Binding affinities for sulfonamide inhibitors with human thrombin using Monte Carlo simulations with a linear response method

Can an optimization/scoring procedure in ligand-protein docking be employed to probe drug-resistant mutations in proteins?

A simple ligand-protein structural optimization and binding evaluation procedure has been routinely used in high-speed ligand-protein docking studies. In this work, we examine whether such an optimization/scoring procedure is useful in indicating possible drug-resistant mutations in proteins. Crystal structures of three wild-type enzymes (HIV-1 protease, HIV-1 reverse transcriptase, and Mycobacterium tuberculosis H37Rv enoyl-ACP reductase) complexed to a variety of inhibitors are studied. Mutations are introduced into these structures by using the molecular modeling software, SYBYL. Structural optimization and scoring of a mutant complex is conducted by a procedure similar to that used in a recent docking study (Wang et al., 1999). The computed results are compared with observed drug resistance data and the profile of nonresistant mutations. Most mutations studied show an energy change in the same direction as those indicated by observed resistance data. 50% of the polar to polar or nonpolar to nonpolar mutations are found to correlate qualitatively with observed drug resistance data. Van der Waals interactions account for most of these changes, which is in agreement with conclusions from structural studies. Substantially larger deviations are found between computed results and observed data for most polar to nonpolar or nonpolar to polar mutations, which result from deficiency in modelling and scoring ligand-protein interactions in our procedure. Our results suggest that an optimization/docking scoring procedure is useful for qualitatively probing polar to polar or nonpolar to nonpolar resistant mutations in addition to its application in screening active compounds. More accurate description of ligand-protein interactions and the use of methods such as free energy perturbation and Poisson-Boltzmann may be needed to further improve the quality of prediction.

Very empirical treatment of solvation and entropy: a force field derived from log Po/w

A non-covalent interaction force field model derived from the partition coefficient of 1-octanol/water solubility is described. This model, HINT for Hydropathic INTeractions, is shown to include, in very empirical and approximate terms, all components of biomolecular associations, including hydrogen bonding, Coulombic interactions, hydrophobic interactions, entropy and solvation/desolvation. Particular emphasis is placed on: (1) demonstrating the relationship between the total empirical HINT score and free energy of association, deltaGinteraction; (2) showing that the HINT hydrophobic-polar interaction sub-score represents the energy cost of desolvation upon binding for interacting biomolecules; and (3) a new methodology for treating constrained water molecules as discrete independent small ligands. An example calculation is reported for dihydrofolate reductase (DHFR) bound with methotrexate (MTX). In that case the observed very tight binding, deltaGinteraction < or = -13.6 kcal mol(-1), is largely due to ten hydrogen bonds between the ligand and enzyme with estimated strength ranging between -0.4 and -2.3 kcal mol(-1). Four water molecules bridging between DHFR and MTX contribute an additional -1.7 kcal mol(-1) stability to the complex. The HINT estimate of the cost of desolvation is +13.9 kcal mol(-1).

Calculations of free-energy contributions to protein-RNA complex stabilization

The problem of calculating binding affinities of protein-RNA complexes is addressed by analyzing a computational strategy of modeling electrostatic free energies based on a nonlinear Poisson-Boltzmann (NLPB) model and linear response approximation (LRA). The underlying idea is to treat binding as a two-step process. Solutions to the NLPB equation calculate free energies arising from electronic polarizability and the LRA is constructed from molecular dynamics simulations to model reorganization free energies due to conformational transitions. By implementing a consistency condition of requiring the NLPB model to reproduce the solute-solvent free-energy transitions determined by the LRA, a "macromolecule dielectric constant" (epsilon(m)) for treating reorganization is obtained. The applicability of this hybrid approach was evaluated by calculating the absolute free energy of binding and free-energy changes for amino acid substitutions in the complex between the U1A spliceosomal protein and its cognate RNA hairpin. Depending on the residue substitution, epsilon(m) varied from 3 to 18, and reflected dipolar reorientation not included in the polarization modeled by epsilon(m) = 2. Although the changes in binding affinities from substitutions modeled strictly at the implicit level by the NLPB equation with epsilon(m) = 4 reproduced the experimental values with good overall agreement, substitutions problematic to this simple treatment showed significant improvement when solved by the NLPB-LRA approach.

