Absolute binding free energy calculations of sparsomycin analogs to the bacterial ribosome

Druglike Molecules Binding to Large Membrane Proteins: Absolute Binding Free Energy Computation

In this research, we employed the alchemical double-decoupling method alongside restraining potentials, coupled with the FEPMD method, to ascertain the standard binding free energy of a drug-like molecule termed BHQ and three analogous compounds engineered with progressive addition of bulky para-alkyl groups binding to SERCA (Ca2+-ATPase of skeletal muscle sarcoplasmic reticulum). Integral transmembrane proteins represent crucial drug targets in numerous therapeutic interventions, presenting computational challenges due to their considerable system sizes. Our approach integrated the generalized born potential method and the spherical solvent boundary potential method, allowing us to explicitly focus on the active binding site while treating the remainder of the system implicitly. We evaluated contributions to the standard binding free energy from distinct interaction potentials: electrostatic, repulsive, dispersive, and restraining potentials, computed separately. The resulting absolute binding free energy of BHQ (11.63 kcal/mol) closely aligns with experimental measurements (10.56 kcal/mol). Notably, an accurate estimation of the absolute binding free energy was achieved for the simplest analog, created with the addition of a single para-methyl group. However, the analog with two para-methyl groups exhibited the highest binding free energy, which disagreed with experimental results. Determining the binding free energy of the BHQ analog engineered with three para-methyl groups presented challenges in convergence and resulted in the lowest free energy among the three.

Investigating the Dynamic Binding Behavior of PMX53 Cooperating with Allosteric Antagonist NDT9513727 to C5a Anaphylatoxin Chemotactic Receptor 1 through Gaussian Accelerated Molecular Dynamics and Free-Energy Perturbation Simulations

C5a anaphylatoxin chemotactic receptor 1 (C5aR1) is an important target in anti-inflammatory therapeutics. The cyclic peptide antagonist PMX53 binds to the orthosteric site located in the extracellular vestibule of C5aR1, and the non-peptide antagonist NDT9513727 binds to the allosteric site formed by the middle region of TM3 (trans-membrane helix), TM4, and TM5. We catch a sight of the variational binding mode of PMX53 during the Gaussian accelerated molecular dynamic (GaMD) simulations. In the binary complex of C5aR1 and PMX53, the PMX53 takes a dynamic binding mechanism during the simulation. Namely, the side chain of Arg⁶ of PMX53 extends to TM6-TM7 (pose 1) or swings to TM5 (pose 2), forming a salt bridge with Glu199. Meanwhile, in the ternary complex of C5aR1 with PMX53 and NDT9513727, the side chain of Arg⁶ of PMX53 swings to TM5 (pose 2) from extending to TM6-TM7 (pose 1) at the beginning of the GaMD simulation. In subsequent simulation, PMX53 stabilizes in the pose 2 binding mode by forming a stable salt bridge with Glu199. The free-energy perturbation (FEP) calculations demonstrate that pose 1 (ΔG_binding = -10.94 kcal/mol) is more stable in the binary complex and pose 2 (ΔG_binding = -7.91 kcal/mol) is unstable because of highly dynamic TM5. NDT9513727 interacts directly with TM4 and TM5 and stabilizes the hydrophobic stack between the extracellular sides of the two helices. Therefore, pose 2 (ΔG_binding = -16.27 kcal/mol) is notably stable than pose 1 (ΔG_binding = -9.78 kcal/mol) in the ternary complex. The identification of a novel binding mode of PMX53 and the detailed structural information of PMX53 interacting with a receptor obtained by GaMD simulations will be helpful in designing potent antagonists of C5aR1.

