On contribution of known atomic partial charges of protein backbone in electrostatic potential density maps

Partial charges of atoms in a molecule and electrostatic potential (ESP) density for that molecule are known to bear a strong correlation. In order to generate a set of point‐field force field parameters for molecular dynamics, Kollman and coworkers have extracted atomic partial charges for each of all 20 amino acids using restrained partial charge‐fitting procedures from theoretical ESP density obtained from condensed‐state quantum mechanics. The magnitude of atomic partial charges for neutral peptide backbone they have obtained is similar to that of partial atomic charges for ionized carboxylate side chain atoms. In this study, the effect of these known atomic partial charges on ESP is examined using computer simulations and compared with the experimental ESP density recently obtained for proteins using electron microscopy. It is found that the observed ESP density maps are most consistent with the simulations that include atomic partial charges of protein backbone. Therefore, atomic partial charges are integral part of atomic properties in protein molecules and should be included in model refinement.     

Application of a universal solvation model to nucleic acid bases: comparison of semiempirical molecular orbital theory, ab initio Hartree-Fock theory, and density functional theory

The free energies of solvation of six nucleic acid bases (adenine, cytosine, hypoxanthine, guanine, thymine, and uracil) in water and chloroform are calculated using CM2 class IV charges and SM5.42R atomic surface tensions. Using any of three approximations to the electronic wave function (AM1, Hartree-Fock, or DFT), we obtain good agreement with experiment for five cases where the experimental results are known for the partition coefficients between the two solvents. Decomposition of the solvation effects into bulk electrostatic contributions and first-solvation-shell effects shows that the partitioning is dominated by the former, and this illustrates the importance of using accurate partial atomic charges for modeling these molecules in aqueous solution.     

The sensitivity of conformational free energies of the alanine dipeptide to atomic site charges

Different atomic point charge sets are obtained for the α_R and C_7.eq conformations of the alanine dipeptide by fitting the charges of each conformation to the respective ab initio electrostatic potential surfaces both individually and simultaneously, in both the united atom and the all-atom representations. Using these charge sets, the sensitivity of the relative conformational aqueous free energies to the atomic site charges is investigated. For this particular system, we find that the solute-water contributions to the conformational free energy differences have a rather weak dependence on site charges; the calculated intramolecular contributions, however, show a rather strong dependence on the atomic site charges. It is suggested that the calculated results for the alanine dipeptide using a single, simultaneously fit set of charges for both conformations are in better agreement with experiments than the calculations carried out with charges determined individually for each conformation. © 1997 John Wiley & Sons, Inc.     

Calculations of the charge distribution in dodecyltrimethylammonium: a quantum chemical investigation

In this work we report the atomic partial charges evaluated on dodecyltrimethylammonium ion. The values obtained from 17 quantum methods [CHELP, CHELPG, MK, NPA at (HF, LDA, PBE, B3LYP)//6-31G++(d,p) level and APT at B3LYP//6-31G++(d,p)] on the molecule optimised at B3LYP/6-31G++(d,p) level were compared to two semiempirical methods (Gasteiger and Qeq) and the commercial force field PCFF. All methods based on quantum calculation gave a positive charge delocalised on at least the first four alkyl groups of the tail. However, those deriving partial charges from the electrostatic potential gave an unrealistic set of alternative positive and negative alkyl group charges along the tail. In comparison, the NPA and APT methods lead to a steady decrease in the partial charges from the third alkyl group, and agreed closely with the representation of the electrostatic potential mapped onto the 0.002 au isodensity surface. The choice of the exchange correlation treatment does not drastically influence the atomic partial charges.     

Large variation in electrostatic contours upon addition of steric parameters and the effect of charge calculation schemes in CoMFA on mutagenicity of MX analogues

Partial atomic charge is a useful concept to describe physico-chemical properties of a molecule. For this, various schemes have been devised to get reasonable values. Mutagen X is an ideal set to test the effect of partial atomic charge variation. Therefore, we collected data from previous reports and studied various charge schemes. Our systematic study covers 26 charge calculation schemes along with a broad range of levels of theory. Charge calculation schemes include charges from charge equalisation, electrostatic potential fitting, molecular orbital and atomic polar tensor. Calculation levels span from empirical, semi-empirical, Hartree–Fock, density functional and Møller–Plesset 2. We also used two validation statistics for internal prediction. To observe the electrostatic effect accurately during comparative molecular field analysis (CoMFA) modelling, we first studied isolated electrostatic parameters to avoid interaction effect with steric parameters. The results clearly show that adding steric parameters does change statistical conclusions as well as CoMFA maps. Although there was a weak trend that quantum mechanical (QM)-derived charges gave better statistical values, it is not apparent statistically (alpha = 0.05). Particularly, Mülliken population analysis (MPA) did not produce better results. Therefore, when we excluded MPA schemes from QM calculation, the QM-derived charges were found to be significant, i.e. sophisticated charge schemes other than MPA with QM methods were found to be superior to simple empirical charge schemes. In addition, we demonstrated that in order to test charge schemes properly, excluding steric parameter is more important. This work exemplifies Occam's theorem of parsimony. A simpler model is a better model.     

