Lateral diffusion and percolation in membranes

First-passage behavior of the random-barrier model

The previously proposed transport equation for the random-barrier model, which is the diffusion equation with resetting to positions visited in the past, is used here to calculate the first-passage times. The results obtained are compared with those obtained using the normal diffusion equation with an effective diffusion coefficient. It is shown that, under certain conditions, the equation with the effective diffusion coefficient can greatly overestimate the time of the first passage. In particular, the rate constant of a bimolecular diffusion-controlled reaction calculated from this equation can be significantly lower than the actual rate. This result can serve as one of the possible explanations for the high rates of diffusion-controlled reactions observed in an experiment.

Pore Filled Ion-Conducting Materials Based on Track-Etched Membranes and Sulfonated Polystyrene

Abstract

Synthesis of proton-conducting materials based on track-etched membranes from polyvinylidene fluoride and sulfonated cross-linked polystyrene is described. The synthesis has been carried out by filling the pores of the original or gamma-irradiated track-etched membrane by copolymerization of styrene/divinylbenzene followed by sulfonation of polystyrene with chlorosulfonic acid. The resulting membranes have been studied by scanning electron microscopy and ATR IR spectroscopy. Membrane ionic conductivity, hydrogen gas permeability, ion-exchange capacity, and water absorption were measured. The ionic conductivity at 30°C reaches 51.7 mS/cm, which is almost three times higher than for Nafion®212 membranes; however, the gas permeability of the obtained materials also increases simultaneously.

Molecular transport in systems containing binding obstacles

We studied the movement of particles in crowded environments by means of extensive Monte Carlo simulations. The dynamic lattice liquid model was employed for this purpose. It is based on the cooperative movement concept and allows the study of systems at high densities. The cooperative model of molecular transport is assumed: the motion of all moving particles is highly correlated. The model is supposed to mimic lateral motion in a membrane and therefore the system is two-dimensional with moving objects and traps placed on a triangular lattice. In our study the interaction (binding) of traps with moving particles was assumed. The conditions in which subdiffusive motion appeared in the system were analysed. The influence of the strength of binding on the dynamic percolation threshold was also shown. The differences in the dynamics compared to systems with impenetrable obstacles and with systems without correlation in motion were presented and discussed. It was shown that in the case of correlated motion the influence of deep traps is similar to that of impenetrable obstacles. If the traps are shallow a recovery to normal diffusion was observed for longer time periods.

Understanding biochemical processes in the presence of sub-diffusive behavior of biomolecules in solution and living cells

In order to maintain cellular function, biomolecules like protein, DNA, and RNAs have to diffuse to the target spaces within the cell. Changes in the cytosolic microenvironment or in the nucleus during the fulfillment of these cellular processes affect their mobility, folding, and stability thereby impacting the transient or stable interactions with their adjacent neighbors in the organized and dynamic cellular interior. Using classical Brownian motion to elucidate the diffusion behavior of these biomolecules is hard considering their complex nature. The understanding of biomolecular diffusion inside cells still remains elusive due to the lack of a proper model that can be extrapolated to these cases. In this review, we have comprehensively addressed the progresses in this field, laying emphasis on the different aspects of anomalous diffusion in the different biochemical reactions in cell interior. These experiment-based models help to explain the diffusion behavior of biomolecules in the cytosolic and nuclear microenvironment. Moreover, since understanding of biochemical reactions within living cellular system is our main focus, we coupled the experimental observations with the concept of sub-diffusion from in vitro to in vivo condition. We believe that the pairing between the understanding of complex behavior and structure-function paradigm of biological molecules would take us forward by one step in order to solve the puzzle around diseases caused by cellular dysfunction.

Heterogeneous kinetics of the loop formation of a single polymer chain in crowded and disordered media

