Effect of polydispersity on diffusion in random obstacle matrices

Simulation Studies of Dynamical Heterogeneity in a Dense Two-Dimensional Dimer-Solvent System with Obstacles

A coarse-grained model of a two-dimensional colloidal suspension was designed. The model was athermal and, in addition, a lattice approximation was introduced. It consisted of solvent (monomer) molecules, dimer molecules, and immobile impenetrable obstacles that introduced additional heterogeneity into the system. Dynamic properties were determined by a Monte Carlo simulation using the dynamic lattice liquid simulation algorithm. It is shown that there is a range of obstacle concentrations in which different diffusion characteristics were observed for dimers and solvents. In the system studied, it is possible to define the ranges of concentrations of individual components (solvent, dimers, and obstacles), in which the nature of the movement of dimers and solvents is different (normal diffusion vs. subdiffusion). The ratio of diffusion coefficients of solvent molecules and dimers for short times does not depend on the concentration of obstacles, while for long times, the ratio increases but remains independent of the concentration of the dimer.

The Influence of Local Constraints on Solvent Motion in Polymer Materials

The influence of obstacles in the form of polymer chains on the diffusion of a low-molecular-weight solvent was the subject of this research. Studies were performed by computer simulations. A Monte Carlo model-the Dynamic Lattice Liquid algorithm-based on the idea of cooperative movements was used. The tested materials were polymer networks with an ideal structure (with a uniform mesh size) and real, irregular networks (with a non-uniform mesh size) obtained numerically by copolymerization. The diffusion of the solvent was analyzed in systems with a polymer concentration that did not exceed 16%. The influence of the polymer concentration and macromolecular architecture structure on the mobility and character of the motion of the solvent was discussed. The influence of irregular network morphology on solvent dynamics appeared to be significantly stronger than that of regular networks and star-like polymers.

Effects of polydispersity on the plastic behaviors of dense two-dimensional granular systems under shear

We study particle-scale motion in sheared highly polydisperse amorphous materials, in which the largest particles are as much as ten times the size of the smallest. We find strikingly different behavior from the more commonly studied amorphous systems with low polydispersity. In particular, an analysis of the nonaffine motion of particles reveals qualitative differences between large and small particles: The smaller particles have dramatically more nonaffine motion, which is induced by the presence of the large particles. We characterize how the nonaffine motion changes from the low- to high-polydispersity regimes. We further demonstrate a quantitative way to distinguish between "large" and "small" particles in systems with broad distributions of particle sizes. A macroscopic consequence of the nonaffine motion is a decrease in the energy dissipation rate for highly polydisperse samples, which is due both to a geometric consequence of the changing jamming conditions for higher polydispersity and to the changing character of nonaffine motion.

Short-Time Transport Properties of Bidisperse Suspensions of Immunoglobulins and Serum Albumins Consistent with a Colloid Physics Picture

The crowded environment of biological systems such as the interior of living cells is occupied by macromolecules with a broad size distribution. This situation of polydispersity might influence the dependence of the diffusive dynamics of a given tracer macromolecule in a monodisperse solution on its hydrodynamic size and on the volume fraction. The resulting size dependence of diffusive transport crucially influences the function of a living cell. Here, we investigate a simplified model system consisting of two constituents in aqueous solution, namely, of the proteins bovine serum albumin (BSA) and bovine polyclonal gamma-globulin (Ig), systematically depending on the total volume fraction and ratio of these constituents. From high-resolution quasi-elastic neutron spectroscopy, the separate apparent short-time diffusion coefficients for BSA and Ig in the mixture are extracted, which show substantial deviations from the diffusion coefficients measured in monodisperse solutions at the same total volume fraction. These deviations can be modeled quantitatively using results from the short-time rotational and translational diffusion in a two-component hard sphere system with two distinct, effective hydrodynamic radii. Thus, we find that a simple colloid picture well describes short-time diffusion in binary mixtures as a function of the mixing ratio and the total volume fraction. Notably, the self-diffusion of the smaller protein BSA in the mixture is faster than the diffusion in a pure BSA solution, whereas the self-diffusion of Ig in the mixture is slower than in the pure Ig solution.

