Charge calculations in molecular mechanics 6: the calculation of partial atomic charges in nucleic acid bases and the electrostatic contribution to DNA base pairing.

A previously described scheme for the direct calculation of the partial atomic charges in molecules (CHARGE2) is applied to the nucleic acid bases. It is shown that inclusion of the omega-technique for the calculation of HMO derived pi charges is of particular importance for these highly polar systems. The molecular dipole moments obtained for the resulting charges are in very good agreement with the observed values for a variety of substituted purine and pyrimidine bases. The partial atomic charges for cytosine, thymine, guanine and adenine (as the 1-methyl and 9-methyl forms) are given and compared with values calculated by a variety of molecular orbital and empirical schemes. All the schemes reproduce the same general trends, with the possible exception of those calculated by the Del Re method, though the charges given by Kollman are in general somewhat larger than the others. The electrostatic contribution to the Watson-Crick base pair interaction energies are calculated using these partial atomic charges. The electrostatic contributions obtained from the M.O. derived atomic charges are less than half the observed values, as are those obtained by the Gasteiger method. The electrostatic contributions calculated from the CHARGE2 atomic charges and those of Kollman are in reasonable agreement with the observed values. The influence of a distant-dependent dielectric constant is examined, but no clear pattern emerges.     

Comparative molecular field analysis of flavonoid inhibitors of the PIM-1 kinase

The PIM-1 protein, the product of the pim-1 oncogene, is a serine/threonine kinase. Dysregulation of the PIM-1 kinase has been implicated in the development of human malignancies including lymphomas, leukemias, and prostate cancer. Comparative molecular field analysis (CoMFA) is a 3-D QSAR technique that has been widely used, with notable success, to correlate biological activity with the steric and electrostatic properties of ligands. We have used a set of 15 flavonoid inhibitors of the PIM-1 kinase, aligned de novo by common substructure, to generate a CoMFA model for the purpose of elucidating the steric and electrostatic properties involved in flavonoid binding to the PIM-1 kinase. Partial least squares correlation between observed and predicted inhibitor potency (expressed as -logIC50), using a non-cross-validated partial least squares analysis, generated a non-cross-validated q2=0.805 for the training set (n=15) of flavonoids. The CoMFA generated steric map indicated that the PIM-1-binding site was sterically hindered, leading to more efficient binding of planar molecules over (R) or (S) compounds. The electrostatic map identified that positive charges near the flavonoid atom C8 and negative charges near C4' increased flavonoid binding. The CoMFA model accurately predicted the potency of a test set of flavonoids (n=6), generating a correlation between observed and predicted potency of q2=0.825. CoMFA models generated from additional alignment rules, which were guided by co-crystal structure ligand orientations, did not improve the correlative value of the model. Superimposing the PIM-1 kinase crystal structure onto the CoMFA contours validated the steric and electrostatic maps, elucidating the amino acid residues that potentially contribute to the CoMFA fields. Thus we have generated the first predictive model that may be used for the rational design of small-molecule inhibitors of the PIM-1 kinase.     

CoMFA and CoMSIA studies of angiotensin (AT1) receptor antagonists

Two 3D-QSAR methods--CoMFA and CoMSIA--were applied to a set of 38 angiotensin receptor (AT1) antagonists. The conformation and alignment of molecules were obtained by a novel method - consensus dynamics. The representation of biological activity, partial charge formalism, absolute orientation of the molecules in the grid, and grid spacing were also studied for their effect on the CoMFA models. The models were thoroughly validated through trials using scrambled activities and bootstrapping. The best CoMFA model had a cross-validated correlation coefficient ( q2) of 0.632, which improved with "region focusing" to 0.680. This model had a "predictive" r2 of 0.436 on a test series that was unique and with little representation in the training set. Although the "predictive" r2 of the best CoMSIA model, which included steric, electrostatic, and hydrogen bond acceptor fields was higher than that of the best CoMFA model, the other statistical parameters like q2, r2, F value, and s were unsatisfactory. The contour maps generated using the best CoMFA model were used to identify the structural features important for biological activity in these compounds.     

The 3D-QSAR study of antitumor arylsulfonylimidazolidinone derivatives by CoMFA and CoMSIA

Three-dimensional quantitative structure-activity relationship (3D-QSAR) studies for a series of arylsulfonylimidazolidinone derivatives having antitumor activity were conducted using comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA). The in vitro cytotoxicity against human lung carcinoma (A549) exhibited a strong correlation with steric and electrostatic factors of the molecules. Four different types of models have been built using CoMFA and CoMSIA method with AM1 charge or Gasteiger-Huckel charge. By comparison of the statistical results of these models, model I obtained by CoMFA study with AM1 showed the best predictability of the antitumor activities based on the cross-validated value (0.642), conventional r2 (0.981), standard error of estimate (0.106) and PRESS value (0.170).     

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.     

