Flexible docking in solution using metadynamics

Flexibility and binding affinity in protein-ligand, protein-protein and multi-component protein interactions: limitations of current computational approaches

The recognition process between a protein and a partner represents a significant theoretical challenge. In silico structure-based drug design carried out with nothing more than the three-dimensional structure of the protein has led to the introduction of many compounds into clinical trials and numerous drug approvals. Central to guiding the discovery process is to recognize active among non-active compounds. While large-scale computer simulations of compounds taken from a library (virtual screening) or designed de novo are highly desirable in the post-genomic area, many technical problems remain to be adequately addressed. This article presents an overview and discusses the limits of current computational methods for predicting the correct binding pose and accurate binding affinity. It also presents the performances of the most popular algorithms for exploring binary and multi-body protein interactions.

Substrate binding process and mechanistic functioning of type 1 11β-hydroxysteroid dehydrogenase from enhanced sampling methods

In humans, type 1 11β-hydroxysteroid dehydrogenase (11β-HSD-1) plays a key role in the regulation of the glucocorticoids balance by converting the inactive hormone cortisone into cortisol. Numerous functional aspects of 11β-HSD-1 have been understood thanks to the availability at the Worldwide Protein Data Bank of a number of X-ray structures of the enzyme either alone or in complex with inhibitors, and to several experimental data. However at present, a complete description of the dynamic behaviour of 11β-HSD-1 upon substrate binding is missing. To this aim we firstly docked cortisone into the catalytic site of 11β-HSD-1 (both wild type and Y177A mutant), and then we used steered molecular dynamics and metadynamics to simulate its undocking. This methodology helped shedding light at molecular level on the complex relationship between the enzyme and its natural substrate. In particular, the work highlights a) the reason behind the functional dimerisation of 11β-HSD-1, b) the key role of Y177 in the cortisone binding event, c) the fine tuning of the active site degree of solvation, and d) the role of the S228-P237 loop in ligand recognition.

A Combined Metadynamics and Umbrella Sampling Method for the Calculation of Ion Permeation Free Energy Profiles

Free energy calculations are one of the most useful methods for the study of ion transport mechanisms through confined spaces such as protein ion channels. Their reliability depends on a correctly defined reaction coordinate (RC). A straight line is usually not a proper RC for such complicated processes so in this work a combined metadynamics/umbrella sampling (MTD/US) method is proposed. In the combined method, the ion transport pathway is first identified by the MTD method and then the free energy profile or potential of mean force (PMF) along the path is calculated using umbrella sampling. This combined method avoids the discontinuity problem often associated with normal umbrella sampling calculations that assume a straight line RC and it provides a more physically accurate PMF for such processes. The method is demonstrated for the proton transport process through the protein channel of aquaporin-1.

Complete reconstruction of an enzyme-inhibitor binding process by molecular dynamics simulations

The understanding of protein-ligand binding is of critical importance for biomedical research, yet the process itself has been very difficult to study because of its intrinsically dynamic character. Here, we have been able to quantitatively reconstruct the complete binding process of the enzyme-inhibitor complex trypsin-benzamidine by performing 495 molecular dynamics simulations of free ligand binding of 100 ns each, 187 of which produced binding events with an rmsd less than 2 Å compared to the crystal structure. The binding paths obtained are able to capture the kinetic pathway of the inhibitor diffusing from solvent (S0) to the bound (S4) state passing through two metastable intermediate states S2 and S3. Rather than directly entering the binding pocket the inhibitor appears to roll on the surface of the protein in its transition between S3 and the final binding pocket, whereas the transition between S2 and the bound pose requires rediffusion to S3. An estimation of the standard free energy of binding gives ΔG° = -5.2 ± 0.4 kcal/mol (cf. the experimental value -6.2 kcal/mol), and a two-states kinetic model k(on) = (1.5 ± 0.2) × 10(8) M(-1) s(-1) and k(off) = (9.5 ± 3.3) × 10(4) s(-1) for unbound to bound transitions. The ability to reconstruct by simple diffusion the binding pathway of an enzyme-inhibitor binding process demonstrates the predictive power of unconventional high-throughput molecular simulations. Moreover, the methodology is directly applicable to other molecular systems and thus of general interest in biomedical and pharmaceutical research.

Studies of glutathione transferase P1-1 bound to a platinum(IV)-based anticancer compound reveal the molecular basis of its activation

Platinum-based cancer drugs, such as cisplatin, are highly effective chemotherapeutic agents used extensively for the treatment of solid tumors. However, their effectiveness is limited by drug resistance, which, in some cancers, has been associated with an overexpression of pi class glutathione S-transferase (GST P1-1), an important enzyme in the mercapturic acid detoxification pathway. Ethacraplatin (EA-CPT), a trans-Pt(IV) carboxylate complex containing ethacrynate ligands, was designed as a platinum cancer metallodrug that could also target cytosolic GST enzymes. We previously reported that EA-CPT was an excellent inhibitor of GST activity in live mammalian cells compared to either cisplatin or ethacrynic acid. In order to understand the nature of the drug-protein interactions between EA-CPT and GST P1-1, and to obtain mechanistic insights at a molecular level, structural and biochemical investigations were carried out, supported by molecular modeling analysis using quantum mechanical/molecular mechanical methods. The results suggest that EA-CPT preferentially docks at the dimer interface at GST P1-1 and subsequent interaction with the enzyme resulted in docking of the ethacrynate ligands at both active sites (in the H-sites), with the Pt moiety remaining bound at the dimer interface. The activation of the inhibitor by its target enzyme and covalent binding accounts for the strong and irreversible inhibition of enzymatic activity by the platinum complex.

