An averaged solvent electrostatic potential from molecular dynamics study of the anomeric equilibrium of D-xylose in aqueous solution

We applied the free-energy perturbation method together with the averaged solvent electrostatic potential from molecular dynamics (ASEP/MD) method to study the anomeric equilibrium of d-xylose in aqueous solution. The level of calculation, 6-311G++(2d,2p) basis set and density functional theory, permits one to explain the main characteristics of the anomeric equilibrium of d-xylopyranose: in vacuo, the anomeric effect predominates and the form is the stabler. In water, solvation leads to the form being the stabler. A comparison between the performances of the ASEP/MD and polarizable continuum models is also presented.Contribution to the Jacopo Tomasi Honorary Issue     

Study of solvent effects by means of averaged solvent electrostatic potentials obtained from molecular dynamics data

We present the theory and implementation of a new approach for studying solvent effects. The electronic structure of the solute, calculated at the ab initio level, is obtained in the presence of the surrounding medium. We employ a mean field theory in which the solvent response is described by means of point charges chosen in such a way that they reproduce the average value of the solvent electrostatic potential calculated from molecular dynamics data. In this way, the complete solvent potential can be introduced into the solute Hamiltonian without making use of a one-center multiple expansion of the solute-solvent potential. In the proposed method, only one quantum calculation has to be performed and a great number of configurations can easily be included making the calculation statistically significant. We show that, despite the large fluctuations in the solute charge distribution induced by the solvent, the proposed mean field theory adequately reproduces the energetics and properties of formamide and water molecules in aqueous solution. © 1997 by John Wiley & Sons, Inc.     

Role of solvent in determining conformational preferences of alanine dipeptide in water

Evidence from a variety of spectroscopic probes indicates that (phi, psi) values corresponding to the left-handed polyproline II helix (P(II)) are preferred for short alanine-based peptides in water. On the basis of results from theoretical studies, it is believed that the observed preference is dictated by favorable peptide-solvent interactions, which are realized through formation of optimal hydrogen-bonding water bridges between peptide donor and acceptor groups. In the present study, we address this issue explicitly by analyzing the hydration structure and thermodynamics of 16 low-energy conformers of the alanine dipeptide (N-acetylalanine-N'-methylamide) in liquid water. Monte Carlo simulations in the canonical ensemble were performed under ambient conditions with all-atom OPLS parameters for the alanine dipeptide and the TIP5P model for water. We find that the number of hydrogen-bonded water molecules connecting the peptide group donor and acceptor atoms has no effect on the solvation thermodynamics. Instead, the latter are determined by the work done to fully hydrate the peptide. This work is minimal for conformations that are characterized by a minimal overlap of the primary hydration shells around the peptide donor and acceptor atoms. As a result, peptide-solvent interactions favor "compact" conformations that do not include P(II)-like geometries. Our main conclusion is that the experimentally observed preference for P(II) does not arise due to favorable direct interactions between the peptide and water molecules. Instead, the latter act to unmask underlying conformational preferences that are a consequence of minimizing intrapeptide steric conflicts.     

Optimization of partial multicanonical molecular dynamics simulations applied to an alanine dipeptide in explicit water solvent

The partial multicanonical algorithm for molecular dynamics and Monte Carlo simulations samples a wide range of an important part of the potential energy. Although it is a strong technique for structure prediction of biomolecules, the choice of the partial potential energy has not been optimized. In order to find the best choice, partial multicanonical molecular dynamics simulations of an alanine dipeptide in explicit water solvent were performed with 15 trial choices for the partial potential energy. The best choice was found to be the sum of the electrostatic, Lennard-Jones, and torsion-angle potential energies between solute atoms. In this case, the partial multicanonical simulation sampled all of the local-minimum free-energy states of the P(II), C(5), α(R), α(P), α(L), and C states and visited these states most frequently. Furthermore, backbone dihedral angles ? and ψ rotated very well. It is also found that the most important term among these three terms is the electrostatic potential energy and that the Lennard-Jones term also helps the simulation to overcome the steric restrictions. On the other hand, multicanonical simulation sampled all of the six states, but visited these states fewer times. Conventional canonical simulation sampled only four of the six states: The P(II), C(5), α(R), and α(P) states.     

