Critical parameters and spherical confinement of H atom in screened Coulomb potential

Critical parameters in three screened potentials, namely, Hulthén, Yukawa, and exponential cosine screened Coulomb potential are reported. Accurate estimates of these parameters are given for each of these potentials, for all states having . Comparison with literature results is made, wherever possible. Present values compare excellently with reference values; for higher n, ?, our results are slightly better. Some of these are presented for first time. Further, we investigate the spherical confinement of H atom embedded in a dense plasma modeled by an exponential cosine screened potential. Accurate energies along with their variation with respect to box size and screening parameter are calculated and compared with reference results in literature. Sample dipole polarizabilities are also provided in this case. The generalized pseudospectral method is used for accurate determination of eigenvalues and eigenfunctions for all calculations. © 2016 Wiley Periodicals, Inc.     

The surface potential of solvent and the intraphase pre-existing potential

Using own and literature data, the differences of real solvation energy for ferricenium and ferrocene in six solvents are found. These quantities are confronted with the calculated difference of the dielectric response energies plus nonelectrostatic energies for the redox couple. Such a comparison allows determining the sum of the surface and intraphase potentials. The comparison of these sums with the experimental values of the surface potential differences obtained by the measuring of Volta potentials allowed determining the differences of pre-existing intraphase potentials formed by solvent molecules on the ferrocene molecule. Thus, the intraphase potentials are evaluated for the first time, using an approach not based on the molecular-dynamic modeling. Using some approximations, the surface potentials of the studied solvents are found.     

Free energies of solvation in the context of protein folding: Implications for implicit and explicit solvent models

Implicit solvent models for biomolecular simulations have been developed to use in place of more expensive explicit models; however, these models make many assumptions and approximations that are likely to affect accuracy. Here, the changes in free energies of solvation upon folding of several fast folding proteins are calculated from previously run μs–ms simulations with a number of implicit solvent models and compared to the values needed to be consistent with the explicit solvent model used in the simulations. In the majority of cases, there is a significant and substantial difference between the values calculated from the two approaches that is robust to the details of the calculations. These differences could only be remedied by selecting values for the model parameters—the internal dielectric constant for the polar term and the surface tension coefficient for the nonpolar term—that were system‐specific or physically unrealistic. We discuss the potential implications of our findings for both implicit and explicit solvent simulations. © 2015 Wiley Periodicals, Inc.     

AGBNP: an analytic implicit solvent model suitable for molecular dynamics simulations and high-resolution modeling

We have developed an implicit solvent effective potential (AGBNP) that is suitable for molecular dynamics simulations and high-resolution modeling. It is based on a novel implementation of the pairwise descreening Generalized Born model for the electrostatic component and a new nonpolar hydration free energy estimator. The nonpolar term consists of an estimator for the solute-solvent van der Waals dispersion energy designed to mimic the continuum solvent solute-solvent van der Waals interaction energy, in addition to a surface area term corresponding to the work of cavity formation. AGBNP makes use of a new parameter-free algorithm to calculate the scaling coefficients used in the pairwise descreening scheme to take into account atomic overlaps. The same algorithm is also used to calculate atomic surface areas. We show that excellent agreement is achieved for the GB self-energies and surface areas in comparison to accurate, but much more expensive, numerical evaluations. The parameter-free approach used in AGBNP and the sensitivity of the AGBNP model with respect to large and small conformational changes makes the model suitable for high-resolution modeling of protein loops and receptor sites as well as high-resolution prediction of the structure and thermodynamics of protein-ligand complexes. We present illustrative results for these kinds of benchmarks. The model is fully analytical with first derivatives and is computationally efficient. It has been incorporated into the IMPACT molecular simulation program.     

Supersymmetric solutions of <Emphasis Type="Italic">PT</Emphasis>-/non-<Emphasis Type="Italic">PT</Emphasis>-symmetric and non-Hermitian screened Coulomb potential via Hamiltonian hierarchy inspired variational method

The supersymmetric solutions of PT -symmetric and Hermitian/non-Hermitian forms of quantum systems are obtained by solving the Schr?dinger equation for the Exponential-Cosine Screened Coulomb potential. The Hamiltonian hierarchy inspired variational method is used to obtain the approximate energy eigenvalues and corresponding wave functions.      

