Estimating the anomalous diffusion exponent for single particle tracking data with measurement errors - An alternative approach.

Krzysztof Burnecki,Yuval Garini,Grzegorz Sikora,Aleksander Weron,Eldad Kepten

doi:10.1038/srep11306

Abstract

Accurately characterizing the anomalous diffusion of a tracer particle has become a central issue in biophysics. However, measurement errors raise difficulty in the characterization of single trajectories, which is usually performed through the time-averaged mean square displacement (TAMSD). In this paper, we study a fractionally integrated moving average (FIMA) process as an appropriate model for anomalous diffusion data with measurement errors. We compare FIMA and traditional TAMSD estimators for the anomalous diffusion exponent. The ability of the FIMA framework to characterize dynamics in a wide range of anomalous exponents and noise levels through the simulation of a toy model (fractional Brownian motion disturbed by Gaussian white noise) is discussed. Comparison to the TAMSD technique, shows that FIMA estimation is superior in many scenarios. This is expected to enable new measurement regimes for single particle tracking (SPT) experiments even in the presence of high measurement errors.

Highlights

Defined here for a trajectory x(t) of length T and the averaging window is τ
We present a comprehensive comparison of the new estimator αFIMA which is obtained by equation (11), with the classical estimator αTAMSD, given by equation (6), based on the time-averaged mean square displacement
Let us notice that both methods often underestimate true values of the anomalous exponent

Summary

Introduction

Defined here for a trajectory x(t) of length T and the averaging window is τ. The second error arises from the inherent measurement error in any experimental procedure[26] This has been shown to insert a bias towards lower α values at short times[27]. Fitting single particle TAMSDs results in anomalous exponents lower than the true physical process. It has been shown that this bias continues even to times where the TAMSD is larger than the measurement noise standard deviation. This effect cannot be corrected through ensemble averaging or measurement of longer trajectories and can be mitigated only under special conditions[28].

Methods

Results

Conclusion