Temporal correlation between oscillating force dipoles drives 3D single cell migration

Directional cell locomotion requires symmetry breaking between the front and rear of the cell. How this manifests itself for cells moving in physiological 3D matrices is often elusive. We take inspiration from the scallop theorem proposed by Purcell for micro-swimmers in Newtonian fluids: self-propelled objects undergoing persistent motion at low Reynolds number must follow a cycle of shape changes that breaks temporal symmetry. We report similar concepts for cells crawling in 3D. We quantified cell motion using a combination of 3D live cell imaging, visualisation of the matrix displacement and a minimal model with multipolar expansion. We show that cells embedded in 3D matrix form myosin-driven force dipoles at both sides of the nucleus, that locally and periodically pinch the matrix. The existence of a phase shift between the two dipoles is required for directed cell motion which manifests itself in cycles in the dipole-quadrupole diagram, a formal equivalence to the Purcell cycle. We confirm this mechanism by triggering local dipolar contractions with a laser, which leads to directed motion. Our study reveals that the cell controls its motility by synchronising dipolar forces distributed at front and back. This result opens new strategies to externally control cell motion as well as for the design of micro-crawlers. ### Competing Interest Statement The authors have declared no competing interest.