Predicting relative binding affinities of non-peptide HIV protease inhibitors with free energy perturbation calculations

The relative binding free energies in HIV protease of haloperidol thioketal (THK) and three of its derivatives were examined with free energy calculations. THK is a weak inhibitor (IC50 = 15 M) for which two cocrystal structures with HIV type 1 proteases have been solved [Rutenber, E. et al., J. Biol. Chem., 268 (1993) 15343]. A THK derivative with a phenyl group on C2 of the piperidine ring was expected to be a poor inhibitor based on experiments with haloperidol ketal and its 2- phenyl derivative (Caldera, P., personal communication). Our calculations predict that a 5-phenyl THK derivative, suggested based on examination of the crystal structure, will bind significantly better than THK. Although there are large error bars as estimated from hysteresis, the calculations predict that the 5-phenyl substituent is clearly favored over the 2-phenyl derivative as well as the parent compound. The unfavorable free energies of solvation of both phenyl THK derivatives relative to the parent compound contributed to their predicted binding free energies. In a third simulation, the change in binding free energy for 5-benzyl THK relative to THK was calculated. Although this derivative has a lower free energy in the protein, its decreased free energy of solvation increases the predicted G(bind) to the same range as that of the 2-phenyl derivative.     

Improved precision and efficiency of free energy calculations for small systems using lambda-scaled atomic masses and separating conformational and transformational sampling

We present results showing the importance of appropriate treatment of atomic masses in molecular dynamics (MD)-based single topology free-energy perturbations (FEPs) on small molecule systems. The reversibility of gas phase simulations is significantly improved by scaling the atomic mass of mutated atoms with the lambda variable normally used for the scaling of energy terms. Because this effect is less pronounced for solvated systems, it will not cancel in estimates of the relative hydration free energy difference. The advantage of mass scaling is demonstrated by a null mutation of ethane to ethane and the calculation of the relative hydration free energy difference between ethane and n-propane. Furthermore, it is found that the simulation time necessary for converged MD/FEPs is prohibitively large for relative hydration free energy calculations on cyclic alkanes. Therefore, we explore an alternative free energy pathway including strongly constrained conformations to improve convergence in FEP simulations of flexible molecules.     

Computation of the binding affinities of catechol‐O‐methyltransferase inhibitors: Multisubstate relative free energy calculations

Alchemical free energy simulations are amongst the most accurate techniques for the computation of the free energy changes associated with noncovalent protein–ligand interactions. A procedure is presented to estimate the relative binding free energies of several ligands to the same protein target where multiple, low‐energy configurational substates might coexist, as opposed to one unique structure. The contributions of all individual substates were estimated, explicitly, with the free energy perturbation method, and combined in a rigorous fashion to compute the overall relative binding free energies and dissociation constants. It is shown that, unless the most stable bound forms are known a priori, inaccurate results may be obtained if the contributions of multiple substates are ignored. The method was applied to study the complex formed between human catechol‐O‐methyltransferase and BIA 9‐1067, a newly developed tight‐binding inhibitor that is currently under clinical evaluation for the therapy of Parkinson's disease. Our results reveal an exceptionally high‐binding affinity (K_d in subpicomolar range) and provide insightful clues on the interactions and mechanism of inhibition. The inhibitor is, itself, a slowly reacting substrate of the target enzyme and is released from the complex in the form of O‐methylated product. By comparing the experimental catalytic rate (k_cat) and the estimated dissociation rate (k_off) constants of the enzyme‐inhibitor complex, one can conclude that the observed inhibition potency (K_i) is primarily dependent on the catalytic rate constant of the inhibitor's O‐methylation, rather than the rate constant of dissociation of the complex. © 2012 Wiley Periodicals, Inc.     

