Note on two-point mean square displacement.

Abstract

When probe molecules of interest are embedded in a substrate 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 a living cell nucleus.