Performance comparison of generalized born and Poisson methods in the calculation of electrostatic solvation energies for protein structures

This study compares generalized Born (GB) and Poisson (PB) methods for calculating electrostatic solvation energies of proteins. A large set of GB and PB implementations from our own laboratories as well as others is applied to a series of protein structure test sets for evaluating the performance of these methods. The test sets cover a significant range of native protein structures of varying size, fold topology, and amino acid composition as well as nonnative extended and misfolded structures that may be found during structure prediction and folding/unfolding studies. We find that the methods tested here span a wide range from highly accurate and computationally demanding PB-based methods to somewhat less accurate but more affordable GB-based approaches and a few fast, approximate PB solvers. Compared with PB solvation energies, the latest, most accurate GB implementations were found to achieve errors of 1% for relative solvation energies between different proteins and 0.4% between different conformations of the same protein. This compares to accurate PB solvers that produce results with deviations of less than 0.25% between each other for both native and nonnative structures. The performance of the best GB methods is discussed in more detail for the application for force field-based minimizations or molecular dynamics simulations.     

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.     

Determination of side‐chain‐rotamer and side‐chain and backbone virtual‐bond‐stretching potentials of mean force from AM1 energy surfaces of terminally‐blocked amino‐acid residues,for coarse‐grained simulations of protein structure and folding. I. The method

In this and the accompanying article, we report the development of new physics‐based side‐chain‐rotamer and virtual‐bond‐deformation potentials which now replace the respective statistical potentials used so far in our physics‐based united‐reside UNRES force field for large‐scale simulations of protein structure and dynamics. In this article, we describe the methodology for determining the corresponding potentials of mean force (PMF's) from the energy surfaces of terminally‐blocked amino‐acid residues calculated with the AM1 quantum‐mechanical semiempirical method. The approach is based on minimization of the AM1 energy for fixed values of the angles λ for rotation of the peptide groups about the C^α ··· C^α virtual bonds, and for fixed values of the side‐chain dihedral angles χ, which formed a multidimensional grid. A harmonic‐approximation approach was developed to extrapolate from the energy at a given grid point to other points of the conformational space to compute the respective contributions to the PMF. To test the applicability of the harmonic approximation, the rotamer PMF's of alanine and valine obtained with this approach have been compared with those obtained by using a Metropolis Monte Carlo method. The PMF surfaces computed with the harmonic approximation are more rugged and have more pronounced minima than the MC‐calculated surfaces but the harmonic‐approximation‐and MC‐calculated PMF values are linearly correlated. The potentials derived with the harmonic approximation are, therefore, appropriate for UNRES for which the weights (scaling factors) of the energy terms are determined by force‐field optimization for foldability. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Accuracy assessment of the linear Poisson–Boltzmann equation and reparametrization of the OBC generalized Born model for nucleic acids and nucleic acid–protein complexes

The generalized Born model in the Onufriev, Bashford, and Case (Onufriev et al., Proteins: Struct Funct Genet 2004, 55, 383) implementation has emerged as one of the best compromises between accuracy and speed of computation. For simulations of nucleic acids, however, a number of issues should be addressed: (1) the generalized Born model is based on a linear model and the linearization of the reference Poisson–Boltmann equation may be questioned for highly charged systems as nucleic acids; (2) although much attention has been given to potentials, solvation forces could be much less sensitive to linearization than the potentials; and (3) the accuracy of the Onufriev–Bashford–Case (OBC) model for nucleic acids depends on fine tuning of parameters. Here, we show that the linearization of the Poisson Boltzmann equation has mild effects on computed forces, and that with optimal choice of the OBC model parameters, solvation forces, essential for molecular dynamics simulations, agree well with those computed using the reference Poisson–Boltzmann model. © 2015 Wiley Periodicals, Inc.     