Meta-Analysis Reveals That Absolute Binding Free-Energy Calculations Approach Chemical Accuracy

Systematic and quantitative analysis of the reliability of formally exact methods that in silico calculate absolute protein-ligand binding free energies remains lacking. Here, we provide, for the first time, evidence-based information on the reliability of these methods by statistically studying 853 cases from 34 different research groups through meta-analysis. The results show that formally exact methods approach chemical accuracy (error = 1.58 kcal/mol), even if people are challenging difficult tasks such as blind drug screening in recent years. The geometrical-pathway-based methods prove to possess a better convergence ability than the alchemical ones, while the latter have a larger application range. We also reveal the importance of always using the latest force fields to guarantee reliability and discuss the pros and cons of turning to an implicit solvent model in absolute binding free-energy calculations. Moreover, based on the meta-analysis, an evidence-based guideline for in silico binding free-energy calculations is provided.

Implicit ligand theory for relative binding free energies: II. An estimator based on control variates

Implicit ligand theory describes the relationship between the noncovalent binding free energy and the binding free energy between a ligand and multiple rigid receptor conformations. We have previously shown that if the receptor conformations are sampled from or reweighed to a holo ensemble, the binding free energy relative to the ligand that defines the ensemble can be calculated. Here, we apply a variance reduction technique known as control variates to derive a new statistical estimator for the relative binding free energy. In applications to a data set of 6 reference ligands and 18 test ligands, statistically significant differences between the estimators are not observed for most systems. However, in cases where such differences are observed, the new estimator is more accurate, precise, and converges more quickly. Performance improvements are most consistent where there is a clear correlation, with a correlation coefficient greater than 0.3, between the control variate and the statistic being averaged.

Combining Machine Learning and Enhanced Sampling Techniques for Efficient and Accurate Calculation of Absolute Binding Free Energies

Calculating absolute binding free energies is challenging and important. In this paper, we test some recently developed metadynamics-based methods and develop a new combination with a Hamiltonian replica-exchange approach. The methods were tested on 18 chemically diverse ligands with a wide range of different binding affinities to a complex target; namely, human soluble epoxide hydrolase. The results suggest that metadynamics with a funnel-shaped restraint can be used to calculate, in a computationally affordable and relatively accurate way, the absolute binding free energy for small fragments. When used in combination with an optimal pathlike variable obtained using machine learning or with the Hamiltonian replica-exchange algorithm SWISH, this method can achieve reasonably accurate results for increasingly complex ligands, with a good balance of computational cost and speed. An additional benefit of using the combination of metadynamics and SWISH is that it also provides useful information about the role of water in the binding mechanism.

On Restraints in End-Point Protein-Ligand Binding Free Energy Calculations

The impact of harmonic restraints on protein heavy atoms and ligand atoms on end-point free energy calculations is systematically characterized for 54 protein-ligand complexes. We observe that stronger restraints reduce the equilibration time and statistical inefficiency, suppress conformational sampling, influence correlation with experiment, and monotonically decrease the estimated loss of entropy upon binding, leading to stronger estimated binding free energies in most systems. A statistical estimator that reweights for the biasing potential and includes data prior to the estimated equilibration time has the highest correlation with experiment. A spring constant of 20 cal mol-1 Å-2 maintains a near-native energy landscape and suppresses artifactual energy minima while minimally limiting thermal fluctuations about the crystal structure. © 2019 Wiley Periodicals, Inc.

Novel MscL agonists that allow multiple antibiotics cytoplasmic access activate the channel through a common binding site

The antibiotic resistance crisis is becoming dire, yet in the past several years few potential antibiotics or adjuvants with novel modes of action have been identified. The bacterial mechanosensitive channel of large conductance, MscL, found in the majority of bacterial species, including pathogens, normally functions as an emergency release valve, sensing membrane tension upon low-osmotic stress and discharging cytoplasmic solutes before cell lysis. Opening the huge ~30Å diameter pore of MscL inappropriately is detrimental to the cell, allowing solutes from and even passage of drugs into to cytoplasm. Thus, MscL is a potential novel drug target. However, there are no known natural agonists, and small compounds that modulate MscL activity are just now being identified. Here we describe a small compound, K05, that specifically modulates MscL activity and we compare results with those obtained for the recently characterized MscL agonist 011A. While the structure of K05 only vaguely resembles 011A, many of the findings, including the binding pocket, are similar. On the other hand, both in vivo and molecular dynamic simulations indicate that the two compounds modulate MscL activity in significantly different ways.