Benchmark of different charges for prediction of the partitioning coefficient through the hydrophilic/lipophilic index

A few different theoretical methods for assigning the partial atomic charges were benchmarked for calculation of the hydrophilic/lipophilic index (HLI). The coefficients were selected to produce the best correlation of the HLI values with the experimental octanol-water partition. Different parameters were checked in calculations of partial charges to get the best performance of the HLI values obtained. Thus, four partitioning schemes (Coulson, Mulliken, Merz-Kollman, Ford-Wang) were benchmarked for calculations of atomic charges with six semiempirical methods (AM1, PM3, RM1, PM6, PM6-D3H4, PM7). Moreover, five distinct types of partial atomic charges (Mulliken, Hirshfeld, Löwdin, CHELPG, NPA), obtained at the Hartree–Fock and DFT levels of theory with three basis sets, were tested for their ability to produce the HLI values with the best correlation to experimental logP coefficients of 50 mono-charged organic anions. In the case of the semiempirical methods, the best correlation between the HLI and logP values (the correlation coefficient r?=?0.9216) was obtained with the AM1 Ford–Wang parametric electrostatic potential charges. The Mulliken and Coulson charges calculated with the PM7 method can be used as an alternative to AM1, with the r values of 0.9107 and 0.8984, respectively. In the case of the DFT, the PBE/def2-TZVP natural population analysis charges produce the best correlation (r?=?0.9220). Nevertheless, in spite of a marginally lower performance (r?=?0.9159), the NPA charges computed at the PBE/def2-SVP level are more robust and can be regarded as the optimum choice for calculating the HLI values.

Open image in new window

Graphical abstract The hydrophilic/lipophilic index (HLI)

     

A Detailed Study of VESPA Electrostatic Potential-Derived Atomic Charges

VESPA, an improved semiempirical method for the calculation of electrostatic potential-derived atomic charges has been tested. It is shown that this approach is even less dependent upon molecular orientation than "high density" CHELPG ab initio ESP-derived charges. The conformational dependence of VESPA charges has been investigated for rotation around the C-N bond in formamide and 11 different conformers of glycerolphosphorylcholine. The results obtained are also compared to the corresponding ab initio values. Finally, VESPA is used to calculate electrostatic potential-derived charges for bioorganic molecules. We discuss the abilities and the limitations of ESP charges in this area.     

Theoretical analysis of deoxycytidine-5'-phosphate protonation

The electron density distribution in deoxycytidine-5'-monophosphate (5'-dCMP) molecule and dianion has been studied by the method of CNDO/2. The comparison between the results of calculation for the neutral molecule and the data obtained by Pearlman and Kim shows that there is a linear correlation between the atomic charges calculated using quantum chemistry and those derived from X-ray results. However, partial charges for the deoxyribose fragment are correlated in a nonlinear manner. The influence of the protons added to the cytosine and phosphate residues on the atomic charges and bond orders of deoxy-cytidine-5'-monophosphate has been analyzed here. The conclusion has been drawn that the semiempirical quantum-chemical CNDO/2 technique is applicable to the mononucleotide studies.     

Hybridization-displaced charges for amino-acids: a new model using two point charges per atom along with bond-center charges

A new charge distribution is proposed for the amino acids where each atom is associated with two point charges while each bond center is associated with one point charge. Centroids of charges arising due to atomic orbital hybridization called hybridization-displaced charges (HDC) and those located at the atomic sites and bond centers obtained by a modified form of the Mulliken scheme were combined. The density matrix calculations required for this analysis were performed at the B3LYP/6-31G** level of density functional theory. The combination of HDC centroids with the modified Mulliken charges was found to yield dipole moments and surface molecular electrostatic potentials (MEP) of the amino acids in good agreement with those obtained by rigorous DFT calculations or those obtained using the MEP-fitted CHelpG charges. This study shows that the combination of HDC centroids with the modified Mulliken charges is significantly superior to the conventional Mulliken charges.     