Solvent models for protein–ligand binding: Comparison of implicit solvent poisson and surface generalized born models with explicit solvent simulations

Solvent effects play a crucial role in mediating the interactions between proteins and their ligands. Implicit solvent models offer some advantages for modeling these interactions, but they have not been parameterized on such complex problems, and therefore, it is not clear how reliable they are. We have studied the binding of an octapeptide ligand to the murine MHC class I protein using both explicit solvent and implicit solvent models. The solvation free energy calculations are more than 10³ faster using the Surface Generalized Born implicit solvent model compared to FEP simulations with explicit solvent. For some of the electrostatic calculations needed to estimate the binding free energy, there is near quantitative agreement between the explicit and implicit solvent model results; overall, the qualitative trends in the binding predicted by the explicit solvent FEP simulations are reproduced by the implicit solvent model. With an appropriate choice of reference system based on the binding of the discharged ligand, electrostatic interactions are found to enhance the binding affinity because the favorable Coulomb interaction energy between the ligand and protein more than compensates for the unfavorable free energy cost of partially desolvating the ligand upon binding. Some of the effects of protein flexibility and thermal motions on charging the peptide in the solvated complex are also considered. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 591–607, 2001     

The SGB/NP hydration free energy model based on the surface generalized born solvent reaction field and novel nonpolar hydration free energy estimators

The development and parameterization of a solvent potential of mean force designed to reproduce the hydration thermodynamics of small molecules and macromolecules aimed toward applications in conformation prediction and ligand binding free energy prediction is presented. The model, named SGB/NP, is based on a parameterization of the Surface Generalized Born continuum dielectric electrostatic model using explicit solvent free energy perturbation calculations and a newly developed nonpolar hydration free energy estimator motivated by the results of explicit solvent simulations of the thermodynamics of hydration of hydrocarbons. The nonpolar model contains, in addition to the more commonly used solvent accessible surface area term, a component corresponding to the attractive solute-solvent interactions. This term is found to be important to improve the accuracy of the model, particularly for cyclic and hydrogen bonding compounds. The model is parameterized against the experimental hydration free energies of a set of small organic molecules. The model reproduces the experimental hydration free energies of small organic molecules with an accuracy comparable or superior to similar models employing more computationally demanding estimators and/or a more extensive set of parameters.     

Spherical confinement of coulombic systems inside an impenetrable box: H atom and the Hulthén potential

The generalized pseudospectral method is used to study spherical confinement in two simple Coulombic systems: (i) well celebrated and heavily studied H atom (ii) relatively less explored Hulthén potential. In both instances, arbitrary cavity size as well as low and higher states are considered. Apart from bound state eigenvalues, eigenfunctions, expectation values, quite accurate estimates of the critical cage radius for H atom for all the 55 states corresponding to , are also examined. Some of the latter are better than previously reported values. Degeneracy and energy ordering under the isotropic confinement situation are discussed as well. The method produces consistently high‐quality results for both potentials for small as well as large cavity size. For the H atom, present results are comparable to best theoretical values, while for the latter, this work gives considerably better estimates than all existing work so far. © 2014 Wiley Periodicals, Inc.     

An anisotropic coarse‐grained model based on Gay–Berne and electric multipole potentials and its application to simulate a DMPC bilayer in an implicit solvent model

In this work, we aim at optimizing the performance of the anisotropic GBEMP model, which adopts a framework by combining a Gay–Berne (GB) anisotropic potential with an electric multipole (EMP) potential, in simulating a DMPC lipid bilayer in an implicit solvent model. First, the Gay–Berne parameters were initially obtained by fitting to atomistic profiles of van der Waals interactions between homodimers of molecular fragments while EMP parameters was directly derived from the expansion of point multipoles at predefined EMP sites. Second, the GB and EMP parameters for DMPC molecule were carefully optimized to be comparable to AMBER atomistic model in the calculations of the dipole moments of DMPC monomers adopting different conformations as well as the nonbonded interactions between two DMPC molecules adopting different conformations and separated at various distances. Finally, the GB parameters for DMPC were slightly adjusted in simulating a 72 DMPC bilayer system so that our GBEMP model would be able to reproduce a few important structural properties, namely, thickness (), area per lipid ( ) and volume per lipid ( ). Meanwhile, the atomistic and experimental results for electron density profiles and order parameters were reproduced reasonably well by the GBEMP model, demonstrating the promising feature of GBEMP model in modeling lipid systems. Finally, we have shown that current GBEMP model is more efficient by a factor of about 25 than AMBER atomistic point charge model. © 2015 Wiley Periodicals, Inc.     

