Molecular dynamics and quantum chemical studies of solvent effects on cyclo glycylglycine and glycylalanine dipeptides

Hydrogen bond (H-bond) interactions between the two cyclo dipeptides, cyclo(glycyl-glycine) (CGG) and cyclo(glycyl-alanine) (CGA), and water have been studied using molecular dynamics (MD) and quantum chemical methods. The MD studies have been carried out on CGG and CGA in water using fixed charge force field (AMBER ff03) for over 10 ns with a MD time step of 2 fs. The results of this study show that the solvation pattern influences the conformations of the cyclo dipeptides. Following molecular simulations, post Hartree–Fock and density functional theory methods have been used to explore the molecular properties of the cyclo dipeptides in gaseous and aqueous phase environments. The self-consistent reaction field theory has been used to optimise the cyclopeptides in diethyl ether (? = 4.3) and water (? = 78.5), and the solvent effects have been analysed. A cluster of eight water molecules leads to the formation of first solvation shell of CGG and CGA and the strong H-bonding mainly contributes to the interaction energies. The H-bond interactions have been analysed by the calculation of electron density ρ(r) and its Laplacian ▽²ρ(r) at bond critical points using atoms in molecules theory. The natural bond orbital analysis was carried out to reveal the nature of H-bond interactions. In the solvated complexes, the keto carbons registered the maximum NMR chemical shifts.     

Investigation of rubidium(I) ion solvation in liquid ammonia using QMCF-MD simulation and NBO analysis of first solvation shell structure

Rb(I) ion solvation in liquid ammonia has been studied by an ab initio quantum mechanical charge field molecular dynamics simulation, and the first solvation shell structure has been analyzed using natural bond orbital. The simulation was performed for an ion and 593 ammonia molecules in a box with a length of 29.03 Å corresponding to a liquid ammonia density of 0.69 g/mL at 235.16 K. The quantum mechanical calculation was carried out for atomic interactions in the radius of 6.4 Å from the ion using LANL2DZ ECP and DZP (Dunning) basis sets for Rb(I) ion and ammonia respectively. The trajectories of the simulation were analyzed in terms of radial, angular, and coordination number distribution functions, vibration, and mean residence time (MRT). Two solvation shell regions are observed for the Rb(I)-N as well as the Rb(I)-H. The maximum distance of Rb(I)-N in the first solvation shell is in accordance with experimental data where a coordination number of 8 is favorable. A non-single coordination number of the first and second shell indicates dynamic solvation structure. It is confirmed by frequent exchange ligand processes observed within a simulation time of 15 ps. The low stabilization energy of donor acceptor ion-ligand interaction with a small Wiberg bond index affirms that the Rb(I)-NH₃ interaction is weak electrostatically.     

Microsolvation of Mg2+, Ca2+: strong influence of formal charges in hydrogen bond networks

A stochastic exploration of the quantum conformational spaces in the microsolvation of divalent cations with explicit consideration of up to six solvent molecules [Mg (H ₂ O) _n )]²⁺, (n?=?3, 4, 5, 6) at the B3LYP, MP2, CCSD(T) levels is presented. We find several cases in which the formal charge in Mg²⁺ causes dissociation of water molecules in the first solvation shell, leaving a hydroxide ion available to interact with the central cation, the released proton being transferred to outer solvation shells in a Grotthus type mechanism; this particular finding sheds light on the capacity of Mg²⁺ to promote formation of hydroxide anions, a process necessary to regulate proton transfer in enzymes with exonuclease activity. Two distinct types of hydrogen bonds, scattered over a wide range of distances (1.35–2.15 Å) were identified. We find that in inner solvation shells, where hydrogen bond networks are severely disturbed, most of the interaction energies come from electrostatic and polarization+charge transfer, while in outer solvation shells the situation approximates that of pure water clusters.

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.     

