- Writing NeuronC programs
- Syntax for node connections
- Cable statement
- Sphere statement
- Synapse statement
- Gap junctions
- Photoreceptor Statement
- Voltage follower
- Channel statement
- Load statement
- Resistor statement
- Gndcap statement
- Cap statement
- Batt statement
- Gndbatt statement
- External compartments
- Stimulus, Electrode, and Record statement
- Plot statement
- Record and Graph statements
- Separate Plots
- Plotting into frames
- Display statement
- Elabl, Ename, and Modify statements
- Modify statement
- Erase statement
- Save and Restore, Run_on_exit
- Run and Step
- NeuronC programming statements
- NeuronC advanced programming statements: Node fields
- Element fields
- Channel fields
- Type() function
- Distance functions: edist
- Fractional distance along cable: efrac
- Foreach statement
- Windowing function: elimit
- Procedure and function definitions
- Assigning procedures and functions
- Exit statement
- Macros (cpp)
- Include and system statements
- NeuronC variables
- Strings and string operators
- Setting variables from command line
- Command line parameters inside script
- Accessing command line parameters with argc and argv
- Local variables
- Arrays and Matrices
- Local Arrays
- Arithmetic operators
- Keywords: "nc -K"
- Read statement (keyboard)
- File open and close
- Printf statement
- Scanf function
- Fread statement
- Fwrite statement
- Unlink statement
- Access to variables from external program
- Test for variable definitions: notinit(), varnum()...
- Run procedure at plot time
- Built-in functions
- Selecting and testing the random number generator
- Gausnn array function
- FFT, acov functions
- LMfit: least-squares fitting
- LMfit2d: 2D least-squares fitting
- Constants
- Graphics statements
- Arranging graphs

- Overview
- Interpreted vs. compiled version
- "Construct" mode
- Run mode
- Simulation time and run mode
- Order of stimuli, time integration and plots
- Run time translation from elements to compartments
- Nodes, neural elements
- Declaring parameters
- Default parameters
- Units

interpreted:and the equivalent compiled versions are presented as:

compiled:The difference between the 2 modes is that the interpreted version depends on a set of precompiled functions to accomplish standard programming features such as subroutines, loops, conditionals, and arithmetic using a stack. Therefore the intepreter runs several-fold slower than the compiled version when executing loops and arithmetic. The advantage of the interpreted version is that it runs immediately and can be used like a calculator as in the original version of "hoc" described in Kernighan and Pike (1984) "The Unix Programming Environment".

In the "construction" mode, one can perform simple calculations, program loops, procedures and subroutines to define neural elements. You may organize these procedures to create a neuron or circuits of many neurons. You may also include stimuli and records in loops and procedures. "Construction" mode is familiar to computer programmers because it is similar to a language like "C" in which procedures are used to accomplish tasks.

A simple calculation:

(interpreted only:) print 54/7; (prints simple calculations)A print statement within a loop:

for (i=0; i<10; i++) print i, sqrt(i); (prints square roots)To define a circuit, add a neural element definition:

(interpreted:) for (i=1; i<=5; i++) (makes a tapered cable) conn i to i-1 cable dia 10-i length 10; (compiled:) for (i=1; i<=5; i++) {c = conn(nd(i), nd(i-1), CABLE); c->dia=10-i; c->length=10;}

statement 1; (these statements construct neural circuit) statement 2; statement 3; . . . step .05; (stops circuit construction, runs 50 msec)

Normally you want to run a simulation as fast as possible. In Neuron-C it is faster to set stimuli and plots before exiting from "construction mode" into "run mode". Then the stimuli and plots run automatically at the correct times in the way you have defined:

Normal order of simulation script: timinc = <expr> /* set integration time step (default 1e-4 s) */ endexp = <expr> /* set end of simulation */ set_stimuli(); set_plots(); run; /* run simulation until end, set by "endexp". */

Sometimes, a simulation is organized as a set of trials, where a stimulus is repeated and plots are overlaid. Often in this case you want to plot the data always starting at the same time. An easy way to do this is to set "time" back to 0 at the beginning of each trial.

Each time "run mode" stops at the end of a "step" statement, the variable "time" is set to a new value. You can use this variable like any other variable for arithmetic expressions. It is possible to set it backwards or forwards to a different value, however if you do this and start "run mode" again you will change the next starting time of the simulation.

timinc = <expr> /* set integration time step (default 1e-4 s) */ set_plots(); for (i=0; i<=ntrials; i++) { /* repeating trials */ time = 0; set_stimuli(); step trial_dur; /* run simulation extended time interval */ };

Note that incrementing the "time" variable does not move the simulation forward, since this happens only during a "step" or "run" statement. Although you can change "time" to a new value in construction mode, and you can use this value in expressions, e.g. to define the start time for stimuli, this new value only affects stimuli when run mode starts inside the step statement. The value of the "time" variable is given to the simulator for its internal value of "simulation time" only when run mode starts inside a "step" or "run" statement.

If you have created stimuli, you may lose part of the stimuli and generate unpredictable results if you set time backwards before you run the simulation long enough to play all the stimuli:

TO = 1; FRO = -1; predur = .01; /* equilibration time before model runs */ time = 0 - predur; /* sets time negative to allow equilib. time */ setxmin = 0; /* sets x-axis beginning at time=0 */ sdur = 0.1; durtotal = sdur + predur; stim sine contrast 0.4 inten .01 tfreq 10 drift TO start time dur durtotal; step sdur; (this is incorrect) time = 0; stim sine contrast 0.4 inten .01 tfreq 10 drift FRO start time dur sdur; step sdur;

This above example doesn't run the stimulus correctly because the step after the first stim statement doesn't play all the stimuli before time is reset. The reason this is important is that typically in a sine wave stimulus each time step runs a intensity increment and an intensity decrement. If not all the intensity increments are run, invariably the last decrements are not added. The correct way to run a stimulus is:

TO = 1; FRO = -1; predur = .01; /* equilibration time before model runs */ time = 0 - predur; /* sets time negative to allow equilib. time */ setxmin = 0; /* sets x-axis beginning at time=0 */ sdur = 0.1; durtotal = sdur + predur; stim sine contrast 0.4 inten .01 tfreq 10 drift TO start time dur durtotal; step durtotal; (correct) time = 0; stim sine contrast 0.4 inten .01 tfreq 10 drift FRO start time dur sdur; step sdur;

Another way to use the simulator is to run the simulation time steps inside a loop in construction mode:

time_incr = timinc; set_plots(); for (i=0; i<=ntrials; i++) { time = 0; set_stimuli(); for (t=0; t<=endexp; t+= time_incr) { modify_circuit(); step time_incr; }; };

This way allows you to modify the circuit each time step, for example, to continuously change the structure or function of the neural circuit. However, this method runs slower since construction mode runs interpreted line by line.

Each time the simulation is run with a "run" or "step" statement the time step cycles through simulation events in a certain order:

1) Stimuli 2) Synapses 3) Photoreceptors 4) Time integration in compartments 5) Onplot procedure 6) Plots 7) Time incremented to next step

This means, for example, that if you run a voltage clamp for 0.1 ms, and set up a voltage plot during runtime, and "step" to run the simulation, you will only record a current during the time the voltage clamp is on:

(interpreted:) ploti=0.0001; /* set plot time increment */ at [0][0] cone (0,0); at [0][0] sphere dia 1 rm=1000; stim spot 10 loc(0,0) inten=1000 start 0 dur .0001; stim node [0][0] vclamp -.01 start 0 dur .0001; plot V[0][0]; /* run-time plots */ plot I[0][0]; plot L[0][0]; step 0.0002; (compiled:) ploti=0.0001; /* set plot time increment */ c = make_cone(nd(0,0), dia=1); c->xloc=0; c->yloc=0; s = make_sphere(nd(0,0), dia=1, rm=1000); stim_spot(10, 0, 0, inten=1000, start=0, dur=0.0001); vclamp(ndn(0,0),clamp=-0.01, start=0, dur=0.0001); plot (V,ndn(0,0)); /* run-time plots */ plot (I,ndn(0,0)); plot (L,ndn(0,0)); step (0.0002);If you would like to record the current at the end of the voltage clamp time, you can stop "run" mode by limiting the step statement to the duration of the voltage clamp. Then you can record the final values of any of the parameters of the simulation since stopping "run" mode stops simulation time from running forward:

(interpreted:) at [0][0] cone (0,0); at [0][0] sphere dia 1 rm=1000; stim spot 10 loc(0,0) inten=1000 start 0 dur .0001; stim node [0][0] vclamp -.01 start 0 dur .0001; step .0001; print "time",time, "V",V[0][0], "I",I[0][0]; /* construction-mode plot */ (compiled:) c = make_cone(nd(0,0), dia=1); c->xloc=0; c->yloc=0; s = make_sphere(nd(0,0), dia=1, rm=1000); stim_spot(10, 0, 0, inten=1000, start=0, dur=0.0001); vclamp(ndn(0,0),clamp=-0.01, start=0, dur=0.0001); step (0.0001); printf ("time %g V %g I %g\n",time,v(nd(0,0)),i(nd(0,0)));

The result of the translation at run-time is a set of linked lists of compartments, connections and pointers between them which the computer scans at high speed for every time step of the simulation run. Each compartment has a linked list of pointers (no limit on the number) which define its connections. Each connection has a set of pointers to the compartments it connects. Every type of connection to a compartment has its own set of mathematical instructions that describe the voltage and current flow through the connection.

NeuronC defines several types of neural elements. Each element connects to either 1 or 2 nodes, and the nodes must be given when the element is defined. The types are:

Type Nodes Description cable 2 defines multiple compartments. sphere 1 defines one compartment. synapse 2 defines connection between 2 nodes. gap junc 2 defines resistive connection between 2 nodes. rod,cone 1 transduction apparatus connected to node. transducer 1 voltage clamp controlled by light itransducer 1 current clamp controlled by light vbuf 2 buffer (voltage follower). load 1 resistor to ground. resistor 2 defines resistive conn. between 2 nodes (same as g.j.) electrode 2 defines resistive conn. between 2 nodes and cap at first cap 2 series capacitor between 2 nodes. gndcap 1 capacitor to ground; adds capacitance to node. batt 2 series battery between 2 nodes. gndbatt 1 battery to ground. chan 1 active set of channels in membrane.

It is often useful to change the default value of a parameter that you have defined in your script. You can do this with the "setvar()" function, which sets variables in your script from values you give on the command line with the "-s variable xx" option (see Setting variables from command line below).

The syntax for the neural elements is given below. Extra spaces (not needed for separating words) are ignored, as are newlines (line feeds or the "enter" key). Words not inside angle brackets must be spelled exactly. The angle brackets indicate a category of input, for example, "<expr> means an expression:

Symbol What to type in: word Must be spelled exactly. <expr> Expression needed here. | Logical OR (either this stmt or another). 'word' Optional part of statement. <node> Node number, either simple expression, or a 1- 2- 3- or 4-dimensional number inside square brackets (see below). Can also include "loc" statement (see below).Each element has either "conn" or "at" as its required first word, followed by node expressions:

(interpeted:) at <expr>conn <expr> to <expr> (compiled:) at (nd(<expr>), <elemtype>); conn (nd(<expr>), nd(<expr>), <elemtype>);

In the compiled version, nodes are defined using the "nd()" function call, listed in "ncfuncs.h". This call returns a pointer to the node and if necessary creates a node. A similar function, "ndn()" retrieves a node pointer if possible, but does not create a new node. These two functions require that the specfied node exist or return a NULL to indicate when it is not found. A third function "ndt()" allows specifying a node number without actually requiring that the node exist. This third form is used in the "display" statement (see below).

Node numbers can also be 2-, 3- or 4-dimensional, but in this case the node numbers must be enclosed with 2 or 3 sets of square brackets "[]"; for example:

(interpeted:) at [<expr>][<expr>][<expr>]Since the node number may be specified either as a simple expression or as a 2-, 3- or 4-dimensional number inside square brackets, node numbers in this manual appear like this:conn [<expr>][<expr>][<expr>] to [<expr>][<expr>] (compiled:) at (nd(<expr>,<expr>,<expr>), <elemtype>); conn (nd(<expr>,<expr>,<expr>), nd(<expr>,<expr>), <elemtype>);

(interpeted:) at <node>Three- and four-dimensional node numbers are useful for specifying which presynaptic cells should connect to a post- synaptic cell. To design your circuit this way, you can specify connections to a neuron based on its type and cell number, without explicitly keeping track of the total number of nodes or compartments defined (which in many cases is a distraction) . To do this, assign the first node dimension to mean "neuron type", the second dimension to mean "cell number", and the third dimension to mean "node number within the cell". If you have an array of cells, you can assign a 2-dimensional "cell number" (dimensions 2 and 3), leaving the fourth to describe the "node within the cell".conn <node> to <node> (compiled:) at(<node>, <elemtype>); conn(<node>, <node>, <elemtype>);

(interpeted:) at <node> loc (<expr>,<expr>)However, locations of both nodes need not be defined in every "cable" statement. It is unnecessary to define the location of a node more than once. For example, if you are defining a cable with several segments, you can define the locations this way:conn <node> loc (<expr>,<expr>) to <node> loc (<expr>,<expr>) (compiled:) at ( loc (<node>, <expr>, <expr>), <elemtype>); conn(loc (<node>, <expr>, <expr>), loc(<node>, <expr>, <expr>), <elemtype>);

(interpeted:) connor:loc (10,0) to conn loc (20,0) to (compiled:) conn(loc (<node1>, 10, 0), <node2>, <elemtype>); conn(loc (<node2>, 20, 0), <node3>, <elemtype>);

(interpeted:) for (i=0; i<10; i++) { conn [i] loc (i*10,0) to [i+1]Also, the node locations may be specified in a "dummy" definition statement:}; (compiled:) for (i=0; i<10; i++) { conn(loc (nd(i), i*10, 0), nd(i+1), <elemtype>); }

(interpeted:) at <node> loc (<expr>,<expr>) (compiled:) at (loc (<node>, <expr>, <expr>));This defines no neural elements but defines the node and sets the node's location. This method is useful when you have a list of cables with absolute locations. In this case, you can specify the locations of the nodes all at once, and then define the cables and their diameters. The lengths are then determined automatically from the node locations.

Photoreceptors are required to have a location in their definition (see "photoreceptors" below). But the photoreceptor location is for the purpose of light stimuli only.

(interpeted:) seglen = 50; conn <node> to <node> cable length=seglen rm=9500; is equivalent to: conn <node> to <node> cable length 50 rm 9500; (compiled:) seglen = 50; c = conn(nd(<node>), nd(<node>), CABLE); c->length=seglen; c->Rm = 9500; is equivalent to: c = make_cable(nd(<node>), nd(<node>)); c->length=seglen; c->Rm=9500;Whenever an optional parameter is not specified, its corresponding default value is used instead. Default values are listed in Section 7, "Predefined variables". Setting an optional variable does not change the value of its default. An attempt to set a variable other than one of the valid parameters inside a neural element statement will be trapped as an error.

To find errors, run NeuronC in "text mode" for printing the errors on the screen:

nc -t fileThis prints out the graph commands as a set of numbers on the screen, instead of graphics. If an error is discovered, the line number and position of the error on the line are printed, too. See section 5 for more information about how to run NeuronC.

(interpeted:) conn <node> to <node> cable dia <expr> 'parameters' (compiled:) make_cable(nd(<node>), nd(<node>)); 'parameter code' optional parameters: -------------------------------------------------------------------------- dia = <expr> [ note that these "cable" params must come first ] dia2 = <expr> length = <expr> cplam = <expr> rm = <expr> [ "membrane" params, come after any "cable" params ] ri = <expr> cm = <expr> vrev = <expr> vrest = <expr> jnoise = <expr> rsd = <expr> (interpeted:) Na type <expr> 'vrev=<expr> 'density=<expr> 'offset=<expr>' 'tau=<expr>' K type <expr> 'vrev=<expr> 'density=<expr> 'offset=<expr>' 'tau=<expr>' KCa type <expr> 'vrev=<expr> 'density=<expr> 'offset=<expr>' 'tau=<expr>' cGMP type <expr> 'vrev=<expr> 'density=<expr> 'offset=<expr>' 'tau=<expr>' Ca type <expr> 'vrev=<expr> 'density=<expr> 'offset=<expr>' 'tau=<expr>' (compiled:) a = make_chan(<elem>, Na, na_type); 'a->vrev=<expr>' 'a->density=<expr>' 'a->voffsetm=<expr>' 'a->tau=<expr>' a = make_chan(<elem>, K, k_type); 'a->vrev=<expr>' 'a->density=<expr>' 'a->voffsetm=<expr>' 'a->tau=<expr>' a = make_chan(<elem>, KCa, kca_type); 'a->vrev=<expr>' 'a->density=<expr>' 'a->voffsetm=<expr>' 'a->tau=<expr>' a = make_chan(<elem>, cGMP, cgmp_type);'a->vrev=<expr>' 'a->density=<expr>' 'a->voffsetm=<expr>' 'a->tau=<expr>' a = make_chan(<elem>, Ca, ca_type); 'a->vrev=<expr>' 'a->density=<expr>' 'a->voffsetm=<expr>' 'a->tau=<expr>' Where: <elem> is the cable or sphere element.where:

parm: default: meaning: ------------------------------------------------------------- length um (def by "loc()") length of cable segment dia 1 um diameter of cable segment (= "dia1") dia2 um defines taper, along with "dia1" (optional) cplam 0.1 (complam) fraction of lambda per compartment. rm 40000 Ohm-cm2 (drm) membrane leakage resistance. ri 200 Ohm-cm (dri) axial cytoplasmic resistivity. cm 1e-6 F/cm2 (dcm) membrane capacitance. vrev -.07 V (vcl) battery voltage for leakage cond. vrest -.07 V (vrev) initial startup voltage for cable seg. jnoise 0 (off) (djnoise) Johnson noise in membrane resistance rsd set by rseed random seed for Johnson noise density .25 S/cm2 (dnadens) density of channel in membrane. .07 S/cm2 (dkdens) .005 S/cm2 (dcadens) ndensity 10-30/um2 numeric density of channels in membrane. (interpreted:) Na type n 'vrev <expr>' 'density <expr>' 'thresh <expr> 'tau <expr>' K type n 'vrev <expr>' 'density <expr>' 'thresh <expr> 'tau <expr>' KCa type n 'vrev <expr>' 'density <expr>' 'thresh <expr> 'tau <expr>' CGMP type n 'vrev <expr>' 'density <expr>' 'thresh <expr> 'tau <expr>' Ca type n 'vrev <expr>' 'density <expr>' 'thresh <expr>' 'tau <expr>' (compiled:) a = make_chan(<elem>, Na, na_type); 'a->vrev=<expr>' 'a->ndensity=<expr>' 'a->voffsetm=<expr>' 'a->voffseth=<expr>' 'a->tau=<expr>' a = make_chan(<elem>, K, k_type); 'a->vrev=<expr>' 'a->ndensity=<expr>' 'a->voffsetm=<expr>' 'a->voffseth=<expr>' 'a->tau=<expr>' = additional voltage-sensitive macroscopic channel conductance in cable membrane. Vrev and density both have default values appropriate for their channel types. Type 0 channels are the HH type and are taken from Hodkgin and Huxley, 1952. Type 1 channels are the exact sequential state equivalent to the type 0 channels. See the "chan" statement below for a more complete description. Channel densities can be specificed as a conductance density or a numeric density. A numeric density is preferred to allow the temperature dependence (Q10) to function correctly. density .07 S/cm2 (dna) = density of channel conductance membrane. ndensity 10 chan/um2 = typical numeric density of channels.

A "cable" statement defines a cable segment, normally used to construct the dendritic tree or axon of a neuron. At runtime, the cable is broken up into compartments, each with the length of the cable's "space constant" multiplied by the value of the parameter "cplam" (default set by the variable "complam", initally 0.1. See "predefined variables"). If the parameter "length" is not specified, the length of the cable is calculated as the distance between the two nodes at the cable ends, minus the radius of any spheres connected to those nodes. For this to work properly you must define the (x,y) or (x,y,z) locations of the nodes. If you specify the cable length, the subtraction of sphere radius at either end is not performed. The specified length may be different than the distance between the location of its ends. To define taper in a cable, you can specify the diameter at both ends with "dia1" and "dia2". If "dia2" isn't specified, the cable is not tapered. Any "cable" params (length, dia, dia2, cplam) must be specified before you specify any membrane parameters.

Each compartment consists of a chunk of membrane, which defines capacitance and leakage values, and internal cytoplasm, which defines axial resistance. A string of connected compartments is created automatically from the cable. The compartments are equal in size except for the two end compartments, which are 1/2 the size of the others. Each compartment is connected to its neighbors with resistors defined by the axial resistances. The membrane capacitance and resistance assigned to the end compartments are added to the capacitance and resistance values of the existing compartments defined for the cable's 2 nodes. If these compartments do not exist yet, they are created new.

You can set the membrane resistance and axial conductance for a cable to be sensitive to temperature using "dqrm" and "dqri". See "Temperature Dependence" below.

noise (std. deviation) = sqrt(4kTBG) Where: k = Boltzmann's constant T = temperature (deg K) B = bandwidth (set to inverse timinc) G = membrane conductance in compartmentTo turn on Johnson noise in all compartments, set the global variable "djnoise". Its value is a multiplier for the basal level of noise, i.e. jnoise=10 gives a standard deviation 10 times higher than normal. Each compartment has its own individual random number generator for Johnson noise so turning on "jnoise" does not affect the random sequence of other noise sources.

Note that the amplitude of Johnson noise in a compartment is dependent on the total conductance in the compartment, including all channels and synapses.

node1 <----------- cable1 ----------> node2 (nodes) ^ ^ comp1 - comp2 - comp3 - ... compN-1 - compN (compartments) 1/2 1 1 1 1/2 (comp. sizes) these comps add (nodes) node2 <------ cable2 --- > node3 ^ ^ (compartments) comp21 - comp22 - comp23 - ...comp2N (comp. sizes) 1/2 1 1 1/2

(interpreted:) at <node> sphere dia <expr> 'params' (same params as cable) (compiled:) at (nd(<node>), SPHERE); 'param code' (same params as cable) make_sphere (nd(<node>),dia=<expr>); 'param code' (same as cable)

The "sphere" statement defines an isopotential sphere, normally used for the soma or axon terminal of a neuron, that has membrane capacitance and leakage resistance but no internal resistance. Thus it is basically a shunting impedance. The values of resistance and capacitance are derived from the surface area of the sphere and the appropriate definition of membrane capacitance and resistance (default or specified). A sphere connects to 1 node, thus the resistance and capacitance are added to the compartment defined for the node. Macroscopic channel conductances are available for spheres just as for cables.

- 1) Synapse parameters and defaults
- 2) Synaptic time step
- 3) Synaptic transfer function
- 4) Vesicle release sensitivity from presynaptic calcium
- 5) Presynaptic delay function
- 6) Speeding up the synapse to save time
- 7) Readily releasible pool
- 8) Synaptic vesicle noise
- 9) Setting random seed for synapse
- 10) Setting randomness of releas
- 11) Post-release delay function for release of neurotransmitter
- 12) Binding of transmitter to postsynaptic receptor: saturation
- 13) Effect of synaptic transmitter
- 14) Postsynaptic delay function
- 15) Postsynaptic Markov sequential state function
- 16) Synaptic channel noise
- 17) Channel noise and time constant
- 18) Synaptic conductance
- 19) Synaptic reversal potential
- 20) Postsynaptic second messenger
- 21) Dyad synapse: multiple postsynaptic mechanisms
- 22) Spost synapse: multiple presynaptic mechanisms

(interpreted:) conn <node> to <node> synapse 'parameters' (compiled:) conn (nd(<node>), nd(<node>), SYNAPSE) 'parameters' make_synpse (nd(<node>), nd(<node>)) 'parameter code' optional parameters: default: meaning: -------------------------------------------------------- open | close open Neurotrans opens or closes chans. linear = <expr> | expon can be either linear or expon expon = <expr> 5 mv exponential const (1/b) (mvolt) vrev = <expr> -.00 V (vna, vk) reversal pot. (battery) (Volts) thresh = <expr> -.05 V (dst) threshold for transfer (Volts) sens = V | Ca V vesicle release sensitivity vgain = <expr> 1 (dvg) vesicle release gain (linear multiplier) rrpool = <expr> 500 (dsrrp) maximum readily releasible pool rrpoolg= <expr> 0 (dsrrg) release gain mul 0->conrolled by rrpool, 1->constant maxsrate=<expr> 0 (dsms) maximum sustainable rate (ves/sec, default 0=>off) cgain = <expr> 1 (dsc) synaptic cGMP gain (after sat.) chc = <expr> 1 (dchc) Hill coeff for cGMP binding nfilt1 = <expr> 2 (dsfa) number of presynaptic filters. timec1 = <expr> .2 msec (dfta) synaptic low pass filter (msec). timec1h= <expr> 1 msec (dftah) synaptic high pass filter (msec). nfilt1h= <expr> 0 no. of presyn. high pass filters. hgain = <expr> 0 gain of high pass filter ( < 0 => rel gain) nfilt2 = <expr> 1 (dsfa) no. of filters after nt release. timec2 = <expr> .2 msec (dfta) synaptic low pass filter (msec). tfall2 = <expr> timec2 tau for falling phase (msec). nfilt3 = <expr> 0 no. of filts for cond. after binding. timec3 = <expr> 0 msec conductance low pass filter (msec). tfall3 = <expr> timec3 tau for falling phase (msec). kd = <expr> 1 (dskd) saturation point: cond/(cond+kd) hcof = <expr> 1 (dshc) Hill coefficient: cond^h/(cond^h+kd^h) trconc = <expr> 1e-4 M (dstr) Transmitter conc factor for AMPA, etc.(Molar) mesgconc = <expr> 1e-5 M (dsmsgc) Transmitter conc factor for CGMP, etc.(Molar) maxcond= <expr> 200e-12 S(dmaxsyn) Conductance when chans fully open (Siemens) mesgout cAMP synapse controls local cAMP level. mesgout cGMP synapse controls local cGMP level. (interpreted:) vesnoise = <expr> 0 (off) = 1 -> define vesicle noise N = <expr> 5 (dsvn) number of vesicle release sites vsize = <expr> 100 (dvsz) size of vesicles released vcov = <expr> 0 stdev/mean of vesicle size rsd = <expr> set by rseed,srseed random seed CoV = <expr> Poisson mult * stdev / mean ves rate refr = <expr> 0 sec minimum time betw vesicle release resp Postsyn sequential-state receptors. AMPA AMPA receptor possibly with desensitization, Ca permeability. NMDA NMDA receptor with voltage-sens. GABA GABA receptor. cGMP cGMP receptor. SYN2 Simple 2-state channel. <chanparm> = <expr> "vrev", "offsetm/h", "taum/h", "chnoise", etc. (params taken from "channel") chnoise = <expr> 0 (off) = 1 -> define chan noise (after "resp") N = <expr> 100 (dscn) number of channels unit = <expr> 50e-12 (dscu) unitary channel conductance tauf = <expr> 1 (dsyntau) rel. time const for noise (abs=.001) rsd = <expr> set by rseed,srseed random seed (compiled:) n = make_vesnoise(epnt); n->N=<expr>; n->vsize=<expr>; ... c = make_chan(epnt, chantype, stype); c->maxcond=<expr>; n->unit=<expr>; ... n = make_chnoise(epnt); n->N=<expr>; n->vsize=<expr>; ... (See "ncelem.h" for synapse, channel and noise parameter definitions.)

Synaptic gain is specified by the value of the "linear" parameter. When set to 1.0, the neurotransmitter released is 1 for a presynaptic voltage of 100 mv above threshold. This value of Trel=1 half-saturates the saturation function (see below). For voltages less than the threshold, no transmitter is released. Larger values reduce the range over which the input voltage operates, i.e. a value of 2 increases the synaptic gain so that 50 mv above threshold releases transmitter of 1.

Trel = 0.01 * (Vpre - Vthresh) * gain * vgain (1)where:

Trel = transmitter released to postsynaptic receptor. (limited to be non-negative) Vpre = presynaptic voltage (normalized to mv). Vthresh = synaptic threshold (normalized to mv). gain,vgain = linear transfer gain.

The transfer function may also be exponential, defined by the equation

Trel = .025 * e(Vpre-Vthresh) * vgain /expon (2)where:

Trel = transmitter released, delayed to postsynaptic receptor. Vpre = presynaptic voltage (mv). Vthresh = synaptic threshold (mv). expon = constant defining mvolts per e-fold increase (1/b). vgain = linear transfer gain. Reference: Belgum and Copenhagen, 1988For exponential transfer, the transmitter released is equal to the exponential function of the presynaptic voltage above threshold. The value of "expon" sets how many millivolts cause an e-fold increase in transmitter release. Exponential release implies a gradual increase with voltage, and it also implies that release is gradually shut off below the threshold voltage. A synapse with exponential release may require a presynaptic voltage 10 to 20 mv. below threshold to extinguish transmitter release.

Note that "Trel", the signal representing released neurotransmitter, normally ranges from 0 to 1, or greater for saturation (maximum=1000). These values are "normalized" so that a value of Trel=1, when passed through the saturation function 5) below, causes a conductance of 0.5 of the maximum conductance ("maxcond"). Thus a value of Trel=5 is necessary to reach 80% of the maximum conductance.

The "vgain" parameter sets the proportion of neurotransmitter released. It is useful for keeping the vesicle release rate constant when you change the vesicle size (which otherwise modulates both size and rate). If you change the "vsize" parameter and the "vgain" parameter proportionately, the rate stays unchanged. If you change "vgain" alone, only the rate changes.

With "sens Ca", the amount of neurotransmitter released is the calcium concentration multiplied by a constant ("dscavg", default = 1e6) multiplied by the "vgain" parameter (default=1) and a power function (default 1):

(interpreted:) synapse ... sens Ca ... (compiled:) synapse *spnt; spnt->sens = CA; in the synapse code: Trel = [Ca]i * dscavg * vgain * exp ( log([Ca]i * dscavg) * caegain) Where: caegain is the power (default=1)To set a cooperative effect of [Ca]i, you can set caegain to a non-zero value. For example, a value of caegain=2 will simulate two calcium binding sites on the release mechanism.

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Each filter (from 1 to 4) is represented by the following equation:

Each stage is described by:

Vout (t+1) = Vout (t) + (Vin (t) - Vout(t)) * (1 - exp(-1/tau))where:

Vout = output of delay filter. Vin = input to filter. t = time in increments of basic timestep tau = time constant of filter (timec1) in increments of timestep.

This equation gives the behavior that one would expect from a filter with a time constant of "tau". The form of the equation corrects a discretization error that occurs with short time constants.

To minimize the lowpass filter effect of this function, use a short time constant. To maximize delay use all 4 filters. Total time delay is approximately equal to the sum of the individual time constants. The default setting is 2 filters with 0.2 msec time constants. If the time step is 1 sec. or greater, then the low-pass filter is removed and the synapse becomes a static transfer function.The signal that passes through the presynaptic delay function represents the steps that lead to transmitter release such as calcium entry and vesicle fusion. The signal that is actually filtered in this function represents the voltage above threshold, and so may range from -100 mV to 100 mV. The static release function 2) below converts this voltage into transmitter released. The signal values in the presynaptic filters may be recorded using the "FA0-4" notation (see "record").

It is possible to set several different time constants in any of the filters, with a different form of the "timec" parameter, for example, for 2 5-msec delays and 1 2-msec delay:

timec1 [5 5 1]Defaults

The presynaptic delay function is set by default to 2 filters of 0.2 msec time constant. If the time step is 1 sec. or greater, then the low-pass filter is removed and the synapse becomes a static transfer function.

conn 1 to 2 synapse ... synaptau = .01; step .05; ( set 50 msec for equilibration ) synaptau = 1; run;Click here to return to Synapse statement index

When the rate of vesicle release at a synapse is high, the synapse's ability to release neurotransmitter is reduced. The ability to release vesicles is thought to be regulated by the number of vesicles that are near to the synaptic site and therefore available for binding and membrane fusion. The number of vesicles available for immediate release is often described as the "readily releasible pool". At a ribbon synapse (e.g. in the retina or auditory nerve) this pool is thought to be the number of vesicles tethered to the ribbon. The pool is continually enlarged by endocytosis of old vesicles and also by creation of new ones.

This behavior is simulated by a first-order differential equation in which pool size controls the rate of release:

pool -= trel pool += maxsrate * timeinc * (1 - pool/rrpool) Trel = trel * (rrpoolg + pool / rrpool * (1 - rrpoolg))

where:

pool = actual pool of vesicles (with or without vesicle noise). rrpool = maximum "readily releasible pool", defined by user. maxsrate = maximum "sustainable release rate", defined by user. timeinc = synaptic time step. trel = neurotransmitter release available, i.e. before this computation. Trel = actual neurotransmitter released. rrpoolg = gain for rrpool release, 1-> regulated by rrpool, 0-> constant gainTo simulate the "readily releasible pool", you can set the "rrpool" and "maxsrate" parameters. The "rrpool" parameter (default=dsrrp) sets the maximum size of the readily releasibile pool, and the "maxsrate" parameter (default=dsms) sets the "maximum sustained rate", i.e. the rate at which the readily releasible pool is enlarged. The rrpoolg parameter sets to what extent the readily releasable pool's filled fraction controls release. For a rrpoolg = 0, the gain is controlled by the size of the readily releasable pool. For a rrpoolg = 1, the gain is constant, controlled by the voltage gain (sometimes set by [Ca]i). Of course, in any case, the readily releasable pool cannot release more vesicles than it contains which is an upper limit on the synaptic transient gain.

By default the "maxsrate" parameter is set to zero so the readily releasible pool is not included in the synaptic release function.

3) Click here to return to Synapse statement indexVesicle noise is defined by one parameter, the size of a vesicle (size). The number of vesicles released is a random function (poisson distribution) of the release rate. Quantal release probability is calculated with the following equations:

n = Trel / size q = poisdev(n) Tnoise = q * sizewhere:

p = probability of release. Trel = transmitter released (amount / 100 usec timestep; 1=half-sat). size = size of release events (1=half saturating). n = average (instantaneous) number of vesicles per time step. q = number of quantal vesicles released per time step. binom = random binomial deviation funtion of p, n. Tnoise = transmitter released (Trel) with noise. Reference: Korn, et al., 1982.For a given amount of transmitter released (Trel) (and therefore a given postsynaptic conductance) the "size" parameter affects the size of quantal vesicles released. A higher value of "size" means a lower probability of a vesicle being released per time step which implies fewer quantal vesicles released and but larger vesicle size. Changing "size" does not change the average amount of transmitter released. The only other parameters affected by "size" are vesicle rate and "amount" of noise.

The "size" parameter sets the amount of neurotransmitter in a vesicle released in a 100 usec timestep (the timestep used in calculating synaptic noise). Normally one doesn't want a vesicle's effect to disappear so quickly so one sets the vesicle duration by setting the time constant of the filter between neurotransmitter release and saturation (i.e. the "second" filter).

