Intervals and the deduction of drug binding site models

In the search for new drugs, it often occurs that the binding affinities of several compounds to a common receptor macromolecule are known experimentally, but the structure of the receptor is not known. This article describes an extraordinarily objective computer algorithm for deducing the important geometric and energetic features of the common binding site, starting only from the chemical structures of the ligands and their observed binding. The user does not have to propose a pharmacophore, guess the bioactive conformations of the ligands, or suggest ways to superimpose the active compounds. The method takes into account conformational flexibility of the ligands, stereospecific binding, diverse or unrelated chemical structures, inaccurate or qualitative binding data, and the possibility that chemically similar ligands may or may not bind to the receptor in similar orientations. The resulting model can be viewed graphically and interpreted in terms of one or more binding regions of the receptor, each preferring to be occupied by various sorts of chemical groups. The model always fits the given data completely and can predict the binding of any other ligand, regardless of chemical structure. The method is an outgrowth of distance geometry and Voronoi polyhedra site modeling but incorporates several novel features. The geometry of the ligand molecules and the site is described in terms of intervals of internal distances. Determining the site model consists of reducing the uncertainty in the interregion distance intervals, and this uncertainty is described as intervals of intervals. Similarly, the given binding affinities and their experimental uncertainties are treated as intervals in the affinity scale. The final site model specifies an entire region of interaction energy parameters that satisfy the training set rather than a single set of parameters. Predicted binding for test compounds results in an interval which, when compared to the experimental interval, may be correct, incorrect, or vague. There is a pervasive ternary logic involved in the assessment of predictions, in the search for a satisfactory model, and in judging whether a given molecule may bind in a particular orientation: true, false, or maybe. The approach is illustrated on an extremely simple artificial example and on a real data set of cocaine analogues binding to a nerve membrane receptor in vitro. © 1995 by John Wiley & Sons, Inc.     

Voronoi binding site models

A frequently occurring problem in drug design and enzymology is that the binding constants for several compounds to the same site are known, but the geometry and energetic interactions of the site are not. This paper presents in detail a novel approach to the problem which accurately but compactly represents the allowed conformation space of each ligand, accurately depicts their three-dimensional structures, and realistically allows each ligand to adopt the conformation and positioning in the site which is most favorable energetically. The investigator supplies only the ligand structures and observed binding free energies, along with a proposed site geometry. With no further assumptions about how the ligands bind and what parts of the ligands are important in determining the binding, the algorithm fits the observed binding energies without leaving outliers, predicts exactly how each of the given ligands binds in the site, and predicts the strength and mode of binding of new compounds, regardless of chemical similarity to the original set of ligands. The method is illustrated by devising a simple site that accounts for the binding of five polychlorinated biphenyls to thyroxine binding prealbumin. This model then predicts the binding energies correctly for an additional six biphenyls, and fails on one compound.     

Geometrically feasible binding modes of a flexible ligand molecule at the receptor site

A very efficient algorithm for determining the geometrically feasible binding modes of a flexible ligand molecule at the receptor site is presented. It is based on distance geometry but maintains the requirements of three dimensions. The distance geometry manipulation can superimpose two bodies without explicitly calculating the necessary rigid rotation and translation. The whole conformation space of a flexible molecule can be efficiently examined by considering only a finite number of conformational points. The method is suitable only when the criterion for superposition is some minimum distance limit. It cannot, however, give the exact distance between two points in two different bodies.     

Competitive mass spectrometry binding assay for characterization of three binding sites of tubulin

