Axon voltage-clamp simulations. I. Methods and tests.

This is the first in a series of four papers in which we present the numerical simulation of the application of the voltage clamp technique to excitable cells. In this paper we describe the application of the Crank-Nicolson (1947) method for the solution of the parabolic partial differential equations that describe a cylindrical cell in which the ionic conductances are functions of voltage and time (Hodgkin and Huxley, 1952). This method is compared with other methods in terms of accuracy and speed of solution for a propagated action potential. In addition, differential equations representing a simple voltage-clamp electronic circuit are presented. Using the voltage clamp circuit equations, we simulate the voltage clamp of a single isopotential membrane patch and show how the parameters of the circuit affect the transient response of the patch to a step change in the control potential. The stimulation methods presented in this series of papers allow the evaluation of voltage clamp control of an excitable cell or a syncytium of excitable cells. To the extent that membrane parameters and geometrical factors can be determined, the methods presented here provide solutions for the voltage profile as a function of time.