Statistical mechanical treatment of the structural hydration of biological macromolecules: Results for B-DNA

Triplet correlation functions in liquid water

Triplet correlations have been shown to play a crucial role in the transformation of simple liquids to anomalous tetrahedral fluids [M. Singh, D. Dhabal, A. H. Nguyen, V. Molinero, and C. Chakravarty, Phys. Rev. Lett. 112, 147801 (2014)]. Here we examine triplet correlation functions for water, arguably the most important tetrahedral liquid, under ambient conditions, using configurational ensembles derived from molecular dynamics (MD) simulations and reverse Monte Carlo (RMC) datasets fitted to experimental scattering data. Four different RMC data sets with widely varying hydrogen-bond topologies fitted to neutron and x-ray scattering data are considered [K. T. Wikfeldt, M. Leetmaa, M. P. Ljungberg, A. Nilsson, and L. G. M. Pettersson, J. Phys. Chem. B 113, 6246 (2009)]. Molecular dynamics simulations are performed for two rigid-body effective pair potentials (SPC/E and TIP4P/2005) and the monatomic water (mW) model. Triplet correlation functions are compared with other structural measures for tetrahedrality, such as the O-O-O angular distribution function and the local tetrahedral order distributions. In contrast to the pair correlation functions, which are identical for all the RMC ensembles, the O-O-O triplet correlation function can discriminate between ensembles with different degrees of tetrahedral network formation with the maximally symmetric, tetrahedral SYM dataset displaying distinct signatures of tetrahedrality similar to those obtained from atomistic simulations of the SPC/E model. Triplet correlations from the RMC datasets conform closely to the Kirkwood superposition approximation, while those from MD simulations show deviations within the first two neighbour shells. The possibilities for experimental estimation of triplet correlations of water and other tetrahedral liquids are discussed.

Implicit solvent models

Implicit solvent models for biomolecular simulations are reviewed and their underlying statistical mechanical basis is discussed. The fundamental quantity that implicit models seek to approximate is the solute potential of mean force, which determines the statistical weight of solute conformations, and which is obtained by averaging over the solvent degrees of freedom. It is possible to express the total free energy as the reversible work performed in two successive steps. First, the solute is inserted in the solvent with zero atomic partial charges; second, the atomic partial charges of the solute are switched from zero to their full values. Consequently, the total solvation free energy corresponds to a sum of non-polar and electrostatic contributions. These two contributions are often approximated by simple geometrical models (such as solvent exposed area models) and by macroscopic continuum electrostatics, respectively. One powerful route is to approximate the average solvent density distribution around the solute, i.e. the solute-solvent density correlation functions, as in statistical mechanical integral equations. Recent progress with semi-analytical approximations makes continuum electrostatics treatments very efficient. Still more efficient are fully empirical, knowledge-based models, whose relation to explicit solvent treatments is not fully resolved, however. Continuum models that treat both solute and solvent as dielectric continua are also discussed, and the relation between the solute fluctuations and its macroscopic dielectric constant(s) clarified.

Solvation Model Based on Order Parameters and a Fast Sampling Method for the Calculation of the Solvation Free Energies of Peptides

An analytical solvation model is proposed as a function of an order parameter, which represents the local arrangement of water molecules in the first solvation shell of peptide atoms. The model is combined with a fast sampling method, rotational isomeric state Monte Carlo, to sample efficiently the torsional degrees of freedom on a peptide backbone. This order parameter solvation model is shown to reproduce without ad hoc fitting parameters the solvation free energies of single amino acids and tripeptides with slightly better accuracy than the generalized Born model but with several orders of magnitude improvement in efficiency. This method is a potential candidate for efficiently and accurately tackling some important issues in biophysical chemistry that are related to solvation, for example, protein folding, ligand binding, etc. Our results also present fundamental new insights into solvation. Specifically, the local water geometry, represented in this work by a properly defined order parameter, carries the majority, if not all, of the energetic information of solvation, including solute-solvent interactions and solvent reorganization in the presence of the solute.

Protein side-chain motion and hydration in proton-transfer pathways. Results for cytochrome p450cam

Proton-transfer reactions form an integral part of bioenergetics and enzymatic catalysis. The identification of proton-conducting pathways inside a protein is a key to understanding the mechanisms of biomolecular proton transfer. Proton pathways are modeled here as hydrogen bonded networks of proton-conducting groups, including proton-exchanging groups of amino acid side chains and bound water molecules. We focus on the identification of potential proton-conducting pathways inside a protein of known structure. However, consideration of the static structure alone is often not sufficient to detect suitable proton-transfer paths, leading, for example, from the protein surface to the active site buried inside the protein. We include dynamic fluctuations of amino acid side chains and water molecules into our analysis. To illustrate the method, proton transfer into the active site of cytochrome P450cam is studied. The cooperative rotation of amino acids and motion of water molecules are found to connect the protein surface to the molecular oxygen. Our observations emphasize the intrinsic dynamical nature of proton pathways where critical connections in the network may be transiently provided by mobile groups.