Tubulin is an attractive and established target for anticancer therapy. To date, the only method to determine the binding of inhibitor to tubulin has been competitive radioligand binding assays. We developed a non‐radioactive mass spectrometry (MS) binding assay to study the tubulin binding of colchicine, vinblastine and paclitaxel and to identify which of these three binding sites that a novel inhibitor binds. The method involves a very simple step of separating the unbound ligand from macromolecules using ultrafiltration. The unbound ligand in the filtrate can be accurately determined using highly sensitive and specific liquid chromatography tandem mass spectrometry (LC‐MS/MS) method using multiple reaction monitoring (MRM) mode. The assay was validated using podophyllotoxin, vincristine and docetaxel, drugs that compete to the colchicine‐, vinblastine‐ and paclitaxel‐binding sites in tubulin, respectively. This competitive binding assay allowed the reliable detection of interactions of these drugs with three binding sites on tubulin. This method was subsequently applied to determine the tubulin‐binding site of 4‐substituted methoxylbenzoyl‐aryl‐thiazoles (SMART‐H), a potent antitubulin agent developed in our laboratory. The results indicated that SMART‐H specifically and reversibly bound only to the colchicine‐binding site, but not to vinblastine‐ or paclitaxel sites. This new non‐radioligand binding method to determine the binding site on tubulin will function as a useful tool to study the binding sites of tubulin inhibitors. Copyright © 2010 John Wiley & Sons, Ltd.     

Resolving the problem of trapped water in binding cavities: prediction of host–guest binding free energies in the SAMPL5 challenge by funnel metadynamics

The funnel metadynamics method enables rigorous calculation of the potential of mean force along an arbitrary binding path and thereby evaluation of the absolute binding free energy. A problem of such physical paths is that the mechanism characterizing the binding process is not always obvious. In particular, it might involve reorganization of the solvent in the binding site, which is not easily captured with a few geometrically defined collective variables that can be used for biasing. In this paper, we propose and test a simple method to resolve this trapped-water problem by dividing the process into an artificial host-desolvation step and an actual binding step. We show that, under certain circumstances, the contribution from the desolvation step can be calculated without introducing further statistical errors. We apply the method to the problem of predicting host–guest binding free energies in the SAMPL5 blind challenge, using two octa-acid hosts and six guest molecules. For one of the hosts, well-converged results are obtained and the prediction of relative binding free energies is the best among all the SAMPL5 submissions. For the other host, which has a narrower binding pocket, the statistical uncertainties are slightly higher; longer simulations would therefore be needed to obtain conclusive results.     

Quantitative structure-based design: formalism and application of receptor-dependent RD-4D-QSAR analysis to a set of glucose analogue inhibitors of glycogen phosphorylase

A method for performing quantitative structure-based design has been developed by extending the current receptor-independent RI-4D-QSAR methodology to include receptor geometry. The resultant receptor-dependent RD-4D-QSAR approach employs a novel receptor-pruning technique to permit effective processing of ligands with the lining of the binding site wrapped about them. Data reduction, QSAR model construction, and identification of possible pharmacophore sites are achieved by a three-step statistical analysis consisting of genetic algorithm optimization followed by backward elimination multidimensional regression and ending with another genetic algorithm optimization. The RD-4D-QSAR method is applied to a series of glucose inhibitors of glycogen phosphorylase b, GPb. The statistical quality of the best RI- and RD-4D-QSAR models are about the same. However, the predictivity of the RD- model is quite superior to that of the RI-4D-QSAR model for a test set. The superior predictive performance of the RD- model is due to its dependence on receptor geometry. There is a unique induced-fit between each inhibitor and the GPb binding site. This induced-fit results in the side chain of Asn-284 serving as both a hydrogen bond acceptor and donor site depending upon inhibitor structure. The RD-4D-QSAR model strongly suggests that quantitative structure-based design cannot be successful unless the receptor is allowed to be completely flexible.     

Approximation of slow attracting manifolds in chemical kinetics by trajectory-based optimization approaches

