Improved estimation of anomalous diffusion exponents in single particle tracking experiments

TL;DR

This paper introduces a method to accurately estimate anomalous diffusion exponents in single particle tracking by correcting measurement errors and heterogeneity effects, enabling analysis of short, noisy data sets.

Contribution

The authors develop a novel correction technique for measurement errors and heterogeneity, improving the estimation of anomalous diffusion parameters in single particle tracking experiments.

Findings

Corrected estimation method reduces bias in diffusion exponent measurement.

Method successfully characterizes heterogeneity in particle populations.

Applied to telomere data, reveals subdiffusive behavior with normally distributed exponents.

Abstract

The Mean Square Displacement is a central tool in the analysis of Single Particle Tracking experiments, shedding light on various biophysical phenomena. Frequently, parameters are extracted by performing time-averages on single particle trajectories followed by ensemble averaging. This procedure however, suffers from two systematic errors when applied to particles that perform anomalous diffusion. The first is significant at short time lags and is induced by measurement errors. The second arises from the natural heterogeneity in biophysical systems. We show how to estimate and correct these two errors and improve the estimation of the anomalous parameters for the whole particle distribution. As a consequence we manage to characterize ensembles of heterogeneous particles even for rather short and noisy measurements where regular time averaged mean square displacement analysis fails. We apply this method to both simulations and in vivo measurements of telomere diffusion in 3T3 mouse embryonic fibroblast cells. The motion of telomeres is found to be subdiffusive with an average exponent constant in time. Individual telomere exponents are normally distributed around the average exponent. The proposed methodology has the potential to improve experimental accuracy while maintaining lower experimental costs and complexity.