Prediction of enzyme binding: human thrombin inhibition study by quantum chemical and artificial intelligence methods based on X-ray structures

Thrombin is a serine protease which plays important roles in the human body, the key one being the control of thrombus formation. The inhibition of thrombin has become a target for new antithrombotics. The aim of our work was to (i) construct a model which would enable us to predict Ki values for the binding of an inhibitor into the active site of thrombin based on a database of known X-ray structures of inhibitor-enzyme complexes and (ii) to identify the structural and electrostatic characteristics of inhibitor molecules crucially important to their effective binding. To retain as much of the 3D structural information of the bound inhibitor as possible, we implemented the quantum mechanical/molecular mechanical (QM/MM) procedure for calculating the molecular electrostatic potential (MEP) at the van der Waals surfaces of atoms in the protein's active site. The inhibitor was treated quantum mechanically, while the rest of the complex was treated by classical means. The obtained MEP values served as inputs into the counter-propagation artificial neural network (CP-ANN), and a genetic algorithm was subsequently used to search for the combination of atoms that predominantly influences the binding. The constructed CP-ANN model yielded Ki values predictions with a correlation coefficient of 0.96, with Ki values extended over 7 orders of magnitude. Our approach also shows the relative importance of the various amino acid residues present in the active site of the enzyme for inhibitor binding. The list of residues selected by our automatic procedure is in good correlation with the current consensus regarding the importance of certain crucial residues in thrombin's active site.

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.

Computational analysis of binding of P1 variants to trypsin

The binding of P1 variants of bovine pancreatic trypsin inhibitor (BPTI) to trypsin has been investigated by means of molecular dynamics simulations. The specific interaction formed between the amino acid at the primary binding (P1) position of the binding loop of BPTI and the specificity pocket of trypsin was estimated by use of the linear interaction energy (LIE) method. Calculations for 13 of the naturally occurring amino acids at the P1 position were carried out, and the results obtained were found to correlate well with the experimental binding free energies. The LIE calculations rank the majority of the 13 variants correctly according to the experimental association energies and the mean error between calculated and experimental binding free energies is only 0.38 kcal/mole, excluding the Glu and Asp variants, which are associated with some uncertainties regarding protonation and the possible presence of counter-ions. The three-dimensional structures of the complex with three of the P1 variants (Asn, Tyr, and Ser) included in this study have not at present been solved by any experimental techniques and, therefore, were modeled on the basis of experimental data from P1 variants of similar size. Average structures were calculated from the MD simulations, from which specific interactions explaining the broad variation in association energies were identified. The present study also shows that explicit treatment of the complex water-mediated hydrogen bonding network at the protein-protein interface is of crucial importance for obtaining reliable binding free energies. The successful reproduction of relative binding energies shows that this type of methodology can be very useful as an aid in rational design and redesign of biologically active macromolecules.

Sensitivity of an empirical affinity scoring function to changes in receptor-ligand complex conformations

A combination of empirical scoring and conformational sampling for ligand binding affinity prediction is examined. The behaviour of a scoring function with respect to the sensitivity to conformational changes is investigated using ensembles of structures generated by molecular dynamics simulation. The correlation between the calculated score and the coordinate deviation from the experimental structure is clear for the complex of arabinose with arabinose-binding protein, which is dominated by hydrogen bond interactions, while the score calculated for the hydrophobic complex between retinol and retinol binding protein is rather insensitive to ligand conformational changes. For typical ensembles of structures generated by molecular dynamics at 300 K, the variation of the calculated score is considerably smaller than that of the underlying molecular mechanics interaction energies.