Large-scale simulations of nucleoprotein complexes: ribosomes, nucleosomes, chromatin, chromosomes and CRISPR

Recent advances in biotechnology such as Hi-C, CRISPR/Cas9 and ribosome display have placed nucleoprotein complexes at center stage. Understanding the structural dynamics of these complexes aids in optimizing protocols and interpreting data for these new technologies. The integration of simulation and experiment has helped advance mechanistic understanding of these systems. Coarse-grained simulations, reduced-description models, and explicit solvent molecular dynamics simulations yield useful complementary perspectives on nucleoprotein complex structural dynamics. When combined with Hi-C, cryo-EM, and single molecule measurements, these simulations integrate disparate forms of experimental data into a coherent mechanism.

An Overview of Molecular Modeling for Drug Discovery with Specific Illustrative Examples of Applications

In this paper we review the current status of high-performance computing applications in the general area of drug discovery. We provide an introduction to the methodologies applied at atomic and molecular scales, followed by three specific examples of implementation of these tools. The first example describes in silico modeling of the adsorption of small molecules to organic and inorganic surfaces, which may be applied to drug delivery issues. The second example involves DNA translocation through nanopores with major significance to DNA sequencing efforts. The final example offers an overview of computer-aided drug design, with some illustrative examples of its usefulness.

A Streamlined, General Approach for Computing Ligand Binding Free Energies and Its Application to GPCR-Bound Cholesterol

The theory of receptor-ligand binding equilibria has long been well-established in biochemistry, and was primarily constructed to describe dilute aqueous solutions. Accordingly, few computational approaches have been developed for making quantitative predictions of binding probabilities in environments other than dilute isotropic solution. Existing techniques, ranging from simple automated docking procedures to sophisticated thermodynamics-based methods, have been developed with soluble proteins in mind. Biologically and pharmacologically relevant protein-ligand interactions often occur in complex environments, including lamellar phases like membranes and crowded, nondilute solutions. Here, we revisit the theoretical bases of ligand binding equilibria, avoiding overly specific assumptions that are nearly always made when describing receptor-ligand binding. Building on this formalism, we extend the asymptotically exact Alchemical Free Energy Perturbation technique to quantifying occupancies of sites on proteins in a complex bulk, including phase-separated, anisotropic, or nondilute solutions, using a thermodynamically consistent and easily generalized approach that resolves several ambiguities of current frameworks. To incorporate the complex bulk without overcomplicating the overall thermodynamic cycle, we simplify the common approach for ligand restraints by using a single distance-from-bound-configuration (DBC) ligand restraint during AFEP decoupling from protein. DBC restraints should be generalizable to binding modes of most small molecules, even those with strong orientational dependence. We apply this approach to compute the likelihood that membrane cholesterol binds to known crystallographic sites on three GPCRs (β₂-adrenergic, 5HT-2B, and μ-opioid) at a range of concentrations. Nonideality of cholesterol in a binary cholesterol:phosphatidylcholine (POPC) bilayer is characterized and consistently incorporated into the interpretation. We find that the three sites exhibit very different affinities for cholesterol: The site on the adrenergic receptor is predicted to be high affinity, with 50% occupancy for 1:10⁹ CHOL:POPC mixtures. The sites on the 5HT-2B and μ-opioid receptor are predicted to be lower affinity, with 50% occupancy for 1:10³ CHOL:POPC and 1:10² CHOL:POPC, respectively. These results could not have been predicted from the crystal structures alone.

