Flexible docking in solution using metadynamics

The structural impact of DNA mismatches

The structure and dynamics of all the transversion and transition mismatches in three different DNA environments have been characterized by molecular dynamics simulations and NMR spectroscopy. We found that the presence of mismatches produced significant local structural alterations, especially in the case of purine transversions. Mismatched pairs often show promiscuous hydrogen bonding patterns, which interchange among each other in the nanosecond time scale. This therefore defines flexible base pairs, where breathing is frequent, and where distortions in helical parameters are strong, resulting in significant alterations in groove dimension. Even if the DNA structure is plastic enough to absorb the structural impact of the mismatch, local structural changes can be propagated far from the mismatch site, following the expected through-backbone and a previously unknown through-space mechanism. The structural changes related to the presence of mismatches help to understand the different susceptibility of mismatches to the action of repairing proteins.

Synthesis and antiplatelet activity of antithrombotic thiourea compounds: biological and structure-activity relationship studies

The incidence of hematological disorders has increased steadily in Western countries despite the advances in drug development. The high expression of the multi-resistance protein 4 in patients with transitory aspirin resistance, points to the importance of finding new molecules, including those that are not affected by these proteins. In this work, we describe the synthesis and biological evaluation of a series of N,N'-disubstituted thioureas derivatives using in vitro and in silico approaches. New designed compounds inhibit the arachidonic acid pathway in human platelets. The most active thioureas (compounds 3d, 3i, 3m and 3p) displayed IC₅₀ values ranging from 29 to 84 µM with direct influence over in vitro PGE₂ and TXA₂ formation. In silico evaluation of these compounds suggests that direct blockage of the tyrosyl-radical at the COX-1 active site is achieved by strong hydrophobic contacts as well as electrostatic interactions. A low toxicity profile of this series was observed through hemolytic, genotoxic and mutagenic assays. The most active thioureas were able to reduce both PGE₂ and TXB₂ production in human platelets, suggesting a direct inhibition of COX-1. These results reinforce their promising profile as lead antiplatelet agents for further in vivo experimental investigations.

The liquid-liquid transition in supercooled ST2 water: a comparison between umbrella sampling and well-tempered metadynamics

We investigate the metastable phase behaviour of the ST2 water model under deeply supercooled conditions. The phase behaviour is examined using umbrella sampling (US) and well-tempered metadynamics (WT-MetaD) simulations to compute the reversible free energy surface parameterized by density and bond-orientation order. We find that free energy surfaces computed with both techniques clearly show two liquid phases in coexistence, in agreement with our earlier US and grand canonical Monte Carlo calculations [Y. Liu, J. C. Palmer, A. Z. Panagiotopoulos and P. G. Debenedetti, J Chem Phys, 2012, 137, 214505; Y. Liu, A. Z. Panagiotopoulos and P. G. Debenedetti, J Chem Phys, 2009, 131, 104508]. While we demonstrate that US and WT-MetaD produce consistent results, the latter technique is estimated to be more computationally efficient by an order of magnitude. As a result, we show that WT-MetaD can be used to study the finite-size scaling behaviour of the free energy barrier separating the two liquids for systems containing 192, 300 and 400 ST2 molecules. Although our results are consistent with the expected N(2/3) scaling law, we conclude that larger systems must be examined to provide conclusive evidence of a first-order phase transition and associated second critical point.

Investigating drug-target association and dissociation mechanisms using metadynamics-based algorithms

