Reduction of the Diffusion Equations of Ion Channel Clusters with Virtually No Increase in the Error Bound

Abstract

A stochastic differential formulation for the collective dynamics of ion channel clusters in excitable membranes is developed from the so-called reduced strong diffusion formulation. In this error bound optimizing reduced formulation, the potassium channel states n(4) and n(3), and, the sodium channel states m(3)h(1) and m(2)h(1) are the retained states; consequently, the formulation accommodates only four channel variables and five white noises. The accuracy of the formulation is tested over the standard deviations and autocorrelation times of the channel density fluctuations. The findings are seen to be virtually identical to the corresponding results from the exact microscopic Markov simulations. The formulation arises as the most accurate model with that structural simplicity, thus making it an important model for both analytic analyses and numerical simulations in the study of finite-sized membranes.