Resampling single-particle tracking data eliminates localization errors and reveals proper diffusion anomalies.

Abstract

Single-particle tracking (SPT) is a versatile tool for quantifying diffusional motion in complex soft-matter systems, e.g., in biological specimen. Evaluating SPT data often invokes the fitting of a trajectory's time-averaged mean-square displacement (TA-MSD) with a simple power law, 〈r^{2}(τ)〉_{t}∼τ^{α}, where the scaling exponent α can yield important insights into the nature of the transport process. Biological specimen, for example, frequently feature a diffusion anomaly, i.e., an exponent α<1 ("subdiffusion"). However, due to SPT-inherent static and dynamic localization errors, in combination with typically short trajectories, it is often a real challenge to determine the value of α reliably by simply fitting TA-MSDs. Here a straightforward resampling approach is presented and tested that eliminates both localization errors in the TA-MSD of trajectories originating from subdiffusive fractional Brownian motion processes. As a result, the mean anomaly exponent 〈α〉_{E} of an ensemble of trajectories is revealed in a robust fashion.