The cytoplasmic volume of cells is occupied and crowded by a variety of macromolecules, such as proteins and cytoskeleton structures. Such diverse macromolecules make the cell cytoplasm not only structurally heterogeneous but also dynamically heterogeneous: Some macromolecules may diffuse freely inside cell cytoplasm at certain timescales while others hardly diffuse. Studies on the effects of the dynamic heterogeneity on reaction kinetics have been limited even though the effects of the crowdedness and structural heterogeneity were investigated extensively. In this study, we employ a simple model of mixtures of mobile and immobile matrix particles, tune the degree of dynamic heterogeneity by changing the fraction of immobile matrix particles, and investigate reaction kinetics in such heterogeneous media. We employ the loop formation of a single polymer chain as a model reaction and perform Langevin dynamics simulations. We find that the free-energy barrier of the loop formation is decreased as the systems become more crowded with matrix particles. But the free-energy barrier is not sensitive to the dynamic heterogeneity. As dynamic heterogeneity increases with an increase in the fraction of immobile matrix particles, however, the diffusivity of the system decreases significantly. The decrease in the diffusion (due to the dynamic heterogeneity) and the decrease in the free-energy barrier (due to the crowdedness) lead together to a complicated trend of the loop formation kinetics. As the volume fraction of immobile matrix particles reaches a critical value at the percolation transition, the reaction kinetics becomes significantly heterogeneous and the survival probability distribution of the chain loop formation becomes stretched-exponential. We also illustrate that the heterogeneous reaction rate near the percolation transition relates closely to the structures of local pores in which the polymer is located.

Anomalous transport in the soft-sphere Lorentz model

The sensitivity of anomalous transport in crowded media to the form of the inter-particle interactions is investigated through computer simulations. We extend the highly simplified Lorentz model towards realistic natural systems by modeling the interactions between the tracer and the obstacles with a smooth potential. We find that the anomalous transport at the critical point happens to be governed by the same universal exponent as for hard exclusion interactions, although the mechanism of how narrow channels are probed is rather different. The scaling behavior of simulations close to the critical point confirm this exponent. Our result indicates that the simple Lorentz model may be applicable to describing the fundamental properties of long-range transport in real crowded environments.

Non-universality of the dynamic exponent in two-dimensional random media

The diffusion of solutes in two-dimensional random media is important in diverse physical situations including the dynamics of proteins in crowded cell membranes and the adsorption on nano-structured substrates. It has generally been thought that the diffusion constant, D, should display universal behavior near the percolation threshold, i.e., D ~ (ϕ − ϕ_c)^μ, where ϕ is the area fraction of the matrix, ϕ_c is the value of ϕ at the percolation threshold, and μ is the dynamic exponent. The universality of μ is important because it implies that very different processes, such as protein diffusion in membranes and the electrical conductivity in two-dimensional networks, obey similar underlying physical principles. In this work we demonstrate, using computer simulations on a model system, that the exponent μ is not universal, but depends on the microscopic nature of the dynamics. We consider a hard disc that moves via random walk in a matrix of fixed hard discs and show that μ depends on the maximum possible displacement Δ of the mobile hard disc, ranging from 1.31 at Δ ≤ 0.1 to 2.06 for relatively large values of Δ. We also show that this behavior arises from a power-law singularity in the distribution of transition rates due to a failure of the local equilibrium approximation. The non-universal value of μ obeys the prediction of the renormalization group theory. Our simulations do not, however, exclude the possibility that the non-universal values of μ might be a crossover between two different limiting values at very large and small values of Δ. The results allow one to rationalize experiments on diffusion in two-dimensional systems.

Hierarchical Morphology of Polymer Blend Films Induced by Convection-Driven Solvent Evaporation

Homogeneous thin films of polymer blends with a desired morphology are necessary because of their applications in the fields such as optoelectronics, sensors, biomedicine, and so on. The frequently employed approach for the thin film preparation, spin coating is only able to achieve a homogeneous film for a small area because of the overwhelming spin-driven solvent evaporation with increased size. Here, a convection-guided morphology formation for polystyrene:poly(methyl methacrylate) blend films is reported. In situ observation shows that the morphology changed from homogeneous deposition with a scale less than 10 μm to a self-organized cellular pattern with a scale of more than 100 μm after the fluid flow is involved. Selective dissolution of the hierarchical films reveals that the cellular morphology is attributed to the flow-field-guided deposition of sequentially generated precipitates. The coupling of phase separation and fluid convection results in the hierarchical morphology that includes Voronoi cellular division as the primary structure and the detailed heterogeneous inner-cell features as the secondary structure. Isolated modulation of either micro- or mesoscale in the hierarchical morphology could be carried out via adjusting phase interaction or the convection disturbance correspondingly, providing a flexible and straightforward strategy to construct designed hierarchical structures for polymer thin films toward desired function or property.

