Potential energy surfaces for small alcohol dimers. II. Propanol, isopropanol, t-butanol, and sec-butanol

Potential energy landscapes for homogeneous dimers of propanol, isopropanol, tert-butanol, and sec-butanol were obtained using 735 counterpoise-corrected energies at the MP2/6-311+G(2df,2pd) level. The landscapes were sampled at 15 dimer separation distances for different relative monomer geometries, or routes, given in terms of the yaw, pitch, and roll of one monomer relative to the other and the spherical angles between the two monomer centers (taken as the C atom attached to the O). The resultant individual energy surfaces and their complex topographies were also regressed using a site-site pair potential model using a modified Morse potential that provides a mathematically simple representation of the landscapes suitable for use in molecular simulations. Generalized Morse parameters were also obtained for this model from a composite regression of these energy landscapes and those previously reported for methanol and ethanol. The quality of fit for all these energy landscapes suggests that these site parameters have transferability for possible use on other alcohols.     

Critical and phase-equilibrium properties of an ab initio based potential model of methanol and 1-propanol using two-phase molecular dynamics simulations

Two-phase molecular dynamics simulations employing a Monte Carlo volume sampling method were performed using an ab initio based force field model parameterized to reproduce quantum-mechanical dimer energies for methanol and 1-propanol at temperatures approaching the critical temperature. The intermolecular potential models were used to obtain the binodal vapor-liquid phase dome at temperatures to within about 10 K of the critical temperature. The efficacy of two all-atom, site-site pair potential models, developed solely from the energy landscape obtained from high-level ab initio pair interactions, was tested for the first time. The first model was regressed from the ab initio landscape without point charges using a modified Morse potential to model the complete interactions; the second model included point charges to separate Coulombic and dispersion interactions. Both models produced equivalent phase domes and critical loci. The model results for the critical temperature, density, and pressure, in addition to the sub-critical equilibrium vapor and liquid densities and vapor pressures, are compared to experimental data. The model's critical temperature for methanol is 77 K too high while that for 1-propanol is 80 K too low, but the critical densities are in good agreement. These differences are likely attributable to the lack of multi-body interactions in the true pair potential models used here.     

Dependency of ligand free energy landscapes on charge parameters and solvent models

We performed replica-exchange molecular dynamics (REMD) simulations of six ligands to examine the dependency of their free energy landscapes on charge parameters and solvent models. Six different charge parameter sets for each ligand were first generated by RESP and AM1-BCC methods using three different conformations independently. RESP charges showed some conformational dependency. On the other hand, AM1-BCC charges did not show conformational dependency and well reproduced the overall trend of RESP charges. The free energy landscapes obtained from the REMD simulations of ligands in vacuum, Generalized-Born (GB), and TIP3P solutions were then analyzed. We found that even small charge differences can produce qualitatively different landscapes in vacuum condition, but the differences tend to be much smaller under GB and TIP3P conditions. The simulations in the GB model well reproduced the landscapes in the TIP3P model using only a fraction of the computational cost. The protein-bound ligand conformations were rarely the global minimum states, but similar conformations were found to exist in aqueous solution without proteins in regions close to the global minimum, local minimum or intermediate states.     

齐墩果酸分子印迹聚合物预组装体系的分子模拟及聚合物制备

以齐墩果酸(OA)为模板分子,三氟甲基丙烯酸(TFMAA)、α-甲基丙烯酸(MAA)、丙烯酰胺(AM)、4-乙烯基吡啶(4-VP)为功能单体,三氯甲烷、四氢呋喃、乙醇、甲醇和丙酮为溶剂,基于量子化学密度泛函理论(DFT)和ONIOM方法,采用Gaussian09软件模拟计算了模板分子与不同功能单体的印迹聚合物预组装体系的构型,探讨了模板分子与功能单体在不同印迹比例时所形成复合物的成键情况以及反应过程中的结合能,并采用自洽反应场极化连续模型(CPCM)计算了功能单体与模板分子在不同溶剂中的溶剂化能。结果表明,TFMAA与模板分子OA以1:1摩尔比形成复合物的结合能ΔE最高(-70.99kJ·mol~(-1)),结构最稳定,模板分子和功能单体在三氯甲烷中的溶剂化能最小。同时,采用实验方法验证模拟结果,并利用扫描电镜、傅里叶红外光谱仪和静态吸附实验对印迹聚合物的形貌、化学基团和吸附性能等进行表征。结果表明,模拟结果与实验结果完全一致,计算机模拟对分子印迹体系的筛选和机理研究提供了理论依据。     

