Long range and multi process coordination in a two scale cellular automata model of cells

Paulien Hogeweg

We use the 2-scale asynchronous stochastic CA-like model first proposed ny Glazier and Graner (1993}. In this model biological cells are represented by many CA cells with identical states. Transitions rules are goverend by energy minimisation and (average) volume conservation of the biological cells. Thus the dynamics is defined at 2 scales. We show that this model structure leads to interactions at all scales. Moreover we show that a number of qualitatively different macroscopic processes can be defined on the outcome of the processes on these 2 scales. This way automatic coordination of cell migration, cell growth, cell death, and cell differentiation can be achieved. Due to this coordination interesting morphogies can be generated and dynamically maintained. We show a number of qualitatively different examples which examplify the morphogenetic power of the system. These examples where obatined as side-effect of an evolutionary process maximizing cell differentation.

References

Glazier J.A. and Graner, F. (1993) Simulation of the differential driven rearrangement of biological cells. Phys.Rev.E. 47:2128-21254

Hogeweg (1999) Evolving Mechanisms of Morphogenesis: on the interplay between surface energy minimization and cell differentiation J. Theor Biol. (submitted).

Savill, N. J. and Hogeweg, P (1997a) Modeling morphogenesis: from single cells to crawling slugs J. theor. Biol 184:229-235

Marée, A. F. M. , Panfilov, A. V., Hogeweg, P. (1999) Migration and thermotaxis of Dictyostelium discoideum slugs, a model study Submitted to J. theor. Biol.

Marée, A. F. M. , Panfilov, A. V., Hogeweg, P. (1999) Phototaxis during the sluc stage of Dictyostelium discoideum: a model study. Proc. Royal Soc B (submitted).

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