Diffusion of tagged particles in a crowded medium

Abstract

The influence of crowding on the diffusion of tagged particles in a dense medium is investigated in the framework of a mean-field model, derived in the continuum limit from a microscopic stochastic process with exclusion. The probability distribution function of the tagged particles obeys to a nonlinear Fokker-Planck equation, where the drift and diffusion terms are determined self-consistently by the concentration of crowders in the medium. Transient sub-diffusive or super-diffusive behaviours are observed, depending on the selected initial conditions, that bridge normal diffusion regimes characterized by different diffusion coefficients. These anomalous crossovers originate from the microscopic competition for space and reflect the peculiar form of the non-homogeneous advection term in the governing Fokker-Planck equation. Our results strongly warn against the overly simplistic identification of crowding with anomalous transport tout court.

Multiscale Modeling of Diffusion in a Crowded Environment

“…In [12, 24, 60] it was shown that diffusion in a crowded environment can be modeled by a temporal change of the diffusion constant. First the molecule diffuses normally with rate γ 0 for very short time-scales, before it undergoes a transient anomalous phase with a changing diffusion coefficient γ and finally stagnates into normal diffusion at a lower diffusion rate γ ∞ .…”

Macroscopic Transport Equations in Many-Body Systems from Microscopic Exclusion Processes in Disordered Media: A Review

“…Only for inequivalent sites and/or in the presence of a field the microscopic exclusion constraint does survive in the mean-field limit. Different is the case of multiple species [86] or recognizable agents [34], where crossterms appear in the mean field limit due to the fact that particles are made distinguishable. In general, we can state that crowding reflects in the macroscopic limit of the point-like description only if some degree of inhomogeneity is enforced at the microscopic level.…”

“…In fact, despite meanfield descriptions for the inhomogeneous ASEP are known to provide imperfect descriptions of certain non-equilibrium observables in one dimension, e.g., the current-density relation and critical exponents [71], continuum descriptions can be employed reliably to track the time-evolution of large-wavelength density fluctuations [34,[72][73][74][75][76][77][78] …”

“…However, strong evidences also exist in favor of normal (Brownian) diffusion, crowding, and confinement resulting in this scenario in (often nontrivial) modifications of the diffusion coefficient [10,27,32,33]. Moreover, as shown in Galanti et al [34], the effect of crowding can result in crossovers between normal and anomalous diffusion, leading to different descriptive scenarios which appear to depend on the selected initial conditions and on the specific time scale of observation.…”

Crowding in Cellular Environments at an Atomistic Level from Computer Simulations

“…122 Anomalous diffusion results in diffusion rates varying on different time scales due to confinement within cellular compartments and caging effects due to temporary encapsulation by larger crowders. 34,123,125−128 However, details of how diffusion is modulated by different cellular microenvironments and by the presence of DNA or membrane surfaces have remained unclear. 77 There is also an incomplete understanding of how smaller molecules, metabolites and other ligands navigate the dense cellular environments where available space is not just limited and solvent viscosity may be altered but where the various macromolecular surfaces also provide ample opportunities for distractions that could, for example, slow down diffusion toward an enzyme active site.…”