Dominant solvation effects from the primary shell of hydration: Approximation for molecular dynamics simulations

A simple approximation is developed to account for the dominant effects of solvation in molecular dynamics simulations of biopolymers. A small number of water molecules are included explicitly in the primary hydration shell around the biopolymer. A nonspherical confining potential responding dynamically to the conformational changes of the biopolymer is applied to prevent evaporation and to approximate the conditions of constant pressure of a bulk solution. Simulations of a spherical system of 25 water molecules are lined to adjust the empirical restraining potential to yield a uniform density distribution close to that in the bulk liquid. The primary hydration shell approach is tested with molecular dynamics simulations of simple hydrated peptides. The conformational equilibrium of alanine dipeptide and alanine tripeptide is examined using umbrella sampling calculations. The relative free energies of the C_7ax (? = 60, ψ = ?80) and α_L (? = 60, ψ = 60) conformations of the alanine dipeptide and the opened and closed conformations of a reversed β-turn modeled with the alanine tripeptide were calculated. The results indicate that the primary hydration shell can reproduce the influence of solvent on small peptides that was observed in simulations involving a much larger number of water molecules. © 1995 John Wiley & Sons, Inc.     

Integral equation theories for predicting water structure around molecules

Water plays a crucial role in the structure and function of proteins and other biological macromolecules; thus, theories of aqueous solvation for these molecules are of great importance. However, water is a complex solvent whose properties are still not completely understood. Statistical mechanical integral equation theories predict the density distribution of water molecules around a solute so that all particles are fully represented and thus potentially both molecular and macroscopic properties are included. Here we discuss how several theoretical tools we have developed have been integrated into an integral equation theory designed for globular macromolecular solutes such as proteins. Our approach predicts the three-dimensional spatial and orientational distribution of water molecules around a solute. Beginning with a three-dimensional Ornstein-Zernike equation, a separation is made between a reference part dependent only on the spatial distribution of solvent and a perturbation part dependent also on the orientational distribution of solvent. The spatial part is treated at a molecular level by a modified hypernetted chain closure whereas the orientational part is treated as a Boltzmann prefactor using a quasi-continuum theory we developed for solvation of simple ions. A potential energy function for water molecules is also needed and the sticky dipole models of water, such as our recently developed soft-sticky dipole (SSD) model, are ideal for the proposed separation. Moreover, SSD water is as good as or better than three point models typically used for simulations of biological macromolecules in structural, dielectric and dynamics properties and yet is seven times faster in Monte Carlo and four times faster in molecular dynamics simulations. Since our integral equation theory accurately predicts results from Monte Carlo simulations for solvation of a variety of test cases from a single water or ion to ice-like clusters and ion pairs, the application of this theory to biological macromolecules is promising.     

Acceptable protein and solvent behavior in primary hydration shell simulations of hen lysozyme

The "primary hydration shell" method in molecular dynamics simulations uses a two- to three-layer thick shell of explicitly represented water molecules as the solvent around the protein of interest. We show that despite its simplicity, this computationally cheap model is capable of predicting acceptable water and protein behavior using the CHARMM22/CMAP potential function. For protein dynamics, comparisons are made with Lipari-Szabo order parameters. These have been derived from NMR relaxation parameters for pico-nano second motions of the NH groups in the main-chain and NH(2) groups in Asn/Gln side chains in hen lysozyme. It is also shown that an even simpler, and therefore faster, water-shell model leads to results in similarly good agreement with experiments, and also compared with simulations using a full box of water with periodic boundary conditions or with an implicit solvation model. Thus, the primary hydration shell method should be useful in making larger systems accessible to extensive simulations.     

Application of the primary hydration shell approach to locally enhanced sampling simulated annealing: computer simulation of thyrotropin-releasing hormone in water

A unified model of simulated annealing with locally enhanced sampling (LES) in a primary hydration shell (PHS) aqueous environment is developed and tested by predicting the structure of the tripeptide thyrotropin-releasing hormone (TRH) in solution. The model extends the formulation of the restraining force in the PHS method as a function of temperature, number of copies in the LES method, and shell thickness. The dependence of the restraining force on temperature can be shown to follow the relationship c(1)T - c(2), which can be derived from the expression for kinetic energy in molecular dynamics simulations. The calibration of the restraining force for different simulation conditions reveals the dependence of c(1) and c(2) on the number of copies in the LES method and the thickness of the PHS. The predicted structure of TRH is in very good agreement with results from NMR experiments and from a 10-ns PHS simulation at 300 K. The method promises to be useful in predicting structure of peptides and proteins in an aqueous environment.     

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.     

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.     

