Dynamics of a membrane interacting with an active wall

TL;DR

This paper investigates how a biological membrane's dynamics are affected by hydrodynamic interactions with an active wall, revealing unique membrane fluctuation behaviors and mean squared displacement growth patterns.

Contribution

It derives a dynamic equation for membrane fluctuations interacting with active walls and analyzes the resulting correlation functions and MSD behaviors under different wall activity conditions.

Findings

MSD exhibits $t^{2/3}$ and $t^{1/3}$ regimes for static walls.

Active walls induce a linear MSD growth at early times.

Finite intrinsic time scales in active walls extend the linear MSD regime.

Abstract

Active motions of a biological membrane can be induced by non-thermal fluctuations that occur in the outer environment of the membrane. We discuss the dynamics of a membrane interacting hydrodynamically with an active wall that exerts random velocities on the ambient fluid. Solving the hydrodynamic equations of a bound membrane, we first derive a dynamic equation for the membrane fluctuation amplitude in the presence of different types of walls. Membrane two-point correlation functions are calculated for three different cases; (i) a static wall, (ii) an active wall, and (iii) an active wall with an intrinsic time scale. We focus on the mean squared displacement (MSD) of a tagged membrane describing the Brownian motion of a membrane segment. For the static wall case, there are two asymptotic regimes of MSD ($\sim t^{2/3}$ and $\sim t^{1/3}$) when the hydrodynamic decay rate changes monotonically. In the case of an active wall, the MSD grows linearly in time ($\sim t$) in the early stage, which is unusual for a membrane segment. This linear-growth region of the MSD is further extended when the active wall has a finite intrinsic time scale.