Simple Entropy Terms for End-Point Binding Free Energy Calculations

We introduce a number of computationally inexpensive modifications to the MM/PBSA and MM/GBSA estimators for binding free energies, which are based on average receptor-ligand interaction energies in simulations of a noncovalent complex, to improve the treatment of entropy: second- and higher-order terms in a cumulant expansion and a confining potential on ligand external degrees of freedom. We also consider a filter for snapshots where ligands have drifted from the initial binding pose. The variations were tested on six sets of systems for which binding modes and free energies have previously been experimentally determined. For some data sets, none of the tested estimators led to results significantly correlated with measured free energies. In data sets with nontrivial correlation, a ligand RMSD cutoff of 3 Å and a second-order truncation of the cumulant expansion was found to be comparable or better than the average interaction energy by several statistical metrics.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Implicit ligand theory for relative binding free energies

Implicit ligand theory enables noncovalent binding free energies to be calculated based on an exponential average of the binding potential of mean force (BPMF)-the binding free energy between a flexible ligand and rigid receptor-over a precomputed ensemble of receptor configurations. In the original formalism, receptor configurations were drawn from or reweighted to the apo ensemble. Here we show that BPMFs averaged over a holo ensemble yield binding free energies relative to the reference ligand that specifies the ensemble. When using receptor snapshots from an alchemical simulation with a single ligand, the new statistical estimator outperforms the original.

Using the fast fourier transform in binding free energy calculations

According to implicit ligand theory, the standard binding free energy is an exponential average of the binding potential of mean force (BPMF), an exponential average of the interaction energy between the unbound ligand ensemble and a rigid receptor. Here, we use the fast Fourier transform (FFT) to efficiently evaluate BPMFs by calculating interaction energies when rigid ligand configurations from the unbound ensemble are discretely translated across rigid receptor conformations. Results for standard binding free energies between T4 lysozyme and 141 small organic molecules are in good agreement with previous alchemical calculations based on (1) a flexible complex ( R≈0.9 for 24 systems) and (2) flexible ligand with multiple rigid receptor configurations ( R≈0.8 for 141 systems). While the FFT is routinely used for molecular docking, to our knowledge this is the first time that the algorithm has been used for rigorous binding free energy calculations. © 2017 Wiley Periodicals, Inc.

Absolute Binding Free Energies between T4 Lysozyme and 141 Small Molecules: Calculations Based on Multiple Rigid Receptor Configurations

We demonstrate the feasibility of estimating protein-ligand binding free energies using multiple rigid receptor configurations. On the basis of T4 lysozyme snapshots extracted from six alchemical binding free energy calculations with a flexible receptor, binding free energies were estimated for a total of 141 ligands. For 24 ligands, the calculations reproduced flexible-receptor estimates with a correlation coefficient of 0.90 and a root-mean-square error of 1.59 kcal/mol. The accuracy of calculations based on Poisson-Boltzmann/surface area implicit solvent was comparable to that of previously reported free energy calculations.

Ligand binding to telomeric G-quadruplex DNA investigated by funnel-metadynamics simulations

A thorough characterization of the binding interaction between a drug and its molecular target is fundamental to successfully lead drug design. We demonstrate that this characterization is also possible using the recently developed method of funnel-metadynamics (FM), here applied to investigate the binding of berberine to DNA G-quadruplex. We computed a quantitatively well-characterized free-energy landscape that allows identifying two low-energy ligand binding modes and the presence of higher energy prebinding states. We validated the accuracy of our calculations by steady-state fluorescence experiments. The good agreement between the theoretical and experimental binding free-energy value demonstrates that FM is a most reliable method to study ligand/DNA interaction.

