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Virtually all docking methods include some local continuous minimization of an energy/scoring function in order to remove steric clashes and obtain more reliable energy values. In this paper, we describe an efficient rigid-body optimization algorithm that, compared to the most widely used algorithms, converges approximately an order of magnitude faster to conformations with equal or slightly lower energy. The space of rigid body transformations is a nonlinear manifold, namely, a space which locally resembles a Euclidean space. We use a canonical parametrization of the manifold, called the exponential parametrization, to map the Euclidean tangent space of the manifold onto the manifold itself. Thus, we locally transform the rigid body optimization to an optimization over a Euclidean space where basic optimization algorithms are applicable. Compared to commonly used methods, this formulation substantially reduces the dimension of the search space. As a result, it requires far fewer costly function and gradient evaluations and leads to a more efficient algorithm. We have selected the LBFGS quasi-Newton method for local optimization since it uses only gradient information to obtain second order information about the energy function and avoids the far more costly direct Hessian evaluations. Two applications, one in protein-protein docking, and the other in protein-small molecular interactions, as part of macromolecular docking protocols are presented. The code is available to the community under open source license, and with minimal effort can be incorporated into any molecular modeling package.

Motivation: An effective docking algorithm for antibody-protein antigen complex prediction is an important first step toward design of biologics and vaccines. We have recently developed a new class of knowledge-based interaction potentials called Decoys as the Reference State (DARS) and incorporated DARS into the docking program PIPER based on the fast Fourier transform correlation approach. Although PIPER was the best performer in the latest rounds of the CAPRI protein docking experiment, it is much less accurate for docking antibody-protein antigen pairs than other types of complexes, in spite of incorporating sequence-based information on the location of the paratope. Analysis of antibody-protein antigen complexes has revealed an inherent asymmetry within these interfaces. Specifically, phenylalanine, tryptophan and tyrosine residues highly populate the paratope of the antibody but not the epitope of the antigen., Results: Since this asymmetry cannot be adequately modeled using a symmetric pairwise potential, we have removed the usual assumption of symmetry. Interaction statistics were extracted from antibody-protein complexes under the assumption that a particular atom on the antibody is different from the same atom on the antigen protein. The use of the new potential significantly improves the performance of docking for antibody-protein antigen complexes, even without any sequence information on the location of the paratope. We note that the asymmetric potential captures the effects of the multi-body interactions inherent to the complex environment in the antibody-protein antigen interface., Availability: The method is implemented in the ClusPro protein docking server, available at http://cluspro.bu.edu.

Formaldehyde has long been recognized as a hazardous environmental agent highly reactive with DNA. Recently, it has been realized that due to the activity of histone demethylation enzymes within the cell nucleus, formaldehyde is produced endogenously, in direct vicinity of genomic DNA. Should it lead to extensive DNA damage? We address this question with the aid of a computational mapping method, analogous to X-ray and nuclear magnetic resonance techniques for observing weakly specific interactions of small organic compounds with a macromolecule in order to establish important functional sites. We concentrate on the leading reaction of formaldehyde with free bases: hydroxymethylation of cytosine amino groups. Our results show that in B-DNA, cytosine amino groups are totally inaccessible for the formaldehyde attack. Then, we explore the effect of recently discovered transient flipping of Watson-Crick (WC) pairs into Hoogsteen (HG) pairs (HG breathing). Our results show that the HG base pair formation dramatically affects the accessibility for formaldehyde of cytosine amino nitrogens within WC base pairs adjacent to HG base pairs. The extensive literature on DNA interaction with formaldehyde is analyzed in light of the new findings. The obtained data emphasize the significance of DNA HG breathing.

The goal of this article is to reduce the complexity of the side chain search within docking problems. We apply six methods of generating side chain conformers to unbound protein structures and determine their ability of obtaining the bound conformation in small ensembles of conformers. Methods are evaluated in terms of the positions of side chain end groups. Results for 68 protein complexes yield two important observations. First, the end-group positions change less than 1 Å on association for over 60% of interface side chains. Thus, the unbound protein structure carries substantial information about the side chains in the bound state, and the inclusion of the unbound conformation into the ensemble of conformers is very beneficial. Second, considering each surface side chain separately in its protein environment, small ensembles of low-energy states include the bound conformation for a large fraction of side chains. In particular, the ensemble consisting of the unbound conformation and the two highest probability predicted conformers includes the bound conformer with an accuracy of 1 Å for 78% of interface side chains. As more than 60% of the interface side chains have only one conformer and many others only a few, these ensembles of low-energy states substantially reduce the complexity of side chain search in docking problems. This approach was already used for finding pockets in protein-protein interfaces that can bind small molecules to potentially disrupt protein-protein interactions. Side-chain search with the reduced search space will also be incorporated into protein docking algorithms., (Copyright © 2011 Wiley Periodicals, Inc.)

