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

ADP-ribose and analogues bound to the deMARylating macrodomain from the bat coronavirus HKU4

Macrodomains are proteins that recognize and hydrolyze ADP ribose (ADPR) modifications of intracellular proteins. Macrodomains are implicated in viral genome replication and interference with host cell immune responses. They are important to the infectious cycle of Coronaviridae and Togaviridae viruses. We describe crystal structures of the conserved macrodomain from the bat coronavirus (CoV) HKU4 in complex with ligands. The structures reveal a binding cavity that accommodates ADPR and analogs via local structural changes within the pocket. Using a radioactive assay, we present evidence of mono-ADPR (MAR) hydrolase activity. In silico analysis presents further evidence on recognition of the ADPR modification for hydrolysis. Mutational analysis of residues within the binding pocket resulted in diminished enzymatic activity and binding affinity. We conclude that the common structural features observed in the macrodomain in a bat CoV contribute to a conserved function that can be extended to other known macrodomains.

Protein-protein binding affinity prediction on a diverse set of structures

MOTIVATION

Accurate binding free energy functions for protein-protein interactions are imperative for a wide range of purposes. Their construction is predicated upon ascertaining the factors that influence binding and their relative importance. A recent benchmark of binding affinities has allowed, for the first time, the evaluation and construction of binding free energy models using a diverse set of complexes, and a systematic assessment of our ability to model the energetics of conformational changes.

RESULTS

We construct a large set of molecular descriptors using commonly available tools, introducing the use of energetic factors associated with conformational changes and disorder to order transitions, as well as features calculated on structural ensembles. The descriptors are used to train and test a binding free energy model using a consensus of four machine learning algorithms, whose performance constitutes a significant improvement over the other state of the art empirical free energy functions tested. The internal workings of the learners show how the descriptors are used, illuminating the determinants of protein-protein binding.

AVAILABILITY

The molecular descriptor set and descriptor values for all complexes are available in the Supplementary Material. A web server for the learners and coordinates for the bound and unbound structures can be accessed from the website: http://bmm.cancerresearchuk.org/~Affinity.

CONTACT

paul.bates@cancer.org.uk.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Prediction and analysis of binding affinities for chemically diverse HIV-1 PR inhibitors by the modified SAFE_p approach

One of the biggest challenges in the "in silico" screening of enzyme ligands is to have a protocol that could predict the ligand binding free energies. In our group we have developed a very simple screening function (referred to as solvent accessibility free energy of binding predictor, SAFE_p) which we have applied previously to the study of peptidic HIV-1 protease (HIV-1 PR) inhibitors and later to cyclic urea type HIV-1 PR inhibitors. In this work, we have extended the SAFE_p protocol to a chemically diverse set of HIV-1 PR inhibitors with binding constants that differ by several orders of magnitude. The resulting function is able to reproduce the ranking and in many cases the value of the inhibitor binding affinities for the HIV-1 PR, with accuracy comparable with that of costlier protocols. We also demonstrate that the binding pocket SAFE_p analysis can contribute to the understanding of the physical forces that participate in ligand binding. The analysis tools afforded by our protocol have allowed us to identify an induced fit phenomena mediated by the inhibitor and have demonstrated that larger fragments do not necessarily contribute the most to the binding free energy, an outcome partially brought about by the substantial role the desolvation penalty plays in the energetics of binding. Finally, we have revisited the effect of the Asp dyad protonation state on the predicted binding affinities.

Inhibitor docking screened by the modified SAFE_p scoring function: Application to cyclic urea HIV-1 PR inhibitors

Our laboratory has in the past developed a method for the prediction of ligand binding free energies to proteins, referred to as SAFE_p (Solvent free energy predictor). Previously, we have applied this protocol for the prediction of the binding free energy of peptidic and cyclic urea HIV-1 PR inhibitors, whose X-ray structures bound to enzyme are known. In this work, we present the first account of a docking simulation, where the ligand conformations were screened and inhibitor ranking was predicted on the basis of a modified SAFE_p approach, for a set of cyclic urea-HIV-1 PR complexes whose structures are not known. We show that the optimal dielectric constant for docking is rather high, in line with the values needed to reproduce some protein residue properties, like pKa's. Our protocol is able to reproduce most of the observed binding ranking, even in the case that the components of the equation are not fitted to experimental data. Partition of the binding free energy into pocket and residue contributions sheds light into the importance of the inhibitor's fragments and on the prediction of "hot spots" for resistance mutations.