CONSPECTUS: This Account highlights recent advances and discusses major challenges in the field of drug-target recognition, binding, and unbinding studied using metadynamics-based approaches, with particular emphasis on their role in structure-based design. Computational chemistry has significantly contributed to drug design and optimization in an extremely broad range of areas, including prediction of target druggability and drug likeness, de novo design, fragment screening, ligand docking, estimation of binding affinity, and modulation of ADMET (absorption, distribution, metabolism, excretion, toxicity) properties. Computationally driven drug discovery must continuously adapt to keep pace with the evolving knowledge of the factors that modulate the pharmacological action of drugs. There is thus an urgent need for novel computational approaches that integrate the vast amount of complex information currently available for small (bio)organic compounds, biologically relevant targets and their complexes, while also accounting accurately for the thermodynamics and kinetics of drug-target association, the intrinsic dynamical behavior of biomolecular systems, and the complexity of protein-protein networks. Understanding the mechanism of drug binding to and unbinding from biological targets is fundamental for optimizing lead compounds and designing novel biologically active ones. One major challenge is the accurate description of the conformational complexity prior to and upon formation of drug-target complexes. Recently, enhanced sampling methods, including metadynamics and related approaches, have been successfully applied to investigate complex mechanisms of drugs binding to flexible targets. Metadynamics is a family of enhanced sampling techniques aimed at enhancing the rare events and reconstructing the underlying free energy landscape as a function of a set of order parameters, usually referred to as collective variables. Studies of drug binding mechanisms have predicted the most probable association and dissociation pathways and the related binding free energy profile. In addition, the availability of an efficient open-source implementation, running on cost-effective GPU (i.e., graphical processor unit) architectures, has considerably decreased the learning curve and the computational costs of the methods, and increased their adoption by the community. Here, we review the recent contributions of metadynamics and other enhanced sampling methods to the field of drug-target recognition and binding. We discuss how metadynamics has been used to search for transition states, to predict binding and unbinding paths, to treat conformational flexibility, and to compute free energy profiles. We highlight the importance of such predictions in drug discovery. Major challenges in the field and possible solutions will finally be discussed.

Kinetics of protein-ligand unbinding: Predicting pathways, rates, and rate-limiting steps

The ability to predict the mechanisms and the associated rate constants of protein-ligand unbinding is of great practical importance in drug design. In this work we demonstrate how a recently introduced metadynamics-based approach allows exploration of the unbinding pathways, estimation of the rates, and determination of the rate-limiting steps in the paradigmatic case of the trypsin-benzamidine system. Protein, ligand, and solvent are described with full atomic resolution. Using metadynamics, multiple unbinding trajectories that start with the ligand in the crystallographic binding pose and end with the ligand in the fully solvated state are generated. The unbinding rate k off is computed from the mean residence time of the ligand. Using our previously computed binding affinity we also obtain the binding rate k on. Both rates are in agreement with reported experimental values. We uncover the complex pathways of unbinding trajectories and describe the critical rate-limiting steps with unprecedented detail. Our findings illuminate the role played by the coupling between subtle protein backbone fluctuations and the solvation by water molecules that enter the binding pocket and assist in the breaking of the shielded hydrogen bonds. We expect our approach to be useful in calculating rates for general protein-ligand systems and a valid support for drug design.

Elucidating the conformational energetics of glucose and cellobiose in ionic liquids

The energetics driving the conformational preference of the ω dihedral of glucose and the φ–ψ dihedrals of cellobiose solvated in imidazolium acetate ionic liquids and water are elucidated and compared.

Computational structural biology of opioid receptors

The publication of high-resolution structures for all of the opioid receptor subfamilies has unveiled exciting opportunities for mechanistic insight into the molecular mechanisms underlying the biology of nociception, reward, and higher cognitive functions, as well as promises for progress in several clinical areas such as pain management, physiological dependence, addiction, and mood disorders. To turn this promise into novel and improved therapeutic entities, however, this information needs to be supplemented with research strategies that explore the dynamic behavior of the proteins and their interactions with other receptors and ligands in their physiological environment.Here we describe state-of-the-art molecular dynamics computational protocols, based on all-atom and coarse-grained modeling techniques, designed to estimate crucial thermodynamic and kinetic parameters describing the binding of small-molecule ligands and the formation of supramolecular complexes.

Enhanced sampling techniques in biomolecular simulations

Biomolecular simulations are routinely used in biochemistry and molecular biology research; however, they often fail to match expectations of their impact on pharmaceutical and biotech industry. This is caused by the fact that a vast amount of computer time is required to simulate short episodes from the life of biomolecules. Several approaches have been developed to overcome this obstacle, including application of massively parallel and special purpose computers or non-conventional hardware. Methodological approaches are represented by coarse-grained models and enhanced sampling techniques. These techniques can show how the studied system behaves in long time-scales on the basis of relatively short simulations. This review presents an overview of new simulation approaches, the theory behind enhanced sampling methods and success stories of their applications with a direct impact on biotechnology or drug design.