Estimating kinetic rates from accelerated molecular dynamics simulations: alanine dipeptide in explicit solvent as a case study

Molecular dynamics (MD) simulation is the standard computational technique used to obtain information on the time evolution of the conformations of proteins and many other molecular systems. However, for most biological systems of interest, the time scale for slow conformational transitions is still inaccessible to standard MD simulations. Several sampling methods have been proposed to address this issue, including the accelerated molecular dynamics method. In this work, we study the extent of sampling of the phi/psi space of alanine dipeptide in explicit water using accelerated molecular dynamics and present a framework to recover the correct kinetic rate constant for the helix to beta-strand transition. We show that the accelerated MD can drastically enhance the sampling of the phi/psi conformational phase space when compared to normal MD. In addition, the free energy density plots of the phi/psi space show that all minima regions are accurately sampled and the canonical distribution is recovered. Moreover, the kinetic rate constant for the helix to beta-strand transition is accurately estimated from these simulations by relating the diffusion coefficient to the local energetic roughness of the energy landscape. Surprisingly, even for such a low barrier transition, it is difficult to obtain enough transitions to accurately estimate the rate constant when one uses normal MD.     

An application of coupled reference interaction site model/molecular dynamics to the conformational analysis of the alanine dipeptide

We present an application of our recently proposed coupled reference interaction site model (RISM) molecular dynamics (MD) solvation free energy methodology [Freedman and Truong, Chem. Phys. Lett. 381, 362 (2003); J. Chem. Phys. 121, 2187 (2004)] to study the conformational stability of alanine dipeptide in aqueous solution. In this methodology, radial distribution functions obtained from a single MD simulation are substituted into a RISM expression for solvation free energy. Consequently, iterative solution of the RISM equation is not needed. The relative solvation free energies of seven different conformations of the alanine dipeptide in aqueous solution are calculated. Results from the coupled RISM/MD methodology are in good agreement with those from earlier simulations using the accurate free energy perturbation approach, showing that the alphaR conformation is most stabilized by solution. This study establishes a framework for applying this coupled RISM/MD method to larger biological systems.     

Temperature and pressure dependence of alanine dipeptide studied by multibaric-multithermal molecular dynamics simulations

We applied the multibaric-multithermal (MUBATH) molecular dynamics (MD) algorithm to an alanine dipeptide in explicit water. The MUBATH MD simulation covered a wide range of conformational space and sampled the states of PII, C5, alphaR, alphaP, alphaL, and C7(ax). On the other hand, the conventional isobaric-isothermal simulation was trapped in local-minimum free-energy states and sampled only a few of them. We calculated the partial molar enthalpy difference DeltaH and partial molar volume difference DeltaV among these states by the MUBATH simulation using the AMBER parm99 and AMBER parm96 force fields and two sets of initial conditions. We compared these results with those from Raman spectroscopy experiments. The Raman spectroscopy data of DeltaH for the C5 state against the PII state agreed with both MUBATH data with the AMBER parm96 and parm99 force fields. The partial molar enthalpy difference DeltaH for the alphaR state and the partial molar volume difference DeltaV for the C5 state by the Raman spectroscopy agreed with those for the AMBER parm96 force field. On the other hand, DeltaV for the alphaR state by the Raman spectroscopy was consistent with our AMBER-parm99 force-field result. All the experimental results fall between those of simulations using AMBER parm96 and parm99 force fields, suggesting that the ideal force-field parameters lie between those of AMBER parm96 and parm99.     

