Unraveling trajectories of diffusive particles on networks

Abstract

The analysis of single-particle trajectories plays an important role in elucidating dynamics within complex environments such as those found in living cells. However, the characterization of intracellular particle motion is often confounded by confinement of the particles within nontrivial subcellular geometries. Here we focus specifically on the case of particles undergoing Brownian motion within a network of narrow tubules, as found in some cellular organelles. A computational unraveling algorithm is developed to uncouple particle motion from the confining network structure, allowing for an accurate extraction of the underlying one-dimensional diffusion coefficient, as well as differentiating between Brownian and fractional Langevin motion. We validate the algorithm with simulated trajectories and then highlight its application to an example system: analyzing the motion of membrane proteins confined in the tubules of the peripheral endoplasmic reticulum in mammalian cells. We show that these proteins undergo diffusive motion and provide a quantitative estimate of their diffusion coefficient. Our algorithm provides a generally applicable approach for disentangling geometric morphology and particle dynamics in networked architectures.