Many common kinetic model reduction approaches are explicitly based on inherent multiple time scales and often assume and directly exploit a clear time scale separation into fast and slow reaction processes. They approximate the system dynamics with a dimension-reduced model after eliminating the fast modes by enslaving them to the slow ones. The corresponding restrictive assumption of full relaxation of fast modes often renders the resulting approximation of slow attracting manifolds inaccurate as a representation of the reduced model and makes the numerical solution of the nonlinear "reduction equations" particularly difficult in many cases where the gap in intrinsic time scales is not large enough. We demonstrate that trajectory optimization approaches can avoid such severe restrictions by computing numerical solutions that correspond to "maximally relaxed" dynamical modes in a suitable sense. We present a framework of trajectory-based optimization for model reduction in chemical kinetics and a general class of reduction criteria characterizing the relaxation of chemical forces along reaction trajectories. These criteria can be motivated geometrically exploiting ideas from differential geometry and fundamental physics and turn out to be highly successful in example applications. Within this framework, we provide results for the computational approximation of slow attracting low-dimensional manifolds in terms of families of optimal trajectories for a six-component hydrogen combustion mechanism.     

Application of a simple calorimetric data analysis on the binding study of calcium ions by human growth hormone

A simple graphical linear method was introduced for isothermal titration calorimetric data analysis in the protein-ligand interaction. The number of binding sites, the dissociation binding constant and the molar enthalpy of binding site can be obtained by using this new isothermal titration calorimetric data analysis method. The method was applied to the study of the interaction of human growth hormone (hGH) with divalent calcium ion at 27°C in NaCl solution, 50 mM. hGH has a set of three identical and independent binding sites for Ca ²⁺ . The intrinsic dissociation equilibrium constant and the molar enthalpy of binding are 52 μMand -17.4, respectively. Results obtained by this new calorimetric data analysis are in good agreement with results obtained using our previous method.     

Molecular docking and competitive binding study discovered different binding modes of microsomal prostaglandin E synthase-1 inhibitors

Microsomal prostaglandin E synthase-1 (mPGES-1) is a newly recognized therapeutic target for the treatment of inflammation, pain, cancer, atherosclerosis, and stroke. Many mPGES-1 inhibitors have been discovered. However, as the structure of the binding site is not well-characterized, none of these inhibitors was designed based on the mPGES-1 structure, and their inhibition mechanism remains to be fully disclosed. Recently, we built a new structural model of mPGES-1 which was well supported by experimental data. Based on this model, molecular docking and competition experiments were used to investigate the binding modes of four representive mPGES-1 inhibitors. As the inhibitor binding sites predicted by docking overlapped with both the substrate and the cofactor binding sites, mPGES-1 inhibitors might act as dual-site inhibitors. This inhibitory mechanism was further verified by inhibitor-cofactor and inhibitor-substrate competition experiments. To investigate the potency-binding site relationships of mPGES-1 inhibitors, we also carried out molecular docking studies for another series of compounds. The docking results correlated well with the different inhibitory effects observed experimentally. Our data revealed that mPGES-1 inhibitors could bind to the substrate and the cofactor binding sites simultaneously, and this dual-site binding mode improved their potency. Future rational design and optimization of mPGES-1 inhibitors can be carried out based on this binding mechanism.     

Mapping the binding site of a large set of quinazoline type EGF-R inhibitors using molecular field analyses and molecular docking studies

In the current work, three-dimensional QSAR studies for one large set of quinazoline type epidermal growth factor receptor (EGF-R) inhibitors were conducted using two types of molecular field analysis techniques: comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA). These compounds belonging to six different structural classes were randomly divided into a training set of 122 compounds and a test set of 13 compounds. The statistical results showed that the 3D-QSAR models derived from CoMFA were superior to those generated from CoMSIA. The most optimal CoMFA model after region focusing bears significant cross-validated r(2)(cv) of 0.60 and conventional r(2) of 0.92. The predictive power of the best CoMFA model was further validated by the accurate estimation to these compounds in the external test set, and the mean agreement of experimental and predicted log(IC(50)) values of the inhibitors is 0.6 log unit. Separate CoMFA models were conducted to evaluate the influence of different partial charges (Gasteiger-Marsili, Gasteiger-Hückel, MMFF94, ESP-AM1, and MPA-AM1) on the statistical quality of the models. The resulting CoMFA field map provides information on the geometry of the binding site cavity and the relative weights of various properties in different site pockets for each of the substrates considered. Moreover, in the current work, we applied MD simulations combined with MM/PBSA (Molecular mechanics/Possion-Boltzmann Surface Area) to determine the correct binding mode of the best inhibitor for which no ligand-protein crystal structure was present. To proceed, we define the following procedure: three hundred picosecond molecular dynamics simulations were first performed for the four binding modes suggested by DOCK 4.0 and manual docking, and then MM/PBSA was carried out for the collected snapshots. The most favorable binding mode identified by MM/PBSA has a binding free energy about 10 kcal/mol more favorable than the second best one. The most favorable binding mode identified by MM/PBSA can give satisfactory explanation of the SAR data of the studied molecules and is in good agreement with the contour maps of CoMFA. The most favorable binding mode suggests that with the quinazoline-based inhibitor, the N3 atom is hydrogen-bonded to a water molecule which, in turn, interacts with Thr 766, not Thr 830 as proposed by Wissner et al. (J. Med. Chem. 2000, 43, 3244). The predicted complex structure of quinazoline type inhibitor with EGF-R as well as the pharmacophore mapping from CoMFA can interpret the structure activities of the inhibitors well and afford us important information for structure-based drug design.     

