Relative differences in the binding free energies of human immunodeficiency virus 1 protease inhibitors: a thermodynamic cycle-perturbation approach

Tinker-OpenMM: Absolute and relative alchemical free energies using AMOEBA on GPUs

The capabilities of the polarizable force fields for alchemical free energy calculations have been limited by the high computational cost and complexity of the underlying potential energy functions. In this work, we present a GPU-based general alchemical free energy simulation platform for polarizable potential AMOEBA. Tinker-OpenMM, the OpenMM implementation of the AMOEBA simulation engine has been modified to enable both absolute and relative alchemical simulations on GPUs, which leads to a ∼200-fold improvement in simulation speed over a single CPU core. We show that free energy values calculated using this platform agree with the results of Tinker simulations for the hydration of organic compounds and binding of host-guest systems within the statistical errors. In addition to absolute binding, we designed a relative alchemical approach for computing relative binding affinities of ligands to the same host, where a special path was applied to avoid numerical instability due to polarization between the different ligands that bind to the same site. This scheme is general and does not require ligands to have similar scaffolds. We show that relative hydration and binding free energy calculated using this approach match those computed from the absolute free energy approach. © 2017 Wiley Periodicals, Inc.

Identification of HIV inhibitors guided by free energy perturbation calculations

Free energy perturbation (FEP) theory coupled to molecular dynamics (MD) or Monte Carlo (MC) statistical mechanics offers a theoretically precise method for determining the free energy differences of related biological inhibitors. Traditionally requiring extensive computational resources and expertise, it is only recently that its impact is being felt in drug discovery. A review of computer-aided anti-HIV efforts employing FEP calculations is provided here that describes early and recent successes in the design of human immunodeficiency virus type 1 (HIV-1) protease and non-nucleoside reverse transcriptase inhibitors. In addition, our ongoing work developing and optimizing leads for small molecule inhibitors of cyclophilin A (CypA) is highlighted as an update on the current capabilities of the field. CypA has been shown to aid HIV-1 replication by catalyzing the cis/trans isomerization of a conserved Gly-Pro motif in the Nterminal domain of HIV-1 capsid (CA) protein. In the absence of a functional CypA, e.g., by the addition of an inhibitor such as cyclosporine A (CsA), HIV-1 has reduced infectivity. Our simulations of acylurea-based and 1-indanylketone-based CypA inhibitors have determined that their nanomolar and micromolar binding affinities, respectively, are tied to their ability to stabilize Arg55 and Asn102. A structurally novel 1-(2,6-dichlorobenzamido) indole core was proposed to maximize these interactions. FEP-guided optimization, experimental synthesis, and biological testing of lead compounds for toxicity and inhibition of wild-type HIV-1 and CA mutants have demonstrated a dose-dependent inhibition of HIV-1 infection in two cell lines. While the inhibition is modest compared to CsA, the results are encouraging.

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.

Modeling Protein-Ligand Binding by Mining Minima

We present the first application of the mining minima algorithm to protein-small molecule binding. This end-point approach use an empirical force field and implicit solvent models, treats the protein binding-site as fully flexible and estimates free energies as sums over local energy wells. The calculations are found to yield encouraging agreement with experiment for three sets of HIV-1protease inhibitors and a set of phosphodiesterase 10a inhibitors. The contributions of various aspects of the model to its accuracy are examined, and the Poisson-Boltzmann correction is found to be the most critical. Interestingly, the computed changes in configurational entropy upon binding fall roughly along the same entropy-energy correlation previously observed for smaller host-guest systems. Strengths and weaknesses of the method are discussed, as are the prospects for enhancing accuracy and speed.

An analysis of hydrophobic interactions of thymidylate synthase with methotrexate: free energy calculations involving mutant and native structures bound to methotrexate

Since the human body for many reasons can adapt and become resistant to drugs, it is important to develop and validate computer aided drug design (CADD) methods that could help predict binding affinity changes that can result from these resistant enzymes. The free energy perturbation (FEP) methodology is the most accurate means of estimating relative binding affinities between inhibitors and protein variants. In this paper, we describe the role played by hydrophobic residues lining the active site region, particularly (79)Ile and (176)Phe, in the binding of methotrexate to the Escherichia coli (E. coli) thymidylate synthase (TS) enzyme, using the thermodynamic cycle perturbation (TCP) approach. The computed binding free energy differences on the binding of methotrexate to the native and some mutant E. coli TS structures have been compared with experimental results. Computationally, four different 'mutations' have been simulated on the TS enzyme with methotrexate (MTX): (79)Ile --> (79)Val; (79)Ile --> (79)Ala; (79)Ile --> (79)Leu; and (176)Phe --> (176)Ile. The calculated results indicate that in each of these cases, the native residues ((79) Ile and (176) Phe) interact more favorably with methotrexate than the mutant residues and these results are corroborated by experimental measurements. Binding preference to wild type residues can be rationalized in terms of their better hydrophobic contacts with the phenyl ring of methotrexate.