Water solvent effects using continuum and discrete models: The nitromethane molecule,CH3NO2

The first three valence transitions of the two nitromethane conformers (CH₃NO₂) are two dark n → π* transitions and a very intense π → π* transition. In this work, these transitions in gas‐phase and solvated in water of both conformers were investigated theoretically. The polarizable continuum model (PCM), two conductor‐like screening (COSMO) models, and the discrete sequential quantum mechanics/molecular mechanics (S‐QM/MM) method were used to describe the solvation effect on the electronic spectra. Time dependent density functional theory (TDDFT), configuration interaction including all single substitutions and perturbed double excitations (CIS(D)), the symmetry‐adapted‐cluster CI (SAC‐CI), the multistate complete active space second order perturbation theory (CASPT2), and the algebraic‐diagrammatic construction (ADC(2)) electronic structure methods were used. Gas‐phase CASPT2, SAC‐CI, and ADC(2) results are in very good agreement with published experimental and theoretical spectra. Among the continuum models, PCM combined either with CASPT2, SAC‐CI, or B3LYP provided good agreement with available experimental data. COSMO combined with ADC(2) described the overall trends of the transition energy shifts. The effect of increasing the number of explicit water molecules in the S‐QM/MM approach was discussed and the formation of hydrogen bonds was clearly established. By including explicitly 24 water molecules corresponding to the complete first solvation shell in the S‐QM/MM approach, the ADC(2) method gives more accurate results as compared to the TDDFT approach and with similar computational demands. The ADC(2) with S‐QM/MM model is, therefore, the best compromise for accurate solvent calculations in a polar environment. © 2015 Wiley Periodicals, Inc.     

Solvation free energies calculated using the GB/SA model: Sensitivity of results on charge sets,protocols, and force fields

The sensitivity of aqueous solvation free energies (SFEs), estimated using the GB/SA continuum solvent model, on charge sets, protocols, and force fields, was studied. Simple energy calculations using the GB/SA solvent model were performed on 11 monofunctional organic compounds. Results indicate that calculated SFEs are strongly dependent on the charge sets. Charges derived from electrostatic potential fitting to high level ab initio wave functions using the CHELPG procedure and “class IV” charges from AM1/CM1a or PM3/CM1p calculations yielded better results than the corresponding Mulliken charges. Calculated SFEs were similar to MC/FEP energies obtained in the presence of explicit TIP4P water. Further improvements were obtained by using GVB/6-31G** and MP2/6-31+G** (CHELPG) charge sets that included correlation effects. SFEs calculated using charge sets assigned by the OPLSA* force field gave the best results of all standard force fields (MM2*, MM3*, MMFF, AMBER*, and OPLSA*) implemented in MacroModel. Comparison of relative and absolute SFEs computed using either the GB/SA continuum model or MC/FEP calculations in the presence of explicit TIP4P water showed that, in general, relative SFEs can be estimated with greater accuracy. A second set of 20 mono- and difunctional molecules was also studied and relative SFEs estimated using energy minimization and thermodynamic cycle perturbation (TCP) protocols. SFEs calculated from TCP calculations using the GB/SA model were sensitive to bond lengths of dummy bonds (i.e., bonds involving dummy atoms). In such cases, keeping the bond lengths of dummy bonds close to the corresponding bond lengths of the starting structures improved the agreement of TCP-calculated SFEs with energy minimization results. Overall, these results indicate that GB/SA solvation free energy estimates from simple energy minimization calculations are of similar accuracy and value to those obtained using more elaborate TCP protocols. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 769–780, 1998     

Screened potential in π-electron systems and its application to the estimation of excitation energies

A diagrammatic technique was developed for the estimation of the screened potential of -electron systems. The screened potential was expanded in terms of the polarization propagators which were constructed from either the singlet, , or triplet vertex part, . These vertex parts correspond to the singlet or triplet excitations, respectively, in the Random Phase Approximation (RPA) containing exchange diagrams. The excitation energies were calculated by using the screened potential in the framework of RPA with exchange. The excitation energies of several conjugated molecules with or without a hetero atom are in agreement with the experimental data.     

