Gompertzian growth and decay: a powerful descriptive tool for neuroscience

First-order kinetics is based on simple exponential decay, usually expressed in base e (Naperian) notation. "Nonexponential" processes, for example, S-shaped functions, are frequently modeled as sums of that elemental construct, and the number of rate constants increases with the number of such terms. A powerful descriptive alternative to sums of simple exponentials is the Gompertz function. In Gompertz kinetics, the rate coefficient of an exponential process is assumed to change exponentially with the independent variable. Nonexponential processes are easily modeled, more efficiently and more accurately than is possible with standard kinetics. Application of Gompertz kinetics to neuroscience research topics ranging from cognitive to molecular is presented to illustrate the power of the model: distribution of nerve fiber diameters, conditioning-testing responses of excitable nerve, psychophysical estimates of taste intensity magnitude, time course of synaptic current, and behavior of membrane conductance during voltage clamp of squid axon.