Numerical calculation on a two-step subdiffusion behavior of lateral protein movement in plasma membranes

A two-step subdiffusion behavior of lateral movement of transmembrane proteins in plasma membranes has been observed by using single-molecule experiments. A nested double-compartment model where large compartments are divided into several smaller ones has been proposed in order to explain this observation. These compartments are considered to be delimited by membrane-skeleton "fences" and membrane-protein "pickets" bound to the fences. We perform numerical simulations of a master equation using a simple two-dimensional lattice model to investigate the heterogeneous diffusion dynamics behavior of transmembrane proteins within plasma membranes. We show that the experimentally observed two-step subdiffusion process can be described using fence and picket models combined with decreased local diffusivity of transmembrane proteins in the vicinity of the pickets. This allows us to explain the two-step subdiffusion behavior without explicitly introducing nested double compartments.

Comparison of different models of motion in a crowded environment: a Monte Carlo study

In this paper we investigate the motion of molecules in crowded environments for two dramatically different types of molecular transport. The first type is realized by the dynamic lattice liquid model, which is based on a cooperative movement concept and thus, the motion of molecules is highly correlated. The second one corresponds to a so-called motion of a single agent where the motion of molecules is considered as a random walk without any correlation with other moving elements. The crowded environments are modeled as a two-dimensional triangular lattice with fixed impenetrable obstacles. Our simulation results indicate that the type of transport has an impact on the dynamics of the system, the percolation threshold, critical exponents, and on molecules' trajectories.

Simulation of Molecular Transport in Systems Containing Mobile Obstacles

In this paper, we investigate the movement of molecules in crowded environments with obstacles undergoing Brownian motion by means of extensive Monte Carlo simulations. Our investigations were performed using the dynamic lattice liquid model, which was based on the cooperative movement concept and allowed to mimic systems at high densities where the motion of all elements (obstacles as well as moving particles) were highly correlated. The crowded environments are modeled on a two-dimensional triangular lattice containing obstacles (particles whose mobility was significantly reduced) moving by a Brownian motion. The subdiffusive motion of both elements in the system was analyzed. It was shown that the percolation transition does not exist in such systems in spite of the cooperative character of the particles' motion. The reduction of the obstacle mobility leads to the longer caging of liquid particles by mobile obstacles.

Non-Gaussian rotational diffusion in heterogeneous media

We employ a simple model for rotational diffusivity DR of dumbbells in porous media in order to study spatially heterogeneous and non-Gaussian dynamics at Fickian time scales. We obtain the distribution P(DR) of DR's of single dumbbells for both ergodic and nonergodic systems. When a pore percolating network disappears beyond the pore percolation transition and the rotational dynamics becomes nonergodic, each single dumbbell undergoes Gaussian rotational dynamics but with different DR, which depends solely on the local pore structure. We also construct a map of heterogeneous dynamic regions and illustrate that such seemingly Fickian but non-Gaussian dynamics could be understood as the linear combination of the Gaussian rotational displacement distribution functions of each dumbbell. With a percolating pore network, the rotational dynamics becomes ergodic, and P(DR) is a δ function at the average value of DR.

Simulation of diffusion in a crowded environment

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.

APL@Voro: a Voronoi-based membrane analysis tool for GROMACS trajectories

APL@Voro is a new program developed to aid in the analysis of GROMACS trajectories of lipid bilayer simulations. It can read a GROMACS trajectory file, a PDB coordinate file, and a GROMACS index file to create a two-dimensional geometric representation of a bilayer. Voronoi diagrams and Delaunay triangulations--generated for different selection models of lipids--support the analysis of the bilayer. The values calculated on the geometric structures can be visualized in a user-friendly interactive environment and, then, plotted and exported to different file types. APL@Voro supports complex bilayers with a mix of various lipids and proteins. For the calculation of the projected area per lipid, a modification of the well-known Voronoi approach is presented as well as the presentation of a new approach for including atoms into an existing triangulation. The application of the developed software is discussed for three example systems simulated with GROMACS. The program is written in C++, is open source, and is available free of charge.

Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.