Conserved core substructures in the overlay of protein-ligand complexes

The method of conserved core substructure matching (CSM) for the overlay of protein-ligand complexes is described. The method relies upon distance geometry to align structurally similar substructures without regard to sequence similarity onto substructures from a reference protein empirically selected to include key determinants of binding site location and geometry. The error in ligand position is reduced in reoriented ensembles generated with CSM when compared to other overlay methods. Since CSM can only succeed when the selected core substructure is geometrically conserved, misalignments only rarely occur. The method may be applied to reliably overlay large numbers of protein-ligand complexes in a way that optimizes ligand position at a specific binding site or subsite or to align structures from large and diverse protein families where the conserved binding site is localized to only a small portion of either protein. Core substructures may be complex and must be chosen with care. We have created a database of empirically selected core substructures to demonstrate the utility of CSM alignment of ligand binding sites in important drug targets. A Web-based interface can be used to apply CSM to align large collections of protein-ligand complexes for use in drug design using these substructures or to evaluate the use of alternative core substructures that may then be shared with the larger user community. Examples show the benefit of CSM in the practice of structure-based drug design.     

Gaussian mapping of chemical fragments in ligand binding sites

We present a new approach to automatically define a quasi-optimal minimal set of pharmacophoric points mapping the interaction properties of a user-defined ligand binding site. The method is based on a fitting algorithm where a grid of sampled interaction energies of the target protein with small chemical fragments in the binding site is approximated by a linear expansion of Gaussian functions. A heuristic approximation selects from this expansion the smallest possible set of Gaussians required to describe the interaction properties of the binding site within a prespecified accuracy. We have evaluated the performance of the approach by comparing the computed Gaussians with the positions of aromatic sites found in experimental protein-ligand complexes. For a set of 53 complexes, good correspondence is found in general. At a 95% significance level, approximately 65% of the predicted interaction points have an aromatic binding site within 1.5 A. We then studied the utility of these points in docking using the program DOCK. Short docking times, with an average of approximately 0.18 s per conformer, are obtained, while retaining, both for rigid and flexible docking, the ability to sample native-like binding modes for the ligand. An average 4-5-fold speed-up in docking times and a similar success rate is estimated with respect to the standard DOCK protocol.     

Identifying the binding mode of a molecular scaffold

We describe a method for docking of a scaffold-based series and present its advantages over docking of individual ligands, for determining the binding mode of a molecular scaffold in a binding site. The method has been applied to eight different scaffolds of protein kinase inhibitors (PKI). A single analog of each of these eight scaffolds was previously crystallized with different protein kinases. We have used FlexX to dock a set of molecules that share the same scaffold, rather than docking a single molecule. The main mode of binding is determined by the mode of binding of the largest cluster among the docked molecules that share a scaffold. Clustering is based on our 'nearest single neighbor' method [J. Chem. Inf. Comput. Sci., 43 (2003) 208-217]. Additional criteria are applied in those cases in which more than one significant binding mode is found. Using the proposed method, most of the crystallographic binding modes of these scaffolds were reconstructed. Alternative modes, that have not been detected yet by experiments, could also be identified. The method was applied to predict the binding mode of an additional molecular scaffold that was not yet reported and the predicted binding mode has been found to be very similar to experimental results for a closely related scaffold. We suggest that this approach be used as a virtual screening tool for scaffold-based design processes.     