The water molecule arrangement over the side chain of some aliphatic amino acids: A quantum chemical and bottom-up investigation

The geometry of surrounding water molecules on the side chain of glycine, alanine, α-aminoisobutyric acid, α-aminobutyric acid, valine, and related hydrocarbons has been analyzed combining bottom-up and quantum chemical methodologies. To minimize the cavity size and to prevent water-water hydrogen bonding loss, the water molecules adopt a shape, resembling the one found in crystal structure of gas clathrate hydrates, with water molecules tangentially oriented to the surface of hydrophobic side chain. The cage is directly hydrogen bonded to the backbone's polar groups, thus hydration shells around hydrophobic and hydrophilic groups are folded together in amphiphilic molecules. The hydrophobe enclathration implies a substantial freedom degree reduction which makes it entropically disfavored. This disadvantageous entropic contribution is partially compensated by the favorable van der Waals interactions with guest in stabilizing clathrate hydrate formation. The water shell around the side chain relates intimately with the side-chain rotational isomerism. Present data are correlated with the experimental determined populations of the three rotamers, yielding promising results for both α-aminobutyric acid and valine.     

Theoretical calculations of homoconjugation equilibrium constants in systems modeling acid-base interactions in side chains of biomolecules using the potential of mean force

The potentials of mean force (PMFs) were determined for systems forming cationic and anionic homocomplexes composed of acetic acid, phenol, isopropylamine, n-butylamine, imidazole, and 4(5)-methylimidazole, and their conjugated bases or acids, respectively, in three solvents with different polarity and hydrogen-bonding propensity: acetonitrile (AN), dimethyl sulfoxide (DMSO), and water (H(2)O). For each pair and each solvent a series of umbrella-sampling molecular dynamics simulations with the AMBER force field, explicit solvent, and counterions added to maintain a zero net charge of a system were carried out and the PMF was calculated by using the Weighted Histogram Analysis Method (WHAM). Subsequently, homoconjugation-equilibrium constants were calculated by numerical integration of the respective PMF profiles. In all cases but imidazole stable homocomplexes were found to form in solution, which was manifested as the presence of contact minima corresponding to hydrogen-bonded species in the PMF curves. The calculated homoconjugation constants were found to be greater for complexes with the OHO bridge (acetic acid and phenol) than with the NHN bridge and they were found to decrease with increasing polarity and hydrogen-bonding propensity of the solvent (i.e., in the series AN > DMSO > H(2)O), both facts being in agreement with the available experimental data. It was also found that interactions with counterions are manifested as the broadening of the contact minimum or appearance of additional minima in the PMF profiles of the acetic acid-acetate, phenol/phenolate system in acetonitrile, and the 4(5)-methylimidazole/4(5)-methylimidzole cation conjugated base system in dimethyl sulfoxide.     

The treatment of solvation by a generalized Born model and a self-consistent charge-density functional theory-based tight-binding method

We present a model to calculate the free energies of solvation of small organic compounds as well as large biomolecules. This model is based on a generalized Born (GB) model and a self-consistent charge-density functional theory-based tight-binding (SCC-DFTB) method with the nonelectrostatic contributions to the free energy of solvation modeled in terms of solvent-accessible surface areas (SA). The parametrization of the SCC-DFTB/GBSA model has been based on 60 neutral and six ionic molecules composed of H, C, N, O, and S, and spanning a wide range of chemical groups. Effective atomic radii as parameters have been obtained through Monte Carlo Simulated Annealing optimization in the parameter space to minimize the differences between the calculated and experimental free energies of solvation. The standard error in the free energies of solvation calculated by the final model is 1.11 kcal mol(-1). We also calculated the free energies of solvation for these molecules using a conductor-like screening model (COSMO) in combination with different levels of theory (AM1, SCC-DFTB, and B3LYP/6-31G*) and compared the results with SCC-DFTB/GBSA. To assess the efficiency of our model for large biomolecules, we calculated the free energy of solvation for a HIV protease-inhibitor complex containing 3,204 atoms using the SCC-DFTB/GBSA and the SCC-DFTB/COSMO models, separately. The computed relative free energies of solvation are comparable, while the SCC-DFTB/GBSA model is three to four times more efficient, in terms of computational cost.     

The generalized Born/volume integral implicit solvent model: estimation of the free energy of hydration using London dispersion instead of atomic surface area

A new generalized Born model for estimating the free energy of hydration is presented. The new generalized Born/volume integral (GB/VI) estimates the free energy of hydration as a classical electrostatic energy plus a cavitation energy that is not based upon atomic surface area (SA) used in GB/SA hydration models but on a VI London dispersion energy estimated from quantities already calculated in the classical electrostatic energy. The (relatively few) GB/VI model parameters are fitted to experimental data, and parameterizations for two different atomic partial charge models are presented. Comparison of the calculated and experimental free energies of hydration for 560 small molecules (both neutral and charged) shows good agreement (r(2) = 0.94).     

