Abstract
Single particle tracking is an essential tool in the study of complex systems and biophysics and it is commonly analyzed by the time-averaged mean square displacement (MSD) of the diffusive trajectories. However, past work has shown that MSDs are susceptible to significant errors and biases, preventing the comparison and assessment of experimental studies. Here, we attempt to extract practical guidelines for the estimation of anomalous time averaged MSDs through the simulation of multiple scenarios with fractional Brownian motion as a representative of a large class of fractional ergodic processes. We extract the precision and accuracy of the fitted MSD for various anomalous exponents and measurement errors with respect to measurement length and maximum time lags. Based on the calculated precision maps, we present guidelines to improve accuracy in single particle studies. Importantly, we find that in some experimental conditions, the time averaged MSD should not be used as an estimator.
Highlights
The analysis of single particle trajectories has become a standard procedure in the analysis of experimental and theoretical systems [1,2,3,4,5,6,7]
In what follows we study the performance of the time averaged mean square displacement (TAMSD) as an estimator for the anomalous exponent, depending on trajectory length, measurement error and the true anomalous exponent
The results allows us to identify an optimal M in each case and by taking all the extracted information together, we identify several guidelines, or best practices, for fitting of anomalous TAMSDs
Summary
The analysis of single particle trajectories has become a standard procedure in the analysis of experimental and theoretical systems [1,2,3,4,5,6,7]. Since cellular environments are complex microscopic systems with a strong thermal component [17], the motion of single particles, even if directed, incorporates a random diffusive component, which must be characterized in order to build a physical picture of the system [18,19,20,21,22,23,24]. A common tool by which the diffusion of a single particle is classified is the time averaged mean square displacement (TAMSD) [14,15,16,17, 25,26,27,28,29,30,31]: d2 ðtÞ 1⁄4. On the Fitting of Anomalous Diffusion Mean Square Displacement Graphs
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