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Mammalian cell migration in open spaces requires F-actin polymerization and myosin contraction. While many studies have focused on myosin’s coupling to focal adhesion and stress fibers, the indirect effect of myosin contraction on cell migration through actin depolymerization is not well studied. In this work, we quantified how cell velocity and effective power output are influenced by the rate of actin depolymerization, which is affected by myosin contraction. In addition, we derived scaling laws to provide physical insights into cell migration. Model analysis shows that the cell migration velocity displays a biphasic dependence on the rate of actin depolymerization and myosin contraction. Our model further predicts that the effective cell energy output depends not only on the cell velocity but also on myosin contractility. The work has implications on in vivo processes such as immune response and cancer metastasis, where cells overcome barriers imposed by the physical environment. 

We consider a classical elastohydrodynamic model of an inextensible filament undergoing planar motion in${\mathbb{R}}^3$. The hydrodynamics are described by resistive force theory, and the fibre elasticity is governed by Euler–Bernoulli beam theory. Our aim is twofold: (1) Serve as a starting point for developing the mathematical analysis of filament elastohydrodynamics, particularly the analytical treatment of an inextensibility constraint, and (2) As an application, prove conditions on internal fibre forcing that allow a free-ended filament to swim. Our analysis of fibre swimming speed is supplemented with a numerical optimization of the internal fibre forcing, as well as a novel numerical method for simulating an inextensible swimmer.