Challenges in determining anomalous diffusion in crowded fluids

Abstract

Anomalous diffusion in crowded fluids, e.g. in the cytoplasm of living cells, is a frequent phenomenon. Despite manifold observations of anomalous diffusion with several experimental techniques, a thorough understanding of the underlying microscopic causes is still lacking. Here, we have quantitatively compared two popular techniques with which anomalous diffusion is typically assessed. Using extensive computer simulations of two prototypical random walks with stationary increments, i.e. fractional brownian motion and obstructed diffusion, we find that single particle tracking (SPT) yields results for the diffusion anomaly that are equivalent to those obtained by fluorescence correlation spectroscopy (FCS). We also show that positional uncertainties, inherent to SPT experiments, lead to a systematic underestimation of the diffusion anomaly, regardless of the underlying random walk and measurement technique. This effect becomes particularly relevant when the position uncertainty is larger than the average positional displacement between two successive frames.

Chromosomal locus tracking with proper accounting of static and dynamic errors

“…Static error is known to cause the log-log MSD curve (which otherwise has constant slope α ) to bend upward at early times, causing potential underestimation of α [18–20]. It is easy to show that the static error presents itself as an additive offset of 2 σ 2 as in the pure Brownian case, and so the static error is sometimes accounted for by assuming an MSD of the form…”

“…Biologically oriented studies often neglect both sources of error, while more quantitative studies sometimes consider the static error but not the dynamic error. We show that the dynamic error must also be considered for anomalous diffusion, especially when the static error has been carefully removed or mitigated as the leading literature advises [18–20]. The expression presented here for the VAC in the presence of errors represents a generalization of the corresponding MSD.…”

Anomalous diffusion: Testing ergodicity breaking in experimental data

“…Several techniques including fluorescence correlation spectroscopy, single-particle tracking, and fluorescence recovery after photobleaching have been used to uncover anomalous diffusion in crowded fluids, for example, in the cytoplasm of living cells [1,2]. Ergodicity and the related Boltzmann ergodic hypothesis are the fundamental concepts in statistical physics [3].…”

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

“…This process will serve us as a basic model for a SPT. The choice of the FBM is well justified in the literature2121329303132. Now, we assume that a measurement error is given in the form of white Gaussian noise, namely i.i.d.…”