Distributions of diffusion measures from a local mean-square displacement analysis.

In cell biology, time-resolved fluctuation analysis of tracer particles has recently gained great importance. One such method is the local mean-square displacement (MSD) analysis, which provides an estimate of two parameters as functions of time: the exponent of growth of the MSD and the diffusion coefficient. Here, we study the joint and marginal distributions of these parameters for Brownian motion with Gaussian velocity fluctuations, including the cases of vanishing correlations (overdamped Brownian motion) and of a finite negative velocity correlation (as observed in intracellular motion). Numerically, we demonstrate that a small number of MSD points is optimal for the estimation of the diffusion measures. Motivated by this observation, we derive an analytic approximation for the joint and marginal probability densities of the exponent and diffusion coefficient for the special case of two MSD points. These analytical results show good agreement with numerical simulations for sufficiently large window sizes. Our results might promote better statistical analysis of intracellular motility.