Inference of hopping rates of anisotropic random walk on a 2D lattice via covariance-based estimators of diffusion parameters

TL;DR

This paper extends covariance-based estimators to infer hopping rates of anisotropic 2D random walks from trajectory data, providing a robust method that accounts for noise and motion blur.

Contribution

It introduces a novel extension of covariance-based estimators to two-dimensional biased random walks, linking hopping rates to higher-order moments of displacements.

Findings

Estimator accurately infers hopping rates from noisy data

Method is robust against motion blur

Numerical simulations validate the approach

Abstract

Traditionally, time-development of the mean square displacement has been employed to determine the diffusion coefficient from the trajectories of single particles. However, this approach is sensitive to the noise and the motion blur upon image acquisition. Recently, Vestergaard et al. has proposed a novel method based on the covariance between the shifted displacement series. This approach gives a more robust estimator of the diffusion coefficient of one-dimensional diffusion without bias, i.e., when mean velocity is zero. Here, we extend this approach to a potentially biased random walk on a two-dimensional lattice. First, we describe the relationship between the hopping rates to the eight adjacent sites and the time development of the higher-order moments of the stochastic two-dimensional displacements. Then, we derive the covariance-based estimators for these higher-order moments. Numerical simulations confirmed that the procedure presented here allows inference of the stochastic hopping rates from two-dimensional trajectory data with location error and motion blur.