Optimized Potential of Mean Force Calculations for Standard Binding Free Energies

The prediction of protein-ligand binding free energies is an important goal of computational biochemistry, yet accuracy, reproducibility, and cost remain a problem. Nevertheless, these are essential requirements for computational methods to become standard binding prediction tools in discovery pipelines. Here, we present the results of an extensive search for an optimal method based on an ensemble of umbrella sampling all-atom molecular simulations tested on the phosphorylated tetrapeptide, pYEEI, binding to the SH2 domain, resulting in an accurate and converged binding free energy of -9.0 ± 0.5 kcal/mol (compared to an experimental value of -8.0 ± 0.1 kcal/mol). We find that a minimum of 300 ns of sampling is required for every prediction, a target easily achievable using new generation accelerated MD codes. Convergence is obtained by using an ensemble of simulations per window, each starting from different initial conformations, and by optimizing window-width, orthogonal restraints, reaction coordinate harmonic potentials, and window-sample time. The use of uncorrelated initial conformations in neighboring windows is important for correctly sampling conformational transitions from the unbound to bound states that affect significantly the precision of the calculations. This methodology thus provides a general recipe for reproducible and practical computations of binding free energies for a class of semirigid protein-ligand systems, within the limit of the accuracy of the force field used.

A High-Throughput Steered Molecular Dynamics Study on the Free Energy Profile of Ion Permeation through Gramicidin A

Steered molecular dynamics (SMD) simulations for the calculation of free energies are well suited for high-throughput molecular simulations on a distributed infrastructure due to the simplicity of the setup and parallel granularity of the runs. However, so far, the computational cost limited the estimation of the free energy typically over just a few pullings, thus impeding the evaluation of statistical uncertainties involved. In this work, we performed two thousand pulls for the permeation of a potassium ion in the gramicidin A pore by all-atom molecular dynamics in order to assess the bidirectional SMD protocol with a proper amount of sampling. The estimated free energy profile still shows a statistical error of several kcal/mol, while the work distributions are estimated to be non-Gaussian at pulling speeds of 10 Å/ns. We discuss the methodology and the confidence intervals in relation to increasing amounts of computed trajectories and how different permeation pathways for the potassium ion, knock-on and sideways, affect the sampling and the free energy estimation.

Physics-based scoring of protein–ligand interactions: explicit polarizability, quantum mechanics and free energies

The ability to accurately predict the interaction of a ligand with its receptor is a key limitation in computer-aided drug design approaches such as virtual screening and de novo design. In this article, we examine current strategies for a physics-based approach to scoring of protein–ligand affinity, as well as outlining recent developments in force fields and quantum chemical techniques. We also consider advances in the development and application of simulation-based free energy methods to study protein–ligand interactions. Fuelled by recent advances in computational algorithms and hardware, there is the opportunity for increased integration of physics-based scoring approaches at earlier stages in computationally guided drug discovery. Specifically, we envisage increased use of implicit solvent models and simulation-based scoring methods as tools for computing the affinities of large virtual ligand libraries. Approaches based on end point simulations and reference potentials allow the application of more advanced potential energy functions to prediction of protein–ligand binding affinities. Comprehensive evaluation of polarizable force fields and quantum mechanical (QM)/molecular mechanical and QM methods in scoring of protein–ligand interactions is required, particularly in their ability to address challenging targets such as metalloproteins and other proteins that make highly polar interactions. Finally, we anticipate increasingly quantitative free energy perturbation and thermodynamic integration methods that are practical for optimization of hits obtained from screened ligand libraries

Structural ensemble in computational drug screening

IMPORTANCE OF THE FIELD

Structure-based in silico drug screening is now widely used in drug development projects. Structure-based in silico drug screening is generally performed using a protein-compound docking program and docking scoring function. Many docking programs have been developed over the last 2 decades, but their prediction accuracy remains insufficient.

AREAS COVERED IN THIS REVIEW

This review highlights the recent progress of the post-processing of protein-compound complexes after docking.

WHAT THE READER WILL GAIN

These methods utilize ensembles of docking poses of compounds to improve the prediction accuracy for the ligand-docking pose and screening results. While the individual docking poses are not reliable, the free energy surface or the most probable docking pose can be estimated from the ensemble of docking poses.

TAKE HOME MESSAGE

The protein-compound docking program provides an arbitral rather than a canonical ensemble of docking poses. When the ensemble of docking poses satisfies the canonical ensemble, we can discuss how these post-docking analysis methods work and fail. Thus, improvements to the docking software will be needed in order to generate well-defined ensembles of docking poses.