Effect of polydispersity on the dynamics of active Brownian particles

We numerically study the dynamics and the phases of self-propelled disk-shaped particles of different sizes with soft repulsive potential in two dimensions. Size diversity is introduced by the polydispersity index (PDI) ε, which is the width of the uniform distribution of the particle's radius. The self-propulsion speed of the particles controls the activity v. We observe enhanced dynamics for large size diversity among the particles. We calculate the effective diffusion coefficient D_{eff} in the steady state. The system exhibits four distinct phases, jammed phase with small D_{eff} for small activity and liquid phase with enhanced D_{eff} for large activity. The number fluctuation is larger and smaller than the equilibrium limit in the liquid and jammed phases, respectively. Further, the jammed phase is of two types: solid jammed and liquid jammed for small and large PDI. Whereas the liquid phase is called motility induced phase separation (MIPS) liquid for small PDI and for large PDI, we find enhanced diffusivity and call it the pure liquid phase. The system is studied for three packing densities ϕ, and the response of the system for polydispersity is the same for all ϕ's. Our study can help understand the behavior of cells of various sizes in a tissue, artificial self-driven granular particles, or living organisms of different sizes in a dense environment.

Theory and simulation of open systems out of equilibrium

We consider the theoretical model of Bergmann and Lebowitz for open systems out of equilibrium and translate its principles in the adaptive resolution simulation molecular dynamics technique. We simulate Lennard-Jones fluids with open boundaries in a thermal gradient and find excellent agreement of the stationary responses with the results obtained from the simulation of a larger locally forced closed system. The encouraging results pave the way for a computational treatment of open systems far from equilibrium framed in a well-established theoretical model that avoids possible numerical artifacts and physical misinterpretations.

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.

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.

Predicting Complex Relaxation Processes in Metallic Glass

Relaxation processes significantly influence the properties of glass materials. However, understanding their specific origins is difficult; even more challenging is to forecast them theoretically. In this study, using microseconds molecular dynamics simulations together with an accurate many-body interaction potential, we predict that an Al_{90}Sm_{10} metallic glass would have complex relaxation behaviors: In addition to the main (α) relaxation, the glass (i) shows a pronounced secondary (β) relaxation at cryogenic temperatures and (ii) exhibits an anomalous relaxation process (α_{2}) accompanying α relaxation. Both of the predictions are verified by experiments. Computational simulations reveal the microscopic origins of relaxation processes: while the pronounced β relaxation is attributed to the abundance of stringlike cooperative atomic rearrangements, the anomalous α_{2} process is found to correlate with the decoupling of the faster motions of Al with slower Sm atoms. The combination of simulations and experiments represents a first glimpse of what may become a predictive routine and integral step for glass physics.

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.

Actin filaments partition primary cilia membranes into distinct fluid corrals

Lee et al. examine the dynamics of membrane proteins within the ciliary membrane using quantum dots and 2P Super FRAP. They show that ciliary membrane proteins diffuse rapidly within highly fluid local membrane domains delimited by actin filaments.

Physical properties of primary cilia membranes in living cells were examined using two independent, high-spatiotemporal-resolution approaches: fast tracking of single quantum dot–labeled G protein–coupled receptors and a novel two-photon super-resolution fluorescence recovery after photobleaching of protein ensemble. Both approaches demonstrated the cilium membrane to be partitioned into corralled domains spanning 274 ± 20 nm, within which the receptors are transiently confined for 0.71 ± 0.09 s. The mean membrane diffusion coefficient within the corrals, D_m1 = 2.9 ± 0.41 µm²/s, showed that the ciliary membranes were among the most fluid encountered. At longer times, the apparent membrane diffusion coefficient, D_m2 = 0.23 ± 0.05 µm²/s, showed that corral boundaries impeded receptor diffusion 13-fold. Mathematical simulations predict the probability of G protein–coupled receptors crossing corral boundaries to be 1 in 472. Remarkably, latrunculin A, cytochalasin D, and jasplakinolide treatments altered the corral permeability. Ciliary membranes are thus partitioned into highly fluid membrane nanodomains that are delimited by filamentous actin.

