An approach to the mathematical biophysics of biological self-regulation and of cell polarity

Abstract

In a cell, in which the permeability to a metabolite is a function of the concentration of that metabolite, situations may occur, in which the diffusion field will exhibit certain assymetric patterns, even though the cell may possess geometrically spherical symmetry. This pattern results in a polarity of the cell. Moreover, the pattern being the result of a dynamic equilibrium, it possesses the property of self-regulation. Dividing the cell in two results in the appearance of a similar patterns in each half-cell.

Another case when such self regulation and polarity occur is given by considerations of the action of the diffusion forces upon colloidal particles, which affect catalytically the metabolic reactions. A simple case is treated mathematically.