Automated calculation of docking of artemisinin to heme

We report automated molecular docking of artemisinin to heme. The effects of atomic charges, and ligand and heme structures on the docking results were investigated. Several charge schemes for both artemisinin and heme, artemisinin structures taken from various optimization methods and X-ray data, and five heme models, were employed for this purpose. The docking showed that artemisinin approaches heme by pointing O1 at the endoperoxide linkage toward the iron center, a mechanism that is controlled by steric hindrance. This result differs from that reported by Shukla et al. which suggested that heme binds with artemisinin at the O2 position. The docking results also depended on the structures of both artemisinin and heme. Moreover, the atomic charges of heme have a significant effect on the docking configurations.     

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.     

Discriminating D1 and D2 agonists with a hydrophobic similarity index

Currently, methods for calculating molecular similarity indices have been developed for comparing steric, charge density, and molecular electrostatic potential (MEP) properties. Much of the existing technology may, however, be applied to the quantitative comparison of molecular hydrophobicities. In this article we present an empirical hydrophobic similarity index. We utilize atomic hydrophobic parameters derived from a quantum mechanical semiempirical wavefunction. Hydrophobicity at points on a grid is computed with a recently introduced “molecular lipophilicity potential”. The overlap of pairs of molecules is calculated with the metric introduced by Carbó. This approach is applied to a case in which steric and electrostatic criteria have already been shown to be inadequate in rationalizing selectivity, namely, requirements for recognition at the dopamine D1 and D2 receptors. We demonstrate that, for a set of dopamine agonists, D1 ligands show higher similarity in this property than D2 analogs. This indicator of similarity is more successful at accounting for D1 selectivity than previous 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.     

Libraries of atomic multipole moments for precise modeling of electrostatic properties of amino acids

Summary Contemporary theoretical models used in describing electrostatic properties of amino acids in polypeptides rely usually on atomic point charges. Recently noted defects of such models in reproducing protein folding originate from the inadequate representation of the electrostatic term, in particular inability of atomic charges to account for local anisotropy of molecular charge distribution. Such defects could be corrected by multicenter multipole moments derived directly from any high quality quantum chemical wavefunctions. This is illustrated by comparison of monopole and multipole electrostatic interactions between some amino acids within glutathione S-transferase.High quality Point Charge Models (PCM) can be derived analytically from multipole moment databases. Preliminary results suggest that torsional potentials are controlled by electrostatic interactions of atomic multipoles.Examples illustrating various uses of multicenter multipole moment databases of protein building blocks in modeling various properties of amino acids and polypeptides have been described, including calculation of molecular electrostatic potentials, electric fields, interactions between amino acid residues, estimates of pK_a shifts and changes in catalytic activity induced by amino acid substitutions in mutated enzymes.     

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.     

Three-dimensional quantitative structure–farnesyltransferase inhibition analysis for some diaminobenzophenones

A 3D-QSAR investigation of 95 diaminobenzophenone yeast farnesyltransferase (FT) inhibitors selected from the work of Schlitzer et al. showed that steric, electrostatic, and hydrophobic properties play key roles in the bioactivity of the series. A CoMFA/CoMSIA combined model using the steric and electrostatic fields of CoMFA together with the hydrophobic field of CoMSIA showed significant improvement in prediction compared with the CoMFA steric and electrostatic fields model. The similarity of the 3D-QSAR field maps for yeast FT inhibition activity (from this work) and for antimalarial activity data (from previous work) and the correlation between those activities are discussed.     

Thermodynamics calculation of protein–ligand interactions by QM/MM polarizable charge parameters

The calculation of protein–ligand binding free energy (ΔG) is of great importance for virtual screening and drug design. Molecular dynamics (MD) simulation has been an attractive tool to investigate this scientific problem. However, the reliability of such approach is affected by many factors including electrostatic interaction calculation. Here, we present a practical protocol using quantum mechanics/molecular mechanics (QM/MM) calculations to generate polarizable QM protein charge (QMPC). The calculated QMPC of some atoms in binding pockets was obviously different from that calculated by AMBER ff03, which might significantly affect the calculated ΔG. To evaluate the effect, the MD simulations and MM/GBSA calculation with QMPC for 10 protein–ligand complexes, and the simulation results were then compared to those with the AMBER ff03 force field and experimental results. The correlation coefficient between the calculated ΔΔG using MM/GBSA under QMPC and the experimental data is .92, while that with AMBER ff03 force field is .47 for the complexes formed by streptavidin or its mutants and biotin. Moreover, the calculated ΔΔG with QMPC for the complexes formed by ERβ and five ligands is positively related to experimental result with correlation coefficient of .61, while that with AMBER ff03 charge is negatively related to experimental data with correlation coefficient of .42. The detailed analysis shows that the electrostatic polarization introduced by QMPC affects the electrostatic contribution to the binding affinity and thus, leads to better correlation with experimental data. Therefore, this approach should be useful to virtual screening and drug design.     

