On the lattice ground state of densely packed hard ellipses.

Among lattice configurations of densely packed hard ellipses, Monte Carlo simulations are used to identify the so-called parallel and diagonal lattices as the two favorable states. The free energies of these two states are computed for several system sizes employing the Einstein crystal method. An accurate calculation of the free energy difference between the two states reveals the parallel lattice as the state with the lowest free energy. The origin of the entropic difference between the two states is further elucidated by assessing the roles of the translational and rotational degrees of freedom.

Kagome lattice made by impenetrable ellipses with attractive walls.

Low-dimensional structures, such as the kagome lattice, are experiencing renewed interest within the physics, chemistry and materials science communities in terms of both basic and applied research. Herein, we show that stable kagome lattices can be made by hard-core ellipses with attractive walls. We study a model in which hard-core ellipse is covered uniformly by an attractive square-well layer. Analytical calculations predict that for certain combinations of the asphericity aspect ratio and the attraction range, the kagome lattice is the ground-state conformation of this model. For one specific set of parameters computer simulations prove that the kagome lattice is the lowest free energy structure at low temperatures. At high temperatures, the conformational ensemble is dominated by liquid states. The temperature at which transition from the liquid to the kagome structure occurs has a maximum as a function of density, indicating that the underlying phase transformation is re-entrant. The maximum is attributed to the energy difference between the liquid and crystalline states. Our study reveals that the kagome lattice can be produced by means of very simple models. No specifically designed molecular shapes or interactions are required. Instead, very basic physical characteristics, such as asphericity and uniform attraction, are sufficient to induce spontaneous transition into this structure. In the context of the general understanding of the self-assembly processes, this finding is encouraging, giving one hope that the requirements for the assembly of other low-dimensional structures could be equally simple.

Liquid-gas critical point of a two-dimensional system of hard ellipses with attractive wells.

In an effort to illuminate the general principles governing the critical behavior of model fluids, we investigate in this study how the shape and the (attractive) interaction range of the molecule affect the gas-liquid equilibrium and the critical behavior of the system. A combination of Monte Carlo simulations and analytical theory is employed to compute critical properties, i.e., temperature and density, of a system of hard-core ellipses with an attractive square-well potential in two-dimensional space. The critical temperature is found to decrease monotonically as the asphericity of the molecule is increased. This trend can be successfully explained in terms of the strength of the effective attraction acting between molecules measured, for instance, by the second virial coefficient. The critical density shows a complex dependence on both the range of attraction and the asphericity of the molecule. We find that the properties of particle clusters formed in near-critical states reproduce some of the most important features of the critical density, including multiple minima and maxima. It is shown that a model based on the extent of the overlap between attractive shells surrounding the ellipses captures the variation of the size of the clusters. Based on the obtained results, we discuss implications of varying the shape of the attraction potential for critical density.

Attraction between Like-Charged Macroions Mediated by Specific Counterion Configurations.

Attraction between like-charged macroions is fundamental to many processes in biology, chemistry, and physics. It also plays an important role in industrial applications such as ion-extraction processes or catalysis. In this work, we report a novel mechanism by which attraction can be realized between spherical macroions at high ionic strength. It consists of specific configurations of two, three, and more counterions that appear between macroions with high statistical probability. The attraction is manifested in a minimum in the potential of mean force between the macroions at short distances. Its depth increases with increasing charge of the macroion, demonstrating that the attraction is electrostatic in nature. It is shown that the implicit solvent model with a distance-dependent dielectric constant can capture both the geometry and thermodynamics of charge-stabilized macroion dimers on the qualitative level. The results obtained for a model colloid with a smooth surface are extrapolated to more realistic systems. Evidence is found that the reported mechanism can be observed in small chemical compounds with encapsulated ions such as fullerenes.

Cluster Crystals Stabilized by Hydrophobic and Electrostatic Interactions.

Cluster crystals are crystalline materials in which each site is occupied by multiple identical particles, atoms, colloids, or polymers. There are two classes of systems that make cluster crystals. One is composed of particles that interact via potentials that are bound at the origin and thus are able to penetrate each other. The other consists of non-interpenetrating particles whose interaction potential diverges at the origin. The goal of this work is to find which systems of the second class can make cluster crystals that are stable at room temperature. First, the general properties of the required potentials are established using an analytical model and Monte Carlo simulations. Next, we ask how such potentials can be constructed by combining hydrophobic attraction and electrostatic repulsion. A colloid model with a hard-sphere core and a repulsive wall is introduced to mimic the hydrophobic interaction. Charge is added to create long-range repulsion. A search in the parameter space of the colloid size, counterion type, and charge configuration uncovers several models for which effective colloid-colloid interaction, determined in explicit solvent as a potential of mean force, has the necessary shape. For the effective potential, cluster crystals are confirmed as low free-energy configurations in replica-exchange molecular dynamics simulations, which also generate the respective transition temperature. The model that exhibits a transition above room temperature is further studied in explicit solvent. Simulations on a 10 ns time scale show that crystalline conformations are stable below the target temperature but disintegrate rapidly above it, supporting the idea that hydrophobic and electrostatic interactions are sufficient to induce an assembly of cluster crystals. Finally, we discuss which physical systems are good candidates for experimental observations of cluster crystals.

