On the existence and strength of stable membrane protrusions

Abstract

We present a mathematical model for the protrusion of lamellipodia in motile cells. The model lamellipodium consists of a viscoelastic actin gel in the bulk and a dynamic boundary layer of newly polymerized filaments at the leading edge called the semiflexible region (SR). The density of filaments in the SR can increase due to nucleation of new filaments and decrease due to capping and severing of existing filaments. Following on from previous publications, we present important approximations that make the model feasible and accessible to fast computational analysis. It reveals that there are three qualitatively different parameter regimes: a stable, stationarily protruding lamellipodium; a stable lamellipodium showing oscillatory motion of the leading edge; and zero filament density and no stable lamellipodium. Hence, the model defines criteria for the existence of lamellipodia and the ability of cells to move effectively, and we discuss which parameter changes can induce transitions between the different states. Furthermore, stable lamellipodia have to be able to exert and withstand substantial forces. We can fit the experimentally measured dynamic force-velocity relation that describes how cells can adapt to increasing external forces when encountering an obstacle in their environment during motion. Moreover, we predict a different stationary force-velocity relation that should apply if cells experience a constant force, e.g. exerted by the surrounding tissue. © IOP Publishing and Deutsche Physikalische Gesellschaft.