A three-dimensional model of cell movement in multicellular systems

A mathematical model for cell movement in multicellular systems has been developed that allows us to simulate and visualize, 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 model is quite adaptable to a number of systems, due to the way it is designed. The building blocks of the model are individual cells, where each cell has certain given properties that are not necessarily the same for all cells. The basic properties are that a cell can deform under force (either stretch or compress), while conserving its volume, it adheres to other cells and it can generate an active motive force. The response of a cell depends on its internal parameter state, and on the information it receives from its external environment, which includes neighbor cells, the extracellular matrix and chemical signals. The net force on a cell is calculated by summing up ail the forces that a cell experiences at its surroundings. Each cell is then moved and deformed according to the equations of motion and deformation. Finally, the net movement of all the cells gives the collective movement of the entire tissue. Here we introduce this model and show examples of its applications and compare the results with experimental data. In the first simulations, we show how different cell types can be sorted out based solely on differences in adhesion. We compare our results to cell sorting experiments done by Steinberg and co-workers [R.A. Foty, C.M. Pfleger, G. Forgacs, M.S. Steinberg, Development 122 (1996) 1611-1620; M.S. Steinberg, Reconstruction of tissues by dissociated cells, Science 141 (1963) 3579] using values for adhesion within the range of the experimental values, acid show that the model reproduces the experiments very well. We also present results from simulations of Dictyostelium movements. We first modeled the aggregation stage, where cells are aggregating chemotactically, towards a signaling center, in response to cAMP waves. In these simulations one can observe stream formation and how the mound arises due to the inward motion of the cells towards the signaling center. Later we studied simulations of 2D slugs, and compared them to observations of 2D slugs done by Bonner [J.T. Bonner, Proc. Natl. Acad. Sci. USA 95 (1998) 9355-9359]. (C) 2001 Elsevier Science B.V. All rights reserved.