Despite the growing number of examples of small-molecule inhibitors that disrupt protein-protein interactions (PPIs), the origin of druggability of such targets is poorly understood. To identify druggable sites in protein-protein interfaces we combine computational solvent mapping, which explores the protein surface using a variety of small "probe" molecules, with a conformer generator to account for side-chain flexibility. Applications to unliganded structures of 15 PPI target proteins show that the druggable sites comprise a cluster of binding hot spots, distinguishable from other regions of the protein due to their concave topology combined with a pattern of hydrophobic and polar functionality. This combination of properties confers on the hot spots a tendency to bind organic species possessing some polar groups decorating largely hydrophobic scaffolds. Thus, druggable sites at PPI are not simply sites that are complementary to particular organic functionality, but rather possess a general tendency to bind organic compounds with a variety of structures, including key side chains of the partner protein. Results also highlight the importance of conformational adaptivity at the binding site to allow the hot spots to expand to accommodate a ligand of drug-like dimensions. The critical components of this adaptivity are largely local, involving primarily low energy side-chain motions within 6 Å of a hot spot. The structural and physicochemical signature of druggable sites at PPI interfaces is sufficiently robust to be detectable from the structure of the unliganded protein, even when substantial conformational adaptation is required for optimal ligand binding.

Our approach to protein-protein docking includes three main steps. First, we run PIPER, a rigid body docking program based on the Fast Fourier Transform (FFT) correlation approach, extended to use pairwise interactions potentials. Second, the 1000 best energy conformations are clustered, and the 30 largest clusters are retained for refinement. Third, the stability of the clusters is analyzed by short Monte Carlo simulations, and the structures are refined by the medium-range optimization method SDU. The first two steps of this approach are implemented in the ClusPro 2.0 protein-protein docking server. Despite being fully automated, the last step is computationally too expensive to be included in the server. When comparing the models obtained in CAPRI rounds 13-19 by ClusPro, by the refinement of the ClusPro predictions and by all predictor groups, we arrived at three conclusions. First, for the first time in the CAPRI history, our automated ClusPro server was able to compete with the best human predictor groups. Second, selecting the top ranked models, our current protocol reliably generates high-quality structures of protein-protein complexes from the structures of separately crystallized proteins, even in the absence of biological information, provided that there is limited backbone conformational change. Third, despite occasional successes, homology modeling requires further improvement to achieve reliable docking results., (© 2010 Wiley-Liss, Inc.)

Structures of the influenza A virus M2 proton channel in the open conformation have been determined by X-ray crystallography, and in the closed conformation by NMR. Whereas the X-ray structure shows a single inhibitor molecule in the middle of the channel, four inhibitor molecules bind the channel's outer surface in the NMR structure. In both structures, the strongest hot spots (i.e., regions that contribute substantially to the free energy of binding any potential ligand) lie inside the pore, and other hot spots are found at exterior locations. By considering all available models, we propose the primary drug binding site is inside the pore, but that exterior binding occurs under appropriate conditions., (Copyright (c) 2010 Elsevier Ltd. All rights reserved.)

The steroid and xenobiotic-responsive human pregnane X receptor (PXR) binds a broad range of structurally diverse compounds. The structures of the apo and ligand-bound forms of PXR are very similar, in contrast to most promiscuous proteins that generally adapt their shape to different ligands. We investigated the structural origins of PXR's recognition promiscuity using computational solvent mapping, a technique developed for the identification and characterization of hot spots, i.e., regions of the protein surface that are major contributors to the binding free energy. Results reveal that the smooth and nearly spherical binding site of PXR has a well-defined hot spot structure, with four hot spots located on four different sides of the pocket and a fifth close to its center. Three of these hot spots are already present in the ligand-free protein. The most important hot spot is defined by three structurally and sequentially conserved residues, W299, F288, and Y306. This largely hydrophobic site is not very specific and interacts with all known PXR ligands. Depending on their sizes and shapes, individual PXR ligands extend into two, three, or four more hot spot regions. The large number of potential arrangements within the binding site explains why PXR is able to accommodate a large variety of compounds. All five hot spots include at least one important residue, which is conserved in all mammalian PXRs, suggesting that the hot spot locations have remained largely invariant during mammalian evolution. The same side chains also show a high level of structural conservation across hPXR structures. However, each of the hPXR hot spots also includes residues with moveable side chains, further increasing the size variation in ligands that PXR can bind. Results also suggest a unique signal transduction mechanism between the PXR homodimerization interface and its coactivator binding site.