Effect of sampling on BACE‐1 ligands binding free energy predictions via MM‐PBSA calculations

The BACE‐1 enzyme is a prime target to find a cure to Alzheimer's disease. In this article, we used the MM‐PBSA approach to compute the binding free energies of 46 reported ligands to this enzyme. After showing that the most probable protonation state of the catalytic dyad is mono‐protonated (on ASP32), we performed a thorough analysis of the parameters influencing the sampling of the conformational space (in total, more than 35 μs of simulations were performed). We show that ten simulations of 2 ns gives better results than one of 50 ns. We also investigated the influence of the protein force field, the water model, the periodic boundary conditions artifacts (box size), as well as the ionic strength. Amber03 with TIP3P, a minimal distance of 1.0 nm between the protein and the box edges and a ionic strength of I = 0.2 M provides the optimal correlation with experiments. Overall, when using these parameters, a Pearson correlation coefficient of R = 0.84 (R ² = 0.71) is obtained for the 46 ligands, spanning eight orders of magnitude of K _d (from 0.017 nm to 2000 μM, i.e., from −14.7 to −3.7 kcal/mol), with a ligand size from 22 to 136 atoms (from 138 to 937 g/mol). After a two‐parameter fit of the binding affinities for 12 of the ligands, an error of RMSD = 1.7 kcal/mol was obtained for the remaining ligands. © 2017 Wiley Periodicals, Inc.     

Modeling of novel CDK7 inhibitors activity by molecular dynamics and free energy perturbation methods

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Localization and quantification of hydrophobicity: The molecular free energy density (MolFESD) concept and its application to sweetness recognition

A method for the localization, the quantification, and the analysis of hydrophobicity of a molecule or a molecular fragment is presented. It is shown that the free energy of solvation for a molecule or the transfer free energy from one solvent to another can be represented by a surface integral of a scalar quantity, the molecular free energy surface density (MolFESD), over the solvent accessible surface of that molecule. This MolFESD concept is based on a model approach where the solvent molecules are considered to be small in comparison to the solute molecule, and the solvent can be represented by a continuous medium with a given dielectric constant. The transfer energy surface density for a 1-octanol/water system is empirically determined employing a set of atomic increment contributions and distance dependent membership functions measuring the contribution of the increments to the surface value of the MolFESD. The MolFESD concept can be well used for the quantification of the purely hydrophobic contribution to the binding constants of molecule-receptor complexes. This is demonstrated with the sweeteners sucrose and sucralose and various halogen derivatives. Therein the relative sweetness, which is assumed to be proportional to the binding constant, nicely correlates to the surface integral over the positive, hydrophobic part of the MolFESD, indicating that the sweetness receptor can be characterized by a highly flexible hydrophobic pocket instead of a localized binding site.     

Homology modeling,force field design,and free energy simulation studies to optimize the activities of histone deacetylase inhibitors

As an effort to develop therapeutics for cancer treatments, a number of effective histone deacetylase inhibitors with structural diversity have been discovered. To gain insight into optimizing the activity of an identified lead compound, a computational protocol sequentially involving homology modeling, docking experiments, molecular dynamics simulation, and free energy perturbation calculations was applied for rationalizing the relative activities of known histone deacetylase inhibitors. With the newly developed force field parameters for the coordination environment of the catalytic zinc ion in hand, the computational strategy proved to be successful in predicting the rank orders for 12 derivatives of three hydroxamate-based inhibitor scaffolds with indole amide, pyrrole, and sulfonamide moieties. The results showed that the free energy of an inhibitor in aqueous solution should be an important factor in determining the binding free energy. Hence, in order to enhance the inhibitory activity by adding or substituting a chemical group, the increased stabilization in solution due to the structural changes must be overcome by a stronger enzyme-inhibitor interaction. It was also found that to optimize inhibitor potency, the hydrophobic head of an inhibitor should be elongated or enlarged so that it can interact with Pro29 and His28 that are components of the flexible loop at the top of the active site.     

Ermod: Fast and versatile computation software for solvation free energy with approximate theory of solutions

ERmod is a software package to efficiently and approximately compute the solvation free energy using the method of energy representation. Molecular simulation is to be conducted at two condensed‐phase systems of the solution of interest and the reference solvent with test‐particle insertion of the solute. The subprogram ermod in ERmod then provides a set of energy distribution functions from the simulation trajectories, and another subprogram slvfe determines the solvation free energy from the distribution functions through an approximate functional. This article describes the design and implementation of ERmod, and illustrates its performance in solvent water for two organic solutes and two protein solutes. Actually, the free‐energy computation with ERmod is not restricted to the solvation in homogeneous medium such as fluid and polymer and can treat the binding into weakly ordered system with nano‐inhomogeneity such as micelle and lipid membrane. ERmod is available on web at http://sourceforge.net/projects/ermod . © 2014 Wiley Periodicals, Inc.     

