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ABSTRACT: 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.
Physical Review Letters 10/2012; 109(15):155901. · 7.37 Impact Factor
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ABSTRACT: The self-assembly behavior of Gemini (dimeric or twin-tail) dicarboxylate disodium surfactants is studied using molecular dynamics simulations. A united atom model is employed for the surfactants with fully atomistic counterions and water. This gemini architecture, in which two single tailed surfactants are joined through a flexible hydrophobic linker, has been shown to exhibit concentration-dependent aqueous self-assembly into lyotropic phases including hexagonal, gyroid, and lamellar morphologies. Our simulations reproduce the experimentally observed phases at similar amphiphile concentrations in water, including the unusual ability of these surfactants to form gyroid phases over unprecedentedly large amphiphile concentration windows. We demonstrate quanitative agreement between the predicted and experimentally observed domain spacings of these nanostructured materials. Through careful conformation analyses of the surfactant molecules, we show that the gyroid phase is electrostatically stabilized related to the lamellar phase. By starting with a lamellar phase, we show that decreasing the charge on the surfactant headgroups by carboxylate protonation or use of a bulkier N(CH3)4 counterion in place of Na+ drives the formation of a gyroid phase. Using our models, we show that the translational diffusion of water and the Na+ counterions is decreased by several orders of magnitude over the studied concentration range, and we attribute these effects to strong correlations between the mobile species and the surfactant headgroups.
The Journal of Physical Chemistry B 09/2012; · 3.70 Impact Factor
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ABSTRACT: The effect of salt on the dynamics of water molecules follows the Hofmeister series. For some "structure-making" salts, the self-diffusion coefficient of the water molecules, D, decreases with increasing salt concentration. For other "structure-breaking" salts, D increases with increasing salt concentration. In this work, the concentration and temperature dependence of the self-diffusion of water in electrolyte solutions is studied using molecular dynamics simulations and pulsed-field-gradient NMR experiments; temperature-dependent viscosities are also independently measured. Simulations of rigid, nonpolarizable models at room temperature show that none of the many models tested can reproduce the experimentally observed trend for the concentration dependence of D; that is, the models predict that D decreases with increasing salt concentration for both structure-breaking and structure-making salts. Predictions of polarizable models are not in agreement with experiment either. These results suggest that many popular water models do not accurately describe the dynamic nature of the hydrogen bond network of water at room temperature. The simulations are in qualitative agreement, however, with experimental results for the temperature dependence of water dynamics; simulations and experiment show an Arrhenius dependence of D with temperature, T, with added salt, that is, ln D ∼ 1/T, over a range of temperatures above the freezing point of water.
The Journal of Physical Chemistry B 09/2012; 116(39):12007-13. · 3.70 Impact Factor
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ABSTRACT: The properties of short chains of poly-(styrene)-co-(styrene sulfonate) are studied using atomistic molecular dynamics simulations with explicit solvent. We study single 8-mers and 16-mers with two species of counterions, Na(+) and Mg(2+), and for various degrees of sulfonation, f. We find that single trajectories do not efficiently sample configurational space, even for fairly long 100-ns simulations, because of rotational barriers caused by nonbonded interactions. Hamiltonian replica exchange molecular dynamics (HREMD) simulations or averages over multiple trajectories are required in order to obtain equilibrium properties. A polystyrene sulfonate chain adopts collapsed conformations at low f, in which the sulfonate groups are located outside the globule and benzene rings form the inner region, and adopts extended conformations as f is increased. Interestingly, the pair correlation functions between side groups of polystyrene chains are not sensitive to f and species of counterion, i.e., the balance of electrostatic repulsion between charged groups and hydrophobic attraction between benzene rings is achieved by conformational change in a way preserving pair correlations between side groups in a polymer chain. For Na(+) counterions, no localization is observed in the simulations. For Mg(2+) counterions, there is a large free energy barrier to contact pair formation between the sulfonate groups and the Mg(2+) counterions. As a consequence we do not observe the formation or breaking of contact pairs during the course of a simulation. The simulations provide insight into the important interactions and correlations in polyelectrolyte solutions.