A molecular dynamics study of the dielectric properties of aqueous solutions of alanine and alanine dipeptide

Molecular dynamics simulations were used to compute the frequency-dependent dielectric susceptibility of aqueous solutions of alanine and alanine dipeptide. We studied four alanine solutions, ranging in concentration from 0.13-0.55 mol/liter, and two solutions of alanine dipeptide (0.13 and 0.27 mol/liter). In accord with experiment we find a strong dielectric increment for both solutes, whose molecular origin is shown to be the zwitterionic nature of the solutes. The dynamic properties were analyzed based on a dielectric component analysis into solute, a first hydration shell, and all remaining (bulk) waters. The results of this three component decomposition were interpreted directly, as well as by uniting the solute and hydration shell component to a "suprasolute" component. In both approaches three contributions to the frequency-dependent dielectric properties can be discerned. The quantitatively largest and fastest component arises from bulk water [i.e., water not influenced by the solute(s)]. The interaction between waters surrounding the solute(s) (the hydration shell) and bulk water molecules leads to a relaxation process occurring on an intermediate time scale. The slowest relaxation process originates from the solute(s) and the interaction of the solute(s) with the first hydration shell and bulk water. The primary importance of the hydration shell is the exchange of shell and bulk waters; the self-contribution from bound water molecules is comparatively small. While in the alanine solutions the solute-water cross-terms are more important than the solute self-term, the solute contribution is larger in the dipeptide solutions. In the latter systems a much clearer separation of time scales between water and alanine dipeptide related properties is observed. The similarities and differences of the dielectric properties of the amino acid/peptide solutions studied in this work and of solutions of mono- and disaccharides and of the protein ubiquitin are discussed.     

Toward the correction of effective electrostatic forces in explicit-solvent molecular dynamics simulations: restraints on solvent-generated electrostatic potential and solvent polarization

Despite considerable advances in computing power, atomistic simulations under nonperiodic boundary conditions, with Coulombic electrostatic interactions and in systems large enough to reduce finite-size associated errors in thermodynamic quantities to within the thermal energy, are still not affordable. As a result, periodic boundary conditions, systems of microscopic size and effective electrostatic interaction functions are frequently resorted to. Ensuing artifacts in thermodynamic quantities are nowadays routinely corrected a posteriori, but the underlying configurational sampling still descends from spurious forces. The present study addresses this problem through the introduction of on-the-fly corrections to the physical forces during an atomistic molecular dynamics simulation. Two different approaches are suggested, where the force corrections are derived from special potential energy terms. In the first approach, the solvent-generated electrostatic potential sampled at a given atom site is restrained to a target value involving corrections for electrostatic artifacts. In the second approach, the long-range regime of the solvent polarization around a given atom site is restrained to the Born polarization, i.e., the solvent polarization corresponding to the ideal situation of a macroscopic system under nonperiodic boundary conditions and governed by Coulombic electrostatic interactions. The restraints are applied to the explicit-water simulation of a hydrated sodium ion, and the effect of the restraints on the structural and energetic properties of the solvent is illustrated. Furthermore, by means of the calculation of the charging free energy of a hydrated sodium ion, it is shown how the electrostatic potential restraint translates into the on-the-fly consideration of the corresponding free-energy correction terms. It is discussed how the restraints can be generalized to situations involving several solute particles. Although the present study considers a very simple system only, it is an important step toward the on-the-fly elimination of finite-size and approximate-electrostatic artifacts during atomistic molecular dynamics simulations.     

Quantum mechanical calculation of the effects of stiff and rigid constraints in the conformational equilibrium of the alanine dipeptide

If constraints are imposed on a macromolecule, two inequivalent classical models may be used: the stiff and the rigid one. This work studies the effects of such constraints on the conformational equilibrium distribution (CED) of the model dipeptide HCO-L-Ala-NH(2)without any simplifying assumption. We use ab initio quantum mechanics calculations including electron correlation at the MP2 level to describe the system, and we measure the conformational dependence of all the correcting terms to the naive CED based in the potential energy surface that appear when the constraints are considered. These terms are related to mass-metric tensors determinants and also occur in the Fixman's compensating potential. We show that some of the corrections are non-negligible if one is interested in the whole Ramachandran space. On the other hand, if only the energetically lower region, containing the principal secondary structure elements, is assumed to be relevant, then, all correcting terms may be neglected up to peptides of considerable length. This is the first time, as far as we know, that the analysis of the conformational dependence of these correcting terms is performed in a relevant biomolecule with a realistic potential energy function.     

