Revisiting Anomalous Diffusion Due To Molecular Crowding

Abstract

Molecular diffusion is called anomalous when the mean-squared displacement of a moving particle does not increase linearly with time. Several simulation works demonstrated anomalous diffusion, as opposed to normal (i.e., Brownian) diffusion, in crowded environments with fixed and/or mobile obstacles. Experimental measurements often report a reduction of molecular diffusion but not necessarily anomalous diffusion in the cytoplasm. Here we propose two possible reasons for the discrepancy between simulations and experiments on diffusion in crowded environments. First, some of the previously developed algorithms might not accurately simulate three-body or higher order molecular collisions in the crowded environment. To this end, we have developed an event-driven, exact collision detection algorithmic scheme and systematically studied the impact of crowding on molecular diffusion. When these higher-order collisions are explicitly taken into account, the anomalous diffusion in 3D seen with the previously developed algorithms becomes less prominent or disappears. Second, experimental analyses that suggested anomalous diffusion might have been problematic. This is particularly relevant to fluorescence correlation spectroscopy (FSC). Unlike single-particle tracking (SPT), FCS does not provide direct information about trajectories of individual molecules. It relies on the analysis of fluctuations in the number of fluorescent particles in a focused laser spot. The diffusion of molecule is inferred from the shape of the autocorrelated fluorescent signals fitted to a mathematical formula purportedly representing anomalous diffusion. However, the latter formula was derived from a modified diffusion equation, which may not have physical basis, thus leading to potentially erroneous data analysis. We propose a new FCS autocorrelation formula based on continuous time random walk theory and fractional diffusion equation. Finally, we use this new FCS formula and the novel event-driven algorithm to simulate diffusion in crowded environments and discuss possible reconciliation of discrepancies between previous simulations and experimental data.