Femtosecond Hydration Map of Intrinsically Disordered α-Synuclein

Protein hydration water plays a fundamentally important role in protein folding, binding, assembly, and function. Little is known about the hydration water in intrinsically disordered proteins that challenge the conventional sequence-structure-function paradigm. Here, by combining experiments and simulations, we show the existence of dynamical heterogeneity of hydration water in an intrinsically disordered presynaptic protein, namely α-synuclein, implicated in Parkinson’s disease. We took advantage of nonoccurrence of cysteine in the sequence and incorporated a number of cysteine residues at the N-terminal segment, the central amyloidogenic nonamyloid-β component (NAC) domain, and the C-terminal end of α-synuclein. We then labeled these cysteine variants using environment-sensitive thiol-active fluorophore and monitored the solvation dynamics using femtosecond time-resolved fluorescence. The site-specific femtosecond time-resolved experiments allowed us to construct the hydration map of α-synuclein. Our results show the presence of three dynamically distinct types of water: bulk, hydration, and confined water. The amyloidogenic NAC domain contains dynamically restrained water molecules that are strikingly different from the water molecules present in the other two domains. Atomistic molecular dynamics simulations revealed longer residence times for water molecules near the NAC domain and supported our experimental observations. Additionally, our simulations allowed us to decipher the molecular origin of the dynamical heterogeneity of water in α-synuclein. These simulations captured the quasi-bound water molecules within the NAC domain originating from a complex interplay between the local chain compaction and the sequence composition. Our findings from this synergistic experimental simulation approach suggest longer trapping of interfacial water molecules near the amyloidogenic hotspot that triggers the pathological conversion into amyloids via chain sequestration, chain desolvation, and entropic liberation of ordered water molecules.     

Simulation of peptide folding with explicit water--a mean solvation method

A new approach to efficiently calculate solvent effect in computer simulation of macromolecular systems has been developed. Explicit solvent molecules are included in the simulation to provide a mean solvation force for the solute conformational search. Simulations of an alanine dipeptide in aqueous solution showed that the new approach is significantly more efficient than conventional molecular dynamics method in conformational search, mainly because the mean solvation force reduced the solvent damping effect. This approach allows the solute and solvent to be simulated separately with different methods. For the macromolecule, the rigid fragment constraint dynamics method we developed previously allows large time-steps. For the solvent, a combination of a modified force-bias Monte Carlo method and a preferential sampling can efficiently sample the conformational space. A folding simulation of a 16-residue peptide in water showed high efficiency of the new approach.     

Structure of hydration water in proteins: a comparison of molecular dynamics simulations and database analysis

Hydration layer water molecules play important structural and functional roles in proteins. Despite being a critical component in biomolecular systems, characterizing the properties of hydration water poses a challenge for both experiments and simulations. In this context we investigate the local structure of hydration water molecules as a function of the distance from the protein and water molecules respectively in 188 high resolution protein structures and compare it with those obtained from molecular dynamics simulations. Tetrahedral order parameter of water in proteins calculated from previous and present simulation studies show that the potential of bulk water overestimates the average tetrahedral order parameter compared to those calculated from crystal structures. Hydration waters are found to be more ordered at a distance between the first and second solvation shell from the protein surface. The values of the order parameter decrease sharply when the water molecules are located very near or far away from the protein surface. At small water-water distance, the values of order parameter of water are very low. The average order parameter records a maximum value at a distance equivalent to the first solvation layer with respect to the water-water radial distribution and asymptotically approaches a constant value at large distances. Results from present analysis will help to get a better insight into structure of hydration water around proteins. The analysis will also help to improve the accuracy of water models on the protein surface.     

A solvent model for simulations of peptides in bilayers. I. Membrane-promoting alpha-helix formation

We describe an efficient solvation model for proteins. In this model atomic solvation parameters imitating the hydrocarbon core of a membrane, water, and weak polar solvent (octanol) were developed. An optimal number of solvation parameters was chosen based on analysis of atomic hydrophobicities and fitting experimental free energies of gas-cyclohexane, gas-water, and octanol-water transfer for amino acids. The solvation energy term incorporated into the ECEPP/2 potential energy function was tested in Monte Carlo simulations of a number of small peptides with known energies of bilayer-water and octanol-water transfer. The calculated properties were shown to agree reasonably well with the experimental data. Furthermore, the solvation model was used to assess membrane-promoting alpha-helix formation. To accomplish this, all-atom models of 20-residue homopolypeptides-poly-Leu, poly-Val, poly-Ile, and poly-Gly in initial random coil conformation-were subjected to nonrestrained Monte Carlo conformational search in vacuo and with the solvation terms mimicking the water and hydrophobic parts of the bilayer. All the peptides demonstrated their largest helix-forming tendencies in a nonpolar environment, where the lowest-energy conformers of poly-Leu, Val, Ile revealed 100, 95, and 80% of alpha-helical content, respectively. Energetic and conformational properties of Gly in all environments were shown to be different from those observed for residues with hydrophobic side chains. Applications of the solvation model to simulations of peptides and proteins in the presence of membrane, along with limitations of the approach, are discussed.     