Computation of affinity and selectivity: Binding of 2,4-diaminopteridine and 2,4-diaminoquinazoline inhibitors to dihydrofolate reductases

Binding energy calculations for complexes of mutant and wild-type human dihydrofolate reductases with 2,4-diaminopteridine and 2,4-diaminoquinazoline inhibitors are reported. Quantitative insight into binding energetics of these molecules is obtained from calculations based on force field energy evaluation and thermal sampling by molecular dynamics simulations. The calculated affinity of methotrexate for wild-type and mutant enzymes is reasonably well reproduced. Truncation of the methotrexate glutamate tail results in a loss of affinity by several orders of magnitude. No major difference in binding strength is predicted between the pteridines and the quinazolines, while the N-methyl group present in methotrexate appears to confer significantly stronger binding. The recent improvement, which is used here, of our linear interaction energy method for binding affinity prediction, as well as problems with treating charged and flexible ligands are discussed. This approach should be suitable in a drug discovery context for prediction of binding energies of new inhibitors prior to their synthesis, when some information about the binding mode is available.     

Peptide mimetics as enzyme inhibitors: Use of free energy perturbation calculations to evaluate isosteric replacement for amide bonds in a potent HIV protease inhibitor

Summary We present the application of free energy perturbation theory/molecular dynamics to predict the consequence of replacing each of the seven peptide bonds in the potent HIV protease inhibitor JG365: ACE (acetyl)-Ser-Leu-Asn-HEA (hydroxyethylamine analog of Phe-Pro)-Ile-Val-NME (N-methyl) by ethylene or fluoroethylene isosteres. Replacing two of these bonds may well lead to significantly tighter binding; replacing two others is predicted to significantly diminish the binding affinity. Also, for three of the peptide bonds fluoroethylene replacements could lead to increased binding of free energies of the inhibitors. Our results should be considered as predictive since there are, as yet, no experimental results on such peptide replacements as enzyme inhibitors.     

Minimum MD simulation length required to achieve reliable results in free energy perturbation calculations: Case study of relative binding free energies of fructose‐1,6‐bisphosphatase inhibitors

In an attempt to establish the criteria for the length of simulation to achieve the desired convergence of free energy calculations, two studies were carried out on chosen complexes of FBPase‐AMP mimics. Calculations were performed for varied length of simulations and for different starting configurations using both conventional‐ and QM/MM‐FEP methods. The results demonstrate that for small perturbations, 1248 ps simulation time could be regarded a reasonable yardstick to achieve convergence of the results. As the simulation time is extended, the errors associated with free energy calculations also gradually tapers off. Moreover, when starting the simulation from different initial configurations of the systems, the results are not changed significantly, when performed for 1248 ps. This study carried on FBPase‐AMP mimics corroborates well with our previous successful demonstration of requirement of simulation time for solvation studies, both by conventional and ab initio FEP. The establishment of aforementioned criteria of simulation length serves a useful benchmark in drug design efforts using FEP methodologies, to draw a meaningful and unequivocal conclusion. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

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).     

Using the local elevation method to construct optimized umbrella sampling potentials: Calculation of the relative free energies and interconversion barriers of glucopyranose ring conformers in water

