A thermodynamic analysis of solvation

Size effects in nonpolar solvation: lessons from two simple models

Size dependence of the solute chemical potential mu(u) is examined using the Ornstein-Zernike equation for two models of the nonpolar solute-solvent interactions. Simple Lennard-Jones interactions are assumed in the first model while the Lennard-Jones potential is distributed over the solute volume in the second model similar to the Hamaker theory for the colloid dispersion forces. In both models, while mu(u) rises asymptotically as the third power of the solute size in agreement with asymptotic solution of the scaled particle theory, it increases faster at smaller sizes. Deviations from the cubic law are more pronounced at higher solvent densities and stronger molecular interactions. Within a relatively narrow size range typical for small organic molecules, mu(u) can be approximated with a polynomial of the third or even the second power. However, the latter approximation is less accurate and cannot be employed for extrapolation to the larger size region.

First-principles calculation of the folding free energy of a three-helix bundle protein

The folding and unfolding of a three-helix bundle protein were explored with molecular-dynamics simulations, cluster analysis, and weighted-histogram techniques. The folding-unfolding process occurs by means of a "folding funnel," in which a uniform and broad distribution of conformational states is accessible outside of the native manifold. This distribution narrows near a transition region and becomes compact within the native manifold. Key thermodynamic steps in folding include initial interactions around the amino-terminal helix-turn-helix motif, interactions between helices I and II, and, finally, the docking of helix III onto the helix I-II subdomain. A metastable minimum in the calculated free-energy surface is observed at approximately 1.5 times the native volume. Folding-unfolding thermodynamics are dominated by the opposing influences of protein-solvent energy, which favors unfolding, and the overall entropy, which favors folding by means of the hydrophobic effect.

Free energy simulations: the meaning of the individual contributions from a component analysis

A theoretical analysis is made of the decomposition into contributions from individual interactions of the free energy calculated by thermodynamic integration. It is demonstrated that such a decomposition, often referred to as "component analysis," is meaningful, even though it is a function of the integration path. Moreover, it is shown that the path dependence can be used to determine the relation of the contribution of a given interaction to the state of the system. To illustrate these conclusions, a simple transformation (Cl- to Br- in aqueous solution) is analyzed by use of the Reference Interaction Site Model-Hypernetted Chain Closure integral equation approach; it avoids the calculational difficulties of macromolecular simulation while retaining their conceptual complexity. The difference in the solvation free energy between chloride and bromide is calculated, and the contributions of the Lennard-Jones and electrostatic terms in the potential function are analyzed by the use of suitably chosen integration paths. The model is also used to examine the path dependence of individual contributions to the double free energy differences (delta delta G or delta delta A) that are often employed in free energy simulations of biological systems. The alchemical path, as contrasted with the experimental path, is shown to be appropriate for interpreting the effects of mutations on ligand binding and protein stability. The formulation is used to obtain a better understanding of the success of the Poisson-Boltzmann continuum approach for determining the solvation properties of polar and ionic systems.

Enthalpy-entropy compensation in the thermodynamics of hydrophobicity

Using Widom's potential distribution theory (J. Chem. Phys. 39 (1963) 2808; J. Phys. Chem. 86 (1982) 869), a general and a special theorems are derived, by means of which one can judge whether a particular sub-process of an overall process will produce compensating changes in enthalpy and entropy. The enthalpy-entropy compensation phenomena that are observed in the transfer process of a hydrophobic molecule from a non-aqueous phase to water are examined in the light of these theorems. It is concluded that most sub-processes involved in the hydrophobic transfer process are compensating except one, that of inserting a cavity corresponding to the solute molecule in the liquid. The reason that this process is non-compensating, and therefore most responsible for the hydrophobicity, is traced to the hard core overlap between solvent and the solute molecules.

Integral equation approaches to structure and thermodynamics of aqueous salt solutions

Results for free energy, entropy, enthalpy and internal energy of solvation for monovalent ions in water have been studied by comparing DRISM theory results to those of RISM and ARISM theories. The greatly improved dielectric behavior in the DRISM case enabled the examination of realistically modeled salts at finite concentrations. The link between solvent structure and the entropy of solvent co-spheres was examined. Finally comparison with the Born free energy equation shows its virtues and flaws due to ignoring cavity formation and asymmetric solvation terms which together always contribute significantly to the free energy of hydration of ions.

Role of hydrogen bonds in hydrophobicity: the free energy of cavity formation in water models with and without the hydrogen bonds

The free energies of cavity formation in water with and without hydrogen bonding potential were computed from the results of a set of Monte Carlo simulation calculations on pure liquid TIP4P water model and on the same model but with the electrostatic charges turned off (Lennard-Jones liquid). The free energies of cavity formation in the Lennard-Jones liquids are higher than or approximately equal to those in TIP4P water, depending, respectively, on whether the Lennard-Jones size parameter sigma is set equal to 3.15 A, which is the value of sigma for TIP4P water, or to 2.8 A, which is the commonly assumed value for the oxygen-oxygen distance between two hydrogen-bonded water molecules. This result indicates that changes in the hydrogen-bonded structure of water and/or in the orientational degree of freedom of water are not essential features in the production of the large free energy change upon cavity formation.

Molecular recognition in proteins. Simulation analysis of substrate binding by a tyrosyl-tRNA synthetase mutant

Alchemical molecular dynamics simulations are performed to determine the difference in the free energy of binding of the tyrosine substrate between the wild type of tyrosyl-tRNA synthetase (TyrRS) from Bacillus stearothermophilus and the mutant Tyr169-->Phe. The results are of general interest because the Tyr169 hydroxyl group interacts with the ammonium group of the substrate in a manner corresponding to that found in other amino acid binding proteins (e.g. the Asp receptor of the chemotactic bacterium Salmonella typhimurium and class I major histocompatibility complex molecules). The calculated free-energy change due to the Tyr169-->Phe mutation is 3.4 kcal/mol (the statistical error is +/- 0.5 kcal/mol) in satisfactory agreement with the experimental value of 3(+/- 0.5) kcal/mol. By use of thermodynamic integration, the contribution of the different terms to the free energy change are estimated. The path dependence of such a decomposition is discussed and it is suggested that the alchemical choice is of primary interest for understanding the interactions involved. There are large protein contributions to the alchemical free energy difference of the bound and free enzyme that cancel in the overall result. Due to this cancellation, the essential interactions contributing to the free-energy change are those between the OH group of Tyr169 and water in the free enzyme and those between the OH group of Tyr169 and the ammonium group of the substrate in the bound system. The results thus support simple models based on a balance of hydrogen bonding interactions.

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.

Hidden thermodynamics of mutant proteins: a molecular dynamics analysis

A molecular dynamics simulation method is used to determine the contributions of individual amino acid residues and solvent molecules to free energy changes in proteins. Its application to the hemoglobin interface mutant Asp G1(99) beta----Ala shows that some of the contributions to the difference in the free energy of cooperativity are as large as 60 kilocalories (kcal) per mole. Since the overall free energy change is only -5.5 kcal/mole (versus the experimental value of -3.4 kcal/mole), essential elements of the thermodynamics are hidden in the measured results. By exposing the individual contributions, the free energy simulation provides new insights into the origin of thermodynamic changes in mutant proteins and demonstrates the role of effects beyond those usually considered in structural analyses.