A statistical mechanical description of biomolecular hydration

A mixed radial, angular, three-body distribution function as a tool for local structure characterization: Application to single-component structures

A mixed radial, angular three-body distribution function g₃(r_BC, θ_ABC) is introduced, which allows the local atomic order to be more easily characterized in a single graph than with conventional correlation functions. It can be defined to be proportional to the probability of finding an atom C at a distance r_BC from atom B while making an angle θ_ABC with atoms A and B, under the condition that atom A is the nearest neighbor of B. As such, our correlation function contains, for example, the likelihood of angles formed between the nearest and the next-nearest-neighbor bonds. To demonstrate its use and usefulness, a visual library for many one-component crystals is produced first and then employed to characterize the local order in a diverse body of elemental condensed-matter systems. Case studies include the analysis of a grain boundary, several liquids (argon, copper, and antimony), and polyamorphism in crystalline and amorphous silicon including that obtained in a tribological interface.

Probing the triplet correlation function in liquid water by experiments and molecular simulations

Three-body information of liquid water is extracted using X-ray diffraction experiment as well as in molecular simulations via isothermal pressure derivative of structure factor term.

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.

Triplet correlations dominate the transition from simple to tetrahedral liquids

The total, triplet, and pair contributions to the entropy with increasing tetrahedrality are mapped out for the Stillinger-Weber liquids to demonstrate the qualitative and quantitative differences between triplet-dominated, tetrahedral liquids and pair-dominated, simple liquids with regard to supercooling and crystallization. The heat capacity anomaly of tetrahedral liquids originates in local ordering due to both pair and triplet correlations. The results suggest that structural correlations can be directly related to thermodynamic anomalies, phase changes, and self-assembly in other atomic and colloidal fluids.

Solvent-induced free energy landscape and solute-solvent dynamic coupling in a multielement solute

Molecular dynamics simulations using a simple multielement model solute with internal degrees of freedom and accounting for solvent-induced interactions to all orders in explicit water are reported. The potential energy landscape of the solute is flat in vacuo. However, the sole untruncated solvent-induced interactions between apolar (hydrophobic) and charged elements generate a rich landscape of potential of mean force exhibiting typical features of protein landscapes. Despite the simplicity of our solute, the depth of minima in this landscape is not far in size from free energies that stabilize protein conformations. Dynamical coupling between configurational switching of the system and hydration reconfiguration is also elicited. Switching is seen to occur on a time scale two orders of magnitude longer than that of the reconfiguration time of the solute taken alone, or that of the unperturbed solvent. Qualitatively, these results are unaffected by a different choice of the water-water interaction potential. They show that already at an elementary level, solvent-induced interactions alone, when fully accounted for, can be responsible for configurational and dynamical features essential to protein folding and function.

Ion atmosphere around nucleic acid

The poyion-ion preferential interaction coefficient Gamma describes the exclusion of coions and accumulations of counterions in the vicinity of a polyion in an aqueous solution. We give tight upper and lower bounds for Gamma when the polyion can be modeled by a cylinder of infinite length but of arbitrary charge density. This case can be used as a model for long strands of DNA or RNA in an aqueous solution containing univalent cations. The salt dependence of Gamma is predicted from low to intermediate and high salt concentrations. We also indicate how the bounds for the infinite polyion can be exploited to place bounds for polyions of length greater than a constant on the order of the inverse Debye screening length.

Proton transfer pathways in the mutant His-64–Ala of human carbonic anhydrase II

We have investigated the possible proton transfer pathways from the surface of the protein to the zinc-bound water molecule in the mutant His-64-Ala of human carbonic anhydrase II. Starting with an input of known crystallographic structures of the mutant, we model the proton pathways as hydrogen-bonded networks of proton conducting groups and bound solvent molecules. No proton path is detected in the mutant, in close agreement with the experimental observation of a 20-fold decrease in its catalytic efficiency compared to the wild-type enzyme. We also investigate in detail changes in hydration structure at the active site of the mutant and the resulting proton paths in the presence of an exogenous proton donor 4-methylimidazole (4-MI). The proton transfer pathways thus detected are correlated to the observed chemical rescue of catalytic activity by 4-MI.

H-bonding in protein hydration revisited

H-bonding between protein surface polar/charged groups and water is one of the key factors of protein hydration. Here, we introduce an Accessible Surface Area (ASA) model for computationally efficient estimation of a free energy of water-protein H-bonding at any given protein conformation. The free energy of water-protein H-bonds is estimated using empirical formulas describing probabilities of hydrogen bond formation that were derived from molecular dynamics simulations of water molecules at the surface of a small protein, Crambin, from the Abyssinian cabbage (Crambe abyssinica) seed. The results suggest that atomic solvation parameters (ASP) widely used in continuum hydration models might be dependent on ASA for polar/charged atoms under consideration. The predictions of the model are found to be in qualitative agreement with the available experimental data on model compounds. This model combines the computational speed of ASA potential, with the high resolution of more sophisticated solvation methods.