Enhanced sampling techniques in molecular dynamics simulations of biological systems

BACKGROUND

Molecular dynamics has emerged as an important research methodology covering systems to the level of millions of atoms. However, insufficient sampling often limits its application. The limitation is due to rough energy landscapes, with many local minima separated by high-energy barriers, which govern the biomolecular motion.

SCOPE OF REVIEW

In the past few decades methods have been developed that address the sampling problem, such as replica-exchange molecular dynamics, metadynamics and simulated annealing. Here we present an overview over theses sampling methods in an attempt to shed light on which should be selected depending on the type of system property studied.

MAJOR CONCLUSIONS

Enhanced sampling methods have been employed for a broad range of biological systems and the choice of a suitable method is connected to biological and physical characteristics of the system, in particular system size. While metadynamics and replica-exchange molecular dynamics are the most adopted sampling methods to study biomolecular dynamics, simulated annealing is well suited to characterize very flexible systems. The use of annealing methods for a long time was restricted to simulation of small proteins; however, a variant of the method, generalized simulated annealing, can be employed at a relatively low computational cost to large macromolecular complexes.

GENERAL SIGNIFICANCE

Molecular dynamics trajectories frequently do not reach all relevant conformational substates, for example those connected with biological function, a problem that can be addressed by employing enhanced sampling algorithms. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Challenges in computational studies of enzyme structure, function and dynamics

In this review we give an overview of the field of Computational enzymology. We start by describing the birth of the field, with emphasis on the work of the 2013 chemistry Nobel Laureates. We then present key features of the state-of-the-art in the field, showing what theory, accompanied by experiments, has taught us so far about enzymes. We also briefly describe computational methods, such as quantum mechanics-molecular mechanics approaches, reaction coordinate treatment, and free energy simulation approaches. We finalize by discussing open questions and challenges.

Molecular Recognition of Platinated DNA from Chromosomal HMGB1

Cisplatin cures testicular and ovarian cancers with unprecedented potency. It induces its beneficial activity by covalently binding to DNA. Repair enzymes, which remove the platinated lesions from DNA, cause drug resistance. Chromosomal High Mobility Group Box proteins (HMGB) may interfere with this process by binding to platinated DNA. Using 8 μs multiple-walker well-tempered metadynamics simulations, here, we investigated the structural and the energetic determinants of one of the HMGB proteins (HMGB1A) in complex with the platinated oligonucleotide [Pt(NH3)2](2+)-d(CCUCTCTG*G*ACCTTCC)-d(GGAGAGACCTGGAAGG) (*G are platinated guanines), for which experimental structural information is available. The calculated affinity is in good agreement with experiment. The process is predicted to be enthalpy-driven, as found for other protein/DNA complexes. The Lys7 residue, whose side-chain was not resolved in the X-ray structure, is found to interact with the C4 5'-phosphate and this interaction emerges as a key facet for the molecular recognition process. In addition, our calculations provide a molecular basis for the experimentally measured decreased affinity of HMGB1A for platinated DNA, as a consequence of Cys22-Cys44 S-S bridge formation (such an oxidation cannot take place in some members of this protein family present in the testis, where the drug is particularly effective). This decrease is likely to be caused by a small yet significant rearrangement of helices H1 and H2 with consequent alteration of the Phe37 juxtaposition.

Well-tempered metadynamics converges asymptotically

Metadynamics is a versatile and capable enhanced sampling method for the computational study of soft matter materials and biomolecular systems. However, over a decade of application and several attempts to give this adaptive umbrella sampling method a firm theoretical grounding prove that a rigorous convergence analysis is elusive. This Letter describes such an analysis, demonstrating that well-tempered metadynamics converges to the final state it was designed to reach and, therefore, that the simple formulas currently used to interpret the final converged state of tempered metadynamics are correct and exact. The results do not rely on any assumption that the collective variable dynamics are effectively Brownian or any idealizations of the hill deposition function; instead, they suggest new, more permissive criteria for the method to be well behaved. The results apply to tempered metadynamics with or without adaptive Gaussians or boundary corrections and whether the bias is stored approximately on a grid or exactly.

