The thermodynamics of solvophobic effects: A molecular‐dynamics study of n‐butane in carbon tetrachloride and water

Hofmeister Order of Anions on Protein Stability Originates from Lifshitz-van der Waals Dispersion Interaction with the Protein Phase

The mechanism underpinning the Hofmeister order of anions on protein stability and other physical and biological processes has been a mystery since its discovery in 1888. In the present study, we investigated electrostatic and Lifshitz-van der Waals (L-vdW) dispersion (electrodynamic) interactions between Hofmeister salts and four monomeric globular proteins. It is shown that structure-stabilizing salts exerted positive L-vdW pressure, whereas structure-destabilizing salts exerted negative L-vdW pressure on proteins. The relative order of the L-vdW pressure followed the Hofmeister series and it overshadowed the electrostatic pressure at high salt concentrations. The net change in the thermal denaturation temperature (ΔT_d) of proteins in 0.8 M Hofmeister salt solutions followed a linear relationship (r² > 0.8) with the net electrodynamic pressure regardless of the physicochemical differences between proteins. This study also revealed that segregation of anions into structure stabilizers and destabilizers depended on the dielectric susceptibility of the anion in the ultraviolet region: ions having absorbtion spectrum in the ultraviolet region (e.g., Cl^-, Br^-, I^-, and SCN^-) exerted a negative electrodynamic pressure, whereas those with absorbtion spectrum only in the infrared region, for example, SO₄^2-, exerted a positive electrodynamic pressure. The lack of ultraviolet absorption of SO₄^2- ions was because of quenching of ultraviolet radiation by water at below 170 nm.

Evaluations of the Absolute and Relative Free Energies for Antidepressant Binding to the Amino Acid Membrane Transporter LeuT with Free Energy Simulations

The binding of ligands to protein receptors with high affinity and specificity is central to many cellular processes. The quest for the development of computational models capable of accurately evaluating binding affinity remains one of the main goals of modern computational biophysics. In this work, free energy perturbation/molecular dynamics simulations were used to evaluate absolute and relative binding affinity for three different antidepressants to a sodium-dependent membrane transporter, LeuT, a bacterial homologue of human serotonin and dopamine transporters. Dysfunction of these membrane transporters in mammals has been implicated in multiple diseases of the nervous system, including bipolar disorder and depression. Furthermore, these proteins are key targets for antidepressants including fluoxetine (aka Prozac) and tricyclic antidepressants known to block transport activity. In addition to being clinically relevant, this system, where multiple crystal structures are readily available, represents an ideal testing ground for methods used to study the molecular mechanisms of ligand binding to membrane proteins. We discuss possible pitfalls and different levels of approximation required to evaluate binding affinity, such as the dependence of the computed affinities on the strength of constraints and the sensitivity of the computed affinities to the particular partial charges derived from restrained electrostatic potential fitting of quantum mechanics electrostatic potential. Finally, we compare the effects of different constraint schemes on the absolute and relative binding affinities obtained from free energy simulations.

CHARMM: the biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

Thermodynamics of a conformational change using a random walk in energy-reaction coordinate space: Application to methane dimer hydrophobic interactions

A random walk sampling algorithm allows the extraction of the density of states distribution in energy-reaction coordinate space. As a result, the temperature dependences of thermodynamic quantities such as relative energy, entropy, and heat capacity can be calculated using first-principles statistical mechanics. The strategies for optimal convergence of the algorithm and control of its accuracy are proposed. We show that the saturation of the error [Q. Yan and J. J. de Pablo, Phys. Rev. Lett. 90, 035701 (2003); E. Belardinelli and V. D. Pereyra, J. Chem. Phys. 127, 184105 (2007)] is due to the use of histogram flatness as a criterion of convergence. An application of the algorithm to methane dimer hydrophobic interactions is presented. We obtained a quantitatively accurate energy-entropy decomposition of the methane dimer cavity potential. The presented results confirm the previous results, and they provide new information regarding the thermodynamics of hydrophobic interactions. We show that the finite-difference approximation, which is widely used in molecular dynamic simulations for the energy-entropy decomposition of a free energy potential, can lead to a significant error.

