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PLoS Comput Biol. 2017 Nov 14;13(11):e1005862. doi: 10.1371/journal.pcbi.1005862. eCollection 2017 Nov.

A free-boundary model of a motile cell explains turning behavior.

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Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, CT, United States of America.
Center for Engineering Learning & Teaching, University of Washington, Seattle, WA, United States of America.
Department of Computer Science, Cornell University, Ithaca, NY, United States of America.
Department of Mathematics, Adrian College, Adrian, MI, United States of America.
Courant Institute and Department of Biology, New York University, New York, NY, United States of America.


To understand shapes and movements of cells undergoing lamellipodial motility, we systematically explore minimal free-boundary models of actin-myosin contractility consisting of the force-balance and myosin transport equations. The models account for isotropic contraction proportional to myosin density, viscous stresses in the actin network, and constant-strength viscous-like adhesion. The contraction generates a spatially graded centripetal actin flow, which in turn reinforces the contraction via myosin redistribution and causes retraction of the lamellipodial boundary. Actin protrusion at the boundary counters the retraction, and the balance of the protrusion and retraction shapes the lamellipodium. The model analysis shows that initiation of motility critically depends on three dimensionless parameter combinations, which represent myosin-dependent contractility, a characteristic viscosity-adhesion length, and a rate of actin protrusion. When the contractility is sufficiently strong, cells break symmetry and move steadily along either straight or circular trajectories, and the motile behavior is sensitive to conditions at the cell boundary. Scanning of a model parameter space shows that the contractile mechanism of motility supports robust cell turning in conditions where short viscosity-adhesion lengths and fast protrusion cause an accumulation of myosin in a small region at the cell rear, destabilizing the axial symmetry of a moving cell.

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