Noise-induced drift in two-dimensional anisotropic systems

TL;DR

This paper investigates how particles drift in two-dimensional anisotropic systems with spatially varying diffusivity, revealing a new drift effect from principal axes rotation and confirming findings with simulations.

Contribution

It derives a general expression for noise-induced drift in 2D anisotropic systems, including a novel effect from principal axes rotation, extending previous 1D results.

Findings

Derived a general mean displacement expression for 2D anisotropic systems.

Identified a new drift effect from principal axes rotation.

Simulated protein diffusion showing rapid increase in inter-protein distance.

Abstract

We study the isothermal Brownian dynamics of a particle in a system with spatially varying diffusivity. Due to the heterogeneity of the system, the particle's mean displacement does not vanish even if it does not experience any physical force. This phenomenon has been termed "noise-induced drift", and has been extensively studied for one-dimensional systems. Here, we examine the noise-induced drift in a two-dimensional anisotropic system, characterized by a symmetric diffusion tensor with unequal diagonal elements. A general expression for the mean displacement vector is derived and presented as a sum of two vectors, depicting two distinct drifting effects. The first vector describes the tendency of the particle to drift toward the high diffusvity side in each orthogonal principal diffusion direction. This is a generalization of the well-known expression for the noise-induced drift in one-dimensional systems. The second vector represents a novel drifting effect, not found in one-dimensional system, originating from the spatial rotation in the directions of the principal axes. The validity of the derived expressions is verified by using Langevin dynamics simulations. As a specific example, we consider the relative diffusion of two transmembrane proteins, and demonstrate that the average distance between them increases at a surprisingly fast rate of several tens of micrometers per second.