The interactions of beta2 glycoprotein I (B2GPI) with the receptors of the low-density lipoprotein receptor (LDLR) family are implicated in the clearance of negatively charged phospholipids and apoptotic cells and, in the presence of autoimmune anti-B2GPI antibodies, in cell activation, which might play a role in the pathology of antiphospholipid syndrome (APS). The ligand-binding domains of the lipoprotein receptors consist of multiple homologous LA modules connected by flexible linkers. In this study, we investigated at the atomic level the features of the LA modules required for binding to B2GPI. To compare the binding interface in B2GPI/LA complex to that observed in the high-resolution co-crystal structure of the receptor associated protein (RAP) with a pair of LA modules 3 and 4 from the LDLR, we used LA4 in our studies. Using solution NMR spectroscopy, we found that LA4 interacts with B2GPI and the binding site for B2GPI on the (15)N-labeled LA4 is formed by the calcium coordinating residues of the LA module. We built a model for the complex between domain V of B2GPI (B2GPI-DV) and LA4 without introducing any experimentally derived constraints into the docking procedure. Our model, which is in the agreement with the NMR data, suggests that the binding interface of B2GPI for the lipoprotein receptors is centered at three lysine residues of B2GPI-DV, Lys 308, Lys 282, and Lys317., (2009 Wiley-Liss, Inc.)

Structures of truncated versions of the influenza A virus M2 proton channel have been determined recently by x-ray crystallography in the open conformation of the channel, and by NMR in the closed state. The structures differ in the position of the bound inhibitors. The x-ray structure shows a single amantadine molecule in the middle of the channel, whereas in the NMR structure four drug molecules bind at the channel's outer surface. To study this controversy we applied computational solvent mapping, a technique developed for the identification of the most druggable binding hot spots of proteins. The method moves molecular probes--small organic molecules containing various functional groups--around the protein surface, finds favorable positions using empirical free energy functions, clusters the conformations, and ranks the clusters on the basis of the average free energy. The results of the mapping show that in both structures the primary hot spot is an internal cavity overlapping the amantadine binding site seen in the x-ray structure. However, both structures also have weaker hot spots at the exterior locations that bind rimantadine in the NMR structure, although these sites are partially due to the favorable interactions with the interfacial region of the lipid bilayer. As confirmed by docking calculations, the open channel binds amantadine at the more favorable internal site, in good agreement with the x-ray structure. In contrast, the NMR structure is based on a peptide/micelle construct that is able to accommodate the small molecular probes used for the mapping, but has a too narrow pore for the rimantadine to access the internal hot spot, and hence the drug can bind only at the exterior sites.

The identification of hot spots, i.e., binding regions that contribute substantially to the free energy of ligand binding, is a critical step for structure-based drug design. Here we present the application of two fragment-based methods to the detection of hot spots for DJ-1 and glucocerebrosidase (GCase), targets for the development of therapeutics for Parkinson's and Gaucher's diseases, respectively. While the structures of these two proteins are known, binding information is lacking. In this study we employ the experimental multiple solvent crystal structures (MSCS) method and computational fragment mapping (FTMap) to identify regions suitable for the development of pharmacological chaperones for DJ-1 and GCase. Comparison of data derived via MSCS and FTMap also shows that FTMap, a computational method for the identification of fragment binding hot spots, is an accurate and robust alternative to the performance of expensive and difficult crystallographic experiments.