Effect of N-acetylaspartic acid on the diffusion coefficient of water: a proton magnetic resonance phantom method for measurement of osmolyte-obligated water

N-acetyl-L-aspartic acid (NAA) is an amino acid present in the vertebrate brain that is synthesized and stored primarily in neurons, although it cannot be hydrolyzed in these cells. Nonetheless, neuronal NAA is dynamic and turns over more than once each day by cycling, via extracellular fluids (ECF), between neurons and catabolic compartments in oligodendrocytes. One important role of the NAA intercompartmental cycle appears to be osmoregulatory, and in this role it may be the primary mechanism for the removal of metabolic water, against a water gradient, from myelinated neurons. However, the number of water molecules that might be cotransported to ECF per NAA molecule released is as yet unclear. In this investigation, using a proton nuclear magnetic resonance method and diffusion measurements at two magnetic field strengths on water and NAA phantoms in vitro, the effect of NAA on the diffusion coefficient of water has been measured, and a ratio (K) of obligated water molecules per molecule of NAA has been determined. For NAA measured at 100mM and 3 Tesla K=24 and at 7 Tesla K=14. Based on these results, apparent K(NAA) varies inversely with field strength, and with a computed field strength factor of 2.55mmol water/unit Tesla, K(NAA) in the absence of any applied magnetic field strength would be 32.

RNA solvation: a molecular dynamics simulation perspective

With the availability of accurate methods to treat the electrostatic long-range interactions, molecular dynamics simulations have resulted in refined dynamical models of the structure of the hydration shell around RNA motifs. The models reviewed here range from basic Watson-Crick to more specific noncanonical base pairs, from "simple" double helices to RNA molecules displaying more complex tertiary folds, and from DNA/RNA hybrid double helices to RNA hybrids formed with a chemically modified strand.

Dynamics of a protein and water molecules surrounding the protein: hydrogen-bonding between vibrating water molecules and a fluctuating protein

Internal and rigid-body motions of bovine pancreatic trypsin inhibitor (BPTI) and of water molecules surrounding the BPTI are studied in a vicinity of an energy minimum using a normal mode analysis proposed as the independent molecule model. Water's rigid-body motion is predominant in comparison to its internal motions. We have derived information about the relationship between the magnitude of a thermal ellipsoid of an H-bonding atom and the anisotropy of its ellipsoid, and the relationship between the magnitude of the ellipsoid and the H-bond strength. We see a relationship between vibrational frequencies (assuming rigid-body motion of the water molecules) and the H-bond strength of the water taking part in this H-bonding. Analyzing the H-bond strength, we found that a hydrogen in water is likely to H-bond to oxygen in the protein, whereas an oxygen in water has a less strong preference to H-bond to the protein. For water molecules acting as the hydrogen acceptor, strong H-bonding has longer lifetimes than weak H-bonding.

Water and ion binding around r(UpA)12 and d(TpA)12 oligomers--comparison with RNA and DNA (CpG)12 duplexes

The structural and dynamic properties of the water and ion first coordination shell of the r(A-U) and d(A-T) base-pairs embedded within the r(UpA)12 and d(TpA)12 duplexes are described on the basis of two 2.4 ns molecular dynamics simulations performed in a neutralizing aqueous environment with 0.25 M added KCl. The results are compared to previous molecular dynamics simulations of the r(CpG)12 and d(CpG)12 structures performed under similar conditions. It can be concluded that: (i) RNA helices are more rigid than DNA helices of identical sequence, as reflected by the fact that RNA duplexes keep their initial A-form shape while DNA duplexes adopt more sequence-specific shapes. (ii) Around these base-pairs, the water molecules occupy 21 to 22 well-defined hydration sites, some of which are partially occupied by potassium ions. (iii) These hydration sites are occupied by an average of 21.9, 21.0, 20.1, and 19.8 solvent molecules (water and ions) around the r(G=C), r(A-U), d(G=C), and d(A-T) pairs, respectively. (iv) From a dynamic point of view, the stability of the hydration shell is the strongest for the r(G=C) pairs and the weakest for the d(A-T) pairs. (v) For RNA, the observed long-lived hydration patterns are essentially non-sequence dependent and involve water bridges located in the deep groove and linking OR atoms of adjacent phosphate groups. Maximum lifetimes are close to 400 ps. (vi) In contrast, for DNA, long-lived hydration patterns are sequence dependent and located in the minor groove. For d(CpG)12, water bridges linking the (G)N3 and (C)O2 with the O4' atoms of adjacent nucleotides with 400 ps maximum lifetimes are characterized while no such bridges are observed for d(TpA)12. (vii) Potassium ions are observed to bind preferentially to deep/major groove atoms at RpY steps, essentially d(GpC), r(GpC), and r(ApU), by forming ion-bridges between electronegative atoms of adjacent base-pairs. On average, about half an ion is observed per base-pair. Positive ion-binding determinants are related to the proximity of two or more electronegative atoms. Negative binding determinants are associated with the electrostatic and steric hindrance due to the proximity of electropositive amino groups and neutral methyl groups. Potassium ions form only transient contacts with phosphate groups.

