A physical model of cellular self-organization

Abstract

The formation of spatial patterns is a phenomenon that we can and in nonequilibrium systems. Here we model the dynamics of phytohormone auxin, responsible for plant growth, in a one-dimensional ring of 100 cells. Through the numerical integration of the differential equations that control the dynamics of auxin concentration and through a linear stability analysis of these dynamics, we determine the conditions for the homogeneous stationary state of auxin concentration to be linearly unstable and dynamically evolve to a spatial periodic pattern, in which there are spatial regions with high auxin concentration alternating with spatial zones with low auxin concentration. Finally we establish a comparison with a prototype model of pattern formation, the Swift-Hohenberg model