When setting "size", remember that a vesicle size of 1 means a the vesicle will produce a 1/2 max. conductance for a 100 usec timestep if there is no low-pass filter activated. When a low- pass filter is activated (nfilt2,timec2), the "energy" of the vesicle is maintained, i.e. its duration is increased and its amplitude is decreased. If you want to set the size of the vesicle after filtering, multiply the "size" by the time constant of the filter in 100 usec steps. For example, a size of 100 is required to produce a 1/2 max conductance with a filter time constant of 10 msec (i.e. (10 msec)/(100 usec) = 100).

The instantaneous rate of neurotransmitter release is always a function of synaptic activation (i.e. presynaptic voltage and gain). Since the "size" parameter also affects the rate of release of vesicles, normally during the course of testing a simulation one chooses a "size" that gives correct vesicle release rate (i.e. rate at 1/2 max total conductance). To lower the release rate without changing the vesicle size, change the synaptic gain, with the "vgain" or "expon" parameters. This affects probability of release (and therefore postsynaptic conductance) but not vesicle size or the vesicle rate necessary to produce a 1/2 max conductance.

Vesicle size is thought to vary because the amplitude distribution of mini quantal events recorded in a postsynaptic cell is highly variable. The distribution looks like a Gaussian distribution whose values are cubed (Bekkers et al., 1990). This behavior can be simulated with the "vcov" parameter (vesicle coefficient of variation), which sets the variability (stdev/mean) of vesicle size. The variability is calculated as:

r = gaussdist() * vcov + 1 vol = r*r*r size = vsize * vol Where: r = radius of vesicle. vol = volume of vesicle. vsize = vesicle size set by user. gaussdist = stochastic Gaussian distribution function with zero mean and unit standard deviation.You can set vcov from almost no variability (vcov=.01) to very large variability (vcov=.5). The higher values (above .2) increase the mean value by 10-30%.

If you want to fit data to the third-power Gaussian distribution function, use this PDF function as a start:

y = exp ( (x^(1/3) - m)^2 / (2 * r*r)) * x^(-2/3);for a sixth-power rule, use:

y = exp ( (x^(1/6) - m)^2 / (2 * r*r)) * x^(-5/6); Where: y = histogram of distribution function. x = quantal size. m = mean of Gaussian. r = standard deviation of Gaussian.The "N" parameter describes the number of independent release sites for the purpose of the noise computation but does not affect conductance. The effect of varying N is noticeable only when the probability of releasing a vesicle is high (i.e. when N is small and Trel is high), and this normally happens only when the release rate is higher than 1000/sec/synapse. The maximum rate of release is set (internally by the simulator) to 10 vesicles/release site/timestep (100 usec), a value that should never be reached in practice. When release rates are lower than this (the usual case) the timing of release is "Poisson", meaning that the standard deviation of the rate (i.e. its "noise") is proportional to the square root of the mean. When N is set to zero, noise is turned off.

Note that saturation can affect a noisy synaptic signal differently than one without noise: the high amplitude noise peaks may saturate and cause the signal mean to be lower than a similar synapse without noise. To minimize this effect, 1) add filters at stage 2 to reduce fluctuation noise, or 2) reduce the amount of saturation by decreasing gain and increasing synaptic conductance ("maxcond").

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Note that the activity of multiple synapses with random noise will not affect each other's random sequence, even though their sequences are set from the main random sequence "rseed". If you want to change one synapse's sequence without changing any others, you can set the pseudo-random sequence for that each synapse with the "rsd" parameter. When set, the "rsd = <expr> parameter keeps the random noise sequence constant for the synapse. The vesicle and channel noises can be initialized separately. Any synapses (or vesicle or channel noise generators within any synapses) that are not initilized with "rsd" are set by the overall "rseed" random number seed.

In addition, the "srseed" variable ("stimulus rseed") modifies the random seed for synapses (and for photoreceptors). This is useful when you want to use the main "rseed" to construct a neural circuit, but you want to vary the synaptic noise random sequence for different stimuli, while keeping the neural circuit constant. The "srseed" variable is added to "rseed" when each synapse's random sequence is defined. Its default value is 0, and any other integer value will change the synaptic noise. A typical use is to set it to the contrast of the stimulus multiplied by 1000.

gorder = 1.0 / (CoV*CoV);The gamma order is a floating point value, so practically you can set the value of CoV to any positive number. The vesicle release rate is set by the simulator from the presynaptic voltage and the neurotransmitter release function, so you only control the relative "regularity" of release with CoV, not the absolute regularity, exact standard deviation, or mean rate. Note that release is more regular with higher rates.

The "refr" parameter is an alternate way to specify regularity in vesicle release. It is specified in seconds and if non-zero it causes an absolute refractory period to be set up so that no vesicles are released during that period after each vesicle event. This causes release at high rates to be more regular than at low rates. Note that release will stop if the refractory period is equal to the mean period between vesicle events.

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The neurotransmitter signal is passed through a second delay function that represents the delay between release at the presynaptic membrane and binding at postsynaptic receptors. The function also slows the rate of rise and fall of neurotransmitter binding to the post- synaptic receptor. The function is identical to the first one described above: it consists of up to 4 variable "resistor-capacitor" filters in series. As in the first delay function, the filters may use the same time constant or can be set to different time constants. In addition, the last filter in the series has an optional falling phase time constant that allows the duration of neurotransmitter action to be prolonged. The last filter connects to the static saturation function, described in 5) below.

The signal that passes through the post-release delay function represents the "neurotransmitter" released by the presynaptic terminal. This signal normally ranges from 0 to 10, where a value of 1 is half-saturated (see "saturation" below). The signal values in the filters may be recorded using the "FB0-4" notation (see "record").When a Markov function is used instead of a saturation function, the signal in the post-release delay function is calibrated in "M" or "Molar", determined by the "trconc" parameter (set for the Markov function) multiplied times the normalized signal used in the post-release delay filter.

This delay function is useful for defining a delay that affects the properties of the (optional) vesicle noise. There are 3 parameters, the number of filters ("nfilt2"), the time constant for the filters ("timec2"), and the optional falling phase parameter ("tfall"). To minimize the lowpass filter effect of this function, use a short time constant. To maximize delay, use all 4 filters. To pass all frequencies but maximize delay, use a short time constant with all 4 filters.

Each filter (from 1 to 4) is represented by the following equation:

Tdel (t+1) = Tdel (t) + (Trel (t) - Tdel(t)) * (1-exp(-1/tau))where:

Tdel = output of delay filter. Trel = input to filter. t = time in increments of basic timestep tau = time constant of filter (timec2) in increments of timestep.Falling phase tau

To use the optional falling phase, set the "tfall" parameter to the time constant you want for neurotransmitter removal. This time constant replaces the falling phase time constant in the last filter and gives an exponential decay to neurotransmitter action.

Note: nonlinear interactions with delay function

Note that if the synapse is set up for substantial saturation, any low-pass "averaging" filtering action in the post-release filter function will interact with the saturation in a "non-intuitive" nonlinear fashion. For example, if the function is given 1 msec delay, a large presynaptic signal may cause the post-synaptic signal to rise quickly (because the initial rise to saturation happens in less than 1 msec) but to fall with 5-10 msec delay because the "averaged" filtered signal keeps the synapse saturated even while the neurotransmitter release is falling.

A similar action can happen when a Markov function is substituted for the saturation function. When the postsynaptic delay filter is set for substantial averaging, a high rate of neurotransmitter released can saturate the postsynaptic Markov function receptor, even when neurotransmitter release is falling.

Defaults

The postsynaptic delay function is set by default to 0 filters (no filter) with 0.2 msec time constant. If the time step is 1 sec. or greater, then the low-pass filter is removed and the synapse becomes a static transfer function.

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Rbound = Tdel^h / (Tdel^h + kd^h) (3)where:

Rbound = Fraction of receptors bound with transmitter. Tdel = transmitter (delayed and filtered Trel). kd = binding constant for synaptic saturation. (default = 1) h = Hill coefficient, representing cooperativity.The released transmitter, delayed and averaged, is delivered to the saturation function which allows the conductance of the postsynaptic membrane to be limited to the maximum defined by the "maxcond" parameter. The default value for the binding constant (kd) is 1, so saturation occurs when the transmitter released is greater than 1, defined in equations (1) and (2) above.

With a synapse set to use the standard saturation function, saturation is dependent on both "gain" and "kd". To change the level of presynaptic voltage at which saturation occurs, increase "gain". For an exponential synapse, the saturation occurs at a presynaptic level dependent on "gain", "expon", and "kd".

When a Markov function is used instead of the standard saturation function, the "kd" parameter is not relevant and the amount of saturation is dependent only on the neurotransmitter release and the Markov function.

The Hill coefficient, defined by the "hcof" parameter, represents the number of molecules of neurotransmitter that must be bound to a receptor for it to be activated, and describes the "degree of cooperativity". A Hill coefficient greater than 1 gives the saturation curve an S-shape, which means a "toe" at low concentrations of neurotransmitter, and a steeper slope in the mid-portion of the curve. Typical Hill coefficients are 2 or 3, although commonly a non-integer Hill coefficient is reported when measured from a pharmacological preparation.

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cGMP = (1 - Rbound * cgain) (5) cGMP >= 0 Gpost = cGMP / (cGMP + ckd) * (1 + ckd) * maxcondwhere

cGMP = the second messenger concentration Gpost = postsynaptic conductance ckd = saturation constant for the 2nd messenger the default level of ckd is set by "dckd" (default 0.1)

If the neurotransmitter action at the synapse has been set to "close", the "cgain" parameter represents the biochemical gain that couples bound receptors to the closing of membrane channels. Amplification in the biochemical cascade after saturation (i.e. cgain > 0) reduces the effect of saturation near the point where all the channels are closed. Gain may be very high at such a synapse with modest values of cgain (e.g. voltage gain = 100). The intermediate parameter "cGMP" represents the level of second-messenger that binds to the membrane ion channel. Since in the "generic" synapse this is limited to a range of 0 to 1, Gpost is multiplied by the factor "(1 + ckd)" in equation (5) above to give a reasonable amount of saturation when ckd=0.1. Normally this default value for ckd should not be changed. Note that the value of "Gpost" above is limited to the range 0 to maxcond.

The default action for neurotransmitter in NeuronC is to open channels, but this may be explicitly stated with the keyword "open".

If a "resp cGMP" is added in the parameter list after the "synapse" keyword, a cGMP channel becomes the output for the synapse's action:

... synapse close maxcond=1e-9 resp cGMP chnoise=1This would generate a synapse in which neurotransmitter closed a cGMP channel through a second-messenger system, with 40 channels having a unitary conductance of 25 pS (default for cGMP). The description of the channel type determines the properties of cGMP binding and channel opening.

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The signal that passes through the post-saturation delay function represents normalized conductance and ranges from 0 to 1. The signal values in the filters may be recorded using the "FC0-4" notation (see "record").

This delay function is useful for defining a delay that affects both (optional) vesicle noise and (optional) channel noise. There are 3 parameters, the number of filters ("nfilt3"), the time constant for the filters ("timec3"), and the optional falling phase parameter ("tfall"). To minimize the lowpass filter effect of this function, use a short time constant. To maximize delay, use all 4 filters.

Each filter (from 1 to 4) is represented by the following equation:

Gdel(t+1) = Gdel(t) + (Gi(t) - Gdel(t)) * (1-exp(-1/tau))where:

Gdel = output of delay filter, goes to "Reversal Potential" below. Gi = input to filter, from Gpost above or previous filter. t = time in increments of basic timestep tau = time constant of filter (timec3) in increments of timestepFalling phase tau

To use the optional falling phase, set the "tfall" parameter to the time constant you want for neurotransmitter removal. This time constant replaces the falling phase time constant in the last filter and gives an exponential decay to neurotransmitter action.

Defaults

The postsynaptic delay function is set by default to 0 filters (no filter). If the time step is 1 sec. or greater, then the low-pass filter is removed and the synapse becomes a static transfer function.

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The discrete state Markov function for AMPA and NMDA channels is placed between neurotransmitter concentration (i.e. temporal filter 2) and channel opening. Calibration of the absolute concentration of neurotransmitter at the postsynaptic receptor is set by the "trconc" parameter. This allows changing the response amplitude and amount of saturation of the receptor. During the simulation, the actual concentration is computed by multiplying "trconc" by the output of the second temporal filter. The level of neurotransmitter bound to the receptor drives the Markov function through the rate constants which are functions of neurotransmitter. (In the NMDA receptor, they're also functions of voltage). Output from the Markov function drives the postsynaptic channels. When channel noise is added to a Markov channel, the kinetics of channel opening and closing are set by the Markov state transitions but can be tuned with the "taua-tauf" parameters (see below). The cGMP Markov function is placed after postsynaptic binding and the third temporal filter. Calibration of the second messenger concentration is set by the "mesgconc" parameter, similar to the "trconc" parameter.

When a channel type is not explicitly defined by the "resp" clause, the trconc parameter can be used in the same way as specified above to vary the amplitude of the response and the amount of saturation specified by "kd". In this case, the default value of trconc is still "dstr" (as defined above) but the multiplier value is trconc/dstr, i.e. it is by default 1.0.

Channel noise can be defined without the "resp" keyword. When this is done a "syn2" channel is created automatically. This example defines a synapse that opens a 2-state Markov channel with 20 channels (with a default unitary conductance of 25 pS):

... synapse ... open chnoise=1 N=20

The order of most synaptic parameters is arbitrary (you can specify them in any order) but any "resp" parameters to specify the postsynaptic channel should all be sequential, starting after "resp", i.e you should specify "resp" and then place all the "channel parameters" ("vrev", "offsetm/h", "taum/h", "caperm", etc.).

(interpreted:) OK: conn node1 to node2 synapse presynaptic options... ; OK: conn node1 to node2 synapse presynaptic options... vesnoise options .... ; OK: conn node1 to node2 synapse presynaptic options... vesnoise options .... chnoise options ... ; OK: conn node1 to node2 synapse presynaptic options... vesnoise options .... resp AMPA taum=2 chnoise=1 unit=20e-12 ; OK: conn node1 to node2 synapse presynaptic options ... vesnoise options ... resp AMPA taum=2 caperm = .2 chnoise=1 unit=20e-12 ; Gives error message: conn node1 to node2 synapse presynaptic options ... vesnoise options ... caperm = .2 (caperm specified before "resp AMPA") resp AMPA taum=2 chnoise=1 unit=20e-12 ; (compiled:) synapse *s; chattrib *c; nattrib *n; s = make_synpse (nd(node1), nd(node2)) presynaptic options: s->vrev=-0.045; s->thresh=-0.045; ... vesnoise options: n = make_vesnoise(s); ... postsynaptic options: c = make_chan(s, AMPA, 0); c->taum=2; c->maxcond = 100e-12; ... chnoise options: n = make_chnoise(s); n->unit=20e-12; Note that vesnoise, channel noise, and a channel attribute are optional. If no channel is specified, generic postsynaptic binding/saturation and conducance functions are created.

The "chnoise" parameter can be specified without "resp", i.e. you don't need to use the "resp" parameter if you only want to add noise. But in that case, a simple postsynaptic 2-state channel type will be created to allow the synapse to have noise properties.

Note that the "N" and "unit" parameters can be placed before, after, or without "chnoise". If placed before "chnoise", they define the conductance of the channel. If placed after chnoise, they define only the noise properties of the channel, not its conductance:

... synapse ... open N=20 chnoise=1You can modify the behavior of the Markov functions with the "tau" and "offset" parameters (similar to those in "channel"): "offset" defines a voltage to be added to the membrane voltage for the NMDA channel, and "tau" defines a multiplier for the time constant functions (i.e. a divider for rate functions). You can separately specify a relative "taum" (activation) and "tauh" (inactivation) multiplier for some channels and "taua-tauf" provide a way to tune 6 separate rate functions.

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The "unit" parameter describes the unitary conductance of a single channel and allows the simulator to calculate the number of channels from the maximum total conductance "maxcond". If you specify a value for "N", the value of "unit" is ignored, otherwise, the total number of channels is calculated as:

N = maxcond / unitThe "N" parameter describes the number of independent channels for the purpose of the noise computation but does not affect conductance. The instantaneous number of open channels is a random function (binomial deviation) of the probability of each channel opening and the number of channels. Defaults for "unit" (the unitary conductance) are:

dscu = 25e-12 @22 default 2-state synaptic channel dampau=25e-12 @22 default AMPA unitary conductance dcgmpu=25e-12 @22 default cGMP unitary conductance dnau = 22e-12 @22 default Na unitary cond, gives 32 pS @33 deg (Lipton & Tauck, 1987) dku = 11.5e-12 @22 default K unitary conductance gives 15 pS @30 deg dkau = 22e-12 @22 default KA unitary conductance gives 30 pS @30 deg dkcabu= 74.3e-12 @22 default BKCa unitary cond, gives 115 pS @ 35 deg dkcasu= 14.2e-12 @22 default SKCa unitary cond, gives 22 pS @ 35 degNote that the default unitary conductances have a temperature coefficient, set by the Q10 for channel conductance "dqc" (default = 1.4). The base temperature at which the unitary conductance is defined is set by the "qt" field of the channel constants. For HH-type rate functions, the orginal temperature was 6.3 deg C, and these original equations are multiplied by a standard factor to normalize them to 22 deg C. For synapses it is also 22 deg C. For more details, look in "Adding New Channels".

You can change the default base temperature for unitary conductances (and kinetics) with the following variables:

var default meaning ------------------------------------------------------------------------------ dbasetc 22 deg C base temp for membrane channel kinetics, conductances dbasetsyn 22 deg C base temp for synaptic kinetics dbasetca 22 deg C base temp for ca pumps dbasetdc 22 deg C base temp for Ca diffusion constantClick here to return to Synapse statement index

The time constant controls the frequency spectrum of the channel noise. The default time constant for the "syn2" simple 2-state channel is 1 ms and this can be changed (multiplied) with the "tauf" parameter. The time constant defines a noise event with an average single exponential time course (single Lorenzian), whose "roll-off" frequency is:

fc = 1 / ( 2 * PI * tau)The power spectral density at frequency = fc is half of that at lower frequencies.

See the description of vesicle noise above for a discussion of the random "seed" and how to change it.

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Gpost = G * maxcond (4)where:

Gpost = postsynaptic conductance. G = Fraction of receptors bound, after saturation and noise. maxcond = maximum postsynaptic conductance (default = 1e-8 S)The fraction receptor bound is always less than 1, so the postsynaptic conductance can only approach the level specified by "maxcond". The instantaneous conductance may be recorded with the "G0" notation (see "record").

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The post-synaptic current reverses when the intracellular voltage passes above or below the synaptic battery potential; thus the name "reversal potential".

Ipost = (Vcell - Vrev) * Gdelwhere:

Ipost = postsynaptic current Vcell = intracellular voltage Vrev = reversal (battery) voltage for synapse Gdel = postsynaptic conductance, (Gpost delayed)Click here to return to Synapse statement index

If you specify a cGMP-gated postsynaptic channel with the "resp" option it will automatically receive its signal from the synapse in the same manner as if you use the "mesgout" option and a separate "chan cGMP" statement.

Note that the third temporal filter can approximate the low-pass filtering action of a second-messenger without the need to specify one with the "mesgout" option (see "Postsynaptic delay function" above).

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The "dyad" parameter allows you to connect 2 or more postsynaptic mechanisms to one presynaptic release mechanism. Photoreceptors and bipolar cells of the retina have such synapses, where the neurotransmitter from each vesicle is thought to diffuse to 2 sets of receptors each on a different postsynaptic neuron. The effect of this is to preserve the vesicle release timing in both postsynaptic cells.

To use the "dyad" parameter, you need to create one synapse first, and name it with the "ename" parameter. This stores the synapse's "element number" in the ename parameter (actually it's an ordinary variable that holds an integer number). Then you create a second synapse, but instead of specifying presynaptic parameters such as gain and release function, you specify "dyad name" where "name" is the variable that you set with the "ename" parameter from the first synapse:

(interpreted:) conn 1 to 10 synapse open expon 5 /* first synapse */ thresh = -.045 maxcond=1e-10 timec2=2 nfilt2=2 ename syn1; /* save element number in "syn1" */ conn 2 to 10 synapse dyad syn1 /* second synapse, dyad to first */ maxcond=1e-10 /* only specify postsynaptic params */ timec3=10 nfilt3=2; (compiled:) int nfilt; synapse *s; s = make_synpse (nd(1), nd(10)); s->ntact=OPEN; s->ngain=5; /* first synapse */ s->thresh= -.045 s->maxcond=1e-10 s->timec2=2 nfilt2=2 nfilt=2; s->nfilt2 = (short int)nfilt; s->timec2 = makfiltarr(nfilt,0,s->timec2,2); syn1=spnt->elnum; /* save element number in "syn1" */ s = make_synpse (nd(2), nd(10)); s->ntact=DYAD; s->ngain=syn1; /* second synapse, dyad to first */ s->maxcond=1e-10; nfilt=3; s->nfilt3=(short int)nfilt; s->timec3 = makfiltarr(nfilt,0,s->timec3,10);

Note that for the second synapse (labeled "dyad"), you can only specify postsynaptic parameters such as filter 2, filter 3, saturation, conductance, and channel noise. You can also specify a Markov channel with "resp" (see above). Both postsynaptic cells will receive a signal whose envelope has identical timing, but they can have different conductances and channel noise.

Click here to return to Synapse statement indexThe "spost" parameter allows you to connect 2 or more presynaptic mechanisms to one postsynaptic release mechanism. It is thought that at some synpses the neurotransmitter can diffuse with enough concentration a few microns away that it can modulate other "extrasynaptic" ligand-binding sites. Photoreceptors are thought to have such synapses, where the neurotransmitter from the ribbon synapse (where neurotransmitter is released onto invaginating dendrites from horizontal and on-bipolar cells) is thought to diffuse to the "flat" contacts from off bipolar cells up to 3-5 microns away. Each vesicle is thought to diffuse to several sets of receptors each on a different postsynaptic neuron. The effect of this is to mix together the vesicle release timing from several release sites in one postsynaptic cell.

To use the "spost" parameter, you need to create one synapse first, and name it with the "ename" parameter. This stores the synapse's "element number" in the ename parameter (see "dyad" above). Then you create a second synapse, but instead of specifying postsynaptic parameters such as saturation, binding, and conductance, you specify "spost name" where "name" is the variable that you set with the "ename" parameter from the first synapse:

(interpreted:) conn (1) to (10) synapse open /* first synapse */ expon 20 maxcond 200e-12 thresh -.04 timec1 .5 nfilt2=2 timec2 2 vgain=5 vesnoise=1 vsize=50 ename syn1; /* save element number in syn1 */ conn (2) to (10) synapse open /* second synapse, uses postsyn from first */ expon 20 /* only specify presynaptic params */ thresh= -.04 timec1=.5 nfilt2=2 timec2=2 vgain=5 vesnoise=1 vsize=50 spost syn1; (compiled:) See example of "dyad" for compiled above.

Note that for the second synapse (with the "spost" parameter), you can only specify presynaptic parameters such as expon (gain), conductance, thresh, etc. The second filter "filt2" for this purpose can be either presynaptic or postsynaptic, i.e. it can be used with either "dyad" or "spost" parameters.

You can use both "dyad" and "spost" at the same time to specify a situation where there are several presynaptic and postsynaptic mechanisms that share a common neurotransmitter pool.

Click here to return to Synapse statement index

(interpreted:) conn <node> to <node> gj <expr> 'parameters' (compiled:) gapjunc *gj; gj *make_gj (nd(<expr<), nd(<expr<), <maxcond>); 'parameter code' ---------------------------------------------- parameters: units: default: meaning: gj <expr> S conductance of gap junction. area = <expr> um2 membrane area of gap junction (alt.). dia = <expr> um diameter of gap junc(alt. to area). rg = <expr> Ohm-um2 5e6 (drg) specific resistance of gj membrane. vgain = <expr> mV 1.0 mV per e-fold change in rate. offset= <expr> V 0.015 (dgjoff) offset voltage. taun = <expr> ratio 1.0 (dgjtau) divider for rate function. gmax = <expr> S conductance of gap junction. gnv = <expr> ratio 0.2 (dgjnv) non-voltage-sensitive fraction. rev 'params' rectifying params for neg voltage. mesgin cAMP modulation by cAMP at local node. mesgin cGMP modulation by cGMP at local node. mesgin cAMP <node> modulation by cAMP from remote node. mesgin cGMP <node> modulation by cGMP from remote node. mesgin 'params' open (close) cAMP/cGMP opens the gj channel. mesgin 'params' close (default) cAMP/cGMP closes the gj channel.A gap junction is implemented as a resistive connection between two nodes, much like the connection between compartments along the length of a cable. Its conductance can change as a function of the cross-junctional voltage. The change is small and slow in response to a voltage step of less than 10 mV, but increasingly strong and rapid above 15 mV. The maximum conductance can be defined immediately after the keyword "gj" (in Siemens), or alternately can be defined by its area, or diameter:

gmax = area / specific resistance gmax = PI*dia*dia/ (4 * specific resistance)To calibrate "area" as a conductance, set the specific resistance "rg" (or drg, its default) to 1. Then the value you supply after "area" is interpreted as the conductance in Siemens.

Optional parameters define the specific resistance, defined in units of ohm-um2 (default 5e6 ohm-um2), voltage gain ("vgain"), the number of mV per e-fold change in rate, and the time constant "taun", which changes the opening and closing rates proportionately. The opening and closing rates are also influenced by temperature (set by "tempcel") with a Q10 of 3, in a manner similar to other membrane channels (Hodgkin and Huxley, 1952). To disable the voltage sensitivity, set the Gmin/Gmax ratio ("gnv") to 1.0, or set its default ("dgjnv") to 1.0.

alpha = tempcoeff * taun * exp(-Aa * (vj - offset) / vgain); beta = tempcoeff * taun * exp( Ab * (vj - offset) / vgain); n += -beta * n + alpha * (1.0 - n) * t; Ggj = (gnv + n * (1.0-gnv)) * (1.0-cyc) Where: tempcoeff = temperature coefficient determined by Q10 of 3. Aa = power coefficient for alpha, set to 0.077 Ab = power coefficient for beta, set to 0.14 t = time increment for synapses (always 100 usec). n = normalized voltage-gated conductance from 0 to 1.0. gnv = non-voltage-gated fraction, from 0 to 1.0 cyc = level of cyclic nucleotide "second-messenger". Ggj = normalized total gap junction conductance.You can change the rate for opening and closing (alpha and beta) by setting taun, offset, and vgain. Because offset and vgain are within the exp() function, they have a larger effect when the voltage is greater. Taun will linearly change the rate.

For details on the voltage gating properties, see Harris, Spray, Bennett, J. Gen Physiol. 77:95-117, 1981.

The "reverse" parameters are vgain, offset, and taun. If any of these are set, the gap junction is effectively split in half with the forward parameters defined before the "rev" keyword, and the reverse parameters defined after the "rev" keyword. In this case, the reverse parameters are used when the voltage across the gap junction is negative. Defaults for the reverse parameters are specified by the forward ones.

The "cAMP" and "cGMP" parameters set modulation by these second- messengers. If no node is specified, the second-messenger levels at both nodes connected by the gap junction will influence the gap junction conductance. When a node is specified for the second messenger, the gap junction is modulated by second-messenger at only that single node.

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- Photoreceptor parameters and defaults
- Description of photoreceptor parameters
- Setting random seed
- Aperture and spatial filtering
- Save, restore photoreceptors
- Difference equations
- Pigment sensitivity functions

(interpreted:) at <node> rod (<xloc>,<yloc>) 'parameters' at <node> cone (<xloc>,<yloc>) 'parameters' at <node> chr (<xloc>,<yloc>) 'parameters' at <node> transducer (<xloc>,<yloc>) 'parameters' at <node> itransducer (<xloc>,<yloc>) 'parameters' (compiled:) photorec *p; p = make_rod (nd(<node>)); p->xloc=<xloc>; p->yloc=<yloc>;'parameters' p = make_cone (nd(<node>)); p->xloc=<xloc>; p->yloc=<yloc>;'parameters' p = make_chr (nd(<node>)); p->xloc=<xloc>; p->yloc=<yloc>;'parameters' p = make_transducer (nd(<node>)); p->xloc=<xloc>; p->yloc=<yloc>;'parameters' p = make_itransducer (nd(<node>));p->xloc=<xloc>; p->yloc=<yloc>;'parameters' p = make_rod (nd(<node>)); p->xloc=<xloc>; p->yloc=<yloc>; p->stimchan=<expr>; p = make_cone (nd(<node>)); p->xloc=<xloc>; p->yloc=<yloc>; p->stimchan=<expr>; p = make_chr (nd(<node>)); p->xloc=<xloc>; p->yloc=<yloc>; p->stimchan=<expr>; p = make_transducer (nd(<node>)); p->xloc=<xloc>; p->yloc=<yloc>; p->stimchan=<expr>; p = make_itransducer (nd(<node>));p->xloc=<xloc>; p->yloc=<yloc>; p->stimchan=<expr>;optional parameters:

----------------------------------- units: default: <xloc>,<yloc> um location of receptor in (x,y) plane. maxcond=<expr> S 1.4e-9 S dark cond of light-modulated channels. dia = <expr> um 2 um dia of receptor used for phot. flux. pigm = <expr> 1 0=rod, 1-3=cone l,m,s, default 1; see below for more pathl = <expr> um 35 um path length for light through receptor attf = <expr> .9 light attenuation factor (lens, etc.) filt = <expr> 0 0=none; 1=macular pigm, 2=lens, 3=macular+lens timec1= <expr> 1.0 time constant multiplier. loopg = <expr> 1.0 gain of ca feedback loop, sets stability linit = <expr> ph/um2/sec 0.0 initial light value for equilibration photnoise = <expr> 0 0->off; 1->on, Poisson photon noise from light flux. darknoise = <expr> 0 0->off; 1->SNR=5; 0-10, ampl Gaussian cont noise. stimchan = <expr> 0 private stimulus channel 0-9, (default 0=>none). rsd = <expr> set by node # Individual random seed, -1 -> set by rseed save save current values for later "restore" restore restore values from previous "save"A rod or cone photoreceptor is a transduction mechanism which responds to light and modulates a channel with certain gain, saturation, and time properties. The channel is added (in parallel) to the membrane properties for the compartment of the node which the receptor connects. A "chr" photoreceptor is a channel-rhodopsin which responds to light but directly controls a membrane ion channel. Its "pigm" parameter has a default of 23, the "ChR2" pigment.

A transducer photoreceptor converts a light stimulus directly into a voltage or current that it injects (through a voltage or current clamp) into the node's compartment. Otherwise it is similar to the rod and cone photoreceptors.

To stop the voltage clamp in a transducer, set the light intensity to a value less outside of the range of the variables "stimonh" and "stimonl" (default= 1, -1), which define the high and low values for a "stimulus-on" window. When the transducer sees a more positive value than "stimonl" and a more negative value than "stimonh", it activates the voltage clamp. For all other values, the voltage clamp is turned off, allowing the voltage to be controlled by other neural circuit elements. If the values are reversed, i.e. "stimonh" is more negative than or equal to "stimonl", the values describe a "stimulus-off" window, i.e. when the transducer sees a more positive value than "stimonh" and a value more negative than "stimonl", the voltage clamp is turned off.

An itransducer is similar to a transducer but converts the light intensity into a current that it injects into the node's compartment.

Click here to return to Photoreceptor statement index

Click here to return to Photoreceptor statement index

If you would prefer to set each noise generator, you
can independently set the pseudo-random sequence that each
photoreceptor receives with the "rsd" parameter. When set, the
"rsd =

Click here to return to Photoreceptor statement index

To specify a non-zero aperture for simulating low-pass spatial filtering, you can add the effect of the aperture to either the stimulus or the optical blur. For instance, if you are using a point-source stimulus (with or without blur), enlarging the point-source into a spot the size of the photoreceptor aperture simulates the spatial-filtering effect of the aperture in the photoreceptor. Alternately, if the optical blur Gaussian is at least twice the diameter (at 1/e) of the aperture, you can "pre-convolve" the optical blur with the aperture. This can be accomplished using either a separate convolution algorithm or the "root-mean- square rule" for convolution of 2 Gaussians (the resulting Gaussian diameter is the square root of the sum of the squares of the two constituent Gaussian diameters).

Click here to return to Photoreceptor statement index

Example:

(interpreted:) dim ncone [100]; at n cone (50,0) attf .75 ename ncone[i]; . . . modify ncone[i] cone () save; code for stimulus here. . step xtime; . code for recording response here. . modify ncone[i] cone () restore; (compiled:) int ncone [100]; photorec *p; p= make_cone(nd(n)); p->xloc=50; p->yloc=0; p->attf=.75; ncone[i]=p->elnum; . . . p=make_cone(nd(0)); p->modif = ncone[i]; p->save = 1; code for stimulus here. . step (xtime); . code for recording response here. . p=make_cone(nd(0)); p->modif = ncone[i]; p->restore = 1;The element number of the original photoreceptor is saved in the array "ncone[]" and this number is used to access the element later in the program. The "save" is placed just before the stimulus, and the "restore" is placed just after the response has been recorded.

Note that the entire model including the photoreceptors
can be saved and restored using the "save model (

By varying the "timec1" parameter, you can run the photoreceptor faster or slower. The photoreceptors are set by default to have a time to peak appropriate for mammals, or about 200 msec for rods and 60 msec for cones. You can lengthen these values to be appropriate for lower vertebrates (1 sec time to peak for rods). Or you can shorten the time to peak, which is useful to minimize the amount of computation in a simulation that records the response to a quick flashed light stimulus. Somemetimes, waiting around for 100 msec to get the response seems wasteful. Remember that membrane time constants will reduce the amplitude of the quicker voltage response recorded inside a neuron.

By varying the "loopg" parameter, you can run the photoreceptor calcium feedback loop with more or less gain. This sets the conditional stability of the loop. The default value for loopg is 1.0, which sets the Ca feedback loop a little unstable, so that the response overshoots during recovery. This type of behavior has been reported by Schneeweis & Schnapf (1999). A value less than 1 will reduce the amount of overshoot. The minimum value is 0.2, which causes a long recovery phase.

Photoreceptor light-modulated conductances are set with the "maxcond" parameter. The total bound fraction is always less than 1 so the maximum conductance is never exactly reached. Actual rod and cone conductances are non-linear but they are approximated by linear conductances in NeuronC. The rod conductance is nearly a current source (Baylor and Nunn, 1986) so that the light-modulated current is nearly constant over the physiological range (-20 to -60 mv). Thus the rod reversal potential is set to a large value (+720 mv). The cone conductance is more linear (Attwell et al., 1982), and reversal potential is predefined to be -8 mv. In order to give physiologically correct intracellular voltages, the rod and cone transduction mechanisms must be used with an appropriate leakage conductance (see definition files "rod.m" and "cone.m").

The rod and cone receptors are similar but the rod is approximately 100 times more sensitive. The rod mechanism responds to 1 photon with a voltage bump of about 0.5 mv and the cone mechanism responds to a 100 photon flash similarly. The cone response also is somewhat faster (peak in 60 msec), and has a negative undershoot on the recovery phase. New types of photoreceptors can be created (using the same set of difference equations) by adding a new set of "receptor constants" to the subroutine "initrec()" in the file "ncmak.c" and recompiling.