Electrostatic Interactions in Aminoglycoside-RNA Complexes

Electrostatic interactions often play key roles in the recognition of small molecules by nucleic acids. An example is aminoglycoside antibiotics, which by binding to ribosomal RNA (rRNA) affect bacterial protein synthesis. These antibiotics remain one of the few valid treatments against hospital-acquired infections by Gram-negative bacteria. It is necessary to understand the amplitude of electrostatic interactions between aminoglycosides and their rRNA targets to introduce aminoglycoside modifications that would enhance their binding or to design new scaffolds. Here, we calculated the electrostatic energy of interactions and its per-ring contributions between aminoglycosides and their primary rRNA binding site. We applied either the methodology based on the exact potential multipole moment (EPMM) or classical molecular mechanics force field single-point partial charges with Coulomb formula. For EPMM, we first reconstructed the aspherical electron density of 12 aminoglycoside-RNA complexes from the atomic parameters deposited in the University at Buffalo Databank. The University at Buffalo Databank concept assumes transferability of electron density between atoms in chemically equivalent vicinities and allows reconstruction of the electron densities from experimental structural data. From the electron density, we then calculated the electrostatic energy of interaction using EPMM. Finally, we compared the two approaches. The calculated electrostatic interaction energies between various aminoglycosides and their binding sites correlate with experimentally obtained binding free energies. Based on the calculated energetic contributions of water molecules mediating the interactions between the antibiotic and rRNA, we suggest possible modifications that could enhance aminoglycoside binding affinity.     

Importance of substrate and cofactor polarization in the active site of dihydrofolate reductase

By using a combined quantum-mechanical and molecular-mechanical potential in molecular dynamics simulations, we have investigated the effects of the enzyme electric field of dihydrofolate reductase on the electronic polarization of its 5-protonated dihydrofolate substrate at various stages of the catalyzed hydride transfer reaction. Energy decomposition of the total electrostatic interaction energy between the ligands and the enzyme shows that the polarization effect is 4% of the total electrostatic interaction energy, and, significantly, it accounts for 9kcal/mol of transition state stabilization relative to the reactant state. Therefore it is essential to take account of substrate polarization for quantitative interpretation of enzymatic function and for calculation of binding free energies of inhibitors to a protein. Atomic polarizations are calculated as the differences in the average atomic charges on the atoms in gas phase and in molecular simulations of the enzyme; this analysis shows that the glutamate tail and the pterin ring are the highly polarized regions of the substrate. Electron density difference plots of the reactant and product complexes at instantaneous configurations in the enzyme active center confirm the inferences made on the basis of partial atomic charges.     

Implicit solvent models

Implicit solvent models for biomolecular simulations are reviewed and their underlying statistical mechanical basis is discussed. The fundamental quantity that implicit models seek to approximate is the solute potential of mean force, which determines the statistical weight of solute conformations, and which is obtained by averaging over the solvent degrees of freedom. It is possible to express the total free energy as the reversible work performed in two successive steps. First, the solute is inserted in the solvent with zero atomic partial charges; second, the atomic partial charges of the solute are switched from zero to their full values. Consequently, the total solvation free energy corresponds to a sum of non-polar and electrostatic contributions. These two contributions are often approximated by simple geometrical models (such as solvent exposed area models) and by macroscopic continuum electrostatics, respectively. One powerful route is to approximate the average solvent density distribution around the solute, i.e. the solute-solvent density correlation functions, as in statistical mechanical integral equations. Recent progress with semi-analytical approximations makes continuum electrostatics treatments very efficient. Still more efficient are fully empirical, knowledge-based models, whose relation to explicit solvent treatments is not fully resolved, however. Continuum models that treat both solute and solvent as dielectric continua are also discussed, and the relation between the solute fluctuations and its macroscopic dielectric constant(s) clarified.     