Atomic picture of ligand migration in toluene 4-monooxygenase

Computational modeling combined with mutational and activity assays was used to underline the substrate migration pathways in toluene 4-monooxygenase, a member of the important family of bacterial multicomponent monooxygenases (BMMs). In all structurally defined BMM hydroxylases, several hydrophobic cavities in the α-subunit map a preserved path from the protein surface to the diiron active site. Our results confirm the presence of two pathways by which different aromatic molecules can enter/escape the active site. While the substrate is observed to enter from both channels, the more hydrophilic product is withdrawn mainly from the shorter channel ending at residues D285 and E214. The long channel ends in the vicinity of S395, whose variants have been seen to affect activity and specificity. These mutational effects are clearly reproduced and rationalized by the in silico studies. Furthermore, the combined computational and experimental results highlight the importance of residue F269, which is located at the intersection of the two channels.

The free energy landscape of pseudorotation in 3'-5' and 2'-5' linked nucleic acids

The five-membered furanose ring is a central component of the chemical structure of biological nucleic acids. The conformations of the furanose ring can be analytically described using the concept of pseudorotation, and for RNA and DNA they are dominated by the C2'-endo and C3'-endo conformers. While the free energy difference between these two conformers can be inferred from NMR measurements, a free energy landscape of the complete pseudorotation cycle of nucleic acids in solution has remained elusive. Here, we describe a new free energy calculation method for molecular dynamics (MD) simulations using the two pseudorotation parameters directly as the collective variables. To validate our approach, we calculated the free energy surface of ribose pseudorotation in guanosine and 2'-deoxyguanosine. The calculated free energy landscape reveals not only the relative stability of the different pseudorotation conformers, but also the main transition path between the stable conformations. Applying this method to a standard A-form RNA duplex uncovered the expected minimum at the C3'-endo state. However, at a 2'-5' linkage, the minimum shifts to the C2'-endo conformation. The free energy of the C3'-endo conformation is 3 kcal/mol higher due to a weaker hydrogen bond and a reduced base stacking interaction. Unrestrained MD simulations suggest that the conversion from C3'-endo to C2'-endo and vice versa is on the nanosecond and microsecond time scale, respectively. These calculations suggest that 2'-5' linkages may enable folded RNAs to sample a wider spectrum of their pseudorotation conformations.

Study of the B1-B2 transition in colloidal clusters

The possible mechanisms for the B1 (NaCl-type) to B2 (CsCl-type) transition in crystalline colloidal clusters of equally sized particles are studied by means of two computational techniques: metadynamics and nudged elastic band calculations. The system is modelled by a screened Coulomb potential. Different interaction ranges are considered. The transition from a perfect NaCl cubic cluster to a full CsCl cluster is forced by metadynamics, revealing a transition path with intermediate metastable configurations in which planes are shifted one by one. The presence of metastable configurations in the transition path, corresponding to a certain number of NaCl planes turned into CsCl, has clear analogies with the known Hyde and O'Keeffe mechanism for ionic crystals, with some important differences due to finite-size effects. These comprise the fact that the transition starts by shifting a surface plane by means of a row-by-row mechanism that has no analog in bulk crystals. The energy barriers between the local minima in the transition path are calculated, showing that the barriers strongly depend on the screening length, in such a way that the B1 metastable phase can have very long lifetimes when the interaction is sufficiently long-ranged.