Calculation of relative binding affinities of fructose 1,6-bisphosphatase mutants with adenosine monophosphate using free energy perturbation method

The free energy perturbation (FEP) methodology is the most accurate means of estimating relative binding affinities between inhibitors and protein variants. In this article, the importance of hydrophobic and hydrophilic residues to the binding of adenosine monophosphate (AMP) to the fructose 1,6-bisphosphatase (FBPase), a target enzyme for type-II diabetes, was examined by FEP method. Five mutations were made to the FBPase enzyme with AMP inhibitor bound: 113Tyr --> 113Phe, 31Thr --> 31Ala, 31Thr --> 31Ser, 177Met --> 177Ala, and 30Leu --> 30Phe. These mutations test the strength of hydrogen bonds and van der Waals interactions between the ligand and enzyme. The calculated relative free energies indicated that: 113Tyr and 31Thr play an important role, each via two hydrogen bonds affecting the binding affinity of inhibitor AMP to FBPase, and any changes in these hydrogen bonds due to mutations on the protein will have significant effect on the binding affinity of AMP to FBPase, consistent to experimental results. Also, the free energy calculations clearly show that the hydrophilic interactions are more important than the hydrophobic interactions of the binding pocket of FBPase.

Ab initio quantum mechanics-based free energy perturbation method for calculating relative solvation free energies

A free energy perturbation (FEP) method was developed that uses ab initio quantum mechanics (QM) for treating the solute molecules and molecular mechanics (MM) for treating the surroundings. Like our earlier results using AM1 semi empirical QMs, the ab initio QM/MM-based FEP method was shown to accurately calculate relative solvation free energies for a diverse set of small molecules that differ significantly in structure, aromaticity, hydrogen bonding potential, and electron density. Accuracy was similar to or better than conventional FEP methods. The QM/MM-based methods eliminate the need for time-consuming development of MM force field parameters, which are frequently required for drug-like molecules containing structural motifs not adequately described by MM. Future automation of the method and parallelization of the code for Linux 128/256/512 clusters is expected to enhance the speed and increase its use for drug design and lead optimization.

Development of a Quantum Mechanics-Based Free-Energy Perturbation Method: Use in the Calculation of Relative Solvation Free Energies

Free-energy perturbation (FEP) is considered the most accurate computational method for calculating relative solvation and binding free-energy differences. Despite some success in applying FEP methods to both drug design and lead optimization, FEP calculations are rarely used in the pharmaceutical industry. One factor limiting the use of FEP is its low throughput, which is attributed in part to the dependence of conventional methods on the user's ability to develop accurate molecular mechanics (MM) force field parameters for individual drug candidates and the time required to complete the process. In an attempt to find an FEP method that could eventually be automated, we developed a method that uses quantum mechanics (QM) for treating the solute, MM for treating the solute surroundings, and the FEP method for computing free-energy differences. The thread technique was used in all transformations and proved to be essential for the successful completion of the calculations. Relative solvation free energies for 10 structurally diverse molecular pairs were calculated, and the results were in close agreement with both the calculated results generated by conventional FEP methods and the experimentally derived values. While considerably more CPU demanding than conventional FEP methods, this method (QM/MM-based FEP) alleviates the need for development of molecule-specific MM force field parameters and therefore may enable future automation of FEP-based calculations. Moreover, calculation accuracy should be improved over conventional methods, especially for calculations reliant on MM parameters derived in the absence of experimental data.

Biomolecular simulations: recent developments in force fields, simulations of enzyme catalysis, protein-ligand, protein-protein, and protein-nucleic acid noncovalent interactions

Computer modeling has been developed and widely applied in studying molecules of biological interest. The force field is the cornerstone of computer simulations, and many force fields have been developed and successfully applied in these simulations. Two interesting areas are (a) studying enzyme catalytic mechanisms using a combination of quantum mechanics and molecular mechanics, and (b) studying macromolecular dynamics and interactions using molecular dynamics (MD) and free energy (FE) calculation methods. Enzyme catalysis involves forming and breaking of covalent bonds and requires the use of quantum mechanics. Noncovalent interactions appear ubiquitously in biology, but here we confine ourselves to review only noncovalent interactions between protein and protein, protein and ligand, and protein and nucleic acids.

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.