Ligand recognition by RAR and RXR receptors: binding and selectivity

Fundamental biological functions, most notably embriogenesis, cell growth, cell differentiation, and cell apoptosis, are in part regulated by a complex genomic network that starts with the binding (and activation) of retinoids to their cognate receptors, members of the superfamily of nuclear receptors. We have studied ligand recognition of retinoic receptors (RXRalpha and RARgamma) using a molecular-mechanics-based docking method. The protocol used in this work is able to rank the affinity of pairs of ligands for a single retinoid receptor, the highest values corresponding to those that adapt better to the shape of the binding site and generate the optimal set of electrostatic and apolar interactions with the receptor. Moreover, our studies shed light onto some of the energetic contributions to retinoid receptor ligand selectivity. In this regard we show that there is a difference in polarity between the binding site regions that anchor the carboxylate in RAR and RXR, which translates itself into large differences in the energy of interaction of both receptors with the same ligand. We observe that the latter energy change is canceled off by the solvation energy penalty upon binding. This energy compensation is borne out as well by experiments that address the effect of site-directed mutagenesis on ligand binding to RARgamma. The hypothesis that the difference in binding site polarity might be exploited to build RXR-selective ligands is tested with some compounds having a thiazolidinedione anchoring group.

Modified solvent accessibility free energy prediction analysis of cyclic urea inhibitors binding to the HIV-1 protease

One of the most successful drug targets against AIDS in the last decade has been the HIV-1 protease (HIV-1 PR), an enzyme that processes the polyprotein gene products into active replicative viral proteins. In our quest for a wide-ranging, binding free energy function we have extended the solvent accessibility free energy predictor (SAFE_p) method, recently developed for peptidic HIV-1 PR inhibitors, to the study of the binding of cyclic urea (CU) HIV-1 PR inhibitors. Our results show that there is a need for a specific term depicting polar contacts to be added to the original SAFE_p analytical expression, an outcome not seen in our studies of HIV-1 PR peptidic inhibitors. Nevertheless, despite the higher profile of the electrostatic interactions in the binding of the CU inhibitors, our analysis indicates that CU inhibitor binding is still driven by the hydrophobic entropic contribution, as much as for the peptidic inhibitors.

A fast empirical approach to binding free energy calculations based on protein interface information

Three useful variables from the interfaces of 20 protein-protein complexes were investigated. These variables are the side-chain accessible number (N(b)), the number of hydrophilic pairs (N(pair)) and buried a polar solvent accessible surface areas (DeltaDeltaASA(apol)). An empirical model based on the three variables was developed to describe the free energy of protein associations. As the results show, the side-chain accessible numbers characterize the loss of side-chain conformational entropy of protein interactions and the effective empirical function presented here has great capability for estimating the binding free energy. It was found that the variables of interface information capture most of the significant features of protein-protein association. Also, we applied the model based on the variables as a rescoring function to docking simulations and found that it has the potential to distinguish the 'true' binding mode. It is clear that the simple and empirical scale developed here is an attractive target function for calculating binding free energy for various biological processes to rational protein design.

Solvation energy density occlusion approximation for evaluation of desolvation penalties in biomolecular interactions

