Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes

Abstract

h i g h l i g h t s• Stochastic simulations of individual and collective motion through a crowded environment. • Crowded environments populated by mixtures of obstacles of different shapes and sizes.• Transport properties depend on the obstacle volume fraction and details of the obstacle shape and size distribution. • Standard fractional diffusion equation descriptions ought to be used with care. a b s t r a c tMany biological environments are crowded by macromolecules, organelles and cells which can impede the transport of other cells and molecules. Previous studies have sought to describe these effects using either random walk models or fractional order diffusion equations. Here we examine the transport of both a single agent and a population of agents through an environment containing obstacles of varying size and shape, whose relative densities are drawn from a specified distribution. Our simulation results for a single agent indicate that smaller obstacles are more effective at retarding transport than larger obstacles; these findings are consistent with our simulations of the collective motion of populations of agents. In an attempt to explore whether these kinds of stochastic random walk simulations can be described using a fractional order diffusion equation framework, we calibrate the solution of such a differential equation to our averaged agent density information. Our approach suggests that these kinds of commonly used differential equation models ought to be used with care since we are unable to match the solution of a fractional order diffusion equation to our data in a consistent fashion over a finite time period.

Anomalous Diffusion with an Irreversible Linear Reaction and Sorption-Desorption Process

“…In particular, for species 2, we obtained different diffusive behaviors. We have also shown that the intermediated behavior exhibited by the mean square displacement before reaching the asymptotic limit depends on the choice of the parameters present in (3). We have shown the influence of the boundary condition on the system and, in this sense, we also analyzed the behavior of the survival probability for these situations and showed that it depends on the choice of the boundary conditions, that is, ( ), which is directly proportional to the flux of particles through the surface.…”

“…Examples can be found in dynamics of biological cell [1][2][3], crowding in living cell [4,5], and diffusion in random fractal geometries [6,7]. In these situations, ⟨(Δ ) 2 ⟩ ∼ ( > 1 superdiffusion and < 1 subdiffusion), in contrast to the usual diffusion characterized by the linear time growing for the mean square displacement; that is, ⟨(Δ ) 2 ⟩ ∼ .…”

Effects of soft interactions and bound mobility on diffusion in crowded environments: a model of sticky and slippery obstacles

“…Above this percolation threshold, diffusion is anomalous at long times. The effects of tracer and obstacle size [26,37,38] and adhesion and repulsion to sites adjacent to obstacles [22] on transient subdiffusion and long-time diffusion have been studied. Extensions to mobile obstacles which interact with each other have demonstrated how obstacle clustering dynamics can influence the diffusivity of tracers [39].…”

“…2b). The dynamics can be quantified using a phenomenological approximation in which the exponent α is treated as time dependent [19,26,37,38,42,53]. Thus, r 2 ∼ t α holds only over particular time scales.…”

Spatial moment description of birth-death-movement processes incorporating the effects of crowding and obstacles

“…Cell migration in living tissues involves complicated heterogeneous environments that are occupied by various biological structures and scaffolds, including macromolecules and cells of varying size, shape and adhesive properties (Ellery et al 2014; Ellery et al 2016). Such obstacles and scaffolds can have a significant impact on the migration of cells due to the interplay between crowding and cell-to-substrate adhesion (Welch 2015; Sun and Zaman 2017; Simpson and Plank 2017).…”