Molecular motions in drug design: the coming age of the metadynamics method

Metadynamics is emerging as a useful free energy method in physics, chemistry and biology. Recently, it has been applied also to investigate ligand binding to biomolecules of pharmacological interest. Here, after introducing the basic idea of the method, we review applications to challenging targets for pharmaceutical intervention. We show that this methodology, especially when combined with a variety of other computational approaches such as molecular docking and/or molecular dynamics simulation, may be useful to predict structure and energetics of ligand/target complexes even when the targets lack a deep binding cavity, such as DNA and proteins undergoing fibrillation in neurodegenerative diseases. Furthermore, the method allows investigating the routes of molecular recognition and the associated binding energy profiles, providing a molecular interpretation to experimental data.

Free-energy-based methods for binding profile determination in a congeneric series of CDK2 inhibitors

Free-energy pathway methods show great promise in computing the mode of action and the free energy profile associated with the binding of small molecules with proteins, but are generally very computationally demanding. Here we apply a novel approach based on metadynamics and path collective variables. We show that this combination is able to find an optimal reaction coordinate and the free energy profile of binding with explicit solvent and full flexibility, while minimizing human intervention and computational costs. We apply it to predict the binding affinity of a congeneric series of 5 CDK2 inhibitors. The predicted binding free energy profiles are in accordance with experiment.

Computer-aided drug-discovery techniques that account for receptor flexibility

Protein flexibility plays a critical role in ligand binding to both orthosteric and allosteric sites. We here review some of the computer-aided drug-design techniques currently used to account for protein flexibility, ranging from methods that probe local receptor flexibility in the region of the protein immediately adjacent to the binding site, to those that account for general flexibility in all protein regions.

Protein dynamics and ligand migration interplay as studied by computer simulation

Since proteins are dynamic systems in living organisms, the employment of methodologies contemplating this crucial characteristic results fundamental to allow revealing several aspects of their function. In this work, we present results obtained using classical mechanical atomistic simulation tools applied to understand the connection between protein dynamics and ligand migration. Firstly, we will present a review of the different sampling schemes used in the last years to obtain both ligand migration pathways and the thermodynamic information associated with the process. Secondly, we will focus on representative examples in which the schemes previously presented are employed, concerning the following: i) ligand migration, tunnels, and cavities in myoglobin and neuroglobin; ii) ligand migration in truncated hemoglobin members; iii) NO escape and conformational changes in nitrophorins; iv) ligand selectivity in catalase and hydrogenase; and v) larger ligand migration: the P450 and haloalkane dehalogenase cases. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.

Prediction of protein-ligand binding affinity by free energy simulations: assumptions, pitfalls and expectations

Many limitations of current computer-aided drug design arise from the difficulty of reliably predicting the binding affinity of a small molecule to a biological target. There is thus a strong interest in novel computational methodologies that claim predictions of greater accuracy than current scoring functions, and at a throughput compatible with the rapid pace of drug discovery in the pharmaceutical industry. Notably, computational methodologies firmly rooted in statistical thermodynamics have received particular attention in recent years. Yet free energy calculations can be daunting to learn for a novice user because of numerous technical issues and various approaches advocated by experts in the field. The purpose of this article is to provide an overview of the current capabilities of free energy calculations and to discuss the applicability of this technology to drug discovery.

Molecular basis of cyclooxygenase enzymes (COXs) selective inhibition

The widely used nonsteroidal anti-inflammatory drugs block the cyclooxygenase enzymes (COXs) and are clinically used for the treatment of inflammation, pain, and cancers. A selective inhibition of the different isoforms, particularly COX-2, is desirable, and consequently a deeper understanding of the molecular basis of selective inhibition is of great demand. Using an advanced computational technique we have simulated the full dissociation process of a highly potent and selective inhibitor, SC-558, in both COX-1 and COX-2. We have found a previously unreported alternative binding mode in COX-2 explaining the time-dependent inhibition exhibited by this class of inhibitors and consequently their long residence time inside this isoform. Our metadynamics-based approach allows us to illuminate the highly dynamical character of the ligand/protein recognition process, thus explaining a wealth of experimental data and paving the way to an innovative strategy for designing new COX inhibitors with tuned selectivity.

Substrate binding mechanism of HIV-1 protease from explicit-solvent atomistic simulations

The binding mechanism of a peptide substrate (Thr-Ile-Met-Met-Gln-Arg, cleavage site p2-NC of the viral polyprotein) to wild-type HIV-1 protease has been investigated by 1.6 micros biased all-atom molecular dynamics simulations in explicit water. The configuration space has been explored biasing seven reaction coordinates by the bias-exchange metadynamics technique. The structure of the Michaelis complex is obtained starting from the substrate outside the enzyme within a backbone rmsd of 0.9 A. The calculated free energy of binding is -6 kcal/mol, and the kinetic constants for association and dissociation are 1.3 x 10(6) M(-1) s(-1) and 57 s(-1), respectively, consistent with experiments. In the main binding pathway, the flaps of the protease do not open sizably. The substrate slides inside the enzyme cavity from the tight lateral channel. This may contrast with the natural polyprotein substrate which is expected to bind by opening the flaps. Thus, mutations might influence differently the binding kinetics of peptidomimetic ligands and of the natural substrate.

