Sub-Diffusive Dynamics Lead to Depleted Particle Densities Near Cellular Borders

Abstract

It has long been known that the complex cellular environment leads to anomalous motion of intracellular particles. At a gross level, this is characterized by mean squared displacements that deviate from the standard linear profile. Statistical analysis of particle trajectories has helped further elucidate how different characteristics of the cellular environment can introduce different types of anomalousness. A significant majority of this literature has however focused on characterizing the properties of trajectories that do not interact with cell borders (e.g. cell membrane or nucleus). Numerous biological processes ranging from protein activation to exocytosis however require particles to be near a membrane. This study investigates the consequences of a canonical type of sub-diffusive motion, Fractional Brownian Motion (FBM), and its physical analogue Generalized Langevin Equation (GLE) Dynamics, on the spatial localization of particles near reflecting boundaries. Results show that this type of sub-diffusive motion leads to the formation of significant zones of depleted particle density near boundaries, and that this effect is independent of the specific model details encoding those dynamics. Rather these depletion layers are a natural and robust consequence of the anti-correlated nature of motion increments that is at the core of FBM / GLE dynamics. If such depletion zones are present, it would be of profound importance given the wide array of signaling and transport processes that occur near membranes. If not, that would suggest our understanding of this type of anomalous motion may be flawed. Either way, this result points to the need to further investigate the consequences of anomalous particle motions near cell borders from both theoretical and experimental perspectives.