The Journal of Physical Chemistry B 03/2012; 116(14):4319-27. · 3.70 Impact Factor
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ABSTRACT: The self-assembly of amphiphilic molecules is of interest from a fundamental and practical standpoint. There has been recent interest in a class of molecules made from β-amino acids (which contain an additional backbone carbon atom when compared with natural amino acids). Block copolymers of β-peptides, where one block is hydrophobic and the other is hydrophilic, self-assemble into micelles. In this work, we use computer simulations to provide insight into the effect of secondary structure on the self-assembly of these molecules. Atomistic simulations for the free energy of association of a pair of molecules show that a homochiral hydrophobic block promotes self assembly compared to a heterochiral hydrophobic block, consistent with experiment. Simulations of a coarse-grained model show that these molecules spontaneously form spherical micelles.
The Journal of chemical physics 02/2012; 136(8):084902. · 3.09 Impact Factor
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ABSTRACT: The control of catalytic activity using molecular self-assembly is of fundamental interest. Recent experiments (Muller et al., Angew. Chem., Int. Ed., 2009, 48, 922-925) have demonstrated that two sequence isomers of β-peptides show remarkably different activity as an amine catalyst for a retro-aldol cleavage reaction, a difference attributed to the ability of one of the sequences to form large aggregates. The self-assembly and catalytic activity of these two isomers are investigated using constant pH molecular dynamics (CPHMD), for an atomistic model of β-peptides in implicit solvent. Simulations show that the globally amphiphilic (GA) isomer, which experimentally has high activity, forms large aggregates, while the non-GA isomer forms aggregates that are at most three or four molecules in size. The pK(a) shift of the βK-residues is significantly higher in the GA isomers that make a large aggregate. Since the decrease in pK(a) of the side-chain ammonium group is the main driving force for amine catalysis, the calculations are consistent with experiment. We find that the buried βK residues become entirely deprotonated, and the pK(a) shift for other titratable βK residues is accompanied mainly by a clustering of solvent exposed βK residues. We conclude that simulations can be used to understand catalytic activity due to self-assembly.
The Journal of Physical Chemistry B 11/2011; 116(1):491-5. · 3.70 Impact Factor
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ABSTRACT: We present a new coarse-grained (CG) model for simulations of lipids and peptides. The model follows the same topology and parametrization strategy as the MARTINI force field but is based on our recently developed big multipole water (BMW) model for water (J. Phys. Chem. B2010, 114, 10524–10529). The new BMW-MARTINI force field reproduces many fundamental membrane properties and also yields improved energetics (when compared to the original MARTINI force-field) for the interactions between charged amino acids with lipid membranes, especially at the membrane–water interface. A stable attachment of cationic peptides (e.g., Arg8) to the membrane surface is predicted, consistent with experiment and in contrast to the MARTINI model. The model predicts electroporation when there is a charge imbalance across the lipid bilayer, an improvement over the original MARTINI. Moreover, the pore formed during electroporation is toroidal in nature, similar to the prediction of atomistic simulations but distinct from results of polarizable MARTINI for small charge imbalances. The simulations emphasize the importance of a reasonable description of the electrostatic properties of water in CG simulations. The BMW-MARTINI model is particularly suitable for describing interactions between highly charged peptides with lipid membranes, which is crucial to the study of antimicrobial peptides, cell penetrating peptides, and other proteins/peptides involved in the remodeling of biomembranes.
