Evaluation of Poisson solvation models using a hybrid explicit/implicit solvent method

Implicit solvent methods have become popular tools in the field of protein dynamics simulations, yet evaluation of their validity has been primarily limited to comparisons with experimental and theoretical data for small molecules. In this paper, we use a recently developed hybrid explicit/implicit solvent methodology to evaluate the accuracy of several Poisson-based implicit solvent models. Specifically, we focus on the calculation of electrostatic solvation free energies of various fixed conformations for two proteins. We show that, among various dielectric boundary definitions, the Lee-Richards molecular surface has the best agreement with hybrid solvent results. Furthermore, certain modifications of the molecular surface Poisson protocol provide varied results. For instance, simple modifications of atomic radii on charged residues generally improve absolute errors but do not significantly reduce relative errors among conformations. On the other hand, using a water-probe radius of 1.0 A, as opposed to the standard value of 1.4 A, to generate the molecular surface, moderately improves both absolute and relative results.     

Density functional theory based molecular-dynamics study of aqueous fluoride solvation

We use density functional theory based molecular-dynamics simulations to study the aqueous solvation of the fluoride anion. Our studies are focused on the first solvation shell and have resulted in detailed information on its structural and dynamical properties. The fluoride ion leads to the formation of a rigid solvation shell, qualitatively consistent with simulation and experimental studies, classifying fluoride as a "structure making" particle. However, quantitatively we find the solvation shell to be less structured and more mobile than predicted from empirical force-field simulation. The influence on the intramolecular electronical and structural properties of water is minimal, as observed for other halogens. We propose two distinct mechanisms for the exchange of bulk and first solvation shell water molecules.     

Density functional theory based molecular-dynamics study of aqueous iodide solvation

We study the solvation of iodide in water using density functional theory based molecular-dynamics simulations. Detailed analysis of the structural and dynamical properties of the first solvation shell is presented, showing a disruptive influence of the ion on the local water structure. Iodide-water hydrogen bonding is weak, compared to water-water hydrogen bonds. This effective repulsive ion-water interaction leads to the formation of a quite unstructured solvation shell. The dynamics of water molecules surrounding the iodide is relatively fast. The intramolecular structural and electronical properties of water molecules around the ion are not affected.     

Fragment density functional theory calculation of NMR chemical shifts for proteins with implicit solvation

Fragment density functional theory (DFT) calculation of NMR chemical shifts for several proteins (Trp-cage, Pin1 WW domain, the third IgG-binding domain of Protein G (GB3) and human ubiquitin) has been carried out. The present study is based on a recently developed automatic fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach but the solvent effects are included by using the PB (Poisson-Boltzmann) model. Our calculated chemical shifts of (1)H and (13)C for these four proteins are in excellent agreement with experimentally measured values and represent clear improvement over that from the gas phase calculation. However, although the inclusion of the solvent effect also improves the computed chemical shifts of (15)N, the results do not agree with experimental values as well as (1)H and (13)C. Our study also demonstrates that AF-QM/MM calculated results accurately reproduce the separation of α-helical and β-sheet chemical shifts for (13)C(α) atoms in proteins, and using the (1)H chemical shift to discriminate the native structure of proteins from decoys is quite remarkable.     

Density functional theory of the chemical potential of atoms and its relation to electrostatic potentials and bonding distances

Using an approximate density functional pseudopotential method we have confirmed several relations proposed earlier by P. Politzer, R.G. Parr and D.R. Murphy (J. Chem. Phys.79, 3859 (1983)), who combined theoretical and experimental information. The main result is that the radial distancer _μ where the chemical potential μ is equal to the electrostatic potential in the free atom, is of especial significance for the bonding properties of the atom.r _μ is linearly related to the nonpolar covalent radius and to the Wigner-Seitz radius of the solid phase. On the other hand μ is linearly related to the electrostatic potentialV _Q (r _μ ) due to the net charge inside a sphere of radiusr _μ in the free atom. Finally we have discovered that a linear relation exists in the free atom between (?μ)^1/2 and ρ(r _μ )^1/3.     

