Figure 1.

Two-dimensional model of the actin network flow. (A) Motile keratocyte cell, view from above. The cargo of the cell body is depicted by the gray ellipse at the rear. The lamellipod glides with the steady shape and velocity V, while the branched actin network (crisscross segments) grows at the leading edge and retracts at the rear due to the contractile action of myosin (thick double-arrows). (Inset) Mechanical model of the actin-myosin lamellipodial network. Actin filaments (segments, density ρ) glide with velocity u, undergo relative viscoelastic sliding (spring and dashpot in series, viscoelastic stress τ), and are contracted by working myosins (density m₁). Adhesion results in effective viscous drag (dashpot, density ξ). Myosin molecules cycle between the working and free (density m₀) states. (B) Hypothesized maintenance of the lamellipodial shape: The actin network grows at the front and sides (solid arrows), while the centripetal actin flow is fast at the rear and sides and slow at the front (dashed arrows). At the sides, the outward growth and inward flow cancel each other. At the rear, there is no actin growth, and the centripetal actin flow is equal to the cell speed (dotted arrow). The front advances with the cell speed equal to the difference between the local rates of actin growth and centripetal flow. To maintain the steady shape, the net local normal extension rate at the lamellipodial boundary has to obey the equation (V_n − V^c · n) = V × cosθ, where V_n is the local actin growth rate, V^c is the local actin centripetal flow velocity, n is the local normal unit vector, and θ is the angle between n and the direction of movement. (C) Characteristic map of the actin centripetal flow, u(r), in the lab coordinate system. (D) In the framework of the steadily moving cell, there is the kinematic flow of F-actin to the rear with constant rate V equal to the cell speed. (E) In the framework of the cell, the actin-myosin network drift is the geometric sum, (u(r) − V), of the flows shown in panels C and D. If V > |u(r)|, then the resulting drift sweeps the myosin to the rear.