July 13, 2004 21:58 WSPC/Trim Size: 9in x 6in for Review Volume bio˙pattern˙format˙7˙14 CHAPTER 1 BIOLOGICAL LATTICE GAS MODELS Mark Alber * , Maria Kiskowski * , Yi Jiang † , and Stuart Newman + * Department of Mathematics, 255 Hurley Building, University of Notre Dame, Notre Dame, IN 46556-4618, USA E-mail: malber@nd.edu † Theoretical Division, Los Alamos National Laboratory Los Alamos, NM 87545, USA E-mail: yi@t7.lanl.gov + Department of Cell Biology & Anatomy, Basic Science Building New York Medical College, Valhalla, NY 10595, USA E-mail: stuart newman@nymc.edu Modelling pattern formation and morphogenesis are fundamental prob- lems in biology. One useful approach involves lattice gases (LGCA) sys- tems. This paper reviews several stochastic lattice gas models for pattern formation in myxobacteria fruiting body morphogenesis and vertebrate limb skeletogenesis. The formation of fruiting bodies in myxobacteria is a complex mor- phological 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 cell-cell interactions rather than of chemotaxis. An model is described for the aggregation stage of fruiting body formation. Limb bud precartilage mesenchymal cells in micromass culture, un- dergo chondrogenic pattern formation which results in the formation of regularly-spaced “islands” of cartilage analogous to the cartilage primor- dia of the developing limb skeleton. An LGCA model is described for this process based on reaction-diffusion coupling and cell-matrix adhesion. 1. Introduction Two main approaches have characterized mathematical modeling pattern formation (generation of specific arrangements of cells or other biolocgical agents) and morphogesesis (generation of 3D forms from such agents) in 1