Softness and non-spherical shape define the phase behavior and the structural properties of lysozyme in aqueous solutions.

In this study, Boltzmann inversion is applied in conjunction with molecular dynamics simulations to derive inter-molecular potential for protein lysozyme in aqueous solution directly from experimental static structure factor. The potential has a soft repulsion at short distances and an attraction well at intermediate distances that give rise to the liquid-liquid phase separation. Moreover, Gibbs ensemble Monte Carlo simulations demonstrate that a non-spherical description of lysozyme is better suited to correctly reproduce the experimentally observed properties of such a phase separation. Our findings shed new light on the common problem in molecular and cell biology: "How to model proteins in their natural aqueous environments?"

Free energy landscapes for amyloidogenic tetrapeptides dimerization.

The oligomerization of four peptide sequences, KFFE, KVVE, KLLE, and KAAE is studied using replica-exchange molecular dynamics simulations with an atomically detailed peptide model. Previous experimental studies reported that of these four peptides, only those containing phenylalanine and valine residues form fibrils. We show that the fibrillogenic propensities of these peptides can be rationalized in terms of the equilibrium thermodynamics of their early oligomers. Thermodynamic stability of dimers, as measured by the temperature of monomer association, is seen to be higher for those peptides that are able to form fibrils. Although the relative high and low stabilities of the KFFE and KAAE dimers arise from their respective high and low interpeptide interaction energies, the higher stability of the KVVE dimer over the KLLE system results from the smaller loss of configurational entropy accompanying the dimerization of KVVE. Free energy landscapes for dimerization are found to be strongly sequence-dependent, with a high free energy barrier separating the monomeric and dimeric states for KVVE, KLLE, and KAAE sequences. In contrast, the most fibrillogenic peptide, KFFE, displayed downhill assembly, indicating enhanced kinetic accessibility of its dimeric states. The dimeric phase for all peptide sequences is found to be heterogeneous, containing both antiparallel beta-sheet structures that can grow into full fibrils as well as disordered dimers acting as on- or off-pathway intermediates for fibrillation.

Viscoelastic model for the dynamic structure factors of binary systems.

This paper presents the viscoelastic model for the Ashcroft-Langreth dynamic structure factors of liquid binary mixtures. We also provide expressions for the Bhatia-Thornton dynamic structure factors and, within these expressions, show how the model reproduces both the dynamic and the self-dynamic structure factors corresponding to a one-component system in the appropriate limits (pseudobinary system or zero concentration of one component). In particular we analyze the behavior of the concentration-concentration dynamic structure factor and longitudinal current, and their corresponding counterparts in the one-component limit, namely, the self-dynamic structure factor and self-longitudinal current. The results for several lithium alloys with different ordering tendencies are compared with computer simulation data, leading to a good qualitative agreement, and showing the natural appearance in the model of the fast sound phenomenon.

Accelerated folding in the weak hydrophobic environment of a chaperonin cavity: creation of an alternate fast folding pathway.

Recent experiments suggest that the folding of certain proteins can take place entirely within a chaperonin-like cavity. These substrate proteins experience folding rate enhancements without undergoing multiple rounds of ATP-induced binding and release from the chaperonin. Rather, they undergo only a single binding event, followed by sequestration into the chaperonin cage. The present work uses molecular dynamics simulations to investigate the folding of a highly frustrated protein within this chaperonin cavity. The chaperonin interior is modeled by a sphere with a lining of tunable degree of hydrophobicity. We demonstrate that a moderately hydrophobic environment, similar to the interior of the GroEL cavity upon complexion with ATP and GroES, is sufficient to accelerate the folding of a frustrated protein by more than an order of magnitude. Our simulations support a mechanism by which the moderately hydrophobic chaperonin environment provides an alternate pathway to the native state through a transiently bound intermediate state.

Improved theoretical description of protein folding kinetics from rotations in the phase space of relevant order parameters.

A method is introduced to construct a better approximation for the reaction coordinate for protein folding from known order parameters. The folding of a two-state off-lattice alpha helical Go-type protein is studied using molecular dynamics simulations. Folding times are computed directly from simulation, as well as theoretically using an equation derived by considering Brownian-type dynamics for the putative reaction coordinate. Theoretical estimates of the folding time using the number of native contacts (Qn) as a reaction coordinate were seen to differ quite significantly from the true folding time of the protein. By considering the properties of the bimodal free energy surface of this protein as a function of Qn and another relevant coordinate for folding Q (the total number of contacts), we show that by introducing a rotation in the phase space of the order parameters Q and Qn, we can construct a new reaction coordinate q that leads to a fivefold improvement in the estimate of the folding rate. This new coordinate q, resulting from the rotation, lies along the line connecting the unfolded and folded ensemble minima of the free energy map plotted as a function of the original order parameters Q and Qn. Possible reasons for the remaining discrepancy between the folding time computed theoretically and from folding simulations are discussed.

