Note on two-point mean square displacement

TL;DR

This paper analyzes two-point mean square displacement methods to better understand probe mobility, non-Gaussian behavior, and correlations, with applications to polymer and chromatin dynamics in cells.

Contribution

It introduces a comparative analysis of two two-point MSD methods and proposes techniques to extract non-Gaussianity and probe correlations.

Findings

Two-point MSD methods differ in properties and applications.

Proposed methods can quantify non-Gaussianity in displacement.

Application to polymer and chromatin reveals insights into intracellular dynamics.

Abstract

When probe molecules of interest are embedded in a container or aggregate under stochastic motion, one needs to rely on the so-called two-point mean square displacement (MSD) measurement to extract the intrinsic mobility of the probes. We discuss two versions, based on the time series of relative vector or distance between two probes, and summarize their basic properties compared to the standard MSD. We also propose a way to extract (i) the non-Gaussianity in the displacement statistics and (ii) the motional correlation between probes from the two-point MSD. The results are presented not only for independent probes, but also for intramolecular probes within a long polymer, which could be useful in quantifying the dynamics of chromatin loci in living cell nucleus.