Solvent coarse-graining and the string method applied to the hydrophobic collapse of a hydrated chain

Using computer simulations of over 100,000 atoms, the mechanism for the hydrophobic collapse of an idealized hydrated chain is obtained. This is done by coarse-graining the atomistic water molecule positions over 129,000 collective variables that represent the water density field and then using the string method in these variables to compute the minimum free energy pathway (MFEP) for the collapsing chain. The dynamical relevance of the MFEP (i.e. its coincidence with the mechanism of collapse) is validated a posteriori using conventional molecular dynamics trajectories. Analysis of the MFEP provides atomistic confirmation for the mechanism of hydrophobic collapse proposed by ten Wolde and Chandler. In particular, it is shown that lengthscale-dependent hydrophobic dewetting is the rate-limiting step in the hydrophobic collapse of the considered chain.Comment: 11 pages, 7 figures, including supporting informatio

Symmetry effects and equivalences in lattice models of hydrophobic interaction

We establish the equivalence of a recently introduced discrete model of the hydrophobic interaction, as well as its extension to continuous state variables, with the Ising model in a magnetic field with temperature-dependent strength. In order to capture the effect of symmetries of the solvent particles we introduce a generalized multi-state model. We solve this model - which is not of the Ising type - exactly in one dimension. Our findings suggest that a small increase in symmetry decreases the amplitude of the solvent-mediated part of the potential of mean force between solute particles and enhances the solubility in a very simple fashion. High symmetry decreases also the range of the attractive potential. This weakening of the hydrophobic effect observed in the model is in agreement with the notion that the effect is entropic in origin.Comment: 19 pages, 2 figure

Warm and Cold Denaturation in the Phase Diagram of a Protein Lattice Model

Studying the properties of the solvent around proteins, we propose a much more sophisticated model of solvation than temperature-independent pairwise interactions between monomers, as is used commonly in lattice representations. We applied our model of solvation to a 16-monomer chain constrained on a two-dimensional lattice. We compute a phase diagram function of the temperature and a solvent parameter which is related to the pH of the solution. It exhibits a native state in which the chain coalesces into a unique compact conformation as well as a denatured state. Under certain solvation conditions, both warm and cold denaturations occur between the native and the denatured states. A good agreement is found with the data obtained from calorimetric experiments, thereby validating the proposed model.Comment: 7 pages, 2 figure

The superheated Melting of Grain Boundary

Based on a model of the melting of Grain Boundary (GB), we discuss the possibility of the existence of superheated GB state. A Molecular Dynamics simulation presented here shows that the superheated GB state can realized in the high symmetric tilt GB. Whether the sizes of liquid nuclei exceed a critical size determined the superheating grain boundary melting or not. Our results also indicate that the increase of melting point due to pressure is smaller than the superheating due to nucleation mechanism.Comment: Accepted by PRB, 7 pages and 5 figure

Elasticity and metastability limit in supercooled liquids: a lattice model

We present Monte Carlo simulations on a lattice system that displays a first order phase transition between a disordered phase (liquid) and an ordered phase (crystal). The model is augmented by an interaction that simulates the effect of elasticity in continuum models. The temperature range of stability of the liquid phase is strongly increased in the presence of the elastic interaction. We discuss the consequences of this result for the existence of a kinetic spinodal in real systems.Comment: 8 pages, 5 figure

Kinetic glass behavior in a diffusive model

Three properties of the Edwards-Anderson model with mobile bonds are investigated which are characteristic of kinetic glasses. First is two-time relaxation in aged systems, where a significant difference is observed between spin and bond autocorrelation functions. The spin subsystem does not show two-time behavior, and the relaxation is stretched exponential. The bond subsystem shows two-time behavior, with the first relaxation nearly exponential and the second similar to the spin one. Second is the two-temperature behavior, which can be tuned by bond dilution through the full range reported in the literature. Third is the rigid-to-floppy transition, identified as a function of bond dilution. Simple Glauber Monte Carlo evolution without extraneous constraints reproduces the behavior of classical kinetic simulations, with the bond (spin) degree of freedom corresponding to configurational (orientational) disorder.Comment: 4 pages, 3 figures, minimal corrections, to appear in Phys. Rev. B (RC

Are Protein Folds Atypical?

Protein structures are a very special class among all possible structures. It was suggested that a ``designability principle'' plays a crucial role in nature's selection of protein sequences and structures. Here we provide a theoretical base for such a selection principle, using a novel formulation of the protein folding problem based on hydrophobic interactions. A structure is reduced to a string of 0's and 1's which represent the surface and core sites, respectively, as the backbone is traced. Each structure is therefore associated with one point in a high dimensional space. Sequences are represented by strings of their hydrophobicities and thus can be mapped into the same space. A sequence which lies closer to a particular structure in this space than to any other structures will have that structure as its ground state. Atypical structures, namely those far away from other structures in the high dimensional space, have more sequences which fold into them, and are thermodynamically more stable. We argue that the most common folds of proteins are the most atypical in the space of possible structures.Comment: 15 pages, 5 figure

Inquiries into the Nature of Free Energy and Entropy in Respect to Biochemical Thermodynamics

Free energy and entropy are examined in detail from the standpoint of classical thermodynamics. The approach is logically based on the fact that thermodynamic work is mediated by thermal energy through the tendency for nonthermal energy to convert spontaneously into thermal energy and for thermal energy to distribute spontaneously and uniformly within the accessible space. The fact that free energy is a Second-Law, expendable energy that makes it possible for thermodynamic work to be done at finite rates is emphasized. Entropy, as originally defined, is pointed out to be the capacity factor for thermal energy that is hidden with respect to temperature; it serves to evaluate the practical quality of thermal energy and to account for changes in the amounts of latent thermal energies in systems maintained at constant temperature. A major objective was to clarify the means by which free energy is transferred and conserved in sequences of biological reactions coupled by freely diffusible intermediates. In achieving this objective it was found necessary to distinguish between a 'characteristic free energy' possessed by all First-Law energies in amounts equivalent to the amounts of the energies themselves and a 'free energy of concentration' that is intrinsically mechanical and relatively elusive in that it can appear to be free of First-Law energy. The findings in this regard serve to clarify the fact that the transfer of chemical potential energy from one repository to another along sequences of biological reactions of the above sort occurs through transfer of the First-Law energy as thermal energy and transfer of the Second-Law energy as free energy of concentration.Comment: 18-page PDF; major correction in APPENDIX; minor corrections elsewher

Dynamical heterogeneity in a glass forming ideal gas

We conduct a numerical study of the dynamical behavior of a system of three-dimensional crosses, particles that consist of three mutually perpendicular line segments rigidly joined at their midpoints. In an earlier study [W. van Ketel et al., Phys. Rev. Lett. 94, 135703 (2005)] we showed that this model has the structural properties of an ideal gas, yet the dynamical properties of a strong glass former. In the present paper we report an extensive study of the dynamical heterogeneities that appear in this system in the regime where glassy behavior sets in. On the one hand, we find that the propensity of a particle to diffuse is determined by the structure of its local environment. The local density around mobile particles is significantly less than the average density, but there is little clustering of mobile particles, and the clusters observed tend to be small. On the other hand, dynamical susceptibility results indicate that a large dynamical length scale develops even at moderate densities. This suggests that propensity and other mobility measures are an incomplete measure of dynamical length scales in this system.Comment: 11 pages, 7 figure