Static vs dynamic rough energy landscapes: Where is diffusion faster?

TL;DR

This paper introduces a discrete-state model for molecules diffusing in environments with both spatial and temporal energy fluctuations, revealing that many dynamic features are unaffected by fluctuation timescales and align with static landscape models.

Contribution

The study develops a unified model of fluctuating energy landscapes that includes back-reaction effects, bridging static and dynamic perspectives on diffusion.

Findings

Many observable dynamics are independent of temporal fluctuation timescales.

Static rough potential models capture key features of dynamic landscapes.

Back-reaction effects are significant in the model.

Abstract

Molecules in dense environments, such as biological cells, are subjected to forces that fluctuate both in time and in space. While spatial fluctuations are captured by Lifson-Jackson-Zwanzig's model of "diffusion in a rough potential", and temporal fluctuations are often viewed as leading to additional friction effects, a unified view where the environment fluctuates both in time and in space is currently lacking. Here we introduce a discrete-state model of a landscape fluctuating both in time and in space. Importantly, the model accounts for the back-reaction of the diffusing particle on the landscape. As a result we find, surprisingly, that many features of the observable dynamics do not depend on the temporal fluctuation timescales and are already captured by the model of diffusion in a rough potential, even though this assumes a static energy landscape.