Comparative assessment of computational methods for the determination of solvation free energies in alcohol‐based molecules

The determination of differences in solvation free energies between related drug molecules remains an important challenge in computational drug optimization, when fast and accurate calculation of differences in binding free energy are required. In this study, we have evaluated the performance of five commonly used polarized continuum model (PCM) methodologies in the determination of solvation free energies for 53 typical alcohol and alkane small molecules. In addition, the performance of these PCM methods, of a thermodynamic integration (TI) protocol and of the Poisson–Boltzmann (PB) and generalized Born (GB) methods, were tested in the determination of solvation free energies changes for 28 common alkane‐alcohol transformations, by the substitution of an hydrogen atom for a hydroxyl substituent. The results show that the solvation model D (SMD) performs better among the PCM‐based approaches in estimating solvation free energies for alcohol molecules, and solvation free energy changes for alkane‐alcohol transformations, with an average error below 1 kcal/mol for both quantities. However, for the determination of solvation free energy changes on alkane‐alcohol transformation, PB and TI yielded better results. TI was particularly accurate in the treatment of hydroxyl groups additions to aromatic rings (0.53 kcal/mol), a common transformation when optimizing drug‐binding in computer‐aided drug design. © 2013 Wiley Periodicals, Inc.     

On the use of electrostatic potential derived charges in molecular mechanics force fields. The relative solvation free energy of cis- and trans-N-methyl-acetamide

We have carried out free energy perturbation calculations on the relative solvation free energy of cis- and trans-N-methyl-acetamide (NMA). Experimentally, the solvation free energy difference has been found to be near zero. Using 6-31G* ab initio electrostatic potential derived charges for both the cis and trans conformations, we calculate a solvation free energy difference of 0.1 ± 0.1 kcal/mol. Using the 6-31G* charges derived for the trans conformation for both the cis and trans models leads to a solvation free energy difference of 0.9 ± 0.1 kcal/mol, compared to the value of 2.2 kcal/mol determined for the OPLS model for trans-NMA.     

Protein environment facilitates O2 binding in non-heme iron enzyme. An insight from ONIOM calculations on isopenicillin N synthase (IPNS)

Binding of dioxygen to a non-heme enzyme has been modeled using the ONIOM combined quantum mechanical/molecular mechanical (QM/MM) method. For the present system, isopenicillin N synthase (IPNS), binding of dioxygen is stabilized by 8-10 kcal/mol for a QM:MM (B3LYP:Amber) protein model compared to a quantum mechanical model of the active site only. In the protein system, the free energy change of O2 binding is close to zero. Two major factors consistently stabilize O2 binding. The first effect, evaluated at the QM level, originates from a change in coordination geometry of the iron center. The active-site model artificially favors the deoxy state (O2 not bound) because it allows too-large rearrangements of the five-coordinate iron site. This error is corrected when the protein is included. The corresponding effect on binding energies is 3-6 kcal/mol, depending on the coordination mode of O2 (side-on or end-on). The second major factor that stabilizes O2 binding is van der Waals interactions between dioxygen and the surrounding enzyme. These interactions, 3-4 kcal/mol at the MM level, are neglected in models that include only the active site. Polarization of the active site by surrounding amino acids does not have a significant effect on the binding energy in the present system.     

