Discrete Stochastic Models for Morphological Pattern Formation in Biology

Modeling morphogenesis is a fundamental problem in biological pattern formation. Biology pattern formation may be modeled using continuous or discrete approaches. Cellular automata are discrete particle systems which are defined on a lattice and have a finite number of states. Lattice gases (LGCA) are a type of cellular automata in which particles move on a lattice and change state following particle collisions.This thesis focuses on three stochastic lattice gas models for pattern formation in limb and myxobacteria fruiting body morphogenesis. In micromass cell culture, limb bud precartilage mesenchymal cells undergo chondrogenic pattern formation which results in the formation of regularly spaced chondrogenenic ``islands'. This thesis describes a model for limb chondrogenesis based on reaction-diffusion and cell-matrix adhesion. The formation of fruiting bodies in myxobacteria is a complex morphological process that requires the organized, collective effort of tens of thousands of cells. Myxobacteria morphogenesis provides new insight into collective microbial behavior since morphogenic pattern formation is governed by mechanical, cell-cell interactions. Two models are described for the rippling and aggregation stages of fruiting body formation. Local rules result in either rippling or aggregation depending on the choice of key biologically motivated cell-cell interactions.