A theoretical investigation on the conformation and the interaction of CHF2OCF2CHF2 (desflurane II) with one water molecule

The conformation and the interaction of CHF₂OCF₂CHF₂ (desflurane II) with one water molecule is investigated theoretically using the ab initio MP2/aug-cc-pvdz and DFT-based M062X/6-311++G(d,p) methods. The calculations include the optimized geometries, the harmonic frequencies of relevant vibrational modes along with a natural bond orbital (NBO) analysis including the NBO charges, the hybridization of the C atom and the intra- and intermolecular hyperconjugation energies. In the two most stable conformers, the CH bond of the F₂HCO- group occupies the gauche position. The hyperconjugation energies are about the same for both conformers and the conformational preference depends on the interaction between the non-bonded F and H atoms. The deprotonation enthalpies of the CH bonds are about the same for both conformers, the proton affinity of the less stable conformer being 3 kcal mol^?1 higher. Both conformers of desflurane II interact with water forming cyclic complexes characterized by CH…O and OH…F hydrogen bonds. The binding energies are moderate, ranging from ?2.4 to ?3.2 kcal mol^?1 at the MP2 level. The origin of the blue shifts of the ν(CH) vibrations is analyzed. In three of the complexes, the water molecule acts as an electron donor. Interestingly, in these cases a charge transfer is also directed to the non bonded OH group of the water molecule. This effect seems to be a property of polyfluorinated ethers.     

Conformational analysis of enkephalin analogs containing a disulfide bond. Models for delta- and mu-receptor opioid agonists

Conformational analysis of the cyclic opioids H-Tyr-D-Pen-Gly-Phe-D-Pen-OH (DPDPE) and H-Tyr-D-Cys-Gly-Phe-D-Cys-OH (DCDCE) have been performed using the AMBER program. DPDPE is considerably more selective for delta-receptors than DCDCE. Using the RNGCFM program, a large number of ways were found to close the 14-membered disulfide-containing ring structure. However, intramolecular hydrogen bonds were only possible in gamma-turn and inverse gamma-turn conformations centered on the glycine residue which were associated with opposite chiralities of the disulfide bond. With the cyclic part of the molecules in either a gamma-turn or inverse gamma-turn, a systematic conformational analysis was performed on the tyrosine and phenylalanine sidechains. This showed that conformers with the tyrosine and phenylalanine phenyl rings in the vicinity of the disulfide bond were preferred due to attractive van der Waals forces. For DPDPE, however, this was only possible with a positive dihedral angle for the disulfide bond due to the presence of the beta-carbon methyls of Pen2. In contrast, these preferred conformers were possible with both chiralities of the disulfide bond in DCDCE. Conformational entropies and free energies were computed from the translational, rotational, and vibrational energy levels available to each conformer. The conformational entropies were found to vary significantly and to result in a re-ordering of the lowest energy minima. Based on these conformational differences in DPDPE and DCDCE and their differing pharmacological selectivities, tentative conformational preferences for delta- and mu-receptor opioid peptides are proposed.     

Calculation of the total electrostatic energy of a macromolecular system: solvation energies, binding energies, and conformational analysis

In this report we describe an accurate numerical method for calculating the total electrostatic energy of molecules of arbitrary shape and charge distribution, accounting for both Coulombic and solvent polarization terms. In addition to the solvation energies of individual molecules, the method can be used to calculate the electrostatic energy associated with conformational changes in proteins as well as changes in solvation energy that accompany the binding of charged substrates. The validity of the method is examined by calculating the hydration energies of acetate, methyl ammonium, ammonium, and methanol. The method is then used to study the relationship between the depth of a charge within a protein and its interaction with the solvent. Calculations of the relative electrostatic energies of crystal and misfolded conformations of Themiste dyscritum hemerythrin and the VL domain of an antibody are also presented. The results indicate that electrostatic charge-solvent interactions strongly favor the crystal structures. More generally, it is found that charge-solvent interactions, which are frequently neglected in protein structure analysis, can make large contributions to the total energy of a macromolecular system.     

Peptides and Peptoids - A Systematic Structure Comparison

A systematic analysis of the conformational space of the basic structure unit of peptoids in comparison to the corresponding peptide unit was performed based on ab initio MO theory and complemented by molecular mechanics (MM) and molecular dynamics (MD) calculations both in the gas phase and in aqueous solution.The calculations show three minimum conformations denoted as C_7ß, a_D and a that do not correspond to conformers on the gas phase peptide potential energy hypersurface. The influence of aqueous solvation was estimated by means of continuum models. The MD simulations indicate the a_D form as the preferred conformation in solution both in cis and trans peptide bond orientations.     