Mechanism of OMP decarboxylation in orotidine 5'-monophosphate decarboxylase

Despite extensive experimental and theoretical studies, the detailed catalytic mechanism of orotidine 5'-monophosphate decarboxylase (ODCase) remains controversial. In particular simulation studies using high level quantum mechanics have failed to reproduce experimental activation free energy. One common feature of many previous simulations is that there is a water molecule in the vicinity of the leaving CO2 group whose presence was only observed in the inhibitor bound complex of ODCase/BMP. Various roles have even been proposed for this water molecule from the perspective of stabilizing the transition state and/or intermediate state. We hypothesize that this water molecule is not present in the active ODCase/OMP complex. Based on QM/MM minimum free energy path simulations with accurate density functional methods, we show here that in the absence of this water molecule the enzyme functions through a simple direct decarboxylation mechanism. Analysis of the interactions in the active site indicates multiple factors contributing to the catalysis, including the fine-tuned electrostatic environment of the active site and multiple hydrogen-bonding interactions. To understand better the interactions between the enzyme and the inhibitor BMP molecule, simulations were also carried out to determine the binding free energy of this special water molecule in the ODCase/BMP complex. The results indicate that the water molecule in the active site plays a significant role in the binding of BMP by contributing approximately -3 kcal/mol to the binding free energy of the complex. Therefore, the complex of BMP plus a water molecule, instead of the BMP molecule alone, better represents the tight binding transition state analogue of ODCase. Our simulation results support the direct decarboxylation mechanism and highlight the importance of proper recognition of protein bound water molecules in the protein-ligand binding and the enzyme catalysis.     

Accurate pK(a) calculations for carboxylic acids using complete basis set and Gaussian-n models combined with CPCM continuum solvation methods

Complete Basis Set and Gaussian-n methods were combined with CPCM continuum solvation methods to calculate pK(a) values for six carboxylic acids. An experimental value of -264.61 kcal/mol for the free energy of solvation of H(+), DeltaG(s)(H(+)), was combined with a value for G(gas)(H(+)) of -6.28 kcal/mol to calculate pK(a) values with Cycle 1. The Complete Basis Set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. The use of Cycle 1 and the Complete Basis Set models combined with the CPCM solvation methods yielded pK(a) values accurate to less than half a pK(a) unit.     

Experimentation with different thermodynamic cycles used for pKa calculations on carboxylic acids using complete basis set and Gaussian‐n models combined with CPCM continuum solvation methods

Complete basis set and Gaussian‐n methods were combined with Barone and Cossi's implementation of the polarizable conductor model (CPCM) continuum solvation methods to calculate pK_a values for six carboxylic acids. Four different thermodynamic cycles were considered in this work. An experimental value of ?264.61 kcal/mol for the free energy of solvation of H⁺, ΔG_s(H⁺), was combined with a value for G_gas(H⁺) of ?6.28 kcal/mol, to calculate pK_a values with cycle 1. The complete basis set gas‐phase methods used to calculate gas‐phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed‐phase free energies are slightly less accurate than the gas‐phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. Thermodynamic cycles that include an explicit water in the cycle are not accurate when the free energy of solvation of a water molecule is used, but appear to become accurate when the experimental free energy of vaporization of water is used. This apparent improvement is an artifact of the standard state used in the calculation. Geometry relaxation in solution does not improve the results when using these later cycles. The use of cycle 1 and the complete basis set models combined with the CPCM solvation methods yielded pK_a values accurate to less than half a pK_a unit. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

A novel quantum mechanical/molecular mechanical approach to the free energy calculation for isomerization of glycine in aqueous solution

The free energy change associated with the isomerization reaction of glycine in water solution has been studied by a hybrid quantum mechanical/molecular mechanical (QM/MM) approach combined with the theory of energy representation (QM/MM-ER) recently developed. The solvation free energies for both neutral and zwitterionic form of glycine have been determined by means of the QM/MM-ER simulation. The contributions of the electronic polarization and the fluctuation of the QM solute to the solvation free energy have been investigated. It has been found that the contribution of the density fluctuation of the zwitterionic solute is estimated as -4.2 kcal/mol in the total solvation free energy of -46.1 kcal/mol, while that of the neutral form is computed as -3.0 kcal/mol in the solvation free energy of -15.6 kcal/mol. The resultant free energy change associated with the isomerization of glycine in water has been obtained as -7.8 kcal/mol, in excellent agreement with the experimental data of -7.3 or -7.7 kcal/mol, implying the accuracy of the QM/MM-ER approach. The results have also been compared with those computed by other methodologies such as the polarizable continuum model and the classical molecular simulation. The efficiency and advantage of the QM/MM-ER method has been discussed.     