Effect of polydispersity on diffusion in random obstacle matrices

The dynamics of tracers in disordered matrices is of interest in a number of diverse areas of physics such as the biophysics of crowding in cells and cell membranes, and the diffusion of fluids in porous media. To a good approximation the matrices can be modeled as a collection of spatially frozen particles. In this Letter, we consider the effect of polydispersity (in size) of the matrix particles on the dynamics of tracers. We study a two dimensional system of hard disks diffusing in a sea of hard disk obstacles, for different values of the polydispersity of the matrix. We find that for a given average size and area fraction, the diffusion of tracers is very sensitive to the polydispersity. We calculate the pore percolation threshold using Apollonius diagrams. The diffusion constant, D, follows a scaling relation D~(φ(c)-φ(m))(μ-β) for all values of the polydispersity, where φ(m) is the area fraction and φ(c) is the value of φ(m) at the percolation threshold.

Obstructed diffusion propagator analysis for single-particle tracking

We describe a method for the analysis of the distribution of displacements, i.e., the propagators, of single-particle tracking measurements for the case of obstructed subdiffusion in two-dimensional membranes. The propagator for the percolation cluster is compared with a two-component mobility model against Monte Carlo simulations. To account for diffusion in the presence of obstacle concentrations below the percolation threshold, a propagator that includes the transient motion in finite percolation clusters and hopping between obstacle-induced compartments is derived. Finally, these models are shown to be effective in the analysis of Kv2.1 channel diffusive measurements in the membrane of living mammalian cells.

Anomalous transport of a tracer on percolating clusters

We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport, which extends to infinite times precisely at the critical obstacle density. The slowing down of the diffusion coefficient exhibits power-law behavior for densities close to the critical point and we show that the mean-square displacement fulfills a scaling hypothesis. Furthermore, we calculate the dynamic conductivity as a response to an alternating electric field. Last, we discuss the non-gaussian parameter as an indicator for heterogeneous dynamics.

Diffusion amid random overlapping obstacles: similarities, invariants, approximations

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.

Two-dimensional continuum percolation threshold for diffusing particles of nonzero radius

Lateral diffusion in the plasma membrane is obstructed by proteins bound to the cytoskeleton. The most important parameter describing obstructed diffusion is the percolation threshold. The thresholds are well known for point tracers, but for tracers of nonzero radius, the threshold depends on the excluded area, not just the obstacle concentration. Here thresholds are obtained for circular obstacles on the continuum. Random obstacle configurations are generated by Brownian dynamics or Monte Carlo methods, the obstacles are immobilized, and the percolation threshold is obtained by solving a bond percolation problem on the Voronoi diagram of the obstacles. The percolation threshold is expressed as the diameter of the largest tracer that can cross a set of immobile obstacles at a prescribed number density. For random overlapping obstacles, the results agree with the known analytical solution quantitatively. When the obstacles are soft disks with a 1/r(12) repulsion, the percolating diameter is approximately 20% lower than for overlapping obstacles. A percolation model predicts that the threshold is highly sensitive to the tracer radius. To our knowledge, such a strong dependence has so far not been reported for the plasma membrane, suggesting that percolation is not the factor controlling lateral diffusion. A definitive experiment is proposed.

Statistical mechanics of homogeneous partly pinned fluid systems

The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture. In this paper, their configurational properties are investigated. It is shown that a peculiar complementarity exists between the mobile and immobile phases, which originates from the fact that the solid is prepared in presence of and in equilibrium with the adsorbed fluid. Simple identities follow, which connect different types of configurational averages, either relative to the fluid-matrix system or to the bulk fluid from which it is prepared. Crucial simplifications result for the computation of important structural quantities, both in computer simulations and in theoretical approaches. Finally, possible applications of the model in the field of dynamics in confinement or in strongly asymmetric mixtures are suggested.

Structure of void space in polymer solutions

The structure of void space in two- and three-dimensional (3D) polymer solutions is studied using Voronoi tessellation and percolation theory. The polymer molecules are modeled as freely jointed chains of N tangent hard disks (two dimensions) or spheres (three dimensions). Polymer chains are equilibrated via Monte Carlo simulations and the pore space in configurations of equilibrated chains is mapped using Voronoi tessellation. In d dimensions a Voronoi vertex is the center of the sphere tangent to the d+1 nearest monomers. An edge of the Voronoi diagram is the shortest route between two neighboring vertices. The edge is considered connected if a monomer can pass through and disconnected otherwise. The Voronoi construction is used to calculate the percolation threshold of the void space. The most interesting result is that the polymer area fraction at the percolation threshold is a nonmonotonic function of N in two dimensions but monotonically reaches a constant value in three dimensions. The crossover behavior of the percolation threshold is also observed in pseudo-3D. The pore size distribution decreases monotonically with increasing pore size. This is markedly different from that in configurations of hard disks (monomeric fluid) where the pore size distribution is peaked at finite size.

