Systems-level approach to uncovering diffusive states and their transitions from single particle trajectories

TL;DR

This paper presents advanced statistical methods, including MLE and pEMv2, to accurately identify and classify diverse diffusive states and transitions from single particle trajectories, improving analysis over traditional methods.

Contribution

It introduces a maximum likelihood estimator for complex diffusion modes and a novel pEMv2 algorithm for analyzing multiple trajectories to uncover diffusive states and transitions.

Findings

MLE improves diffusion parameter estimation.

pEMv2 effectively classifies diffusive states.

Method performance validated on simulated data.

Abstract

The stochastic motions of a diffusing particle contain information concerning the particle's interactions with binding partners and with its local environment. However, accurate determination of the underlying diffusive properties, beyond normal diffusion, has remained challenging when analyzing particle trajectories on an individual basis. Here, we introduce the maximum likelihood estimator (MLE) for confined diffusion and fractional Brownian motion. We demonstrate that this MLE yields improved estimation over traditional mean square displacement analyses. We also introduce a model selection scheme (that we call mleBIC) that classifies individual trajectories to a given diffusion mode. We demonstrate the statistical limitations of classification via mleBIC using simulated data. To overcome these limitations, we introduce a new version of perturbation expectation-maximization (pEMv2), which simultaneously analyzes a collection of particle trajectories to uncover the system of interactions which give rise to unique normal and/or non-normal diffusive states within the population. We test and evaluate the performance of pEMv2 on various sets of simulated particle trajectories, which transition among several modes of normal and non-normal diffusion, highlighting the key considerations for employing this analysis methodology.