In silico footprinting of ligands binding to the minor groove of DNA

The sequence selectivity of small molecules binding to the minor groove of DNA can be predicted by "in silico footprinting". Any potential ligand can be docked in the minor groove and then moved along it using simple simulation techniques. By applying a simple scoring function to the trajectory after energy minimization, the preferred binding site can be identified. We show application to all known noncovalent binding modes, namely 1:1 ligand:DNA binding (including hairpin ligands) and 2:1 side-by-side binding, with various DNA base pair sequences and show excellent agreement with experimental results from X-ray crystallography, NMR, and gel-based footprinting.     

Calculating electron binding energies for quadratic fermion Hamiltonian by virtue of the IEO method

In this work, we discuss how to use the invariant eigen‐operator (IEO) method to derive the electron binding energies for the quadratic fermion Hamiltonian. We find that the task of solving the energy gap of fermion Hamiltonian can be ascribed to simply solving a standard eigenvalue problem of a numerical matrix, which is determined by the parameters of the given Hamiltonian. The IEO method provides us with a new approach for solving quadratic Hamiltonians in a more convenient and concise way. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Activation state-dependent binding of small molecule kinase inhibitors: structural insights from biochemistry

Interactions between kinases and small molecule inhibitors can be activation state dependent. A detailed understanding of inhibitor binding therefore requires characterizing interactions across multiple activation states. We have systematically explored the effects of ABL1 activation loop phosphorylation and PDGFR family autoinhibitory juxtamembrane domain docking on inhibitor binding affinity. For a diverse compound set, the affinity patterns correctly classify inhibitors as having type I or type II binding modes, and we show that juxtamembrane domain docking can have dramatic negative effects on inhibitor affinity. The results have allowed us to associate ligand-induced conformational changes observed in cocrystal structures with specific energetic costs. The approach we describe enables investigation of the complex relationship between kinase activation state and compound binding affinity and should facilitate strategic inhibitor design.     

Structure-based identification of small molecule binding sites using a free energy model

We separately have shown that the maximal druglike affinity of a given binding site on a protein can be calculated on the basis of the binding-site structure alone by using a desolvation-based free energy model along with the notion that druglike ligands fall into certain physiochemical property ranges. Here, we present an approach where we reformulate the calculated druggability affinity as an additive free energy to facilitate the searching of whole protein surfaces for druglike binding sites. The highest-scoring patches in many cases represent known ligand-binding sites for druggable targets, but not for difficult targets. This approach differs from other approaches in that it does not simply identify pockets with the greatest volume but instead identifies pockets that are likely to be amenable to druglike small-molecule binding. Combining the method with a functional residue prediction method called SCA (statistical coupling analysis) results in the prediction of potentially druggable allosteric binding sites on p38alpha kinase.     

Designed compounds for recognition of 10 base pairs of DNA with two at binding sites

Short AT base pair sequences that are separated by a small number of GCs are common in eukaryotic parasite genomes. Cell-permeable compounds that bind effectively and selectively to such sequences present an attractive therapeutic approach. Compounds with linked, one or two amidine-benzimidazole-phenyl (ABP) motifs were designed, synthesized, and evaluated for binding to adjacent AT sites by biosensor-surface plasmon resonance (SPR). A surprising feature of the linked ABP motifs is that a set of six similar compounds has three different minor groove binding modes with the target sequences. Compounds with one ABP bind independently to two separated AT sites. Unexpectedly, compounds with two ABP motifs can bind strongly either as monomers or as cooperative dimers to the full site. The results are supported by mass spectrometry and circular dichroism, and models to explain the different binding modes are presented.