Conformation and Solvation Structure for an Isolated n-Octadecane Chain in Water, Methanol, and Their Mixtures

Configurational-bias Monte Carlo simulations in the isobaric-isothermal ensemble (T = 323 K and p = 10 atm) were carried out to probe structural properties of an isolated n-octadecane chain solvated in water, methanol, water-rich, or methanol-rich mixtures and, for comparison, of an isolated chain in the gas phase and for neat liquid n-octadecane. The united-atom version of the TraPPE (transferable potentials for phase equilibria) force field was used to represent n-octadecane and methanol and the TIP-4P model was used for water. In all six environments, broad conformational distributions are observed and the n-octadecane chains are found to predominantly adopt extended, but not all-trans conformations. In addition, a small fraction of more collapsed conformations in which the chain ends approach each other is observed for aqueous hydration, the water-rich solvent mixture and the gas phase, but the simulation data do not support a simple two-state picture with folded and unfolded basins of attraction. For chains in these three "poor" solvent environments, the dihedral angles near the center of the chain show an enhancement of the gauche population. The ensemble of water-solvated chains with end-to-end contacts is preferentially found in a U-shaped conformation rather than a more globular state. An analysis of the local solvation structures in the water-methanol mixtures shows, as expected, an enrichment of the methyl group of methanol near the methylene and methyl segments of the n-octadecane chain. Interestingly, these local bead fractions are enhanced by factors of 2.5 and 1.5 for methyl and methylene segments reflecting the more hydrophobic nature of the former segments.

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 solution.

Conformational equilibria of alkanes in aqueous solution: relationship to water structure near hydrophobic solutes

Conformational free energies of butane, pentane, and hexane in water are calculated from molecular simulations with explicit waters and from a simple molecular theory in which the local hydration structure is estimated based on a proximity approximation. This proximity approximation uses only the two nearest carbon atoms on the alkane to predict the local water density at a given point in space. Conformational free energies of hydration are subsequently calculated using a free energy perturbation method. Quantitative agreement is found between the free energies obtained from simulations and theory. Moreover, free energy calculations using this proximity approximation are approximately four orders of magnitude faster than those based on explicit water simulations. Our results demonstrate the accuracy and utility of the proximity approximation for predicting water structure as the basis for a quantitative description of n-alkane conformational equilibria in water. In addition, the proximity approximation provides a molecular foundation for extending predictions of water structure and hydration thermodynamic properties of simple hydrophobic solutes to larger clusters or assemblies of hydrophobic solutes.

Effective energy function for proteins in solution

A Gaussian solvent-exclusion model for the solvation free energy is developed. It is based on theoretical considerations and parametrized with experimental data. When combined with the CHARMM 19 polar hydrogen energy function, it provides an effective energy function (EEF1) for proteins in solution. The solvation model assumes that the solvation free energy of a protein molecule is a sum of group contributions, which are determined from values for small model compounds. For charged groups, the self-energy contribution is accounted for primarily by the exclusion model. Ionic side-chains are neutralized, and a distance-dependent dielectric constant is used to approximate the charge-charge interactions in solution. The resulting EEF1 is subjected to a number of tests. Molecular dynamics simulations at room temperature of several proteins in their native conformation are performed, and stable trajectories are obtained. The deviations from the experimental structures are similar to those observed in explicit water simulations. The calculated enthalpy of unfolding of a polyalanine helix is found to be in good agreement with experimental data. Results reported elsewhere show that EEF1 clearly distinguishes correctly from incorrectly folded proteins, both in static energy evaluations and in molecular dynamics simulations and that unfolding pathways obtained by high-temperature molecular dynamics simulations agree with those obtained by explicit water simulations. Thus, this energy function appears to provide a realistic first approximation to the effective energy hypersurface of proteins.

