Modeling the electrical behavior of anatomically complex neurons using a network analysis program: excitable membrane

We present methods for using the general-purpose network analysis program, SPICE, to construct computer models of excitable membrane displaying Hodgkin-Huxley-like kinetics. The four non-linear partial differential equations of Hodgkin and Huxley (H-H; 1952) are implemented using electrical circuit elements. The H-H rate constants, alpha and beta, are approximated by polynomial functions rather than exponential functions, since the former are handled more efficiently by SPICE. The process of developing code to implement the H-H sodium conductance is described in detail. The Appendix contains a complete listing of the code required to simulate an H-H action potential. The behavior of models so constructed is validated by comparison with the space-clamped and propagating action potentials of Hodgkin and Huxley. SPICE models of multiply branched axons were tested and found to behave as predicted by previous numerical solutions for propagation in inhomogeneous axons. New results are presented for two cases. First, a detailed, anatomically based model is constructed of group Ia input to an alpha-motoneuron with an excitable soma, a myelinated axon and passive dendrites. Second, we simulate interactions among clusters of mixed excitable and passive dendritic spines on an idealized neuron. The methods presented in this paper and its companion (Segev et al. 1985) should permit neurobiologists to construct and explore models which simulate much more closely the real morphological and physiological characteristics of nerve cells.