TY - JOUR
T1 - A free-boundary model of a motile cell explains turning behavior
AU - Nickaeen, Masoud
AU - Novak, Igor L.
AU - Pulford, Stephanie
AU - Rumack, Aaron
AU - Brandon, Jamie
AU - Slepchenko, Boris M.
AU - Mogilner, Alex
N1 - Funding Information:
This work was supported by the National Institutes of Health grants: 2 P41 RR013186-15 from the National Center for Research Resources and 9 P41 GM103313-15 and U54 GM64346 from the National Institute of General Medical Sciences. AR and JB were supported by the National Science Foundation grant DMS 1460967. AM was supported by the National Institutes of Health grant GM068952 and by US Army Research Office grant W911NF-17-1-0417. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. M.N., I.L.N. and B.M.S. thank Leslie Loew for his continuing support and helpful discussions.
Publisher Copyright:
© 2017 Nickaeen et al.
PY - 2017/11
Y1 - 2017/11
N2 - 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.
AB - 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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U2 - 10.1371/journal.pcbi.1005862
DO - 10.1371/journal.pcbi.1005862
M3 - Article
C2 - 29136638
AN - SCOPUS:85036554634
SN - 1553-734X
VL - 13
JO - PLoS computational biology
JF - PLoS computational biology
IS - 11
M1 - e1005862
ER -