Gompertz kinetics model of fast chemical neurotransmission currents

At a chemical synapse, transmitter molecules ejected from presynaptic terminal(s) bind reversibly with postsynaptic receptors and trigger an increase in channel conductance to specific ions. This paper describes a simple but accurate predictive model for the time course of the synaptic conductance transient, based on Gompertz kinetics. In the model, two simple exponential decay terms set the rates of development and decline of transmitter action. The first, r, triggering conductance activation, is surrogate for the decelerated rate of growth of conductance, G. The second, r', responsible for Y, deactivation of the conductance, is surrogate for the decelerated rate of decline of transmitter action. Therefore, the differential equation for the net conductance change, g, triggered by the transmitter is dg/dt=g(r-r'). The solution of that equation yields the product of G(t), representing activation, and Y(t), which defines the proportional decline (deactivation) of the current. The model fits, over their full-time course, published records of macroscopic ionic current associated with fast chemical transmission. The Gompertz model is a convenient and accurate method for routine analysis and comparison of records of synaptic current and putative transmitter time course. A Gompertz fit requiring only three independent rate constants plus initial current appears indistinguishable from a Markov fit using seven rate constants.