Entropic predictions for cellular networks

Abstract

Diverse cellular systems evolve to remarkably similar stationary states. We therefore have studied and simulated a purely topological model. We use a maximum-entropy argument to predict that the average number of l-sided cells adjacent to an n-sided cell, ${\mathit{M}}_{\mathit{l}}$(n), will be linear in n. One consequence is the empirically observed linearity of the total number of edges of cells adjacent to an n-sided cell, known as the Aboav-Weaire law. The prevailing justification of that law is shown to be incorrect, and thus the apparently universal experimental slope of \ensuremath{\sim}5 remains unexplained.