Single-Particle Tracking Analysis using the Radius of Gyration Tensor, Revisited

Abstract

A key problem in the analysis of trajectories from two-dimensional single-particle tracking experiments is distinguishing actual structure due to anomalous subdiffusion, confinement, or directed motion from apparent structure due to fluctuations in random walks. To better analyze these trajectories we examine properties of descriptors based on the radius of gyration tensor of the trajectory. This work revisits and updates my work [Saxton, Biophys J 64 (1993) 1776] and work from the Amblard laboratory [Coscoy et al., Bull Math Biol 69 (2007) 2467]. The descriptors are chosen to be the time-scaled eigenvalues of the radius of gyration tensor. Both individual and joint probability density functions of the descriptors are considered, using analytical results from the literature and Monte Carlo simulations. Particular attention is paid to the time scaling of the histograms so one can easily obtain the histogram for a given number of experimental time steps.The current view in the physics literature on single-particle tracking is that the analysis should be done entirely in terms of the displacement over single time steps, Δt = 1. This approach is clearly appropriate for pure random walks. These are Markovian, and displacements for Δt > 1 by definition cannot add any information. But for non-Markovian motion, Δt > 1 is directly relevant, as the method of Thiel et al. [PRL 111 (2013) 010601] to identify the mechanism of anomalous diffusion by scaling analysis of displacements over pairs of Δt's. Biophysically interesting forms of non-Markovian motion include directed motion, which is positively correlated; anomalous subdiffusion, which is anticorrelated on all time scales; and confined motion, which is anticorrelated on the time scales of individual collisions with the corral walls and diffusive crossing of the corral. (Supported in part by NIH grant GM038133)