Subdiffusive 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 subdiffusive motion, fractional Brownian motion, and its physical analog, generalized Langevin equation dynamics, on the spatial localization of particles near reflecting boundaries. Results show that this type of subdiffusive 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 anticorrelated nature of motion increments that is at the core of fractional Brownian motion (or alternatively generalized Langevin equation) 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.

Probability density of the fractional Langevin equation with reflecting walls

“…Recently, Holmes [26] performed simulations of an overdamped FLE on a finite interval. In contrast to our results and in violation of the Boltzmann distribution expected in thermal equilibrium, he reports that the steady-state density is not uniform but develops depletion zones close to the boundaries.…”

Microtubules Regulate Localization and Availability of Insulin Granules in Pancreatic Beta Cells

“…Although this would be a general phenomenon in any system in which viscoelastic subdiffusion is present (46), it is specifically relevant here because of the dependence of this depletion effect on the speed of motion. The gray bars in Fig.…”

Chemical Langevin equation: A path-integral view of Gillespie's derivation

“…• The thermodynamic limit may not apply to most biochemical systems of interest, given that molecule numbers are often large but not overwhelmingly so, and that the system volume (for example, of a cell) is not large enough to prevent crowding [109][110][111][112] and boundary effects [113][114][115] from being important.…”