Some mathematical problems of excitability

The description of the electrical behaviour of nerve and muscle is one of the most quantitative areas of cellular physiology. There are detailed biophysical measurements of currents and potentials, that may be summarised as Master equations or stochastic differential equations for membrane channel and noise recordings, and nonlinear differential equations for macroscopic voltage clamp recordings. Propagation in excitable media is described by nonlinear reaction-diffusion equations. Computational approaches can provide solutions to these equations, but without qualitative studies on simplified caricatures contribute little to mathematical or physiological understanding.