Simulation of diffusion in a crowded environment

Abstract

We performed extensive and systematic simulation studies of two-dimensional fluid motion in a complex crowded environment. In contrast to other studies we focused on cooperative phenomena that occurred if the motion of particles takes place in a dense crowded system, which can be considered as a crude model of a cellular membrane. Our main goal was to answer the following question: how do the fluid molecules move in an environment with a complex structure, taking into account the fact that motions of fluid molecules are highly correlated. The dynamic lattice liquid (DLL) model, which can work at the highest fluid density, was employed. Within the frame of the DLL model we considered cooperative motion of fluid particles in an environment that contained static obstacles. The dynamic properties of the system as a function of the concentration of obstacles were studied. The subdiffusive motion of particles was found in the crowded system. The influence of hydrodynamics on the motion was investigated via analysis of the displacement in closed cooperative loops. The simulation and the analysis emphasize the influence of the movement correlation between moving particles and obstacles.

Motion in a crowded environment: the influence of obstacles’ size and shape and model of transport

“…Slopes of the MSD curves for long time periods are approximately equal to 0.77 for the SAM model and 0.45 for the DLL model. This is more than in the case of small obstacles, where the slope was found to be 0.70 and 0.37, respectively [50,52]. This is possibly because the distribution of small obstacles is rather uniform when compared with the structure of a polymer film (like those presented in Fig.…”

“…However, one can distinguish clear differences between the two cases: for the SAM model the decrease of PAF takes place more rapidly, which is related to the lack of correlations between moving elements in this case. The correlation between moving elements in the case of the DLL model leads to a situation where some potentially movable elements become temporary obstacles [50]; therefore, the Fig. 7 The position autocorrelation function ρ(time) for various chain lengths near the percolation threshold for both models: SAM (solid symbols) and DLL (empty symbols) effect of trapping some of the moving elements in the case of a DLL is much stronger than in the case of SAM.…”

“…Simulations of such dense systems were performed using molecular dynamics and Brownian dynamics techniques employing both coarse-grained and atomistic models [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. The results of initial Monte Carlo simulations of dense systems where cooperative motions were taken under consideration were recently published [50][51][52].…”

Diffusive properties of solvent molecules in the neighborhood of a polymer chain as seen by Monte-Carlo simulations

“…60,61 The DLL model has been successfully used to characterize many complex phenomena, like: diffusion limited aggregation, 62 reaction diffusion front problems, 63 polymer solution dynamics, 64 gelation in crosslinked polymeric systems, [65][66][67][68] spinodal decomposition 69,70 and diffusion in crowed environments. 71 The Monte Carlo Step (MCS) applied to realize the DLL model in the athermal case reflects discrete time. The single MCS unit includes four operations: (1) random generation of movement attempts vectors (represented in Fig.…”

Statistical mechanics of high-density bond percolation

“…A number of physical properties of disordered materials depend on the structure of the clusters they contain. Among them are the ferromagnetism of dilute semiconductors [1], the catalytic ability of random films [2], electrolytic dissolution of binary alloys [3], diffusion in a crowded environment [4] and many others. Phase transitions in such materials often result from percolation transitions -emergence of giant cluster of specific sort, relevant for specific property of the material.…”