Unravelling Heterogeneous Transport of Endosomes

Abstract

A major open problem in biophysics is to understand the highly heterogeneous transport of many structures inside living cells, such as endosomes. We find that mathematically it is described by spatio-temporal heterogeneous fractional Brownian motion (hFBM) which is defined as FBM with a randomly switching anomalous exponent and random generalized diffusion coefficient. Using a comprehensive local analysis of a large ensemble of experimental endosome trajectories (> 10 5 ), we show that their motion is characterized by power-law probability distributions of displacements and displacement increments, exponential probability distributions of local anomalous exponents and power-law probability distributions of local generalized diffusion coefficients of endosomes which are crucial ingredients of spatio-temporal hFBM. The increased sensitivity of deep learning neural networks for FBM characterisation corroborates the development of this multi-fractal analysis. Our findings are an important step in understanding endosome transport. We also provide a powerful tool for studying other heterogeneous cellular processes.

Local Analysis of Heterogeneous Intracellular Transport: Slow and Fast moving Endosomes

“…Notice that two sub-diffusive regimes characterize the MSD time behavior for fast and all trajectories. The first, at small time scales (t ≤ 10 −1 s) can be attributed to the measurement errors [42,45,46]; the second, at longer time scales (t > 10 s) was shown to be spurious and originate from the coupling of the trajectories' duration and their diffusivities [39,43]. We suggest that, due to this coupling, the anomalous exponents deduced from the power-law fit of EMSD and E-TMSD, do not capture the essential characteristics of the endosome superdiffusive motility, nor shed light on its fundamental aspects.…”

“…We suggest that, due to this coupling, the anomalous exponents deduced from the power-law fit of EMSD and E-TMSD, do not capture the essential characteristics of the endosome superdiffusive motility, nor shed light on its fundamental aspects. Therefore, in order to reveal the effect of the duration of trajectories on the statistical analysis, we consider only trajectories longer than a certain threshold T [39].…”

“…Thus, it was possible to track the centres of endosomes with sub-pixel accuracy, but not the sizes of the smaller endosomes (less than 200 nm). The duration of all trajectories, T , has a good fit to a power law distribution, T −1.85 [39], which is a manifestation of the heterogeneity of the trajectories. Slow moving endosomes stay longer within the observation volume and therefore have longer trajectories than fast moving endosomes, leading to the emergence of the power-law probability distribution for the trajec-tories’ duration.…”

“…Recently, the intracellular transport of endosomes in eukaryotic cells was shown to be described by spatio-temporal heterogeneous fractional Brownian motion (hFBM) with non-constant Hurst exponents [39]. By analysing the local motion of endosomes, we found that it is characterized by power-law probability distributions of displacements and displacement increments, exponential probability distributions of local anomalous exponents and power-law probability distributions of local generalized diffusion coefficients.…”

“…In this paper, we split the ensemble of endosomes into slow and fast moving vesicles which is the main difference between this study and Ref. [39]. This splitting allows us to study sub-ensembles separately in addition to studying of the ATP driven active transport of endosomes.…”