Changes in water structure induced by a hydrophobic solute probed by simulation of the water hydrogen bond angle and radial distribution functions

In order to better characterize changes in water structure induced by a hydrophobic solute the oxygen-oxygen and hydrogen-hydrogen radial distribution functions (goo(r), ghh(r)) and the hydrogen bond angle distribution function p(theta) for water molecules in the first hydration shell of the tetramethyl ammonium (TMA) cation were computed using Monte Carlo simulations. goo(r) and ghh(r) were corrected for the effect of solute volume exclusion on the local solvent density so that intrinsic structural changes independent of local solvent density variations could be detected. Comparison of ghh(r) of TMA's first hydration shell water with ghh(r) for bulk water shows subtle but clear evidence of structure formation induced by the ion. These changes in ghh(r) are very similar to those seen experimentally for larger tetra-alkyl ammonium ions in previous neutron diffraction experiments. Larger changes in p(theta) in the first hydration shell of TMA were seen. Comparison of changes in p(theta) with changes in goo(r) and ghh(r) show that the angle distribution function provides the most sensitive way to analyze water structure changes associated with hydrophobic solvation.

Computer simulations with explicit solvent: recent progress in the thermodynamic decomposition of free energies and in modeling electrostatic effects

This review focuses on recent progress in two areas in which computer simulations with explicit solvent are being applied: the thermodynamic decomposition of free energies, and modeling electrostatic effects. The computationally intensive nature of these simulations has been an obstacle to the systematic study of many problems in solvation thermodynamics, such as the decomposition of solvation and ligand binding free energies into component enthalpies and entropies. With the revolution in computer power continuing, these problems are ripe for study but require the judicious choice of algorithms and approximations. We provide a critical evaluation of several numerical approaches to the thermodynamic decomposition of free energies and summarize applications in the current literature. Progress in computer simulations with explicit solvent of charge perturbations in biomolecules was slow in the early 1990s because of the widespread use of truncated Coulomb potentials in these simulations, among other factors. Development of the sophisticated technology described in this review to handle the long-range electrostatic interactions has increased the predictive power of these simulations to the point where comparisons between explicit and continuum solvent models can reveal differences that have their true physical origin in the inherent molecularity of the surrounding medium.

Hydration and conformational equilibria of simple hydrophobic and amphiphilic solutes

We consider whether the continuum model of hydration optimized to reproduce vacuum-to-water transfer free energies simultaneously describes the hydration free energy contributions to conformational equilibria of the same solutes in water. To this end, transfer and conformational free energies of idealized hydrophobic and amphiphilic solutes in water are calculated from explicit water simulations and compared to continuum model predictions. As benchmark hydrophobic solutes, we examine the hydration of linear alkanes from methane through hexane. Amphiphilic solutes were created by adding a charge of +/-1e to a terminal methyl group of butane. We find that phenomenological continuum parameters fit to transfer free energies are significantly different from those fit to conformational free energies of our model solutes. This difference is attributed to continuum model parameters that depend on solute conformation in water, and leads to effective values for the free energy/surface area coefficient and Born radii that best describe conformational equilibrium. In light of these results, we believe that continuum models of hydration optimized to fit transfer free energies do not accurately capture the balance between hydrophobic and electrostatic contributions that determines the solute conformational state in aqueous solution.

Free-energy simulations of the retinal cis --> trans isomerization in bacteriorhodopsin