Force-field parametrization of retro-inverso modified residues: Development of torsional and electrostatic parameters

Summary Torsional and the electrostatic parameters for molecular mechanics studies of retro-inverso modified peptides have been developed using quantum mechanical calculations. The resulting parameters have been compared with those calculated for conventional peptides. Rotational profiles, which were obtained spanning the corresponding dihedral angle, were corrected by removing the energy contributions associated to changes in interactions different from torsion under study. For this purpose, the torsional energy associated to each point of the profiles was estimated as the corresponding quantum mechanical energy minus the bonding and nonbonding energy contributions produced by the perturbations that the variation of the spanned dihedral angle causes in the bond distances, bond angles and the other dihedral angles. These energies were calculated using force-field expressions. The corrected profiles were fitted to a three-term Fourier expansion to derive the torsional parameters. Atomic charges for retro-inverso modified residues were derived from the rigorously calculated quantum mechanical electrostatic potential. Furthermore, the reliability of electrostatic models based on geometry-dependent charges and fixed charges has been examined.     

Unfolding the conformational behavior of peptide dendrimers: insights from molecular dynamics simulations

We present here the first comprehensive structural characterization of peptide dendrimers using molecular simulation methods. Multiple long molecular dynamics simulations are used to extensively sample the conformational preferences of five third-generation peptide dendrimers, including some known to bind aquacobalamine. We start by analyzing the compactness of the conformations thus sampled using their radius of gyration profiles. A more detailed analysis is then performed using dissimilarity measures, principal coordinate analysis, and free energy landscapes, with the aim of identifying groups of similar conformations. The results point to a high conformational flexibility of these molecules, with no clear "folded state", although two markedly distinct behaviors were found: one of the dendrimers displayed mostly compact conformations clustered into distinct basins (rough landscape), while the remaining dendrimers displayed mainly noncompact conformations with no significant clustering (downhill landscape). This study brings new insight into the conformational behavior of peptide dendrimers and may provide better routes for their functional design. In particular, we propose a yet unsynthesized peptide dendrimer that might exhibit enhanced ability to coordinate aquocobalamin.     

Molecular dynamics simulations of liquid methanol and methanol-water mixtures with polarizable models

A polarizable model for simulation of liquid methanol, compatible with the COS/G2 water model, has been developed using the Charge-on-Spring (COS) technique. The model consists of three point charges, with one polarizable center on the oxygen atom. The Lennard-Jones parameters on the oxygen atom together with the molecular polarizability were varied to reproduce the experimental heat of vaporization and density of liquid methanol at ambient conditions. We examined the energies of various methanol dimers in the gas phase and compared them with values obtained from ab initio calculations. The model was then used to study the thermodynamic, dynamic, structural, and dielectric properties of liquid methanol as well as of a methanol-water mixture. A microscopic picture of the structure of pure liquid methanol and of the methanol-water mixture is provided. Good agreement was found between the results from our model simulations and available experimental and ab initio calculation data. In particular, the experimental dielectric permittivity of 32 could be reproduced, which had been shown to be difficult when using nonpolarizable models.     