Effective water model for Monte Carlo simulations of proteins

We present an effective theory for water. Our goal is to formulate on accurate model for the effects of solvation on protein dynamics, without incurring the huge computational cost and the slow temporal evolution typical of molecular dynamics simulations of liquids. We replace the individual water molecules in an all-atom potential with a local dielectric density field, with self interactions given by the Landau-Ginzburg free energy and external interactions by Lennard-Jones forces at the surface of the protein atoms. We explore conformational space with finite temperature Monte Carlo dynamics, using parallel Langevin and Fourier acceleration algorithms well suited to data-parallel computer architectures such as the Connection Machine. To establish the validity of our approximations, we compare our electrostatic contribution to the solvalion energy with the results of Lim, Bashford, and Karplus using a conventional static continuum dielectric cavity model, and the non electrostatic contributions with estimates of hydrophohic surface free energy. Our model can also accommodate ionic charges and temperature fluctuations, We propose future investigations extending our effective theory of solvation to include explicit orientational entropy and hydroxen-bonding terms. © 1995 John Wiley & Sons, Inc.     

Molecular simulation of dioleoylphosphatidylcholine lipid bilayers at differing levels of hydration.

The structure and dynamics of the lipid and water components of dioleoylphosphatidylcholine bilayers at various levels of hydration were studied using molecular dynamics (MD) simulations. Equilibration of these systems proceeded by use of a hybrid MD and configurational-bias Monte Carlo technique using one atmosphere of pressure normal to the membrane and a set point for the lateral area derived from experimental Bragg spacings, combined with experimentally derived specific volumes for each of the system components. Membrane surface tensions were observed to be of the order of tens of dyn/cm. The transbilayer molecular fragment peak positions at low hydration were found to agree with experimental neutron and x-ray scattering profiles and previously published simulations. For hydration levels of 5.4, 11.4, and 16 waters/lipid, molecular fragment distributions and order parameters for the headgroup, lipid chains, and water were quantified. Spin-lattice relaxation rates and lateral self-diffusion coefficients of water agreed well with results from experimental nuclear magnetic resonance studies. Relaxation rates of the choline segments and chemical shift anisotropies for the phosphate and carbonyls were computed. Headgroup orientation, as measured by the P-N vector, showed enhanced alignment with the membrane surface at low hydration. The sign of the membrane dipole potential reversed at low hydration, with the membrane interior negative relative to the interlamellar region. Calculation of the number of water molecules in the headgroup hydration shell, as a function of hydration level, supports the hypothesis that the break point in the curve of Bragg spacing versus hydration level near 12 waters/lipid, observed experimentally by Hristova and White (1988. Biophys. J. 74:2419-2433), marks the completion of the first hydration shell.     

Effects of metal ion and solute conformation change on hydration of small amino acid

The effects of metal ion and solute conformation change on the structures, energetic and dynamics of water molecules in the first hydration shell of amino acid were studied, using three forms of alanine (Ala) and Li(+)/Ala as model molecules. The theoretical investigations were started with construction of the test-particle model (T-model) potentials for all molecules involved and followed by molecular dynamics (MD) simulations of [Ala](aq) and [Li(+)/Ala](aq) at 298 K. The MD results showed that the hydrogen bond (H-bond) networks of water at the functional groups of Ala are strengthened by the metal ion binding, whereas the rotation of the N-C(alpha) bond from the angle phi=0 degrees to 180 degrees brings about smaller effects which cannot be generalized. It was also shown that the dynamics of water molecule in the first hydration shell of amino acid could be estimated from the total-average potential energy landscapes and the water exchange diagrams. The MD results suggested inclusion of an additional dynamic step in the water exchange process, in which water molecule moves inside a channel within the first hydration shell of solute, before leaving the channel at some point. The theoretical results reported in the present work iterated the necessity to include explicit water molecules in the model calculations.     

Proteins maintain hydration at high [KCl] concentration regardless of content in acidic amino acids

Proteins of halophilic organisms, which accumulate molar concentrations of KCl in their cytoplasm, have a much higher content in acidic amino acids than proteins of mesophilic organisms. It has been proposed that this excess is necessary to maintain proteins hydrated in an environment with low water activity, either via direct interactions between water and the carboxylate groups of acidic amino acids or via cooperative interactions between acidic amino acids and hydrated cations. Our simulation study of five halophilic proteins and five mesophilic counterparts does not support either possibility. The simulations use the AMBER ff14SB force field with newly optimized Lennard-Jones parameters for the interactions between carboxylate groups and potassium ions. We find that proteins with a larger fraction of acidic amino acids indeed have higher hydration levels, as measured by the concentration of water in their hydration shell and the number of water/protein hydrogen bonds. However, the hydration level of each protein is identical at low (b_KCl = 0.15 mol/kg) and high (b_KCl = 2 mol/kg) KCl concentrations; excess acidic amino acids are clearly not necessary to maintain proteins hydrated at high salt concentration. It has also been proposed that cooperative interactions between acidic amino acids in halophilic proteins and hydrated cations stabilize the folded protein structure and would lead to slower dynamics of the solvation shell. We find that the translational dynamics of the solvation shell is barely distinguishable between halophilic and mesophilic proteins; if such a cooperative effect exists, it does not have that entropic signature.     