Free-energy profiles for ground-state cis --> trans isomerization of retinal in vacuum, in solution, and in the protein bacteriorhodopsin are calculated using free-energy simulations. The free-energy barriers in the protein were 9 kcal/mol for ionized Asp85 and 14 kcal/mol for neutral Asp85, significantly lower than those found in solution (18 kcal/mol) or vacuum (19 kcal/mol). Therefore, bacteriorhodopsin can be said to act as a catalyst in the isomerization. The barrier in the protein is due mainly to stabilization of the transition state through favorable nonbonded interactions with the protein part of the system, with internal strain and interactions with solvent playing minor roles. The protonated Asp85 simulation models the behavior of the system in the N --> O transition. Our calculated 14 kcal/mol barrier and 4-ms relaxation time for this process are in excellent agreement with experimentally measured values of 12 kcal/mol and 5 ms, respectively. The ionized Asp85 simulation models two hypothetical processes: the N --> O transition with a proton removed from Asp85 and the initial BR568 --> L transition on the ground-state energy surface. The cis-trans isomerization barrier in this system is 9 kcal/mol, the lowest of all the studied cases. The presence of the charged carboxylate group in the ionized Asp85 system leads to strong stabilization of the transition state by interactions with the surroundings and changes the distance between Asp85 and the Schiff base proton compared to the corresponding distance in the neutral Asp85 system. This suggests that the protonation of Asp85 plays an important role in regulating access to the Schiff base proton. For both Asp85 ionization states the calculated cis-trans free-energy difference was close to 0, indicating that the protein can accommodate both retinal isomers equally well. The computed negligible difference between the N and O free-energy levels is in accord with experimental data.

Free energy simulations of axial contacts in sickle-cell hemoglobin

Molecular dynamics simulations have been used to investigate the thermodynamic stability of axial contacts in sickle-cell hemoglobin (HbS). Free energy changes were evaluated for the point mutation beta 121 Glu --> Gln in the axial contact region of HbS crystals. The calculations predict a free energy change of-3.6 kcal/mol per contact for the mutation, which is in qualitative agreement with experimental observations of aggravated sickling found in the double mutant Hb D Los Angeles (beta 6 Glu --> Val. beta 121 Glu --> Gln) relative to HbS (beta 6 Glu --> Val). The beta 121 Glu is sequestered in a salt link with beta 17 Lys located on the same polypeptide chain, making the Glu interactions with its surroundings similar in aggregates and individual hemoglobins. Due to this cancellation of the large electrostatic Glu contributions, the weak nonspecific interactions between the Gln and the neighboring polypeptide chain are the main contributing factor to the enhanced aggregation of Hb D Los Angeles relative to HbS. Together with the previous study of the lateral contact [K. Kuczera et al. (1990) Proceedings of the National Academy of Science USA, Vol. 87, pp, 8481-8485], the present results provide a more complete picture of the forces driving the sickling aggregation. A comparison of different treatments of internal flexibility in free energy simulations and analysis of rate of convergence of the different calculated properties has also been performed.

Reverse turns in blocked dipeptides are intrinsically unstable in water

We have carried out molecular dynamics simulations to study the conformational equilibria of two blocked dipeptides, Ac-Ala-Ala-NHMe and trans-Ac-Pro-Ala-NHMe, in water (Ac, amino-terminal blocking group COCH3; NHMe, carboxy-terminal blocking group NHCH3). Using specialized sampling techniques we computed free-energy surfaces as functions of a conformation co-ordinate that corresponds to hydrogen-bonded reverse turns at small values and to extended conformations at large values. The free-energy difference between hydrogen-bonded reverse turn conformations and extended conformations, determined from the equilibrium constants for reverse turn unfolding, is approximately -5 kcal/mole for Ac-Ala-Ala-NHMe, and -10 kcal/mole for Ac-Pro-Ala-NHMe. These results demonstrate that reverse turns in blocked dipeptides are intrinsically unstable in water. That is, in the absence of strongly stabilizing sequence-specific inter-residue interactions involving side-chains and/or charged terminal groups, the extended conformations of small peptides are highly favored in solution. By thermodynamically decomposing the free-energy differences, we found that the peptide-water entropy is the primary reason for the exceptional stability of the extended conformations of both peptides, and that the differences between the two peptides are primarily due to differences in the peptide-water interactions. In addition, we assessed the "proline effect" on the conformational equilibria by comparing the differences in configurational entropies between the reverse turn and extended conformations of the two peptides. As expected, the extended conformation of the Pro-Ala peptide is destabilized by reduced configurational entropy, but the effect is negligible in the blocked dipeptides. Finally, we compared our results with the results of several other experimental studies to identify some of the specific interactions that may be responsible for stabilizing reverse turns in small peptides in solution.