Colloidal permeability of liquid membranes consisting of hard particles by nonequilibrium simulations

A novel particulate membrane, comprised of a confined fluid of colloidal hard spheres, is presented and studied by means of simulations. Using a fluid of smaller hard spheres as feed, the transport properties of the membrane are studied as a function of the volume fractions of both the feed solution and membrane and the size ratio between both types of particles. Our simulations show that the fluid in the membrane is compressed to the permeate side due to the pressure of the feed. This effect controls the permeability behavior of the membrane: impermeable when the feed pressure is too low, or when the pressure is high enough to induce crystallization of the membrane fluid. Thus, the permeability first increases and then decreases, upon increasing the feed concentration. Finally we focus in systems with high concentrations of the feed and membrane fluids, where completely impermeable membranes are obtained only when the feed spheres are big enough (sigma(f)>0.38sigma(m)).

Computer simulations of protein diffusion in compartmentalized cell membranes

The diffusion of proteins in the cell membrane is investigated using computer simulations of a two-dimensional model. The membrane is assumed to be divided into compartments, with adjacent compartments separated by a barrier of stationary obstacles. Each compartment contains traps represented by stationary attractive disks. Depending on their size, these traps are intended to model either smaller compartments or binding sites. The simulations are intended to model the double-compartment model, which has been used to interpret single molecule experiments in normal rat kidney cells, where five regimes of transport are observed. The simulations show, however, that five regimes are observed only when there is a large separation between the sizes of the traps and large compartments, casting doubt on the double compartment model for the membrane. The diffusive behavior is sensitive to the concentration and size of traps and the strength of the barrier between compartments suggesting that the diffusion of proteins can be effectively used to characterize the structure of the membrane.

Tagged-particle dynamics in a fluid adsorbed in a disordered porous solid: interplay between the diffusion-localization and liquid-glass transitions

A mode-coupling theory for the slow single-particle dynamics in fluids adsorbed in disordered porous media is derived, which complements previous work on the collective dynamics [V. Krakoviack, Phys. Rev. E 75, 031503 (2007)]. Its equations, such as the previous ones, reflect the interplay between confinement-induced relaxation phenomena and glassy dynamics through the presence of two contributions in the slow part of the memory kernel, which are linear and quadratic in the density correlation functions, respectively. From numerical solutions for two simple models with pure hard-core interactions, it is shown that two different scenarios result for the diffusion-localization transition depending on the strength of the confinement. For weak confinement, this transition is discontinuous and coincides with the ideal glass transition, such as in one-component bulk systems, while, for strong confinement, it is continuous and occurs before the collective dynamics gets nonergodic. In the latter case, the glass transition manifests itself as a secondary transition, which can be either continuous or discontinuous, in the already arrested single-particle dynamics. The main features of the anomalous dynamics found in the vicinity of all these transitions are reviewed and illustrated with detailed computations.

Crowding effects on diffusion in solutions and cells

We review the effects of molecular crowding on solute diffusion in solution and in cellular aqueous compartments and membranes. Anomalous diffusion, in which mean squared displacement does not increase linearly with time, is predicted in simulations of solute diffusion in media crowded with fixed or mobile obstacles, or when solute diffusion is restricted or accelerated by a variety of geometric or active transport processes. Experimental measurements of solute diffusion in solutions and cellular aqueous compartments, however, generally show Brownian diffusion. In cell membranes, there are examples of both Brownian and anomalous diffusion, with the latter likely produced by lipid-protein and protein-protein interactions. We conclude that the notion of universally anomalous diffusion in cells as a consequence of molecular crowding is not correct and that slowing of diffusion in cells is less marked than has been generally assumed.

