Heavy-tailed jumps induce intermittent patterns and gradual transitions in interacting cell populations

It has been widely accepted, that a key step in cancer invasion and metastasis is the so-called epithelial-mesenchymal transition (EMT), where cells lose contacts with their neighbors and start moving freely, colonizing new tissues in the process. However, it has been found that cancer cells may retain cellular contacts and become highly metastasizing without undergoing EMT. Furthermore, single cancerous cells may reach far away tissues by displaying superdiffusive Lévy dynamics. Here, we study a system of collectively migrating cells with attracting (adhesive) interactions and heavy-tailed distributed jump lengths. To this end, we develop a multi-speed lattice-gas cellular automaton model, and analyze it both computationally and analytically. To study the effect of Lévy dynamics on collective behavior, we consider three migration scenarios: (classic) single-jump migration, corresponding to a “healthy” scenario, where cells move a single site per time step, block migration, where cells that move together remain together for the total duration of the jump but jump lengths are random and power-law distributed, corresponding to the case where leader cells can guide cell clusters through strong cell junctions, and cell-wise migration, where each cell in a group may perform jumps of different lengths, independently of other cells, corresponding to the case where cell junctions are dynamic enough to allow single cells to escape clusters. We show that, while in the classic case, destabilization of the homogeneous steady state only depends on cell density and/or adhesion strength, in the multi-speed case, increasing the probability of long jump lengths leads to a gradual order-disorder transition, as opposed to the sharp transition with increasing cell density and/or adhesiveness. Furthermore, observed spatial patterns formed are stable when jumps are preferentially small, unstable when long jumps are highly probable, and metastable at intermediate regimes.