Accurate and efficient generalized born model based on solvent accessibility: derivation and application for LogP octanol/water prediction and flexible peptide docking

A novel method for fast and accurate evaluation of the generalized Born radii in macromolecular solvation electrostatics calculations is proposed, based on the solvent accessibility of the first two solvation layers around an atom. The reverse generalized Born radii calculated by the method have correlation coefficient of 98.7% and RMSD of 0.031 A(-1) with the values obtained using a precise but significantly slower numerical boundary element solution. The method is applied to derive an estimate of the free solvation energy difference between octanol and water and to predict LogP octanol-water. A nine-parameter model is optimized on an 81 compound training set and applied to predict LogP(ow) for an external evaluation set of 19 drug molecules with RMSD of 0.9. The new GB approximation is also tested in Monte Carlo docking simulations of the fully flexible p53 peptide fragment to MDM2. The best energy solution found in the simulations has RMSD of 2.8 A to the X-ray structure.     

Identification of novel nt-MGAM inhibitors for potential treatment of type 2 diabetes: Virtual screening,atom based 3D-QSAR model,docking analysis and ADME study

In this study, a virtual screening procedure was applied to identify new potential nt-MGAM inhibitors as a possible medication for type 2 diabetes. To this aim, a series of salacinol analogues were first investigated by docking analysis for their binding to the X-ray structure of the biological target nt-MGAM. Key interactions for ligand binding into the receptor active site were identified which shared common features to those found for other known inhibitors, which strengthen the results of this study. 3D QSAR model was then built and showed to be statistically significant and with a good predictive power for the training (R² = 0.99, SD = 0.17, F = 555.3 and N = 27) and test set (Q² = 0.81, Pearson(r) = 0.92, RMSE = 0.52, N = 08). The model was then used to virtually screen the ZINC database with the aim of identifying novel chemical scaffolds as potential nt-MGAM inhibitors. Further, in silico predicted ADME properties were investigated for the most promising molecules. The outcome of this investigation sheds light on the molecular characteristics of the binding of salacinol analogues to nt-MGAM enzyme and identifies new possible inhibitors which have the potential to be developed into drugs, thus significantly contributing to the design and optimization of therapeutic strategies against type 2 diabetes.     

Accelerating molecular Monte Carlo simulations using distance and orientation-dependent energy tables: tuning from atomistic accuracy to smoothed "coarse-grained" models

Typically, the most time consuming part of any atomistic molecular simulation is the repeated calculation of distances, energies, and forces between pairs of atoms. However, many molecules contain nearly rigid multi-atom groups such as rings and other conjugated moieties, whose rigidity can be exploited to significantly speed-up computations. The availability of GB-scale random-access memory (RAM) offers the possibility of tabulation (precalculation) of distance- and orientation-dependent interactions among such rigid molecular bodies. Here, we perform an investigation of this energy tabulation approach for a fluid of atomistic-but rigid-benzene molecules at standard temperature and density. In particular, using O(1) GB of RAM, we construct an energy look-up table, which encompasses the full range of allowed relative positions and orientations between a pair of whole molecules. We obtain a hardware-dependent speed-up of a factor of 24-50 as compared to an ordinary ("exact") Monte Carlo simulation and find excellent agreement between energetic and structural properties. Second, we examine the somewhat reduced fidelity of results obtained using energy tables based on much less memory use. Third, the energy table serves as a convenient platform to explore potential energy smoothing techniques, akin to coarse-graining. Simulations with smoothed tables exhibit near atomistic accuracy while increasing diffusivity. The combined speed-up in sampling from tabulation and smoothing exceeds a factor of 100. For future applications, greater speed-ups can be expected for larger rigid groups, such as those found in biomolecules.