A method is proposed to combine the local elevation (LE) conformational searching and the umbrella sampling (US) conformational sampling approaches into a single local elevation umbrella sampling (LEUS) scheme for (explicit‐solvent) molecular dynamics (MD) simulations. In this approach, an initial (relatively short) LE build‐up (searching) phase is used to construct an optimized biasing potential within a subspace of conformationally relevant degrees of freedom, that is then used in a (comparatively longer) US sampling phase. This scheme dramatically enhances (in comparison with plain MD) the sampling power of MD simulations, taking advantage of the fact that the preoptimized biasing potential represents a reasonable approximation to the negative of the free energy surface in the considered conformational subspace. The method is applied to the calculation of the relative free energies of β‐D ‐glucopyranose ring conformers in water (within the GROMOS 45A4 force field). Different schemes to assign sampled conformational regions to distinct states are also compared. This approach, which bears some analogies with adaptive umbrella sampling and metadynamics (but within a very distinct implementation), is shown to be: (i) efficient (nearly all the computational effort is invested in the actual sampling phase rather than in searching and equilibration); (ii) robust (the method is only weakly sensitive to the details of the build‐up protocol, even for relatively short build‐up times); (iii) versatile (a LEUS biasing potential database could easily be preoptimized for small molecules and assembled on a fragment basis for larger ones). © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Effect of the R119G mutation on human P5CR structure and its interactions with NAD: Insights derived from molecular dynamics simulation and free energy analysis

Pyrroline-5-carboxylate reductase (P5CR), an enzyme with conserved housekeeping roles, is involved in the etiology of cutis laxa. While previous work has shown that the R119G point mutation in the P5CR protein is involved, the structural mechanism behind the pathology remains to be elucidated. In order to probe the role of the R119G mutation in cutis laxa, we performed molecular dynamics (MD) simulations, essential dynamics (ED) analysis, and Molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) binding free energy calculations on wild type (WT) and mutant P5CR-NAD complex. These MD simulations and ED analyses suggest that the R119G mutation decreases the flexibility of P5CR, specifically in the substrate binding pocket, which could decrease the kinetics of the cofactor entrance and egress. Furthermore, the MM-PBSA calculations suggest the R119G mutant has a lower cofactor binding affinity for NAD than WT. Our study provides insight into the possible role of the R119G mutation during interactions between P5CR and NAD, thus bettering our understanding of how the mutation promotes cutis laxa.     

Insight into herbicide resistance of W574L mutant Arabidopsis thaliana acetohydroxyacid synthase:molecular dynamics simulations and binding free energy calculations

Acetohydroxyacid synthase(AHAS) is the target enzyme of several classes of herbicides,such as sulfonylureas and imidazolinones.Now many mutant AHASs with herbicide resistance have emerged along with extensive use of herbicides,therefore it is imperative to understand the detailed interaction mechanism and resistance mechanism so as to develop new potent inhibitors for wild-type or resistant AHAS.With the aid of available crystal structures of the Arabidopsis thaliana(At) AHAS-inhibitor complex,molecular dyn...     

A novel rhenium(III) complex with bis(pyrazol-1-yl)methane: X-ray structure and DFT calculations for [ReCl3(bpzm)(PPh3)]

The [ReCl₃(MeCN)(PPh₃)₂] complex reacts with bis(pyrazol-1-yl)methane (bpzm) to give [ReCl₃(bpzm)(PPh₃)]. This compound has been studied by IR, UV–Vis spectroscopy, magnetic measurement and X-ray crystallography. The molecular orbital diagram of [ReCl₃(bpzm)(PPh₃)] has been calculated with the density functional theory (DFT) method. The spin-allowed triplet–triplet electronic transitions of [ReCl₃(bpzm)(PPh₃)] have been calculated with the time-dependent DFT method, and the UV–Vis spectrum of the title compound has been discussed on this basis. The magnetic behavior is characteristic of a mononuclear d⁴ low-spin octahedral Re(III) complex (³T_1g ground state) and arises because of the large spin–orbit coupling (ζ = 2500 cm⁻¹), which gives a diamagnetic ground state.     

Combined application of 2D NMR correlation methods and ab initio chemical shift calculations to the structure determination of new heterocyclic compounds

The combined use of 2D NMR correlation methods and ab initio chemical shift calculations is efficient and, in some cases, virtually the only way to determine the structures of new organic compounds. This approach enabled us to establish the structure of the major unusual product of the three-component reaction of imidazo[1,5-a]quinoxalin-4-one, bis(2-chloroethyl)amine hydrochloride, and potassium carbonate in DMF. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2172–2179, December, 2006. Dedicated to Professor A. V. Il’yasov on the occasion of his 70th birthday.