Effects of electric charges on hydrophobic forces. II

We study by molecular-dynamics simulations the effect of electric charges of either sign on hydrophobic interactions and on the dynamics of hydration water, using explicit water and very simplified solutes. Results show that the presence of a charged solute can disrupt the "hydrophobic contact bond" between two apolar solutes nearby, by forcing them towards a different configuration. As a consequence of different structural changes of the solvent caused by charges of opposite sign, the effect is markedly charge-sign-dependent. Analogous weaker effects appear to be induced by the presence of one additional apolar element. The dynamics of hydration water around each solute is also seen to be strongly influenced by the presence of other (charged or uncharged) nearby solutes. Comparison between our results on hydration water dynamics around charged solutes and available experimental data allows sorting out the effects of solute charge sign and size. Our results also offer a plain interpretation of the equivalence of the effects on water structure due to solute ions and to high pressures. These results reflect at a basic paradigmatic level the immensely more complex cases of well-known phenomena such as salting-in and salting-out, and of protein conformational changes caused, e.g., by the arrival of a charged or of an apolar group (phosphorilation or methylation). As it will be discussed, they help in the direction of Delbruck's desirable "progress towards a radical physical explanation" for this class of phenomena.

A molecular dynamics study of the 41-56 beta-hairpin from B1 domain of protein G

The structural and dynamical behavior of the 41-56 beta-hairpin from the protein G B1 domain (GB1) has been studied at different temperatures using molecular dynamics (MD) simulations in an aqueous environment. The purpose of these simulations is to establish the stability of this hairpin in view of its possible role as a nucleation site for protein folding. The conformation of the peptide in the crystallographic structure of the protein GB1 (native conformation) was lost in all simulations. The new equilibrium conformations are stable for several nanoseconds at 300K (>10 ns), 350 K (>6.5 ns), and even at 450 K (up to 2.5 ns). The new structures have very similar hairpin-like conformations with properties in agreement with available experimental nuclear Overhauser effect (NOE) data. The stability of the structure in the hydrophobic core region during the simulations is consistent with the experimental data and provides further evidence for the role played by hydrophobic interactions in hairpin structures. Essential dynamics analysis shows that the dynamics of the peptide at different temperatures spans basically the same essential subspace. The main equilibrium motions in this subspace involve large fluctuations of the residues in the turn and ends regions. Of the six interchain hydrogen bonds, the inner four remain stable during the simulations. The space spanned by the first two eigenvectors, as sampled at 450 K, includes almost all of the 47 different hairpin structures found in the database. Finally, analysis of the hydration of the 300 K average conformations shows that the hydration sites observed in the native conformation are still well hydrated in the equilibrium MD ensemble.

Local water bridges and protein conformational stability

Recent studies have pointed out the important role of local water structures in protein conformational stability. Here, we present an accurate and computationally effective way to estimate the free energy contribution of the simplest water structure motif--the water bridge. Based on the combination of empirical parameters for accessible protein surface area and the explicit consideration of all possible water bridges with the protein, we introduce an improved protein solvation model. We find that accounting for water bridge formation in our model is essential to understand the conformational behavior of polypeptides in water. The model formulation, in fact, does not depend on the polypeptide nature of the solute and is therefore applicable to other flexible biomolecules (i.e., DNAs, RNAs, polysaccharides, etc.).

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.

Function of the N-acetyl-L-histidine system in the vertebrate eye. Evidence in support of a role as a molecular water pump

