Molecular Theory of Hydrophobic Effects: ``She is too mean to have her name repeated.''

This paper reviews the molecular theory of hydrophobic effects relevant to biomolecular structure and assembly in aqueous solution. Recent progress has resulted in simple, validated molecular statistical thermodynamic theories and clarification of confusing theories of decades ago. Current work is resolving effects of wider variations of thermodynamic state, e.g. pressure denaturation of soluble proteins, and more exotic questions such as effects of surface chemistry in treating stability of macromolecular structures in aqueous solutionComment: submitted to Ann. Rev. Phys. Chem., 31 pages, 245 references, 2 figure

Exploring the Free Energy Landscape: From Dynamics to Networks and Back

The knowledge of the Free Energy Landscape topology is the essential key to understand many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers are, how the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times or rate constants, and the hierarchical relationship among basins, complete the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, the dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press

Ensemble preconditioning for Markov chain Monte Carlo simulation

We describe parallel Markov chain Monte Carlo methods that propagate a collective ensemble of paths, with local covariance information calculated from neighboring replicas. The use of collective dynamics eliminates multiplicative noise and stabilizes the dynamics thus providing a practical approach to difficult anisotropic sampling problems in high dimensions. Numerical experiments with model problems demonstrate that dramatic potential speedups, compared to various alternative schemes, are attainable

Comparison of approximate quantum simulation methods applied to normal liquid helium at 4 K.

The Feynman-Kleinert linearized path integral molecular dynamics (FK-LPI), ring polymer molecular dynamics (RPMD), and centroid molecular dynamics (CMD) methods are applied to the simulation of normal liquid helium. Comparisons of the simulation results at the T = 4 K and rho = 0.01873 A-3 state point are presented. The calculated quantum correlation functions for the three methods show significant differences, both in the short time and in the intermediate regions of the spectrum. Our simulation results are also compared to the recent results of other approximate quantum simulation methods. We find that FK-LPI qualitatively agrees with other approximate quantum simulation results while CMD and RPMD predict a qualitatively different impulsive rebound in the velocity autocorrelation function. Frequency space analysis reveals that RPMD exhibits a broad high-frequency tail similar to that from quantum mode coupling theory and numerical analytic continuation approaches, while FK-LPI provides a somewhat more rapid decay at high frequency than any of these three methods. CMD manifests a high-frequency component that is greatly reduced compared with the other methods

Predicting cavity formation free energy: how far is the Gaussian approximation valid?

We examine the range of validity of the Gaussian model for various water-like liquids whose intermolecular potentials differ from SPC/E water, to provide insight into the temperature dependence of the hydrophobic effect for small hard sphere solutes. We find that low compressibility liquids that have more close-packed network structures show much larger deviations from Gaussian fluctuations for low or zero occupancies relative to more compressible fluids with more open networks. Water appears to be a unique molecular fluid in possessing equilibrium density fluctuations that are faithfully described by the Gaussian theory. We ascribe this success to the fact, shown here, that the orientational correlations near a small hard sphere solute involve remarkably little reorganization from the bulk, which is a consequence of water's low solvent reorganization enthalpy and entropy

Predicting cavity formation free energy: how far is the Gaussian approximation valid?

We examine the range of validity of the Gaussian model for various water-like liquids whose intermolecular potentials differ from SPC/E water, to provide insight into the temperature dependence of the hydrophobic effect for small hard sphere solutes. We find that low compressibility liquids that have more close-packed network structures show much larger deviations from Gaussian fluctuations for low or zero occupancies relative to more compressible fluids with more open networks. Water appears to be a unique molecular fluid in possessing equilibrium density fluctuations that are faithfully described by the Gaussian theory. We ascribe this success to the fact, shown here, that the orientational correlations near a small hard sphere solute involve remarkably little reorganization from the bulk, which is a consequence of water's low solvent reorganization enthalpy and entropy

Hydrogen bond strength and network structure effects on hydration of non-polar molecules.

We measure the solvation free energy, Δμ*, for hard spheres and Lennard-Jones particles in a number of artificial liquids made from modified water models. These liquids have reduced hydrogen bond strengths or altered bond angles. By measuring Δμ* for a number of state points at P = 1 bar and different temperatures, we obtain solvation entropies and enthalpies, which are related to the temperature dependence of the solubilities. By resolving the solvation entropy into the sum of the direct solute-solvent interaction and a term depending on the solvent reorganisation enthalpy we show that, although the hydrophobic effect in water at 300 K arises mainly from the small molecular size, its temperature dependence is anomalously low because the reorganisation enthalpy of liquid water is unusually small. We attribute this to the strong tetrahedral network which results from both the molecular geometry and the hydrogen bond strength