Reversed stereochemical preference in binding of Ro 31-8959 to HIV-1 proteinase: A free energy perturbation analysis

Ro 31-8959 is a highly potent inhibitor of HIV-1 proteinase in phase III clinical trials for treatment of AIDS. It is also the first subnanomolar inhibitor that demonstrated reversed stereochemical preference at the central hydroxyl group. Free energy perturbation calculations have been carried out to rationalize the preference for the R-diastereomer by consideration of two models of the (weaker) S-diastereomer. In the first model, the central hydroxyl group makes only one hydrogen bond with the active site aspartates, whereas the hydroxyl group in the second model makes at least three strong hydrogen bonds. Using the first model, the free energy difference in binding of Ro 31-8959 and its S-diastereomer is calculated to be 3.4 kcal/mol, which is in close agreement with the experimental value. Although the second model has a more favorable interaction with the active site aspartates compared to the first model, it has a higher energy N-axial conformation at the decahydroisoquinoline group in P. We show here that the two contributions cancel each other and the two models of S-diastereomer are predicted to have equivalent binding. The stereochemical preference in a hydroxyethylamine series of inhibitors appears to be affected by both intermolecular and intramolecular (conformational) energies. The binding data on the proline containing inhibitors are rationalized based on these results. © 1994 by John Wiley & Sons, Inc.     

Prediction of the potency of inhibitors of adenosine deaminase by QM/MM calculations

QM/MM calculations show that the potency of a range of inhibitors of adenosine deaminase correlates with the relative stability of the reaction intermediate at the active site, rather than with the inhibitor binding energy.     

Inhibitory activity of hibifolin on adenosine deaminase- experimental and molecular modeling study

Adenosine deaminase (ADA) is an enzyme involved in purine metabolism. ADA converts adenosine to inosine and liberates ammonia. Because of their critical role in the differentiation and maturation of cells, the regulation of ADA activity is considered as a potential therapeutic approach to prevent malignant and inflammatory disorders. In the present study, the inhibitory activity of a plant flavonoid, hibifolin on ADA is investigated using enzyme kinetic assay and isothermal titration calorimetry. The inhibitory constant of hibifolin was found to be 49.92 μM ± 3.98 and the mode of binding was reversible. Isothermal titration calorimetry showed that the compound binds ADA with binding energy of −7.21 Kcal/mol. The in silico modeling and docking studies showed that the bound ligand is stabilized by hydrogen bonds with active site residues of the enzyme. The study reveals that hibifolin can act as a potential inhibitor of ADA.     

Does a diol cyclic urea inhibitor of HIV-1 protease bind tighter than its corresponding alcohol form? A study by free energy perturbation and continuum electrostatics calculations

The cyclic urea inhibitors of HIV-1 protease generally have two hydroxyl groups on the seven-membered ring. In this study, free energy perturbation and continuum electrostatic calculations were used to study the contributions of the two hydroxyl groups to the binding affinity and solubility of a cyclic urea inhibitor DMP323. The results indicated that the inhibitor with one hydroxyl group has better binding affinity and solubility than the inhibitor with two hydroxyl groups. Therefore, removal of one hydroxyl group from DMP323 may help to improve the properties of DMP323. This is also likely to be true for other cyclic urea inhibitors. The study also illustrated the difficulty in accurate modeling of the binding affinities of HIV-1 protease inhibitors, which involves many possible protonation states of the two catalytic aspartic acids in the active site of the enzyme.     

Continuum solvation models in the linear interaction energy method

The linear interaction energy (LIE) method in combination with two different continuum solvent models has been applied to calculate protein-ligand binding free energies for a set of inhibitors against the malarial aspartic protease plasmepsin II. Ligand-water interaction energies are calculated from both Poisson-Boltzmann (PB) and Generalized Born (GB) continuum models using snapshots from explicit solvent simulations of the ligand and protein-ligand complex. These are compared to explicit solvent calculations, and we find close agreement between the explicit water and PB solvation models. The GB model overestimates the change in solvation energy, and this is caused by consistent underestimation of the effective Born radii in the protein-ligand complex. The explicit solvent LIE calculations and LIE-PB, with our standard parametrization, reproduce absolute experimental binding free energies with an average unsigned error of 0.5 and 0.7 kcal/mol, respectively. The LIE-GB method, however, requires a constant offset to approach the same level of accuracy.     