Monte Carlo Free Ligand Diffusion with Markov State Model Analysis and Absolute Binding Free Energy Calculations

Obtaining absolute binding free energies from unbiased ligand diffusion has attracted a significant amount of attention due to its implications in drug design. Several studies have used special purpose computers and software to achieve microsecond molecular dynamics which, combined with a Markov state model analysis, are capable of providing absolute binding free energies. We have recently developed a Monte Carlo based technique, PELE, capable of performing a dynamical exploration of the protein-ligand energy landscape including free ligand diffusion into the active site, at a fraction of the computational cost of molecular dynamics techniques. We demonstrate here the capabilities of our Monte Carlo technique in obtaining absolute binding free energies for a series of benzamidine like inhibitors into trypsin. Our results are in good agreement with experimental data and other molecular dynamics simulations, indicating that PELE can be a useful tool for quick estimates of binding free energies and mechanisms.

Computational modeling of an epidermal growth factor receptor single-mutation resistance to cetuximab in colorectal cancer treatment

Extracellular S468R mutation of the epidermal growth factor receptor (EGFR) was recently identified as the cause of resistance to cetuximab, a widely used drug in colorectal cancer treatment. Here, we have determined the binding free energies of cetuximab's Fab V(H)-V(L) domains and endogenous EGF ligand to wild type and S468R EGFR by high-throughput molecular dynamics. This work provides a possible mechanism of resistance in terms of increased competition, an hypothesis that can be further validated experimentally.

Role of the protein in the DNA sequence specificity of the cleavage site stabilized by the camptothecin topoisomerase IB inhibitor: a metadynamics study

Camptothecin (CPT) is a topoisomerase IB (TopIB) selective inhibitor whose derivatives are currently used in cancer therapy. TopIB cleaves DNA at any sequence, but in the presence of CPT the only stabilized protein–DNA covalent complex is the one having a thymine in position −1 with respect to the cleavage site. A metadynamics simulation of two TopIB–DNA–CPT ternary complexes differing for the presence of a thymine or a cytosine in position −1 indicates the occurrence of two different drug’s unbinding pathways. The free-energy difference between the bound state and the transition state is large when a thymine is present in position −1 and is strongly reduced in presence of a cytosine, in line with the different drug stabilization properties of the two systems. Such a difference is strictly related to the changes in the hydrogen bond network between the protein, the DNA and the drug in the two systems, indicating a direct role of the protein in determining the specificity of the cleavage site sequence stabilized by the CPT. Calculations carried out in presence of one compound of the indenoisoquinoline family (NSC314622) indicate a comparable energy difference between the bound and the transition state independently of the presence of a thymine or a cytosine in position −1, in line with the experimental results.

Binding free-energy calculation of an ion-peptide complex by constrained dynamics

Binding free energy is the most important physical parameter that describes the binding affinity of a receptor-ligand complex. Conventionally, it was obtained based on the thermodynamic cycle or alchemical reaction. These strategies have been widely used, but they would be problematic if the receptors and/or ligands have large conformational changes during the binding processes. In this paper, we present a way to calculate the binding free energy: constrained dynamics along a fragmental and high-dimensional transition path. This method directly considers unbound states in the simulation. The application to the calmodulin loop-calcium complexes shows that it is practical and the calculated relative binding affinities are in good agreement with experimental results.

Accounting for receptor flexibility and enhanced sampling methods in computer-aided drug design

Protein flexibility plays a major role in biomolecular recognition. In many cases, it is not obvious how molecular structure will change upon association with other molecules. In proteins, these changes can be major, with large deviations in overall backbone structure, or they can be more subtle as in a side-chain rotation. Either way the algorithms that predict the favorability of biomolecular association require relatively accurate predictions of the bound structure to give an accurate assessment of the energy involved in association. Here, we review a number of techniques that have been proposed to accommodate receptor flexibility in the simulation of small molecules binding to protein receptors. We investigate modifications to standard rigid receptor docking algorithms and also explore enhanced sampling techniques, and the combination of free energy calculations and enhanced sampling techniques. The understanding and allowance for receptor flexibility are helping to make computer simulations of ligand protein binding more accurate. These developments may help improve the efficiency of drug discovery and development. Efficiency will be essential as we begin to see personalized medicine tailored to individual patients, which means specific drugs are needed for each patient's genetic makeup.

