Biological Lattice Gas Models

Abstract

Modelling pattern formation and morphogenesis are fundamental problems in biology. One useful approach involves lattice gases (LGCA) systems. 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 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 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, undergo chondrogenic pattern formation which results in the formation of regularly-spaced "islands" of cartilage analogous to the cartilage primordia of the developing limb skeleton. An LGCA model is described for this process based on reaction-diffusion coupling and cell-matrix adhesion.

On Modeling Complex Collective Behavior in Myxobacteria

“…In Secs. 3.1-3.3, we use 2-D and 3-D LGCA models based on an extended cell representation [1][2][3][4]32]. Namely, each cell is represented as (i) a single node which corresponds to the position of the cell's center (or "center of mass"), (ii) the choice of occupied channel at the cell's position designating the cell's orientation and (iii) a local neighborhood defining the physical size and shape of the cell with associated interaction neighborhoods (see Fig.…”

A three-dimensional model of myxobacterial fruiting-body formation

“…Biological LGCA employ a regular, finite lattice and include a finite set of cell states, an interaction neighborhood, and probabilistic local rules that determine the cells' movements and transitions between states (for a review, see ref. 3).…”