# Interplay between surface and bending energy helps membrane protrusion formation

## TL;DR

This study investigates how the combined effects of surface and bending energies influence membrane protrusion formation, revealing counterintuitive behavior where increased surface tension can facilitate protrusions.

## Contribution

It uncovers the nontrivial interplay between surface and bending energies in membrane dynamics, explaining unusual protrusion formation behavior.

## Key findings

- Protrusions form more easily with higher surface tension at fixed bending rigidity.
- Membrane velocity exhibits a dip and peak as a function of surface tension.
- Shape changes in the membrane are driven by energy interplay.

## Abstract

We consider a one-dimensional elastic membrane, which is pushed by growing filaments. The filaments tend to grow by creating local protrusions in the membrane and this process has surface energy and bending energy costs. Although it is expected that with increasing surface tension and bending rigidity, it should become more difficult to create a protrusion, we find that for a fixed bending rigidity, as the surface tension increases, protrusions are more easily formed. This effect also gives rise to nontrivial dependence of membrane velocity on the surface tension, characterized by a dip and a peak. We explain this unusual phenomenon by studying in detail the interplay of the surface and the bending energy and show that this interplay is responsible for a qualitative shape change of the membrane, which gives rise to the above effect.