Effect of partial atomic charges on the calculated free energy of solvation of poly(vinyl alcohol) in selected solvents

It is well-known that properties of poly(vinyl alcohol) (PVA) in the pure and solution states depend largely on the hydrogen bonding networks formed. In the context of molecular simulation, such networks are handled through the Coulombic interactions. Therefore, a good set of partial atom charges (PACs) for simulations involving PVA is highly desirable. In this work, we calculated the PACs for PVA using a few commonly used population analysis schemes with a hope to identify an accurate set of PACs for PVA monomers. To evaluate the quality of the calculated parameters, we have benchmarked their predictions for free energy of solvation (FES) in selected solvents by molecular dynamics simulations against the ab initio calculated values. Selected solvents were water, ethanol and benzene as they covered a range of size and polarity. Also, PVA with different tacticities were used to capture their effect on the calculated FESs. Based on our results, neither PACs nor FESs are affected by the chain tacticity. While PACs predicted by the Merz-Singh-Kollman scheme were close to original values in the OPLS-AA force field in way that no significant difference in properties of pure PVA was observed, free energy of solvation calculated using such PACs showed greater agreement with ab initio calculated values than those calculated by OPLS-AA (and all other schemes used in this work) in all three solvents considered.     

A reinterpretation of the infrared linear dichroism of oriented nucleic acid films and a calculation of some effective partial changes on the ribose phosphate backbone.

In this paper we show, based on symmetry considerations, that structural information cannot be obtained from the linear infrared dichroism of the dioxy vibrations of the phosphate group of nucleic acids. Consequently, the discrepancies between the results of x-ray structure measurements and linear dichroism measurements are not meaningful. The linear dichroism measurements are instead important for a calculation of transition dipole moments that involve both the vibrations of all the atoms of the nucleotide and their charges. Independent information on either the atomic displacements contributing to a given vibration or the atomic charges permits a refinement of the unknown quantities. Based on the molecular dynamics calculations of Prohofsky et al., atomic charges of DNA are calculated to reproduce the observed linear dichroism results. Some of the resulting charges are unexpected and may reflect the inadequacy of the molecular dynamic calculation.     

A precise analytical method for calculating the electrostatic energy of macromolecules in aqueous solution

A new method for calculating the total electrostatic free energy of a macromolecule in solution is presented. It is applicable to molecules of arbitrary shape and size, including membranes or macromolecular assemblies with substrate molecules and ions. The method is derived from integrating the energy density of the electrostatic field and is termed the field energy method. It is based on the dielectric model, in which the solute and the surrounding water are regarded as different continuous dielectrics. The field energy method yields both the interaction energy between all charge pairs and the self energy of single charges, effectively accounting for the interaction with water. First, the dielectric boundary and mirror charges are determined for all charges of the solute. The energy is then given as a simple function of the interatomic distances, and the standard atomic partial charges and volumes. The interaction and self energy are shown to result from three-body and pairwise interactions. Both energy terms explicitly involve apolar atoms, revealing that apolar groups are also subject to electrostatic forces. We applied the field energy method to a spherical model protein. Comparison with the Kirkwood solution shows that errors are within a small percentage. As a further test, the field energy method was used to calculate the electrostatic potential of the protein superoxide dismutase. We obtained good agreement with the result from a program that implements the numerical finite difference algorithm. The field energy method provides a basis for energy minimization and dynamics programs that account for the solvent and screening effect of water at little computational expense.     

Calculation and measurement of the dipole moment of small proteins: Use of protein data base

The dipole moments of small protein molecules were determined experimentally in order to validate the calculated dipole moments by previous investigators. We found that the agreements are satisfactory for some proteins. There are, however, many proteins for which the agreement is less than satisfactory. In order to find the cause of the disagreement, the dipole moments of these proteins were recalculated using the Brookhaven Protein Data Bank. We calculated the dipole moment due to fixed surface charges and the bond moments of all the carbonyl groups in main chain and side chains. The calculation consists of the mean moments and their mean square fluctuations. In addition, we investigated the effect of electrostatic interactions between charged sites for several proteins. These results show that incorporation of the interactions does not affect substantially the calculated dipole moments. The rms fluctuation of the dipole moment is found to be small but not negligible. In conclusion, recalculated dipole moments are in good agreement with the observed values. © 1993 John Wiley & Sons, Inc.     

