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

TL;DR

This study investigates how actin filaments grow against elastic membranes, revealing different behaviors in membrane velocity and stability depending on the elastic model and parameters, with implications for understanding cellular protrusions.

Contribution

It introduces two lattice models for membrane dynamics under actin filament forces, analyzing their effects on membrane velocity, stability, and protrusion interactions, which was not previously explored.

Findings

Membrane velocity peaks at a specific elastic constant in the gradient model.

The Gaussian model always reaches a steady state with decreasing velocity as elasticity increases.

Protrusions merge due to membrane elasticity, forming a single wide protrusion.

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 non-monotonic function of the elastic constant $\mu$, and reaches a peak at $\mu=\mu^\ast$. For $\mu < \mu^\ast$ 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 $\nu$ for all nonzero values of $\nu$. 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.