You can plot the values in the transduction cascade with:

(interpreted:) plot G(n) <element expr> G(0) conductance G(1) isomerized rhodopsin G(2) meta rhodopsin I G(3) meta rhodopsin II (R*) activates G protein G(4) G protein G(5) PDE G(6) G cyclase G(7) cGMP G(8) Ca feedback for recovery and adaptation G(9) Cax (protein between Ca and G cyclase) G(10) Rhodopsin kinase (turns off rhod in response to decrement in Ca) For mouse rod (Invergo et al. 2014), pigm=22: G(1) conductance G(1) isomerized rhodopsin G(2) rhodopsin bound to G protein G(3) rhodopsin bound to rhodopsin kinase G(4) activated G protein bound to ATP G(5) activated PDE G(6) activated RGS-PDE-G protein complex G(7) cGMP G(8) Rec protein bound to Ca2+ G(9) Free Ca++ G(10) Buffered Ca++ G(11) rhodopsin kinase (turns off rhodopsin) (compiled:) plot (G, n, <elnum>,<max>,<min>); Where: n=0-10 (as above). elnum = ename, element number. max, min = max and min for plot.Click here to return to Photoreceptor statement index

0 rod 1,2,3 cone l,m,s 4,5,6 turtle l,m,s 10,11,12 rabbit 13,14,15 guinea pig 16,17,18 goldfish 19,20,21 van_Hateren cone with adaptation (2007) 22 mouse rod with adaptation from Invergo et al (2014) 23 mouse channel-rhodopsin-2 from Williams et al (2013) 100 simple default 1 ->coneRod and cone type pigments are specified with the "pigm" parameter. The first 4 pigment sensitivity functions (rod=0, l,m,s = 1,2,3) are from Baylor, et al, 1984 and 1987 (monkey) and operate between 380 and 800 nm. The functions are implemented using a lookup table with values every 5 nm, quadratically interpolated between points. Default path length is dependent on pigment type: rods have a 25 um path, red, green and blue cones 35 um path. These can be overridden using the "pathl=x" parameter. The absolute sensitivity of a photoreceptor is calculated from tables of specific density vs. wavelength, multiplied by the path length. This calculation takes into account the photoreceptor's absolute density and its consequent self-screening.

The macular pigment is a yellow filter that excludes blue light from foveal cones, and the lens filter cuts off sharply in violet. The macular+lens filter adds the filtering properties of both filters in series (by adding their optical densities). The transmission spectrum for these filters is determined by table lookup, and the tables are from standard references. See the source code in "ncstim.cc", "wave.cc", "odconv.n", "macul.txt", and "lens.txt".

The turtle pigment sensitivity functions (pigm=4,5,6) are narrower than the corresponding primate pigments because turtles have colored oil droplets in the inner segment of the M and S cones that selectively filter the light reaching the outer segment. The turtle data are from Perlman, Itzhaki, Malik, and Alpern (1994), Visual Neuroscience, 11:247, Figs.4, 10, as digitized by Amermuller et al, Oldenburg, DE. The peaks were modified for smoothness, and the curves extrapolated from 400 to 380 nm and from 700 to 800 nm. The longwave extrapolation was done by the method of Lewis (1955) (J.Physiol 130:45) in which the log(sens) of a visual pigment is linear when plotted against wavenumber. (See "turtlesens.n" which was used to make "turtle.h", which contains the log(sensitivity) functions included in "wave.cc", which generates log(specific OD) functions in "wave.h" for "ncstim.cc".)

The goldfish pigment sensitivity functions (pigm=16,17,18) are from fundamentals defined in van Dijk and Spekreijse, 1984, fitted to equations from Govardovskii et al. (2000). See "goldfish.n" which was used to make "goldfish.h", which contains the log(sensitivity) tables included in "wave.cc". Then wave.cc generates log(specific OD) functions in "wave.h" for "ncstim.cc".)

The 19,20,21 pigment functions are a cone from van Hateren & Snippe (2007) and include the inner segment along with the outer segment. This model includes adaptation and bleaching at high light levels

The 22 pigment function is a mouse rod from Invergo et al (2014) that includes adaptation. It runs slow because it uses 96 differential equations.

The 23 pigment function is a channel-rhodopsin2 from Williams et al (2013) that includes adaptation. It is run through the channel sequential-state function which allows it to be run with or without gating noise.

The "simple" pigment has no sensitivity function and little transduction apparatus. Its conductance is modulated by a simple saturation function:

G = Isat / (Iflux + Isat) Where: Isat = 50000 R*/sec [for cones] 500 R*/sec [for rods]This provides a simple intensity response and allows photon noise but has no temporal filtering action. All the efficiency factors and pigment absorption factors are taken to be the same as in monkey "L" (red-absorbing) cones.

The light absorbed by a photoreceptor is calculated from:

sod = function of pigment and wavelength (table lookup) od = sod * path length T = exp10 ( -od ) Labs = photons/sec * ( 1 - T ) * mfilt * attf * dqeffWhere:

sod = specific optical density (extinction coeff. x concentration) od = optical density T = fraction Transmitted light mfilt = macular filter (if defined, 1.0 by default) attf = miscellaneous attenuation factor (set in photrec only, default 0.9) dqeff = default quantum efficiency (global variable "dqeff", set at .67) Labs = Light absorbed (absolute sensitivity)

Note that the L <node> expression plots the amount of light absorbed by a photorreceptor, i.e. it includes the effect of the attenuation factors "attf", "dqeff", and the photoreceptor sensitivity function. Click here to return to Photoreceptor statement index

(interpreted:) conn <node> to <node> vbuf <options> conn <node> to <node> vbuf gain=<expr> offset=<expr> tau=<expr> delay=<expr>; (compiled:) vbuf *make_vbuf (node *node1, node *node2, double offset, double gain, double delay, double tau) or vb = (vbuf *)conn(ct1, cn1, nd1, ct2, cn2, nd2, BUF); vb->offset = offset; vb->gain = gain; vb->tau = tau;Where:

option units: default: gain 1 Gain, Vout = (Vnode1 - Voffset) * gain offset V 0 Voltage offset tau sec 0 Low past time const in sec. delay sec 0 Time delay in sec.A "vbuf" is a connection between two nodes that causes the voltage at the second node to exactly duplicate the voltage at the first node. In effect, it functions as a voltage clamp but also has the ability to function as an amplifier (op-amp).

The "gain" parameter sets the gain of the amplifier, by default=1. The "offset" parameter (default=0) is a voltage that is subtracted from the voltage at node 1 and multiplied by the gain. The "tau" parameter is the low-pass cutoff frequency. The "delay" parameter allows a "vbuf" to function as an axon of a neuron to carry an action potential from one node to another node instead of requiring a set of compartments normally generated by a cable. This scheme greatly reduces computation.

The voltages are passed through a "circular buffer" that holds the data. The storage requirements are 10 floating-point values for each msec of delay.

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- Channel parameters and defaults
- Setting the channel conductance
- Voltage offset parameters
- Tau parameters
- Functions to plot Minf, Mtau, Tau[a-f]
- Temperature dependence (rates, conductances)
- Setting unitary conductance and N
- caperm parameter
- List of channel types
- Channel types: type 0, Hodgkin-Huxley
- Channel types: type 1
- KA (fast inactivating K channel)
- KCa (calcium-activated potassium channel)
- Ih channel (activated by hyperpolarization)
- Kir channel (activated by hyperpolarization)
- Integrate-and-Fire Na channel
- Calcium channels
- Calcium compartment
- Calcium buffering
- Calcium pumps
- Calcium induced calcium release (CICR)
- Calcium binding to inhibit channel
- Current through Ca channels
- Setting Nernst and GHK reversal potentials
- Strategy for computing reversal and Nernst potentials.
- Voltage offset of channel gating from external calcium
- Use of GHK current equation for channel current
- Voltage offset of reversal potential external calcium
- Markov channel noise
- Two-state channels
- Multi-state channels
- Recording conductance and state concentration
- Setting the rate functions
- Definition of alpha and beta for the "m" parameter
- Adding new channel types
- Channel condensation

(interpreted:) at <node> chan Na type <expr> 'parameters' at <node> chan K type <expr> 'parameters' at <node> chan CGMP type <expr> 'parameters' at <node> chan Ca type <expr> 'parameters' 'caexch params' 'pump params' 'cicr params' 'ip3 params' at <node> cacomp 'Ca parameters' 'caexch params' 'pump params' 'cicr params' 'ip3 params' (compiled:) elem *e; chattrib *c; cattrib *ca; e = at (nd(<node>), CHAN); a = make_chan (e, Na, <expr>); 'parameter code' a = make_chan (e, K, <expr>); 'parameter code' a = make_chan (e, cGMP, <expr>); 'parameter code' ca = (cattrib*)make_chan (e, Ca, <expr>); 'parameter code' ca = (cattrib*)make_chan (e, CACOMP,<expr>); 'parameter code' parameters: default: -------------------------------------------------------------------- (interpreted:) vrev = <expr> .04 V (Na) (~vna) Na reversal potential (Volts) -.08 V (K) (~vk) K reversal potential (Volts) .05 V (Ca) from cao/i and [K]i offsetm = <expr> 0.0 V (dnaoffsm) relative threshold for Na chan activation (Volts) offseth = <expr> 0.0 V (dnaoffsh) relative threshold for Na chan inactivation (Volts) offsetm = <expr> 0.0 V (dkoffsm) relative threshold for K chan activation (Volts) offseth = <expr> 0.0 V (dkoffsh) relative threshold for K chan inactivation (Volts) offset = <expr> 0.0 V (dcaoffs) relative threshold for Ca chan activation (Volts) tau = <expr> 1.0 relative act & inact 1/rate. taum = <expr> 1.0 (dnataum) relative activation 1/rate. taun = <expr> 1.0 (dktaun) relative activation 1/rate. tauh = <expr> 1.0 (dnatauh) relative inactivation 1/rate. taua = <expr> 1.0 relative activation alpha 1/rate. taub = <expr> 1.0 relative activation beta 1/rate. tauc = <expr> 1.0 relative inact 1/rate. taud = <expr> 1.0 relative inact recovery 1/rate. taue = <expr> 1.0 relative flicker 1/rate. tauf = <expr> 1.0 relative flicker 1/rate. maxcond= <expr> 1e-9 S (dmaxna) maximum conductance (Siemens) 2e-10 S (dmaxk) 1e-10 S (dmaxca) density= <expr> no default membrane chan density (S/cm2). ndensity=<expr> no default membrane chan density (N/um2). N = <expr> no default Number of channels. unit = <expr> (set by chan type) Unitary channel conductance caperm = <expr> (set by chan type) rel Ca permeability (NMDA,AMPA,cGMP). cakd = <expr> 1e10(=none)(dcakd) Kd for Ca binding to block channel. cahc = <expr> 1 (dcahc) Hill coefficient for Ca binding. k1 = <expr> 1e-7 M (dsk1), 1e-6 (dbk1) mult for Ca sens of KCa type 0,1,2,3 chan (KCa) k2 = <expr> 1e-7 M (dsk2), 1e-6 (dbk2) mult for Ca sens of KCa type 0,1,2,3 chan (KCa) d1 = <expr> 0 (dsd1), 1 (dbd1) mult for volt sens of KCa type 0,1,2,3 chan (KCa, type SK, BK) d2 = <expr> 0 (dsd2), 1 (dbd2) mult for volt sens of KCa type 0,1,2,3 chan (KCa, type SK, BK) cao = <expr> 0.005 M (dcao) extracellular Calcium conc (Molar) cai = <expr> 50e-9 M (dcai) intracellular Calcium conc (Molar) tcai = <expr> 10e-9 M (dtcai) intracellular Calcium conc threshold (Molar) cbound = <expr> 5 (dcabnd) ratio of bound to free Ca cshell = <expr> 10 (dcashell) number of int Ca diffusion shells caoshell = <expr> 10 (dcaoshell) number of ext Ca diffusion shells cabuf off use Ca buffer kd = <expr> 1e-6 M (dcabr/dcabf) Kd for Ca buffer (rev/forw rates) vmax = <expr> 1e8 /M/s (dcabf) Forward rate for Ca binding buffer btot = <expr> 3e-6 M (dcabt) Buffer concentration in shells btoti = <expr> 30e-6 M (dcabti) Buffer concentration in first shell caexch off use Na-Ca exchanger kex = <expr> 5e-9 A/mM4/cm2 (dcakex) exchanger current density capump off use Calcium pump vmax = <expr> 1e-4 A/cm2 (dcavmax) pump maximum velocity km = <expr> 2e-7 M (dcapkm) pump 1/2 max conc cicr off use Calcium-induced calcium release cas = <expr> 1.6e-6 M (casStart) CICR [Ca] init vm2 = <expr> 65e-6/ms (vm2CICR) CICR maximum uptake velocity vm3 = <expr> 500e-6/ms (vm2CICR) CICR maximum release velocity kf = <expr> 5e-6/s (kfCICR) CICR leak rate k2 = <expr> 1e-6 M (k2CICR) CICR thresh uptake kr = <expr> 2e-6 M (krCICR) CICR thresh release ka = <expr> 0.9e-6 (kaCICR) CICR thresh release ip3 off use IP3 internal store cas2 = <expr> 1.6e-6M (cas2Start) IP3 [Ca] init ip3i = <expr> 0.4e-6M (ip3iStart) IP3 [IP3] init vip3 = <expr> 7.3e-6/s (v1IP3) IP3 static flux rate bip3 = <expr> 0.31 (betaIP3) IP3 static frac chnoise = <expr> 0 (off) = 1 -> set channel noise on N = <expr> set by unitary cond Number of channels unit = <expr> (set by chan type) Unitary channel conductance rsd = <expr> set by rseed,srseed random seed (compiled:) elem *e; chattrib *c; cattrib *ca; nattrib *n; e = at (nd(<node>), CHAN); e = make_sphere(nd(soma),dia=10); ca = (cattrib *)make_chan(e,cGMP); ca->pump=1; ca->vmax=<expr> ... ca = (cattrib *)make_chan(e,CACOMP); ca->pump=1; ca->vmax=<expr> ... ca = (cattrib *)make_chan(e,CACOMP); ca->cicr=1; ca->vm3=<expr> ... n = make_chnoise(e); n->unit=<expr> ...These statements define a macroscopic conductance at a node. Several classes of ion-selective channels can be created: Na, K, Ca. Within each class there are several types. Type 0 is the Hodgkin-Huxley (1952) standard type. Type 1 is a discrete-state version of the H-H type, and other types have different behavior (see below). Type 0 channels' conductance is the product of activation (m or n) and inactivation (h) variables in the form m3h for Na, and n4 for K. Standard rate constants (alpha, beta) are calculated from look-up tables generated at the beginning of each run, based on the temperature (set by "tempcel") and a Q10 set by a default variable (see below).

The "maxcond" and "density" parameters define the open conductance of the channels. If you need to create a channel of a specific conductance at a node, specify the conductance with the "maxcond" parameter. Otherwise, use the "density" or "ndensity" parameters to specify a conductance density. The "ndensity" parameter along with a unitary conductance (either specified or default) defines the maximum conductance (see "see setting unitary conductance and N" below. You should not use both "maxcond" and "density" in the same statement, because they both define the channel conductance.

If you define a maxcond of zero, the channel won't be created, except if the parameter "nozerochan" is set to zero (default=1).

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If you prefer your "offset" parameters to define absolute voltages instead of relative offsets, set the default offset values in the beginning of your script to the voltage thresholds you determine for your default condition.

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If you prefer an "absolute" calibration for tau, just set the value for "base tau" in the beginning of your script to the time constant you determine for your default condition. Then you can then specify the "tau" as an actual time constant.

base_tau = time constant you find for default tau actual rate = rate * base_tau / tau"taum" corresponds to the sodium activation time constant, "tauh" corresponds to sodium inactivation, and taun corresponds to activation of potassium. If you want to change all of the rates proportionately, set the "tau" parameter.

A longer tau than the default value causes the action potential to be lengthened in time. A shorter tau shortens the action potential. If both "taum" and "tauh" are changed by the same factor, the action potential will retain the same general shape. If they are not changed by the same factor, the action potential shape will change and may fail entirely. If the time constants are too short, the action potential will fail because capacitive membrane charging shunts the ion currents and prevents voltage from changing quickly.

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minf (v, ename); /* returns equilibrium value of "m" */ mtau (v, ename); /* returns time constant of "m" */ hinf (v, ename); /* returns equilibrium value of "h" */ htau (v, ename); /* returns time constant of "h" */ ctaua (v, ename); /* returns time constant of alpham */ ctaub (v, ename); /* returns time constant of betam */ ctauc (v, ename); /* returns time constant of alphah */ ctaud (v, ename); /* returns time constant of betah */ ctaue (v, ename); /* returns time constant of flicker */ ctauf (v, ename); /* returns time constant of flicker */Click here to return to Channel statement index

Ea = [(R T1 T2) / (T2-T1)] ln (tau1/tau2) (see Kirsh and Sykes, 1987) Q10 = exp (10 Ea / (R T1 T2) (method of computing Q10)Where:

R = gas const, 1.987 cal/deg/mol. T1,T2 = Temperatures, deg K. tau1 = time constant of channel at T1. tau2 = time constant of channel at T2.Once the Q10 value for a temperature sensitive function (rate or conductance) is known, the function is multiplied by a factor defined by the Q10 equation:

rate multplier = exp(log(dqx) * (tempcel - dbasetc) / 10)Where:

dqx = the Q10 temperature dependence (dqm=2, dqh=3, dqc=1.4, etc.) tempcel = temperature of the simulation dbasetc = base temperature for channel, default = 22 deg. C.The temperature dependence of most of the rate functions is set to a default Q10 value of 3, as assumed by Hogkin and Huxley (1952), except for alpham and betam which are set to a default of 2, and for alphan, 3.2, and for betan, 2.8 (Frankenhaeuser and Moore, 1963).

The default values are: dqm = 2.3 (alpham, betam) dqh = 2.3 (alphah, betah) dqna = 2.3 (alphan) dqnb = 2.3 (betan) dqn = 2.3 (alphan,betan) (set this to override dqna, dqnb) dqca = 3 (alphac, betac) dqd = 3 (alphad, betad, for KA h) dqkca = 3 (for Kca chan) dqsyn = 3 (synaptic channels) dqcab = 2 (Ca buffer) dqcavmax=2 (Ca pump) dqdc = 1.3 (Ca diffusion constant) dqc = 1.4 (channel unitary conductance) dqrec = 2.7 (photorecptor transduction shape, not currently used) dqcrec = 1.8 (photorecptor transduction cond) dqrm = 1 (membrane conductance 1/Rm) dqri = 1 (axial conductance 1/Ri)For each channel type the rate function is defined at a certain temperature (the "base temperature"). At other temperatures the rate is multiplied by the increase or decrease calculated from the Q10 over the change in temperature from the original definition. Since voltage gated channels have a well-known temperature depency, it is always used, even when you specify a change in rate (with the dividers "taum", "tauh", etc.) from the original absolute rate.

In their classic study of channel kinetics, Hodgkin and Huxley (1952) used a temperature of 6.3 degrees Celsius. Since many recent studies of channel kinetics have been done at 22 degrees, this is the standard temperature for defining their rate functions and unitary conductance. To simplify the kinetic and conductance parameters, the Hodgkin-Huxley kinetic functions are normalized to 22 deg C. For channels whose rate functions have been studied at some other temperature, that temperature can be entered as the standard temperature for the channel, or the channel's kinetics can be normalized for 22 deg C by assuming a temperature sensitivity (Q10) for its kinetics and unitary conductance. For synaptic conductances the base temperature is 22 degrees C.

You can change the default base temperature for channel kinetics (and unitary conductances) with the following variables:

var default meaning ------------------------------------------------------------------------------ dbasetc 22 deg C base temp for membrane channel kinetics, conductances dbasetsyn 22 deg C base temp for synaptic kinetics dbasetca 22 deg C base temp for ca pumps dbasetdc 22 deg C base temp for Ca diffusion constantNormally it is not necessary to change the base temperature for channel kinetics because the rate functions are automatically adjusted when you change temperature (with the "tempcel" parameter).

The Hodgkin-Huxley type channels are normalized by multiplying their rate functions by a constant factor ("dratehhx") that increases their rate from the original (defined at 6.3 deg. Celsius) to the correct rate for the base temperature (dbasetc = 22 deg C). This factor is computed by default from the standard default "dqm, dqh, dqna, dqnb" values. However, it is not affected if you change the value of "dqm, dqh, dqna, dqnb". Instead, you can change it by setting the "dbasehhx" rate multiplier variables:

var default Q10 meaning ------------------------------------------------------------------------------ dratehhm 2.9690 2.0 multiplier for normalizing alpham, betam from 6.3 to 22 deg C dratehhh 5.6115 3.0 multiplier for normalizing alphah, betah from 6.3 to 22 deg C dratehhna 6.2099 3.2 multiplier for normalizing alphan from 6.3 to 22 deg C dratehhna 5.0354 2.8 multiplier for normalizing betan from 6.3 to 22 deg CThese values are computed from the Q10 equation:

dbasehhh = exp(log(3.0) * (22 - 6.3) / 10)The temperature sensitivities for channel gating and conductance have recently been determined for mammalian ganglion cells by Fohlmeister, Cohen and Newman (2009). They are nearly constant from 22 deg C to 37 deg C, but below 22 deg the changes are larger, and below 10 deg C they are much larger. To work in the range of 10-22 deg, you can set dqm, dqh, and dqn to 3.5.

chan default Q10 Q10 @22-37deg @10-22 deg Gating dqm 2.3 1.95 3.5 (alpham, betam) dqh 2.3 1.95 3.5 (alphah, betah) dqn 2.3 1.9 3.5 (alphan, betan) dqca 2.3 1.95 3.5 (alphac, betac) conductance dqc(Na) 1.44 1.85 3.0 (channel unitary conductance) dqc(K) 1.44 1.8 3.5 (channel unitary conductance) dqri 1.0 0.8 (axial conductance 1/Ri) dqrm 1.0 1.85 (membrane conductance 1/Rm)You can set these values according to the temperature ("tempcel") by calling the function:

(interpreted:) set_q10s() (compiled:) setq10s() which returns the current temperature ("tempcel");For the calcium buffer and pump the Q10 has been arbitrarily set to 2. The rates will change with temperature only when the default rates for the buffer and pump are used, i.e. if you specify a rate, it will not change with temperature.

dqcab = 2 (Q10 for Ca buffer) dqcavmax = 2 (Q10 for Ca pump)When a unitary conductance for a channel is not specified by the user, a default value defined for the channel type is used. The default rate changes according to the temperature and the Q10 set by "dqc". If you specify a unitary conductance, this value is used directly, i.e. it will not change with temperature.

unitary conductance = dxu * exp(log(dqc) * (tempcel - dbasetc) / 10)Where:

dxu = default unitary conductance for the channel (dnau, dku, etc.) dqc = Q10 for unitary conductances, default = 1.4 tempcel = temperature of the simulation dbasetc = base temperature for channel, default = 22 deg. C.Unitary conductances reported in the literature generally have a Q10 between 1.3 (for diffusion in water) to 1.6, so the value of 1.4 is a compromise (it can be changed for any channel in the source code).

The Q10s for Rm and Ri are active when the default values (drm, dri) are used. When you set a "local Rm" or "local Ri" in a cable or sphere statement its value is used unchanged. The default values for "dqri" and "dqrm" are set to 1, and their base temperature is "dbasetc", as above for channels. To activate temperature compensation for these conductances, set the value of "dqri" and/or "dqrm" to 1.3.

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If "unit" and "N" are both set and "maxcond" is not, the conductance is set by the product of N times unit:

chan .... chnoise=1 N=25 unit=10e-12 N = you define unit = you define channel conductance is then calculated as = N * unitIf you define "N" but not "unit" or "maxcond", the conductance will be determined from the N you set along with the default "unit" for the channel type:

chan .... chnoise=1 N=25 N = you define unit = default for channel channel conductance is then calculated as = N * unitIf you place the "N" parameter before or without "chnoise", it will define the channel conductance. You can place a second "N" after "chnoise" and it will define N for the noise properties only.

chan .... N=100 chnoise=1 N=25 N = you define unit = default for channel channel conductance is calculated as = N * unit Noise is calculated from second N (25).Note that you can turn off noise by setting "N" or "chnoise" to zero.

You can use the "ndensity" parameter instead of the "N" parameter to define the conductance and noise properties automatically:

chan .... ndensity=10 chnoise=1 ndensity = you define unit = default for channel N is calculated as = ndensity * membrane surface area channel conductance is calculated as = N * unit Noise is calculated from N (from ndensity).If you use a channel's default unitary conductance (by not defining "unit"), the unitary conductance will have a temperature dependence (Q10 set by "dqc", default=1.4)

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Na (green) and Kdr (red) channels voltage clamped in steps from -70 to +20 mV. Note that Na currents are inward, activate quickly, and inactivate after 1-2 msec, whereas Kdr currents activate slowly and do not inactivate.

Na type 0 rate functions: Given Vm in mV, calculate rate /sec: Activation: alpham = taum ( -100 (V- -40.) / (exp ( -0.1 (V- -40.) - 1)) betam = taum ( 4000 exp ((V- -65) / -18.)) alphah = 70 exp ((V- -65) / -20.) betah = 1000 / (exp (-0.1(V - -35)) + 1.0) Inactivation: alphah = tauh ( 70 exp ((V- -65) / -20.)) betah = tauh (1000 / (exp (-0.1(V - -35)) + 1.0)) Where: V = Vm - voffset voffset = voltage voffset (set by user) taum = activation rate function divider (set by user) tauh = inactivation rate function divider (set by user)Click here to return to Channel statement index

Channel types ion type states characteristics Na 0 0 Standard Hodgkin-Huxley kinetics, m3h. 1 8 Standard Hodgkin-Huxley kinetics, Markov discrete-state. 2 9 NaV1.2, Markov, modified from Vandenberg and Bezanilla, 1991 3 12 NaV1.2, Markov, from Kuo and Bean (1994). 4 12 NaV1.2, Markov, persistent, from Taddese and Bean (2002). 5 9 NaV1.1, Markov, SCN1A, slow recovery from inactivation, from Clancy and Kass (2004). 6 13 NaV1.6, Markov, persistent, rapid recovery from inactivation, from Raman and Bean (2001). 8 9 NaV1.8, Markov, TTX-resistant, similar to type 2 but slower 20 6 Simple Markov, similar to Type 1. 21 2 Integrate-and-fire, Markov. K 0 0 Standard Hodgkin-Huxley kinetics, n4, non-inactivating. 1 5 Standard Hodgkin-Huxley kinetics, Markov discrete-state 2 0 KA channel, inactivating, HH-type, n3h. 3 8 KA current, inactivating, HH-type, Markov discrete-state 4 3 Ih channel, hyperpolarization-activated, depolarizing from Hestrin (1987), see chank4.cc. 5 3 Kir channel, hyperpolarization-activated, hyperpolarizing 6 5 Duplicate of type 1 Markov, used for slower version 7 5 Duplicate of type 1 Markov, used for slower version 8 10 HCN (Ih) channel, from Altomare et al. (2001), see chank4.cc. 9 6 HCN (Ih) channel, like Altomare et al. (2001), but only 1 cond state. KCa 0 0 SKCa, Hodgkin-Huxley-like, no voltage sensitivity. 1 2 SKCa, Markov discrete-state. Ca-sensitivity can be varied, see below. 2 0 BKCa Hodgkin-Huxley-like. 3 2 BKCa channel, Markov discrete-state. Voltage- and Ca-sensitivity can be varied, see below. 4 6 SKCa channel, Markov discrete-state, from Hirshberg et al. (1998). 5 6 SKCa channel, Markov discrete-state, from Sah and Clements (1999). Insensitive to apamin. 6 10 BKCA channel, Markov discrete-state, voltage sensitivity, from Cox et al. (1999). (Best BK model yet) ClCa 1 12 ClCa, like KCa type 4, after Lalonde Kelley, Barnes (2008) ClCa 2 12 ClCa, like type 1 but senses [Ca]i shell set by "dsclcac" (default 10) Ca 0 0 L-type Ca, c3 (high voltage activated, tonic) Ca 1 4 L-type Ca, discrete state, like type 0. Ca 2 0 T-type Ca, c2h, (low voltage activated, fast inactivating) Ca 3 6 T-type Ca, discrete state, like type 2. Ca 4 0 T-type Ca, c3h, (low voltage activated, fast inactivating) Ca 5 8 T-type Ca, discrete state, like type 4. Ca 6 12 T-type Ca, low threshold, from Serrano et al, 1999 Ca 7 12 T-type Ca, low threshold, modified after Lee et al., 2003 cGMP 1 8 cGMP-gated chan from rod outer segment (Taylor & Baylor 1995) cGMP 2 9 cGMP-gated chan, inhibited by Ca binding AMPA 1 7 AMPA-gated chan, zero Ca perm (Jonas et al 1993) AMPA 2 7 AMPA-gated chan, Ca perm, independent gating (Jonas et al 1993) AMPA 3 9 AMPA-gated chan, Ca perm, (Raman and Trussel 1995) AMPA 4 9 AMPA-gated chan, Ca perm, (simple state diagram, based on Jonas 1993) AMPA 5 9 AMPA-gated chan, Ca perm, (non-desensitizing, based on Jonas 1993) GABA 1 5 GABA-gated chan (Busch and Sakmann, 1990) GABA 2 7 GABA-gated chan (based on AMPA chan Jonas et al 1993) GABA 3 7 GABA-gated chan (based on Jones and Westbrook 1995) GABA 4 5 GABA-gated chan, GABA-C, longer decay (mod. from Busch and Sakmann, 1990) GLY 1 5 GLY-gated chan (based on GABA chan, Busch and Sakmann, 1990)The type 1 Na channel has an 8 state transition table with four inactivated states. The K channel has 5 states with no inactivated states. They produce identical results to the HH (or type 0) channels, but run a little slower. The type 2 Na channel has "improved" kinetics that are defined by a 9-state Markov diagram. It is the "extended type 3" model of Vandenberg and Bezanilla, (1991) and is more biologically accurate than HH type models. It is slightly modified from the published version to have a higher slope on the activation vs. voltage curve. This reduces the amount of activation at voltages hyperpolarized from -50 mV. The type 3 Na channel is from Kuo & Bean (1994) and has a 12 state transition table with 6 activated and 6 inactivated states, and is also more realistic than the HH (type 0) channel. The Na type 4 channel is from Taddese & Bean (2002) and is a "normal" current that persists to allow pacemaking. The Na type 6 channel is from Raman & Bean (2001) and is a persistent current that reactivates rapidly to give burstiness. The Na type 21 channel is an "integrate-and-fire" model (see below).

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Other discrete-state channels (type 1 and above) are macroscopic descriptions of sets of channels in a membrane. The population of a state represents its "concentration" as a fraction of 1. The concentration of all states always sums to 1. Each state also has a fractional conductance which when multiplied by the effective maximum conductance "maxcond" produces the instantaneous channel conductance. Microscopic descriptions of channels are possible for the same transition state diagram using noise parameters (see below).

When noise is added to these discrete-state channel types (with the "chnoise" parameter), the population of a state is an integer that represents the actual number of channels in the state, and the number of channels that move between between different states is an integer number calculated from the binomial function. The total number of channels (i.e. from all the states) remains constant. This scheme gives a very accurate representation of the channel kinetics and noise. A time step of 50 usec or less must be used when discrete state channels are given noise properties or the numerical integration becomes unstable.

Top, eight-state Markov state diagram for Na type 1 channel. Time courses of 6 of the 8 states are illustrated below. Middle, average state populations for a typical action potential. Each state varies between 0 and 1, and the total of all states is 1. Bottom, same plot except noise for 100 channels added. Transition between states is computed from binomial distribution based on population of the source state and the probability of the transition (rate function).

The function of the KA current in some neurons is to stablize the membrane in combination with Na and Kdr channels. Since KA activates and inactivates rapidly it is active during the time when Kdr channels are building up activation, but during a prolonged stimulus KA inactivates when Kdr is fully active. This action tends to dampen oscillatory behavior. In a spike generator, KA helps to terminate the spike, and is quickly inactivated on hyperpolarization. In some neurons, it activates at a more hyperpolarized voltage than Na channels, so it slows down repolarization in the interspike interval.

KA rate functions: Given Vm in mV, calculate rate /sec: Activation: y = -0.1 * (V+90); alphan = taun * 10.7 * y / (exp(y) - 1) betan = taun * 17.8 * exp ((V+30) / -10.) Inactivation: alphad = tauh * 007.1 * exp (-0.05 * (V+70)) betad = tauh * 10.7 / (exp (-0.1 * (V+40)) + 1.0) Where: V = Vm - voffset voffset = voltage voffset (set by user) taun = activation rate divider (set by user) tauh = inactivation rate divider (set by user)

Activation of K type 2 and 3 channels by a voltage clamp from -70 mV to -10 mV. Dark blue traces show conductance. On top, green trace is the "m" state variable (activation), and the light blue trace is the "h" state variable (inactivation). At bottom, each trace represents the fractional population of one of the 8 states.

Gk = maxcond * n dn/dt = alphakca - (alphakca + betakca) * n alphakca = taun / (1 + k1 / [Ca] * exp(d1 * -V / 10) ) betakca = taun / (1 + [Ca]/ (k2 * exp(d2 * -V / 10) ) ) Where: d1, d2 are voltage coefficients k1, k2 are calcium coefficients V = membrane voltage in mV V = Vm - voffset (set by user) taun = rate divider (set by user)The constants maxcond, tau, voffset, d1,d2,k1,k2 can be specified by the user. The d1 and d2 constants set the voltage sensitivity, and k1 and k2 set calcium sensitivity.

Reasonable values of d1 and d2 are between .5 and 5. To eliminate voltage sensitivity, set both d1 and d2 to 0 (which is default for KCa types 0 and 1). A good start for the k1 and k2 values is the average range of internal [Ca] expected. Above this average Ca level, alphakca increases, and below the average betakca increases.

Some KCa channels have minimal voltage sensitivity (SK type), a small unitary conductance (~20 pS), and are thought to be involved in lengthening the interspike interval. Other types involved in spike termination have a large unitary conductance, and both voltage and calcium sensitivity (BK type). If you specify KCa type 0 or 1 channels (SK type) they will have no voltage sensitivity by default. If you specify KCa type 2 or 3 channels (BK type) they will have voltage and calcium sensitivity by default. You can change this default behavior by setting d1, d2, k1, and k2.

The KCa type 2, 3 channels are similar to the 0, 1 channels except that they are the "BK" type (sensitive to voltage and Ca, with large conductance = 200 pS). They have different default values for the unitary conductance and the d1, d2, k1, k2 constants.

The KCa type 4 channel is a sequential-state channel with 6 states that has no voltage sensitivity and is the best model so far for the SKCa channel (apamin-sensitive). This channel is derived from Hirshberg et al, 1998 (see chankca.cc for details). As in the other sequential state channels, when noise is added the states become populated with an integer number of channels with the changes in population computed from the binomial function. You can modify the activation and inactivation rates with the parameters "taua" (Ca binding), "taub" (Ca unbinding), "tauc" (opening flicker rate), and "taud" (closing rate).