Postprocessing of docked protein-ligand complexes using implicit solvation models

Molecular docking plays an important role in drug discovery as a tool for the structure-based design of small organic ligands for macromolecules. Possible applications of docking are identification of the bioactive conformation of a protein-ligand complex and the ranking of different ligands with respect to their strength of binding to a particular target. We have investigated the effect of implicit water on the postprocessing of binding poses generated by molecular docking using MM-PB/GB-SA (molecular mechanics Poisson-Boltzmann and generalized Born surface area) methodology. The investigation was divided into three parts: geometry optimization, pose selection, and estimation of the relative binding energies of docked protein-ligand complexes. Appropriate geometry optimization afforded more accurate binding poses for 20% of the complexes investigated. The time required for this step was greatly reduced by minimizing the energy of the binding site using GB solvation models rather than minimizing the entire complex using the PB model. By optimizing the geometries of docking poses using the GB(HCT+SA) model then calculating their free energies of binding using the PB implicit solvent model, binding poses similar to those observed in crystal structures were obtained. Rescoring of these poses according to their calculated binding energies resulted in improved correlations with experimental binding data. These correlations could be further improved by applying the postprocessing to several of the most highly ranked poses rather than focusing exclusively on the top-scored pose. The postprocessing protocol was successfully applied to the analysis of a set of Factor Xa inhibitors and a set of glycopeptide ligands for the class II major histocompatibility complex (MHC) A(q) protein. These results indicate that the protocol for the postprocessing of docked protein-ligand complexes developed in this paper may be generally useful for structure-based design in drug discovery.     

Secondary structure bias in generalized Born solvent models: comparison of conformational ensembles and free energy of solvent polarization from explicit and implicit solvation

The effects of the use of three generalized Born (GB) implicit solvent models on the thermodynamics of a simple polyalanine peptide are studied via comparing several hundred nanoseconds of well-converged replica exchange molecular dynamics (REMD) simulations using explicit TIP3P solvent to REMD simulations with the GB solvent models. It is found that when compared to REMD simulations using TIP3P the GB REMD simulations contain significant differences in secondary structure populations, most notably an overabundance of alpha-helical secondary structure. This discrepancy is explored via comparison of the differences in the electrostatic component of the free energy of solvation (DeltaDeltaG(pol)) between TIP3P (via thermodynamic Integration calculations), the GB models, and an implicit solvent model based on the Poisson equation (PE). The electrostatic components of the solvation free energies are calculated using each solvent model for four representative conformations of Ala10. Since the PE model is found to have the best performance with respect to reproducing TIP3P DeltaDeltaG(pol) values, effective Born radii from the GB models are compared to effective Born radii calculated with PE (so-called perfect radii), and significant and numerous deviations in GB radii from perfect radii are found in all GB models. The effect of these deviations on the solvation free energy is discussed, and it is shown that even when perfect radii are used the agreement of GB with TIP3P DeltaDeltaG(pol) values does not improve. This suggests a limit to the optimization of the effective Born radius calculation and that future efforts to improve the accuracy of GB models must extend beyond such optimizations.     

Treatment of geometric singularities in implicit solvent models

Geometric singularities, such as cusps and self-intersecting surfaces, are major obstacles to the accuracy, convergence, and stability of the numerical solution of the Poisson-Boltzmann (PB) equation. In earlier work, an interface technique based PB solver was developed using the matched interface and boundary (MIB) method, which explicitly enforces the flux jump condition at the solvent-solute interfaces and leads to highly accurate biomolecular electrostatics in continuum electric environments. However, such a PB solver, denoted as MIBPB-I, cannot maintain the designed second order convergence whenever there are geometric singularities, such as cusps and self-intersecting surfaces. Moreover, the matrix of the MIBPB-I is not optimally symmetrical, resulting in the convergence difficulty. The present work presents a new interface method based PB solver, denoted as MIBPB-II, to address the aforementioned problems. The present MIBPB-II solver is systematical and robust in treating geometric singularities and delivers second order convergence for arbitrarily complex molecular surfaces of proteins. A new procedure is introduced to make the MIBPB-II matrix optimally symmetrical and diagonally dominant. The MIBPB-II solver is extensively validated by the molecular surfaces of few-atom systems and a set of 24 proteins. Converged electrostatic potentials and solvation free energies are obtained at a coarse grid spacing of 0.5 A and are considerably more accurate than those obtained by the PBEQ and the APBS at finer grid spacings.     

