Analysis of a model of membrane potential for a skin receptor nerve

The analysis of the membrane potential of the Pacinian corpuscle is presented. A system of partial differential equations, boundary and initial conditions form a linear model. The unknowns of the model are the receptor potential and the filopodia membrane potential. The input to the system is a mechanical stimulus. One of the major parameters is the filopodia density. The points of interest are the value of the receptor potential in the heminode and the role played by the filopodia distribution and the stimulus in the potential dynamics. These goals are approached analytically and numerically. A general theory of existence and uniqueness of a solution of the one dimensional diffusion equation with the oblique boundary conditions is developed. Some useful estimates of the potential based on the Green function and the strong maximum principle are derived. Two finite difference schemes are used to obtain more information about the time dependent and the stationary models. An explicit solution of the stationary problem with the uniform filopodia distribution and the constant stimulus is extensively discussed.