Communication: Quantum polarized fluctuating charge model: a practical method to include ligand polarizability in biomolecular simulations

We present a simple and practical method to include ligand electronic polarization in molecular dynamics (MD) simulation of biomolecular systems. The method involves periodically spawning quantum mechanical (QM) electrostatic potential (ESP) calculations on an extra set of computer processors using molecular coordinate snapshots from a running parallel MD simulation. The QM ESPs are evaluated for the small-molecule ligand in the presence of the electric field induced by the protein, solvent, and ion charges within the MD snapshot. Partial charges on ligand atom centers are fit through the multi-conformer restrained electrostatic potential (RESP) fit method on several successive ESPs. The RESP method was selected since it produces charges consistent with the AMBER/GAFF force-field used in the simulations. The updated charges are introduced back into the running simulation when the next snapshot is saved. The result is a simulation whose ligand partial charges continuously respond in real-time to the short-term mean electrostatic field of the evolving environment without incurring additional wall-clock time. We show that (1) by incorporating the cost of polarization back into the potential energy of the MD simulation, the algorithm conserves energy when run in the microcanonical ensemble and (2) the mean solvation free energies for 15 neutral amino acid side chains calculated with the quantum polarized fluctuating charge method and thermodynamic integration agree better with experiment relative to the Amber fixed charge force-field.     

Comparison of charge models for fixed-charge force fields: small-molecule hydration free energies in explicit solvent

In molecular simulations with fixed-charge force fields, the choice of partial atomic charges influences numerous computed physical properties, including binding free energies. Many molecular mechanics force fields specify how nonbonded parameters should be determined, but various choices are often available for how these charges are to be determined for arbitrary small molecules. Here, we compute hydration free energies for a set of 44 small, neutral molecules in two different explicit water models (TIP3P and TIP4P-Ew) to examine the influence of charge model on agreement with experiment. Using the AMBER GAFF force field for nonbonded parameters, we test several different methods for obtaining partial atomic charges, including two fast methods exploiting semiempirical quantum calculations and methods deriving charges from the electrostatic potentials computed with several different levels of ab initio quantum calculations with and without a continuum reaction field treatment of solvent. We find that the best charge sets give a root-mean-square error from experiment of roughly 1 kcal/mol. Surprisingly, agreement with experimental hydration free energies does not increase substantially with increasing level of quantum theory, even when the quantum calculations are performed with a reaction field treatment to better model the aqueous phase. We also find that the semiempirical AM1-BCC method for computing charges works almost as well as any of the more computationally expensive ab initio methods and that the root-mean-square error reported here is similar to that for implicit solvent models reported in the literature. Further, we find that the discrepancy with experimental hydration free energies grows substantially with the polarity of the compound, as does its variation across theory levels.     

Dispersion energy evaluated by using locally projected occupied and excited molecular orbitals for molecular interaction

The dispersion terms are evaluated with the perturbation theory based on the locally projected molecular orbitals. A series of model systems, including some of the S22 set, is examined, and the calculated binding energies are compared with the published results. The basis set dependence is also examined. The dispersion energy correction is evaluated by taking into account the double excitations only of the dispersion type electron configurations and is added to the 3rd order single excitation perturbation energy, which is a good approximation to the counterpoise (CP) corrected Hartree-Fock (HF) binding energy. The procedure is the approximate "CP corrected HF + D" method. It ensures that the evaluated binding energy is approximately free of the basis set superposition error without the CP procedure. If the augmented basis functions are used, the evaluated binding energies for the predominantly dispersion-bound systems, such as rare gas dimers and halogen bonded clusters, agree with those of the reference calculations within 1 kcal mol(-1) (4 kJ mol(-1)). The limitation of the present method is also discussed.     

Effect of atomic charge,solvation, entropy,and ligand protonation state on MM-PB(GB)SA binding energies of HIV protease

The molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) and MM-generalized-Born surface area (MM-GBSA) approaches are commonly used in molecular modeling and drug design. Four critical aspects of these approaches have been investigated for their effect on calculated binding energies: (1) the atomic partial charge method used to parameterize the ligand force field, (2) the method used to calculate the solvation free energy, (3) inclusion of entropy estimates, and (4) the protonation state of the ligand. HIV protease has been used as a test case with six structurally different inhibitors covering a broad range of binding strength to assess the effect of these four parameters. Atomic charge methods are demonstrated to effect both the molecular dynamics (MD) simulation and MM-PB(GB)SA binding energy calculation, with a greater effect on the MD simulation. Coefficients of determination and Spearman rank coefficients were used to quantify the performance of the MM-PB(GB)SA methods relative to the experimental data. In general, better performance was achieved using (i) atomic charge models that produced smaller mean absolute atomic charges (Gasteiger, HF/STO-3G and B3LYP/cc-pVTZ), (ii) the MM-GBSA approach over MM-PBSA, while (iii) inclusion of entropy had a slightly positive effect on correlations with experiment. Accurate representation of the ligand protonation state was found to be important. It is demonstrated that these approaches can distinguish ligands according to binding strength, underlining the usefulness of these approaches in computer-aided drug design. © 2012 Wiley Periodicals, Inc.     

