Our NSF funded Biocomplexity Group studies multicellular aggregates, such as embryonic and mature tissues, which often share the properties of "excitable media" and "soft matter," familiar to modern condensed matter physics and dynamical systems theory. Changes in tissue shape and form during development and repair-skeletal formation, gastrulation, segmentation, are well suited to analysis by physical and mathematical concepts, particularly in conjunction with modern knowledge of cells' adhesive forces and the molecular composition and rheology of cytoplasm and extracellular matrix.
We developed a package CompuCell3D which provides a framework for multimodel simulations of complex biological problems. It has been developed as an ongoing project for the Interdisciplinary Center for the study of Biocomplexity at the University of Notre Dame. By biocomplexity we mean the study of complex structures and behaviors that arise from the interaction of biological (biophysical!) entities (molecules, cells, organisms). The complex interplay of physical and chemical processes give rise to a great variety of spatial and temporal structures, resulting in rich complexity of even the simplest biological phenomena. CompuCell currently uses a combination of "extended Potts model" for cell sorting and clustering, and "Reaction Diffusion" equations to establish the underlying chemical field to which cells respond and form typical patterns found in such biological systems as a growing chicken limb.
Fruiting body formation in bacteria occurs in response to adverse conditions and is critical for species survival.When starved, myxobacteria undergo a process of alignment, rippling, streaming, and aggregation that culminates in a three-dimensional fruiting body (Fig. 1). This complex morphogenesis must be robust despite internal and external noise.
Canonically, models for bacteria (e.g., E. Coli and B. subtilis ) and amoebae (e.g., D. discoideum ) aggregation have been based on chemotaxis, a long range cell interaction that shares many features of chemical reaction-diffusion dynamics. Initialization of chemotactic signals plays an important role in the initial position of aggregates and subsequent signaling biases cell motion towards developing aggregates. Cells following the maximal chemical gradient navigate towards aggregates that are large and near. In myxobacteria there are no chemotactic cues, yet cells travel large distances to enter an aggregate.
Our lattice cell model is based on simple local rules by which cells align by turning preferentially to make end to end contacts. On average this rule results in cells following the tails of other cells, mimicking the effect of C signaling in myxobacteria that drives aggregation. In our simulations, distinct aggregate types form that have different behaviors and roles even though they are composed of identical cells following identical rules. Large, stationary aggregates are stable, while intermediate motile aggregates (streams) can aid in large aggregate formation. An interesting discovery is that the presence of internal noise is required for efficient streaming. It is as if the cells must make short-term mistakes to form unstable transients that ultimately results in more efficient aggregation. Our analysis of streams and noise suggests some new experiments.
Myxococcus xanthus is a Gram-negative rod-shaped bacterium. Under
starvation conditions, it undergoes a magnificent developmental process
in which roughly 100,000 individual cells aggregate to form a structure
called the fruiting body over the course of several hours (see the
following page for details:
LGCA models were originally developed to describe idealized fluids and gases composed of point-like interacting particles. We describe several extensions of the classical LGCA model to self-directed biological cells. In particular, we review recent models for the rippling stage of fruiting body formation in myxobacteria, aggregation of cells and swarming. These LGCA-based models show the versatility of CA in modeling and their utility in attacking basic biological questions.
The CPM is a more sophisticated CA which describes the shapes of individual cells. We use the CPM to simulate morphogenesis, the development of a complex spatial structure by a collection of cells. We review various extensions to the original Potts model and describe their application to three phenomena: cell sorting in aggregates of embryonic chicken cells, morphological development of the slime mold Dictyostelium discoideum and avascular tumor growth. These models include intracellular and extracellular interactions cell growth and cell death.
Last Updated: September 20, 2006 by Tanya Kazakova.