The effect of matrix structure on the diffusion of fluids in porous media

The effect of matrix structure on the transport properties of adsorbed fluids is studied using computer simulations and percolation theory. The model system consists of a fluid of hard spheres diffusing in a matrix of hard spheres fixed in space. Three different arrangements of the fixed spheres, random, templated, and polymeric, are investigated. For a given matrix volume fraction the diffusion coefficient of the fluid, D, is sensitive to the manner in which the matrix is constructed, with large differences between the three types of matrices. The matrix is mapped onto an effective lattice composed of vertices and bonds using a Voronoi tessellation method where the connectivity of bonds is determined using a geometric criterion, i.e., a bond is connected if a fluid particle can pass directly between the two pores the bond connects, and disconnected otherwise. The percolation threshold is then determined from the connectivity of the bonds. D displays universal scaling behavior in the reduced volume fraction, i.e., D approximately (1-phi(m)phi(c))(gamma), where phi(m) is the matrix volume fraction and phi(c) is the matrix volume fraction at the percolation threshold. We find that gamma approximately 2.2, independent of matrix type, which is different from the result gamma approximately 1.53 for diffusion in lattice models, but similar to that for conduction in Swiss cheese models. Lattice simulations with biased hopping probabilities are consistent with the continuous-space simulations, and this shows that the universal behavior of diffusion is sensitive to details of local dynamics.

Tobacco mosaic virus (TMV) replicase and movement protein function synergistically in facilitating TMV spread by lateral diffusion in the plasmodesmal desmotubule of Nicotiana benthamiana

Virus spread through plasmodesmata (Pd) is mediated by virus-encoded movement proteins (MPs) that modify Pd structure and function. The MP of Tobacco mosaic virus ((TMV)MP) is an endoplasmic reticulum (ER) integral membrane protein that binds viral RNA (vRNA), forming a vRNA:MP:ER complex. It has been hypothesized that (TMV)MP causes Pd to dilate, thus potentiating a cytoskeletal mediated sliding of the vRNA:MP:ER complex through Pd; in the absence of MP, by contrast, the ER cannot move through Pd. An alternate model proposes that cell-to-cell spread takes place by diffusion of the MP:vRNA complex in the ER membranes which traverse Pd. To test these models, we measured the effect of (TMV)MP and replicase expression on cell-to-cell spread of several green fluorescent protein-fused probes: a soluble cytoplasmic protein, two ER lumen proteins, and two ER membrane-bound proteins. Our data support the diffusion model in which a complex that includes ER-embedded MP, vRNA, and other components diffuses in the ER membrane within the Pd driven by the concentration gradient between an infected cell and adjacent noninfected cells. The data also suggest that the virus replicase and MP function together in altering Pd conductivity.

Cellular ion channel-pump system modeling using switched stochastic differential equations

This paper identifies a multidimensional random switched process model of a neuron with embedded Ca++ ion channel and pump molecules adiabatically interacting based on local ion concentrations near the cell membrane. The model interprets known physiology of the channels as a coupled set of switched random processes and derives mechanical equations based on concentration flow among different states of the system. Rapid changes to channel barrier energies occurring during channel opening and closing transitions are modeled as another degree of freedom commutating the state of the overall system. An ion reservoir model is used as the primary tool to incorporate stochastic effects in channel operation. The complete model is analyzed numerically and then the equations are used to motivate a stochastic model for closed state dwell times. The result is compared against expected results of a leaky-integrator and known single-channel histograms.

Permeation of a hard sphere fluid into a quenched matrix

The permeation of a hard sphere fluid through a model membrane, composed of quenched (in space) hard spheres, is studied using molecular dynamics simulations. The fluid is initially placed outside the porous matrix and their initial intake is investigated and found to be non-Fickian. This non-Fickian behavior can be attributed to the high concentration difference between the fluid in the bulk and in the membrane. Once the system is equilibrated, the authors mark fluid particles that are outside the membrane and investigate their diffusion (color diffusion). Color diffusion is Fickian, and the mass intake and density profiles are well described by a continuum composite medium model with no adjustable parameters, i.e., with self-diffusion coefficients obtained from simulations. The matrix becomes impermeable when there are no percolating paths for the fluid.

Dynamics of probes in model glassy matrices

The dynamics of diatomic probe molecules in matrices composed of hard spheres are studied using molecular dynamics simulations. The matrix particles are connected to fixed attachment points by strings of length, l, which is varied from l-->infinity (fluid) to 0 ("glass"). The probe diffusion coefficient, D interpolates smoothly between these limits when l is changed. As l is decreased, D displays a transition from a power-law l dependence, which is well fit by the mode-coupling theory expression, to an Arrhenius l dependence. Single particle analysis shows that the hopping motion sets in for l much larger than a critical length, l(c), and Arrhenius behavior occurs when hopping becomes the dominant mode of transport. The system displays dynamic heterogeneity even though there is no growing dynamic correlation length of any kind.