The Henry's law constants of water in the binary mixtures of benzene,carbon tetrachloride,and cyclohexane at 25°C

The solubilities of water in each of the three binary mixtures benzene-carbon tetrachloride, benzene-cyclohexane, and carbon tetrachloride-cyclohexane were determined as a function of solvent composition at 25°C. It was found that, as with the pure solvents, water in the 0.50 mole fraction binary mixtures of these solvents obeyed Henry's law up to saturation. The experimentally determined solubilities were converted to Henry's law constants of water for the entire range of solvent compositions. These values for the Henry's law constants were compared with theoretically calculated values. The comparisons indicated that water in the benzene-cyclohexane and in the benzene-carbon tetrachloride mixtures was preferentially solvated by benzene. Preferential solvation of water was not indicated for the carbon tetrachloride-cyclohexane mixtures.     

The salting coefficient and size of alkylamines in saline media at different temperatures: estimation from Pitzer equations and the mean spherical approximation

The renewed theoretical interest in the proton transfer associated to the amino group together with the scarcity of acid-base studies of amines in moderate to concentrated saline media focussed our attention on the study of the basicities of some alkylamines, namely monomethyl, dimethyl and trimethylamine, in aqueous saline solutions of KCl at various temperatures.

A non-conventional analysis of stoichiometric equilibrium constants versus ionic strength data is carried out. On one hand, Pitzer’s model is easily applied to calculate the salting coefficient and the thermodynamic equilibrium constant of the alkylamines. On the other hand, the mean spherical approximation has the advantage over the Debye–Hückel based theories that it can account for effects produced by species of different sizes. Here, it is applied to predict the dependence of the salting behavior on the size of the alkylamines.     

Equation of state for aqueous electrolyte systems based on the semirestricted non-primitive mean spherical approximation

The semirestricted non-primitive mean spherical approximation (npmsa) is used in combination with the PC-SAFT equation of state to model completely dissociating aqueous alkali halide systems. The salts are described using ion-specific parameters from tables and correlations. Upon analyzing aqueous electrolyte systems at infinite dilution of the salt it was concluded that for the arithmetic mean ion diameter of anion and cation, the semirestricted npmsa contribution gives no reliable results. Therefore, this parameter is adjusted in this work. The model was applied to aqueous alkali halide systems up to the solubility limit at T = 298.15 K. Mean ionic activity coefficients and osmotic coefficients were correlated with good results. The model was subsequently applied to temperatures up to T = 373.15 K and compared to liquid densities and to system pressures up to the solubility limit of the salts in water. The agreement between experimental data and the proposed equation of state is satisfactory for the liquid densities and excellent in case of the system pressures.     

Thermodynamic and spectroscopic study of the interaction of Cu(II), Ni(II), Zn(II) and Ca(II) ions with 2-amino-N-(2-oxo-2-(2-(pyridin-2-yl)ethyl amino)ethyl)acetamide,a pseudo-mimic of human serum albumin

The protonation equilibria of 2-amino-N-(2-oxo-2-(2-(pyridin-2-yl)ethyl amino)ethyl)acetamide ([H₂(556)–N]) and the complexation of this ligand with Cu(II) Ca(II), Zn(II) and Ni(II) have been studied by glass electrode potentiometry and UV–visible spectrophotometry. From pH ∼2.00–11.00, five models for Cu(II) with the following complexes; MLH, ML, MLH₋₁, MLH₋₂ and MLH₋₃ were generated and observed to describe the experimental data equally well as far as the statistical criteria were concerned. The MLH₋₂ complex predominates at physiological pH in all five models, while the MLH₋₁ complex species exists only at low concentration in two models. The coordination in the MLH₋₂ complex suggested the involvement of one amino, two deprotonated peptides and one pyridyl nitrogen atoms. Molecular mechanics (MM) calculations confirmed the MLH₋₂ complex as the most stable species. Speciation calculations, using a blood plasma model, predicted that the Cu(II)–[H₂(556)–N] complex is able to mobilize Cu(II). Octanol/water partition of CuLH₋₂ showed that 30% of the complex went into the octanol phase, hence promoting percutaneous absorption of copper. The complex is a poor mimic of native copper–zinc superoxide dismutase.