A Mathematical Model of Two Cells Via Turing’s Equation

Abstract

Here we describe a mathematical model in the field of cellular biology. It is a model for two similar cells which interact via diffusion past a membrane. Each cell by itself is inert or dead in the sense that the concentrations of its enzymes achieve a constant equilibrium. In interaction however, the cellular system pulses (or expressed perhaps over dramatically, becomes alive!) in the sense that the concentrations of the enzymes in each cell will oscillate indefinitely. Of course we are using an extremely simplified picture of actual cells.