10/2011;
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ABSTRACT: In Escherichia coli, ribosomes concentrate near the cylindrical wall and at the endcaps, whereas the chromosomal DNA segregates in the more centrally located nucleoid. A simple statistical model recovers the observed ribosome-nucleoid segregation remarkably well. Plectonemic DNA is represented as a hyperbranched hard-sphere polymer, and multiple ribosomes that simultaneously translate the same mRNA strand (polysomes) are represented as freely jointed chains of hard spheres. There are no attractive interactions between particles, only excluded-volume effects. At realistic DNA and ribosome concentrations, segregation arises primarily from two effects: the DNA polymer avoids walls to maximize conformational entropy, and the polysomes occupy the empty space near the walls to maximize translational entropy. In this complex system, maximizing total entropy results in spatial organization of the components. Due to coupling of mRNA to DNA through RNA polymerase, the same entropic effects should favor the placement of highly expressed genes at the interface between the nucleoid and the ribosome-rich periphery. Such a placement would enable efficient cotranscriptional translation and facile transertion of membrane proteins into the cytoplasmic membrane. Finally, in the model, monofunctional DNA polymer beads representing the tips of plectonemes preferentially locate near the cylindrical wall. This suggests that initiation of transcription may occur preferentially near the ribosome-rich periphery.
Biophysical Journal 06/2011; 100(11):2605-13. · 3.65 Impact Factor
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Journal of Polymer Science Part B Polymer Physics 04/2011; 49(11):818 - 825. · 1.53 Impact Factor
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ABSTRACT: The cell cytoplasm is a dense environment where the presence of inert cosolutes can significantly alter the rates of protein folding and protein association reactions. Most theoretical studies focus on hard sphere crowding agents and quantify the effect of excluded volume on reaction rates. In this work the effect of interactions between the crowding agents on the thermodynamics of protein association is studied using computer simulation. Three cases are considered, where the crowding agents are (i) hard spheres, (ii) hard spheres with additional attractive or repulsive interactions, and (iii) chains of hard spheres. Reactants and products of the protein association are modeled as hard spheres. Although crowding effects are sensitive to the shape of the reaction product, in most cases the excess free energy difference between the product and reactants (nonideality factor) is insensitive to the interactions between crowding agents, due to a cancellation of effects. The simulations therefore suggest that the hard sphere model of crowding agents has a surprisingly large regime of validity and should be sufficient for a qualitative understanding of the thermodynamics of crowding effects when the interactions of associating proteins with crowding agents other than excluded volume interactions are not significant.
The Journal of Physical Chemistry B 01/2011; 115(2):347-53. · 3.70 Impact Factor
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The Journal of Physical Chemistry B 09/2010; · 3.70 Impact Factor
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ABSTRACT: Recent experimental studies have revealed interesting sequence dependence in the antimicrobial activity of β-peptides, which suggests the possibility of a rational design of new antimicrobial agents. To obtain insight into the mechanism of membrane activity, we present a computer simulation study of the adsorption of these molecules to a single-component lipid membrane. Two classes of molecules are investigated: 10-residue oligomers of 14-helical sequences, and four sequences of random copolymeric β-peptides. The oligomers of interest are globally amphiphilic (GA) and nonglobally amphiphilic (non-GA) sequences of 10-residue, 14-helical sequences. In solution and at the interface, all oligomers maintain a helical structure throughout the simulation. The penetration of the molecules into the membrane and the orientation of the molecules at the interface depend strongly on the sequence. We attribute this to the propensity of the β-phenylalanine (βF) residues for membrane penetration. For the four sequences of random copolymeric β-peptides, simulations of an implicit solvent and membrane model show that the strength of adsorption of the polymers is strongly correlated with their efficiency to segregate the hydrophobic and cationic residues. The simulations suggest simple strategies for the design of candidates for antimicrobial β-peptides. Collectively, these results further support the conclusion from several recent studies that neither global amphiphilicity nor regular secondary structure is required for short peptides to effectively interact with the membrane. Moreover, although we study only the binding process, the fact that there is a correlation between the sequence dependence in the calculated binding properties and the experimentally observed antimicrobial activity suggests that efficient binding to the membrane might be a good predictor for high antimicrobial activity.