Computational investigation on microsolvation of the osmolyte glycine betaine [GB (H2O)1-7]

The preferential interactions of glycine betaine (GB) with solvent components and the effect of solvent on its stability have been examined. In particular, the microsolvation of organic osmolyte and widely important osmoprotectant in nature as glycine betaine has been reported by using M06 method. A number of configurations (b_X (a-z)) of the clusters for one to seven water molecules (×?=?1-7) have been considered for the microsolvation. Structures of stable conformers are obtained and denoted as b1a, b2a, b3a, b4a, b5a, b6a and b7a. It is observed from the interaction energy difference (?E) that only seven water molecules can be accommodated in the first solvation shell to stabilize GB. It is also observed that the calculated relative energy using M06 is in close agreement with calculations at the MP2 level of theory.

Reversible scaling of dihedral angle barriers during molecular dynamics to improve structure prediction of cyclic peptides.

Peptide cyclization or chemical cross-linking has frequently been used to restrict the conformational freedom of a peptide, for example, to enhance its capacity for selective binding to a target receptor molecule. Structure prediction of cyclic peptides is important to evaluate possible conformations prior to synthesis. Because of the conformational constraints imposed by cyclization low energy conformations of cyclic peptides can be separated by large energy barriers. In order to improve the conformational search properties of molecular dynamics (MD) simulations a potential scaling method has been designed. The approach consists of several consecutive MD simulations with a specific lowering of dihedral energy barriers and reduced nonbonded interactions between atoms separated by three atoms followed by gradually scaling the potential until the original barriers are reached. Application to four cyclic penta- and hexa-peptide test cases and a protein loop of known structure indicates that the potential scaling method is more efficient and faster in locating low energy conformations than standard MD simulations. Combined with a generalized Born implicit solvation model the low energy cyclic peptide conformations and the loop structure are in good agreement with experiment. Applications in the presence of explicit water molecules during the simulations showed also improved convergence to structures close to experiment compared with regular MD.     

Molecular dynamics simulations of void defects in the energetic material HMX

A molecular dynamics (MD) simulation was carried out to characterize the dynamic evolution of void defects in crystalline octahydro-1, 3, 5, 7-tetranitro-1, 3, 5, 7-tetrazocine (HMX). Different models were constructed with the same concentration of vacancies (10 %) to discuss the size effects of void. Energetic ground state properties were determined by annealing simulations. The void formation energy per molecule removed was found to be 55–63 kcal/mol^?1, and the average binding energy per molecule was between 32 and 34 kcal/mol^?1 according to the change in void size. Voids with larger size had lower formation energy. Local binding energies for molecules directly on the void surface decreased greatly compared to those in defect-free lattice, and then gradually increased until the distance away from the void surface was around 10 Å. Analysis of 1 ns MD simulations revealed that the larger the void size, the easier is void collapse. Mean square displacements (MSDs) showed that HMX molecules that had collapsed into void present liquid structure characteristics. Four unique low-energy conformers were found for HMX molecules in void: two whose conformational geometries corresponded closely to those found in HMX polymorphs and two, additional, lower energy conformers that were not seen in the crystalline phases. The ratio of different conformers changed with the simulated temperature, in that the ratio of α conformer increased with the increase in temperature.     

Many-body energies during proton transfer in an aqueous system

The energetics of the mechanism of proton transfer from a hydronium ion to one of the water molecules in its first solvation shell are studied using density functional theory and the Møller–Plesset perturbation (MP2) method. The potential energy surface of the proton transfer mechanism is obtained at the B3LYP and MP2 levels with the 6-311++G** basis set. Many-body analysis is applied to the proton transfer mechanism to obtain the change in relaxation energy, two-body, three-body and four-body energies when proton transfer occurs from the hydronium ion to one of the water molecules in its first solvation shell. It is observed that the binding energy (BE) of the complex decreases during the proton transfer process at both levels of theory. During the proton transfer process, the % contribution of the total two-body energy to the binding energy of the complex increases from 62.9 to 68.09% (39.9 to 45.95%), and that of the total three-body increases from 25.9 to 27.09% (24.16 to 26.17%) at the B3LYP/6-311++G** (MP2/ 6-311++G**) level. There is almost no change in the water–water–water three-body interaction energy during the proton transfer process at both levels of theory. The contribution of the relaxation energy and the total four-body energy to the binding energy of the complex is greater at the MP2 level than at the B3LYP level. Significant differences are found between the relaxation energies, the hydronium–water interaction energies and the four-body interaction energies at the B3LYP and MP2 levels.     

