Program
| CTC1c | |
|---|---|
| Christophe Deroulers | |
| University Paris Diderot-Paris 7 | |
| Title | The phase diagram of elongated migrating cells: aggregation without attraction |
| Abstract | Many migrating cells have an elongated shape, e.g. cancerous astrocytes diffusing out of a spheroid [1] or myxobacteria [2], and they tend to migrate in a preferred directions, with changes of direction, or even complete reversal [2], from time to time. It is well known from simple models that a population of point-like migrating cells behaves, at large time scales, in a diffusive manner [3], unless the cells exert some kind of attraction on their neighbours. Here, we investigate the collective behaviour in two dimensions of elongated cells with preferred migration in the direction of elongation, random rotations at a fixed rate, and hard-core repulsion (to prevent cells from penetrating one another). We find, on the basis of numerical simulations on a regular lattice, that the cells may spontaneously form aggregates if the random rotations occur not frequently enough and if the density of cells is high enough. This happens even though there is no attraction between cells, and even for cells that do not migrate always in the forward direction, but are allowed to make random backward steps. The parameter space is divided into two regions with nontrivial boundaries, one where cells form aggregates, and the other one where their population behaves in a simple diffusive way. The change of behaviour is abrupt when the boundaries are crossed. Finally, we establish approximate equations for the density of cells. They enable us to give an analytical model of this phenomenon. [1] M. Aubert, M. Badoual, S. Féréol, C. Christov, and B. Grammaticos, Phys. Biol. 3, 93 (2006); C. Deroulers, M. Aubert, M. Badoual, and B. Grammaticos, Phys. Rev. E 79, 031917 (2009) [2] Y. Wu, A. Dale Kaiser, Y. Jiang, and M. S. Alber, PNAS 106, 1222 (2009) [3] H. G. Othmer, S. R. Dunbar, and W. Alt, J. Math. Biol. 26, 263 (1988) |
| Coauthors | Mathilde Badoual, Basil Grammaticos |
| Location | Woodward 1 |