The Journal of Physical Chemistry B 09/2010; 114(42):13585-92. · 3.70 Impact Factor
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ABSTRACT: A new coarse-grained (CG) model is developed for water. Each CG unit consists of three charged sites, and there is an additional nonelectrostatic soft interaction between central sites on different units. The interactions are chosen to mimic the properties of 4-water clusters in atomistic simulations: the nonelectrostatic component is modeled using a modified Born-Mayer-Huggins potential, and the charges are chosen to reproduce the dipole moment and quadrupole moment tensor of 4-water clusters from atomistic simulations. The parameters are optimized to reproduce experimental data for the compressibility, density, and permittivity of bulk water and the surface tension and interface potential for the air-water interface. This big multipole water (BMW) model represents a qualitative improvement over existing CG water models; for example, it reproduces the dipole potential in membrane-water interface when compared to experiment, with modest additional computational cost as compared to the popular MARTINI CG model.
The Journal of Physical Chemistry B 08/2010; 114(32):10524-9. · 3.70 Impact Factor
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ABSTRACT: Oligomers of β-peptides with cyclic residues make very stable helices where the amphiphilicity can be tailored via the sequence. These molecules display large-scale hierarchical self-assembly that is very sensitive to the sequence. For example, the globally amphiphilic (GA) sequence of one molecule, βY−(ACHC−ACHC−βK)3 (model A), self-assembles into long cylinders, which can display a nematic phase, but the nonglobally amphiphilic (non-GA) sequence does not. Interestingly, for a closely related sequence, βY−(ACHC−βF−βK)3 (model B), the opposite is true; that is, the non-GA sequence self-assembles into long hollow cylinders, and the GA sequence does not. In this work, the pair and many-body potential of mean force (PMF) between β-peptides is studied using computer simulations with explicit and implicit solvent. The PMF studies rationalize the experimentally observed trends. In particular, for the sequences that form hollow cylinders, the most stable configuration of a pair of molecules is when they are side-to-side and parallel. The two sequences that do make cylinders have side-to-side parallel configurations with a slight curvature at the minimum in the triplet PMF. The implicit solvent simulations are in qualitative accord with explicit solvent simulations for the pair PMF, suggesting that one could use multibody PMF studies with implicit solvent models to provide insight into the self-assembly of complex molecules.
07/2010;
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ABSTRACT: The effect of macromolecular crowding on the binding of ligands to a receptor near membranes is studied using Brownian dynamics simulations. The receptor is modeled as a reactive patch on a hard surface and the ligands and crowding agents are modeled as spheres that interact via a steep repulsive interaction potential. When a ligand collides with the patch, it reacts with probability p(rxn). The association rate constant (k(infinity)) can be decomposed into contributions from diffusion-limited (k(D)) and reaction-limited (k(R)) rates, i.e., 1/k(infinity) = 1/k(D) + 1/k(R). The simulations show that k(D) is a nonmonotonic function of the volume fraction of crowding agents for receptors of small sizes. k(R) is always an increasing function of the volume fraction of crowding agents, and the association rate constant k(infinity) determined from both contributions has a qualitatively different dependence on the macromolecular crowding for high and low values of the reaction probability p(rxn). The simulation results are used to predict the velocity of the membrane protrusion driven by actin filament elongation. Based on the simple model where the protrusive force on the membrane is generated by the intercalation of actin monomers between the membrane and actin filament ends, we predict that crowding increases the local concentration of actin monomers near the filament ends and hence accelerates the membrane protrusion.
Biophysical Journal 03/2010; 98(6):951-8. · 3.65 Impact Factor
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ABSTRACT: 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.