Energy decomposition in molecular complexes: implications for the treatment of polarization in molecular simulations

This study examines the contribution of electrostatic and polarization to the interaction energy in a variety of molecular complexes. The results obtained from the Kitaura-Morokuma (KM) energy decomposition analysis at the HF/6-31G(d) level indicate that, for intermolecular distances around the equilibrium geometries, the polarization energy can be determined as the addition of the polarization energies of interacting blocks, as the mixed polarization term is typically negligible. Comparison of KM and QM/MM results shows that the electrostatic energy determined in the KM method is underestimated (in absolute value) by QM/MM methods. The reason of such underestimation can be attributed to the simplified representation of treating the interaction between overlapping charge distribution by the interaction of a QM molecule with a set of point charges. Nevertheless, the polarization energies calculated by KM and QM/MM methods are in close agreement. Finally, a consistent, automated strategy to derive charge distributions that include implicitly polarization effects in pairwise, additive force fields is presented. The strategy relies in the simultaneous fitting of electrostatic and polarization energies computed by placing a suitable perturbing particle at selected points around the molecule. The suitability of these charges to describe molecular interactions is discussed.     

Charge asymmetries in hydration of polar solutes

We study the solvation of polar molecules in water. The center of water's dipole moment is offset from its steric center. In common water models, the Lennard-Jones center is closer to the negatively charged oxygen than to the positively charged hydrogens. This asymmetry of water's charge sites leads to different hydration free energies of positive versus negative ions of the same size. Here, we explore these hydration effects for some hypothetical neutral solutes, and two real solutes, with molecular dynamics simulations using several different water models. We find that, like ions, polar solutes are solvated differently in water depending on the sign of the partial charges. Solutes having a large negative charge balancing diffuse positive charges are preferentially solvated relative to those having a large positive charge balancing diffuse negative charges. Asymmetries in hydration free energies can be as large as 10 kcal/mol for neutral benzene-sized solutes. These asymmetries are mainly enthalpic, arising primarily from the first solvation shell water structure. Such effects are not readily captured by implicit solvent models, which respond symmetrically with respect to charge.     

Implicit nonpolar solvent models

We have systematically analyzed a new nonpolar solvent model that separates nonpolar solvation free energy into repulsive and attractive components. Our analysis shows that either molecular surfaces or volumes can be used to correlate with repulsive free energies of tested molecules in explicit solvent with correlation coefficients higher than 0.99. In addition, the attractive free energies in explicit solvent can also be reproduced with the new model with a correlation coefficient higher than 0.999. Given each component optimized, the new nonpolar solvent model is found to reproduce monomer nonpolar solvation free energies in explicit solvent very well. However, the overall accuracy of the nonpolar solvation free energies is lower than that of each component. In the more challenging dimer test cases, the agreement of the new model with explicit solvent is less impressive. Nevertheless, it is found that the new model works reasonably well for reproducing the relative nonpolar free energy landscapes near the global minimum of the dimer complexes.     

A multipole approximation of the electrostatic potential of molecules

The problem of approximating three-dimensional spatial distributions of quantum-mechanical electrostatic potentials of molecules by analytic potentials on the basis of atomic charges, real dipoles, and atomic multipoles up to quadrupoles inclusive was considered. Real dipole potentials are created by pairs of point charges of opposite signs, and the search for their arrangement in the volume of a molecule is part of the approximation problem. A FitMEP program was developed for the optimization of the parameters of models of the types specified taking into account molecular symmetry. It was shown for the example of several molecules (HF, CO, H₂O, NH₃, CH₄, formaldehyde, methanol, formamide, ethane, cyclopropane, cyclobutane, cyclohexane, tetrahedrane, cubane, adamantane, ethylene, and benzene) that the real dipole and atomic multipole models gave errors in approximated quantum-mechanical electrostatic potential values smaller by one or two orders of magnitude compared with the atomic charge model. The atomic charge model was shown to be virtually inoperative as applied to saturated hydrocarbons. Real dipole models were slightly inferior to atomic multipole models in quality but had all the advantages of the potential of point charges as concerned simplicity and compactness, and their use in potential energy calculations did not require changes in the existing program codes.     