Calculation of weak protein-protein interactions: the pH dependence of the second virial coefficient

Interactions between proteins are often sufficiently weak that their study through the use of conventional structural techniques becomes problematic. Of the few techniques capable of providing experimental measures of weak protein-protein interactions, perhaps the most useful is the second virial coefficient, B(22), which quantifies a protein solution's deviations from ideal behavior. It has long been known that B(22) can in principle be computed, but only very recently has it been demonstrated that such calculations can be performed using protein models of true atomic detail (Biophys. J. 1998, 75:2469-2477). The work reported here extends these previous efforts in an attempt to develop a transferable energetic model capable of reproducing the experimental trends obtained for two different proteins over a range of pH and ionic strengths. We describe protein-protein interaction energies by a combination of three separate terms: (i) an electrostatic interaction term based on the use of effective charges, (ii) a term describing the electrostatic desolvation that occurs when charged groups are buried by an approaching protein partner, and (iii) a solvent-accessible surface area term that is used to describe contributions from van der Waals and hydrophobic interactions. The magnitude of the third term is governed by an adjustable, empirical parameter, gamma, that is altered to optimize agreement between calculated and experimental values of B(22). The model is applied separately to the proteins lysozyme and chymotrypsinogen, yielding optimal values of gamma that are almost identical. There are, however, clear difficulties in reproducing B(22) values at the extremes of pH. Explicit calculation of the protonation states of ionizable amino acids in the 200 most energetically favorable protein-protein structures suggest that these difficulties are due to a neglect of the protonation state changes that can accompany complexation. Proper reproduction of the pH dependence of B(22) will, therefore, almost certainly require that account be taken of these protonation state changes. Despite this problem, the fact that almost identical gamma values are obtained from two different proteins suggests that the basic energetic formulation used here, which can be evaluated very rapidly, might find use in dynamical simulations of weak protein-protein interactions at intermediate pH values.     

Calculation of atom-centered partial charges for heme

Atom-centered partial charges are calculated for the Fe-heme in cytochrome P450cam for use in molecular dynamics simulations of polar substrates bound in the active site of the enzyme. Charges are fit to the electrostatic potential produced by ab initio UHF wavefunctions for an Fe-porphine model. Basis set dependence of these charges is observed using the LANL1DZ, LANL2DZ and augmented 6–31G levels of theory. Upon geometry optimization of the enzyme, these charge sets cause varying degrees of distortion of the porphyrin from its crystallographically observed conformation. Scaling the charges calculated from the augmented 6–31G basis by 75% reduces the heme distortion while preserving reasonable interactions with a polar substrate. A comparison of the calculated charges with other published values is presented.     

An optimized potential function for the calculation of nucleic acid interaction energies I. Base stacking

An optimized potential function for base-stacking interaction is constructed. Stacking energies between the complementary pairs of a dimer are calculated as a function of the rotational angle and separation distance. Using several different sets of atomic charges, the electrostatic component in the monopole-monopole approximation (MMA) is compared to the more refined segmented multipole–multipole representation (SMMA); the general features of the stacking minima are found to be correctly reproduced with IEHT or CNDO atomic charges. The electrostatic component is observed to control the location of stacking minima. The MMA, in general, is not a reliable approximation of the SMMA in regions away from minima; however, the MMA is reliable in predicting the location and nature of stacking minima. The attractive part of the Lennard-Jones 6–12 potential is compared to and parameterized against the expression for the second-order interaction terms composed of multipole-bond polarizability for the polarization energy and transition-dipole bond polarizabilities for approximation of the dispersion energy. The repulsive part of the Lennard-Jones potential is compared to a Kitaygorodski-type repulsive function; changing the exponent from its usual value of 12 to 11.7 gives significantly better agreement with the more refined repulsive function. Stacking minima calculated with the optimized potential method are compared with various perturbation-type treatments. The optimized potential method yields results that compare as well with melting data as do any of the more recent and expensive perturbation methods.     

Incorporation of lone pairs into the electrostatic term in the empirical intra- and intermolecular energy calculations

The method hitherto used for estimating the electrostatic term in empirical intramolecular calculations of stable conformations of biologically important molecules and macromolecules and intermolecular calculations of molecular associations or packing energy in molecular crystals had been analyzed. It has been shown that the contribution of atomic hybridization moments is omitted in the calculation of electrostatic interactions from net atomic charges localized on nuclei which have been determined by standard quantum-chemical methods. This contribution plays an important part in determining electrostatic interactions, mainly in molecules containing atoms with lone pairs. Simultaneously, a modified method for calculating the electrostatic term comprising the interaction of the lone pairs, which are represented by atomic hybridization moments, has been proposed. The relationship between the atomic hybridization moment and the bond angle has been expressed for some typical configurations occurring in biologically important molecules. Finally, this new approach is illustrated by results of the conformational analysis of some model compounds for biomolecules and compared with the approach used so far for the estimation of the electrostatic interaction in empirical methods of calculation of the intra- and intermolecular energy.