Conformational free energy surface of alpha-N-acetylneuraminic acid: an interplay between hydrogen bonding and solvation

The conformational free energy surface of alpha-N-acetylneuraminic acid (Neu5Ac, sialic acid) in the space of ring-puckering coordinates was calculated using the metadynamics method. Free energy surfaces in vacuum and with an explicit solvent were calculated in GLYCAM 06 force field. In vacuum three structures are almost equivalently populated, namely, the (2)C(5) chair and the B(3,6)/(2)S(6) and (O)S(3) boat/skew-boat conformations. The B(3,6)/(2)S(6) structure is stabilized by an ionic hydrogen bond between the amide N-H bond and the carboxylic group. However, this structure is unfavorable in a water environment in which the experimentally observed (2)C(5) chair conformation is predicted to be more stable than the other structures. These results indicate that environment significantly influences conformation of Neu5Ac and that Neu5Ac-processing enzymes might modify a conformation of their substrates solely by a changing polarity of the environment. The structure of Neu5Ac bound in influenza neuraminidase ((4)S(2)/B(2,5)) belongs to conformations preferred in a water environment. The free energy penalty of this conformational change was calculated (relative to (2)C(5)) as 10.2 +/- 2.0 and 17.3 +/- 2.0 kJ/mol for (4,O)B/(O)S(3) and (4)S(2), respectively. This result indicates that mimicking of the enzyme-bound conformation is likely to be a viable strategy for the design of neuraminidase inhibitors.

Docking Ligands on Protein Surfaces: The Case Study of Prion Protein

Molecular docking of ligands targeting proteins undergoing fibrillization in neurodegenerative diseases is difficult because of the lack of deep binding sites. Here we extend standard docking methods with free energy simulations in explicit solvent to address this issue in the context of the prion protein surface. We focus on a specific ligand (2-pyrrolidin-1-yl-N-[4-[4-(2-pyrrolidin-1-yl-acetylamino)-benzyl]-phenyl]-acetamide), which binds to the structured part of the protein as shown by NMR (Kuwata, K. et al. Proc Natl Acad Sci U.S.A. 2007, 104, 11921-11926). The calculated free energy of dissociation (7.8 ± 0.9 kcal/mol) is in good agreement with the value derived by the experimental dissociation constant (Kd = 3.9 μM, corresponding to ΔG(0) = -7.5 kcal/mol). Several binding poses are predicted, including the one reported previously. Our prediction is fully consistent with the presence of multiple binding sites, emerging from NMR measurements. Our molecular simulation-based approach emerges, therefore, as a useful tool to predict poses and affinities of ligand binding to protein surfaces.

Mechanism and energetics of charybdotoxin unbinding from a potassium channel from molecular dynamics simulations

Ion channel-toxin complexes are ideal systems for computational studies of protein-ligand interactions, because, in most cases, the channel axis provides a natural reaction coordinate for unbinding of a ligand and a wealth of physiological data is available to check the computational results. We use a recently determined structure of a potassium channel-charybdotoxin complex in molecular dynamics simulations to investigate the mechanism and energetics of unbinding. Pairs of residues on the channel protein and charybdotoxin that are involved in the binding are identified, and their behavior is traced during umbrella-sampling simulations as charybdotoxin is moved away from the binding site. The potential of mean force for the unbinding of charybdotoxin is constructed from the umbrella sampling simulations using the weighted histogram analysis method, and barriers observed are correlated with specific breaking of interactions and influx of water molecules into the binding site. Charybdotoxin is found to undergo conformational changes as a result of the reaction coordinate choice--a nontrivial decision for larger ligands--which we explore in detail, and for which we propose solutions. Agreement between the calculated and the experimental binding energies is obtained once the energetic consequences of these conformational changes are included in the calculations.

Consistent improvement of cross-docking results using binding site ensembles generated with elastic network normal modes

The representation of protein flexibility is still a challenge for the state-of-the-art flexible ligand docking protocols. In this article, we use a large and diverse benchmark to prove that is possible to improve consistently the cross-docking performance against a single receptor conformation, using an equilibrium ensemble of binding site conformers. The benchmark contained 28 proteins, and our method predicted the top-ranked near native ligand poses 20% more efficiently than using a single receptor. The multiple conformations were derived from the collective variable space defined by all heavy-atom elastic network normal modes, including backbone and side chains. We have found that the binding site displacements for best positioning of the ligand seem rather independent from the global collective motions of the protein. We also found that the number of binding site conformations needed to represent nonredundant flexibility was < 100. The ensemble of receptor conformations can be generated at our Web site at http://abagyan.scripps.edu/MRC.

Standard Free Energy of Binding from a One-Dimensional Potential of Mean Force

A practical approach that enables one to calculate the standard free energy of binding from a one-dimensional potential of mean force (PMF) is proposed. Umbrella sampling and the weighted histogram analysis method are used to generate a PMF along the reaction coordinate of binding. At each point, a restraint is applied orthogonal to the reaction coordinate to make possible the determination of the volume sampled by the ligand. The free energy of binding from an arbitrary unbound volume to the restrained bound form is calculated from the ratio of the PMF integrated over the bound region to that of the unbound. Adding the free energy changes from the standard-state volume to the unbound volume and from the restrained to the unrestrained bound state gives the standard free energy of binding. Exploration of the best choice of binding paths is also made. This approach is first demonstrated on a model binding system and then tested on the benzamidine-trypsin system for which reasonable agreement with experiment is found. A comparison is made with other methods to obtain the standard free energy of binding from the PMF.