Treatment of charge singularities in implicit solvent models

This paper presents a novel method for solving the Poisson-Boltzmann (PB) equation based on a rigorous treatment of geometric singularities of the dielectric interface and a Green's function formulation of charge singularities. Geometric singularities, such as cusps and self-intersecting surfaces, in the dielectric interfaces are bottleneck in developing highly accurate PB solvers. Based on an advanced mathematical technique, the matched interface and boundary (MIB) method, we have recently developed a PB solver by rigorously enforcing the flux continuity conditions at the solvent-molecule interface where geometric singularities may occur. The resulting PB solver, denoted as MIBPB-II, is able to deliver second order accuracy for the molecular surfaces of proteins. However, when the mesh size approaches half of the van der Waals radius, the MIBPB-II cannot maintain its accuracy because the grid points that carry the interface information overlap with those that carry distributed singular charges. In the present Green's function formalism, the charge singularities are transformed into interface flux jump conditions, which are treated on an equal footing as the geometric singularities in our MIB framework. The resulting method, denoted as MIBPB-III, is able to provide highly accurate electrostatic potentials at a mesh as coarse as 1.2 A for proteins. Consequently, at a given level of accuracy, the MIBPB-III is about three times faster than the APBS, a recent multigrid PB solver. The MIBPB-III has been extensively validated by using analytically solvable problems, molecular surfaces of polyatomic systems, and 24 proteins. It provides reliable benchmark numerical solutions for the PB equation.     

Limitations of atom-centered dielectric functions in implicit solvent models

Many recent advances in Poisson-Boltzmann and generalized Born implicit solvent models have used atom-centered polynomial or Gaussian functions to define the boundary separating low and high dielectric regions. In contrast to the Lee and Richards molecular surface, atom-centered surfaces result in interatomic crevices and buried pockets of high dielectric which are too small for a solvent molecule to occupy. We show that these interstitial high dielectric regions are of significant magnitude in globular proteins, that they artificially increase solvation energies, and that they distort the free energy surface of nonbonded interactions. These results suggest that implicit solvent dielectric functions must exclude interstitial high dielectric regions in order to yield physically meaningful results.     

Density functional theory calculations of dynamic first hyperpolarizabilities for organic molecules in organic solvent: comparison to experiment

Against experimental values obtained from solution-phase dc electric field induced second-harmonic generation measurements at a fundamental wavelength of 1910 nm, the performance of 20 exchange-correlation functionals in density functional theory in evaluation of solvent modulated dynamic first hyperpolarizabilities of 82 organic molecules in chloroform, 1,4-dioxane, and/or dichloromethane was evaluated. The used exchange-correlation functionals consisted of generalized gradient approximation (GGA), meta-GGA, global hybrids, and range-separated hybrids. The PCM-X/6-311+G(2d,p)//PCM-B3LYP/6-31G(2df,p) level of theory was employed. The calculated results showed functionals with the exact asymptote of the exchange potential gave satisfying linear correlation with R(2) of 0.95 between experimental data and theoretical values. With a linear correction, these functionals also provided a better accuracy with mean absolute error of 5 × 10(-30) esu than other functionals. The solvent effect and solvation scheme on the calculated property were also studied.     