Evaluation of the conformational free energies of loops in proteins

In this paper we discuss the problem of including solvation free energies in evaluating the relative stabilities of loops in proteins. A conformational search based on a gas-phase potential function is used to generate a large number of trial conformations. As has been found previously, the energy minimization step in this process tends to pack charged and polar side chains against the protein surface, resulting in conformations which are unstable in the aqueous phase. Various solvation models can easily identify such structures. In order to provide a more severe test of solvation models, gas phase conformations were generated in which side chains were kept extended so as to maximize their interaction with the solvent. The free energies of these conformations were compared to that calculated for the crystal structure in three loops of the protein E. coli RNase H, with lengths of 7, 8, and 9 residues. Free energies were evaluated with a finite difference Poisson-Boltzmann (FDPB) calculation for electrostatics and a surface area-based term for nonpolar contributions. These were added to a gas-phase potential function. A free energy function based on atomic solvation parameters was also tested. Both functions were quite successful in selecting, based on a free energy criterion, conformations quite close to the crystal structure for two of the three loops. For one loop, which is involved in crystal contacts, conformations that are quite different from the crystal structure were also selected. A method to avoid precision problems associated with using the FDPB method to evaluate conformational free energies in proteins is described. © 1994 John Wiley & Sons, Inc.     

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.     

The influences of water solvent on the structures and stabilities of Na+–AD conformers

The influences of water solvent on the structures and stabilities of the complex ion conformers formed by the coordination of alanine dipeptide (AD) and Na⁺ have been investigated using supramolecular and polarizable continuum solvation models at the level of B3LYP/6-311++G**, respectively; 12 monohydrated and 12 dihydrated structures of Na⁺–AD complex ion were obtained after full geometrical optimization. The results showed that H₂O molecules easily bind with Na⁺ of Na⁺–AD complex ion, forming an ion-lone pair interaction with the Na–O bond length of 2.1–2.3 Å. Besides, H₂O molecules also can form hydrogen bonds O_W–H_W···O(1), O_W–H_W···O(2), N(1)–H(1)···O_W or N(2)–H(2)···O_W with O or N groups of the Na⁺–AD backbone. The most stable gaseous bidentate conformer C7AB of Na⁺–AD is still the most stable one in the solvent of water. However, the structure of the most unstable gaseous conformer α′B of Na⁺–AD collapses under the attack of H₂O molecules and changes into C7AB conformation. Computations with IEFPCM solvation model of self-consistent reaction field theory give that aqueous C5A is more stable than C7_eqB and that the stabilization energies of water solvent on monodentate conformers of Na⁺–AD complex ion (about 272–294 kJ/mol) are more than those on bidentate ones (about 243 kJ/mol).     

Continuum solvent studies of the stability of RNA hairpin loops and helices

We apply continuum solvent models to investigate the relative stability of various conformational forms for two RNA sequences, GGAC(UUCG)GUCC and GGUG(UGAA)CACC. In the first part, we compare alternate hairpin conformations to explore the reliability of these models to discriminate between different local conformations. A second part looks at the hairpin-duplex conversion for the UUCG sequence, identifying major contributors to the thermodynamics of a much large scale transition. Structures were taken as snapshots from multi-nanosecond molecular dynamics simulations computed in a consistent fashion using explicit solvent and with long-range electrostatics accounted for using the Particle-Mesh Ewald procedure. The electrostatic contribution to solvation energies were computed using both a finite-difference Poisson-Boltzmann (PB) model and a pairwise Generalized Born model; non-electrostatic contributions were estimated with a surface-area dependent term. To these solvation free energies were added the mean solute internal energies (determined from a molecular mechanics potential) and estimates of the solute entropy (from a harmonic analysis). Consistent with experiment and with earlier solvated molecular dynamics simulations, the UUCG hairpin was found to prefer conformers close to a recent NMR structure determination in preference to those from an earlier NMR study. Similarly, results for the UGAA hairpin favored an NMR-derived structure over that to be expected for a generic GNRA hairpin loop. Experimental free energies are not known for the hairpin/duplex conversion, but must be close to zero since hairpins are seen in solution and duplexes in crystals; out calculations find a value near zero and illustrate the expected interplay of solvation, salt effects and entropy in affecting this equilibrium.     