Progress in ab initio QM/MM free-energy simulations of electrostatic energies in proteins: accelerated QM/MM studies of pKa, redox reactions and solvation free energies

Hybrid quantum mechanical/molecular mechanical (QM/MM) approaches have been used to provide a general scheme for chemical reactions in proteins. However, such approaches still present a major challenge to computational chemists, not only because of the need for very large computer time in order to evaluate the QM energy but also because of the need for proper computational sampling. This review focuses on the sampling issue in QM/MM evaluations of electrostatic energies in proteins. We chose this example since electrostatic energies play a major role in controlling the function of proteins and are key to the structure-function correlation of biological molecules. Thus, the correct treatment of electrostatics is essential for the accurate simulation of biological systems. Although we will be presenting different types of QM/MM calculations of electrostatic energies (and related properties) here, our focus will be on pKa calculations. This reflects the fact that pKa's of ionizable groups in proteins provide one of the most direct benchmarks for the accuracy of electrostatic models of macromolecules. While pKa calculations by semimacroscopic models have given reasonable results in many cases, existing attempts to perform pKa calculations using QM/MM-FEP have led to discrepancies between calculated and experimental values. In this work, we accelerate our QM/MM calculations using an updated mean charge distribution and a classical reference potential. We examine both a surface residue (Asp3) of the bovine pancreatic trypsin inhibitor and a residue buried in a hydrophobic pocket (Lys102) of the T4-lysozyme mutant. We demonstrate that, by using this approach, we are able to reproduce the relevant side chain pKa's with an accuracy of 3 kcal/mol. This is well within the 7 kcal/mol energy difference observed in studies of enzymatic catalysis, and is thus sufficient accuracy to determine the main contributions to the catalytic energies of enzymes. We also provide an overall perspective of the potential of QM/MM calculations in general evaluations of electrostatic free energies, pointing out that our approach should provide a very powerful and accurate tool to predict the electrostatics of not only solution but also enzymatic reactions, as well as the solvation free energies of even larger systems, such as nucleic acid bases incorporated into DNA.

Alpha7 nicotinic acetylcholine receptor agonists: prediction of their binding affinity through a molecular mechanics Poisson-Boltzmann surface area approach

A group of agonists for the alpha7 neuronal nicotinic acetylcholine receptors (nAChRs) was investigated, and their free energies of binding DeltaG(bind) were calculated by applying the molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) approach. This method, based on molecular dynamics simulations of fully solvated protein-ligand complexes, allowed us to estimate the contribution of both polar and nonpolar terms as well as the entropy to the overall free energy of binding. The calculated results were in a good agreement with the experimentally determined DeltaG(bind) values, thereby pointing to the MM-PBSA protocol as a valuable computational tool for the rational design of specific agents targeting the neuronal alpha7 nAChR subtypes.

Metadynamic sampling of the free-energy landscapes of proteins coupled with a Monte Carlo algorithm

Metadynamics is a powerful computational tool to obtain the free-energy landscape of complex systems. The Monte Carlo algorithm has proven useful to calculate thermodynamic quantities associated with simplified models of proteins, and thus to gain an ever-increasing understanding on the general principles underlying the mechanism of protein folding. We show that it is possible to couple metadynamics and Monte Carlo algorithms to obtain the free energy of model proteins in a way which is computationally very economical.

Dissociation of minor groove binders from DNA: insights from metadynamics simulations

We have used metadynamics to investigate the mechanism of noncovalent dissociation from DNA by two representatives of alkylating and noncovalent minor groove (MG) binders. The compounds are anthramycin in its anhydrous form (IMI) and distamycin A (DST), which differ in mode of binding, size, flexibility and net charge. This choice enables to evaluate the influence of such factors on the mechanism of dissociation. Dissociation of IMI requires an activation free energy of approximately 12 kcal/mol and occurs via local widening of the MG and loss of contacts between the drug and one DNA strand, along with the insertion of waters in between. The detachment of DST occurs at a larger free energy cost, approximately 16.5 or approximately 18 kcal/mol depending on the binding mode. These values compare well with that of 16.6 kcal/mol extracted from stopped-flow experiments. In contrast to IMI, an intermediate is found in which the ligand is anchored to the DNA through its amidinium tail. From this conformation, binding and unbinding occur almost at the same rate. Comparison between DST and with kinetic models for the dissociation of Hoechst 33258 from DNA uncovers common characteristics across different classes of noncovalent MG ligands.

Adaptively biased molecular dynamics for free energy calculations

We present an adaptively biased molecular dynamics (ABMD) method for the computation of the free energy surface of a reaction coordinate using nonequilibrium dynamics. The ABMD method belongs to the general category of umbrella sampling methods with an evolving biasing potential and is inspired by the metadynamics method. The ABMD method has several useful features, including a small number of control parameters and an O(t) numerical cost with molecular dynamics time t. The ABMD method naturally allows for extensions based on multiple walkers and replica exchange, where different replicas can have different temperatures and/or collective variables. This is beneficial not only in terms of the speed and accuracy of a calculation, but also in terms of the amount of useful information that may be obtained from a given simulation. The workings of the ABMD method are illustrated via a study of the folding of the Ace-GGPGGG-Nme peptide in a gaseous and solvated environment.