The KCa type 5 channel is a sequential-state channel with 6 states that describes an sKCa channel with no voltage sensitivity but insensitive to apamin. This channel is derived from Sah and Clements, 1999 (see chankca.cc for details). Its affinity for Ca++ is relatively high, so Ca++ unbinds slowly, which accounts for the slow deactivation of the channel. You can change the Ca++ binding rate with "taua", the unbinding rate with the parameter "taub", and the open/close flicker rate with "taud". You can test these channels with the "tcomp/chantestkca.n" script.

The KCa type 6 channel is a sequential-state channel with 10 states that describes a bKCa channel with voltage- and calcium-dependent gating. It is taken from Cox et al, 1997 (see chankca.cc for details) in which a cloned "mslo" channel is analyzed and an allosteric Markov model developed. The model starts opening at ~100 nM [Ca]i but at a relatively high voltage ( > +30 mV), and at higher [Ca] it opens at more hyperpolarized voltages.

You can change the Ca++ binding rate with "taua", the unbinding rate with the parameter "taub", and the rates for the voltage gating functions with "tauc" and "taud". You can change the range of voltage gating with the d1 and d2 constants (as in the other KCa channel types). You can test this channel with the "tcomp/chantestkca2.n" script.

The Cox et al. Markov model is valid for a wide physiological range of [Ca]i and voltage, but is recognized to be incorrect for zero [Ca]i or for extremes of voltage. In this MWC-type model, 4 subunits have independent binding of Ca++, can remain closed during Ca binding, and the channel has a concerted voltage-gated opening. The effect of [Ca] on opening is to shift the channel to liganded states which have different forward and reverse rate functions for voltage gating, effectively changing the voltage range of gating, though the gating function is unchanged. Gating of the BK channel is among the most complex known, since the channel has numerous open and closed states and can open almost fully in the absence of [Ca]. More recent studies have ruled out this MWC-type model, and we are awaiting a better Markov model for the BK channel.

The ClCa type 2 channel is identical to the ClCa type 1 channel except that it senses [Ca]i in any shell or the Ca core, set by the parameter "dsclcac" (default=10). Its voltage sensitivity is controlled by "dclcavsc" (default=2.0) which multiplies the forward rate of binding by [Ca]i at the shell described by "dsclcac" over the range of 120 mv, starting at -40 mV.

Currents through a K type 4 channel (Ih current). The cell is clamped to -30 mV and then stepped to -50 down to -110 mV for 500 msec, then stepped to +30 mV. Note that the activation currents have a long time constant but deactivation is short, and that the channel does not inactivate.

The K type 4 channel is a sequential-state version of the Ih channel from photoreceptors. It is activated when the membrane voltage hyperpolarizes beyond -50 mV, and has a slow activation time constant, between 50 and 200 msec. It does not inactivate, but deactivates at voltages more depolarized than -30 mV with a time constant between 20 and 50 msec. Normally K channels have a default reversal potential set by the K Nernst potential to near -80 mV, however for the Ih channel the default is -20 mV. You can change the reversal potential with the "vrev=" option.

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Since the channel imitates a Na channel it can only depolarize so another channel (typically a K channel) is required to set up a working spike generator. This channel can therefore be used in combination with other channel types to test out hypotheses in a way not possible with standard integrate-and-fire spike generators (because they don't work with a standard compartment that sums the synaptic inputs and the spike currents).

To look inside the operation of the IF NA channel, you can plot the G1 and G2 values to show the population of the two states; G2 is the conducting state. Plot G3 and G4 to look at the integration and state switching.

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Type 0 Gca = c3 * maxcond = L-type calcium dc/dt = alphac - (alphac + betac) * c high threshold Type 1 same as type 0 but Markov sequential-state Type 2 Gca = c2h * maxcond = T-type calcium dc/dt = alphac - (alphac + betac) * c low threshold dh/dt = alphah - (alphah + betah) * h Type 3 same as type 2 but Markov sequential-state Type 4 Gca = c3h * maxcond = T-type calcium dc/dt = alphac - (alphac + betac) * c low threshold dh/dt = alphah - (alphah + betah) * h Type 5 same as type 4 but Markov sequential-state Type 6 Markov 12 states = T-type calcium From Serrano et al (1999), low threshold J Gen Physiol 114:185-201 Type 7 Markov 12 states = T-type calcium Like Serrano et al, but modified low threshold for retinal ganglion cell. Taken from Lee SC, Hayashida Y, and Ishida AT (2003), J Neurophysiol 90:3888-3901.The alpha and beta rate equations are similar to those for the Na conductance (look in "initchan.c" for "accalc()" and "bccalc()").

The calcium compartment contains a series of concentric shells
of "cytoplasm", each 0.1 um thick, that restrict the flow of
calcium into the interior of the cell according to the law of
diffusion. The parameter "cshell" sets the number of shells
(default 10). The inner part of the cell is considered to be a
well-stirred "core" with a uniform concentration of calcium. In
a dendrite that's too small to fit the number of specified or
default shells, the number of shells is reduced so they fit.
Only the calcium concentration at the outer shell "Ca(1)",
next to the membrane, affects the membrane reversal potential.
The parameters "cao" and "cai" define the starting concentrations
of calcium in extra- and intra-cellular space, respectively. The
parameter "caoshell" sets the number of shells in extracellar
space (default 1). The parameter "ddiacao" sets the effective
diameter of the extracellular "core" for calcium diffusion. The
parameter "ddcao" sets the diffusion constant for extracellular
calcium. The parameter "dcasarea" sets the effective area
of the shells for calculating the Ca flux (default set by morphology).
The parameter "tcai" specifies the threshold below which internal
calcium is not pumped. You may also specify a calcium compartment
with the "at

At each time step, the calcium flux through the membrane is computed from the sum of the current through the calcium channel, the calcium pump, and the sodium-calcium exchanger. This flux is then added to the compartment and calcium diffusion between the concentric shells is computed.

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Dynamic calcium buffering in the shells is specified with the "cabuf" parameter. The total concentration of buffer is set by the "btot" parameter ("btoti" for the first shell). Calcium binds to the buffer at a high rate that is proportional to the concentration of both calcium and buffer:

f> Ca + B <--------> Ca.B <rYou specify the forward (binding) and reverse (unbinding") rates (default values "dcabf", "dcabr") using the "kd" (= ratio of reverse/forward rates) and "vmax" (=forward rate) parameters. Many different effects can be set up by varying the forward binding rate, kd, and the buffer concentration.

The forward rate is dependent on the concentration of calcium and buffer. The reverse rate is a function of time and is independent of concentration. If the forward rate is not set (with "vmax"), the default values are dependent on temperature (Q10 set by "dqcab", default=2).

Note that when the "cabuf" parameter is defined, the "cbound" parameter is ignored.

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Its current is:

Ica = Vmax * ([Ca]-[CaB]) / ( Km + ([Ca]-CaB] )Where:

Ica = calcium current from this pump (outward). [Ca] = calcium concentration at inner surface of membrane. [CaB]= basal level of calcium below which it is not pumped = tcai. Vmax = Maximum rate of calcium current (density: mA/cm2). km = concentration for 1/2 max rate.The pump's calcium current is added to the total current in the voltage compartment and also to the total calcium flux in the calcium compartment. The parameter "dicafrac" sets the fraction of Ica (default=1) that is added to the current. Seting this parameter to 0 allows you to set the calcium pump's rate of calcium flux without affecting current flow.

Note that the pump current is independent of membrane voltage but is dependent on the internal Ca concentration. If the pump "vmax" is not set, its default value is "dcavmax". It is dependent on temperature (set by its Q10 value, "dqcavmax" default=2).

For a simple model, you can set up exponential decay for [Ca]i by setting just one shell, and eliminating diffusion to the internal core. For this purpose, set the Ca pump Km a little higher than the expected maximum [Ca]i (so the pump rate is proportional to [Ca]), like this:

tempcel=35; /* pump is temperature-dependent */ ddca = 1e-12; /* set to low value to eliminate diffusion */ catau = 50e-3; /* Sets Ca decay tau (used here only) */ at 1 sphere dia 10; at 1 chan Ca density 1e-5 capump vmax=5e-7/catau km=5e-6 /* gives 50 msec tau @ 35 deg C */ cshell 1;A second type of calcium pump is the "exchanger". It is a low-affinity, high-volume calcium transporter that exchanges Na ions for Ca ions. Its currents are:

Ica = Kex * [ Cao * Nai * Nai * Nai exp (EG * V * F/RT) - Cai * Nao * Nao * Nao exp ((EG-1) * V * F/RT) ] Ina = -r * Ica / 2Where:

Ica = calcium current from this exchanger (outward). Ina = sodium current from this exchanger (inward). Cao = external calcium concentration. Cai = calcium concentration at inner surface of membrane. Nao = external sodium concentration. Nai = internal sodium concentration. Kex = defines rate of calcium current (density: A/mM4/cm2). EG = partition parameter representing position of V sensor (0.38). r = exchange ratio (3 Na+ per Ca++)The exchanger's calcium and sodium currents are added to the total current in the voltage compartment. The calcium current is added to the total calcium flux in the calcium compartment. The parameter "dicaexchfrac" sets the fraction of the calcium exchanger's current that is added to the total current. Setting this parameter to zero allows setting the calcium flux rate without affecting the current flow.

Note that the exchanger current is dependent on membrane voltage and on the concentration of both internal and external Ca and Na and temperature. At low internal Ca concentrations the exchanger supplies Ca to the cell which raises internal Ca and generates a net outward current. At high internal Ca concentrations the exchanger extrudes Ca from the cell which lowers internal Ca and generates a net inward current.

For simulations with typical concentrations and temperatures (temp = 22-35 deg C, dcao = 1.15 mM, dnao = 143 mM, dnai = 12.5 mM, i.e. Ena = +65 mV), the equilibrium point ranges from 90 to 150 nM, so typically the exchanger tends to deplolarize. The pump and exchanger rates therefore can be adjusted to achieve a balance at one concentration:

at 1 sphere dia 10; at 1 chan Ca density 1e-5 capump vmax=1e-5 km=5e-6 caex kex=5e-9 cshell 1;Click here to return to Channel statement index

This behavior is controlled by several parameters:

casStart /* init ryanodine [Ca] store = 1.6e-6 M */ kfCICR /* passive leak rate const from ryanodine store, 1/s (Goldbeter 1990) */ vm2CICR /* max rate of Ca pump into ryanodine store, 65e-6/ms (Goldbeter 1990) */ vm3CICR /* max rate of Ca pump from ryanodine store,500e-6/ms (Goldbeter 1990) */ k2CICR /* assoc thresh pump const, ryan store uptake,1e-6 M (Goldbeter 1990) */ krCICR /* assoc thresh pump const, ryan store release,2e-6 M (Goldbeter 1990) */ kaCICR /* assoc thresh pump const, ryan store release,0.9e-6 M (Goldbeter 1990) */ nCICR /* Hill coeff, coop pump binding ryan store uptake, 1 (Goldbeter 1990 */ mCICR /* Hill coeff, coop pump binding ryan store release, 1 (Goldbeter 1990 */ pCICR /* Hill coeff, coop pump binding ryan store release, 4 (Goldbeter 1990 */ cas2Start /* init IP3 [calcium] store = 1.6e-6 M */ ip3iStart /* init [IP3] intracellular = 0.4e-6 M */ betaIP3 /* init fractional rate of constant IP3 store release, default 0.31 */ v1IP3 /* init constant IP3 store flux to 7.3e-6/ms (Goldbeter 1990) */Click here to return to Channel statement index

When you specify the "cakd" parameter, calcium binds to the channel and causes it to close. It uses the following equation:

go = gc * ( 1 - Ca^n) / ( Ca^n + kd^n) Where: go = output conductance limited by Ca binding gc = channel conductance without Ca binding kd = Kd for Ca binding "cakd" n = Hill Coeff for Ca binding "cahc" Ca = [Ca]i, internal Ca concentration kd^n = kd to the n power Ca^n = [Ca]i to the n powerThe cooperativity of the binding is first-order by default but it can be set with the "cahc" parameter (default dcahc=1). This works for the "syn2" and "cGMP type 1" channels, and is a very simple implementation that does not give correct channel noise properties. The "cGMP type 2" channel is a Markov implementation that gives more accurate noise properties (see "chancgmp.cc"). Click here to return to Channel statement index

if((cratio=(cai + dpki) / cao) < 1.0) { if (abs(vm) > 1e-5) { vfact = exp(vm* 2F/R/T); df = -vm * (1.0-cratio*vfact) / (1.0 - vfact); } else df = r2ft * (1-cratio); } else df = capnt->vrev - vm; /* driving force */ Where: df = driving force for calculating current vm = membrane voltage cai = internal Ca cao = external Ca dpki = internal KClick here to return to Channel statement index

However, the Nernst potentials "vna", "vk", "vcl", etc. are not equal to the reversal potential that is experienced by a channel, for several reasons. Other ions besides the channel's major ion can pass through the channel and this affects the reversal potential, defined by the "GHK voltage equation" (see "Reversal potentials, Nernst and GHK equation" in the first section of the manual). Also, when the internal and external concentrations of an ion such as Ca are very different, the effective driving force for the channel changes with membrane voltage (see "Current through Ca channels" above).

The reversal potential for a NeuronC channel is set by default to its GHK voltage, calculated from the concentrations of various ions and their permeabilities through the channel. The internal and external concentrations for an ion are set by default from predefined Nernst potentials for the ion (i.e. vna, vk, vcl), but you can change these values to give arbitrary Nernst and reversal potentials. Note that the default reversal potential for a channel and the Nernst potential for an ion are functions of "tempcel" = temperature (see "Reversal potentials, Nernst and GHK equation" in the first section of the manual). They are also functions of the "surface potential" that is created when external calcium concentration is high (see "Voltage offset from external calcium" below).

If you want to ignore the GHK voltage equation and set reversal potentials from the Nernst voltages vna, vk, and vcl, you can set the relative permeabilities of channels to their minor ions to zero:

dpkna = 0; ( sets K permeability in Na chans to 0 ) dpcana = 0; ( sets Ca permeability in Na chans to 0 ) dpnak = 0; ( sets Na permeability in K chans to 0 ) dpcak = 0; ( sets Ca permeability in K chans to 0 ) dpnaca = 0; ( sets Na permeability in Ca chans to 0 ) dpkca = 0; ( sets K permeability in Ca chans to 0 ) dpcaampa= 0; ( sets Ca permeability in AMPA chans to 0 ) dpcacgmp= 0; ( sets Ca permeability in cGMP chans to 0 ) dpcanmda= 0; ( sets Ca permeability in NMDA chans to 0 ) dpcasyn2= 0; ( sets Ca permeability in syn2 chans to 0 )If you want to keep the Nernst potentials constant without being redefined automatically with temperature, you can set:

calcnernst = 0; ( do not recalculate Nernst potentials ) ( after set by user )The reversal potential issue is especially important for Ca channels because internal [Ca] is normally so low that even a slight permeability to [K] ions is a large factor in the Ca channel's reversal potential (see "Current through Ca channels" above).

If you specify the internal Ca level (cai) this will override the default internal concentration at the Ca compartment associated with the channel, and the Ca channel's current and reversal potential will be modified accordingly from the GHK current and voltage equations assuming a default level of K permeability (dpkca = 0.001 by default). If you set the Ca channel's reversal potential (vrev) this will set the internal calcium for the compartment also assuming a default level of K permeability.

If you specify both internal calcium and reversal potential (cai and vrev) the calcium flux will be set by the levels of cao and cai, and the Ca channel's total current will be set by vrev, assuming for both the GHK current equation but not K permeability. This would be the case, for example, if you don't want to use relative K permeability in Ca channels (dpkca) but want to define the reversal potential and the resulting total current through a Ca channel.

If you set:

chan Ca ... vrev=0.05 (sets cai, controls caflux and Ica) chan Ca ... cai=100e-9 (sets vrev, controls caflux and Ica) chan Ca ... vrev=0.05 cai=100e-9 (vrev sets Ica, cai controls caflux)Click here to return to Channel statement index

Setting the right internal and external ion concentrations is a bit tricky, and has been designed to be automatic so no changes are necessary for most simulations.

Here's the sequence: the vna, vk, and vcl values are set arbitrarily to +65, -98, and -70 mV. Then the external ion concentrations are specified (from Ames & Nesbett, 1981, i.e. the composition of Ames medium, and Hille, 2nd ed and some retinal papers: dnao=143, dko=3.6, dclo=125.4 mM). Then using the vna, vk, and vcl values and the external concentrations, the internal concentrations are set from the Nernst equation at 37 degrees C. These are the default values.

If the user wants to set the Nernst potentials vna, vk, or vcl, these values could then be used to recompute the internal ion concentrations from the Nernst equation at whatever temperature is currently set. One problem with this method of setting the internal ion concentrations is that internal K+ concentration varies a lot when temperature ("tempcel") is changed. This is not really correct, as a typical cell regulates its membrane potential and ion concentrations quite tightly. Howver it is not known exactly which parameters in the real physiology of a cell have priority over others when external ion concentrations or temperature change.

One would like a method for simulating control of ion concentrations and reversal potentials that mimics various types of physiological dependence of Nernst potential and internal ion concentrations on temperature. This strategy is implemented in NeuronC with the variable "calcnernst" which sets the simulator's priority for ion concentrations and Nernst potentials. If calcnernst = 0 (the default), the internal ion concentrations are recomputed from the temperature and the Nernst potentials. However, when calcnernst = 1, Nernst potentials are recomputed from temperature and ion concentrations.

If "calcnernst" is set between 0 and 1, (default 0.6) a hybrid strategy is used where Nernst potentials and ion concentrations both change. A new reversal potential is calculated from the temperature and ion concentrations, but "calcnernst" sets the "fraction" of this value that is used. The difference is made up by a change in internal ion concentration. For example, if calcnernst=0.9, most of the change is assigned to the Nernst potential, and the ion concentrations change only a little.

Note that for this strategy to be useful, you should not change both Nernst potentials (vna, vk, vcl) and ion concentrations (dnai, dki, dko), since these parameters are automatically set at run time. If you want to precisely define the Nernst potentials at different temperatures, then you can set "calcnernst=0" and the ion concentrations will be recomputed. Otherwise, if you want to keep ion concentrations precisely defined, you can set calcnernst=1, and the Nernst potentials will be recomputed.

Of course at any time "vrev" for a synapse or channel can be defined which overides the Nernst potential and the channel's default value.

These additions have the effect of making the simulator more realistic, but there is a *price* for it. The default reversal potentials for the channels are not vna, vk, or vcl. They are calculated from the GHK voltage equation so they represent all the ion currents that flow through a channel. The currents are defined by setting permeabilities for several ions for each channel.

What this means in practice is that vrev for an Na channel is *near* +40 mv (43 at 22 deg and 47 at 37 deg), and *near* -80 for a K channel (83 at 22 deg, and 82 at 37 deg). So the reversal potentials are close but not exact to the usual values, and they change with temperature and the ion concentrations and permeabilities.

If you would prefer to have the Nernst potentials define the reversal potentials for channels, you can set the permeability for each channel type to be exclusively for the major ion, (i.e. set dpnak, dpkna = 0). Then you can set the reversal potentials for all the channels with vna, vk, and vcl.

The permeabilities are set to default values (dpkna, dpnak, dpkca, etc.) in the channel definitions (in "chanxxx.cc"). However, to change the value of the Ca permeability for a channel, you can set its "caperm" parameter. This overrides the channel's default Ca permeability. Note that caperm and the default parameters range from 0 to 1.

dpkna relative permeability for K in Na channels 0.08, Hille (1992) dpcana relative permeability for Ca in Na channels 0.01, Baker et al, (1971), Meves and Vogel, (1973) dpnak relative permeability for Na in K channels 0.01, Hille (1992) dpcak relative permeability for Ca in K channels 0.0001,Hille (1992) dpnaca relative permeability for Na in Ca channels 0.001, Hille (1992) dpkca relative permeability for K in Ca channels 0.0003,Hille (1992) dpcaampa relative permeability for Ca in AMPA channels 0.1 dpcacgmp relative permeability for Ca in cGMP channels 0.1 dpcanmda relative permeability for Ca in NMDA channels 0.1 dpcasyn2 relative permeability for Ca in syn2 channels 0.1Click here to return to Channel statement index

When the internal and external ion concentrations are different, the instantaneous current through an ion-selective channel is a nonlinear function of the voltage. This is computed using the GHK current equation. The "nc" simulator uses the GHK current equation when the variable "use_ghki" is set to 1 (default 0). The GHK current equation calculates the effective conductance from the voltage and the internal and external ion concentrations. The internal ion concentration is set for each channel type by the Nernst equation, from the external ion concentration and the reversal potential. The reversal potential is set by default for each channel type but can be overridden in several ways.

One way to set the reversal potential for a channel is to set its corresponding "ion reversal potential":

vna for all Na channels (default +65 mV) vk for all K channels (default -89 mV) vcl for all chloride, GABA, and glycine channels (default -70 mV)As described above, when you change the global variables vna, vk, or vcl from their default values (with default calcnernst=0) this causes the corresponding internal ions concentrations to be recalculated. These new values for ion concentrations will affect all of the channels that have permeabilities for these ions. If you set vna, vk, or vcl variables at the beginning of your program, their values will be used to generate the reversal potentials for all of the channel types that are programmed to use these global variables. If you set "use_ghki = 1", then the current for each channel type will be determined by the GHK current equation using the relevant ions and permeabilities for each channel.

Channels such as AMPA and NMDA channels are non-selective and have permeabilities to both Na+ and K+ ions. When the concentration gradients for the 2 ions are equal and opposite, the channel acts like a linear conductance, with current proportional to the membrane potential.

When a channel has such a major permeability to 2 ions, their permeabilities and concentrations are both taken into account when computing the GHK equation. The permeabilities are computed from the reversal potential and the original default permeabilities using the GHK voltage equation in an iterative procedure.

Another way to set the reversal potential for a channel is to individually set the reversal potential "vrev" for each channel when it is created. If this reversal potential is different than the default value, the channel gets an individual copy of the reversal potential. If you set "use_ghki=1", then the channel also gets a new set of ion concentrations and permeabilities from its default channel type definition. These are used the GHK voltage equation to generate a new set of permeabilities and internal concentrations specific to that channel. Then the "slope conductance" and "slope reversal potential" are computed as described above and lookup tables are created for that individual channel. This is relatively fast at run time but requires a lot more memory to store the lookup tables when many individual channels are set. When the channel has only 1 major permeability, the reversal potential is used to set the internal concentration. When the channel has 2 major permeabilities (as described above), they are revised and iteratively from the concentrations which are not changed.

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To disable the automatic computation of voltage offset, set "dcavoff=0" in the beginning of your script. This is not normally necessary, however, as the voltage offset is zero if "dcao" or "dcoo" is not changed. If you want to set the [Ca]o for some channels without causing a voltage offset, set the "cao" parameter for the channel without changing "dcao":

dcavoff = 0; ( External Ca does not produce voltage offset ) chan Ca ... cao=0.004 ( Set external Ca for local Ca compartment )The effect of an increase in external divalent cations on the reversal potential of channels is less than on gating but is positive, and is set by the "dcaspvrev" variable (default = 0.18), which multiplies dcavoff (0.018) for a value of 3.2 mV positive shift in a channel's reversal potential for each factor of 10 increase in cao. See "Reversal potentials, Nernst and GHK equation" in section 1 of the manual.

To turn off this feature, you can set either "dcavoff" or "dcaspvrev" to zero, or you can leave "dcao" set to its default value:

dcavoff = 0; ( External Ca does not produce voltage offset ) dcaspvrev = 0; ( Voltage offset does not affect reversal potential ) chan Ca ... cao=0.004 ( Set external Ca for local Ca compartment )Click here to return to Channel statement index

Trace of a K channel in a small patch of membrane (green) that contains channel noise (large jumps) and Johnson noise (small fluctuations) filtered at 1000 Hz, and an identical channel on a separate patch of membrane (red) without Johnson noise. Channels are voltage clamped to -20 mV. Note that the K current is outward.

at .... chan .... chnoise=1 [noise parameters] noise parameters: default N = <expr> (no default) number of channels for noise unit = <expr> (set by chan type) size of unitary conductance rsd = <expr> (set by rseed) random seed for noise tauc = <expr> 1.0 rate divider for Mg noise tauf = <expr> 1.0 rate divider for noise flickerThe "unit" parameter describes the unitary conductance of a single channel and allows the simulator to calculate the number of channels from the maximum total conductance "maxcond". When N is set to zero, channel noise is turned off. If you specify a value for "N", the value of "unit" is ignored:

maxcond = you specify N = you specify unit is calculated as = maxcond / NOtherwise, if you specify both "maxcond" and "unit", the total number of channels is calculated as:

maxcond = you specify unit = you specify N is calculated as = maxcond / unitIf you don't define "N" or "unit", but do specify "chnoise", the value of N will be computed from either the value of "maxcond" specified or its default value, and the unitary conductance will also come from its default:

channel conductance = maxcond or its default unit = you define or default for channel type N is calculated as = maxcond / unitDefaults for "unit" (the unitary conductance) are:

dnau = 12e-12 @22 default Na unitary cond, gives 32 pS @ 33 deg (Lipton & Tauck, 1987) dku = 11.5e-12 @22 default K unitary cond, gives 15 pS @ 30 deg dkau = 22e-12 @22 default KA unitary conductance, gives 30 ps @30 deg dkcabu= 74.3e-12 @22 default BKCa unitary cond, gives 115 pS @ 35 deg dkcasu= 14.2e-12 @22 default SKCa unitary cond, gives 22 pS @ 35 deg dampau = 25e-12 @22 default AMPA unitary conductance dcgmpu = 25e-12 @22 default cGMP unitary conductance dscu = 25e-12 @22 default 2-state synaptic channelNote that the default unitary conductances have a temperature coefficient, set by the Q10 for channel conductance "dqc" (default = 1.4). The base temperature at which the unitary conductance is defined is set by the "qt" field of the channel constants. For membrane channels, the base temperature is normally 22 deg C, and for synapses it is also 22 deg C. For more details, look in "Adding New Channels".

You can change the default base temperature for unitary conductances (and channel kinetics) with the following variables:

var default meaning ------------------------------------------------------------------------------ dbasetc 22 deg C base temp for membrane channel kinetics, conductances dbasetsyn 22 deg C base temp for synaptic kinetics dbasetca 22 deg C base temp for ca pumps dbasetdc 22 deg C base temp for Ca diffusion constantClick here to return to Channel statement index

pa = conduct / tau; /* tau for close -> open */ pb = (1.0-conduct) / tau; /* tau for open -> close */ nco = bnldev(pa,nc); /* delta closed to open */ noc = bnldev(pb,no); /* delta open to closed */ no += nco - noc; conduct = no / nchan; where: pa = probability of opening pb = probability of closing tau = average frequency of channel opening no = number of open channels nco = number of channels opened per time step noc = number of channels closed per time step nchan = number of channels bnldev = random binomial distribution funtion conduct = channel conductanceClick here to return to Channel statement index

See the description of "synaptic vesicle noise" above for a discussion of the random "seed" and how to change it.

For all channel types:

G channel conductance (Same as G(0) or G0) G(I) ionic current through channel G(vrev) vrev (reversal potential, from GHK V eqn. and permeabilities) G(Ca) Calcium current through channel (if Ca, NMDA, cGMP chan)For HH channel types:

G(M) m (if Na chan) or n (if K chan), or c (if Ca chan), frac of 1. G(H) h (if inactivating type)For sequential-state Markov types:

G channel conductance (Siemens) G(0) channel conductance (Siemens) G(1) amplitude of state 1 (Fraction of 1, or population if "chnoise") G(2) amplitude of state 2 . . . G(n) amplitude of state n.Note that the number inside the parentheses is a numerical expression and can be a variable or a function. At a node with a calcium channel:

Ca cai = [Ca] at first Ca shell, same as Ca(1) Ca (0) cao = [Ca] at first exterior Ca shell (next to membrane) Ca (1) cai = [Ca] at first interior Ca shell (next to membrane) Ca (2) [Ca] at second shell . . . Ca (n) [Ca] at nth interior shell Ca (100) [Ca] in inner core Ca (-1) same as Ca[0], = [Ca] at first exterior Ca shell (next to membrane) Ca (-2) cao = [Ca] at second exterior shell . . . Ca (-n) [Ca] at nth exterior shell Ca (-100) [Ca] at exterior core Ca (vrev) local reversal potential for Ca (Nernst potential) Ca (I) total Ca current through Ca channels and pumps Ca (IP) Ca current through pump Ca (IE) Ca current through exchanger Ca (IPE) Ca current through Ca pump and exchanger[ Note that exchanger current Ca(IE) includes Ca and Na currents, and that it is dependent on Vrev of Ca and Na.]

If the channel is a Na type 4 (Integrate-and-Fire)

G(0) channel conductance G(1) population of state 1 G(2) population of state 2 G(3) integration state G(4) state switchingClick here to return to Channel statement index

You can also define your own rate functions for existing channels by writing the functions in a simulation script. These functions are used instead of the default ones at the beginning and also whenever the time increment changes during a run. For example, you could change the sensitivity to voltage for activation (the alpha rate function) and this would modify the range over which the channel would start to activate.

The default transition rate functions in "nc" are exactly as defined by Hodgkin and Huxley (1952), from the membrane voltage in mV. A channel's default rate functions are defined in the file containing the channel data structures (e.g. channa1.cc for Na type 0 and 1 channels).

To replace these predefined functions, make your own functions that define the alpha and beta rates, normally called "calcna0m" (calculate m for Na type 0), "calcna0h", etc., in your script file that you run with "nc". For the interpreted version, whenever any of these functions are defined inside your file, they are used automatically instead of the default ones. For the compiled version, you must call set_chancalc() to replace the default kinetic function for the channel before the channel is defined or used. The functions return their respective rate constants and have two parameters: a) membrane voltage, and b) a number describing the function (e.g. 1 = alpha, 2 = beta, etc.). Voltage is calibrated here in mV, using the modern definition of "membrane voltage" (i.e. cell membrane voltages are negative when hyperpolarized). This definition of voltage differs from the original Hodgkin and Huxley (1952) paper but is more convenient. The functions define rate per sec.

Example:

(interpreted:) func calcna1m (v, func) /* Calculate Na rate functions given voltage in mv. All rates are calculated exactly as in HH (1952) paper. Original rates were 1/msec, we multiply by 1000 here (MSSEC) to convert to 1/sec. The "func" parameter defines: 1 alpha m 2 beta m */ { local val,x,y; if (func==1) { /* alpha m */ y = -0.1 * (v+40.); x = exp (y) - 1.; if (abs(x) > 1e-5) /* singularity at v = -40 mv */ val = y / x * MSSEC else val = 1.0 * MSSEC; } else if (func==2) { /* beta m */ val = MSSEC * 4 * exp ((v+65) / -18.); }; return val; }; ------------------------------------------------------------------------ (compiled:) double calcna1m (v, func) /* Calculate Na rate functions given voltage in mv. All rates are calculated exactly as in HH (1952) paper. Original rates were 1/msec, we multiply by 1000 here (MSSEC) to convert to 1/sec. The "func" parameter defines: 1 alpha m 2 beta m */ { double val,x,y; if (func==1) { /* alpha m */ y = -0.1 * (v+40.); x = exp (y) - 1.; if (abs(x) > 1e-5) /* singularity at v = -40 mv */ val = y / x * MSSEC else val = 1.0 * MSSEC; } else if (func==2) { /* beta m */ val = MSSEC * 4 * exp ((v+65) / -18.); } return val; } /* call before channel is defined or run: */ set_chancalc(NA,1,0,calcna1m); /* sets the 0 (m) param for Na type 1 */At the beginning of each simulation run, this subroutine is used to calculate alpha for "m" to make the lookup table used by the channels during the run. The name used to define the function is set in the "mak???()" procedure that defines each channel type. For more details on adding new channels, see Section 6, "Adding new channels".

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Distributed macroscopic channels are available for cable membranes and are defined much like the "chan" statement, except that their maximum conductance is defined as a function of the membrane area and not as an absolute conductance. Multiple types of channels may be defined by including multiple channel options in sequence after the "cable" statement. See "cable".

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Each channel is checked against every other one in the compartment to see if they are identical in their properties (vrev, voltage offset, tau, unitary conductance). If they are, their conductances and values of "N" (number of unitary conductances) are added together. The value of N is a floating point number so if the channel conductance is low, the fractional channels from several compartments can add to give a final value of N greater than 1 (or higher integer). After this process, the value of N is rounded up to the nearest integer so the channel stochastic noise computations can be correctly run with the binomial distribution (see "Markov noise") below.

To see this process work, you can set the "lamcrit" variable or the "-l" command-line option: a lamcrit value of 0 prevents condensation of any kind so you get lots of compartments. Setting lamcrit to .001 prevents compartment condensation but activates channel condensation, and a value of lamcrit in the range 0.1-1 will give both compartment and channel condensation. Use the "nc -p 1" option to print out the compartments and channels.

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at <node> load <expr> [vrev <expr>This defines a load resistor in series with a battery which connects to the membrane leakage at a node. Calibrated in ohms. Can be used to simulate a synapse, photoreceptor, or membrane channel.

conn <node> to <node> resistor <expr>This defines a series resistor between two nodes which acts exactly like a gap junction. Calibrated in ohms.

at <node> gndcap <expr>This defines a capacitor which adds to the membrane capacitance in a node's compartment. Calibrated in farads.

conn <node> to <node> cap <expr>This defines a capacitor which connects two compartmemnts. The addition of this element makes the model unstable and it must be run slowly with the "implicit" mode turned on for stability. Calibrated in farads.

conn <node> to <node> batt <expr>This defines a battery connected between two compartments. The addition of this element makes the model slightly unstable and it must be run with "implicit" mode turned on for stability. Calibrated in volts.

at <node> gndbatt <expr>This defines a battery connected between a node and ground. Calibrated in volts.

You can set up a channel to sense the external compartment using the function "addchan_extern()". For calcium channels, you use the function "addchan_extern_ca()

Note that every node contains a pointer to the compartment that represents the node. The compartments are created after a "step()" statement.

comp *extern_comp; extern_comp = nd(x,y)->compnt; predur = 0.01; step(predur); addchan_extern (extern_comp, chan); addchan_extern_ca (extern_comp, chan); Where: extern_comp = pointer to the external compartment, often a node's compartment pointer. chan = pointer to the channel.Another effect of external voltages is capacitive coupling via the membrane capacitance. A positive shift of the external voltage will depolarize the local cytoplasm of the cell, but this alone will not activate or deactivate membrane channels, because the voltage gradient across the membrane does not change. However, if the positive shift is applied to only one region of a cell, other regions will receive the internal depoarization from that one region, allowing membrane channels to be depolarized by internal current flows within the cell.

