Figure 1.

Interaction between membrane and actin network filaments at the leading edge. The lamellipodial actin network has two functionally different parts: a cross-linked part forming a gel, and a brush of free fluctuating polymer ends extending toward the cell membrane. The position of the membrane is described by the function y(x). The boundary between the brush and the cross-linked network region is described by the function y_g(x). Filaments attach to the membrane at rate k_a, and attached filaments detach at rate k_d. Detached filaments elongate by polymerization with velocity v_p. Cross-linkers continuously bind to the free polymers, so that the gel boundary y_g(x) advances at velocity v_g. (Inset A) Force f_d exerted by detached filaments depends on the contour length l, distance to the membrane tangent z, and angle θ. (Inset B) Force f_a exerted by attached filaments depends on the relation between the distance to the membrane z, the projection R_‖ of the equilibrium end-to-end distance on the membrane normal, and the contour length l. (Inset C) Geometry of the problem: P₁ is the fixed end of the filament and P₁P₂ is the grafting direction. The distance z from P₁ to the local tangent to the membrane at P₂ relates to y – y_g by z/cos(θ₀ + α) = (y – y_g)/cos θ₀, where α = arctan y_x is the local slope of the membrane.