In calculations involving many displacements of an interacting pair of biomolecules, such as brownian dynamics, the docking of a substrate/ligand to an enzyme/receptor, or the screening of a large number of ligands as prospective inhibitors for a particular receptor site, there is a need for rapid evaluation of the desolvation penalties of the interacting pair. Although continuum electrostatic treatments with distinct dielectric constants for solute and solvent provide an account of the electrostatics of solvation and desolvation, it is necessary to re-solve the Poisson equation, at considerable computational cost, for each displacement of the interacting pair. We present a new method that uses a formulation of continuum electrostatic solvation in terms of the solvation energy density and approximates desolvation in terms of the occlusion of this density. We call it the SEDO approximation. It avoids the need to re-solve the Poisson equation, as desolvation is now estimated by an integral over the occluded volume. Test calculations are presented for some simple model systems and for some real systems that have previously been studied using the Poisson equation approach: MHC class I protein-peptide complexes and a congeneric series of human immunodeficiency virus type 1 (HIV-1) protease--ligand complexes. For most of the systems considered, the trends and magnitudes of the desolvation component of interaction energies obtained using the SEDO approximation are in reasonable correlation with those obtained by re-solving the Poisson equation. In most cases, the error introduced by the SEDO approximation is much less than that of the often-used test-charge approximation for the charge-charge components of intermolecular interactions. Proteins 2001;43:12-27.

Scoring docked conformations generated by rigid-body protein-protein docking

Rigid-body methods, particularly Fourier correlation techniques, are very efficient for docking bound (co-crystallized) protein conformations using measures of surface complementarity as the target function. However, when docking unbound (separately crystallized) conformations, the method generally yields hundreds of false positive structures with good scores but high root mean square deviations (RMSDs). This paper describes a two-step scoring algorithm that can discriminate near-native conformations (with less than 5 A RMSD) from other structures. The first step includes two rigid-body filters that use the desolvation free energy and the electrostatic energy to select a manageable number of conformations for further processing, but are unable to eliminate all false positives. Complete discrimination is achieved in the second step that minimizes the molecular mechanics energy of the retained structures, and re-ranks them with a combined free-energy function which includes electrostatic, solvation, and van der Waals energy terms. After minimization, the improved fit in near-native complex conformations provides the free-energy gap required for discrimination. The algorithm has been developed and tested using docking decoys, i.e., docked conformations generated by Fourier correlation techniques. The decoy sets are available on the web for testing other discrimination procedures. Proteins 2000;40:525-537.

Free energy landscapes of encounter complexes in protein-protein association

We report the computer generation of a high-density map of the thermodynamic properties of the diffusion-accessible encounter conformations of four receptor-ligand protein pairs, and use it to study the electrostatic and desolvation components of the free energy of association. Encounter complex conformations are generated by sampling the translational/rotational space of the ligand around the receptor, both at 5-A and zero surface-to-surface separations. We find that partial desolvation is always an important effect, and it becomes dominant for complexes in which one of the reactants is neutral or weakly charged. The interaction provides a slowly varying attractive force over a small but significant region of the molecular surface. In complexes with no strong charge complementarity this region surrounds the binding site, and the orientation of the ligand in the encounter conformation with the lowest desolvation free energy is similar to the one observed in the fully formed complex. Complexes with strong opposite charges exhibit two types of behavior. In the first group, represented by barnase/barstar, electrostatics exerts strong orientational steering toward the binding site, and desolvation provides some added adhesion within the local region of low electrostatic energy. In the second group, represented by the complex of kallikrein and pancreatic trypsin inhibitor, the overall stability results from the rather nonspecific electrostatic attraction, whereas the affinity toward the binding region is determined by desolvation interactions.

Selecting near-native conformations in homology modeling: the role of molecular mechanics and solvation terms

A free energy function, combining molecular mechanics energy with empirical solvation and entropic terms, is used for ranking near-native conformations that occur in the conformational search steps of homology modeling, i.e., side-chain search and loop closure calculations. Correlations between the free energy and RMS deviation from the X-ray structure are established. It is shown that generally both molecular mechanics and solvation/entropic terms should be included in the potential. The identification of near-native backbone conformations is accomplished primarily by the molecular mechanics term that becomes the dominant contribution to the free energy if the backbone is even slightly strained, as frequently occurs in loop closure calculations. Both terms become equally important if a sufficiently accurate backbone conformation is found. Finally, the selection of the best side-chain positions for a fixed backbone is almost completely governed by the solvation term. The discriminatory power of the combined potential is demonstrated by evaluating the free energies of protein models submitted to the first meeting on Critical Assessment of techniques for protein Structure Prediction (CASP1), and comparing them to the free energies of the native conformations.