Two-dimensional infrared spectroscopy of the alanine dipeptide in aqueous solution

The linear-infrared and two-dimensional infrared (2D IR) spectra in the amide-I' region of the alanine dipeptide and its (13)C isotopomers in aqueous solution (D(2)O) are reported. The two amide-I' IR transitions have been assigned unambiguously by using (13)C isotopic substitution of the carbonyl group; the amide unit at the acetyl end shows a lower transition frequency in the unlabeled species. The ratio of their transition dipole strengths remains almost unchanged upon (13)C substitution, indicating the absence of intensity transfer between two vibrators. The 2D IR cross peaks directly associated with intramode coupling in this case show a small off-diagonal anharmonicity (0.2 +/- 0.2 cm(-1)), leading to a small coupling constant (1.5 +/- 0.5 cm(-1)). The coupling and the 2D IR spectra in two different polarizations (zzzz and zxxz) are as expected for a polyproline-II (PP(II))-like conformation for dialanine, with the backbone dihedral angles (phi, psi) determined to be in the range of (-70 degrees +/- 25 degrees, +120 degrees +/- 25 degrees). Ab initio DFT calculations and normal mode decoupling analysis in the Ramachandran subspace in the neighborhood of PP(II) conformation confirm the presence of a region where the coupling is vanishingly small and support these experimental findings. The relationship between the coupling and off-diagonal anharmonicity is consolidated by examining the distribution of the latter from an ensemble averaged Hamiltonian incorporating uncorrelated diagonal frequency distributions and a small coupling (<2 cm(-1)); it is found that the most probable value for the off-diagonal anharmonicity falls into the range of experimental observations. Further, incorporating DFT results, the simulated linear-IR and 2D IR can reproduce the essential features of the measurements, including the transition frequency positions and apparent peak intensities. All the experimental results and simulations are consistent with a PP(II)-like conformation for the alanine dipeptide in aqueous solution, in which two amide-I' modes are highly localized and whose frequency distributions are uncorrelated.     

Statistical mechanically averaged molecular properties of liquid water calculated using the combined coupled cluster/molecular dynamics method

Liquid water is investigated theoretically using combined molecular dynamics (MD) simulations and accurate electronic structure methods. The statistical mechanically averaged molecular properties of liquid water are calculated using the combined coupled cluster/molecular mechanics (CC/MM) method for a large number of configurations generated from MD simulations. The method includes electron correlation effects at the coupled cluster singles and doubles level and the use of a large correlation consistent basis set. A polarizable force field has been used for the molecular dynamics part in both the CC/MM method and in the MD simulation. We describe how the methodology can be optimized with respect to computational costs while maintaining the quality of the results. Using the optimized method we study the energetic properties including the heat of vaporization and electronic excitation energies as well as electric dipole and quadrupole moments, the frequency dependent electric (dipole) polarizability, and electric-field-induced second harmonic generation first and second hyperpolarizabilities. Comparisons with experiments are performed where reliable data are available. Furthermore, we discuss the important issue on how to compare the calculated microscopic nonlocal properties to the experimental macroscopic measurements.     

Generation of OPLS-like charges from molecular electrostatic potential using restraints

A new method for generating atom-centered charges for use in condensed phase computer simulations is presented, which is based on a restrained electrostatic potential (RESP) procedure. Charges are calculated from a least-squares fit to the quantum mechanical electrostatic potential with a restraint applied to reduce their magnitude. The restraint developed here offers advantages over that used in RESP. The magnitude of the restraint is optimized to yield charges as close to the equivalent OPLS values as possible while still reproducing the molecule's electrostatic potential. A cross-validation analysis is used to show that the restraint is insensitive to the selection of OPLS molecules from which it is derived. Thus, with this method, OPLS-like charges may be produced from the electrostatic potential for atom types not in the OPLS force field. In addition, the restraint is shown to reduce the conformational dependence of the charges. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 483–498, 1999     

Solution reaction space Hamiltonian based on an electrostatic potential representation of solvent dynamics

