Michaelis-Menten Equation

This formula has been very useful in modeling biological behavior. It has been refered to using several names and with some subtle and not-so subtle derivations. The Naka-Rushton formula and the pigment depletion formulaes are examples. It is a saturating nonlinearity.

					       n
                                      Intensity
	Response = Response_Max ----------------------
 					  n	     n
			    	 Intensity + half_sat

Response : The mechanism/neural response
Response_Max : the maximum possible response of the mechanism/neuron
Intensity : the signal intensity
half_sat : The level of I which produces half of Response_Max

It is easy to get confused about when to use linear steps and when to use logarithmic steps. To be specific, the above equation is used to create the shown plot with Intensity = 10^(0 to 7) and half-saturation = 10^3.2 = 1584.9 It is then plotted with a linear y axis and a logarithmic x axis.

The example of the Michaelis-Menten function plotted here is taken from Valeton and van Norren (1983)'s paper on light adaptation in primate cones as measured extracellularly. They found that changing the steady background light level did not alter the shape of the increment-response curve. The invariant increment-response curve is plotted here as a Michaelis-Menten function with an exponent of .74 and a half-saturation constant of 3.2 log td (linearly specified as 1584.9 in the equation). They don't give the value of Rmax, so I used the value 700 which produces a range similar to that of their figure 2b.
Understanding parameter manipulations.
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