Prediction of binding constants of protein ligands: a fast method for the prioritization of hits obtained from de novo design or 3D database search programs

A dataset of 82 protein-ligand complexes of known 3D structure and binding constant Ki was analysed to elucidate the important factors that determine the strength of protein-ligand interactions. The following parameters were investigated: the number and geometry of hydrogen bonds and ionic interactions between the protein and the ligand, the size of the lipophilic contact surface, the flexibility of the ligand, the electrostatic potential in the binding site, water molecules in the binding site, cavities along the protein-ligand interface and specific interactions between aromatic rings. Based on these parameters, a new empirical scoring function is presented that estimates the free energy of binding for a protein-ligand complex of known 3D structure. The function distinguishes between buried and solvent accessible hydrogen bonds. It tolerates deviations in the hydrogen bond geometry of up to 0.25 A in the length and up to 30 degrees in the hydrogen bond angle without penalizing the score. The new energy function reproduces the binding constants (ranging from 3.7 x 10(-2) M to 1 x 10(-14) M, corresponding to binding energies between -8 and -80 kJ/mol) of the dataset with a standard deviation of 7.3 kJ/mol corresponding to 1.3 orders of magnitude in binding affinity. The function can be evaluated very fast and is therefore also suitable for the application in a 3D database search or de novo ligand design program such as LUDI. The physical significance of the individual contributions is discussed.

Toward a predictive understanding of molecular recognition

T cells circulate in blood and the lymphatic system, continually engaging cells through transient non-specific adhesion. In a normally functioning immune system, these interactions permit sufficient time for T-cell receptors (TCRs) to sample major histocompatibility complex (MHC)-peptide complexes for the presence of foreign antigen, with detection of the latter to some extent being triggered by a longer dwell time of the receptor on the complex. Precisely how this incremental stability, which may be relatively small, leads to activation is unclear, but it appears to be related to diffusion-mediated formation of ternary complex dimers. The formation of stable dimers can explain the high sensitivity of the response, but leaves a number of questions unaddressed, including the following: i) How can high sensitivity be reconciled with high specificity, and how can a short TCR dwell time be reconciled with a comparably short time for ternary complex pair formation? ii) What is the nature of the early signals on the plasma membrane that determine alternative responses e.g. proliferation at one extreme and apoptosis at the other? iii) What are the cell-surface correlates of biphasic dose response functions i.e. of responses that peak as a function of dose and then descend? This paper has two loosely coupled goals. One is to review and assess the mathematical and computational methods available for analyzing reactions with and between mobile membrane-bound receptors. These methods range from phenomenological to mechanistic, the latter being based on the details of atomic structure. The other is to apply these methods to address biological questions, such as those raised above, part of whose answer may lie in the kinetic competition between alternative reaction paths.

Empirical free energy calculation: comparison to calorimetric data

An effective free energy potential, developed originally for binding free energy calculation, is compared to calorimetric data on protein unfolding, described by a linear combination of changes in polar and nonpolar surface areas. The potential consists of a molecular mechanics energy term calculated for a reference medium (vapor or nonpolar liquid), and empirical terms representing solvation and entropic effects. It is shown that, under suitable conditions, the free energy function agrees well with the calorimetric expression. An additional result of the comparison is an independent estimate of the side-chain entropy loss, which is shown to agree with a structure-based entropy scale. These findings confirm that simple functions can be used to estimate the free energy change in complex systems, and that a binding free energy evaluation model can describe the thermodynamics of protein unfolding correctly. Furthermore, it is shown that folding and binding leave the sum of solute-solute and solute-solvent van der Waals interactions nearly invariant and, due to this invariance, it may be advantageous to use a nonpolar liquid rather than vacuum as the reference medium.

