Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium

TL;DR

This paper compares the effects of different types of diffusion slowdown on ligand-binding equilibrium in membranes, revealing that anomalous and slowed-down Brownian diffusion have distinct impacts on reaction affinity.

Contribution

It demonstrates through theory and simulations that anomalous diffusion and slowed-down Brownian motion differently influence ligand-binding affinity in membranes.

Findings

Continuous-time random walks decrease apparent affinity.

Locally slowed-down Brownian motion increases affinity.

Affinity is maximized when slowdown is localized.

Abstract

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) which converges back to a Brownian motion with reduced diffusion coefficient at long times, after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed-down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in 2d. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte-Carlo simulations, we show that those three scenarios have distinctive effects on the apparent affinity of the reaction. While continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hinderance by obstacles both improve it. However, only in the case of slowed-down Brownian motion, the affinity is maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.