Solvation model dependency of helix-coil transition in polyalanine

Helix-coil transitions in polyalanine molecules of length 10 are studied by multi-canonical Monte Carlo simulations. The solvation effects are included by either a distance-dependent dielectric permittivity or by a term that is proportional to the solvent-accessible surface area of the peptide. We found a strong dependence of the characteristics of the helix-coil transition from the details of the solvation model.     

Grand canonical ensemble Monte Carlo simulation of the dCpG/proflavine crystal hydrate.

The grand canonical ensemble Monte Carlo molecular simulation method is used to investigate hydration patterns in the crystal hydrate structure of the dCpG/proflavine intercalated complex. The objective of this study is to show by example that the recently advocated grand canonical ensemble simulation is a computationally efficient method for determining the positions of the hydrating water molecules in protein and nucleic acid structures. A detailed molecular simulation convergence analysis and an analogous comparison of the theoretical results with experiments clearly show that the grand ensemble simulations can be far more advantageous than the comparable canonical ensemble simulations.     

Polyproline II helix is the preferred conformation for unfolded polyalanine in water

Does aqueous solvent discriminate among peptide conformers? To address this question, we computed the solvation free energy of a blocked, 12‐residue polyalanyl‐peptide in explicit water and analyzed its solvent structure. The peptide was modeled in each of 4 conformers: α‐helix, antiparallel β‐strand, parallel β‐strand, and polyproline II helix (P_II). Monte Carlo simulations in the canonical ensemble were performed at 300 K using the CHARMM 22 forcefield with TIP3P water. The simulations indicate that the solvation free energy of P_II is favored over that of other conformers for reasons that defy conventional explanation. Specifically, in these 4 conformers, an almost perfect correlation is found between a residue's solvent‐accessible surface area and the volume of its first solvent shell, but neither quantity is correlated with the observed differences in solvation free energy. Instead, solvation free energy tracks with the interaction energy between the peptide and its first‐shell water. An additional, previously unrecognized contribution involves the conformation‐dependent perturbation of first‐shell solvent organization. Unlike P_II, β‐strands induce formation of entropically disfavored peptide:water bridges that order vicinal water in a manner reminiscent of the hydrophobic effect. The use of explicit water allows us to capture and characterize these dynamic water bridges that form and dissolve during our simulations. Proteins 2004. © 2004 Wiley‐Liss, Inc.     

Modeling DNA Hydration: Comparison of Calculated and Experimental Hydration Properties of Nuclic Acid Bases

Abstract

Hydration properties of individual nucleic acid bases were calculated and compared with the available experimental data. Three sets of classical potential functions (PF) used in simulations of nucleic acid hydration were juxtaposed: (i) the PF developed by Poltev and Malenkov (PM), (ii) the PF of Weiner and Kollman (WK), which together with Jorgensen's TIP3P water model are widely used in the AMBER program, and (HI) OPLS (optimized potentials for liquid simulations) developed by Jorgensen (J). The global minima of interaction energy of single water molecules with all the natural nucleic acid bases correspond to the formation of two water-base hydrogen bonds (water bridging of two hydrophilic atoms of the base). The energy values of these minima calculated via PM potentials are in somewhat better conformity with mass-spectrometric data than the values calculated via WK PF. OPLS gave much weaker water-base interactions for all compounds considered, thus these PF were not used in further computations. Monte Carlo simulations of the hydration of 9- methyladenine, 1-methyluracil and 1-methylthymine were performed in systems with 400 water molecules and periodic boundary conditions. Results of simulations with PM potentials give better agreement with experimental data on hydration energies than WK PF. Computations with PM PF of the hydration energy of keto and enol tautomers of 9-methyl- guanine can account for the shift in the tautomeric equilibrium of guanine in aqueous media to a dominance of the keto form in spite of nearly equal intrinsic stability of keto and enol tautomers. The results of guanine hydration computations are discussed in relation to mechanisms of base mispairing errors in nucleic acid biosynthesis. The data presented in this paper along with previous results on simulation of hydration shell structures in DNA duplex grooves provide ample evidence for the advantages of PM PF in studies of nucleic-acid hydration.