A molecular docking study of potential inhibitors and repurposed drugs against SARS-CoV-2 main protease enzyme

COVID-19 has affected millions of people. Although many drugs are in use to combat disease, there is not any sufficient treatment yet. Having critical role in propagation of the novel coronavirus (SARS-CoV-2) works Main Protease up into a significant drug target. We have performed a molecular docking study to define possible inhibitor candidates against SARS-CoV-2 Main Protease enzyme. Besides docking Remdesivir, Ribavirin, Chloroquine and 28 other antiviral inhibitors (totally 31 inhibitors) to Main Protease enzyme, we have also performed a molecular docking study of 2177 ligands, which are used against Main Protease for the first time by using molecular docking program Autodock4. All ligands were successfully docked into Main Protease enzyme binding site. Among all ligands, EY16 coded ligand which previously used as EBNA1-DNA binding blocker candidate showed the best score for Main Protease with a binding free energy of −10.83 ​kcal/mol which was also lower than re-docking score of N3 ligand (−10.72 ​kcal/mol) contained in crystal structure of Main Protease. After analyzing the docking modes and docking scores we have found that our ligands have better binding free energy values than the inhibitors in use of treatment. We believe that further studies such as molecular dynamics or Molecular Mechanic Poisson Boltzmann Surface Area studies can make contribution that is more exhaustive to the docking results.     

Solvated interaction energy (SIE) for scoring protein-ligand binding affinities. 1. Exploring the parameter space

We present a binding free energy function that consists of force field terms supplemented by solvation terms. We used this function to calibrate the solvation model along with the binding interaction terms in a self-consistent manner. The motivation for this approach was that the solute dielectric-constant dependence of calculated hydration gas-to-water transfer free energies is markedly different from that of binding free energies (J. Comput. Chem. 2003, 24, 954). Hence, we sought to calibrate directly the solvation terms in the context of a binding calculation. The five parameters of the model were systematically scanned to best reproduce the absolute binding free energies for a set of 99 protein-ligand complexes. We obtained a mean unsigned error of 1.29 kcal/mol for the predicted absolute binding affinity in a parameter space that was fairly shallow near the optimum. The lowest errors were obtained with solute dielectric values of Din = 20 or higher and scaling of the intermolecular van der Waals interaction energy by factors ranging from 0.03 to 0.15. The high apparent Din and strong van der Waals scaling may reflect the anticorrelation of the change in solvated potential energy and configurational entropy, that is, enthalpy-entropy compensation in ligand binding (Biophys. J. 2004, 87, 3035-3049). Five variations of preparing the protein-ligand data set were explored in order to examine the effect of energy refinement and the presence of bound water on the calculated results. We find that retaining water in the final protein structure used for calculating the binding free energy is not necessary to obtain good results; that is the continuum solvation model is sufficient. Virtual screening enrichment studies on estrogen receptor and thymidine kinase showed a good ability of the binding free energy function to recover true hits in a collection of decoys.     

Role of solvation in the reduction of the uranyl dication by water: a density functional study

We have studied the solvation of uranyl, UO(2)(2+), and the reduced species UO(OH)(2+) and U(OH)(2)(2+) systematically using three levels of approximation: direct application of a continuum model (M1); explicit quantum-chemical treatment of the first hydration sphere (M2); a combined quantum-chemical/continuum model approach (M3). We have optimized complexes with varying numbers of aquo ligands (n = 4-6) and compared their free energies of solvation. Models M1 and M2 have been found to recover the solvation energy only partially, underestimating it by approximately 100 kcal/mol or more. With our best model M3, the calculated hydration free energy Delta(h)G degrees of UO(2)(2+) is about -420 kcal/mol, which shifts to about -370 kcal/mol when corrected for the expected error of the model. This value agrees well with the experimentally determined interval, -437 kcal/mol < Delta(h)G degrees < -318 kcal/mol. Complexes with 5 and 6 aquo ligands have been found to be about equally favored with models M2 and M3. The same solvation models have been applied to a two-step reduction of UO(2)(2+) by water, previously theoretically studied in the gas phase. Our results show that the solvation contribution to the reaction free energy, about 60 kcal/mol, dominates the endoergicity of the reduction.     

