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Type of Document Dissertation Author Kiskowski, Maria Audelia Author's Email Address mkiskows@nd.edu URN etd-04162004-112203 Title Discrete Stochastic Models for Morphological Pattern Formation in Biology Degree Doctor of Philosophy Department Mathematics Advisory Committee
Advisor Name Title Edward Hinchcliffe Committee Chair Andrew Sommese Committee Member David Nicholls Committee Member Holly Goodson Committee Member Mark Alber Committee Member Yi Jiang Committee Member Keywords
- pattern formation
- discrete particle systems
- morphogenesis
- mathematical biology
Date of Defense 2004-03-30 Availability restricted Abstract 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 definedon 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.
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