Theoretical Studies of the Electrostatic Effect on Carbocations Adsorbed over Zeolitic Sites

Theoretical studies, at MNDO level, of carbocations adsorbed over a zeolite active site were carried out, taking into account the effect of electrostatic fields. Clusters 1 and 2 were placed between two electrostatic charges of opposite sign. The distance from each charge to the center of the oxygen atom bearing the proton or alkyl group was varied in order to find the minimum in energy. The ionicity, expressed by the decrease in bond order, slightly increased with the inclusion of the charges. A more pronounced effect was observed for a positive charge of +2. The energy of the system decreased with the introduction of electrostatic charges. This fact may be partly explained by the electrostatic interaction between the opposed charges and also to an observed increase in the Si–-O–-Al bond angle, decreasing the steric repulsions between the substituents and the acid site. The bond orders remained high, indicating a predominant covalent character for the adsorption of the carbocations. The calculations are in agreement with experimental data of exchange of polyvalent cations, which pointed to an increase in the acid strength of the zeolite, due to decrease in the electron density in the aluminum atom. This revised version was published online in June 2006 with corrections to the Cover Date.     

Advanced models based on the integral equation theory of molecular liquids for calculating the hydration of ions

An advanced model based on the integral equation theory of molecular liquids has been developed. The model is a modification of the RISM/HNC method in which the solvent electrostatic potential is approximated by a linear dependence on the solute charge, while the solvent response of the solute is calculated by introducing the empirical repulsive bridge function accounting steric constrains. The hydration energies for a series of atomic and molecular ions have been calculated. The results of the calculations deviate only by a few percent from the experimental data.     

3D QSAR CoMFA/CoMSIA, molecular docking and molecular dynamics studies of fullerene-based HIV-1 PR inhibitors

For the first time, a set of experimentally reported [60] fullerene derivatives were subjected to the 3D-QSAR/CoMFA and CoMSIA studies. The aim of this study is to propose a series of novel [60] fullerene-based inhibitors with optimal binding affinity for the HIV-1 PR enzyme. The position of the template molecule at the cavity of HIV-1 PR was optimized and 3D QSAR models were developed. Relative contributions of steric/electrostatic fields of the 3D-QSAR/CoMFA and CoMSIA models have shown that steric effects govern the bioactivity of the compounds, but electrostatic interactions play also an important role.The de novo drug design Leapfrog simulations provided a series of novel compounds with predicted improved inhibition effect.     

Molecular dynamics and QM/MM-based 3D interaction analyses of cyclin-E inhibitors

Abnormal expression of cyclin-dependent kinase 2 (CDK2)/cyclin-E is detected in colorectal, ovarian, breast and prostate cancers. The study of CDK2 with a bound inhibitor revealed CDK2 as a potential therapeutic target for several proliferative diseases. Several highly selective inhibitors of CDK2 are currently undergoing clinical trials, but possibilities remain for the identification and development of novel and improved inhibitors. For example, in silico targeting of ATP-competitive inhibitors of CDKs is of special interest. A series of 3,5-diaminoindazoles was studied using molecular docking and comparative field analyses. We used post-docking short time molecular dynamics (MD) simulation to account for receptor flexibility. The three types of structures, i.e., the highest energy, lowest energy and the structure most resembling the X-ray structure (three complexes) were identified for all ligands. QM/MM energy calculations were performed using a DFT b3lyp/6–31 g* and MM OPLS-2005 force field. Conceptual DFT properties such as the interaction energy of ligand to protein, global hardness (η), HOMO density, electrostatic potential, and electron density were calculated and related to inhibitory activity. CoMFA and CoMSIA were used to account for steric and electrostatic interactions. The results of this study provide insight into the bioactive conformation, interactions involved, and the effect of different drug fragments over different biological activities.     

Importance of polarization effect in the study of metalloproteins: Application of polarized protein specific charge scheme in predicting the reduction potential of azurin

Molecular dynamics (MD) simulation is commonly used in the study of protein dynamics, and in recent years, the extension of MD simulation to the study of metalloproteins is gaining much interest. Choice of force field is crucial in MD studies, and the inclusion of metal centers complicates the process of accurately describing the electrostatic environment that surrounds the redox centre. Herein, we would like to explore the importance of including electrostatic contribution from both protein and solvent in the study of metalloproteins. MD simulations with the implementation of thermodynamic integration will be conducted to model the reduction process of azurin from Pseudomonas aeruginosa. Three charge schemes will be used to derive the partial charges of azurin. These charge schemes differ in terms of the amount of immediate environment, respective to copper, considered during charge fitting, which ranges from the inclusion of copper and residues in the first coordination sphere during density functional theory charge fitting to the comprehensive inclusion of protein and solvent effect surrounding the metal centre using polarized protein‐specific charge scheme. From the simulations conducted, the relative reduction potential of the mutated azurins respective to that of wild‐type azurin (ΔE_cal) were calculated and compared with experimental values. The ΔE_cal approached experimental value with increasing consideration of environmental effect hence substantiating the importance of polarization effect in the study of metalloproteins. This study also attests the practicality of polarized protein‐specific charge as a computational tool capable of incorporating both protein environment and solvent effect into MD simulations. Proteins 2014; 82:2209–2219. © 2014 Wiley Periodicals, Inc.