Quantum chemical solvation models usually rely on the equilibrium solvation condition and is thus not immediately applicable to the study of nonequilibrium solvation dynamics, particularly those associated with chemical reactions. Here we address this problem by considering an effective Hamiltonian for solution-phase reactions based on an electrostatic potential (ESP) representation of solvent dynamics. In this approach a general ESP field of solvent is employed as collective solvent coordinate, and an effective Hamiltonian is constructed by treating both solute geometry and solvent ESP as dynamical variables. A harmonic bath is then attached onto the ESP variables in order to account for the stochastic nature of solvent dynamics. As an illustration we apply the above method to the proton transfer of a substituted phenol-amine complex in a polar solvent. The effective Hamiltonian is constructed by means of the reference interaction site model self-consistent field method (i.e., a type of quantum chemical solvation model), and a mixed quantum/classical simulation is performed in the space of solute geometry and solvent ESP. The results suggest that important dynamical features of proton transfer in solution can be captured by the present approach, including spontaneous fluctuations of solvent ESP that drives the proton from reactant to product potential wells.     

Classical and quantum mechanical/molecular mechanical molecular dynamics simulations of alanine dipeptide in water: comparisons with IR and vibrational circular dichroism spectra

We have implemented the combined quantum mechanical (QM)/molecular mechanical (MM) molecular dynamics (MD) simulations of alanine dipeptide in water along with the polarizable and nonpolarizable classical MD simulations with different models of water. For the QM/MM MD simulation, the alanine dipeptide is treated with the AM1 or PM3 approximations and the fluctuating solute dipole moment is calculated by the Mulliken population analysis. For the classical MD simulations, the solute is treated with the polarizable or nonpolarizable AMBER and polarizable CHARMM force fields and water is treated with the TIP3P, TIP4P, or TIP5P model. It is found that the relative populations of right-handed alpha-helix and extended beta and P(II) conformations in the simulation trajectory strongly depend on the simulation method. For the QM/MM MD simulations, the PM3/MM shows that the P(II) conformation is dominant, whereas the AM1/MM predicts that the dominant conformation is alpha(R). Polarizable CHARMM force field gives almost exclusively P(II) conformation and other force fields predict that both alpha-helical and extended (beta and P(II)) conformations are populated with varying extents. Solvation environment around the dipeptide is investigated by examining the radial distribution functions and numbers and lifetimes of hydrogen bonds. Comparing the simulated IR and vibrational circular dichroism spectra with experimental results, we concluded that the dipeptide adopts the P(II) conformation and PM3/MM, AMBER03 with TIP4P water, and AMBER polarizable force fields are acceptable for structure determination of the dipeptide considered in this paper.     

Influence of solvent on conformational equilibrium in phenyl glycidyl ether

The conformational equilibrium in phenyl glycidyl ether in aprotic solvents was studied by the PMR method over a broad range of changes in the values of the dielectric constant. It was shown that the parameters of the multiplet of noncyclic methylene protons in the PMR spectrum of phenyl glycidyl ether are a sensitive indicator of the position of the conformational equilibrium in the glycidyl fragment. The specific interaction of the molecules of aromatic solvents with the epoxide ring has been discovered.Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 21, No. 2, pp. 245–247, March–April, 1985.     

An NMR study of the conformational equilibrium of 5-fluoro-1,3-dioxan in solution. Dependence on solvent

The ¹H and ¹⁹F NMR parameters of 5-fluoro-1,3-dioxan ( 1 ) dissolved in a number of solvent systems are interpreted on the basis of fast inversion between two chair conformations. In cyclohexane solution the two chair conformations are almost equally populated, whereas in more polar solvents, such as chloroform, the conformation having the fluorine substituent in an axial position is strongly preferred. Addition of acetic acid to a solution of 1 in cyclohexane increases the preference of the fluorine substituent for the axial orientation. Possible reasons for these observations are discussed.     

Effect of solvent on the cis-trans conformational equilibrium of a proline imide bond of short model peptides in solution.