Motivation: The binding sites of proteins generally contain smaller regions that provide major contributions to the binding free energy and hence are the prime targets in drug design. Screening libraries of fragment-sized compounds by NMR or X-ray crystallography demonstrates that such 'hot spot' regions bind a large variety of small organic molecules, and that a relatively high 'hit rate' is predictive of target sites that are likely to bind drug-like ligands with high affinity. Our goal is to determine the 'hot spots' computationally rather than experimentally., Results: We have developed the FTMAP algorithm that performs global search of the entire protein surface for regions that bind a number of small organic probe molecules. The search is based on the extremely efficient fast Fourier transform (FFT) correlation approach which can sample billions of probe positions on dense translational and rotational grids, but can use only sums of correlation functions for scoring and hence is generally restricted to very simple energy expressions. The novelty of FTMAP is that we were able to incorporate and represent on grids a detailed energy expression, resulting in a very accurate identification of low-energy probe clusters. Overlapping clusters of different probes are defined as consensus sites (CSs). We show that the largest CS is generally located at the most important subsite of the protein binding site, and the nearby smaller CSs identify other important subsites. Mapping results are presented for elastase whose structure has been solved in aqueous solutions of eight organic solvents, and we show that FTMAP provides very similar information. The second application is to renin, a long-standing pharmaceutical target for the treatment of hypertension, and we show that the major CSs trace out the shape of the first approved renin inhibitor, aliskiren., Availability: FTMAP is available as a server at http://ftmap.bu.edu/.

ClusPro is the first fully automated, web-based program for docking protein structures. Users may upload the coordinate files of two protein structures through ClusPro's web interface, or enter the PDB codes of the respective structures. The server performs rigid body docking, energy screening, and clustering to produce models. The program output is a short list of putative complexes ranked according to their clustering properties. ClusPro has been participating in CAPRI since January 2003, submitting predictions within 24 h after a target becomes available. In Rounds 6-11, ClusPro generated acceptable submissions for Targets 22, 25, and 27. In general, acceptable models were obtained for the relatively easy targets without substantial conformational changes upon binding. We also describe the new version of ClusPro that incorporates our recently developed docking program PIPER. PIPER is based on the fast Fourier transform correlation approach, but the method is extended to use pairwise interaction potentials, thereby increasing the number of near-native docked structures., ((c) 2007 Wiley-Liss, Inc.)

Our approach to protein-protein docking includes three main steps. First we run PIPER, a new rigid body docking program. PIPER is based on the Fast Fourier Transform (FFT) correlation approach that has been extended to use pairwise interactions potentials, thereby substantially increasing the number of near-native structures generated. The interaction potential is also new, based on the DARS (Decoys As the Reference State) principle. In the second step, the 1000 best energy conformations are clustered, and the 30 largest clusters are retained for refinement. Third, the conformations are refined by a new medium-range optimization method SDU (Semi-Definite programming based Underestimation). SDU has been developed to locate global minima within regions of the conformational space in which the energy function is funnel-like. The method constructs a convex quadratic underestimator function based on a set of local energy minima, and uses this function to guide future sampling. The combined method performed reliably without the direct use of biological information in most CAPRI problems that did not require homology modeling, providing acceptable predictions for targets 21, and medium quality predictions for targets 25 and 26., ((c) 2007 Wiley-Liss, Inc.)

The folding of Ser-Tyr-Pro-Phe-Asp-Val (SYPFDV), and sequence variants of this peptide (SYPYD and SYPFD) are studied computationally in an explicit water environment. An atomically detailed model of the peptide is embedded in a sphere of TIP3P water molecules and its optimal structure is computed by simulated annealing. At distances from the peptide that are beyond a few solvation shells, a continuum solvent model is employed. The simulations are performed using a mean field approach that enhances the efficiency of sampling peptide conformations. The computations predict a small number of conformations as plausible folded structures. All have a type VI turn conformation for the peptide backbone, similar to that found using NMR. However, some of the structures differ from the experimentally proposed ones in the packing of the proline ring with the aromatic residues. The second most populated structure has, in addition to a correctly folded backbone, the same hydrophobic packing as the conformation measured by NMR. Our simulations suggest a kinetic mechanism that consists of three separate stages. The time-scales associated with these stages are distinct and depend differently on temperature. Electrostatic interactions play an initial role in guiding the peptide chain to a roughly correct structure as measured by the end-to-end distance. At the same time or later the backbone torsions rearrange due to local tendency of the proline ring to form a turn: this step depends on solvation forces and is helped by loose hydrophobic interactions. In the final step, hydrophobic residues pack against each other. We also show the existence of an off the pathway intermediate, suggesting that even in the folding of a small peptide "misfolded" structures can form. The simulations clearly show that parallel folding paths are involved. Our findings suggest that the process of peptide folding shares many of the features expected for the significantly larger protein molecules., (Copyright 1997 Academic Press Limited.)