Substrate recognition by norovirus polymerase: microsecond molecular dynamics study

Molecular dynamics simulations of complexes between Norwalk virus RNA dependent RNA polymerase and its natural CTP and 2dCTP (both containing the O5'-C5'-C4'-O4' sequence of atoms bridging the triphosphate and sugar moiety) or modified coCTP (C5'-O5'-C4'-O4'), cocCTP (C5'-O5'-C4'-C4'') substrates were produced by means of CUDA programmable graphical processing units and the ACEMD software package. It enabled us to gain microsecond MD trajectories clearly showing that similar nucleoside triphosphates can bind surprisingly differently into the active site of the Norwalk virus RNA dependent RNA polymerase. It corresponds to their different modes of action (CTP-substrate, 2dCTP-poor substrate, coCTP-chain terminator, cocCTP-inhibitor). Moreover, extremely rare events-as repetitive pervasion of Arg182 into a potentially reaction promoting arrangement-were captured.

Improved estimation of protein-ligand binding free energy by using the ligand-entropy and mobility of water molecules

We previously developed the direct interaction approximation (DIA) method to estimate the protein-ligand binding free energy (DG). The DIA method estimates the DG value based on the direct van der Waals and electrostatic interaction energies between the protein and the ligand. In the current study, the effect of the entropy of the ligand was introduced with protein dynamic properties by molecular dynamics simulations, and the interaction between each residue of the protein and the ligand was also weighted considering the hydration of each residue. The molecular dynamics simulation of the apo target protein gave the hydration effect of each residue, under the assumption that the residues, which strongly bind the water molecules, are important in the protein-ligand binding. These two effects improved the reliability of the DIA method. In fact, the parameters used in the DIA became independent of the target protein. The averaged error of DG estimation was 1.3 kcal/mol and the correlation coefficient between the experimental DG value and the calculated DG value was 0.75.

Funnel metadynamics as accurate binding free-energy method

A detailed description of the events ruling ligand/protein interaction and an accurate estimation of the drug affinity to its target is of great help in speeding drug discovery strategies. We have developed a metadynamics-based approach, named funnel metadynamics, that allows the ligand to enhance the sampling of the target binding sites and its solvated states. This method leads to an efficient characterization of the binding free-energy surface and an accurate calculation of the absolute protein-ligand binding free energy. We illustrate our protocol in two systems, benzamidine/trypsin and SC-558/cyclooxygenase 2. In both cases, the X-ray conformation has been found as the lowest free-energy pose, and the computed protein-ligand binding free energy in good agreement with experiments. Furthermore, funnel metadynamics unveils important information about the binding process, such as the presence of alternative binding modes and the role of waters. The results achieved at an affordable computational cost make funnel metadynamics a valuable method for drug discovery and for dealing with a variety of problems in chemistry, physics, and material science.

Computational study of synthetic agonist ligands of ionotropic glutamate receptors

Neurological glutamate receptors are among the most important and intensely studied protein ligand binding systems in humans. They are crucial for the functioning of the central nervous system and involved in a variety of pathologies. Apart from the neurotransmitter glutamate, several artificial, agonistic and antagonistic ligands are known. Of particular interest here are novel photoswitchable agonists that would open the field of optogenetics to glutamate receptors. The receptor proteins are complex, membrane-bound multidomain oligomers that undergo large scale functional conformational changes, making detailed studies of their atomic structure challenging. Therefore, a thorough understanding of the microscopic details of ligand binding and receptor activation remains elusive in many cases. This topic has been successfully addressed by theoretical studies in the past and in this paper, we present extensive molecular dynamics simulation and free energy calculation results on the binding of AMPA and an AMPA derivative, which is the basis for designing light-sensitive ligands. We provide a two-step model for ligand binding domain activation and predict binding free energies for novel compounds in good agreement to experimental observations.