Diffusion of small particles in polymer films

The motion of small probe molecules in a two-dimensional system containing frozen polymer chains was studied by means of Monte Carlo simulations. The model macromolecules were coarse-grained and restricted to vertices of a triangular lattice. The cooperative motion algorithm was used to generate representative configurations of macromolecular systems of different polymer concentrations. The remaining unoccupied lattice sites of the system were filled with small molecules. The structure of the polymer film, especially near the percolation threshold, was determined. The dynamic lattice liquid algorithm was then employed for studies of the dynamics of small objects in the polymer matrix. The influence of chain length and polymer concentration on the mobility and the character of motion of small molecules were studied. Short- and long-time dynamic behaviors of solvent molecules were also described. Conditions of anomalous diffusions' appearance in such systems are discussed. The influence of the structure of the matrix of obstacles on the molecular transport was discussed.

Dynamics of highly polydisperse colloidal suspensions as a model system for bacterial cytoplasm

There are various kinds of macromolecules in bacterial cell cytoplasm. The size polydispersity of the macromolecules is so significant that the crystallization and the phase separation could be suppressed, thus stabilizing the liquid state of bacterial cytoplasm. On the other hand, recent experiments suggested that the macromolecules in bacterial cytoplasm should exhibit glassy dynamics, which should be also affected significantly by the size polydispersity of the macromolecules. In this work, we investigate the anomalous and slow dynamics of highly polydisperse colloidal suspensions, of which size distribution is chosen to mimic Escherichia coli cytoplasm. We find from our Langevin dynamics simulations that the diffusion coefficient (D_{tot}) and the displacement distribution functions (P(r,t)) averaged over all colloids of different sizes do not show anomalous and glassy dynamic behaviors until the system volume fraction ϕ is increased up to 0.82. This indicates that the intrinsic polydispersity of bacterial cytoplasm should suppress the glass transition and help maintain the liquid state of the cytoplasm. On the other hand, colloids of each kind show totally different dynamic behaviors depending on their size. The dynamics of colloids of different size becomes non-Gaussian at a different range of ϕ, which suggests that a multistep glass transition should occur. The largest colloids undergo the glass transition at ϕ=0.65, while the glass transition does not occur for smaller colloids in our simulations even at the highest value of ϕ. We also investigate the distribution (P(θ,t)) of the relative angles of displacement for macromolecules and find that macromolecules undergo directionally correlated motions in a sufficiently dense system.

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.

Splitting of the Universality Class of Anomalous Transport in Crowded Media

We investigate the emergence of subdiffusive transport by obstruction in continuum models for molecular crowding. While the underlying percolation transition for the accessible space displays universal behavior, the dynamic properties depend in a subtle nonuniversal way on the transport through narrow channels. At the same time, the different universality classes are robust with respect to introducing correlations in the obstacle matrix as we demonstrate for quenched hard-sphere liquids as underlying structures. Our results confirm that the microscopic dynamics can dominate the relaxational behavior even at long times, in striking contrast to glassy dynamics.

Dimensional study of the dynamical arrest in a random Lorentz gas

The random Lorentz gas (RLG) is a minimal model for transport in heterogeneous media. Upon increasing the obstacle density, it exhibits a growing subdiffusive transport regime and then a dynamical arrest. Here, we study the dimensional dependence of the dynamical arrest, which can be mapped onto the void percolation transition for Poisson-distributed point obstacles. We numerically determine the arrest in dimensions d=2-6. Comparison of the results with standard mode-coupling theory reveals that the dynamical theory prediction grows increasingly worse with d. In an effort to clarify the origin of this discrepancy, we relate the dynamical arrest in the RLG to the dynamic glass transition of the infinite-range Mari-Kurchan-model glass former. Through a mixed static and dynamical analysis, we then extract an improved dimensional scaling form as well as a geometrical upper bound for the arrest. The results suggest that understanding the asymptotic behavior of the random Lorentz gas may be key to surmounting fundamental difficulties with the mode-coupling theory of glasses.

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.