Kinetics of the coil-to-helix transition on a rough energy landscape.

The kinetics of folding of a fully atomic seven-residue polyalanine peptide in an implicit solvent are studied using molecular dynamics simulations. The use of an implicit solvent is found to dramatically increase the frustration of the energy landscape relative to simulations performed in an explicit solvent [Phys. Rev. Lett. 85, 2637 (2000)]. While the native state in both implicit and explicit solvent simulations is an alpha-helix, the kinetics of the coil-to-helix transition differ significantly. In contrast to the explicit solvent simulations, the native state in the implicit solvent simulations is not kinetically accessible at temperatures where it is thermodynamically stable and could not be brought into equilibrium with other conformational states. At temperatures where statistical equilibrium was achieved, the conformational diffusion folding mechanism, found earlier to be adequate for this peptide in an explicit solvent [Phys. Rev. Lett. 85, 2637 (2000)], is met with only limited success. Issues relating to the evaluation of the quality of implicit solvent models on the basis of thermodynamic criteria only are reexamined.

Effects of confinement in chaperonin assisted protein folding: rate enhancement by decreasing the roughness of the folding energy landscape.

Chaperonins, such as the GroE complex of the bacteria Escherichia coli, assist the folding of proteins under non-permissive folding conditions by providing a cavity in which the newly translated or translocated protein can be encapsulated. Whether the chaperonin cage plays a passive role in protecting the protein from aggregation, or an active role in accelerating folding rates, remains a matter of debate. Here, we investigate the role of confinement in chaperonin mediated folding through molecular dynamics simulations. We designed a substrate protein with an alpha/beta sandwich fold, a common structural motif found in GroE substrate proteins and confined it to a spherical hydrophilic cage which mimicked the interior of the GroEL/ES cavity. The thermodynamics and kinetics of folding were studied over a wide range of temperature and cage radii. Confinement was seen to significantly raise the collapse temperature, T(c), as a result of the associated entropy loss of the unfolded state. The folding temperature, T(f), on the other hand, remained unaffected by encapsulation, a consequence of the folding mechanism of this protein that involves an initial collapse to a compact misfolded state prior to rearranging to the native state. Folding rates were observed to be either accelerated or retarded compared to bulk folding rates, depending on the temperature of the simulation. Rate enhancements due to confinement were observed only at temperatures above the temperature T(m), which corresponds to the temperature at which the protein folds fastest. For this protein, T(m) lies above the folding temperature, T(f), implying that encapsulation alone will not lead to a rate enhancement under conditions where the native state is stable (T

Glass transition in an off-lattice protein model studied by molecular dynamics simulations.

In this paper we report the results of a numerical investigation of the glass transition phenomenon in a minimalist protein model. The inherent structure theory of Stillinger and Weber was applied to an off-lattice protein model with a native state beta-sheet motif. By using molecular dynamics simulations and the steepest descent method, sets of local potential energy minima were generated for the model over a range of temperatures. The mean potential energy of the inherent structures allowed to make rough estimates of the glass-transition temperature T(K). More accurately T(K) was computed by direct evaluations of the total and vibrational entropies. It is found that for the present model the thermodynamic ratio of the folding and glass-transition temperatures is 1.7 which is in good agreement with experimental observations.

Diffusive dynamics of protein folding studied by molecular dynamics simulations of an off-lattice model.

We report the results of a molecular dynamics study on the kinetic properties of a small off-lattice model of proteins. The model consists of a linear chain of monomers interacting via a number of potentials. These include hydrophobic, bond-angle, and torsion potentials. The ground-state conformation of the studied model is a beta-sheet motif. Molecular dynamics simulations focused on the time evolution of the reaction coordinate measuring the similarity of a given conformation with the native state. Folding time for the studied model is calculated following the diffusive-rate formula of Bryngelson and Wolynes [J. Phys. Chem. 93, 6902 (1989)] by using a computed separately configurational diffusion coefficient. Comparison of the folding time with the mean-first passage time obtained directly from folding simulations shows that the approximation depicting the dynamics of the reaction coordinate in protein folding as a diffusive motion on a free-energy landscape is quantitatively correct for the studied model.

Finite-size dependence of the bridge function extracted from molecular dynamics simulations.

The bridge function for liquid sodium at T=373 K is obtained by using the mean spherical approximation to extrapolate the pair distribution function (PDF), calculated in molecular dynamics (MD) simulations, beyond the half simulation box length for two sizes of the MD system. The bridge function is found to strongly depend on the total number of particles used in the simulation cell. This dependency leads to a spurious maximum of the static structure factor at long wavelengths, obtained from the reference hypernetted-chain approximation (RHNC) with the MD system used as a reference system (RHNC-MD). A simple self-consistent procedure, proposed to account for the finite-size effects in the bridge function, allows one to efficiently correct the RHNC-MD static structure factor for all unphysical manifestations.