You can set up capacitive coupling through the membrane with the function "addcomp_extern(extern_comp, intern_comp):

comp *extern_comp; comp *intern_comp; extern_comp = nd(a,b)->compnt; intern_comp = nd(c,d)->compnt; addcomp_extern (extern_comp, intern_comp); Where: extern_comp = pointer to the external compartment, intern_comp = pointer to the internal compartment,Note that compartments that represent the middle portion of a cable element, i.e. are not linked to nodes at the cable's ends, can be accessed using a "for" loop:

for (pnt=compnt; pnt; pnt=pnt->next) { if (ndn(c,d)->compnt == pnt) { this is one end. } if (ndn(e,f)->compnt == pnt) { this is the other end. } }

stimulus light, voltage or current clamp stimulus electrode make an elecrode with series resistance plot make continuous plot of a node during run graph graph any variables at end of step or run display display the neural circuit on screen step run for short time and stop to allow graphing run run simulation continuously for high speed

V, I, L return voltage (current,light) at a node FA0-4, FA8, FA9, FB0-4, FC0-4, FC9 return synaptic neurotransmitter from filter stage G0-8 return channel conductance or state concentration

(interpreted:) conn [1] to [2] electrode rs=10e7 cap=1e-12; (compiled:) make_electrode (nd(1),nd(2), rs=10e6, cap=1e-12); To define the electrode shape: conn [1] to [2] electrode rs=10e7 cap=1e-12 dia=5 length=100;

noise parameters: default rs = <expr> (10e6 Ohms, set by "drs") series resistance cap = <expr> (1e-12 F, set by "deleccap") electrode parallel capacitance vrest = <expr> (0 mV) starting voltage dia = <expr> (set by rseed) diameter for display length = <expr> (set by rseed) length for displayThen, later in the script you can display it:

display electrode matching [1][-1] color 5 dscale 1;You can also change what your "electrode" looks like by redefining its icon.

(interpreted:) stim node <node> vclamp=<expr> start=<expr> dur=<expr> stim node <node> cclamp=<expr> start=<expr> dur=<expr> stim node <node> puff <ligand>=<expr> start=<expr> dur=<expr> (compiled:) vclamp (nd(<node>), inten, start, dur); cclamp (nd(<node>), inten, start, dur); puff (nd(<node>), ligand, inten, start, dur);where:

unit: vclamp =<expr> (volts) set voltage for clamp cclamp =<expr> (amperes) set current for clamp start =<expr> (sec) time to start stimulus dur =<expr> (sec) duration of stimulus after start puff <nt> =<expr> (M) puff ligand Ligands available for "puffThe "stim node" statements define node stimuli. To stimulate a single node, a voltage or current clamp may be used, in which case the node current or voltage, respectively may be be plotted. An I/V measurement can be performed by placing a "stim node" statement inside a "for" loop. These statements are not interpreted by the program "stim" (see below).": GLU AMPA NMDA CNQX GABA BIC PTX GLY STR cAMP cGMP

(interpreted:) stim cone <node> inten=<expr> start=<expr> dur=<expr> stim rod <node> inten=<expr> start=<expr> dur=<expr> (compiled:) stim_cone (nd(<node>), inten, start, dur, wavel); stim_rod (nd(<node>), inten, start, dur, wavel);where:

inten =<expr> Q/um2/sec intensity of stimulus start =<expr> sec time to start stimulus dur =<expr> sec duration of stimulus after start wavel =<expr> nm wavelength (also, sun, tungsten or xenon)The "stim cone" and "stim rod" statements allow single photoreceptors to be given a point-source light stimulus. These statements are not interpreted by the "stim" program (see below). See below for explanation of parameters.

Most of the stimuli provided in nc come in several different versions. A version with many parameters gives flexibility, and the versions with fewer parameters set some of the parameters with default values. See "ncstimfuncs.cc" for definitions of stimulus procedures.

For the sine wave grating (sine, gabor, sineann, windmill) stimuli, two intensities can be specified (see ncstimfuncs.cc). The "inten_mult" intensity is multiplied with the sine wave and serves as a scaling factor for contrast. The "inten_add" intensity is added to the resulting sine wave to provide a local mean intensity. Both the sine wave and the mean intensity are added to any other stimuli including the background set with "stim_backgr()". The "makenv" parameter controls the outer edge of the stimulus. If it is set to 1, the edge will have a gaussian decay with radius, but if it is set to 0, the edge will decline to 0 immediately with radius.

(interpreted:) stim spot <expr> loc (<expr>,<expr>) blur=<expr> inten=<expr> start=<expr> dur=<expr> mask=<expr> stim bar <expr> loc (<expr>) blur <expr> inten=<expr> start=<expr> dur=<expr> mask=<expr> orient=<expr> stim sine <expr> loc (<expr>,<expr>) blur=<expr> inten=<expr> start=<expr> dur=<expr> sphase=<expr> orient=<expr> tfreq=<expr> drift=<expr> contrast=<expr> xenv=<expr> yenv=<expr> mask=<expr> stim gabor <expr> loc (<expr>,<expr>) blur=<expr> inten=<expr> start=<expr> dur=<expr> sphase=<expr> orient=<expr> tfreq=<expr> drift=<expr> contrast=<expr> xenv=<expr> yenv=<expr> mask=<expr> stim sineann <expr> loc (<expr>,<expr>) blur=<expr> inten=<expr> start=<expr> dur=<expr> sphase=<expr> orient=<expr> tfreq=<expr> drift=<expr> contrast=<expr> renv=<expr> mask=<expr> stim windmill <expr> loc (<expr>,<expr>) blur=<expr> inten=<expr> start=<expr> dur=<expr> sphase=<expr> orient=<expr> tfreq=<expr> drift=<expr> contrast=<expr> xenv=<expr> mask=<expr> stim checkerboard <expr> loc (<expr>,<expr>) blur=<expr> xenv=<expr> yenv=<expr> inten=<expr> start=<expr> dur=<expr> orient=<expr> tfreq=<expr> contrast=<expr> stim simage <filename> loc (<expr> <expr>); blur <expr> inten=<expr> start=<expr> dur=<expr> orient=<expr> xenv=<expr> yenv=<expr> mask=<expr> stim sector <expr> inten=<expr> orient=<expr> start=<expr> dur=<expr> stim file <filename> stim backgr <expr> stim center (<expr>,<expr>) (compiled:) stim_spot (double dia, double xloc, double yloc, double inten, double start, double dur); stim_spot (double dia, double xloc, double yloc, double inten, double start, double dur, double wavel, double mask); stim_ispot (double dia, double xloc, double yloc, double inten, double start, double dur, double wavel, double mask, int invert); stim_annulus (double idia, double odia, double xloc, double yloc, double inten, double start, double dur); stim_bar (double width, double height, double xloc, double yloc, double orient, double inten, double start, double dur, double wavel, double mask, double stimchan); stim_bar (double width, double height, double xloc, double yloc, double orient, double inten, double start, double dur, double mask); stim_bar (double width, double height, double xloc, double yloc, double orient, double inten, double start, double dur); stim_grating (int type, double speriod, double sphase, double orient, double xloc, double yloc, double tfreq, double drift, double inten, double contrast, double wavel, double xenv, double yenv, double mask, double start, double dur); stim_sine(double speriod, double sphase, double orient, double xloc, double yloc, double xcent, double ycent, double tfreq, int drift, double scale, double inten_add, double inten_mult, double contrast, int sq, double start, double dur, double wavel, double mask) stim_sine(double speriod, double sphase, double orient, double xloc, double yloc, double tfreq, int drift, double inten, double contrast, double start, double dur); stim_gabor(double speriod, double sphase, double orient, double xloc, double yloc, double xcent, double ycent, double tfreq, double drift, double scale, double inten_add, double inten_mult, double contrast, double xenv, double yenv, int sq, double start, double dur, double wavel, double mask); stim_gabor(double speriod, double sphase, double orient, double xloc, double yloc, double tfreq, double drift, double inten, double contrast, double xenv, double yenv, double start, double dur); stim_sineann(double speriod, double sphase, double xloc, double yloc, double xcent, double ycent, double tfreq, double drift, double scale, double inten_add, double inten_mult, double contrast, double renv, double makenv, int sq, double start, double dur, double wavel, double mask); stim_sineann(double speriod, double sphase, double xloc, double yloc, double tfreq, double drift, double inten, double contrast, double xenv, double start, double dur); stim_windmill(double speriod, double sphase, double xloc, double yloc, double xcent, double ycent, double tfreq, double drift, double scale, double inten_add, double inten_mult, double contrast, double renv, int sq, double start, double dur, double wavel, double mask); stim_windmill(double speriod, double sphase, double xloc, double yloc, double tfreq, double drift, double inten, double contrast, double xenv, double start, double dur); void stim_checkerboard(double width, double height, int xn, int yn, double orient, double xloc, double yloc, double xcent, double ycent, double scale, double tfreq, double inten, double contrast, double start, double dur, double **stim_rndarr, int *stim_nfr) void sector_mask(double orient, double width, double val, double stimtime, double dur); See definitions of these functions in "ncstimfuncs.cc" and "ncfuncs.h".where:

units: spot <expr> um diameter of spot bar <expr> um width of bar sine <expr> um spatial period of sine wave grating gabor <expr> um spatial period of gabor wave grating sineann <expr> um spatial period of sine wave grating windmill <expr> um number of vanes of sine wave windmill simage <expr> image file loc (<expr>,<expr>) spatial location (x,y) or (xmin,xmax) for stimulus sscale = <expr> default=1 resolution of blur convolution inten = <expr> Q/um2/sec intensity of stimulus inten_add = <expr> Q/um2/sec mean intensity of grating (sine,gabor,sineann,windmill) inten_mult= <expr> Q/um2/sec contrast scaling for of grating (sine,gabor,sineann,windmill) start = <expr> sec time to start stimulus dur = <expr> sec duration of stimulus after start backgr = <expr> Q/um2/sec intensity of background wavel = <expr> nm wavelength (also, sun, tungsten or xenon) contrast =<expr> (L1-L2)/(L1+L2) fractional contrast of grating tfreq = <expr> Hz (cy/sec) Temporal frequency drift = <expr> 0 = 1 -> Drifting grating sphase = <expr> deg [optional] Spatial phase (offset) for grating orient = <expr> deg [optional] Orientation from vertical xenv = <expr> um [optional] Radius of X Gaussian envelope (def=50um), (or grating size, def=inf) yenv = <expr> um [optional] Radius of Y Gaussian envelope (def=50um), (or grating size, def=inf) blur = <expr> um [optional] dia (at 1/e) of Gaussian blur func. mask = <expr> na [optional] masking: 0->transparent, 1->masking stimchan = <expr> na [optional] stimulus channel: 0->default, 1-9 independent masking scatter = <expr>,<expr> um [optional] dia (at 1/e) of Gaussian blur func. sq = <expr> for sine stimuli, sq=1 -> square wave, sq=0 -> sine wave pie_mask = 2 partly overlapping bar masks that together produce a pie-shaped stimulus

The "stim spot", "stim bar", "stim sine", "stim gabor", "stim windmill", and "stim sineann" statements allow large fields of photoreceptors to be given an optical stimulus. These statements are interpreted at run time by "nc" so that the photoreceptor receives the appropriate amount of photon flux. Stimuli are additive so multiple simultaneous stimuli may be given without interaction. "nc" does no blurring at run time.

Note that "nc" can generate all the stimuli correctly except for blur and scatter. The idea is to run "stim" once to generate the stimulus file. When you then run "nc", it will use the stim file to generate the optical stimuli instead of generating the stimulus again each time you run the simulation. Because the stim file defines the light flux for each photoreceptor, each time you change the stimulus or the photoreceptor array you'll need to run stim again.

If you don't have optical blur or scatter, you can just run "nc". But this can in some cases use a lot of memory to store the photon fluxes for each photoreceptor. For example, for a large cone array and a long duration drifting sine wave grating, the stimuli can take many MB of memory. Also, note that "nc" interprets all the non-optical stimuli, i.e. "stim rod", "stim cone", "stim cclamp", "stim vclamp". The stim file only contains optical stimuli.

scatter <expr>, <expr> (amplitude) (diameter) where: amplitude = scatter function's amplitude relative to the blur function diameter = diameter for scatter functionTo describe a non-Gaussian scatter function, it can be described as a radial power function. The value set for its "power" distinguishes it from a Gaussian:

scatter <expr>, <expr>, <expr> (amplitude) (diameter) (power) where: amplitude = scatter function's amplitude relative to the blur function diameter = diameter for scatter function power = power for scatter function scatter function = 1 / (1 + pow(r/(diameter/2), power))If "scatter" is given no arguments, the scatter function from Robson and Enroth-Cugell (1978) is added to the blur function used by the "stim" program to generate a stimulus. This is appropriate for the cat eye. The "blur" and "scatter" functions are added together and the resulting optical blur function is normalized so its volume is 1. Therefore, if the amplitude of the "scatter" function is set greater than 1, it predominates over the "blur" function (see "stimsub.cc"). Some useful blur and scatter functions are:

blur 22 scatter (.15, 45, 2.5) Robson & Enroth-Cugell (1978), 4 mm pupil, cat (default) blur 4.677 scatter (.0427, 20.35) Campbell & Gubisch (1966), 2 mm pupil, human Gaussian scatter function fit by Geisler (1984) Blur=4.677 includes 4.43 blur, 1.5 cone aperture. blur 1.5 scatter (10, 5.4, 1.95) Campbell & Gubisch (1966), 5.7 mm pupil, human scatter (1000, 2.6, 1.85) Guirao et al, (2001), 5.8 mm pupil, "best refracted" average human eye scatter (1000, 3, 1.0) Guirao et al, (2001), 5.8 mm pupil "uncorrected" average human eye

To see how these functions were created, look in "linesp.c" and "linespr.c". A point-spread (2D) scatter function is generated and convolved with a line. The resulting line-spread function is sampled and compared with the original data (which is usually in line-spread form). If the original data is a MTF (modulation transfer function), then the line-spread's Fourier transform must be compared. The point-spread function's parameters are modified until the comparison is satisfactory. The scatter functions given above are within 1-2% of the original data but it is likely that better approximations can be found.

If the original blur and scatter line-spread functions are Gaussian, their radii can be used directly in the 2D point-spread function and only the relative amplitude of the scatter function must be determined by fitting. The reason is that a Gaussian function is (x,y) separable, i.e. a section through a 2D Gaussian (a Gaussian of rotation) looks Gaussian in 1-D. Other radial functions not (x,y) separable can be readily fit using the method described above. Robson & Enroth-Cugell (1987) derived the pow(r,2.5) point-function analytically from the measured pow(r,1.5) line spread function.

To run the convolution at finer resolution than 1 micron in the stimulus position, set the "sscale" parameter which magnifies the resolution of the convolution arrray (e.g. sscale=.2 means magnify by 5 times). Of course, if you don't require blur, you will not require the convolution and therefore don't need to run the "stim" program or the stimulus file it generates. In that case, full "floating-point" precision (6 decimal places) is available for the stimulus position.

The convolution that "stim" performs goes as follows: for each photoreceptor, each element in the "blur" array is multiplied by the corresponding element in the "stimulus" array. The sum of these multiplications becomes the stimulus intensity for the photoreceptor. In order to save space, the "blur" array is made only large enough to hold the Gaussian blur. The array is created with a radius of 5 times the standard deviation of the Gaussian blur specified by the "stim" statement. If the "sscale" factor is defined smaller than 1, the blur array is made larger.

To make the stimulus file, run "stim" on the simulation program that contains the "stim file" statement. "stim" will create the stimulus file automatically. Thereafter, "nc" may be run on the same simulation program, reading its stimulus from the stimulus file defined in the program. The "stim file" contains one line for each change of light intensity for each photorecptor. The "stim file" is a text file and you may view and modify it with a text editor. It is written (by "stim") by the subroutine "stimfmout()" in file "stimsub.c" and is read (by "nc") by the subroutine "readstim()" in file "ncstim.c".

Large stim files may be compressed with "gzip" which will add ".gz" onto the end of the file name. If the compressed stim file exists and the original does not, "nc" will read the .gz file and decompress it with the "zcat" command. The .gz file size is typically 10% of the original text version. For this scheme to work properly, both "gzip" and "zcat" must be avalable in your shell PATH environment variable.

The spatial extent of the grating is defined by the "xenv" and "yenv" parameters, which define the radii of the X and Y dimension Gaussian envelopes for the "Gabor" function. For the "sineann" funtion "xenv" gives the radius of the envelope. Note that many complete sine-wave cycles may exist within the envelope. If no xenv and yenv values are given for the "Gabor" or "sineann" statements, they default to 50 um Gaussian radius. For a "sine" grating, the envelope function is set by default to infinity, and its extent from its center is set by "xenv" and "yenv" (which for "sine" defaults to infinity). In every other respect a "sine" grating is identical to a "Gabor" grating. The "sineann" grating is a concentric sinewave grating, where the extent from the center is given by "xenv". Outwards motion is set by a positive value for "drift". The "windmill" function is identical to the "sineann" function except that it generates a sine windmill orthogonal to the "sineann" stimulus, and the number after "windmill" is the number of windmill vanes.

(interpreted:) stim spot 10 loc (25,25) inten=10 mask=1 start=time dur=.02; (compiled:) stim_spot (dia=10, 25, 25, inten=10, start=time, dur=0.02, wavel=1, mask=1);

This type of masking stimulus is useful when stimulating with a moving grating, to prevent motion in part of the stimulus from being seen. The mask intensities are additive like ordinary stimuli, so a mask can be built up from any comination of spots or bars.

To generate a mask complementary to a stimulus pattern, set the variable "unmaskthr" to a negative value (e.g. -100), and set your masking stimulus to a more negative value (e.g. -200). When the stimulus is processed, any masking values more negative than "unmaskthr" become unmasked. This allows you to generate a mask with a hole in it:

(interpreted:) // Standard stim and backgr statements... stim backgr 1000 stim sine ... // Then, the mask stim and backgr statements... unmaskthr = -100; stim backgr 100 mask=1 start=0; stim spot 10 loc (25,25) inten=-200 mask=1 start=time dur=.02; step 0.001; (compiled:) // Standard stim and backgr statements... stim_backgr (1000); stim_sine (...) // Then, the mask stim and backgr statements... unmaskthr = -100; stim_backgr (backgr=100, wavel=1, mask=1, start=0); stim_spot (dia=10, 25, 25, inten=-200, start=time, dur=0.02, wavel=1, mask=1); step (0.001);

The "backgr" stimulus statement is required to generate the mask surrounding the spot since the spot (mask) statement only generates a mask intensity inside the spot.

interpreted: sector 45 orient=90 inten=1000 start=0.1 dur=2.0; sector 45 orient=90 loc (100,200) inten=1000 start=0.1 dur=2.0; compiled: sector_mask(orient, width, inten, stimtime, dur); sector_mask(orient, width, xloc, yloc, inten, stimtime, dur, stimchan);The sector function sets up 2 masking bars that are oriented to unmask the sector defined by the user. The bars are set to be 1000 microns long, so if your photoreceptor array extends beyond that you should revise the constant BARLENGTH (in ncstimfuncs.cc and modcode.cc).

However, to set a photoreceptor (rod, cone, or transducer) to be sensitive to only one stimulus channel, you can set the stimchan parameter for the photoreceptor. If the stimchan parameter is set to zero (the default), the photoreceptor will be sensitive to all the stimulus channels, but if it is set to a value from 1 to 9, it will ignore any other stimulus channels. This allows you to create different stimuli and blur for different neurons.

timinc = 0.0001; steptime = 0.011111111111; /* not integral mult of timinc */ for (i=1; i<n; i++) { stim .... start=i*steptime dur=steptime; /* correct to 0.0001 sec */ }; for (i=1; i<n; i++) { plotarr[i] = V[node1]; step steptime; /* step 0.0112, but maybe acceptable */ };When the "stim" statements are all executed before the first "step" statement, they are all run in "construction mode" before the model starts, so they are correctly synchronized with the integration time step. Another solution is to use the "time" variable which always has the correct time updated by the "step" statement:

timinc = 0.0001; steptime = 0.011111111111; /* not integral mult of timinc */ for (i=1; i<n; i++) { plotarr[i] = V[node1]; stim .... start=time dur=steptime; /* may give blank betw. stimuli */ step steptime; /* still steps 0.0112 sec */ };

The stimulus on and off times are rounded up using a time step defined by "srtimestep" (default = 0.0001 sec) which can lead to inaccuracy in the start and stop times of stimuli of 0.1 msec. The reason for rounding up the stimulus times is that the simulation time "simtime" is advanced as a continuing sum of small timesteps which has inherent roundoff error -- and the stimulus on and off times are directly compared with this continuing sum, which can cause stimuli to be missed.

For most models, the rounding of stimulus on and off times is is not a problem, but if you need very accurate on and off times, you can set "srtimestep = 1e-6" which will make the stimulus on and off times accurate to 1 usec. The disadvantage of using this smaller roundoff value is that for long simulations with a short time step, roundoff error builds up, causing on and off times of stimuli occasionally to be missed -- which is a serious problem for a model.

If you want to set "srtimestep = 1e-6" you should keep the number of total time steps for the simulation (i.e. endexp / timinc) less than 1e7, which will maintain 10 digits of precision in "simtime" and prevent stimuli from being missed.

Test of accuracy in a continuing sum such as "simtime": test2.cc: ---------------------------------------- #include <stdio.h> double val = 0; double inc = 3e-10; double n = 1e5; main(int argc, char **argv) { int i; for (i=0; iWhen compiled with n set to different values, the accuracy of the accumulated val (a double precision value) goes down by a little less than 1 digit per factor of 10 increase in n.make test2 g++ -c -g -I../libP -I../pl test2.cc cc -g test2.o -o test2 (note: have added spaces to align "val":) n val ---------------------------------------- 1e+04 2.9999999999994338345e-06 1e+05 3.0000000000045564356e-05 1e+06 0.00029999999999524000092 1e+07 0.0030000000006714456005 1e+08 0.030000000036306033457 1e+09 0.30000000203657323228

The printout of the "plot" statement represents the value of stimulus and record parameters at the beginning of the time step, before the simulator integrates to the end of the timestep and computes the voltage values. This means that after a "step" statement, the last plotted values are not always the most recent ones available. Normally this is OK because in a series of "step" statements the next "step" allows the "plot" statement to print out the next set of values. If you want the last plot statement to correctly reflect the ending values, set the "endexp" variable to the ending time of the simulation. When the simulation time equals the value of "endexp", the "plot" statement adds one last printout of the values of stimulus and record parameters that are valid at the end of the last time step. To change the maximum and minimum values for the X axis, set the "setxmax" and "setxmin" parameters.

The plot statment has several forms. If the voltage at several nodes needs to be plotted at the same scale, a combined plot statement may be used:

(interpreted:) plot V [<node>] plot V [<node>], V[<node>] ... plot V [<node>] max <expr> min <expr> plot V [<node>] max <expr> min <expr> <options> plot Vm [<node>] max <expr> min <expr> <options> plot I [<node>] max <expr> min <expr> <options> plot L [<node>] max <expr> min <expr> <options> plot func max <expr> min <expr> <options> plot S variable max <expr> min <expr> <options> plot FAn <element> max <expr> min <expr> <options> plot FBn <element> (same options) plot FCn <element> (same options) plot G(n) <element> (same options) plot Ca(n) [<node>] (same options) (compiled:) plot (V, <node>); plot (V, <node>, max=<expr>, min=<expr>); plot (VM, <node>); plot (I, <node>); plot (L, <node>); plot (V, <element>); plot (FAn, n, <elemnum>, max=<expr>, min=<expr>); plot (FBn, n, <elemnum>, max=<expr>, min=<expr>); plot (FCn, n, <elemnum>, max=<expr>, min=<expr>); plot (Ca, n, <elemnum>, max=<expr>, min=<expr>); plot (G, n, <elemnum>, max=<expr>, min=<expr>); plot_func (double(*func)(double val, double t), double plval, double max, double min); plot_var (double *var, double plval, double maxx, double minx); followed by: plot_param(name=<string>, plnum=<expr>, plsize=<expr>); plot_param(name=<string>, pen=<expr>, plnum=<expr>); plot_param(name=<string>, pen=<expr>, plnum=<expr>, plsize=<expr>); plot_param(name=<string>, pen=<expr>, plnum=<expr>, plsize=<expr>, plval=<expr>); You can also follow these by: void plotchar (int val,int lines, int i); uses char symbol instead of line void plotvpenc (double (vpen)(int,double,double)); inserts virtual pen in plot void plotfilt (int nfilt, float *timec); inserts low-pass filter in plot plot_arr (double *arr, int arrsize); puts xval,yval into array "arr[arrsize][2]"where: (interpreted or compiled:)

[<node>] = 1-, 2- or 3-D node number; must have brackets. max <expr> (volts) = maximum voltage for vertical plot axis min <expr> (volts) = minimum voltage for vertical plot axis plmin, plmax are default values for max and min when not specified. func = a function returing value to plot variable = any variable <options> = pen <expr> sets color of single plot. char 'x' char labels with lines. Char 'x' char labels without lines. size <expr> size of char point label. filt <expr> lowpass filter (tau in sec). filt [<expr>,<expr>] cascade lowpass filter. vpen <func> function returning pen color plname <expr> name for plot plnum <expr> plot number assignment (if plsep) plsize <expr> plot size (if plsep) plval <expr> constant value to pass to func plarr <expr> puts xval,yval into array "arr[arrsize][2]"These statements plot the voltage as a function of time at the nodes specified on a single graph. If "max" and "min" are left out of the statement, the voltage scale (ordinate) is defined by the variables "plmax" and "plmin". These variables are set by default (plmax = 0.04, plmin = -0.07) to the normal physiological range of neurons, and in many cases they need not be changed. The variable "endexp" (length of the experiment) sets the time scale (abscissa), and the "ploti" variable sets the time resolution of the plot. The "plot Vm" statement plots the membrane voltage, that is, the difference between the intracellular voltage and the extracellular voltage at an external compartment.

Several "plot V[]" statements may be used to cause several plots to be displayed on one graph, but with different scales. The first one defined determines the scale actually plotted on the vertical axis, but the rest simply use their own scale and ignore the scale numbers on the graph.

The "filt" option inserts a lowpass filter in the plot to reduce the bandwidth of the recorded signal. The value given sets the time constant of the filter in seconds [1/(2*PI*F)]. You can also set a cascade of filters:

(interpreted:)

plot .... filt [ 3.2e-5, 1.6e-6, .8e-5];(compiled:)

plotfilt(3,make_filt(3.2e-5, 1.6e-6, .8e-5));This plot filter would have a cascade of single-pole filters in series with 3dB cutoff frequencies of 5KHz, 10KHz, and 20KHz. The filter is applied to the previous "plot" statement.

To make a Bessel filter, use this statement:

(compiled:) plotbessfilt(2000); // 4th order bessel filter, cutoff = 2000 HzYou can define a special "pen" function for each plot using the "vpen" option. This function receives the plot number and the X and Y values for the plot, and returns a number which is interpreted as the "pen" number (0-15 = color, -1 = no display). The advantage of this method over the "onplot" method defined below is that if the plot number changes when you add more plots, the color of the plot is defined by the same function.

(interpreted:) func spikplot (nplot, xval, yval) { local retval; if (yval > 25) retval = 7 /* white if > 25 */ else retval = 6; /* brown otherwise */ if (yval < 10) retval = -1; /* disappear if less than 10 */ return (retval); }; After this pen color function is defined, you can call the function from a "plot" statement: plot V[100] max 0.01 min -0.07 vpen spikplot; /* set plot time function */ (compiled:) double spikplot (int nplot, double xval, double yval) { double retval; if (yval > 25) retval = 7 /* white if > 25 */ else retval = 6; /* brown otherwise */ if (yval < 10) retval = -1; /* disappear if less than 10 */ return (retval); } plot_vpen (spikplot); plot (V, nd(100), max=0.01, min=-0.07);The vpen function is called before the plot variables are recorded. You can include other actions in it, much like the "onplot()" procedure.

plot I [<node>] max=<expr> min=<expr> <options>where:

[<node>] = 1-, 2- or 3-D node number; must have brackets max=<expr> (amperes) = maximum current for vertical plot axis min=<expr> (amperes) = minimum current for vertical plot axis <options> = pen and char statements as in plot above.This statement plots the current passed through the electrode of a node which has been voltage clamped. It works exactly like the "plot V[]" statement in that several plots of current and/or voltage can be combined on the same graph with different scales. If a current clamp is connected to the node, without a voltage clamp, the "plot I[]" statement plots the current passed through the current electrode. Note that to record the current at the "end" of a voltage clamp period, the voltage clamp must still be present. One way to assure this is to record the current at a small time step before the voltage clamp stops.

plot L [<node>] max <expr> min <expr>where:

[<node>] = 1-, 2- or 3-D node; must have brackets max <expr> (photons/sec) = maximum "inten" min <expr> (photons/sec) = minimum "inten" <options> = pen and char statements as in plot above.This statement plots the light flux (number of photons/sec) absorbed by a photoreceptor at a node. It is useful for determining single photon events or plotting the stimulus timing on the same graph as the voltage or current in a node. "max" and "min" determine the scale for plotting. Remember, the number of photons absorbed is related to light intensity, photoreceptor absorbing area, and absorption factors ("dqeff"=0.67, "attf"=0.9, and the pigment absorption).

plot <func> max <expr> min <expr>This statement plots the value returned by a function. The function must have 2 input parameters: a number set by "plval=val" (a param on the plot line) or if this has not been set, the number of the plot, and the X value, and must return the Y value.

(interpreted:) dim contrast_array[endexp/ploti+1]; func contrast_val (plval, xval) /* Return and save the contrast value */ { contr = (V[1]- V[0]) / (V[1] + V[0]); contrast_array[xval] = contr; if (contr >= plval) contr = plval; return (contr); }; (compiled:) double contrast_array[1000]; double contrast_val (double plval, double xval) /* Return and save the contrast value */ { contr = (v(nd(1))- v(nd(0))) / (v(nd(1)) + v(nd(0))); contrast_array[(int)xval] = contr; if (contr >= plval) contr = plval; return (contr); }; plot_func (contrast_val, plval=100, max=<expr>, min=<expr>);Note that you can accomplish several things in a plot function, e.g. you can load arrays with recorded values, or modify the neural circuit. Since it runs once every "ploti" time increment (which can be much longer than the integration time increment "timinc") it takes relatively little CPU time.

You can also load an array with plot values using the "plarr

dim plot_array[501][2]; plot V[1] plarr plot_array; . . . run; process data in plot_array here. (compiled:) double plot_array[501][2]; plot_arr (plot_array,501); // puts xval,yval into array "arr[arrsize][2]"

plot S variable max <expr> min <expr>This statement plots the value of any symbol (variable) together with other plot statements.

(interpreted:) plot FAx <element expr> plot FBx <element expr> plot FCx <element expr> plot Gy <element expr> plot FAx <element expr> max=<expr> min=<expr> plot FBx <element expr> max=<expr> min=<expr> plot FCx <element expr> max=<expr> min=<expr> plot G(s) <element expr> max=<expr> min=<expr> plot G(g) <element expr> max=<expr> min=<expr> plot G(hh) <element expr> max=<expr> min=<expr> plot nt [<node>] max=<expr> min=<expr> plot Ca(z) [<node>] max=<expr> min=<expr> (compiled:) plot (FAn, n, <elemnum>, max=<expr>, min=<expr>); plot (FBn, n, <elemnum>, max=<expr>, min=<expr>); plot (FCn, n, <elemnum>, max=<expr>, min=<expr>); plot (G, n, <elemnum>, max=<expr>, min=<expr>); plot (nt, n, <node>, max=<expr>, min=<expr>); plot (Ca, n, <node>, max=<expr>, min=<expr>);where:

x = 0 - 4 = filter number s = 0 - 12 = state number g = vrev, I, CA = params for any channel type hh = H, M = params for HH channels nt = GLU,AMPA,NMDA, = ligands CNQX,GABA,BIC, STR,GLY,STR, cGMP,cAMP z = I,IP,IE,IPE,VREV = params at a node with Ca chans z = 0, 1, 2 ... n = [Ca] in shells, 0=outside, 1=inside, 100=core and: <element expr> = number or variable describing a synapse, from "ename" clause. max=<expr> = maximum for plot, value depends on filter min=<expr> = minimum for plot, value depends on filterThis statement plots the neurotransmitter time functions inside a synapse or channel. The synapse (channel) is identified using an "ename" in its definition statement, when it is first made (see "ename" and "modify" below). Thereafter, the synapse (channel) can be referred to by a unique value (its element number) retrieved from the "element".

The FA0-FA4 values are pre-release time functions, calibrated in "volts above synaptic threshold". FA8 gives the "readily releasible pool", and FA9 gives the instantaneous "trel" (transmitter released) vesicle release rate in vesicles/sec. The FB0-FB4 values are post-release functions and represent the concentration of neurotransmitter in the synaptic cleft. FB0-4 range from 0 to 1000, where a value of 1 represents the half-saturation point for the static post-synaptic saturation function. The FC0-FC4 values are post-saturation conductances. FC9 is the second-messenger level. They return a value normalized to the range 0 - 1. This value is multiplied by the "maxcond" parameter to set the post- synaptic conductance. The values FA0, FB0 and FC0 return the input to their respective filter functions.

Using the "G", "G(1)-G(12)" expressions, the channel internal states may be recorded (see "plot" below). The expression "G(0) <expr> records the channel conductance in a manner similar to the "FCx" expression (calib. in S). For a "sequential-state" type of channel (type 1), the "G(x)" (x=1-12) expression records the channel state concentrations, (dimensionless fractions of 1). Each of these plot expressions has a default max and min to set the graph scale (e.g 2, 0 for states, 100e-6 for nt, etc.)

For all channel types:

G channel conductance (Same as G(0) or G0) G(I) ionic current through channel G(vrev) vrev (reversal potential) G(Ca) Calcium current through channel (if Ca, NMDA, cGMP chan)For HH channel types:

G(M) m (if Na chan) or n (if K chan), or c (if Ca chan), frac of 1. G(H) h (if inactivating type)For sequential-state Markov types:

G channel conductance (Siemens) G(0) channel conductance (Siemens) G(1) amplitude of state 1 (Fraction of 1, or population if "chnoise") G(2) amplitude of state 2 . . . G(n) amplitude of state n.Note that the number inside the parentheses is a numerical expression and can be a variable or a function. At a node with a calcium channel:

Ca (0) cao = [Ca] at first exterior Ca shell (next to membrane) Ca (1) cai = [Ca] at first interior Ca shell (next to membrane) Ca (2) [Ca] at second interior shell . . . Ca (n) [Ca] at nth shell Ca (100) [Ca] in core Ca (vrev) local reversal potential for Ca Ca (I) total Ca current through Ca channels and pumps Ca (IP) Ca current through pump Ca (IE) Ca current through exchanger Ca (IPE) Ca current through Ca pump and exchanger[ Note that exchanger current Ca(IE) includes Ca and Na currents, and that it is dependent on Vrev of Ca and Na.]

