Unravelling Heterogeneous Transport of Endosomes

TL;DR

This paper models the complex, heterogeneous transport of endosomes within cells using a novel spatio-temporal fractional Brownian motion framework, supported by extensive experimental data and advanced deep learning analysis.

Contribution

It introduces a new mathematical model (hFBM) for endosome transport, combining experimental analysis with deep learning to characterize heterogeneity in cellular processes.

Findings

Endosome motion follows power-law distributions of displacements.

Local anomalous exponents are exponentially distributed.

Generalized diffusion coefficients follow power-law distributions.

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.