Capture and quality control mechanisms for adenosine-5'-triphosphate binding

The catalytic events in members of the nucleotidylyl transferase superfamily are initiated by a millisecond binding of ATP in the active site. Through metadynamics simulations on a class I aminoacyl-tRNA synthetase (aaRSs), the largest group in the superfamily, we calculate the free energy landscape of ATP selection and binding. Mutagenesis studies and fluorescence spectroscopy validated the identification of the most populated intermediate states. The rapid first binding step involves formation of encounter complexes captured through a fly casting mechanism that acts upon the triphosphate moiety of ATP. In the slower nucleoside binding step, a conserved histidine in the HxxH motif orients the incoming ATP through base-stacking interactions resulting in a deep minimum in the free energy surface. Mutation of this histidine significantly decreases the binding affinity measured experimentally and computationally. The metadynamics simulations further reveal an intermediate quality control state that the synthetases and most likely other members of the superfamily use to select ATP over other nucleoside triphosphates.

Protein-Ligand Binding from Distancefield Distances and Hamiltonian Replica Exchange Simulations

The calculation of protein-ligand binding free energies is an important goal in the field of computational chemistry. Applying path-sampling methods for this purpose involves calculating the associated potential of mean force (PMF) and gives insight into the binding free energy along the binding process. Without a priori knowledge about the binding path, sampling reversible binding can be difficult to achieve. To alleviate this problem, we introduce the distancefield (DF) as a reaction coordinate for such calculations. DF is a grid-based method in which the shortest distance between the binding site and a ligand is determined avoiding routes that pass through the protein. Combining this reaction coordinate with Hamiltonian replica exchange molecular dynamics (HREMD) allows for the reversible binding of the ligand to the protein. A comparison is made between umbrella sampling using regular distance restraints and HREMD with DF restraints to study aspirin binding to the protein phospholipase A2. Although the free energies of binding are similar for both methods, the increased sampling with HREMD has a significant influence on the shape of the PMF. A remarkable agreement between the calculated binding free energies from the PMF and the experimental estimate is obtained.

Virtual screening in drug design

Virtual screening has become a standard tool in drug discovery to identify novel lead compounds that target a biomolecule of interest. I present several concepts in ligand-based and structure-based virtual screening and discuss some of the current shortcomings and new developments. I also highlight approaches that combine concepts from structure- and ligand-based design.

Molecular docking methodologies

Molecular docking represents an important technology for structure-based drug design. Docking is a computational technique aimed at the prediction of the most favorable ligand-target spatial configuration and an estimate of the corresponding complex free energy, although as stated at the beginning accurate scoring methods remain still elusive. In this chapter, the state of art of molecular docking methodologies and their applications in drug discovery is summarized.

Consensus Induced Fit Docking (cIFD): methodology, validation, and application to the discovery of novel Crm1 inhibitors

We present the Consensus Induced Fit Docking (cIFD) approach for adapting a protein binding site to accommodate multiple diverse ligands for virtual screening. This novel approach results in a single binding site structure that can bind diverse chemotypes and is thus highly useful for efficient structure-based virtual screening. We first describe the cIFD method and its validation on three targets that were previously shown to be challenging for docking programs (COX-2, estrogen receptor, and HIV reverse transcriptase). We then demonstrate the application of cIFD to the challenging discovery of irreversible Crm1 inhibitors. We report the identification of 33 novel Crm1 inhibitors, which resulted from the testing of 402 purchased compounds selected from a screening set containing 261,680 compounds. This corresponds to a hit rate of 8.2 %. The novel Crm1 inhibitors reveal diverse chemical structures, validating the utility of the cIFD method in a real-world drug discovery project. This approach offers a pragmatic way to implicitly account for protein flexibility without the additional computational costs of ensemble docking or including full protein flexibility during virtual screening.

Statistical estimation of the protein-ligand binding free energy based on direct protein-ligand interaction obtained by molecular dynamics simulation

We have developed a method for estimating protein-ligand binding free energy (DG) based on the direct protein-ligand interaction obtained by a molecular dynamics simulation. Using this method, we estimated the DG value statistically by the average values of the van der Waals and electrostatic interactions between each amino acid of the target protein and the ligand molecule. In addition, we introduced fluctuations in the accessible surface area (ASA) and dihedral angles of the protein-ligand complex system as the entropy terms of the DG estimation. The present method included the fluctuation term of structural change of the protein and the effective dielectric constant. We applied this method to 34 protein-ligand complex structures. As a result, the correlation coefficient between the experimental and calculated DG values was 0.81, and the average error of DG was 1.2 kcal/mol with the use of the fixed parameters. These results were obtained from a 2 nsec molecular dynamics simulation.