Empirical scoring functions: I. The development of a fast empirical scoring function to estimate the binding affinity of ligands in receptor complexes

This paper describes the development of a simple empirical scoring function designed to estimate the free energy of binding for a protein-ligand complex when the 3D structure of the complex is known or can be approximated. The function uses simple contact terms to estimate lipophilic and metal-ligand binding contributions, a simple explicit form for hydrogen bonds and a term which penalises flexibility. The coefficients of each term are obtained using a regression based on 82 ligand-receptor complexes for which the binding affinity is known. The function reproduces the binding affinity of the complexes with a cross-validated error of 8.68 kJ/mol. Tests on internal consistency indicate that the coefficients obtained are stable to changes in the composition of the training set. The function is also tested on two test sets containing a further 20 and 10 complexes, respectively. The deficiencies of this type of function are discussed and it is compared to approaches by other workers.

Empirical free energy calculations: a blind test and further improvements to the method

Empirical Gibbs functions estimate free energies of non-covalent reactions (deltaG) from atomic coordinates of reaction products (e.g. antibody-antigen complexes). The function previously developed by us has four terms that quantify the effects of hydrophobic, electrostatic and entropy changes (conformational, association) upon complexation. The function was used to calculate delta deltaG of ten lysozyme mutants affecting the stability of the HyHEL-10 antibody-lysozyme complex. The mutants were computer-modeled from the X-ray structure of the wild-type, and free energy calculations produced a correlation coefficient of 0.5 with the experimental delta deltaG data (average absolute error +/-3 kcal). The following changes were then introduced into the Gibbs function: (1) the hydrophobic force was made proportional to the molecular surface, as calculated by the GEPOL93 algorithm, with the scaling constant of 70 cal/mol/A2; (2) calculation of the electrostatics of binding was carried out by the finite difference Poisson-Boltzmann algorithm, which employed uniform grid charging, dielectric boundary smoothing and charge anti-aliasing; and (3) side-chain conformational entropy was estimated from the CONGEN sampling of torsional degrees of freedom. In the new calculations, correlation with experimental data improved to 0.6 or 0.8 if a single outlying mutant, K96M, was neglected. Analysis of the errors remaining in our calculations indicated that molecular mechanics-based modeling of the mutants, rather than the form of our amended Gibbs function, was the main factor limiting the accuracy of the free energy estimates.

Solvation effects are responsible for the reduced inhibitor affinity of some HIV-1 PR mutants

The formulation of HIV-1 PR inhibitors as anti-viral drugs has been hindered by the appearance of protease strains that present drug resistance to these compounds. The mechanism by which the HIV-1 PR mutants lower their affinity for the inhibitor is not yet fully understood. We have applied a modified Poisson-Boltzmann method to the evaluation of the molecular interactions that contribute to the lowering of the inhibitor affinity to some polar mutants at position 82. These strains present drug resistance behavior and hence are ideally suited for these studies. Our results indicate that the reduction in binding affinity is due to the solvation effects that penalize the binding to the more polar mutants. The inhibitor binding ranking of the different mutants can be explained from the analysis of the different components of our free energy scoring function.

Empirical potentials and functions for protein folding and binding

Simplified models and empirical potentials are being increasingly used for the analysis of proteins, frequently augmenting or replacing molecular mechanics approaches. Recent folding simulations have employed potentials that, in addition to terms assuring proper polypeptide geometry, include only two noncovalent effects-hydrogen bonding and hydrophobicity, with extremely simple approximations to the latter. The potentials that have been used in the free-energy ranking of protein-ligand complexes have generally been more involved. These potentials have more detailed solvation models and account for both local (hydrophobic and polar) solute-solvent phenomena and long range electrostatic solvation effects. The models of solvation that have been used most frequently are surface area related atomic parameters, knowledge-based models extracted from protein-structure data, and continum electrostatics with an additional area-related parameter. The knowledge-based approaches to solvation, although convenient and accurate enough, are suspect of double counting certain free-energy terms.

Modeling protein-ligand complexes

Increasing the rate at which new biologically active compounds are found is a major goal in pharmaceutical chemistry. Recently, several computational methods have been proposed with this intent. For some time, algorithms have been used to direct ligand evolution on the basis of complementarity to the three-dimensional structure of a selected protein. Current research focuses on enhancements to methods for searching chemical databases, proposing sensible modifications to known active compounds, and construction of novel ligands from theoretical principles.