A Model of Growth and Form Based on Adhesion Molecules

A model is given for the generation of pattern and form in living systems, based on the assumption of two types of a single adhesion molecule that form homotypic cell-cell contacts. The time dependence of the model is different from that of the Turing models, instead viewing the change in time as being driven by the change in time of the total areaA, along with the sequential gene activation which is called into play at discrete times as the organism grows and changes shape. Two equations are derived on the assumption of an energy minimum equilibrium being achieved at all times on a scale that is short compared with the rate of change over time of the total area. The two equations derived from the simple assumptions of the model are the (nonlinear) Helmholtz equation and the Laplace equation. It is argued that a suitable “morphogen” should attempt to satisfy certain rather specific conditions.