CIMMS Lunchtime Series:  On Multiscale Approaches to Three-Dimensional Modelling of Morphogenesis

Mark Alber, Mathematics and Physics, The Center for the Study of Biocomplexity, University of Notre Dame

In this talk we will present the foundation of a unified, object-oriented, three-dimensional biomodelling environment, which allows us to integrate multiple submodels at scales from subcellular to those of tissues and organs [1]. Our current implementation combines a modified discrete model from statistical mechanics, the Cellular Potts Model, with a continuum reaction diffusion model [2] and a state automaton with well-defined conditions for cell differentiation transitions to model genetic regulation. This environment allows one to rapidly and compactly create computational models of a class of complex-developmental phenomena. To illustrate model development, we describe simulations of the simplified version of the formation of the skeletal pattern in a growing embryonic vertebrate limb.

In the second half of the talk we will describe the first three-dimensional stochastic model [3,4] based on contact-mediated cell communication, for studying myxobacteria fruiting body development. The myxobacteria under starvation undergo several developmental stages including rippling, streaming, jamming, aggregation, and, finally, developing mature fruiting bodies. Combining contact signaling between cells and slime production mechanisms, our model reproduces all different stages in a transition from 3D traffic jams to aggregates and demonstrates possible structure of cell arrangement within the fruiting body.



References:

1. Chaturvedi, R., C. Huang, B. Kazmierczak, T. Schneider, J. A. Izaguirre, T. Glimm, H.G.E. Hentschel, J. A. Glazier, S. A. Newman, M. Alber [2005], On Multiscale Approaches to 3-Dimensional Modeling of Morphogenesis, Journal of the Royal Society Interface 2 3, 237-253.

2. Alber, M., Glimm, T., Hentschel, H.G.E., Kazmierczak, B., and S. Newman [2005], Stability of n-Dimensional Patterns in a Generalized Turing System: Implications for Biological Pattern Formation, Nonlinearity 18 125-138.

3. Alber, M.S., M.A. Kiskowski, and Y. Jiang [2004], Two-stage aggregate formation via streams in myxobacteria, Phys. Rev. Lett. 93 068301.

4. Sozinova, O., Y. Jiang, D. Kaiser, and M. Alber [2005], A Three-Dimensional Model of Myxobacterial Aggregation by Contact-mediated Interactions, Proc. Natl. Acad. Sci. USA 102 No.32, 11308-11312.