Multidimensional umbrella sampling and replica‐exchange molecular dynamics simulations for structure prediction of transmembrane helix dimers

Structural information of a transmembrane (TM) helix dimer is useful in understanding molecular mechanisms of important biological phenomena such as signal transduction across the cell membrane. Here, we describe an umbrella sampling (US) scheme for predicting the structure of a TM helix dimer in implicit membrane using the interhelical crossing angle and the TM–TM relative rotation angles as the reaction coordinates. This scheme conducts an efficient conformational search on TM–TM contact interfaces, and its robustness is tested by predicting the structures of glycophorin A (GpA) and receptor tyrosine kinase EphA1 (EphA1) TM dimers. The nuclear magnetic resonance (NMR) structures of both proteins correspond to the global free‐energy minimum states in their free‐energy landscapes. In addition, using the landscape of GpA as a reference, we also examine the protocols of temperature replica‐exchange molecular dynamics (REMD) simulations for structure prediction of TM helix dimers in implicit membrane. A wide temperature range in REMD simulations, for example, 250–1000 K, is required to efficiently obtain a free‐energy landscape consistent with the US simulations. The interhelical crossing angle and the TM–TM relative rotation angles can be used as reaction coordinates in multidimensional US and be good measures for conformational sampling of REMD simulations. © 2013 Wiley Periodicals, Inc.     

On the transferability of hydration-parametrized continuum electrostatics models to solvated binding calculations

Using molecular mechanics force field partial atomic charges, we show the nonuniqueness of the parametrization of continuum electrostatics models with respect to solute atomic radii and interior dielectric constant based on hydration (vacuum-to-water transfer) free energy data available for small molecules. Moreover, parameter sets that are optimal and equivalent for hydration free energy calculations lead to large variations of calculated absolute and relative electrostatic binding free energies. Hence, parametrization of solvation effects based on hydration data, although a necessary condition, is not sufficient to guarantee its transferability to the calculation of binding free energies in solution.     

Parameterization and evaluation of a flexible water model

The thermodynamic, dielectric, and dynamic properties of a newly parameterized flexible water model are studied using molecular dynamics simulations. The potential function developed is based on the popular simple point charge (SPC) rigid model with the addition of appropriate harmonic and anharmonic energy terms for stretching and bending. Care was taken to account for the self-polarization and gas-phase monomer energy corrections during the parameterization, which have typically been ignored in past studies. The results indicate that an increased Lennard-Jones repulsive coefficient and slightly scaled partial charges are required when adding flexibility to the rigid model potential to reliably reproduce the experimental density, energy, and O ? O radial distribution function of water at 298 K and 1 atm. Analysis of the power spectrum derived from the H-velocity autocorrelation function allowed the water potential to be evaluated further and refined by adjusting the valence forces to fit the vibrational frequencies of the gas and liquid. Once a consistent set of parameters was determined, the static dielectric properties of the water model were calculated at two temperatures using the reaction field method to treat long-range forces and correlations. The dielectric constant of 75 ± 7 calculated at 300 K is in good agreement with the experimental value of 78.5. The Kirkwood g factor was also examined for temperature dependence and showed the correct increasing behavior with decreasing T. As a final check of the water potential, the free energies of solvation of a flexible water molecule and neon were predicted using thermodynamic perturbation methods. The calculated solvation energies of ?7.0 ± 0.8 for water and 2.7 ± 0.7 for neon are both consistent with the experimental values of ?6.3 and 2.7 kcal/mol. Comparisons are made throughout the study with the results of previous rigid and flexible model simulations. © 1995 by John Wiley & Sons, Inc.