Structure-based drug design approaches for predicting binding affinities of HIV1 protease inhibitors

Computational assessment of the binding affinity of enzyme inhibitors prior to synthesis is an important component of computer-assisted drug design (CADD) paradigms. The free energy perturbation (FEP) methodology is the most accurate means of estimating relative binding affinities between two inhibitors. However, due to its complexity and computation-intensive nature, practical applications are restricted to analysis of structurally-related inhibitors. Accordingly, there is a need for methods that enable rapid assessment of large number of structurally-unrelated molecules in a suitably accurate manner. In this review, the FEP method is compared with regression-based methods that employ multivariate models to assess the advantages of each in the estimation of relative binding affinities of inhibitors to an enzyme. Semiquantitative predictions of relative binding free energies of human immunodeficiency virus 1 (HIV1) protease inhibitors are also presented and compared with the corresponding FEP results. The results indicate that the regression-based methods and the FEP method are useful in the semi-quantitative and quantitative assessment of relative binding affinities of enzyme inhibitors, respectively, prior to synthesis.

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 microM) 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 delta delta G (bind) to the same range as that of the 2-phenyl derivative.

Molecular mechanisms of resistance: free energy calculations of mutation effects on inhibitor binding to HIV-1 protease

The changes in the inhibitor binding constants due to the mutation of isoleucine to valine at position 84 of HIV-1 protease are calculated using molecular dynamics simulations. The calculations are done for three potent inhibitors--KNI-272, L-735,524 (indinavir or MK-639), and Ro 31-8959 (saquinavir). The calculations agree with the experimental data both in terms of an overall trend and in the magnitude of the resulting free energy change. HIV-1 protease is a homodimer, so each mutation causes two changes in the enzyme. The decrease in the binding free energy from each mutated side chain differs among the three inhibitors and correlates well with the size of the cavities induced in the protein interior near the mutated residue. The cavities are created as a result of a mutation to a smaller side chain, but the cavities are less than would be predicted from the wild-type structures, indicating that there is significant relaxation to partially fill the cavities.

Structure-activity correlation study of HIV-1 inhibitors: electronic and molecular parameters

Quantitative structure-activity relationships (QSARs) for 40 HIV-1 inhibitors, 1-[(2-hydroxyethoxy)-methyl]-6-(phenylthio)thymine and its derivatives, were studied. Fully optimized geometries, based on the semiempirical AMl method, were used to calculate electronic and molecular properties of all compounds. In order to examine the relation between biological activities and structural properties, multiple linear regression models were employed. A suitable QSAR model was obtained, showing not only statistical significance, but also predictive ability. The significant molecular descriptors used were atomic charges of two substituted carbon atoms in the thymine ring, hydration energies and molar refractivities of the molecules. These descriptors allowed a physical explanation of electronic and molecular properties contributing to HIV-1 inhibitory potency.

Solvent accessibility as a predictive tool for the free energy of inhibitor binding to the HIV-1 protease

We have developed a simple approach for the evaluation of the free energies of inhibitor binding to the protease of the human immunodeficiency virus (HIV-1 PR). Our algorithm is based on the observation that most groups that line the binding pockets of this enzyme are hydrophobic in nature. Based on this fact, we have likened the binding of an inhibitor to this enzyme to its transfer from water to a medium of lower polarity. The resulting expression produced values for the free energy of binding of inhibitors to the HIV-1 PR that are in good agreement with experimental values. The additive nature of this approach has enabled us to partition the free energy of binding into the contributions of single fragments. The resulting analysis clearly indicates the existence of a ranking in the participation of the enzyme's subsites in binding. Although all the enzyme's pockets contribute to binding, the ones that bind the P2-P'2 span of the inhibitor are in general the most critical for high inhibitor potency. Moreover, our method has allowed us to determine the nature of the functional groups that fit into given enzyme binding pockets. Perusal of the energy contributions of single side chains has shown that a large number of hydrophobic and aromatic groups located in the central portion of the HIV-1 PR inhibitors present optimal binding. All of these observations are in agreement with experimental evidence, providing a validation for the physical relevancy of our model.

Expression of virus-encoded proteinases: functional and structural similarities with cellular enzymes

Many viruses express their genome, or part of their genome, initially as a polyprotein precursor that undergoes proteolytic processing. Molecular genetic analyses of viral gene expression have revealed that many of these processing events are mediated by virus-encoded proteinases. Biochemical activity studies and structural analyses of these viral enzymes reveal that they have remarkable similarities to cellular proteinases. However, the viral proteinases have evolved unique features that permit them to function in a cellular environment. In this article, the current status of plant and animal virus proteinases is described along with their role in the viral replication cycle. The reactions catalyzed by viral proteinases are not simple enzyme-substrate interactions; rather, the processing steps are highly regulated, are coordinated with other viral processes, and frequently involve the participation of other factors.