Docking to RNA via root-mean-square-deviation-driven energy minimization with flexible ligands and flexible targets

Structure-based drug design is now well-established for proteins as a key first step in the lengthy process of developing new drugs. In many ways, RNA may be a better target to treat disease than a protein because it is upstream in the translation pathway, so inhibiting a single mRNA molecule could prevent the production of thousands of protein gene products. Virtual screening is often the starting point for structure-based drug design. However, computational docking of a small molecule to RNA seems to be more challenging than that to protein due to the higher intrinsic flexibility and highly charged structure of RNA. Previous attempts at docking to RNA showed the need for a new approach. We present here a novel algorithm using molecular simulation techniques to account for both nucleic acid and ligand flexibility. In this approach, with both the ligand and the receptor permitted some flexibility, they can bind one another via an induced fit, as the flexible ligand probes the surface of the receptor. A possible ligand can explore a low-energy path at the surface of the receptor by carrying out energy minimization with root-mean-square-distance constraints. Our procedure was tested on 57 RNA complexes (33 crystal and 24 NMR structures); this is the largest data set to date to reproduce experimental RNA binding poses. With our procedure, the lowest-energy conformations reproduced the experimental binding poses within an atomic root-mean-square deviation of 2.5 A for 74% of tested complexes.

Towards the development of universal, fast and highly accurate docking/scoring methods: a long way to go

Accelerating the drug discovery process requires predictive computational protocols capable of reducing or simplifying the synthetic and/or combinatorial challenge. Docking-based virtual screening methods have been developed and successfully applied to a number of pharmaceutical targets. In this review, we first present the current status of docking and scoring methods, with exhaustive lists of these. We next discuss reported comparative studies, outlining criteria for their interpretation. In the final section, we describe some of the remaining developments that would potentially lead to a universally applicable docking/scoring method.

A new method for ligand docking to flexible receptors by dual alanine scanning and refinement (SCARE)

Protein binding sites undergo ligand specific conformational changes upon ligand binding. However, most docking protocols rely on a fixed conformation of the receptor, or on the prior knowledge of multiple conformations representing the variation of the pocket, or on a known bounding box for the ligand. Here we described a general induced fit docking protocol that requires only one initial pocket conformation and identifies most of the correct ligand positions as the lowest score. We expanded a previously used diverse "cross-docking" benchmark to thirty ligand-protein pairs extracted from different crystal structures. The algorithm systematically scans pairs of neighbouring side chains, replaces them by alanines, and docks the ligand to each 'gapped' version of the pocket. All docked positions are scored, refined with original side chains and flexible backbone and re-scored. In the optimal version of the protocol pairs of residues were replaced by alanines and only one best scoring conformation was selected from each 'gapped' pocket for refinement. The optimal SCARE (SCan Alanines and REfine) protocol identifies a near native conformation (under 2 angstroms RMSD) as the lowest rank for 80% of pairs if the docking bounding box is defined by the predicted pocket envelope, and for as many as 90% of the pairs if the bounding box is derived from the known answer with approximately 5 angstroms margin as used in most previous publications. The presented fully automated algorithm takes about 2 h per pose of a single processor time, requires only one pocket structure and no prior knowledge about the binding site location. Furthermore, the results for conformationally conserved pockets do not deteriorate due to substantial increase of the pocket variability.

Ab initio calculations of free-energy reaction barriers

The theoretical description of chemical reactions was until recently limited to a 'static' approach in which important parameters such as the rate constant are deduced from the local topology of the potential energy surface close to minima and saddle points. Such an approach has, however, serious limitations. The growing computational power allows us now to use advanced simulation techniques to determine entropic effects accurately for medium-sized systems at ab initio level. Recently, we have implemented free-energy simulation techniques based on molecular dynamics, in particular on the blue-moon ensemble technique and on metadynamics, in the popular DFT code VASP. In the thermodynamic integration (blue-moon ensemble) technique, the free-energy profile is calculated as the path integral over the restoring forces along a parametrized reaction coordinate. In metadynamics, an image of the free-energy surface is constructed on the fly during the simulation by adding small repulsive Gaussian-shaped hills to the Lagrangian driving the dynamics. The two methods are tested on a simple chemical reaction-the nucleophilic substitution of methyl chloride by a chlorine anion.

Well-tempered metadynamics: a smoothly converging and tunable free-energy method

We present a method for determining the free-energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting cases. Convergence and errors can be rigorously and easily controlled. The parameters of the simulation can be tuned so as to focus the computational effort only on the physically relevant regions of the order parameter space. The algorithm is tested on the reconstruction of an alanine dipeptide free-energy landscape.

