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

Abstract

We study the force generation by a set of parallel actin filaments growing against an elastic membrane. The elastic membrane tries to stay flat and any deformation from this flat state, either caused by thermal fluctuations or due to protrusive polymerization force exerted by the filaments, costs energy. We study two lattice models to describe the membrane dynamics. In one case, the energy cost is assumed to be proportional to the absolute magnitude of the height gradient (gradient model) and in the other case it is proportional to the square of the height gradient (Gaussian model). For the gradient model we find that the membrane velocity is a nonmonotonic function of the elastic constant μ and reaches a peak at μ=μ^{*}. For μ<μ^{*} the system fails to reach a steady state and the membrane energy keeps increasing with time. For the Gaussian model, the system always reaches a steady state and the membrane velocity decreases monotonically with the elastic constant ν for all nonzero values of ν. Multiple filaments give rise to protrusions at different regions of the membrane and the elasticity of the membrane induces an effective attraction between the two protrusions in the Gaussian model which causes the protrusions to merge and a single wide protrusion is present in the system. In both the models, the relative time scale between the membrane and filament dynamics plays an important role in deciding whether the shape of elasticity-velocity curve is concave or convex. Our numerical simulations agree reasonably well with our analytical calculations.

Interplay between surface and bending energy helps membrane protrusion formation

“…3, we present our data for the variation of membrane velocity V as a function of the surface tension σ, for a fixed value of bending rigidity κ. We find that for small κ, velocity decreases monotonically with σ, as expected [27]. However, as κ is held fixed at a moderate or large value, V shows a rich behavior: starting with a non-zero value at σ = 0, V first decreases with σ and reaches a minimum and then it increases to reach a maximum before finally decreasing exponentially for large σ.…”

“…However, as κ is held fixed at a moderate or large value, V shows a rich behavior: starting with a non-zero value at σ = 0, V first decreases with σ and reaches a minimum and then it increases to reach a maximum before finally decreasing exponentially for large σ. While this non-monotonic behavior is in general interesting [27], the most intriguing observation here is that, there is a range of σ for which V grows with σ. This growth is counter-intuitive because one generally expects that with increasing surface tension, it should become more difficult for the filament to push the membrane.…”

“…As long as this constraint is satisfied, the update rules can be chosen following local detailed balance R + /R − = e −βǫ , where R + is the rate of a process that has a positive energy cost ǫ and R − is the rate of the reverse process. The filaments are modeled as rigid rod-like polymers, composed of monomers of length d [27,[36][37][38]. In Fig.…”

“…VII of [39], we have included our data for the d = δ case. There are two types of filaments in our model: a free filament, which is not in contact with the membrane, and a bound filament, whose tip is in contact with the membrane site [27,36,37,40]. The point of contact is referred to as a binding site.…”

“…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.…”