# Cell motility, synchronization, and cell traction orientational order

## TL;DR

This paper develops a theoretical model for cell motility based on traction forces and synchronization, revealing conditions for spontaneous migration and wave-like synchronization patterns, aligning with experimental observations.

## Contribution

It introduces a novel tensor-based characterization of cell traction that incorporates synchronization, and demonstrates how non-isochrony leads to spontaneous cell motility.

## Key findings

- Spontaneous transition to motility requires non-isochrony.
- Synchronization patterns involve wave propagation.
- Model aligns with experimental actin oscillator data.

## Abstract

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.