Hydration of biological molecules: lipids versus nucleic acids

We used FTIR spectroscopy to comparatively study the hydration of films prepared from nucleic acids (DNA and double-stranded RNA) and lipids (phosphatidylcholines and phosphatidylethanolamines chosen as the most abundant ones) at room temperature by varying the ambient relative humidity in terms of solvent-induced structural changes. The nucleic acids and phospholipids both display examples of polymorphism on the one hand and structural conservatism on the other; even closely related representatives behave differently in this respect. DNA undergoes a hydration-driven A-B conformational transition, but RNA maintains an A-like structure independently of the water activity. Similarly, a main transition between the solid and liquid-crystalline phases can be induced lyotropically in certain phosphatidylcholines, while their phosphatidylethanolamine counterparts do not exhibit chain melting under the same conditions. A principal difference concerning the structural changes that occur in the studied biomolecules is given by the relevant water-substrate stoichiometries. These are rather high in DNA and often low in phospholipids, suggesting different mechanisms of action of the hydration water that appears to induce structural changes on global- and local-mode levels, respectively.

Fast prediction of hydration free energies from molecular interaction fields

A novel empirical model is presented that allows the fast computation of hydration free energies with high accuracy. The linear model is based upon the separation of the free energy of hydration into a cavity and an interaction term. The cavity contribution is modeled as a linear combination of molecular volume and surface terms. The interaction part is derived from the statistical three-dimensional (3D) free energy density and is modeled approximately as a molecular interaction field using the program GRID. A compression scheme is employed to represent this 3D information on the molecular surface by means of a linear combination of surface functions. A set of 81 small organic molecules with known experimental hydration free energies is used to determine the coefficients of the linear model by least squares regression. The fit is statistically significant yielding a correlation coefficient of 0.99, a root mean square error of 0.27 kcal/mol for the 81 molecules belonging to the training set, and 0.63 kcal/mol for an independent test set of 10 molecules.

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.

Potential of mean force treatment of salt-mediated protein crystallization

In the initial stages of crystallization of proteins, monomers aggregate rapidly and form nuclei and large fractal clusters, as previously shown by dynamic light scattering experiments (Georgalis, Y., J. Schüler, J. Frank, D. M. Soumpasis, and W. Saenger. 1995. Protein crystallization screening through scattering techniques. Adv. Colloid Interface Sci. 58:57-86). In this communication we initiate an effort to understand the effective interactions controlling charged protein aggregation and crystallization using the potential of mean force (PMF) theory. We compute the PMFs of the system lysozyme-water-NaCl within the framework of the hypernetted chain approximation for a wide range of protein and salt concentrations. We show that the computed effective interactions can rationalize the experimentally observed aggregation behavior of lysozyme under crystallization conditions.

A statistical mechanical description of biomolecular hydration

An efficient and accurate theoretical description of the structural hydration of biological macromolecules is presented. The hydration of molecules of almost arbitrary size (tRNA, antibody-antigen complexes, photosynthetic reaction centre) can be studied in solution and in the crystalline environment. The biomolecular structure obtained from X-ray crystallography, NMR or modelling is required as input information. The structural arrangement of water molecules near a biomolecular surface is represented by the local water density, analogous to the corresponding electron density in an X-ray diffraction experiment. The water-density distribution is approximated in terms of two- and three-particle correlation functions of solute atoms with water using a potentials-of-mean-force expansion.

Theoretical description of biomolecular hydration. Application to A-DNA

The local density of water molecules around a biomolecule is constructed from calculated two- and three-points correlation functions of polar solvents in water using a Potential-of-Mean-Force (PMF) expansion. As a simple approximation, the hydration of all polar (including charged) groups in a biomolecule is represented by the hydration of water oxygen in bulk water, and the effect of non-polar groups on hydration are neglected, except for excluded volume effects. Pair and triplet correlation functions are calculated by molecular dynamics simulations. We present calculations of the structural hydration for ideal A-DNA molecules with sequences [d(CG)5]2 and [d(C5G5)]2. We find that this method can accurately reproduce the hydration patterns of A-DNA observed in neutron diffraction experiments on oriented DNA fibers (P. Langan et al. J. Biomol. Struct. Dyn., 10, 489 (1992)).