Computationally accessible method for estimating free energy changes resulting from site-specific mutations of biomolecules: systematic model building and structural/hydropathic analysis of deoxy and oxy hemoglobins

A practical computational method for the molecular modeling of free-energy changes associated with protein mutations is reported. The de novo generation, optimization, and thermodynamic analysis of a wide variety of deoxy and oxy hemoglobin mutants are described in detail. Hemoglobin is shown to be an ideal candidate protein for study because both the native deoxy and oxy states have been crystallographically determined, and a large and diverse population of its mutants has been thermodynamically characterized. Noncovalent interactions for all computationally generated hemoglobin mutants are quantitatively examined with the molecular modeling program HINT (Hydropathic INTeractions). HINT scores all biomolecular noncovalent interactions, including hydrogen bonding, acid-base, hydrophobic-hydrophobic, acid-acid, base-base, and hydrophobic-polar, to generate dimer-dimer interface "scores" that are translated into free-energy estimates. Analysis of 23 hemoglobin mutants, in both deoxy and oxy states, indicates that the effects of mutant residues on structurally bound waters (and visa versa) are important for generating accurate free-energy estimates. For several mutants, the addition/elimination of structural waters is key to understanding the thermodynamic consequences of residue mutation. Good agreement is found between calculated and experimental data for deoxy hemoglobin mutants (r = 0.79, slope = 0.78, standard error = 1.4 kcal mol(-1), n = 23). Less accurate estimates were initially obtained for oxy hemoglobin mutants (r = 0.48, slope = 0.47, standard error = 1.4 kcal mol(-1), n = 23). However, the elimination of three outliers from this data set results in a better correlation of r = 0.87 (slope = 0.72, standard error = 0.75, n = 20). These three mutations may significantly perturb the hemoglobin quaternary structure beyond the scope of our structural optimization procedure. The method described is also useful in the examination of residue ionization states in protein structures. Specifically, we find an acidic residue within the native deoxy hemoglobin dimer-dimer interface that may be protonated at physiological pH. The final analysis is a model design of novel hemoglobin mutants that modify cooperative free energy (deltaGc)--the energy barrier between the allosteric transition from deoxy to oxy hemoglobin.

Computational modelling of inhibitor binding to human thrombin

Thrombin is an essential protein involved in blood clot formation and an important clinical target, since disturbances of the coagulation process cause serious cardiovascular diseases such as thrombosis. Here we evaluate the performance of a molecular dynamics based method for predicting the binding affinities of different types of human thrombin inhibitors. For a series of eight ligands the method ranks their relative affinities reasonably well. The binding free energy difference between high and low affinity representatives in the test set is quantitatively reproduced, as well as the stereospecificity for a chiral inhibitor. The original parametrisation of this linear interaction energy method requires the addition of a constant energy term in the case of thrombin. This yields a mean unsigned error of 0.68 kcal/mol for the absolute binding free energies. This type of approach is also useful for elucidating three-dimensional structure-activity relationships in terms of microscopic interactions of the ligands with the solvated enzyme.

Monte Carlo calculations on HIV-1 reverse transcriptase complexed with the non-nucleoside inhibitor 8-Cl TIBO: contribution of the L100I and Y181C variants to protein stability and biological activity

A computational model of the non-nucleoside inhibitor 8-Cl TIBO complexed with HIV-1 reverse transcriptase (RT) was constructed in order to determine the binding free energies. Using Monte Carlo simulations, both free energy perturbation and linear response calculations were carried out for the transformation of wild-type RT to two key mutants, Y181C and L100I. The newer linear response method estimates binding free energies based on changes in electrostatic and van der Waals energies and solvent-accessible surface areas. In addition, the change in stability of the protein between the folded and unfolded states was estimated for each of these mutations, which are known to emerge upon treatment with the inhibitor. Results from the calculations revealed that there is a large hydrophobic contribution to protein stability in the native, folded state. The calculated absolute free energies of binding from both the linear response, and also the more rigorous free energy perturbation method, gave excellent agreement with the experimental differences in activity. The success of the relatively rapid linear response method in predicting experimental activities holds promise for estimating the activity of the inhibitors not only against the wild-type RT, but also against key protein variants whose emergence undermines the efficacy of the drugs.