Proton NMR spectra of proline-containing short peptides with N-terminal sequences of N-acetyl-prolyl- (Ac-Pro-) N-tert-butoxycarbonyl-phenylalanyl-prolyl- (Boc-Phe-Pro-) and N-tert-butoxycarbonyl-leucyl-prolyl- (Boc-Leu-Pro-) were measured in mixed solvents of hexadeuterodimethylsulfoxide and deuterochloroform (CDCl3). Population ratios of cis and trans conformers with respect to the proline imide bond and chemical shifts of NH protons were obtained as a function of a CDCl3 fraction of solvent. With increasing fraction of CDCl3, the trans percentages of the Ac-Pro-imide bonds increased. On the other hand, those of Boc-Phe-Pro- decreased, and those of Boc-Leu-Pro- exhibited middle tendency. From the solvent-dependent variation of the chemical shifts of the NH protons, intramolecular hydrogen bonds that stabilize the trans form of Ac-Pro- and the cis form of Boc-Phe-Pro- were discussed. For the Ac-Pro- peptides, only the trans forms are found to the compatible with 7-, 10-, and 13-membered hydrogen-bonded rings that would be similar to the ordinary secondary structures, gamma- and beta-turns and alpha-helix, respectively. For the cis form of Boc-Phe-Pro-R (R = O-methyl or glycyl-O-ethyl), the hydrogen-bonded structure is found to be similar to the type-VIa beta-turn. On the other hand, for Boc-Phe-Pro-Pro-Leu-Gly-NH2, it has been suggested that two different hydrogen bonds, which are different from that of the type-VIa beta-turn, support each other and cooperatively stabilize the cis form.     

Multiple pathways in conformational transitions of the alanine dipeptide: an application of dynamic importance sampling

We present multiple dynamic transition pathways on the two-dimensional dihedral plane between conformational states of the alanine dipeptide. The method used in this study is dynamic importance sampling (DIMS). To perform DIMS, unbiased molecular dynamic simulations are used to generate equilibrium ensembles for the alanine dipeptide within different states. Free energy surfaces on the dihedral plane are calculated from the equilibrium simulations, and four energy minima defined from the surface are used as the starting and ending points for DIMS dynamics. The DIMS method represents an important step towards finding multiple transition pathways within complex biomolecular systems.     

CHARMM fluctuating charge force field for proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model

A fluctuating charge (FQ) force field is applied to molecular dynamics simulations for six small proteins in explicit polarizable solvent represented by the TIP4P-FQ potential. The proteins include 1FSV, 1ENH, 1PGB, 1VII, 1H8K, and 1CRN, representing both helical and beta-sheet secondary structural elements. Constant pressure and temperature (NPT) molecular dynamics simulations are performed on time scales of several nanoseconds, the longest simulations yet reported using explicitly polarizable all-atom empirical potentials (for both solvent and protein) in the condensed phase. In terms of structure, the FQ force field allows deviations from native structure up to 2.5 A (with a range of 1.0 to 2.5 A). This is commensurate to the performance of the CHARMM22 nonpolarizable model and other currently existing polarizable models. Importantly, secondary structural elements maintain native structure in general to within 1 A (both helix and beta-strands), again in good agreement with the nonpolarizable case. In qualitative agreement with QM/MM ab initio dynamics on crambin (Liu et al. Proteins 2001, 44, 484), there is a sequence dependence of average condensed phase atomic charge for all proteins, a dependence one would anticipate considering the differing chemical environments around individual atoms; this is a subtle quantum mechanical feature captured in the FQ model but absent in current state-of-the-art nonpolarizable models. Furthermore, there is a mutual polarization of solvent and protein in the condensed phase. Solvent dipole moment distributions within the first and second solvation shells around the protein display a shift towards higher dipole moments (increases on the order of 0.2-0.3 Debye) relative to the bulk; protein polarization is manifested via the enhanced condensed phase charges of typical polar atoms such as backbone carbonyl oxygens, amide nitrogens, and amide hydrogens. Finally, to enlarge the sample set of proteins, gas-phase minimizations and 1 ps constant temperature simulations are performed on various-sized proteins to compare to earlier work by Kaminsky et al. (J Comp Chem 2002, 23, 1515). The present work establishes the feasibility of applying a fully polarizable force field for protein simulations and demonstrates the approach employed in extending the CHARMM force field to include these effects.