Mathematical Models for Cellular Organisms

Abstract

During the life of a cellular organism, the individual cells grow, divide and die. Our aim in this paper is to examine various mathematical models that represent this process as a sequence of discrete events.

In section I and ll we give models in which the development of a cell is not affected by the spatial arrangement of the neighbouring cells. In section lll we drop this restriction for one-dimensional organisms to get the Lindenmayer model. The models in the remaining sections represent attempts to generalize the Lindenmayer model to higher dimensions. The Von-Neumann cellular array model of section IV proves unsatisfactory. The geographical models of section V, Vl and Vll are somewhat better for higher dimensional organisms. The final section gives a precise definition of a class of models, that includes those models presented earlier in the paper. The hope is that biologists will find these models suitable for describing real organisms and that mathematicians will be stimulated to prove biologically interesting theorems about them.