In order to allow for real dielectric properties of a solvent in calculating of electrostatic characteristics of strongly charged polyions such as DNA in salt solution we consider a simple model of linear dielectric response of a medium. The interactions between charged particles are treated in the framework of self-consistent-field approximation. The basic characteristic of the problem, electrostatic potential, can be found from the solution of non-linear integro-differential equation. Specifically we consider so-called quasimacroscopic model where dielectric response of a medium depends only on the distance from the polyion. Application of the approach for calculating of the B-to-Z free energy qualitatively retains the main conclusion obtained previously within the model with fixed dielectric constant: non-monotonous behavior of the free energy differences as a function of ionic strength. At the same time, essential sensitivity of the results to specific values of dielectric parameters is observed.

Calculation of long-range electrostatic interactions is the most time-consuming step in theoretical simulation of the structure and dynamics of macromolecules. In practice very short cutoff distances are used, which may distort the behavior of the model system. We describe two accurate approaches to calculation of electrostatic forces based on hierarchical grouping of charges into cubes. The first is similar to the O(NlogN) algorithm developed by Barnes, J. and Hut, P., Nature (London) 324, 446-449 (1986), for simulation of a gravitational motion of N bodies. The second approach we formulate for a system with periodic boundary conditions in the nearest image approximation. The calculation of electrostatic interactions and a charge grouping procedure are faster than O(N2). The average inaccuracy in the force introduced by the grouping does not exceed 1%. We describe a small modification of the same approach which makes it suitable for long strongly charged polymers as well. This accurate approach to calculation of electrostatic interactions is illustrated with an example of the dynamics of ions near DNA. Quick equilibration of the ionic distribution is observed during molecular dynamics simulation if electrostatic forces are properly calculated, while the behavior and distribution of ions are less realistic when the conventional cutoff distances are used.

We consider the problem of the mean field (Poisson-Boltzmann) calculation of the electrostatic free energy for a strongly charged polyelectrolyte such as DNA in a salt solution. We compare two approaches to calculate the free energy: (i) direct one starting from the statistical-mechanical expression for the electrostatic free energy and (ii) the polyion charge variation method. In the infinite dilution limit (in respect to polyion) and in excess salt (IDLES) the two approaches are fully equivalent. This is shown by straight forward algebra. We have performed specific calculations of the free energy difference for the case of B-Z transition in DNA as a function of ionic strength. As expected, the two approaches led to identical results. The ionic strength dependence of the B-to-Z free energy proves to be concaved up and as a result Z-DNA is stabilized at low ionic concentration as well as at high salt, in full agreement with our previous results (M.D.Frank-Kamenetskii et al., J. Biomol. Struct. Dyn. 3, 35-42 (1985]. Our data quantitatively agree with the results of Soumpasis (D.M.Soumpasis, J. Biomol. Struct. Dyn. 6, 563-574 (1988]. However, his claim about the absence of the effect of stabilization of Z-DNA at low salt proves to be groundless, and the criticism of our earlier approach seems to be irrelevant.

Adjacent phosphate oxygen atoms in A and Z-DNA are located much closer together than in the B form and can be hydrated more economically due to the formation of water bridges between them, whereas in the B form phosphates are hydrated individually. This principle of hydration economy of phosphate groups discovered by Saenger and colleagues could not be applied to the B-D transition, which, like the B-A and B-Z transitions, occurs in a situation of water deficiency, because the distances between adjacent phosphates of individual polynucleotide chains in the D form are not much different from B-DNA. It follows from our calculations of B and D-DNA accessibility to solvent performed by the method of Lee & Richards, and from a simulation of solvent structure near DNA, that there is an economy of hydration only for the minor groove atoms. This feature and some experimental data can explain why only a limited range of sequences consisting of A.T or I.C pairs undergo the transition to the D form. The conformational transition in DNAs with such sequences to a poly[d(A]).poly[d(T])-like conformation (Bh-DNA), which is accompanied by a narrowing of the minor groove, can be explained in the same way. Calculations suggest that in the D-form minor groove of different A-T or I-C DNAs there is a double-layer hydration spine similar to that observed by Drew & Dickerson in the A-T tract of the d(C-G-C-G-A-A-T-T-C-G-C-G) dodecamer. The B-D and B-Bh transitions in A + T-rich DNAs can have biological implications, e.g. they can facilitate DNA bending upon the interaction with proteins.