The role of Li + , Na + , and K + in the ligand binding inside the human acetylcholinesterase gorge

Alkali cations can affect the catalytic efficiency of enzymes. This is particularly true when dealing with enzymes whose substrate bears a formal positive charge. Computational and biochemical approaches have been combined to shed light on the atomic aspects of the role of Li(+), Na(+), and K(+) on human acetylcholinesterase (hAChE) ligand binding. In this respect, molecular dynamics simulations and our recently developed metadynamics method were applied to study the entrance of the three cations in the gorge of hAChE, and their effect on the dynamical motion of a ligand (tetramethylammonium) from the bulk of the solvent into the deep narrow enzyme gorge. Furthermore, in order to support the theoretical results, K(M) and k(cat) for the acetylcholine hydrolysis in the presence of the three cations were evaluated by using an approach based on the Ellman's method. The combination of computational and biochemical experiments clearly showed that Li(+), Na(+), and K(+) may influence the ligand binding at the hAChE gorge.

Molecular docking for substrate identification: the short-chain dehydrogenases/reductases

Protein ligand docking has recently been investigated as a tool for protein function identification, with some success in identifying both known and unknown substrates of proteins. However, identifying a protein's substrate when cross-docking a large number of enzymes and their cognate ligands remains a challenge. To explore a more limited yet practically important and timely problem in more detail, we have used docking for identifying the substrates of a single protein family with remarkable substrate diversity, the short-chain dehydrogenases/reductases. We examine different protocols for identifying candidate substrates for 27 short-chain dehydrogenase/reductase proteins of known catalytic function. We present the results of docking >900 metabolites from the human metabolome to each of these proteins together with their known cognate substrates and products, and we investigate the ability of docking to (a) reproduce a viable binding mode for the substrate and (b) to rank the substrate highly amongst the dataset of other metabolites. In addition, we examine whether our docking results provide information about the nature of the substrate, based on the best-scoring metabolites in the dataset. We compare two different docking methods and two alternative scoring functions for one of the docking methods, and we attempt to rationalise both successes and failures. Finally, we introduce a new protocol, whereby we dock only a set of representative structures (medoids) to each of the proteins, in the hope of characterising each binding site in terms of its ligand preferences, with a reduced computational cost. We compare the results from this protocol with our original docking experiments, and we find that although the rank of the representatives correlates well with the mean rank of the clusters to which they belong, a simple structure-based clustering is too naive for the purpose of substrate identification. Many clusters comprise ligands with widely varying affinities for the same protein; hence important candidates can be missed if a single representative is used.

QM/MM metadynamics study of the direct decarboxylation mechanism for orotidine-5'-monophosphate decarboxylase using two different QM regions: acceleration too small to explain rate of enzyme catalysis

Despite decades of study, the mechanism by which orotidine-5'-monophosphate decarboxylase (ODCase) catalyzes the decarboxylation of orotidine monophosphate remains unresolved. A computational investigation of the direct decarboxylation mechanism has been performed using mixed quantum mechanical/molecular mechanical (QM/MM) dynamics simulations. The study was performed with the program CP2K that integrates classical dynamics and ab initio dynamics based on the Born-Oppenheimer approach. Two different QM regions were explored. The free energy barriers for direct decarboxylation of orotidine-5'-monophosphate (OMP) in solution and in the enzyme (using the larger QM region) were determined with the metadynamics method to be 40 and 33 kcal/mol, respectively. The calculated change in activation free energy (DeltaDeltaG++) on going from solution to the enzyme is therefore -7 kcal/mol, far less than the experimental change of -23 kcal/ mol (for k(cat.)/k(uncat.): Radzicka, A.; Wolfenden, R., Science 1995, 267, 90-92). These results do not support the direct decarboxylation mechanism that has been proposed for the enzyme. However, in the context of QM/MM calculations, it was found that the size of the QM region has a dramatic effect on the calculated reaction barrier.

Binding of Organic Cations to Gramicidin A Channel Studied with AutoDock and Molecular Dynamics Simulations

The accurate description of protein-ligand binding energies and configurations is an important problem in molecular biology with many applications in medicine and pharmacology. Molecular dynamics (MD) simulations provide the required accuracy but they are too slow for searching binding positions. Conversely, docking methods are much faster but have limited accuracy. An appropriate combination of the two methods could avoid the shortcomings associated with each, thus offering a better approach to the protein-ligand binding problem. Here we investigate the feasibility of such a combined docking-MD approach in a well-defined system: binding of organic cations to the gramicidin A channel. We use the AutoDock program to generate a set of protein-ligand binding configurations, which are then refined in MD simulations. For each system, we examine the binding configuration in detail and calculate the binding free energy by constructing the potential of mean force for the ligand. Our results show that AutoDock provides suitable initial configurations, which can be used profitably in MD simulations to obtain an accurate description of protein-ligand binding with a reasonable computational effort.

