Cell motility, synchronization, and cell traction orientational order

Suspensions of swimming micro-organisms provide examples of coordinated active dynamics. That has stimulated the study of a phenomenological theory combining synchronization and polar order in active matter. Here, we consider another example inspired by the traction forces of migrating cells. The novelty, in this case, is the global force-free nature of the traction force field. Such a constraint is absent in the case where the vector field describes swimming speeds in micro-organisms suspensions. Cell traction is characterized by means of a complex tensor quantity, that generalizes the nematic orientation tensor to incorporate the ability of particles to synchronize, and cell motility depends on this quantity being non-zero. We provide a realization of migrating cell which comprises an assembly of dipolar elements exerting traction on a fluid substrate. This model indicates that spontaneous transition to the motile state is possible but requires (as in the case of synchronization) non-isochrony of oscillations and involves subtle synchronization patterns, associated to propagation of waves. Such results are consistent with recent experimental work relating motility to the synchronization of actin oscillators at the periphery of migrating cells.