If the channel is a Na type 4 (Integrate-and-Fire)

G(0) channel conductance G(1) population of state 1 G(2) population of state 2 G(3) integration state G(4) state switchingTo look inside a rod or cone transduction element, the G(0) - G(9) values plot:

G(0) conductance G(1) rhodopsin G(2) meta rhodopsin I G(3) meta rhodopsin II (R*) activates G protein G(4) G protein G(5) PDE G(6) G cyclase G(7) cGMP G(8) Ca feedback for recovery and adaptation G(9) Cax (protein between Ca and G cyclase)

(interpreted:) V [<node>] voltage at node V @ cable <element expr> : <expr> voltage along cable I [<node>] current L [<node>] light FAx <element expr> pre-synaptic filters FBx <element expr> post-release filters FCx <element expr> post-saturation filters G(s)These functions return the values of voltage, current, or light absorbed, respectively, at any node. The node may be 1-, 2-, 3-, or 4-dimensional. For instance, the record function "V[]" can be used to find voltages at pre- and post-synaptic nodes, and these voltages may be plotted (see explanation above) or graphed (see programming example below). The "I[]" statement returns the currrent injected at a node through a voltage clamp if present. When a current clamp is present without a voltage clamp (the ususal case), the "I[]" statement returns the current clamp's current. Note that to record the current at the "end" of a voltage clamp period, the voltage clamp must still be present. One way to assure this is to record the current at a small time step before the voltage clamp stops.populations of Markov states G(g) ionic conductance G(hh) HH M and H state variables nt [<node>] concentration of ligand at node Ca(z) [<node>] concentration of Ca in shells (compiled:) v (<node>) voltage at node v (<elemnum>, <expr> voltage along cable i (<node>) current l (<node>) light record_synapse(<elemnum>, nf) synaptic filters record_chan(<elem>, nf, ns) populations of Markov states or conductance record_chan(<elemnum>, nf, ns) populations of Markov states or conductance record_ca(<node>, caval, ns) conc of Ca in shells record_nt(<node>, nt) conc of ligand at node

The synaptic filters return values between 0 and 1 representing the amount of neurotransmitter released (see "plot" above). The "FAx", "FBx", and "FCx" synaptic filter functions require an element number which has been set through the "ename" clause in the original definition of the synapse.

The value G0 returns the total channel conductance, and the values G1-G8 return the concentrations of the states 1-8 respectively, or in the case of Hodgkin-Huxley type channels, G1,G2 return "m","h" for the Na channel, and G1 returns "n" for the K channel.

graph X max=<expr> min=<expr> graph Y max=<expr> min=<expr> <options> For setting X and Y scales of graph axes and initial color. where: <options> = pen <expr> sets color of single plot. char 'x' char labels points with lines. Char 'x' char labels points without lines. filt <expr> lowpass filter (tau in sec) filt [<expr>,<expr>] cascade lowpass filter graph init For drawing graph axes on screen. graph restart For resetting graph so lines don't connect to previous lines. graph pen (<expr>, [<expr>] ... ) where <expr> is the number of color (1-16 on VGA and X screen) For changing pen color of lines on graph between plots, after the axes have been drawn. The differnt <expr> numbers are the colors assigned respectively to different plots. A color of -1 means do not display. graph (<expr>,<expr>) where: (<expr>,<expr>) is an (x,y) point to be graphed. Draws a new point by connecting it to others with line.The graph statement allows the display of variables before or after a "run" or "step" (not while running!). Graphed points are connected by lines, in a color specified by the "graph pen" command. Both x and y axes must be initialized (with "graph X ..." and "graph Y ..." statements) to allow the graph scale to be set up and the graph axes labeled. The "graph (x,y)" statement then plots a sequence of points as connected line segments. The "restart" command allows multiple sets of points connected by lines to be drawn on the same grid. Any variable (or node voltage/current/ intensity) may be plotted. Calibrated in same units used to record.

The graph statement is useful for displaying parametric equations like I/V plots, where both are functions of time. In this case, the "step" statement can be used to set up a short simulation which can be continued to gather further graph points:

Example:

(interpreted:) graph X max -.01 min -.08; /* volts */ graph Y max -2e-11 min -6e-11; /* amps */ graph init; graph pen (4); for (i=0; i<10; i++) { stim node 1 vclamp i * -.01 start i * .02 dur .02; /* sweep voltage */ step .02; /* wait for equilbration */ graph (V[1], I[1]); /* graph result */ }; graph restart; /* this time stim node 2 */ graph pen (2,3); for (i=0; i<10; i++) { stim node 2 vclamp i * -.01 start i * .02 dur .02; /* sweep voltage */ step .02; /* wait for equilbration */ graph (V[1], I[1]); /* graph result */ }; (compiled:) graph_x(max= -0.01, min= -0.08); /* volts */ graph_y(max= -2e-11, min= -6e-11); /* amps */ graph_init(); graph_pen (4); for (i=0; i<10; i++) { vclamp(nd(1), i*-0.01, start=i*0.02, dur=0.02); /* sweep voltage */ step (0.02); /* wait for equilbration */ graph (v(1), i(1)); /* graph result */ } graph_restart(); /* this time stim node 2 */ graph_pen (2,3); for (i=0; i<10; i++) { vclamp( nd(2), i*-0.01, start=i*0.02, dur=0.02); /* sweep voltage */ step (0.02); /* wait for equilbration */ graph (v(1), i(1)); /* graph result */ }; ;

You can set the display to make separate plots for each trace with the "plsep" parameter. If you set "plsep=1" then the screen will be divided into separate plots, each with its own y axis and label, and with a common x axis, so that all the traces can be more easily distinguished. By default, "plsep"=0" so if you want separate plots you will need to set it to 1.

You can set "plsep=1" in the script, or from the command line, like this:

nc --plsep 1 file.n or nc -S file.nThe "-S" or "--plsep 1" command line switches set the "plsep" parameter when you call "setvar()" in the script. If you place "plsep=1" before the "setvar()" statement, then you can turn off separate plots with "--plsep 0" in the command line. See "Setting variables from command line".

If you are using "plsep" mode for separate plots, you can assign more than one trace to a plot with the "plnum x" parameter. Each trace can be assigned to a "logical plot", and more than one trace can be assigned to a logical plot. The logical plots are then assigned to the display in increasing order. For example:

(interpreted:) plot V[1] pen 2 plname "V1" plnum 2; /* the first 2 are on the same plot */ plot V[3] pen 3 plnum 2; plot V[5] pen 5 plname "V5" plnum 10; plot V[6] pen 6 plname "V6" plnum 11; (compiled:) plot (v,ndn(1), max, min); plot_param(name="V1", pen=2, plnum=2); /* the first 2 are on the same plot */ plot (v,ndn(3), max, min); plot_param(name="", pen=3, plnum=2); plot (v,ndn(5), max, min); plot_param(name="V5", pen=5, plnum=10); plot (v,ndn(6), max, min); plot_param(name="V6", pen=6, plnum=11);

In this example there are 3 plots, which are logical plots 2, 10 and 11. They are displayed on the screen starting from the bottom as 1, 2, 3. Each trace can be assigned pen color, but if no pen color is given, its color is assigned from the plot number. A label for V[3] (the second trace in "logical plot" 2 ) could be displayed, but in this case its "plname" is not given so a label is omitted for this trace. If the first trace is not given a "plname", all the traces in the plot are labeled according to their node or element numbers or their "plname". With suitable "max" and "min" parameters, the traces in logical plot 2 can be offset so they overlap a desired amount. Any plot statements without a logical plot assignment are assigned independent plots.

You can also change the size of the separate plots, to make their Y axes bigger or smaller. Use the "plsize x" parameter. The first trace sets the size. All the sizes are scaled to fit inside the window.

(interpreted:) plot V[1] pen 2 plname "V1" plnum 2 plsize 2; /* sets this plot bigger */ plot V[3] pen 3 plnum 2; plot V[5] pen 5 plname "V5" plnum 10; plot V[6] pen 6 plname "V6" plnum 11; (compiled:) plot (v,ndn(1), max, min); plot_param,name="V1", pen=2, plnum=2, plsize=2); /* sets this plot bigger */ plot (v,ndn(3), max, min); plot_param(name="", pen=3, plnum=2); plot (v,ndn(5), max, min); plot_param(name="V5", pen=5, plnum=10); plot (v,ndn(6), max, min); plot_param(name="V6", pen=6, plnum=11);

To simplify placing traces within a plot, you can set the "max" and "min" parameters e.g. like this:

(interpreted:) plg = .3e-6; offtr = .2; offb = 1e-6; plot Ca(1)[soma] max (1-offtr)*plg+offb min (0-offtr)*plg+offb pen 6 plsize .3 plname "[Ca]i" plnum 1; (compiled:) max=(1-offtr)*plg+offb; min=(0-offtr)*plg+offb; plot (Ca, ndn(1,soma), max, min); plot_param(name="[Ca]i",pen=6, plnum=1, plsize=0.3);

In this case, the "plg" variable is the "plot gain", "offtr" is the offset for the trace within the plot (range of 0 to 1 is size of plot), and "offb" is the zero offset in the units for "plg". To make the trace larger, increase "plg", and to shift it up or down, change "offtr" or "offb".

Example:

gframe "gr1"; gorigin (0.2,0.2); gsize (0.5); code that generates graph or plot in smaller frame . . . gframe ".."; code to draw on overall screen . . . gframe "gr2"; gorigin (0.6,0.2); gsize (0.4); code to generate second small graph gframe ".."; etc.

(interpreted:) display matching <node> 'parameters' display <elemtype> matching <node> 'parameters' display range <node> to <node> 'parameters' display <elemtype> range <node> to <node> 'parameters' display connect <node> to <node> 'parameters' display <elemtype> connect <node> to <node> 'parameters' display element <expr> 'parameters' display stim at <expr> 'parameters' (compiled:) display (ELEMENT, MATCHING, ndt(<node>), color, dscale); display (<elemtype>, MATCHING, ndt(<node>), zrange1=-10, zrange2=50, color, dscale); display (<elemtype>, MATCHING, ndt(<node>), VCOLOR, vmax=-0.02, vmin=-0.08); display (CABLE, MATCHING, ndt(<node>), zrange1=-10, zrange2=50, color, dscale); display (SPHERE, MATCHING, ndt(<node>), zrange1=-10, zrange2=50, color, dscale); display (ELEMENT, RANGE, ntd(<node>), ndt(<node>), 'parameters'); display (<elemtype>, RANGEi, ntd(<node>), ndt(<node>), 'parameters'); display (ELEMENT, CONNECT, ndt(<node>) ndt(<node>), 'parameters'); display (<elemtype>, elnum, zrange1, zrange2, color, dscale); display_stim (at_time, scale); set_disp_rot( xrot, yrot, zrot, dxcent, dycent, dzcent, rxcent, rycent, rzcent, dsize); disp_calib (xcalib, ycalib, cline, dsize, dcolor); setcmap (int *parr, int cmapsize); setcmap (int cmap); void display (int elemtype, int disptype, node *nd1, double zrange1, double zrange2, int dcolor, double(*vpenn)(int elnum, int color), int cmap, double vmax,double vmin, double dscale, int hide, int excl, double stime); void display (int elemtype, int disptype, node *nd1, node *nd2, node *nexc, int exceptype, double zrange1, double zrange2, int dcolor, double(*vpenn)(int, int), int cmap, double vmax,double vmin, double dscale, int hide, int excl, double stime); void display (int elemtype, int elnum, double zrange1, double zrange2, int dcolor, double(*vpenn)(int, int), int cmap, double vmax,double vmin, double dscale, int hide); void display (int elemtype, int elnum, double zrange1, double zrange2, int dcolor, double dscale);optional parameters:

xrot = <expr> yrot = <expr> zrot = <expr> color =<expr> max <expr> min <expr> vpen =<func> cmap =<expr> except matching <node> except <elemtype> except <elemtype> matching <node> hide size =<expr> dscale=<expr> rmove (<expr>,<expr>)ltexpr> center (<expr>,<expr>) calibline=<expr> calibline=<expr> loc (<expr>,<expr>) newpagewhere:

parameter: default: meaning xrot,yrot,zrot 0 degrees x,y,z rotation of anatomical circuit. color see below color of matching elements displayed. vpen see below func to compute color of matching elements. except none prevent display of selected elements. size 200 um size of display window. dscale 1.0 display object at different size. rmove (0,0,0) display object displaced by (x,y,z) center 1/2 of size location of display window. z min z1 max n2 none display range from z1 to z2, if backwards, exclude hide no hide hidden-line removal. calibline none calibration line in microns newpage none make new page for movie (use with "vid -P file") <elemtype> = One of: "cable", "sphere", "synapse","gj", "rod", "cone", "transducer", "load", "resistor","cap", "gndcap", "batt", "gndbatt", "chan","vbuf", "node", "comps".The display statement is used to display neural circuit anatomy. The display statement only works in "nc" with the "-d 1" switch (or with "nd"), otherwise all display statements are ignored. This feature allows you to either display or run a neural circuit model without changing its descriptor file. You can display a "photographic" view of your neural circuit using "nc -d 1 -R" (or "nc -R"), in conjunction with "povray", a 3D ray-tracing program.

The selected neural elements appear on the screen with the view selected by appropriate rotation and "center" commands. Each neural element is displayed with a simple icon in a position corresponding to its location in the circuit. In order for neural elements to be displayed in their proper place, the location of each node must be defined with the "loc (x,y)" clause when a node is set up with a statement beginning with "at" or "conn". (If this is not done, the location of a node is 0,0,0). Note that rods and cones also have a location for their transduction element, which is not necessarily the same as their node's location. For example, to set up a cable connected to a sphere, you could say:

(interpreted:) at [1][3] loc (10,10) sphere dia 5; conn [1][3] to [2][4] loc (10,20) cable dia 1 length 10; (compiled:) make_sphere (loc(nd(1,3), 10, 10), dia=5); c = make_cable (nd(1,3), loc(nd(2,4), 10, 20)); c->dia=1;The "display matching <node>" statement displays all the neural elements matching the "<node>" value given, including elements that are located "at" the node or those that are "connected" to it. A "<node>" value in the "display" statement can match a neural element with more node dimensions. In this case, the match ignores the extra node dimensions. For instance, in the example above, the statement:

(interpreted:) display matching [1]; (compiled:) display (ELEMENT, MATCHING, ndt(1));matches a "1" in the first dimension, but ignores the second and third dimensions. In this case, it displays both the sphere at node [1][3] and the cable from [1][3] to [2][4]. Any dimension can be specifically excluded from the match by including a negative number in that dimension. For example,

(interpreted:) display matching [1] [-1] [5]; (compiled:) display (ELEMENT, MATCHING, ndt(1,-1,5));matches any node with 1 in its first dimension and 5 in its third dimension. The second dimension is ignored.

The addition of "only" to the ""display matching <node> statement displays only those neural elements "at" the "<node> given, or those elements that connect exclusively with that "<node> Given the circuit in the example above:

(interpreted:) display matching [1][3] only; (compiled:) void display (ELEMENT, MATCHING, ndt(1,3), zrange1, zrange2, dcolor, vpen, cmap, vmax, vmin, dscale, hide, excl=1, stime);would display only the sphere, not the cable. This is useful to display a neuron but none of its connections to other neurons.

The "display connect <node> to <node> statement displays all the neural elements that match and connect to both "<node> values. For instance, in the example above, the statement:

display connect [1] to [2];would display the cable from [1][3] to [2][4]. Any dimensions not defined by the "display" statement are ignored, as described above.

The "display range

The display element <expr> statement displays one neural element that has been remembered with the "element <expr> statement. This is useful for displaying one specific element of several that connect to identical nodes.

Click here to return to Display statement index

(interpreted:) display matching [5][1]; displays any element type display sphere matching [5][1]; displays only spheres (compiled:) display (ELEMENT, MATCHING, ndt(5,1)); display (SPHERE, MATCHING, ntd(5,1);

(interpreted:) display matching [1][-1][5] except sphere [-1][2]; (compiled:) display (ELEMENT, MATCHING, ndt(1,-1,5)); except=SPHERE, ndt(-1,2));This displays all the elements connected to nodes [1][-1][5] except spheres connected to [1][2][5].

(interpreted:) display Z max -23 min -20; (compiled:) display ( ... zrange1=-23, zrange2=-20, ... );This displays everything but neural elements in the range -20 to -23 (microns).

The "dscale" parameter causes the icon of a neural element to be displayed in a different size than normal, without changing the size of the element. It is sometimes helpful to display the icon larger to make it more visible, or smaller to allow more space between icons in an array.

When displaying nodes (-d 8), the dscale parameter can also select which node number dimension (1-4) is displayed, along with the size. A negative number selects this option. When dscale is negative, the sign is ignored, and the integer part selects the node number dimension, and the fractional part to the right of the decimal point selects the size.

The "rmove (x,y,z)" parameters cause the objects selected to be displaced (translated) during display. This is useful for "pulling apart" a neural circuit into its separate neurons. The move only takes effect for objects displayed within the same statement.

You can display the voltage of a neuron by displaying it with a color of "vcolor". The range of colors is distributed between the range of the "max, min" parameters. The colors range from the cool colors for "min" to the warm for "max". The amount of light received by photoreceptors can be displayed with "color=lcolor", and display of [Ca]i by "color=cacolor". To display different colors for each region, set "color=rcolor".

(interpreted:) func drawv (elnum, color) { /* return color as a func of voltage */ vmin = -0.08; cmax = 100; v = V [element elnum->node1a][element elnum->node1b]; /* voltage at node1 */ vs = v-vmin; if (vs<0) vs=0; if (vs>cmax) vs=cmax; if (color != blue) { color = int(vs*100); } return color; }; display cable matching <node> vpen drawv; (compiled:) double drawv (int elnum, int color) { /* return color as a func of voltage */ int cmax; double v, vs, vmin; elem *e; vmin = -0.08; cmax = 100; e = elempnt(elnum); v = v (e->node1a, e->node1b); /* voltage at node1 */ vs = v-vmin; if (vs<0) vs=0; if (vs>cmax) vs=cmax; if (color != blue) { color = int(vs*100); } return color; } display (CABLE, MATCHING, <node>, drawv);

(interpreted:) stim spot ... disp stim at <time>; (compiled:) stim_spot (...); display_stim (time, dscale);The advantage of this method is that you can see the stimulus at a distant time in the future, without running the full simulation, which is typically much faster.

To display the stimulus during the simulation, you display the light that the photoreceptors currently sense at this instant, using (no "at" clause):

stim spot ... start <expr> dur <expr>; step <expr>; disp stim;

Note that if a "step" or "run" statement comes before a "disp stim" statement, the "disp stim" statement will always show the stimulus at the current simulation time, even if an "at" clause is included.

The display stim" statement displays the light value as the color of a small sphere (default 1 um diameter). Often one wants to display photoreceptors a little larger than the default size with the "dscale" parameter:

disp stim at <time> dscale <expr>;where for good visibility one sets <expr> between 2 and 10.

Each type of "display" has its own default colormap, but you can set another colormap with the "cmap = <expr>" parameter. The "display stim" statement defaults to a grayscale colormap but you can set it to a colormap with colors using "cmap = 3":

Colormap N val 1 16 0-15 (VGA colors, for plots) 2 16 16-31 (blue=low, green=med low, yellow=med hi, red=high, for vcolor, cacolor, etc.) 3 16 32-47 (blue=low, purple=medium, red=high, for vcolor, cacolor, etc.) 4 16 48-63 (black=low, red=high, for vcolor, cacolor, etc.) 5 16 64-79 (black=low, green=high, for vcolor, cacolor, etc.) 6 16 80-95 (black=low, blue=high, for vcolor, cacolor, etc.) 7 100 96-195 (for "display stim" grayscale) 8 100 196-295 (a bigger variety, taken from "rgb.txt" ) 9 (user defined, must use colors defined above, i.e. 0-295)

You can define your own colormap by creating a one-dimensional array and placing sequential color values into it. Note that the color values are the unique colors are already defined in the various drivers (i.e. color "32" is grayvalue 0 from colormap 3, "195" is grayval99).

(interpreted:) dim mycolormap = {{1,2,3,4,5,32,6,65,8}}; display cmap = mycolormap; display matching [2][-1] pen 5; /* displays color 32, dark gray */ (compiled:) int mycolormap[] = {1,2,3,4,5,32,6,65,8}; setcmap(mycolormap,sizeof(mycolormap)); display (ELEMENT, MATCHING, ndt(2,-1), pen=5; dscale=1); /* displays color 32, dark gray */

For more details on the "bigger variety" colormap 8, see "nc/pl/ccols.txt" (taken from "/usr/lib/X11/rgb.txt"). You can see these colors and their names with the program "xcolorsel". To add or modify these colors, see "nc/src/ncdisp.cc", "nc/src/colors.h" and "nc/pl/mprint{x,c,xf}.c"

A display statement runs in "construction" mode. To see the progress of the construction of a neural circuit, a stimulus, or the color display of voltage or calcium, you can place "display" statements between "step" statements:

for (t=0; t<stoptime; t++ ) { modify neural circuit ... step <expr>; disp stim; }or

for (t=0; t<stoptime; t++ ) { display stimulus ... step <expr>; disp stim; }

To make a movie of the spatiotemporal propagation of voltage or calcium concentration in a neuron or in a network, you can place "display" statements inside the "onplot" procedure. This is a special procedure that runs at intervals during the simulation, just after any "plot" statements generate their output:

frameint = 0.001; (interpreted:) proc onplot() /* plot procedure that displays a neuron's voltage */ { if ((int(time/ploti+0.001) % (frameint/ploti)) == 0) { display matching [celltype][cellnum][-1] color=vcolor min=-0.09 max=0.02; draw_color_scalebar(cmin,cmax); display newpage; }; }; (compiled:) void onplot(void) /* plot procedure that displays a neuron's voltage */ { if ((int(time/ploti+0.001) % (frameint/ploti)) == 0) { display (ELEMENT, MATCHING, ndt(celltype,cellnum,-1), color=vcolor, min=-0.09, max=0.02); draw_color_scalebar(cmin,cmax); gpage(); } } . . . setonplot(onplot); /* set onplot() procedure to run at plot time */The basic idea is to display the voltage in the network at an interval that may be slower than the standard plot interval defined by "ploti". In the above example, the display is triggered at an an interval of "frameint", or 1 ms. Note that the statement "display newpage" defines the end of a frame. For other uses of the "onplot()" procedure, see "Run procedure at plot time".

You can add a color definition bar like this:

proc draw_time(dtime) { if (dtime < 1e-6 && dtime > -1e-6) dtime = 0; gframe ("Col_bar"); gpen (0); gmove(0.10,0.025); gtext ("V at time t=%g s",oldtime); gpen (15); gmove(0.10,0.025); gtext ("V at time t=%g s",dtime); oldtime = dtime; gframe (".."); }; proc draw_color_scalebar(cmin,cmax) /* Draw scalebar for vcolor display */ { local colbarlen,dist,wid; local colbase,numcols; local x1,y1,x2,y2,x3,y3,x4,y4; local dim colors[10][2] = {{0,0,0,16,16,16,32,16,48,16,64,16,80,16,96,100,148,100,0,0}}; /* see colormap in manual */ colbarlen=0.40; wid = 0.03; colbase = colors[colrmap][0]; /* lowest color in colormap */ numcols = colors[colrmap][1]; /* number of colors used */ dist = colbarlen/numcols; gframe ("Col_bar"); for (i=0; i<numcols; i++){ gpen(i+colbase); x1 = i*dist; y1 = wid/2; x2 = (i+1)*dist; y2 = y1; x3 = x2; y3 = -wid/2; x4 = x1; y4 = y3; grect(x1,y1,x2,y2,x3,y3,x4,y4,fill=1); }; gmove(-0.1,-0.002); gpen (15); gtext("MIN"); gmove(-0.1,-0.03); sprintf (nbuf,"%.3g",cmin); /* lowest value */ gtext(nbuf); gmove(colbarlen+0.05,-0.002); gtext("MAX"); gmove(colbarlen+0.05,-0.03); sprintf (nbuf,"%.3g",cmax); /* highest value */ gtext(nbuf); gframe (".."); draw_time(time); }; if (make_movie) { gframe ("Col_bar"); gorigin (0.15,0.05); /* set bar position */ gframe (".."); oldtime = 0; };You can view the output in graphics mode as usual by:

nc .... -v script.n | vidTo study the movie more carefully, you may want to slow down the display further, using the "-S" command line option for "vid":

nc .... -v script.n | vid -S 1.5This example displays individual frames with an interval of at least 1.5 seconds. Note that for this to work correctly, individual frames must be defined as in the "display newpage" command in the example above.

To make a movie from separate files, define a file name using the -P command line option:

for a black background: nc .... -v script.n | vid -c -B 0 -P cellmovie or for a white background: nc .... -v script.n | vid -c -B 7 -P cellmovieThis will create the set of files: "cellmovie1.ps, cellmovie2,ps, ... cellmovieN.ps" that you can convert to other image formats. For example, the programs, "makempeg" or "mpeg2encode", available on the web, make movies from "gif" or "ppm" files respectively. You can convert from PS format using a converter like ps2ppm:

#! /bin/tcsh -f # # ps2ppm # # script to make .ppm files from .ps or .eps # foreach i ($argv) echo "converting $i to $i:r.ppm" cat $i | gs -q -dNOPAUSE -r100 -sDEVICE=ppm -sOutputFile=- - > $i:r.ppm endClick here to return to Display statement index

(interpreted:) display node matching [5] dscale 2; displays node numbers (compiled:) display (NODE, MATCHING, ndt(5), color=5, dscale=2);For multidimensional nodes, to display just one of the numbers, negate it and subtract the dscale parameter divided by 10. The example below displays the second node dimension (usually the cell number) with an effective "dscale" of 1.5:

(interpreted:) display node matching [5][-1][-1] dscale -2.15; (compiled:) display (NODE, MATCHING, ndt(5), color=5, dscale= -2.15);You can display these node number sequences:

number displayed node numbers (dimensions) 1 1 2 2 3 3 4 4 5 1,2 6 2,3 7 1,2,3So, for example, to display the cell number (second node dim) and the node number within the cell (third node dim) with a size of 1.5:

display node matching [5][-1][-1] dscale -6.15;

(interpreted:) display comps matching [5][1]; (compiled:) display (COMPS, MATCHING, ndt(5,1));This statement displays only compartments and/or their low- level connections that have been translated from neural elements matching a node. A compartment is displayed as a sphere with a size that would have the compartment's resistance and capacitance. A connection is displayed as a yellow line between compartments. The compartment and connection display is useful for "tuning" the variable "lamcrit" which controls the minimum size of compartments.

Click here to return to Display statement index

(interpreted:) proc phot_dr (type, pigm, color, dscale, dia, foreshorten, hide) { gpen (color); gcirc (dscale*dia/2,0); }; proc gapjunc_dr (color, dscale, length, foreshorten, hide) { gpen (color); gcirc (dscale*dia/2,0); }; proc synapse_dr (color, vrev, dscale, dia, length, foreshorten, hide) { local dx,dy; dx = length; dy = dscale*dia/2; gpen (color); grect (dx,0,dx,dy,-dx,dy,-dx,0); gmove (0,0); gcirc (dscale*dia/2,0); }; proc elec_dr (color, dscale, dia, length, foreshorten, hide, elnum) { gpen (color); gcirc (dscale*dia/2,0); gmove(0,02,0); n2 = elem elnum->node1b; n3 = elem elnum->node1c; sprintf (numbuf,"%d %d",n2,n3); gtext (numbuf); }; (compiled;) void phot_dr (type, pigm, color, dscale, dia, foreshorten, hide) { gpen (color); gcirc (dscale*dia/2,0); }; set_phot_dr(phot_dr); void gapjunc_dr (color, dscale, length, foreshorten, hide) { gpen (color); gcirc (dscale*dia/2,0); }; set_gapjunc_dr(gapjunc_dr); void synapse_dr (synapse *spnt, color, vrev, dscale, dia, length, foreshorten, hide) { double dx,dy; dx = length; dy = dscale*dia/2; gpen (color); grect (dx,0,dx,dy,-dx,dy,-dx,0); gmove (0,0); gcirc (dscale*dia/2,0); }; set_synapse_dr(synapse_dr); void elec_dr (color, dscale, dia, length, foreshorten, hide) { elem *epnt; node *np; gpen (color); gcirc (dscale*dia/2,0); gmove (0.02,0); epnt = findelem(elnum); if (dscale != 1 && np=epnt->nodp1) dr_node(np,dscale); }; set_elec_dr(elec_dr);Currently only photoreceptor ("phot_dr"), gap junction ("gapjunc_dr"), synapse ("synap_dr"), and recording electrode ("elec_dr") icons can be re-defined. It is easy to add new procedures in the "nc" source code for other neural elements.

Within the draw procedure, you can use or ignore any of the parameters. The "pigm" and "dia" parameters are the numbers you set (or were set by default) for the photoreceptor definition. The "type" is "rod" or "cone". The "color" parameter is defined by the following search: if your "display" statement defines a color, then this is used, otherwise a standard color representing the pigment type is used. The "dscale" parameter is a copy of the "dscale" parameter in the "display" statement. It allows you to change the size of an object for display purposes only without changing its actual size. Generally you want to multiply the size by dscale inside your procedure, but other uses are possible, for example, you could have integer values (or negative values) of "dscale" select for a different of icons. The "dist" parameter represents the amount of foreshortening of the object's icon by the rotation it undergoes (see below). The "hide" parameter is set to 1 whenever "hide" is set, in which case the icon should be a closed unfilled outline, i.e. a polygon.

Just before your procedure is called, the "graphics pen" is moved to the (x,y,z) location of the photoreceptor and a graphics sub-frame is initiated that is rotated with respect to the root frame. If the icon is oriented (e.g. extended vertically like a photoreceptor), you draw it horizontally to the right (i.e. horizontal is "zero" degrees rotation). The icon may be foreshortened by some 3D rotations, so to correctly take this foreshortening into account, multiply its length by the "forshortening" parameter. This parameter varies from 0 to 1. If you ignore the foreshortening, your icon will be displayed the same size no matter what rotation.

You can use any graphics commands to draw the icon. The graphics scale is in microns but this can be changed with "gsize()".

#include "gprim.h" void syn_draw2 (synapse *spnt, int color, double vrev, double dscale, double dia, double length, double foreshorten, int hide) /* draw synapse within small oriented frame */ { int fill=1; double tlen; char tbuf[10]; dia *= dscale; /* draw circle with line */ if (dia < 0) dia = -dia; color = -1; if (color < 0) { if (vrev < -0.04) color = RED; else color = CYAN; } gpen (color); if (length > 1e-3) { gmove (length/2.0,0.0); if (dia > 0.001) gcirc (dia/2.0,fill); else gcirc (0.001,fill); gmove (0,0); gdraw (length,0); } else gcirc (0.001,fill); gpen (black); sprintf (tbuf,"%d %d",spnt->node1b,spnt->node2b); /* print pre and postsynaptic cell number */ tlen = strlen(tbuf); gmove (length/2.0 -tlen*0.3, -1.0); gcwidth (1.2); gtext (tbuf); }You can activate this procedure with:

set_synapse_dr (syn_draw2);placed in the script before the display is run.

If you want to draw something on top of a display of a neural circuit, you can use the "transf()" subroutine to give the rotated 2D coordinates of a 3D point:

tarr = transf (x,y,z); xt = tarr[0]; yt = tarr[1]; zt = tarr[2];

You can use the "xt,yt" values passed into the "gmove()" and "gdraw()" functions to draw. The "zt" value can be used to decide whether one object is in front of another.

Click here to return to Display statement index(interpreted:) conn <node1> to <node2> cable <membrane params> elabl <expr> (compiled:) c = conn(<node1>, <node2>, CABLE); <membrane params> c->elabl <string>The "elabl" name can be retrieved later with the

element <expr> -> elablclause (see"element fields" below).

(interpreted:) conn <node1> to <node2> synapse <synaptic params> ename <var> (compiled:) s=conn(<node1>, <node2>, SYNAPSE); <synaptic params> var=s->elnum;A unique identifier is assigned to the variable whose name is given after the "ename" keyword. That specific individual neural element can be referred to later by the variable's value.

Note that a channel specified as a density cannot be named in the same way because a density statement defines channels in multiple compartments. However, channels specified as a density that sit in the compartment associated with a node can be accessed like this:

(interpreted:) at <node> chan Na 2 chset ename <var>In this case, the "chset" parameter specifies that you want to find a channel with the type given and the "ename" saves a reference to it for later use.

A typical use for the ename of a channel is to retrieve the fraction of inactivation of Na+ channels at a node:

(interpreted:) func na_inact () /* returns total inactivated fraction for Na type 2*/ { return (G(7)var + G(8)var + G(9)var); } (compiled:) double na_inact (void) /* returns total inactivated fraction for Na type 2*/ { return (record_chan(var,G,7) + record_chan(var,G,8) + record_chan(var,G,9)); }

In the original declaration: (interpreted:) conn <node1> to <node2> synapse <synaptic params> ename <var>where

<synaptic params> are the optional paramaters originally used for specifying the synapse; <var> is a variable used for remembering the synapse especially for modifying later.In a later declaration:

modify <expr> synapse <new synaptic params>where

<new synaptic params> are the new parameter value specifications; <expr> is an expression having the value of the "var" in the "ename" statement described above. Ordinarily, this expression is simply the variable. (compiled:) In the original declaration: s = (synapse *)conn (nd(<node1>), nd (<node2>), SYNAPSE); <synaptic params> var = s->elnum; In a later declaration: s = (synapse *)makelem(SYNAPSE,modify (var)); <new synaptic params >With the "ename/modify" feature, one can change a synapse as a function of any other recordable or computable parameter in a neural circuit. For instance, one could vary postsynaptic conductance (or presynaptic transmitter release) as a delayed function of postsynaptic voltage to simulate long-term potentiation.

This example constructs a presynaptic terminal that connects to a postsynaptic cell with a synapse. The synapse releases neurotransmitter exponentially with voltage, calculated at the standard time resolution of 0.1 msec. However, every "synstep" (10 msec) time interval, the synapse's conductance is modified according to the function "modsyn" which can be any computable or recordable function (e.g. it may be a function of voltage or conductance at any node in the network). The pre- and post-synaptic nodes are given as parameters to the function. Then the simulation continues to run with the "step" statement, which is similar to the "run" statement except that it stops the simulation after the given time interval:

(interpreted:) pre = 1; post = 2; soma = 3; synstep = .01; /* timestep for synaptic modification */ at [pre] sphere dia 5; conn [pre] to [post] synapse expon 2 thresh= -.045 maxcond=1e-9 ename syn1; conn [post] to [soma] cable dia .2 length 10; at [soma] sphere dia 10; stim node [pre] cclamp 1e-10 start 0.2 dur 10; for (t=0; t<100; t+= synstep) { newcond = modsyn (pre,post); /* function to calc new conductance */ modify syn1 synapse maxcond=newcond; step synstep; }; (compiled:) pre = 1; post = 2; soma = 3; synstep = .01; /* timestep for synaptic modification */ make_sphere(nd(pre), dia=5); s=make_synapse (nd(pre), nd(post)); s->ngain=2 s->thresh= -.045; s->maxcond=1e-9; syn1=s->elnum; c=make_cable(nd(post), nd(soma)); c->dia=0.2; c->length=10; make_sphere(nd(soma), dia=10); cclamp (ndn(pre),1e-10,start=0.2,dur=10); for (t=0; t<100; t+= synstep) { newcond = modsyn (pre,post); /* function to calc new conductance */ s = (synapse *)makelem(SYNAPSE,modify (syn1)); s->maxcond=newcond; step(synstep); }When neither the synapse pointer or its element number are available, you can use the "foreach()" function to search for the right one. For example, if you want to find and modify the output synapses of a population of cells with nodes [prect][precn], you can do it like this:

int prect, precn; for (epnt=elempnt; epnt=foreach(epnt,SYNAPSE,prect,-1, NULL,&precn); epnt=epnt->next) { synapse *s; printf ("found synapse from cell [%d][%d]\n",prect,precn); syn1 = get_efield(epnt,ELNUM); s = (synapse *)makelem(SYNAPSE,modify (syn1)); s->maxcond=newcond; }Or if you want to find the synapse that connects to postsynaptic node [postct][postcn], you could do it like this:

int postct, postcn; for (epnt=elempnt; epnt=foreach(epnt,SYNAPSE,-1,-1, NULL,NULL); epnt=epnt->next) { if (get_efield (epnt,NODE2A)==postct) && get_efield (epnt,NODE2B)==postcn)) syn1 = get_efield(epnt,ELNUM); }Then, you could modify that synapse as above:

s = (synapse *)makelem(SYNAPSE,modify (syn1)); s->maxcond=newcond;

(intepreted:) erase model erase array erase node <node> erase element <element> (compiled:) node *erasenode(node *npnt); void eraseelem(elem *epnt); void erase(node *npnt); void erase(elem *epnt); void eramod(void);

The "erase model" statement erases all arrays and neural circuits, so a simulation can be started over within one session of running "nc". Whenever "nc" runs, of course, everything is already erased, thus normally there's no reason to "erase model".

