Lateral Diffusion and Percolation in Membranes

Sung, Bong June; Yethiraj, Arun

doi:10.1103/physrevlett.96.228103

Cited by 54 publications

(59 citation statements)

References 26 publications

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“…Simple comparison of our results with the results obtained using the continuous model in 2D places them between the results obtained for the Lorentz gas model 33 and the results found using the discontinuous molecular dynamic model. 40 It was also found that the diffusion coefficient for a long time near the percolation threshold scales as D z 3 m where 3 ¼ |c À c c |/c c with m z 4.34. This value of the exponent m is different from the pervious prediction obtained from the percolation theory and simulations, 50 where m ¼ 1.31.…”

Section: Discussionmentioning

confidence: 97%

Simulation of diffusion in a crowded environment

Polanowski

Sikorski

2014

Soft Matter

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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.

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Section: Discussionmentioning

confidence: 97%

Simulation of diffusion in a crowded environment

Polanowski

Sikorski

2014

Soft Matter

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“…In particular, we perform computations for spheroids whose exact values of α are known. Even though we are not concerned with the critical behavior of the system (the latter was recently studied for overlapping spheres 12,14 and for hard spheres and large-size tracers 15 ), we did perform accurate computations of percolation thresholds because this allowed us to assess the accuracy of approximation (1) without resorting to fitting. Having accurate estimates of V c also made it possible to verify the existence of a universal curve for diffusivities in two and three dimensions.…”

Section: Introductionmentioning

confidence: 99%

Diffusion amid random overlapping obstacles: Similarities, invariants, approximations

Novak

Gao

Kraikivski

et al. 2011

The Journal of Chemical Physics

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Efficient and accurate numerical techniques are used to examine similarities of effective diffusion in a void between random overlapping obstacles: essential invariance of effective diffusion coefficients (D eff ) with respect to obstacle shapes and applicability of a two-parameter power law over nearly entire range of excluded volume fractions (φ), except for a small vicinity of a percolation threshold. It is shown that while neither of the properties is exact, deviations from them are remarkably small. This allows for quick estimation of void percolation thresholds and approximate reconstruction of D eff (φ) for obstacles of any given shape. In 3D, the similarities of effective diffusion yield a simple multiplication "rule" that provides a fast means of estimating D eff for a mixture of overlapping obstacles of different shapes with comparable sizes.

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“…For example, recent theoretical advancements have extended Saxton's lattice-based results to lattice-free frameworks [30,35,36], including studying the role of obstacle orientation [37]. Progress has also been made by combining experimental and theoretical approaches, for example, studying overlapping circular and elliptical obstacles [38] and studying more complicated environments containing up to 15 different types of obstacles [31].…”

Section: Introductionmentioning

confidence: 97%

“…Such FDE models have been analyzed in various biological settings including chemical reactions [23], reaction fronts [22,24] and reaction-diffusion mechanisms [25]. We would like to emphasize that the group of studies described here, focusing explicitly on motion through crowded environments using experimental and simulation data [30][31][32][33][35][36][37][38][39], have not attempted to interpret their results using any kind of FDE framework. Conversely, the group of studies described here focusing on FDE models [21][22][23][24][25] have not attempted to connect the solution of any FDE model to measurements from any simulation or experiment which explicitly represents transport through a crowded environment.…”

Section: Introductionmentioning

confidence: 98%

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

Ellery

Baker

McCue

et al. 2016

Physica A: Statistical Mechanics and its Applications

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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.

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Lateral Diffusion and Percolation in Membranes

Cited by 54 publications

References 26 publications

Simulation of diffusion in a crowded environment

Simulation of diffusion in a crowded environment

Diffusion amid random overlapping obstacles: Similarities, invariants, approximations

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

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