A mathematical model for cell movement in multicellular systems has been developed that can simulate and vizualize, in three dimensions, individual cell movements in a number of multicellular systems. These include cell movement during, aggregation and slug stage of Dictyostelium discoideum, embryogenesis, limb formation and wound healing.

The basic unit in the model is an individual cell, each of which has the following properties. It can deform under force, it conserves volume under deformation, it adhers to other cells, it can generate active force, and it responds to chemical signals. The cell can extract infomation from its surroundings, which can be either a substrate or other cells, and it can exert forces on its surroundings. The net force on each cell is calculated and each cell is moved and deformed accordingly, with the result that the collective movement of the entire tissue is determined.

In this talk I will introduce the model and show examples of its applications and compare the results with experimental data. Among the simulations I will show is how how different cell types can sort out based solely on differences in adhesion. We compare our results to cell sorting experiments done by Steinberg et al. [1,2] using values for adhesion within the range of the experimental values, and show that the model reproduces the experiments very vell. We also study cell movement in response to a chemotactic signal and compare the results to experimental observations of cell movements in Dictyostelium discoideum. I will also discuss future applications of the model.

[1] R. Foty et al. Development 122, 1611--1620 (1996), Surface tension of embryonic tissues predict their mutual envelopment.

[2] M.S. Steinberg Science 141, 401--408 (1963), Reconstruction of tissues by dissociated cells.

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1998-1999 Mathematics in Biology