Concentration Profiles of Actin-Binding Molecules in Lamellipodia with Retrograde Flow

Abstract

Motile cells form flat protrusions in the direction of motion called lamellipodia. The actin filament network inside lamellipodia flows opposite to the direction of motion (retrograde flow) due to actin polymerization at the front. Hence, actin binding molecules are subject to transport to the rear in the bound state and diffuse freely in the unbound state. We analyse this non-linear reaction-diffusion-advection process with respect to the concentration profiles of these species and provide analytic approximations for the profiles. Retrograde flow may cause a depletion zone of actin-binding molecules close to the leading edge. The existence of such zone depends on the free molecule concentration in the cell body, on the ratio of the diffusion length to the distance bound molecules travel rearward with the retrograde flow before dissociating, and the ratio of the diffusion length to the width of the region with retrograde flow and actin binding. Our calculations suggest the existence of depletion zones for the F-actin cross-linkers filamin and α-actinin in 3T3-fibroblasts, which is in line with the small elastic moduli of the F-actin network close to the leading edge found in measurements of the force motile cells are able to exert.