Exhaustive mutagenesis in silico: multicoordinate free energy calculations on proteins and peptides

We have extended and applied a multicoordinate free energy method, chemical Monte Carlo/Molecular Dynamics (CMC/MD), to calculate the relative free energies of different amino acid side-chains. CMC/MD allows the calculation of the relative free energies for many chemical species from a single free energy calculation. We have previously shown its utility in host:guest chemistry (Pitera and Kollman, J Am Chem Soc 1998;120:7557-7567)1 and ligand design (Eriksson et al., J Med Chem 1999;42:868-881)2, and here demonstrate its utility in calculations of amino acid properties and protein stability. We first study the relative solvation free energies of N-methylated and acetylated alanine, valine, and serine amino acids. With careful inclusion of rotameric states, internal energies, and both the solution and vacuum states of the calculation, we calculate relative solvation free energies in good agreement with thermodynamic integration (TI) calculations. Interestingly, we find that a significant amount of the unfavorable solvation of valine seen in prior work (Sun et al., J Am Chem Soc 1992;114:6798-6801)3 is caused by restraining the backbone in an extended conformation. In contrast, the solvation free energy of serine is calculated to be less favorable than expected from experiment, due to the formation of a favorable intramolecular hydrogen bond in the vacuum state. These monomer calculations emphasize the need to accurately consider all significant conformations of flexible molecules in free energy calculations. This development of the CMC/MD method paves the way for computations of protein stability analogous to the biochemical technique of "exhaustive mutagenesis." We have carried out just such a calculation at position 133 of T4 lysozyme, where we use CMC/MD to calculate the relative stability of eight different side-chain mutants in a single free energy calculation. Our T4 calculations show good agreement with the prior free energy calculations of Veenstra et al. (Prot Eng 1997;10:789-807)4 and excellent agreement with the experiments of Mendel et al. (Science 1992;256:1798-1802).     

Explicit and implicit water simulations of a beta-hairpin peptide.

The conformational properties of a beta-hairpin peptide (YITNSDGTWT) were studied by using both explicit and implicit water simulations. The conformational space of the peptide was scanned by using a restricted hydrogen-bonding search method. The search method used generated the conformational space with enough diversity and good representation of beta-hairpin structures. By using a total surface area-based treatment of hydrophobic interactions, implicit water simulations failed to discriminate between experimental beta-hairpin structures from the rest of the conformers present in the authors' conformation library. However, with inclusion of vibrational free energy and accounting separately for polar and nonpolar surface areas, the nuclear magnetic resonance structure was ranked successfully as the most stable conformation. There is a loose correlation between the conformational energies by the continuum model and the conformational energies by explicit water simulation for conformers with similar structures. However, in terms of solvation energy, both approaches have a much better correlation. By using proper treatment of surface effect (partition of the surface area into polar and nonpolar areas) and including vibrational free-energy contribution, the continuum models should be reliable. Furthermore, the authors found that, for this peptide, beta-hairpin structures have large vibrational entropy that contributes decisively to the stability of folded beta-hairpin structures. Proteins 1999;37:73-87.     

Microsolvation and hydration enthalpies of CaC2O4(H2O) n (n = 0-16) and C2O4 2-(H2O) n (n = 0-14): an ab initio study

We studied hydrated calcium oxalate and its ions at the restricted Hartree–Fock RHF/6-31G* level of theory. Performing a configurational search seems to improve the fit of the HF/6-31G* level to experimental data. The first solvation shell of calcium oxalate contains 13 water molecules, while the first solvation shell of oxalate ion is formed by 14 water molecules. The first solvation shell of Ca(II) is formed by six water molecules, while the second shell contains five. At 298.15 K, we estimate the asymptotic limits (infinite dilution) of the total standard enthalpies of hydration for Ca(II), oxalate ion and calcium oxalate as ?480.78, –302.78 and –312.73 kcal mol^?1, resp. The dissociation of hydrated calcium oxalate is an endothermic process with an asymptotic limit of +470.84 kcal mol^?1.

Empirical solvation models in the context of conformational energy searches: application to bovine pancreatic trypsin inhibitor.

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.