Towards a Rational Design of Ruthenium CO2 Hydrogenation Catalysts by Ab Initio Metadynamics

Complete reaction pathways relevant to CO2 hydrogenation by using a homogeneous ruthenium dihydride catalyst ([Ru(dmpe)2H2], dmpe=Me2PCH2CH2PMe2) have been investigated by ab initio metadynamics. This approach has allowed reaction intermediates to be identified and free-energy profiles to be calculated, which provide new insights into the experimentally observed reaction pathway. Our simulations indicate that CO2 insertion, which leads to the formation of formate complexes, proceeds by a concerted insertion mechanism. It is a rapid and direct process with a relatively low activation barrier, which is in agreement with experimental observations. Subsequent H2 insertion into the formate--Ru complex, which leads to the formation of formic acid, instead occurs via an intermediate [Ru(eta2-H2)] complex in which the molecular hydrogen coordinates to the ruthenium center and interacts weakly with the formate group. This step has been identified as the rate-limiting step. The reaction completes by hydrogen transfer from the [Ru(eta2-H2)] complex to the formate oxygen atom, which forms a dihydrogen-bonded Ru--HHO(CHO) complex. The activation energy for the H2 insertion step is lower for the trans isomer than for the cis isomer. A simple measure of the catalytic activity was proposed based on the structure of the transition state of the identified rate-limiting step. From this measure, the relationship between catalysts with different ligands and their experimental catalytic activities can be explained.

Insight into the folding inhibition of the HIV-1 protease by a small peptide

It has recently been shown that the highly protected segments 24-34 (S2) and 83-93 (S8) of each of the two 99-mers of human immunodeficiency virus type 1 protease play an essential role in the folding of the monomers, giving rise to the so-called (postcritical) folding nucleus ((FN) minimum condensation unit ensuring folding) when they dock. This scenario received further support from model calculations that demonstrated that the peptide p-S8, displaying an amino acid sequence identical to the corresponding (83-93) segment of the monomer, can be used to interfere with the formation of the FN and eventually to inhibit folding by docking the fragment 24-34. Experiments in vitro and in cells infected with ex vivo wild-type and multiresistant HIV isolates confirm that the inhibition power of p-S8 is robust. On the other hand, there is no direct evidence demonstrating the validity of the proposed mechanism of inhibition associated with p-S8. To shed light on this question and to provide the basis for the design of a molecule mimetic to p-S8, to be used as lead of an eventual drug against AIDS, we study, in this paper, with the help of all-atom simulations in explicit solvent and the novel method of metadynamics combined with parallel tempering: a), the free energy and the equilibrium structure of each of the peptides p-S2 and p-S8; b), the details of the docking mechanism of the two peptides and the free energy associated with this process. Whereas p-S8 is found to be well structured, p-S2 is rather flexible, wrapping itself around p-S8 to give rise to the FN, which is stabilized by three particular hydrogen bonds.

Docking of ATP to Ca-ATPase: considering protein domain motions

Most standard molecular docking algorithms take into account only ligand flexibility, while numerous studies demonstrate that receptor flexibility may be also important. While some efficient methods have been proposed to take into account local flexibility of protein side chains, the influence of large-scale domain motions on the docking results still represents a challenge for computational methods. In this work we compared the results of ATP docking to different models of Ca-ATPase: crystallographic apo- and holo-forms of the enzyme as well as "flexible" target models generated via molecular dynamics (MD) simulations in water. MD simulations were performed for two different apo-forms and one holo-form of Ca2+-ATPase and reveal large-scale domain motions of type "closure", which is consistent with experimental structures. Docking to a set of MD-conformers yielded correct solutions with ATP bound in both domains regardless of the starting Ca2+-ATPase structure. Also, special attention was paid to proper ranking of docking solutions and some particular features of different scoring functions and their applicability for the model of "flexible" receptor. Particularly, the results of docking ATP were ranked by a scoring criterion specially designed to estimate ATP-protein interactions. This criterion includes stacking and hydrophobic interactions characteristic of ATP-protein complexes. The performance of this ligand-specific scoring function was considerably better than that of a standard scoring function used in the docking algorithm.

A Bias-Exchange Approach to Protein Folding

By suitably extending a recent approach [Bussi, G.; et al. J. Am. Chem. Soc. 2006, 128, 13435] we introduce a powerful methodology that allows the parallel reconstruction of the free energy of a system in a virtually unlimited number of variables. Multiple metadynamics simulations of the same system at the same temperature are performed, biasing each replica with a time-dependent potential constructed in a different set of collective variables. Exchanges between the bias potentials in the different variables are periodically allowed according to a replica exchange scheme. Due to the efficaciously multidimensional nature of the bias the method allows exploring complex free energy landscapes with high efficiency. The usefulness of the method is demonstrated by performing an atomistic simulation in explicit solvent of the folding of a Triptophane cage miniprotein. It is shown that the folding free energy landscape can be fully characterized starting from an extended conformation with use of only 40 ns of simulation on 8 replicas.

Can MM-PBSA calculations predict the specificities of protein kinase inhibitors?

An application of the molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) protocol to the prediction of protein kinase inhibitor selectivity is presented. Six different inhibitors are placed in equivalent orientations in each of six different receptors. Fully solvated molecular dynamics is then run for 1 ns on each of the 36 complexes, and the resulting trajectories scored, using the implicit solvent model. The results show some correlation with experimentally-determined specificities; anomalies may be attributed to a variety of causes, including difficulties in quantifying induced fit penalties and variabilities in normal modes calculations. Decomposing interaction energies on a per-residue basis yields more useful insights into the natures of the binding modes and suggests that the real value of such calculations lies in understanding interactions rather than outright prediction.