Morphogenesis is one of three fundamental mechanisms of developmental biology along with cell growth and differentiation. Understanding morphogenesis requires understanding the processes which control the spatial distribution of cells during embryonic development of an organism. The Cellular Potts Model (CPM) is a discrete, lattice-based model of morphogenesis, in which cells consist of domains of lattice sites and system dynamics are modeled based on energy minimization under imposed fluctuations. Biological mechanisms such as haptotaxis and cell adhesivity are described in terms of effective energies. The CPM has been used to study chicken retinal cells, the entire life cycle of Dictyostelium discoideum, liquid flow during foam drainage and foam rheology. Researchers at Indiana University and Purdue University have developed an open-source C++ modeling environment for CPM simulations, CompuCell3D (http://www.simtk.org/home/compucell3d). CompuCell3D models morphogenesis in three dimensions using a combination of the CPM (for cell clustering, growth, division, death, intracellular adhesion, and volume/surface area constraints), PDE solvers (establishing external chemical fields and modeling reaction-diffusion), and cell-state automata (for cell type differentiation). Using the CompuCell 3D implementation, we have modeled skeletal pattern formation in the chicken limb and somitogenesis. Because the CPM is a fixed-grid, real-space method, it is fast and simple, but memory hungry, requiring very large grids in 3D. The simultaneous solutions of multiple, coupled PDEs, the CPM and internal state models inside each CPM cell are also computationally costly. The CPM uses a modified Metropolis algorithm which is simple, but is based on a sequential algorithm designed to run only on a single processor. It does not parallelize trivially, although Baarkema has developed a number of parallel algorithms for the ordinary Potts model. Current processor and core memory availability means that we can model about 100,000 cells (or a voume of about 300microns. Modeling large-scale morphogenesis of entire tissues or organs, e.g. with 107 cells or more, will require parallel computation. The overall objective of this project is to develop an open-source, scalable, parallel version of CompuCell 3D.
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