The "erase array" statement erases a dynamically-allocated array.

The "erase node" statement erases a node and any elements that connect to it.

The "erase element" statement erases an element and any nodes that connect to it.

Note that you can erase elements or nodes within a foreach statement but in this case you may only erase the node or element provided by that iteration of the foreach. If you try to erase any other nodes or elements, undefined behavior may result. The reason for this restriction is that the foreach statement cannot find the next node or element if you erase it. See example in description of "foreach" below).

(interpreted:) save model (<filname>) restore model (<filname>) (compiled:) void savemodel (char *filnam); void restoremodel (char *filnam);

The "save model" and "restore model" statements allow you to run a model, save its state, and later return to that same state. This is useful when you are running a model that takes some time to equilibrate, but then want to repeat an experiment starting each time from the same saved state.

In some model scripts, it may be useful to save and restore more than once. In this case, you must use different file names to keep track of the appropriate state.

When selecting a file name, remember that if you are running several simulator processes on the same model simultaneously, you may want to set a different file name for each separate simulation. The simulator provides you with several ways to generate unique file names. The "getpid()" function returns a 6-digit process number. This number refers to the simulator process which is the same as the "PID" number printed out by the "ps" command (see "getpid()" under "Built-in Functions" below). You can use getpid() to generate a file name like this:

sprintf (savefilnam,"file%06g",getpid()); # to add pid to file name save model (savefilnam); # creates "file024994" or sprintf (savefilnam,"file%04g%06g",int(rand()*10000),getpid()); # to add rand num, pid save model (savefilnam); # creates "file3032024994", pid = 024994 . . . restore model (savefilnam); # restores model to original state

In other cases, you may want to equilibrate a model, then save its state, and use this state to rapidly start up a different model that has the same structure (i.e. equilibrates to the same state) but run different experiments. In this case you may want to create the save, restore without setting a unique filename. This will allow many scripts to read the same save file when restoring to the original file's state.

(interpreted:) proc run_on_exit() /* procedure that runs just before exit */ { sprintf (str,"unlink %s",savefilnam); system(str); # remove the temporary save file }; (compiled:) void on_run_exit (void) /* procedure that runs just before exit */ { unlink (savefilnam); # remove the temporary save file } # Below, at beginning of main model procedure: set_run_on_exit(run_on_exit); # Initialize "run_on_exit()" to run just before exit # when program is stopped with ^C or "kill" command.

(interpreted:) proc run_on_step() /* procedure that runs every time step */ { }; (compiled:) void on_run_step (void) /* procedure that runs every time step */ { } # Below, at beginning of main model procedure: set_run_on_step(run_on_step); # Initialize "run_on_step()" to run each time step

(interpreted:) step <expr> run; (compiled:) step(<expr>); run();where:

step <expr> (sec) = time interval to run simulationThe "step" statement works exactly like the "run" statement (it activates the neural circuit, stimuli, and plots) but stops after a time interval, allowing the network to be restarted with where it stopped. All parameters such as node voltages and the elapsed simulation time retain their values.

timinc = 0.0001; steptime = 0.011111111111; /* not integral mult of timinc */ for (i=1; i<n; i++) { plotarr[i] = V[node1]; stim .... start=i*steptime dur=steptime; /* off by 0.0001 each time */ step steptime; /* steps 0.0112 sec each time */ };For example, if timinc=1e-4 and you give a time step of 0.01111111, the simulator will run for 0.0112 sec which is the next larger interval. This is usually not a problem, but if you place the "step" statement inside a "for" loop along with "stim" statements, you may find that the stimuli are not being started at the correct times because of the "roundoff" problem stated above. The way to correct this problem is to make 2 separate "for" loops, one to generate the stimuli, and one to run the "step" statement:

steptime = 0.011111111111; /* not integral mult of timinc */ for (i=1; i<n; i++) { stim .... start=i*steptime dur=steptime; /* correct to 0.0001 sec */ }; for (i=1; i<n; i++) { plotarr[i] = V[node1]; step steptime; /* step 0.0112, but maybe acceptable */ };When the "stim" statements are all executed before the first "step" statement, they are all run in "construction mode" before the model starts, so they are correctly synchronized with the integration time step. Another solution is to use the "time" variable which always has the correct time updated by the "step" statement:

steptime = 0.011111111111; /* not integral mult of timinc */ for (i=1; i<n; i++) { plotarr[i] = V[node1]; stim .... start=time dur=steptime; /* may give blank betw. stimuli */ step steptime; /* still steps 0.0112 sec */ };

for while if else assignment define procedure, function call procedure, function return break continue formatted print arithmetic and logical operators increment operators numeric expressions trig, log, expon, power, sqrt functions predefined constants (PI, E, etc.) include file edit file run system command automatic variable definition local variables dynamically allocated multidimensional arraysFeatures of C not supported:

structures, unions, bit fields pointers, address operators #define, #ifdef statementsMost of the statements in NeuronC borrowed from C are familiar to most of us who have used C. There are a few significant exceptions. A semicolon must be used after every statement in NeuronC except the first statement after the "if" in an "if () ... else ... " statement. For example:

if (i > 5) x = 0 else x = 1;These two lines comprise a single statement and the semicolon (";") is missing after the first line to allow NeuronC to better sense the upcoming "else".

A statement list enclosed by curly brackets ("{}") must have a semicolon after it (except between an "if ... else" statement):

for (i=0; i>5; i++) { x[i] = i; y[i] = array[i]; }; /* semicolon necessary */

interpreted: node <node> -> exist 1 if node exists, 0 if not node <node> -> numconn Number of connections to elements node <node> -> numsyn Number of connections to synapses node <node> -> xloc X location node <node> -> yloc Y location node <node> -> zloc Z location node <node> -> cacomp 1 if node has cacomp, 0 if not. node <node> -> <expr> Absolute number of an element, given its sequence number at node. node <node> -> synapse <expr> Absolute number of a synapse, given its sequence number at node. compiled: get_nfield (<node>, <nodefield>); get_nfield (<node>, <nodefield>, <elnum>); where: <node> is a pointer to an element <elnum> is the element number, when <nodefield> is the field name (integer), one of: ELNUM EXIST NUMCONN NUMSYN SYNAPSE XLOC YLOC ZLOC CACOMP When the field is ELNUM or SYNAPSE, the <elnum> field is the element relative to the node (i.e. 1...n ).Once nodes are created, they contain information about their location and connections, called "node fields". It is sometimes useful to retrieve this information directly from its storage in the node instead of referring back to the original algorithm that created the node. The concept of a "pointer" serves this purpose. To retrieve information from a node field, enter a node number, then the characters "->" and one of the "node fields". For instance:

node [50][1] -> xlocmeans the numerical x location of node [5][1]. This can be used in any expression where a number would normally be required, and can be part of arithmetic or passed to a function. A node's location is useful when a NeuronC program is determining how close two neurons are to each other when building a circuit. Remember, node numbers may be 1-, 2-, 3-, or 4-dimensional.

To find an element connected to a node, you can make a "for" loop to check for the one you are looking for:

ncon = node [50][2] -> numconn; for (i=0; i<ncon; i++) { /* look for first cable */ elnum = (node [50][2] -> i); if (element elnum->type == "synapse") break; }; othernode = element elnum->node2b;

Another faster way of doing the same thing, using "numsyn" and "synapse <expr>":

if ((nsyn = (node [50][2] -> numsyn)) > 0) elnum = (node [50][2] -> synapse 1); }; othernode = element elnum->node2b;

interpreted: element <element> -> type element type: "cable","sphere","chan", etc. element <element> -> ntype numerical element type. element <element> -> elabl label for element (set by "elabl" clause) element <element> -> dia diameter. element <element> -> length length, given or calculated from nodes. element <element> -> n3dist 3D distance between element's nodes. element <element> -> n2dist 2D (x,y) distance between element's nodes. element <element> -> rm membrane Rm. element <element> -> ri membrane Ri. element <element> -> cplam lambda for compartments in cable. element <element> -> maxcond maxcond for a synapse or channel. element <element> -> node1a number of first node. element <element> -> node1b element <element> -> node1c element <element> -> node1d element <element> -> node2a number of second node. element <element> -> node2b element <element> -> node2c element <element> -> node2dTo retrieve information about a neural element, enter "element", then the element number, then place the characters "->" after the element number, and then place a field name. This expression can be used anywhere instead of a standard numerical expression.

compiled: get_efield (<elem>, <elemfield>); get_efield (<elnum>, <elemfield>); where: <elem> is a pointer to an element <elnum> is the element number (integer) <elemfield> is the field name (integer), one of: ELNUM NTYPE LENGTH N3DIST N2DIST N2DIST DIA DIA2 RM RI CM CPLAM MODIFY MAXCOND SCURVE SDYAD DYAD NUMDYAD NUMSPRE NODE1A NODE1B NODE1C NODE1D NODE2A NODE2B NODE2C NODE2D

chan <element> -> type element type: "Na","K", "KCa" etc. chan <element> -> ntype numerical channel type. chan <element> -> stype numerical channel sub-type. chan <element> -> nstate number of states in Markov channel. chan <element> -> maxcond maxcond for a channel.

x = type (<elemtype>)The numerical "element <element> -> type" expression returns a number unique to the type of the neural element. To find out what type this number is, you can compare it with "type(<elemtype>)", where <elemtype> is one of the neural element types (see <elemtype> in "foreach" below).

(interpreted:) x = n2dist (<node1>, <node2>) 2D (x,y) node distance function x = n3dist (<node1>, <node2>) 3D node distance function x = nzdist (<node1>, <node2>) 1D Z node distance function (compiled:) x = dist2d (<node1>, <node2>) 2D (x,y) node distance function x = dist3d (<node1>, <node2>) 3D node distance function x = distzd (<node1>, <node2>) 1D Z node distance functionThese functions compute the distance between 2 nodes when their locations have been defined. The node numbers may be 1, 2, 3 or 4 dimensional, and the extra dimensions not used are assumed, for the computation, to be zero. n3dist measures 3D distance in (x,y,z), and n2dist measures distance in (x,y) only, useful for developing rules for "growing" neurons.

(interpreted:) x = e2dist ( <node>, <element> ) 2D element distance function x = e3dist ( <node>, <element> ) 3D element distance function x = ezdist ( <node>, <element> ) Z dist element distance function (compiled:) x = endist2d ( <node>, <element> ) 2D element distance function x = endist3d ( <node>, <element> ) 3D element distance function x = endistzd ( <node>, <element> ) Z dist element distance functionThese functions compute the distance between a node and an element. If the closest part of the element is one of its end nodes, the distance to that node is returned. e3dist measures 3D distance in (x,y,z), and e2dist measures distance in (x,y) only, useful for developing rules for "growing" neurons.

x = efrac ( <node>, <element> ) fractional distance on cableThis function finds the point in a cable closest to the given node. It returns the fractional distance from this point to the cable's "first" end node. The distance ranges between 0 and 1, so if the closest part of the element is the first end node, 0 is returned, and if it is the second end node, 1.0 is returned.

at <node> : <element> offset <expr> put <node>This statement puts a new node on a cable at the specified "offset". The offset is a fraction between 0 and 1 and can be computed by the "efrac()" function. The new node splits the cable element into two cables, each with a new length according to the location of the new node with respect to the existing nodes' positions.

This statement is useful when building neural circuits with "developmental rules". When an array of neurons is made, the algorithm that defines them may not include a precise location on the dendritic tree for synaptic connections. Instead, synaptic connection may be defined by a "connection rule" that specifies how to connect two cells based on distance and other factors. In this case, new nodes for connecting the synapses are needed at locations not specified by the algorithm that made the cell. Thus the "at <node> : <element>" statement allows the "connection rule" to make connections wherever it needs to.

(interpreted:) foreach <elemtype> ?var statement (iterate over element type) foreach <elemtype> ?var node <nodedim> statement (iterate over elem, return node) foreach node <nodedim> statement (iterate over matched nodes) foreach <elemtype> ?var within <expr> node <nodedim> statement (iterate over elem type within radius) foreach <elemtype> ?var node <nodedim> within <expr> node <nodedim> statement (iterate over elem, return node within radius) foreach node <nodedim> within <expr> node <nodedim> statement (iterate over matched nodes within radius)where:

<nodedim> = 1 to 4 node dimensions, each in the following syntax: [<expr>] dimension set to a value that must match. ?var dimension free to vary, not to be matched. The "?" in front of the variable means the variable will be replaced with the corresponding value (from the node that matches) for that dimension while the following statement is executed. <elemtype> = One of: "element", "cable", "sphere", "synapse", "gj", "rod", "cone", "load", "resistor", "cap", "gndcap", "batt", "gndbatt", "chan", "vbuf". within = "within2d" or "within3d" (compiled:) for (epnt=elempnt; epnt=foreach(epnt,<elemtype>); epnt=epnt->next) {} (iterate over element type) for (epnt=elempnt; epnt=foreach(epnt,<elemtype>,<nodedim>, <nodedimpnt>); (iterate over elem, return node) epnt=epnt->next) {} for (epnt=elempnt; epnt=foreach(epnt,<elemtype>,<nodedim>, <nodedimpnt>, (iterate over elem, return node within radius) radius, distfunc, <rnode>); epnt=epnt->next) {} for (npnt=nodepnt; npnt=foreach(npnt,<nodedim>, <nodedimpnt>); (iterate over matched nodes) epnt=epnt->next) {} for (npnt=nodepnt; npnt=foreach(npnt,<nodedim>, <nodedimpnt>, (iterate over matched nodes within radius) radius, distfunc, <rnode>); epnt=epnt->next) {}where:

<nodedim> = 4 node dimensions, each a value that much match, except negative numbers don't have to match. <nodedimpnt> = 4 dimensions, each with a pointer to an integer, to allow returning with the value of dimensions that were not specified. A NULL means don't return that dimension. radius = distance within which element/element must match distfunc = distance function, normally "dist2d" or "dist3d" rnode = node defining radius within which match can occurThe "foreach" statement allows you to access neural elements and nodes with a partial specification of their range. It iterates a statement or block of statements (inside "{}") over an element type and/or set of nodes, selected by the <nodedim> value described above. You can select which nodes will match by giving expressions inside square brackets (as you normally would to define a node). For any dimension that you wish to leave free for iteration, place a "?" directly in front of a variable's name. This replaces the expression you would normally enter for the dimension's value. A "within" clause specifies that the elements or nodes must be within the specified distance from the given node.

When the following statement executes, the variables will contain the value from the corresponding unspecified dimensions of the node being considered by the loop. For example:

(interpreted:) i = 50; foreach node [i] ?j ?k { print j, k; }; (compiled:) i = 50; for (epnt=elempnt; epnt=foreach(epnt,i,-1,-1,NULL,&j,&k); epnt=epnt->next) printf ("%d %d\n",j,k);This statement prints the second and third dimension of all nodes that have a value of i (= 50) in their first dimension. The "foreach" statement in many cases is easier to use than its equivalent nested "for" loops (one "for" loop is normally required for each unspecified dimension).

If an element type is specfied, without a node, then all elements of that type are selected. If both element type and node are specified, then only elements of that type with nodes that match the specification are selected. For example:

(interpreted:) foreach sphere ?s { if (s->dia > 5) display element s }; (compiled:) for (epnt=elempnt; epnt=foreach(epnt,SPHERE); epnt=epnt->next) { s = (sphere *)epnt; if (s->dia > 5) display (epnt,1,1); }This statement displays all spheres with a diameter greater than 5 microns. The variable "s" specifies the element number, and is given a new value (another sphere's element number) for each iteration of the loop.

(interpreted:) foreach cable ?x node [i][j] ?k {if (k>10) display element x}; (compiled:) for (epnt=elempnt; epnt=foreach(epnt,CABLE,i,j,-1,NULL,NULL,&k); epnt=epnt->next) { if (k>10) display (epnt, 1,1); }This statement displays all cables that connect to node [i],[j] if their third dimension is greater than 10. The variable "x" specifies the cable's element number, and the third node dimension is specified by variable "k".

(interpreted:) foreach cable ?x node [i][j] ?k within2d 10 node [a][b][c] {if (k>10) display element x}; (compiled:) for (epnt=elempnt; epnt=foreach(epnt,CABLE,i,j,-1,NULL,NULL,&k,10,dist2d,ndn(a,b,c)); epnt=epnt->next) { if (k>10) display (epnt, 1,1); }This statement displays all cables that connect to node [i],[j] if they are closer than 10 um from node [a][b][c]. The variable "x" specifies the cable's element number, and the third node dimension is specified by variable "k". You can specify the distance in 3D with the keyword "within3d".

If you want to erase nodes or elements selectively (see "erase node" and "erase element" above) from within a "foreach" statement, you must erase only the node or element provided by that iteration of the foreach statement. If you try to erase other nodes or elements, you may produce undefined behavior. The reason for this restriction is that the foreach statement cannot find the next node or element if you erase it.

Example: foreach node [i][j] ?k { if (k > nbranches) erase node [i][j][k]; /* Correct */ }; foreach node [i][j] ?k { if (k > nbranches) for (n=0; n<5; n++) erase node [i][j][k+n]; /* Incorrect, undefined */ };

(interpreted:) ymax = xmax = 100; ymin = xmin = -100; elimit X max xmax min xmin Y max ymax min ymin; foreach element ?c node [-1][-1][-1] { elimit element c; }; (compiled:) ymax = xmax = 100; ymin = xmin = -100; elimit (X, max=xmax,min=xmin); /* set bounds */ elimit (Y, max=ymax,min=ymin); for (e=elempnt; e; e=t) { /* cut elems outside bounds */ t = e->next; elimit (e); }

proc makecell (node1, node2) { /* procedure definition */ at node1 sphere dia 10; conn node1 to node2 cable dia 1 length 10; }; func rms (val1, val2) { /* function definition */ return ( sqrt( val1 * val1 + val2 * val2)); }; for (i=0; i<100; i++) val = rms (i,10); /* use of function */ printf ("%g\n", val); };Note that procedures and functions must be defined before they are used, and they must be "external", i.e. they cannot be defined from inside other procedures or functions. They may be defined inside an 'if' statement when it contains no local variable definitions, or when the procedure or function has no arguments or local variables.

Arrays can be passed into procedures and functions. The call is by reference, so that the address of the original array is passed to the procedure, and any modifications it makes on the array will appear in the original array outside the procedure. An array passed into a procedure or function may be assigned to another array, but it must have the same size.

Functions can return scalar or array values.

You can set a new procedure/function to be equal to a previously defined one. The assignment is like a function definition, except that there are no formal arguments or block of statements:

proc oldproc(s,x,y) { /* original procedure definition */ print s,"=",x+2*y+y*y; }; proc newproc = oldproc; /* assign new procedure to old */ newproc("var",1,8); var = 81 func oldfunc(x,y) { /* original function definition */ return log(x+2*y+y*y); }; func newfunc = oldfunc; /* assign new function to old */ newfunc(1,8); 4.3944492 func abc = log; /* assign new function to builtin */ abc(2); 0.69314718

You can define macros (redefine the syntax that NeuronC understands) using the "nc -C" command-line switch. This runs the standard C pre-processor that is included with the "gcc" compiler. The "cpp" pre-processor is run by NeuronC using an internal pipe to process and expand macros before it is parsed by the simulator. You can define a macro at the top of a script file like:

#define maxmin(gain,offs) max (1-offs)*gain min (0-offs)*gainThen, later in the script file, you can put:

plot V[1] maxmin(1e-9,0.3);Then run the script like:

nc -C fileand the pre-processor will expand the macro to:

plot V[1] max (1-0.3)*1e-9 min (0-0.3)*1e-9;Use of the "#define" statement allows you to redefine or shorten the syntax that "nc" understands to simplify your scripts. The cpp pre-processor replaces the text that calls the macro by the macro text, with the arguments replaced by those from the call. To see the changes that the pre-processor makes, run "cpp -P file".

In the example above for the "plot V[]" statement, the "max" and "min" clauses are required but these are supplied by a macro, even though they did not originally appear in the required positions in the statement. The macro changes the text that the simulator actually sees so you can modify the syntax of the language.

The "include" statement allows the inclusion of a text file into a NeuronC program, and is useful for allowing a standard neural circuit definition to be used in several different models. Note that the "include" statement must be "external," i.e. it must not be placed inside a procedure or function. It may be placed inside an "if" statement, but it must be the only statement inside the "if".

The "system" command allows any standard system command such as "ls -l" (list directory) or "vi modelfile" (edit a NeuronC program) to be run.

The "system" command is useful when running NeuronC in interactive mode, but can also be used in a simulation script to run other commands. For example, you can run a series of simulation scripts from a parent script:

system ("nc --var1 23.5 file.n > file.r"); or system ("file.n --var1 23.5 > file.r");

Some other nice things:

rseed = atof(system ("date +%m%d%H%M%S")); /* set random seed from date */ machine = ccstr(system("hostname -s")); /* get machine name, remove CRLF */

If you have a script that prints a number or a small amount of text, you can run an nc script several times, each time returning the output into a variable in the parent script. This method avoids making any output files, and is appropriate when you want to run several closely related simulations (e.g. with a different random seed):

(interpreted:) #! /home/nc/bin/nc -c # # script file run_multsim_1 # /*--------------------------------------------------------*/ func runnc(randnum, lim, td) /* function to run an nc script with different values of parameters */ /* and return its output. */ { fmt = "nc -r %8.8g --limit %g --td %g --info 1 file.n"; sprintf (str,fmt,randnum,lim,td); return system(str); }; /*--------------------------------------------------------*/ proc runtest (lim, td) /* procedure to run an nc script and return a value to an "nc" variable. */ { for (m=i=0; i<nsim; i++) { randum = int(rand()*1e8); m += runnc(randnum, lim, td); }; printf ("lim %g td %g m %-10.5g\n", lim, td, m/nsim); }; . . . (compiled:) // // script file run_multsim_1 // /*--------------------------------------------------------*/ char *runnc(int randnum, double lim, double td) /* function to run an nc script with different values of parameters */ /* and return its output. */ { fmt = "nc -r %8d --limit %g --td %g --info 1 file.n"; sprintf (str,fmt,randnum,lim,td); return xsystem(str); }; /*--------------------------------------------------------*/ void runtest (double lim, double td) /* procedure to run an nc script and return a value to an "nc" variable. */ { int i, randnum; double m; for (m=i=0; i<nsim; i++) { randum = int(rand()*1e8); m += atof(runnc(randnum, lim, td)); }; printf ("lim %g td %g m %-10.5g\n", lim, td, m/nsim); }; . . .

x = "Strings "; y = "make "; z = "useful labels."; String operators (interpreted:) str1 + str2 catenates two strings. str1 = str2 assigns string 2 to string 1. str1 += str2 catenates string 2 to string 1. Logical operators str1 == str2 true if strings are same. str1 != str2 true if strings are different. str1 || str2 true if either string 1 or string 2 exist. str1 || numval true if string 1 exists or numval is non-zero. str1 && str2 true only if string 1 and string 2 both exist. !str true if string does not exist. strlen(str) returns length of string. strtok(str1,str2) returns first substring in str1 delimited by any of the chars in str2. The str1 string can be parsed further by passing a 0 instead of str1; str1 is remembered by "strtok" through several calls. (For further information, look in the Programmer's Reference Manual under "string(3x)"). strcmp(str1,str2) returns 0 if strings are equal, like "strcmp(3x)" strstr(str1,str2) returns position of str2 within str1, 0=start, -1=not found. substr(str,i,n) returns substring of str starting at i, length n. index(s1,ch) returns first char "ch" within s1, 0 = start, -1 => not found rindex(s1,ch) returns last char "ch" within s1, 0 = start, -1 => not found ccstr(str) returns str with all control chars removed.The result of a logical operator is always a numeric value, either 1 (true) or 0 (zero=false).

Some examples:

print x + y + z; Strings make useful labels. print x + "often " + y + z; Strings often make useful labels. x += "used wisely "; print x + y + z; Strings used wisely make useful labels. x = ""; if (x) print x else print "empty string"; empty stringOf course, you can use the "print" statement to format your reports with numbers:

cablediam = 5.6; print "The current diameter is:", cablediam; The current diameter is: 5.6 printf ("The current diameter is: %-.3f.\n",cablediam); The current diameter is: 5.600.You can "add" (catenate) string and numeric variables:

w = 5; print x+"often "+y+5+z; Strings often make 5useful labels. print x+"often "+y+5+" "+z; Strings often make 5 useful labels. print x+"often "+y+"5 "+z; Strings often make 5 useful labels.

/* Program nfile1 */ bsize = 5; nset = setvar(); /* nset is number of params set */ . . other statements that use "bsize".... /* end of program */ Later, when the program is run, the variable may be changed from the command line: nc -s bsize 6 nfile1.n or nc --bsize 6 nfile1.nIn this case "--bsize 6" sets the variable "bsize" to a different value after it has been set to the default value of 5. This is useful doing several runs of a file with different parameter values. The "setvar()" function returns the number of parameters that were set from the command line. If the function is not assigned to a variable then "nc" will print the number to "stdout" (the output file).

In the compiled version of the simulator, it is necessary to specify all parameters that will be given on the command line, so that the simulator can find them and store the values. [The intepreted version accomplishes this automatically with its dynamic symbol table allocation.] You can do this by calling the "setptr()" or "setptrn()" procedures, with the text name of the variable and a pointer to the variable:

(compiled:) double gctheta; char *funcfile; int *ntrials; int make_cone = 1; int make_a17 = 1; int make_gc = 1; void setptrs(void) { setptr("gctheta", &gctheta); /* register command line variables, with init */ setptr("funcfile", &funcfile); setptr("ntrials", &ntrials); setptrn("make_cone", &make_cone); /* register command line variables without init */ setptrn("make_a17", &make_a17); setptrn("make_gc", &make_gc); }Note that in addition to registering the variable, the "setptr()" procedure initializes the variable with a "magic" number (LARGENUM in nc.h) that means it is "not initialized", allowing you to use the "notinit()" function to test whether it has been set. The "setptrn()" procedure does not initialize the value, allowing you to set the value as a default before calling the "setvar()" procedure at the beginning of your program. Then, in your program, you include the following code to initialize the simulator correctly, you call the "ncinit()" procedure:

(compiled:) main(int argc, char **argv) { ncinit(argc,argv); (initializes command-line variables, sets clock, etc.) timinc = 1e-4; endexp = .5; . . (code to set default parameters) . setvar(); . . (code to construct model and experiment) . run(); ncexit(); }The "ncinit()" procedure (inside "ncfuncs.cc") takes the two arguments describing the command line (argc, argv) from "main()", calls the "setptrs()" procedure to define the command-line variables, and sets their values. It also sets the default simulation variables, and sets time to zero.

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interpreted: #! /home/nc/bin/nc -c # # script file "run_func" # . . .Then you can run the script like this:

run_func --t1 233 --t3 422and the variables t1 and t3 will have their values automatically assigned from the command line.

interpreted: #! /home/nc/bin/nc -c # # script "make_types" # print argc, argv; typ = argv[1]; for (f=1; fThen:= 0; f+=2) { /* skip over "--param xx", find file names */ if (f>=argc-2) { print "cellbr: no file name"; exit; }; }; # for (i=f; i<argc; i++) { print argv[i], typ; sprintf (buf,"mv %s %s.%s\n",argv[i+2],argv[i+2],typ); x = system (buf); // print x; };

make_types t2 morph.cell0{4[123]?,44[0-9]}This script can then be run from other scripts.

proc xydistance (x,y) { local x2,y2,rdist; local dim power[100]; code starts here after local def... };Local variables can be defined at the beginning of any "{ }" block, e.g. inside a "{ }" block inside an "if" or "for" statement and within nested blocks. If a variable name has been defined in several nested blocks, and referred to by a statement enclosed in an inner block, the inner definition is used. Note that local variables defined inside a block are visible only to statements inside that block. Local variables defined outside a block are also visible inside the block (if their names are not defined more locally).

Example of nested local definitions: { local x1, y1; x1 = ... if (x1 > 5) { local x2, y2; x2 = ... if (x2 > x1) ... /* x1 is defined outside of inner block */ }; };

dim conearray [30][30][3];The dimension parameters need not be constants but may be variables or expressions:

dim rodarray [xsize] [ysize] [abs(sin(theta))];Arrays may be assigned string values, with the same rules as ordinary variables:

x = "first string"; dim z[10]; z[0] = x; z[1] = "second string"; z[2] = z[0] + z[1]; print z[2]; first stringsecondstringArrays may be initialized when they are defined or afterwards. There are several ways to initialize an array. The initialized values go into memory sequentially, and the right-most array indices increment most rapidly (as in standard C):

dim arr1 [4][2] = {{ 1, 2, 3, 4, 5, 6, 7, 8 }}; print arr1; 1 2 3 4 5 6 7 8 print arr1 [1][1]; 4 arr1 = {{ 10, 9, 8, 7 }}; print arr1 [1][1]; 7 dim arr2 [4][2]= {{0:16}}; print arr2; 0 1 2 3 4 5 6 7To initialize all the array contents to a single value, place just that value in the initialization string. An initialization can assign values to an existing array, but the array remains at least the original size:

dim arr1[6] = {{ 0 }}; print arr1; 0 0 0 0 0 0 arr1 = {{1,2,3,4}}; print arr1; 1 2 3 4 0 0

When the array size is not specified, its size is determined by the initialization:

dim arr2 [] = {{ 1, 2, 3, 4 }}; or dim arr2 [] = {{1:4:1}}; /* {{ low : high : incr }} */ or arr2 = {{1,2,3,4}}; or arr2 = {{1:4}}; dim arr2 []= {{0:16:2}}; print arr2; 0 2 4 6 8 10 12 14 16 dim arr2[] = {{ 0 }}; print arr2; 0 arr2 = {{1:50000:3}}; sizeof(arr2); 16667

Any array values not specifically initialized are set to an undefined value which will generate an error if accessed. That value is "UNINIT" and you can use it to create an unitialized value. dim arr1 [5][2] = {{ 1, 2, 3, 4, 5, 6, 7, 8 }}; print arr1; 1 2 3 4 5 6 7 8 uninit uninit

Arrays can be passed into procedures and functions. The call is by reference, so that the address of the original array is passed to the procedure, and any modifications it makes on the array will appear in the original array outside the procedure. Arrays can also be passed out on return from functions.

dim abc[5][2] = {{1,2,3,4,5,6,7,8,9,10}}; proc printx (x) { print x; }; proc printy(y) { local dim z[5]= {{10,9,8,7,6}}; printx(z); printx(z[3]); printx(y); printx(y[3][1]); }; printy (abc); 10 9 8 7 6 7 1 2 3 4 5 6 7 8 9 10 8

Most operators work on arrays and combinations of arrays and single valued variables. You can add regular variables and arrays. When the type is different (string,number or number,string), the type of the array sets the type of the result:

x = "5"; dim y[] = {{5,6,7,8}}; print x+y; 10 11 12 13 print y+y; 10 12 14 16 print y*y; 25 36 49 64 print pow(y,y); 3125 46656 823543 1.677722e+07 print pow(y,y)+x; 3130 46661 823548 1.677722e+07 x = 5; dim y[] = {{"5","6","7","8"}}; print x+y; 55 56 57 58 print y+x; 55 65 75 85 print y+y; 55 66 77 88

/*--------------------------------------------*/ dim abc[] = {{1,2,3,4,5,6,7,8,9,10}}; proc printd(d) { print(amax(d)); print(fmax(d,5)); print(d*2); print(d++); print(-d++); print((d-9)>0); print((4<=d && d<=9)*d); print(amax(d)); }; printd(abc); 10 5 5 5 5 5 6 7 8 9 10 2 4 6 8 10 12 14 16 18 20 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 0 0 0 0 0 0 0 0 1 1 0 4 5 6 7 8 9 0 0 0 12 /*--------------------------------------------*/ dim a[] = {{"Is", "this", "a", "match","?"}}; dim b[] = {{"Yes", "it's a", "good", "maker", "!"}}; g=(a=="match"); h=(b!="maker"); print a,b; print g; print h; print (a*h + b*g); print (a*g + b*h); Is this a match ? Yes it's a good maker ! 0 0 0 1 0 1 1 1 0 1 Is this a maker ? Yes it's a good match ! dim c[] = {{"Must", "be", "a", "match","."}}; print "Found", (c==a)*c; Found a match /*--------------------------------------------*/

2D arrays can hold matrix values. Several matrix functions allow very powerful solutions to matrix equations:

x = a + b matrix add x = a - b matrix subtract x = a * b matrix scalar multiply x = a / b matrix scalar divide x = matmul(m1,m2) matrix multiply x = transpose(m) matrix transpose x = matinv(m) matrix invert x = matsolve(A,b) solve A * x = b

You can find out how many dimensions an array has with the "dims" statement, and you can find the size of an array with the "sizeof()" function:

dim oldarr[5][3][1]; adim = dims(oldarr); print adim; 5 3 1 print sizeof(adim); 3

Although the standard initializer is "={{...}};", you can also initialize an array by writing a procedure like this:

proc initarr (arr,val) { /* procedure to set an array to a value */ local i,j,k,ndim; adim = dims(arr); /* get dimensions of array */ ndim = sizeof(adim); /* find how many dimensions */ if (ndim==1) { for (i=0; i<adim[0]; i++) { arr[i] = val; }; } else if (ndim==2) { for (i=0; i<adim[0]; i++) { for (j=0; j<adim[1]; j++) { arr[i][j] = val; }; }; } else if (ndim==3) { for (i=0; i<adim[0]; i++) { for (j=0; j<adim[1]; j++) { for (k=0; k<adim[2]; k++) { arr[i][j][k] = val; }; }; }; }; print arr; }; initarr(abc,0); /* set the array to all zeroes */Arrays can be erased with the "erase" statement:

erase rodarray;Array size is limited only by the hardware and "C" compiler. Array access time is slower than simple variable access time because the array indices must be multiplied by the dimension sizes to locate a value in the array.

