Crawling of a driven adherent membrane

Abstract

We discuss motions of an elastic N × M membrane model whose constituents can bind reversibly with strength ε to adhesive sites of a flat substrate. One of the edges of the membrane ("front") is driven in one direction at rate constant p by N stochastically treadmilling short parallel lines ("cortex"). The main conclusions derived from Monte Carlo studies of this model are the following: (a) Since the polymerizing cortex pushes only the leading edge of the membrane, the major part of the membranes is dragged behind. Therefore, the locomotion of the membrane can be described by frictional sliding processes which are asymmetrically distributed between front and rear of the membrane. A signature of this asymmetry is the difference between the life times of adhesion bonds at front and rear, τ(1) and τ(M), respectively, where τ(1) ≫ τ(M). (b) There are four characteristic times for the membrane motion: The first time, T(0) ~ τ(M) ~ e(aε), is the resting time where the displacement of the membrane is practically zero. The second time, T(p) ~ τ(1) ~ M, is the friction time which characterizes the time between two consecutive ruptures of adhesion bonds at the front, and which signalizes the onset of drift ("protrusion") at the leading edge. The third time, T(r) ~ M(γ(ε)) (γ > 1), characterizes the "retraction" of the trailing edge, which is the retarded response to the pulling leading edge. The fourth time, T(L) ~ M(2), is the growth time for fluctuation of the end-to-end distance. (c) The separation of time scales, T(r)/T(p) ~ M(γ(ε) - 1), leads to stretched fluctuations of the end-to-end distance, which are considered as stochastic cycles of protrusion and retraction on the time scale of T(L). (d) The drift velocity v obeys anomalous scaling, v/p~f(p(1/γ(ε))M), where f(z) ~ const. for small drag pM ≪ 1, and f(z) ~ z(-γ(ε)) for pM ≫ 1, which implies v~M(-γ(ε)). These results may also turn out to be useful for the (more difficult) problem of understanding the protrusion-retraction cycle of crawling biological cells. We compare our model and our results to previous two-particle theories for membrane protrusion and to known stochastic friction models.

A Review of Fast Bubble-Driven Micromotors Powered by Biocompatible Fuel: Low-Concentration Fuel, Bioactive Fluid and Enzyme

“…However, most photocatalytic reactions cannot efficiently generate abundant bubbles to enable the autonomous motion of micromotors. Some kinds of active metals, like potassium, calcium, and sodium, are too violent in their water-splitting reactions to be contained in the design of micromotors; however, magnesium [ 76 ] and aluminum (Al) are rather stable due to the formation of a passivation layer on the surface [ 77 ]. Consequently, the problem of the passivation layer must be carefully dealt with to make both metals reactive.…”

Actin filaments growing against an elastic membrane: Effect of membrane tension

“…Towards the end of the paper, we present a discussion on this. In our second model, the membrane is described as a Gaussian surface with the Hamiltonian [16,20]…”

Interplay between surface and bending energy helps membrane protrusion formation

“…In the absence of any external force, the height profile of the membrane follows an equilibrium dynamics with the Helfrich Hamiltonian, which is standardly used to describe the height fluctuations of a plasma membrane [12,[14][15][16]. This Hamiltonian consists of surface interaction and bending interaction of the membrane and in our lattice model, it has the form [29][30][31][32]…”

“…Any variation in the height costs energy and a flat membrane corresponds to the lowest energy configuration. We consider the membrane being pushed by few growing filaments, which tend to create protrusions in the membrane that cost energy [27][28][29][30]. As surface tension σ or bending rigidity κ of the membrane is increased, one would expect that protrusion formation should become more difficult, since the energy cost for creating a protrusion ought to go up monotonically with σ and κ.…”