Calculation of solvation free energy from quantum mechanical charge density and continuum dielectric theory

We have combined ultrasoft pseudopotential density functional theory utilizing plane wave basis with a Poisson-Boltzmann/solvent-accessible surface area (PB/SA) model to calculate the solvation free energy of small neutral organic compounds in water. The solute charge density obtained from density functional theory was directly used in solving the Poisson-Boltzmann equation to obtain the reaction field. The polarized electronic wave function of the solute in the solvent was solved by including the reaction field in the density functional Hamiltonian. The quantum mechanical and Poisson-Boltzmann equations were solved self-consistently until the charge density and reaction field converged. Using the solute charge density directly instead of a point-charge representation permitted asymmetric distortion and spreading out of the electron cloud. Because the electron density could leave the van der Waals surface to penetrate into the high-dielectric solvent, the reaction field generated by this density was generally smaller than that obtained by using the point-charge representation. In applying this model to calculate the solvation free energy of 31 small neutral organic molecules spanning a range of 25 kcal/mol, we obtained a root-mean-square error of only 1.3 kcal/mol if we allowed one adjustable parameter to shift the calculated solvation free energy.     

Combining the polarizable Drude force field with a continuum electrostatic Poisson–Boltzmann implicit solvation model

In this work, we have combined the polarizable force field based on the classical Drude oscillator with a continuum Poisson–Boltzmann/solvent‐accessible surface area (PB/SASA) model. In practice, the positions of the Drude particles experiencing the solvent reaction field arising from the fixed charges and induced polarization of the solute must be optimized in a self‐consistent manner. Here, we parameterized the model to reproduce experimental solvation free energies of a set of small molecules. The model reproduces well‐experimental solvation free energies of 70 molecules, yielding a root mean square difference of 0.8 kcal/mol versus 2.5 kcal/mol for the CHARMM36 additive force field. The polarization work associated with the solute transfer from the gas‐phase to the polar solvent, a term neglected in the framework of additive force fields, was found to make a large contribution to the total solvation free energy, comparable to the polar solute–solvent solvation contribution. The Drude PB/SASA also reproduces well the electronic polarization from the explicit solvent simulations of a small protein, BPTI. Model validation was based on comparisons with the experimental relative binding free energies of 371 single alanine mutations. With the Drude PB/SASA model the root mean square deviation between the predicted and experimental relative binding free energies is 3.35 kcal/mol, lower than 5.11 kcal/mol computed with the CHARMM36 additive force field. Overall, the results indicate that the main limitation of the Drude PB/SASA model is the inability of the SASA term to accurately capture non‐polar solvation effects. © 2018 Wiley Periodicals, Inc.     

Homology modeling and molecular dynamic simulation of UDP-N-acetylmuramoyl-l-alanine-d-glutamate ligase (MurD) from Mycobacterium tuberculosis H37Rv using in silico approach

The present study aimed to identify the prospective inhibitors of MurD, a cytoplasmic enzyme that catalyzes the addition of d-glutamate to the UDP-N-acetylmuramoyl-l-alanine nucleotide precursor in Mycobacterium tuberculosis (MTB), using virtual screening, docking studies, pharmacokinetic analysis, Molecular Dynamic (MD) simulation, and Molecular Mechanics Generalized Born and Surface Area (MM-GBSA) analyses. The three dimensional (3D) structure was determined based on the homology technique using a template from Streptococcus agalactiae. The modeled structure had three binding sites, namely; substrate binding site (Val18, Thr19, Asp39, Asp40, Gly75, Asn147, Gln171 and His192), the ATP binding site (Gly123, Lys124, Thr125, Thr126, Glu166, Asp283, and Arg314) and the glutamic acid binding site (Arg382, Ser463, and Tyr470). These residues mentioned above play a critical role in the catalytic activity of the enzyme, and their inhibition could serve as a stumbling block to the normal function of the enzyme. A total of 10,344 obtained from virtual screened of Zinc and PubChem databases. These compounds further screened for Lipinski rule of five, docking studies and pharmacokinetic analysis. Four compounds with good binding energies (ZINC11881196 = −10.33 kcal/mol, ZINC12247644 = −8.90 kcal/mol, ZINC14995379 =−8.42 kcal/mol, and PubChem6185 = −8.20 kcal/mol), better than the binding energies of the ATP (−2.31 kcal/mol) and the ligand with known IC₅₀, Aminothiazole (−7.11 kcal/mol) were selected for the MD simulation and MM-GBSA analyses. The result of the analyses showed that all the four ligands formed a stable complex and had the binding free energies better than the binding energy of ATP. Therefore, these ligands considered as suitable prospective inhibitors of the MurD after experimental validation.     