N-acetyl-L-histidine (NAH) is a major constituent of poikilotherm brain, eye, heart, and muscle, but for which there is no known function. NAH is characterized by high tissue concentrations, a high tissue/extracellular fluid (ECF) gradient, and by a continuous selective and regulated efflux into ECF. In the eye, there is a complete compartmentalization of the synthetic and hydrolytic enzymes, with synthesis of NAH from AcCoA and L-histidine (His) occurring in the lens, and its hydrolysis to acetate and His restricted to surrounding ocular fluids. Using 14C-isotopes, the cycling of NAH between lens and ocular fluids in a simple support medium consisting of NaCl (0.9%), Ca2+ (4 mEq/L) and D-glucose (5 mM) at pH 7.4 has previously been observed. In the present study, using the isolated lens of the goldfish eye, each of the components of that support medium has been individually varied in order to determine its effect on NAH release down its intercompartmental gradient. As a result of these and related studies, it is suggested that NAH may function as a metabolically recyclable gradient-driven molecular water pump. It is proposed that water influx or generation of metabolic water serves as the trigger mechanism to open a Ca-dependent gate for the release of NAH down its gradient, along with its associated water. Preliminary analyses suggest that in addition to its potential for multiple daily cycles, a strongly ionized hydrophilic molecule, such as NAH, may include a large power function as a result of its attraction to water, and it has been calculated that an aqua complex of each NAH molecule may have 33 dipole-dipole-associated water molecules as it passes into ECF. It is this unique combination of a capacity for multiple cycles per day, coupled with a large power function, that may allow for such an intracellular osmolyte to be present in relatively low concentration in comparison to total cellular osmolality, and yet to perform a large and important task with little expenditure of energy. With each NAH molecule recycled up to 10 times/d, and a power factor of 33, there could be 330 mmol of water transported/mmol of NAH each day. With typical NAH concentrations in brains of poikilothermic vertebrates of 5-10 mmol/kg, there is the potential for up to 3.3 mol (60 mL) of water to be removed each day/kg of brain, a value that represents about 8% of total brain water content. Dewatering of the released osmolyte would occur in two additional steps, consisting of its hydrolysis and the subsequent active uptake of its metabolites. It is also suggested that NAH is the archetype of several metabolically and structurally related cellular osmolytes found in both poikilotherms and homeotherms, for which there is similarly no known function, and these may form a family of cycling hydrophilic osmolytes that serve as molecular water pumps in a variety of tissues. These include the basic His containing derivatives: NAH, carnosine, anserine, ophidine, and homocarnosine, and the acidic aspartate derivatives: N-acetyl-L-aspartate (NAA) and N-acetyl-L-aspartylglutamate (NAAG). In each of these cases, the high intracellular/extracellular osmolyte gradient appears to be maintained by combining a hydrophilic protein amino acid with a nonprotein moiety to block its use in other intracellular metabolic pathways, and by blocking catabolism of the derivative by maintaining its hydrolytic enzyme in an extracytosolic membrane or extracellular compartment. Unlike other known water-regulating mechanisms, the proposed cellular system is unique in that as a water pump, it can function as a water regulator independently of extracellular solute composition or osmolality. Finally, based on the hypothesis developed, the NAH system would represent the first cellular water pump to be identified.

Protein hydration density: theory, simulations and crystallography

Models of protein hydration are becoming increasingly more accurate in comparison with experimental data. The recent success of these models implies that the major features of the solvation layers are dominated by local correlations and that such correlations are universal. The excellent agreement between theoretical and experimental solvent electron density radial distributions marks a significant success in our ability to accurately model macromolecular hydration.

Glutamic acid 286 in subunit I of cytochrome bo3 is involved in proton translocation

Glutamic acid 286 (E286; Escherichia coli cytochrome bo3 numbering) in subunit I of the respiratory heme-copper oxidases is highly conserved and has been suggested to be involved in proton translocation. We report a technique of enzyme reconstitution that yields essentially unidirectionally oriented cytochrome bo3 vesicles in which proton translocation can be measured. Such experiments are not feasible in the E286Q mutant due to strong inhibition of respiration, but this is not the case for the mutants E286D and E286C. The reconstituted E286D mutant enzyme readily translocates protons whereas E286C does not. Loss of proton translocation in the D135N mutant, but not in D135E or D407N, also is verified using proteoliposomes. Stopped-flow experiments show that the peroxy intermediate accumulates in the reaction of the E286Q and E286C mutant enzymes with O2. We conclude that an acidic function of the 286 locus is essential for the mechanism of proton translocation.

Bound water in the proton translocation mechanism of the haem-copper oxidases

We address the molecular mechanism by which the haem-copper oxidases translocate protons. Reduction of O2 to water takes place at a haem iron-copper (CuB) centre, and protons enter from one side of the membrane through a 'channel' structure in the enzyme. Statistical-mechanical calculations predict bound water molecules within this channel, and mutagenesis experiments show that breaking this water structure impedes proton translocation. Hydrogen-bonded water molecules connect the channel further via a conserved glutamic acid residue to a histidine ligand of CuB. The glutamic acid side chain may have to move during proton transfer because proton translocation is abolished if it is forced to interact with a nearby lysine or arginine. Perturbing the CuB ligand structure shifts an infrared mode that may be ascribed to the O-H stretch of bound water. This is sensitive to mutations of the glutamic acid, supporting its connectivity to the histidine. These results suggest key roles of bound water, the glutamic acid and the histidine copper ligand in the mechanism of proton translocation.