Molecular density functional theory of solvation: from polar solvents to water

A classical density functional theory approach to solvation in molecular solvent is presented. The solvation properties of an arbitrary solute in a given solvent, both described by a molecular force field, can be obtained by minimization of a position and orientation-dependent free-energy density functional. In the homogeneous reference fluid approximation, limited to two-body correlations, the unknown excess term of the functional approximated by the angular-dependent direct correlation function of the pure solvent. We show that this function can be extracted from a preliminary MD simulation of the pure solvent by computing the angular-dependent pair distribution function and solving subsequently the molecular Ornstein-Zernike equation using a discrete angular representation. The corresponding functional can then be minimized in the presence of an arbitrary solute on a three-dimensional cubic grid for positions and Gauss-Legendre angular grid for orientations to provide the solvation structure and free-energy. This two-step procedure is proved to be much more efficient than direct molecular dynamics simulations combined to thermodynamic integration schemes. The approach is shown to be relevant and accurate for prototype polar solvents such as the Stockmayer solvent or acetonitrile. For water, although correct for neutral or moderately charged solute, it tends to underestimate the tetrahedral solvation structure around H-bonded solutes, such as spherical ions. This can be corrected by introducing suitable three-body correlation terms that restore both an accurate hydration structure and a satisfactory energetics.     

青蒿素及其衍生物抗疟活性的密度泛函理论研究

为了深入研究青蒿素及其衍生物的抗疟活性和分子结构之间的关系,运用密度泛函理论B3LYP方法,以6-31G*为基组对青蒿素及其衍生物二氢青蒿素、蒿甲醚和青蒿琥酯进行了优化计算.从分子的几何构型、NBO电荷及前线轨道能等方面分析了青蒿素及其衍生物的抗疟活性与结构之间的关系.青蒿素及其衍生物结构中的过氧桥键是其抗疟作用的活性位,O17和O_20带负电荷越多、ΔE_(LUMO-HOMO)越低、E_(HOMO)能级越高,分子的抗疟活性越强.结果表明,4种化合物的抗疟活性顺序为:青蒿素二氢青蒿素蒿甲醚青蒿琥酯,与临床实验结果相吻合.     

Competition between intramolecular hydrogen bonds and solvation in phosphorylated peptides: simulations with explicit and implicit solvent

The atomic-level mechanisms of protein regulation by post-translational phosphorylation remain poorly understood, except in a few well-studied systems. Molecular mechanics simulations can in principle be used to help understand and predict the effects of protein phosphorylation, but the accuracy of the results will of course depend on the quality of the force field parameters for the phosphorylated residues as well as the quality of the solvent model. The phosphorylated residues typically carry a -2 charge at physiological pH; however, the effects of phosphorylation can sometimes be mimicked by substituting Asp or Glu for the phosphorylated residue. Here we examine the suitability of explicit and implicit solvent models for simulating phospho-serine in both the -1 and -2 charge states. Specifically, we simulate a capped phosphorylated peptide, Ace-Gly-Ser-pSer-Ser-Nme, and compare the results to each other and to experimental observables from an NMR experiment. The first major conclusion is that explicit water models (TIP3P, TIP4P and SPC/E) and a Generalized Born implicit solvent model provide reasonable agreement with the experimental observables, given appropriate partial charges for the phosphate group. The Generalized Born results, however, show greater hydrogen bonding propensity than the explicit solvent results. Distance dependent dielectric treatments perform poorly. The second major conclusion is that many ensemble-averaged properties obtained for the phosphopeptide in the -1 and -2 charge states are strikingly similar; the -1 species has a slightly higher propensity to form internal hydrogen bonds. All of the results can be rationalized by quantifying the strength of the P-O/H-N hydrogen bond, which depends on a sensitive balance between strongly favorable charge/dipole and dipole/dipole interactions and strongly unfavorable desolvation.     

Density functional theory study of difluorovinylidene isomerization to difluoroacetylene

The isomerization of difluorovinylidene: C = CF₂ into difluoroacetylene FCCF was systematically studied using density functional theory (DFT) methods with the 6-311 + G(2 p, 2 p) Gaussian-type basis set. The computed geometries for the reactant, product, and transition state as well as the enthalpy and reaction barrier were compared with the previously computed values obtained by the LSD and NLSD DFT methods and the ab initio CCSD method. The suitability of some of the DFT methods for the computation of this system was discussed and the best estimated computational data were selected. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 515–520, 1997