Role of structural water molecule in HIV protease-inhibitor complexes: a QM/MM study

Structural water molecule 301 found at the interface of HIV protease-inhibitor complexes function as a hydrogen bond (H-bond) donor to carbonyl groups of the inhibitor as well as H-bond acceptor to amide/amine groups of the flap region of the protease. In this study, six systems of HIV protease-inhibitor complexes were analyzed, which have the presence of this "conserved" structural water molecule using a two-layer QM/MM ONIOM method. The combination of QM/MM and QM method enabled the calculation of strain energies of the bound ligands as well as the determination of their binding energies in the ligand-water and ligand-water-protease complexes. Although the ligand experiences considerable strain in the protein bound structure, the H-bond interactions through the structural water overcomes this strain effect to give a net stability in the range of 16-24 kcal/mol. For instance, in 1HIV system, the strain energy of the ligand was 12.2 kcal/mol, whereas the binding energy associated with the structural water molecule was 20.8 kcal/mol. In most of the cases, the calculated binding energy of structural water molecule showed the same trend as that of the experimental binding free energy values. Further, the classical MD simulations carried out on 1HVL system with and without structural water 301 showed that this conserved water molecule enhances the H-bond dynamics occurring at the Asp-bound active site region of the protease-inhibitor system, and therefore it will have a direct influence on the mechanism of drug action.     

Periodic density functional theory study of methane activation over La(2)O(3): activity of O(2-), O(-), O(2)(2-), oxygen point defect,and Sr(2+)-doped surface sites

Results of gradient-corrected periodic density functional theory calculations are reported for hydrogen abstraction from methane at O(s)(2-), O(s)(-), O(2)(s)(2-) point defect, and Sr(2+)-doped surface sites on La(2)O(3)(001). The results show that the anionic O(s)(-) species is the most active surface oxygen site. The overall reaction energy to activate methane at an O(s)(-) site to form a surface hydroxyl group and gas-phase (*)CH(3) radical is 8.2 kcal/mol, with an activation barrier of 10.1 kcal/mol. The binding energy of hydrogen at an site O(s)(-) is -102 kcal/mol. An oxygen site with similar activity can be generated by doping strontium into the oxide by a direct Sr(2+)/La(3+) exchange at the surface. The O(-)-like nature of the surface site is reflected in a calculated hydrogen binding energy of -109.7 kcal/mol. Calculations indicate that surface peroxide (O(2(s))(2-)) sites can be generated by adsorption of O(2) at surface oxygen vacancies, as well as by dissociative adsorption of O(2) across the closed-shell oxide surface of La(2)O(3)(001). The overall reaction energy and apparent activation barrier for the latter pathway are calculated to be only 12.1 and 33.0 kcal/mol, respectively. Irrespective of the route to peroxide formation, the O(2)(s)(2-) intermediate is characterized by a bent orientation with respect to the surface and an O-O bond length of 1.47 A; both attributes are consistent with structural features characteristic of classical peroxides. We found surface peroxide sites to be slightly less favorable for H-abstraction from methane than the O(s)(-) species, with DeltaE(rxn)(CH(4)) = 39.3 kcal/mol, E(act) = 47.3 kcal/mol, and DeltaE(ads)(H) = -71.5 kcal/mol. A possible mechanism for oxidative coupling of methane over La(2)O(3)(001) involving surface peroxides as the active oxygen source is suggested.