Role of proximal His93 in nitric oxide binding to metmyoglobin. Application of continuum solvation in Monte Carlo protein simulations

Monte Carlo protein simulations with continuum solvation were used to explore the conformational mobility of NO within the active site of metmyoglobin. To the best of our knowledge this is the first application of a continuum solvation model for exploring protein binding sites. The usefulness of the Monte Carlo conformational analysis was demonstrated in comparative molecular dynamics simulations. Analysis of conformer populations revealed that Monte Carlo conformational analysis is more effective in mapping the relevant region of the potential surface. Distribution of low-energy conformers obtained for the metmyoglobin-NO complex was found to depend on the orientation of proximal His93. Different charge distributions corresponding to the two experimentally verified possible torsions of this proximal residue result in strong binding of NO or its release to a nearby hydrophobic trap. Conformer populations obtained by Monte Carlo conformational analysis were grouped into three main families: one, with the NO directly bound to the iron, appears when the CA-CB-CG-CD2 torsion of His93 is at its ligand binding value (-113 degrees); and two conformers exist where NO is trapped in a nearby hydrophobic pocket, the same cavity that was determined to be the geminate trap of CO in ferrous Mb as a result of the torsional flip of His93 to its ligand releasing state (-125 degrees). Based on this analysis, we suggest that the electrostatic rearrangement coupled to the conformational fluctuation of the proximal His leads to the geminate trapping of the ligand. Conformational rearrangement of the proximal side would provide the possibility of rebinding of the ligand to Fe.

Estimation of the binding affinities of FKBP12 inhibitors using a linear response method

A series of non-immunosuppressive inhibitors of FK506 binding protein (FKBP12) are investigated using Monte Carlo statistical mechanics simulations. These small molecules may serve as scaffolds for chemical inducers of protein dimerization, and have recently been found to have FKBP12-dependent neurotrophic activity. A linear response model was developed for estimation of absolute binding free energies based on changes in electrostatic and van der Waals energies and solvent-accessible surface areas, which are accumulated during simulations of bound and unbound ligands. With average errors of 0.5 kcal/mol, this method provides a relatively rapid way to screen the binding of ligands while retaining the structural information content of more rigorous free energy calculations.

Free energy determinants of binding the rRNA substrate and small ligands to ricin A-chain

A continuum model is provided of the free energy terms that contribute to the molecular association of ricin A-chain (RTA) with the rRNA substrate and several small ligands. The model for RTA interactions with the RNA was taken from a previously proposed complex containing a 29-mer oligonucleotide hairpin (. Proteins 27:80-95), and models for the ligands were constructed from x-ray crystallographic structures. The calculated absolute free energies of complex formation for the RTA-RNA assembly and several single-residue substitutions are in good agreement with experimental data, given the approximations of evaluating the strain energy and conformational entropy. The free energy terms were found to resemble those of protein-protein complexes, with the net unfavorable electrostatic contribution offset by the favorable nonspecific hydrophobic effect. Decomposition of the RTA-RNA binding free energy into individual contributions revealed the electrostatic "hot" spots arising from charge-charge complementarity of the interfacial arginines with the RNA phosphate backbone. Base interactions of the GAGA loop structure dominate the hydrophobic complementarity. A linear-scaling model was parametrized for evaluating the binding of small ligands against the rRNA substrate and illustrates the free energy determinant required for designing specific RTA inhibitors.

Q: a molecular dynamics program for free energy calculations and empirical valence bond simulations in biomolecular systems

A new molecular dynamics program for free energy calculations in biomolecular systems is presented. It is principally designed for free energy perturbation simulations, empirical valence bond calculations, and binding affinity estimation by linear interaction energy methods. Evaluation of ligand-binding selectivity and free energy profiles for nucleophile activation in two protein tyrosine phosphatases as well as absolute binding affinity estimation for a lysine-binding protein are given as examples.

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 quinazolìnes, 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.

Ligand binding affinity prediction by linear interaction energy methods

A recent method for estimating ligand binding affinities is extended. This method employs averages of interaction potential energy terms from molecular dynamics simulations or other thermal conformational sampling techniques. Incorporation of systematic deviations from electrostatic linear response, derived from free energy perturbation studies, into the absolute binding free energy expression significantly enhances the accuracy of the approach. This type of method may be useful for computational prediction of ligand binding strengths, e.g., in drug design applications.

Computational approaches to molecular recognition

Recent advances in the computation of free energies have facilitated the understanding of host-guest and protein-ligand recognition. Rigorous perturbation methods have been assessed and expanded, and more approximate techniques have been developed that allow faster treatment of diverse systems.