Physical Review E 03/2010; 81(3 Pt 1):031801. · 2.26 Impact Factor
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ABSTRACT: The sequence-directed self-assembly of amphiphilic beta-peptides is studied using Monte Carlo simulations. A phenomenological model is employed where each molecule is modeled as a rigid nanorod with side groups located at positions to mimic globally amphiphilic (GA) and nonglobally amphiphilic (non-GA) isomers of beta-peptides. The strength and the range of interactions between side groups are chosen based on the types of residues. The simulations show that the aggregation of beta-peptides is sensitive to the sequence and the residue types. For one type of beta-peptide the GA isomer has a greater tendency to aggregate while for the other the non-GA isomer has a greater tendency to aggregate. The trends observed in the simulations are consistent with recent experiments [Pomerantz et al., J. Am. Chem. Soc. 128, 8730 (2006); Pomerantz et al., Angew. Chem., Int. Ed. 47, 1 (2008)], although the molecules do not spontaneously form the hollow fibers seen in experiment. Simulations with initial configurations as hollow fibers show that the stability of the fibers follows the same trend as the tendency for aggregation. The simulations demonstrate that the details matter: the self-assembly of the molecules is sensitive to the strength of the short-ranged interactions and the size of the side groups, in addition to the global amphiphilicity of the molecules. This suggests the possibility of designing molecules for desired nanostructures.
The Journal of chemical physics 02/2010; 132(6):065103. · 3.09 Impact Factor
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ABSTRACT: The adsorption of strongly charged polyelectrolyte chains to an oppositely charged planar surface is studied using computer simulation. In addition to an explicit solvent model, two implicit solvent models are considered: one where the solvent induces an implicit Lennard-Jones (ILJ) interaction between polymer sites and one where the solvent induces a many body interaction that depends on the solvent accessible surface area (SASA) of the monomers. Molecular and Brownian dynamics simulations are reported for the explicit and implicit solvent models, respectively. All three models give similar results for the adsorption of the chains in good solvent. The electrostatic attraction between the surface and the polymers is not sufficient to drive the strong adsorption that is seen in experiments. In poor solvents, the models give different results for the adsorption excess and the mechanism for polyelectrolyte adsorption. With explicit solvent, thick adsorbed layers are formed at both charged and neutral surfaces. With the SASA model, adsorbed layers are formed on the charged but not on the neutral surface. With the ILJ model, adsorbed layers are not formed on any surfaces. The results show that the solvent plays a dominant role in the adsorption of polyelectrolytes under poor solvent conditions and that many-body solvent effects have a qualitative effect on the adsorption characteristics and mechanism. In particular, SASA and depletion effects could possibly play an important role; the former can be incorporated in the SASA model, but the latter cannot. The results suggest that accurate computational models for polymer adsorption under poor solvent conditions must incorporate the solvent explicitly.
The Journal of chemical physics 02/2010; 132(7):074903. · 3.09 Impact Factor
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ABSTRACT: All-atom molecular mechanics (MM) force field parameters are developed for the backbone of acyclic beta-amino acid using an improved version of the multiobjective evolutionary algorithm (MOEA). The MM model is benchmarked using beta(3)-homo-Alanine (beta(3)-hAla) diamide in water with SCC-DFTB/MM simulations as the reference. Satisfactory agreements are found between the MM and SCC-DFTB/MM results regarding the distribution of key dihedral angles for the beta(3)-hAla diamide in water. The MM model is further applied to a beta-hepta-peptide in methanol solution. The calculated NOE values and (3)J coupling constants averaged over different trajectories are consistent with experimental data. By contrast, simulations using parameters directly transferred from the CHARMM22 force field for proteins lead to much worse agreement, which highlights the importance of careful parameterization for non-natural peptides, for which the improved MOEA is particularly useful. Finally, as an initial application of the new force field parameters, the behaviors of a short random copolymer consisting of beta amino acids in bulk solution and membrane/water interface are studied using a generalized Born implicit solvent model (GBSW). Results for four selected sequences show that segregation of hydrophobic and cationic groups occur easily at the membrane/solution interface for all sequences. The sequence that features alternating short blocks exhibits signs of lower stability at the interface compared to other sequences. These results confirm the hypothesis in recent experimental studies that beta-amino-acid based random copolymers can develop a high degree of amphiphilicity without regular three-dimensional structure.
Journal of Computational Chemistry 02/2010; 31(10):2063-77. · 4.58 Impact Factor
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ABSTRACT: 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.
Biophysical Journal 08/2009; 97(2):472-9. · 3.65 Impact Factor