Using metadynamics and path collective variables to study ligand binding and induced conformational transitions

Large-scale conformational transitions represent both a challenge and an opportunity for computational drug design. Exploring the conformational space of a druggable target with sufficient detail is computationally demanding. However, if it were possible to fully account for target flexibility, one could exploit this knowledge to rationally design more potent and more selective drug candidates. Here, we discuss how molecular dynamics together with free energy algorithms based on Metadynamics and Path Collective Variables can be used to study both large-scale conformational transitions and ligand binding to flexible targets. We show real-life examples of how these methods have been applied in the case of cyclin-dependent kinases, a family of flexible targets that shows promise in cancer therapy.

Density of states-based molecular simulations

One of the central problems in statistical mechanics is that of finding the density of states of a system. Knowledge of the density of states of a system is equivalent to knowledge of its fundamental equation, from which all thermodynamic quantities can be obtained. Over the past several years molecular simulations have made considerable strides in their ability to determine the density of states of complex fluids and materials. In this review we discuss some of the more promising approaches proposed in the recent literature along with their advantages and limitations.

Locating binding poses in protein-ligand systems using reconnaissance metadynamics

A molecular dynamics-based protocol is proposed for finding and scoring protein-ligand binding poses. This protocol uses the recently developed reconnaissance metadynamics method, which employs a self-learning algorithm to construct a bias that pushes the system away from the kinetic traps where it would otherwise remain. The exploration of phase space with this algorithm is shown to be roughly six to eight times faster than unbiased molecular dynamics and is only limited by the time taken to diffuse about the surface of the protein. We apply this method to the well-studied trypsin-benzamidine system and show that we are able to refind all the poses obtained from a reference EADock blind docking calculation. These poses can be scored based on the length of time the system remains trapped in the pose. Alternatively, one can perform dimensionality reduction on the output trajectory and obtain a map of phase space that can be used in more expensive free-energy calculations.

Visualizing the Induced Binding of SH2-Phosphopeptide

Approximately 100 proteins in the human genome contain an SH2 domain recognizing small flexible phosphopeptides. It is therefore important to understand in atomistic detail the way these peptides bind and the conformational changes that take place upon binding. Here, we obtained several spontaneous binding events between the p56 lck SH2 domain and the pYEEI peptide within 2 Å RMSD from the crystal structure and with kinetic rates compatible with experiments using high-throughput molecular dynamics simulations. Binding is achieved in two phases, fast contacts of the charged phospho-tyrosine and then rearrangement of the ligand involving the stabilization of two important loops in the SH2 domain. These observations provide insights into the binding pathways and induced conformations of the SH2-phosphopeptide complex which, due to the characteristics of SH2 domains, should be relevant for other SH2 recognition peptides.

Sampling protein motion and solvent effect during ligand binding

An exhaustive description of the molecular recognition mechanism between a ligand and its biological target is of great value because it provides the opportunity for an exogenous control of the related process. Very often this aim can be pursued using high resolution structures of the complex in combination with inexpensive computational protocols such as docking algorithms. Unfortunately, in many other cases a number of factors, like protein flexibility or solvent effects, increase the degree of complexity of ligand/protein interaction and these standard techniques are no longer sufficient to describe the binding event. We have experienced and tested these limits in the present study in which we have developed and revealed the mechanism of binding of a new series of potent inhibitors of Adenosine Deaminase. We have first performed a large number of docking calculations, which unfortunately failed to yield reliable results due to the dynamical character of the enzyme and the complex role of the solvent. Thus, we have stepped up the computational strategy using a protocol based on metadynamics. Our approach has allowed dealing with protein motion and solvation during ligand binding and finally identifying the lowest energy binding modes of the most potent compound of the series, 4-decyl-pyrazolo[1,5-a]pyrimidin-7-one.