BIRS Workshop Lecture Videos
Mean Cluster Approach to Active Matter Beatrici, Carine
Cell migration is essential to cell sorting, playing a central role in tissue formation, wound healing, and tumor evolution. In a limit where inner cells are diluted when compared to outer cells, cell sorting can be described directly by the evolution of inner cells in a process of diffusion and fusion. Experiments show that far from finite size boundaries the average mass of inner cell clusters grows as a power law. In active matter systems, the dependency of the diffusion constant with the cluster mass does not follow the expected inverse relation but still preserves a simple relation. The diffusion constant depends on the cluster mass as a power law. In this work, we take into account this dependency within a Mean Cluster Approach (MCA). It results that, out of finite size limits, the average cluster mass evolves as a power law and its exponent depends only on the system dimension and on the exponent in the relation between diffusion constant and cluster mass, independent of the specific segregation mechanism. We confirm this simple prediction using simulations with different segregation hypotheses describing cell-cell interaction: differential adhesion hypothesis (DAH) and different velocities hypothesis (DVH). We performed MCA analysis and simulations below the transition to the ordered phase. However, system behavior above the transition is still not explored. Preliminary analytic and simulation results present a non-trivial positive exponent for the diffusion constant in the ordered phase. These results apply for active matter systems in general and, in particular, the mechanisms found underlying the increase in cell sorting speed and in cell crawling certainly has profound implications in biological evolution as a selection mechanism.
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