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{ local dim x[100], dim y[100]; local i,j, z[100][100]; local mcond; local dim cond[mcond=calcval(120)]; z[i][j] = x[i] + y[j] * cond[i+j]; ... };The dimension of a local array must be an expression whose value is known at the time its definition is encountered by the interpreter. As in the example above, the dimension can be a constant, or can be calculated by a function or be the result of an assignment. Except for such assigments, the local definitions must be made before any other statements in the code block. Local arrays can be initialized in the "dim" statement or afterwards (see "Arrays" above").

Local arrays are accessed through the stack but their space is allocated on the heap. A new instance of a local array is defined each time control enters the block. After control exits the block in which a local array was defined the array is erased.

unary operators - negative ! logical NOT (!x true when x==0) x++ post-increment (add one to value after use) x-- post-decrement (subtract one after use) ++x pre-increment (add one to value before use) --x pre-decrement (subtract one before use) binary operators + addition - subtraction * multiplication / division % modulo (as in C/C++) ^ power (A^B == A to the power of B) & bitwise AND (x&1 true when x is odd) | bitwise OR (y|1 sets ones bit in y) ^^ bitwise XOR (y^^1 inverts ones bit in y) && logical AND ("x && y" true if both x and y nonzero) || logical OR ("x || y" true if either x or y nonzero) comparison operators return value of 1 if true or 0 if false > greater than >= greater than or equal to < less than <= less than or equal to == test for equal to (no assignment of value) != not equal to assignment operators = assignment += increment by right hand side (x+=2: add 2 to x). -= decrement by right hand side (x-=2: subtr 2 from x). *= multiply by right hand side. /= divide by right hand side.

abs acos acov allowrev amax amin ampa area asin at atan atan2 atof attf backgr bar batt bic binomdev blur break btot btoti cAMP cGMP cable cabuf cabufb cacolor cacomp caexch cahc cai cakd calcnernst calibline camp cao cap caperm capump cbound cclamp ccstr center cgain cgmp chan char chc checkerboard chinf chnoise chset chtau cinf ckd close cm cmap cnqx coff color complam comps cone conn connect continue contrast copychan cos cplam crit cshell ctau ctaua ctaub ctauc ctaud ctaue ctauf d1 d2 dampau darknoise dash dbasetc dbasetca dbasetdc dbasetsyn dbd1 dbd2 dbk1 dbk2 dcabf dcabnd dcabr dcabt dcabti dcadens dcahc dcai dcakd dcakex dcalu dcao dcaoffs dcapkm dcashell dcaspvrev dcatauf dcatauh dcataum dcatu dcavmax dcavoff dcgmpu dchc dckd dsclcac dclcavs dclcavsc dclcasu dcli dclo dcm dcoo ddca debug debugf debugz delay deleccap density dfta dftah dftb dgjnv dgjoff dgjtau dia dia1 dia2 dim dims dinf diode disp display djnoise dkau dkcabu dkcasu dkcatauh dkcataum dkdens dki dkihu dko dkoffsh dkoffsn dkrseed dktauf dktauh dktaum dku dmaxampa dmaxca dmaxclca dmaxcon dmaxgaba dmaxk dmaxna dmaxnmda dmaxrod dmaxsyn dmgo dnadens dnai dnao dnaoffsh dnaoffsm dnatauf dnatauh dnataum dnau dnmdamg dpcaampa dpcacgmp dpcak dpcana dpcanmda dpcasyn2 dpkca dpkna dpnaca dpnak dqc dqca dqcab dqcavmax dqcrec dqd dqdc dqeff dqh dqkca dqm dqn dqna dqnb dqrec dqri dqrm dqsyn dratehhh dratehhm dratehhna dratehhnb drg dri drift drm drs dsc dscale dscavg dscu dsd1 dsd2 dsfa dsfb dsg dshc dsintinc dsintres dsk1 dsk2 dskd dsms dsmsgc dsn dsrrp dst dstr dsvn dsyntau dsyntauf dtau dtcai dur dvg dvsz dyad e2dist e3dist edist edit efrac elabl elap_time electrode element elimit else ename endexp erase euler except exist exit exp exp10 expon ezdist fclose fft fgetc fgets file filt fmax fmin fopen for foreach fprintf fputc fread fscanf func fwrite gaba gabor gamdev gasdev gausnn gauss gcirc gcrot gcwidth gdash gdraw getflds getpid gframe ginfo gj glu gly gmax gmove gndbatt gndcap gnv gorigin gpen gpurge graph grdraw grect grmove grot gsize gtext glabel gvpen gwindow hcof hgain hide hinf htau if ifft implfk implicit include infile info init initrand int inten jnoise k1 k2 kd kex km label lamcrit lcolor length linear linit lmfit lmfit2d load loc local log log10 loopg makestim mask matching matinv matmul matsolve max maxcond maxsrate mesgconc mesgin mesgout mg min minf model modify mtau n2dist n3dist nacolor ncomps ncversion ndensity ndist newpage nfilt1 nfilt1h nfilt2 nfilt3 ninf nmda nnd nnstd node node1a node1b node1c node1d node2a node2b node2c node2d notinit nozerochan nstate ntau ntype numconn numdyad numsyn nzdist offset offseth offsetm oldsynapz only opamp open orient pathl pen pfft photnoise phrseed pigm plmax plmin plname plnum plot ploti plsep plsize plval plarr poisdev pow print print_version printf printsym prmap proc progname ptx puff put radius rand range rcolor read rect refr reg relax relincr resistor resp restart restore return rev rg rgasdev ri rightyax rm rmove rod rrand rrpool rs rsd rseed run save scanf scatter scurve sdyad sens set_q10s setchan_cond setchan_mul setchan_ntrans setchan_rateo setchan_trans setchan_trate setvar setxmax setxmin setymax setymin sgcolor silent simage simwait sin sine sineann size sizeof sphase sphere spost spot sprintf sqrt srcolor srseed sscale sscanf start stderr stdin stdout step stim stim_elem stimelem stiminc stimonh stimonl strcmp strlen strstr strtok stry stype substr sun syn2 synapse synaptau system system_speed tan tau taua taub tauc taud taue tauf tauh taum taun tcai tempcel tfall2 tfall3 tfreq thresh time timec1 timec1h timec2 timec3 timinc to transducer transf transpose trconc tungsten type unit unlink unmaskthr varchr varnum varstr vbuf vcl vclamp vcolor vcov version vesnoise vgain vidmode vk vmax vna vpen vrest vrev vsize wavel while width windmill window within2d within3d xenon xenv xloc xrot yenv yloc yrot zloc zrot AMPA BIC CNQX Ca Char ClCa CoV DEG E FA0 FA1 FA2 FA3 FA4 FA9 FB0 FB1 FB2 FB3 FB4 FC0 FC1 FC2 FC3 FC4 FC9 FH0 FH1 FH2 FH3 FH4 G G0 G1 G2 GABA GAMMA GLU GLY Gabor H I IE IP IPE Im K KCa L M N NMDA Na PHI PI PTX S STRY UNINIT V X Y ZTo track down these keywords, look in "nc/src/init.cc" and from there look in "nc.y" to understand the details of their usage (if this manual doesn't describe them well enough for you). You can print out all the keywords into a sorted list with the commands

nc -K | sort. nc -K | sort | less nc -K | sort > file

readThis function reads a value from the keyboard (standard input) into a variable. It returns 1 if a variable was read, or 0 if not. Typical usage:

while (read(x)) print "Value is:",x;Note that the familiar "scanf()" statement also exists in NeuronC (see "scanf function" below).

fd = fopen (filename,mode) fclose (fd)The "fopen" statement opens a file, given its name and a mode ("r" = read, "w" = write, "a" = append), exactly as in standard C. It returns a file descriptor which may be used by file read and write statements to refer to the file. The file descriptor is a standard number with a special value. If the file could not be opened, the returned file descriptor is zero. To test for this you can write code like this:

filnam = "test.n"; filmode = "r"; /* to generate an error if file is not found */ if (ftemp=fopen(filnam,filmode)) == 0) { fprintf (stderr,"fopen: can't open file '%s'.\n",filnam); exit; }; /* to try something else if file is not found */ if (ftemp=fopen(filnam,filmode)) > 0) { /* file was found */ ... } /* same thing, testing for non-zero */ if (ftemp=fopen(filnam,filmode)) { /* file was found */ ... }The "fclose" statement closes a file given its file descriptor.

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print <expr> <expr> printf ("format", <expr> ... fprintf (file,"format", <expr> ...) sprintf (stringvar,"format", <expr> ...) sprintf (stringvar,"format", <expr> ...)The "print" statement prints the value of any expression, or list of expressions. The expression may have either a number or string value. A comma-separated list of expressions is printed with spaces separating the values.

The "printf" statement is identical to the familiar library subroutine "printf". It prints a formatted string to the "standard output". It requires a "format" string, which may contain literal characters and formats of numbers or strings to be printed. A number format has a "%" followed by either "f" (floating-point), "e" (with exponent), or "g" (integer, floating point, or with exponent whichever takes fewest chars to print out).

The "fprintf" statement is identical to the "printf" statement except that it prints to a file. The file is defined by a "file descriptor" which you must define before calling "fprintf", exactly like in standard C. The file descriptor is created by a call to "fopen()" (see above). In addition, the file can be "stdout" or "stderr", which are normally the video screen (exactly like in standard C) but can be redirected with shell commands. The file descriptor can also be a filename if you don't need to keep the file open between fprintf() calls. Any message printed to "stderr" is guaranteed to appear on the screen (unless redirected), even if the program terminates prematurely. This is useful for debugging.

The "sprintf" statement is identical to the "printf" statement except that it prints its output into the first argument which is set to string type.

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n = scanf("format", <var> ...) n = sscanf(stringvar,"format", <var> ...) n = fscanf(<fd>,"format", <var> ...) n = fgets(<var>,<n>,<fd>) n = fgetc(<var>,<fd>) n = fputc(<var>,<fd>) n = getflds(<fd>)The "scanf()" function is identical to the familiar library function "scanf()". It reads a formatted string from the "standard input". It requires a "format" string, which may contain literal characters and formats of numbers or strings to be printed. A number format has a "%" followed by "lg" (double), and a string has "%s". "scanf()" returns the number of arguments converted.

The "sscanf" function is identical to the "scanf" function except that it reads its output from the first argument which must be a character string.

The "fscanf" function is identical to the "scanf" function except that it reads from a file. The file is defined by a "file descriptor" that you must define before calling "fscanf", exactly like in standard C. The file descriptor is created by a call to "fopen()". In addition, the file can be "stdin" which is normally the keyboard (exactly like in standard C) but can be redirected with shell commands. The file descriptor can also be a filename if you don't need to keep it open between fscanf() calls. "fscanf" returns the number of arguments converted.

The "fgets" function reads a line from a file, exactly like in standard C. The parameters are "var", the line buffer, "n", the maximum size of the line buffer, and "fd" the file descriptor that has been created by a call to fopen(). If "fd" is "stdin" then the standard input is read, and if it is a filename, the file will be opened and read. If successful, "fgets" returns a 1, and if not it returns 0.

The "fgetc" and "fputc" functions read and write a single character from a file, exactly like in standard C. If "fd" is "stdin" then the standard input is read/written to, and if it is a filename, the file will be opened and read/written to.

The "getflds" function reads a line from a file, and then parses it into text tokens. The parameter is "fd" the file descriptor, set by a call to "fopen()". The text tokens are delimited by " ,:\t\n\r" (i.e. the tokens can be separated by spaces, colons, tabs, LF, CR). It returns the text tokens in an array. The number of tokens is defined by the size of the array. Multiple calls to the same file (with the same file descriptor fd) will parse consecutive lines of text in the file. When getflds() gets to the end of the file, it closes the file and returns with an array of zero size.

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fread ( <filename>, <arrname>, <var>, [>var<] ) freads ( <filename>, <arrname>, <var>, [>var<] )where:

<filename> = name of file that contains numerical array (can be "string" or string variable). <arrname> = name of array (not yet defined). <ar> = variable to contain dimension size of array. [<var>] = optional variable for second dimension size.The fread statement reads a file of numbers (or variables) into an array of one or two dimensions. The file contains a list of numbers separated by spaces. The array must not yet be defined, because the statement defines the array to match the dimension(s) of the list of numbers in the file. The (one or optionally 2) var's are set to the sizes of the array's dimensions. The size of the first dimension is the number of lines (with numbers on them) in the file, and the size of the second dimension is the number of numbers on the first line. The freads statement is similar but reads a file of strings, and does not interpret them as numbers

1) in an assignment statement: x = 87 or 2) in a command line assignment: nc -s x 87

Comment lines may be included in the "fread" file. Any line starting with the "#" character is ignored. Comments are useful for documenting data files.

Examples: 4*3 4*2 4*diam 4*6 (mult OK, no spaces) size+2 size-3 size*4 size/5 (where size is predefined) log(2*x) log(3*x) log(4*x) log(5*x) (where x is predefined)

freads ( <filename>, <arrname>, <var>, [>var<] )The freads statement is similar to the fread statment except that it reads string values from a file of 1 or 2 dimensions and creates an array of string type. It does not intepret the strings as numbers or expressions.

fwrite ( <filename>, <arrname>)where:

<filename> = name of file (can be "string" or string variable). <arrname> = name of array.This statement writes an array of one or two dimensions to a file.

unlink ( <filename>)where:

<filename> = name of file to remove (can be "string" or string variable).This statement removes a file.

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if (notinit(<var1>)) var1 = 100; /* set a default value */ if (notinit(<var1>)) fprintf (stderr,"Error in defining var1, %g\n", <var2>);

The "varnum()", "varstr()", and "varchar" functions return a 1 if a variable is a number, string or char, respectively, otherwise they return 0. They are useful when checking variables set on the command line.

if (varnum(<var1>)) printf ("var is a number\n"); if (varstr(<var1>)) printf ("var is a str\n"); if (varchr(<var1>)) printf ("var is a char\n");

You can do this with the "onplot()" procedure. If the "onplot()" procedure is defined (with the "proc" statement), it is run at increments of the plot time defined by "ploti" (plot increment). You can place any commands you like in the procedure, which has access to any recorded value (voltage, current, light) or variable. For the compiled version, you set the name of the onplot procedure with the "setonplot()" procedure.

(interpreted:) func calctau (tau) /* Function to calculate "k" for digital filter, */ /* given time constant. */ { k = 1.0 - exp (-timinc/tau); return k; }; kf11 = calctau(1.5e-5); /* filter time constants */ kf12 = calctau(2e-5); graph X max endexp min 0; graph Y max 0 min 1e-10; graph Y max 0 min 1e-10; graph init; proc onplot() /* plot procedure that implements 2nd order digital filter */ { graph pen (2,4); /* plots green, red */ val = I[1] f11 += (val - f11) * kf11; /* second-order filter */ f12 += (f11 - f12) * kf12; graph (time, val, f12); }; (compiled:) double calctau (double tau) /* Function to calculate "k" for digital filter, */ /* given time constant. */ { k = 1.0 - exp (-timinc/tau); return k; }; kf11 = calctau(1.5e-5); /* filter time constants */ kf12 = calctau(2e-5); graph_x (max=endexp,min=0); graph_y (max=0,min=1e-10); graph_y (max=0,min=1e-10); graph_init(); void onplot(void) /* plot procedure that implements 2nd order digital filter */ { graph_pen (2,4); /* plots green, red */ val = I[1] f11 += (val - f11) * kf11; /* second-order filter */ f12 += (f11 - f12) * kf12; graph (time, val, f12); } . . . setonplot (onplot); /* set "onplot()" to run at plot time */Click here to return to NeuronC Statements

(interpreted:) x = exp(a) exponential to base e x = exp10(a) exponential to base 10 x = log(a) natural logarithm x = log10(a) logarithm to base 10 x = pow(a,b) power (a to the b power) = a^b x = sin(a) sine a = asin(x) arcsine x = cos(a) cosine x = tan(a) tan a = atan(x) arctan x = gauss(x,r) Gaussian function x = sqrt(a) square root x = int(a) integer value of (a) x = abs(a) absolute value of (a) x = amax(a,b) maximum of (a,b), single number max of array a x = amin(a,b) minimum of (a,b), single number min of array a x = fmax(a,b) maximum of (a,b), array or scalar values x = fmin(a,b) minimum of (a,b), array or scalar values x = atof(s) ascii string to number conversion x = strlen(s) string length (s must have a string value) x = strtok(s1,s2) returns first substring in s1 delimited by any of the chars in s2. The str1 string can be parsed further by passing a 0 instead of s1; s1 is remembered by "strtok" through several calls. (For further information, look in the Programmer's Reference Manual under "string(3x)"). x = strcmp(s1,s2) returns 0 if strings are equal, like "strcmp(3x)". x = strstr(s1,s2) returns position of s2 within s1, 0 = start, -1 => not found x = index(s1,ch) returns first occurence of char "ch" within s1, 0 = start, -1 => not found x = rindex(s1,ch) returns last occurence of char "ch" within s1, 0 = start, -1 => not found s = substr(s,i,n) returns substring of s starting at i, length n. s = ccstr(s) returns s with all control chars removed. x = isnum(s) returns 1 if s is numeric, otherwise 0. x = system_speed() system CPU speed (approx, in MHz). x = wait(nsecs) wait specified time (seconds). x = elap_time() elapsed computation time (minutes). x = getpid() process number, useful to make temporary file names x = setvar() set variables specified on command line. x = print_version() print NeuronC version. x = printsym() print all defined symbols (keywords, variables, functions). (same as "nc -K") x = matmul(m1,m2) matrix multiply x = transpose(m) matrix transpose x = matinv(m) matrix invert x = matsolve(A,b) solve A * x = b x = rand() random function. x = rrand(n) random function from individual random noise generator. x = gasdev() Gaussian distribution with variance of 1. x = rgasdev(n) Gaussian distribution from individual random noise generator. x = poisdev(m) Poisson distribution, m = mean. x = gamdev(n) Gamma interval distribution, n = order (an integer). initrand (n) set up and initialize individual random noise generator. initrand (n) rsd=x set up random noise generator and initialize with seed. (compiled:) (see math funcs defined in) char *xsystem (char *str); system shell command, returns output of command double system_speed (void); system CPU speed (approx in MHz). simwait(nsecs); wait specified time (seconds). char *print_version(void); return NeuronC version. double elap_time(void); return elapsed computation time (in minutes). int getpid(void); process number, useful to make temporary file names setptr(char *name, int *ptr); register variables specified on command line, with init. setptr(char *name, double *ptr); register variables specified on command line, with init. setptr(char *name, float *ptr); register variables specified on command line, with init. setptr(char *name, char *ptr); register variables specified on command line, with init. setptrn(char *name, int *ptr); register variables specified on command line, without init. setptrn(char *name, double *ptr); register variables specified on command line, without init. setptrn(char *name, float *ptr); register variables specified on command line, without init. setptrn(char *name, char *ptr); register variables specified on command line, without init. int setvar(void); set variables specified on command line. double drand(void); random function (default "rnd_taus113()" from GSL) void setrand(int val); set random seed value double rrand(int ngen); numbered random noise generator void initrand (ngen, nrseed); set random seed for numbered noise generator double gasdev(void); Gaussian distribution with variance of 1 double rgasdev(int ngen); Gaussian distribution from numbered noise generator double poisdev(double m); Poisson distribution, m= mean double gamdev(double a); Gamma interval distribution, n = order (an integer)

elapsed_time = elap_time() /* elapsed computation time (minutes) */ estimated_time = total_measured_time * elapsed_time / measured_elapsed_time;

The "elap_time" function returns the number of minutes (accurate to .0001667 min = .01 sec) since the start of the simulation process. It is useful for timing a part of a simulation run, or for estimating how a script will take.

cpuspeed = system_speed() system CPU speed (approx, in MHz) estimated_time = measured_time * actual CPU speed / cpuspeed;

The "getpid()" function returns the current process number of the simulator. This is useful to make a temporary file name when you are running multiple copies of a script:

pid = getpid() process number for simulatorUse this function to make a temporary file name:

sprintf (str,"file%06g",getpid()); # to add pid to file name save model (str); # creates "file024994" or sprintf (str,"file%04g%06g",int(rand()*10000),getpid()); # to add rand num, pid save model (str); # creates "file3032024994", pid = 024994 . . . restore model (str); # restores model to original stateThe first case shows how to add a 6-digit number onto the file name to make it unique to that process, so that the code can be run by several simultaneous simulator processes without conflict. The process number returned by getpid() is the same as the "PID" number displayed by the "ps" command.

The second case shows how to add 4 more random digits onto the file name to make it even more unique. The "rand()" function is seeded by the "rseed" variable. This can be set by the script or "-r x" on the command line (see "rseed" above). To make the "rseed" value different for each simulation run, set it negative, and it will be set instead by a combination of the process number and the system time when the simulator first starts up.

The "system_speed()" function returns the approximate CPU speed. [ You can recalibrate it by following the instructions in "system_speed()" in "ncmain.cc".] It is useful for estimating how long a script will take.

x = setvar() set variables designated on command line, returns number of variables set.The "setvar" function is useful for running a "nc" program with different sets of parameters. Using the "-s" commaend line switch you can set the value of any variables for the script. The variables set by the "-s" switch need not be already defined in the program. Normally the values defined by the "-s" option are set at the beginning of the nc program. However the "setvar()" function also sets the values that you defined on the command line with "-s". Since you can locate the "setvar()" function anywhere, it is convenient when initializing variables for use as default parameters. You merely run "setvar()" once after the default values for variables have been set. This allows you from the command line to override the default parameter values. (see "NeuronC Variables"). This is especially useful when running "nc" from a shell script file.

The "rand()" function returns a number between 0 and 1. The "rseed" variable sets the seed for the random number generator, as does the "-r n" command line switch (See Section 6). The "gasdev()" function returns a Gaussian distributed set of numbers with zero mean and unit variance, and the "poisdev(m)" function returns a poisson rate distribution.

The "gamdev(n)" function returns a gamma interval distribution, where its order "n" is a positive integer. Note that a gamma distribution with order 1 is equal to the intervals in a poisson distribution with mean of 1. To generate a gamma interval distribution normalized to a mean of 1, use:

gamdev(gorder) / gorder

where "gorder" is set greater than 1 to generate an interval distribution more regular than Poisson. This function is used in the simulator to generate synaptic vesicle release from the "CoV" synaptic parameter.

If you set "rseed" to a negative number, its value is changed to a different value every time to randomize the random function sequences. The seed value is computed from the process ID number and the system time, but appears in "rseed" only after the script does a "run" or "step". Similar behavior occurs when you set "rseed" from the command line switch "-r n", but in that case "rseed" contains the randomized value after you run the "setvar()" function.

The "initrand" and "rrand(n)" statements allow you to create lots of individual random functions that produce different sequences. First you run the "initrand(n)" statement which sets up a different random number generator for each "n". It will automatically seed the generator, but including the "rsd=x" parameter allows you to specify the seed (see the "rsd" parameter in the "photoreceptor" statement). The "rgasdev(n)" function allows you to create an individual Gaussian distribution in the same way as "rrand(n)" above.

There are five random sequence generators included in the simulator.

glibc2 (several sizes, small and fast, or large and hi-quality taus2 (12 bytes, good length period (2^88, 10^26), fastest in GSL) taus113 (16 bytes, longer period than taus2 (2^113), only ~2% slower) tinymt (tiny mersenne twister, 32 bytes, period 2^127, many sequences, 40% slower) mt (mersenne twister, longest random period in GSL, fast, only 10% slower) See http://www.gnu.org/software/gsl for more on these random number generators.The "glibc2" generator can be configured with random states of several sizes. The smaller sizes (8, 32 bytes) are very fast but the random sequences have significant correlations. The larger sizes (128, 256) are still very fast and generate sequences of very high quality. The size of 128 is set by default.

The "taus2" generator (from GSL, http://www.gnu.org/software/gsl) is one of the fastest random generators available and is good quality. It has no significant correlations and uses only 12 bytes, and has a sequence period of 2^88 (10^26).

The "taus113" generator (from GSL, http://www.gnu.org/software/gsl) has a longer period (2^113, 10^34) is only ~2% slower than taus2 (see https://patchwork.ozlabs.org/patch/290250), and is one of the highest quality random generators available. It has no significant correlations and uses only 16 bytes. It is the default random sequence generator in "nc".

The "tinymt" generator (from http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/TINYMT/index.html) has a longer period than taus113 (2^127, 10^38) is only a little (~40-50%) slower, and is one of the best good quality random generators available, noting the tradeoff between speed and length of period. It has no significant correlations and its state uses only 32 bytes. One of its interesting features is the use of parameters that can change the sequence, where the seed sets the start of each sequence. In "nc" the seed sets a different start and also a different sequence. This can prevent significant correlations between different noise sequences.

The "mt" generator (from GSL, http://www.gnu.org/software/gsl) has the longest sequence period (2^19937, 10^6000). It is fast, a little slower than taus2 (~6-12%) but because of its complexity its state requires 2500 bytes. Because a state must be saved for each separate random number sequence in "nc" (i.e. for each neuron that has an individual random seed set), this is a significant drawback, but may not be a problem if you have enough RAM.

(intepreted:) n = gausnn (array, <option1,option2,...>);where:

array = Name of array to hold the points. Array should not be previously defined. optional parameters: default: meaning: -------------------------------------------------------- N = <expr> Number of cells in the array. density = <expr> Density of cells in the array (N/um2). nnd = <expr> 20 Mean nearest-neighbor distance (um). nnstd = <expr> Standard deviation of nnd. reg = <expr> 5 Regularity of the array: mean/stdev. rsd = <expr> set by rseed Random seed for separate sequence. center = <expr> (0,0) Location of center of array (um). size = <expr> (200,200) Size of square array's side (um). (compiled:) gausnn (xarr, yarr, ncells, density, rsd, reg, xcent, ycent, ginfo); gausnn (xarr, yarr, density, rsd, reg, xsize, ysize, xcent, ycent, ginfo); gausnn (xarr, yarr, ncells, rsd, reg, xsize, ysize, xcent, ycent, ginfo); gausnn (xarr, yarr, nnd, reg, rsd, xsize, ysize, xcent, ycent, ginfo); Where: xarr, yarr (double) x,y location of cells generated. xsize, ysize (double) size of array (norm. in microns). xcent, ycent (double) center of array (norm. in microns, default; 0,0). density (double) density of cells specified. nnd (double) nearest-neighbor distance specified. reg (double) regularity (nnd/stdev) of cells specified. ncells (int) number of cells specified. rsd (int) random seed specified for the array of cells. ginfo (int) info variable, sets level of debugging printout.

The gausnn function is useful for creating arrays of cells that are randomly placed but have a certain amount of regularity. This function creates a set of points having a Gaussian distribution of mean nearest-neighbor distance, with a given density and degree of regularity within a specified square region. It is useful from a regularity of 3 (almost random) to a regularity of 50 (almost perfect triangular packing), although it is most accurate (better than 5%) for regularities above 5. One can also specify the mean and standard deviation or various combinations of these parameters.

The gausnn algorithm attempts to use the information specified in the most appropriate way and calculates how many cells should fit in the region specified. If "numcells" is set, its value will be used to determine the density, otherwise if "density" is set, its value will be used to determine the number of cells. If neither of these is set, but "nnd" (mean nearest-neighbor distance) is set, its value is used to determine the density and number of cells. If none of these are set, a default value of 20 um is assigned to "nnd" and this is used to determine the density and number of cells. In a similar manner, the regularity of the array can be set with "reg" (mean/std.deviation), or the "nnstd" parameters.

The number of points successfully placed in the region is returned. The points are returned in the array (previously undefined). The array is defined to be a 2-dimensional array with the first dimension equal to the number of points and the second dimension 0 for X and 1 for Y. The array can be written to a file with "fwrite" or used directly by "nc" to create an array of neurons, etc.

The "rsd" parameter is useful to create an array of neurons whose positions are not affected by construction of other parts of a neural circuit. If "rsd" is set to a negative number, its value is set to a different value every time the simulation is run (also the default behavior for the simulator's random number seed "rseed"). If "rsd" is not set, the default random number seed "rseed" is used.

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(interpreted:) fft (array) (amplitude, phase) spectrum ifft (array) inverse transform (amplitude, phase) pfft (array) power spectrum acov (array) autocovariance dim array [2][arraysize]; (compiled:) void fft(double *real, double *imag, int asiz, int param) Where: param = type of transformation: FFT, IFFT, PFFT, ACOV. These functions compute the fast Fourier transform of the array and leave the answer in the same array, which must be defined with two dimensions. The first subarray (array[0][arraysize]) dimension is amplitude, and the second is phase (array[1][arraysize]).Click here to return to NeuronC Statements

The function you want to fit "fit_func" must be a function of 2 arguments, 1) the X-axis value, and 2), an array containing the coefficients to be fitted for the function. You set the initial values of the coefficients (they must not all be zero). You can set constraints on the coefficient values by including range checks in the function (see example below).

(interpreted:)

lmfit (fit_func,data,p);compiled:

void do_lmfit (double (*user_func) (double user_x_point, double *coeff), int m_dat, double *xydata, int n_p, double *coeff, double *coeffc); /* xydata array must be: arr[2][length]; arr[0] is x, and arr[1] is y. The coeff array must be: coeff[n_p], which is starting value of the coefficients for the function. The coeffc array contains constraints L0, U0, L1, U1, .... 2n_p. If coeffc is NULL no constraints are set. */

(interpreted example:) dim data[2][15] = {{ .07, .13, .19, .26, .32, .38, .44, .51, .57, .63, .69, .76, .82, .88, .94, .24, .35, .43, .49, .55, .61, .66, .71, .75, .79, .83, .87, .90, .94, .97 }}; dim p[] = {{1,1,1}}; // use any starting value except {{ 0,0,0 }}; func fit_func(x, p) { return (p[0] * x + (1 - p[0] + p[1] + p[2]) * x * x) / (1 + p[1] * x + p[2] * x * x); }; lmfit (fit_func,data,p); print p;

(compiled example:) #includeRunning this example produces this output:#include "ncinit.h" #include "ncfuncs.h" double data[] = { .07, .13, .19, .26, .32, .38, .44, .51, .57, .63, .69, .76, .82, .88, .94, .24, .35, .43, .49, .55, .61, .66, .71, .75, .79, .83, .87, .90, .94, .97 }; double p[] = { 1, 1, 1 }; // use any starting value except { 0,0,0 } double fit_func(double x, double *p) { if (p[0] > 5) p[0] = 5; return (p[0] * x + (1 - p[0] + p[1] + p[2]) * x * x) / (1 + p[1] * x + p[2] * x * x); } main() { // perform the fit: lmfit (fit_func,15,&data[0],3,&p[0],NULL); fprintf (stderr,"%g %g %g\n",p[0],p[1],p[2]); }

status: success (f) after 42 evaluations 6.259145 16.1219 6.751548You can set constraints in your "fit_func()" by including a test inside your function. The initial values of the coefficients must be within the range of the constraints:

func fit_func(x, p) { if (p[0] < 1) p[0] = 1; if (p[0] > 5) p[0] = 5; return (p[0] * x + (1 - p[0] + p[1] + p[2]) * x * x) / (1 + p[1] * x + p[2] * x * x); };Running this example produces this output:

status: success (f) after 60 evaluations 5 9.531072 2.152715You can control the level of information in the lmfit printout using the "info" variable. The default level is "info = 2", which prints out the coefficients at every iteration of lmfit. A setting of "info = 1" prints out just the final message containing the number of iterations. A setting of "info = 0" prints nothing:

nc --info 0 lm_test.n 6.259145 16.1219 6.751548

A 2D version of lmfit, called "lmfit2d()" is also available. It is similar to the standard 1D version except that the data array has the X,Y values sequentially stored in the first dimension, and the second dimension contains the Z values for fitting.

A test program for 2D fitting called "gaussfit.cc" is provided. It reads in a square array of values from a file and allows you to set initial values for 6 parameters from the command line:

kc center amplitude rc center radius ks surround amplitude rs surround radius xo X offset yo Y offsetYou may also set constraints using the parameters:

kc_max, kc_min rc_max, rc_min ks_max, ks_min rs_max, rs_min xo_max, xo_min yo_max, yo_minSeveral other parameters help in defining the fit:

file filename for square array of z values to be fit dx delta x,y for the array datasize size of one side of the square arrayA standalone version of gaussfit called "gaussfitn.cc" is provided that does not require linking with "libnc.a". Also provided is a useful program to generate test Gaussian arrays is "makgauss.cc".

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PI 3.141592653589793 E 2.71828182845903523536 DEG 57.29577951308232

gmove (x,y) gdraw (x,y) grmove (dx,dy) ( relative move ) grdraw (dx,dy) ( relative draw ) gcirc (rad, fill) ( fill = 0 or 1 ) grect (x1,y1,x2,y2,x3,y3,x4,y4, fill) (4 (x,y) corners, fill = 0-1 ) gpen (color) ( color range: 1-15 ) grot (theta) ( rotate picture, angle in degrees ) gcrot (theta) ( rotate text, angle in degrees ) gcwidth(width) ( character width ) gsize (size) ( size that square screen frame represents ) gdash (dashcode) ( code range 1->8 ) gorigin (x,y) ( origin of new frame in parent's coords ) gframe ("<name>") ( make new sub-frame ) grframe ("<name>") ( remove sub-frame ) gtext ("<char string>") glabel ("<char string>", color, x, y) (draws label with color at x,y )These graphics primitives allow NeuronC to draw to the graphics screen, defined as by coordinates (0,0) to (1.0, 1.0). gmove and gdraw together with gpen allow you to draw a line anywhere in any color (16 colors for VGA). gtext writes text on the graphics screen, in a manner similar to "printf", or you can call it with a string and no other arguments. glabel calls gtext(), gpen(), and gmove(). The string cannot have arguments that would be allowed in gtext(). gcwidth sets the character size as a fraction of the frame, i.e. .02 sets the char size to 1/50th of the frame size. grmove and grdraw are relative move and draw. grot (calib in degrees) rotates the graphics frame defined by gframe so graphics and text can be written at any angle. gorigin translates the current frame.

A frame is a name for a subregion of a window that can be rotated, translated, and scaled separately from its parent. The frame statement causes the named frame to be the current one. If the named frame doesn't exist, then it is created new. If it does already exist as a parent or descendent of the current frame, the current frame is moved appropriately. gsize sets the size of a frame as a fraction of the current frame. This is useful to allow the other graphics statements to scale to the same size as the "display" statements in "nc".

gcrot (calib in radians) rotates only text (not graphics) about the current location. gdash causes a line to be dashed with a certain pattern (0 - 8 are different patterns).

Example:

gframe "graph1"; gorigin (.2,.2); gsize (.4); code to draw points on graph . . . gframe ".."; gframe "graph2"; gorigin (.2 .6); . . . gframe ".."; (at this point, you can go back to either "graph1" or "graph2" and draw more in them.)