# Dynamics of a Bilayer Membrane Coupled to a Two-dimensional Cytoskeleton: Scale Transfers of Membrane Deformations

## TL;DR

This paper models the complex dynamics of a lipid bilayer membrane coupled with a cytoskeleton, revealing how microscopic interactions influence large-scale membrane deformations and relaxation behaviors.

## Contribution

It introduces a theoretical framework accounting for lattice structure, intermonolayer friction, and prestress, highlighting their effects on membrane dynamics and mode coupling.

## Key findings

- Long-wavelength deformations excite short-wavelength modes.
- Slow relaxation is dominated by intermonolayer friction.
- Long-term forces can induce large-scale membrane responses.

## Abstract

We theoretically investigate the dynamics of a floating lipid bilayer membrane coupled with a two-dimensional cytoskeleton network, taking into explicitly account the intermonolayer friction, the discrete lattice structure of the cytoskeleton, and its prestress. The lattice structure breaks lateral continuous translational symmetry and couples Fourier modes with different wavevectors. It is shown that within a short time interval a long-wavelength deformation excites a collection of modes with wavelengths shorter than the lattice spacing. These modes relax slowly with a common renormalized rate originating from the long-wavelength mode. As a result, and because of the prestress, the slowest relaxation is governed by the intermonolayer friction. Reversely, and most interestingly, forces applied at the scale of the cytoskeleton for a sufficiently long time can cooperatively excite large-scale modes.