G-quadruplexes (G4s) are higher-order DNA structures typically present at promoter regions of genes and telomeres. Here, the G4 formation decreases the replicative DNA at each cell cycle, finally leading to apoptosis. The ability to control this mitotic clock, particularly in cancer cells, is fascinating and passes through a rational understanding of the ligand/G4 interaction. We demonstrate that an accurate description of the ligand/G4 binding mechanism is possible using an innovative free-energy method called funnel-metadynamics (FM), which we have recently developed to investigate ligand/protein interaction. Using FM simulations, we have elucidated the binding mechanism of the anticancer alkaloid berberine to the human telomeric G4 (d[AG₃(T₂AG₃)₃]), computing also the binding free-energy landscape. Two ligand binding modes have been identified as the lowest energy states. Furthermore, we have found prebinding sites, which are preparatory to reach the final binding mode. In our simulations, the ions and the water molecules have been explicitly represented and the energetic contribution of the solvent during ligand binding evaluated. Our theoretical results provide an accurate estimate of the absolute ligand/DNA binding free energy (ΔGb0 = −10.3 ± 0.5 kcal/mol) that we validated through steady-state fluorescence binding assays. The good agreement between the theoretical and experimental value demonstrates that FM is a most powerful method to investigate ligand/DNA interaction and can be a useful tool for the rational design also of G4 ligands.

Potential Application of Alchemical Free Energy Simulations to Discriminate GPCR Ligand Efficacy

G protein-coupled receptors (GPCRs) play fundamental roles in physiological processes by modulating diverse signaling pathways and thus have been one of the most important drug targets. Based on the fact that GPCR-mediated signaling is modulated in a ligand-specific manner such as agonist, inverse agonist, and neutral antagonist (termed ligand efficacy), quantitative characterization of the ligand efficacy is essential for rational design of selective modulators for GPCR targets. As experimental approaches for this purpose are time-, cost-, and labor-intensive, computational tools that can systematically predict GPCR ligand efficacy can have a big impact on GPCR drug design. Here, we have performed free energy perturbation molecular dynamics simulations to calculate absolute binding free energy of an inverse agonist, a neutral antagonist, and an agonist to β2-adrenergic receptor (β2-AR) active and inactive states, respectively, in explicit lipid bilayers. Relatively short alchemical free energy calculations reveal that both the time-series of the total binding free energy and decomposed energy contributions can be used as relevant physical properties to discriminate β2-AR ligand efficacy. This study illustrates a merit of the current approach over simple, fast docking calculations or highly expensive millisecond-time scale simulations.

Complex long-distance effects of mutations that confer linezolid resistance in the large ribosomal subunit

The emergence of multidrug-resistant pathogens will make current antibiotics ineffective. For linezolid, a member of the novel oxazolidinone class of antibiotics, 10 nucleotide mutations in the ribosome have been described conferring resistance. Hypotheses for how these mutations affect antibiotics binding have been derived based on comparative crystallographic studies. However, a detailed description at the atomistic level of how remote mutations exert long-distance effects has remained elusive. Here, we show that the G2032A-C2499A double mutation, located > 10 Å away from the antibiotic, confers linezolid resistance by a complex set of effects that percolate to the binding site. By molecular dynamics simulations and free energy calculations, we identify U2504 and C2452 as spearheads among binding site nucleotides that exert the most immediate effect on linezolid binding. Structural reorganizations within the ribosomal subunit due to the mutations are likely associated with mutually compensating changes in the effective energy. Furthermore, we suggest two main routes of information transfer from the mutation sites to U2504 and C2452. Between these, we observe cross-talk, which suggests that synergistic effects observed for the two mutations arise in an indirect manner. These results should be relevant for the development of oxazolidinone derivatives that are active against linezolid-resistant strains.

Computational study of Gleevec and G6G reveals molecular determinants of kinase inhibitor selectivity

Gleevec is a potent inhibitor of Abl tyrosine kinase but not of the highly homologous c-Src kinase. Because the ligand binds to an inactive form of the protein in which an Asp-Phe-Gly structural motif along the activation loop adopts a so-called DFG-out conformation, it was suggested that binding specificity was controlled by a "conformational selection" mechanism. In this context, the binding affinity displayed by the kinase inhibitor G6G poses an intriguing challenge. Although it possesses a chemical core very similar to that of Gleevec, G6G is a potent inhibitor of both Abl and c-Src kinases. Both inhibitors bind to the DFG-out conformation of the kinases, which seems to be in contradiction with the conformational selection mechanism. To address this issue and display the hidden thermodynamic contributions affecting the binding selectivity, molecular dynamics free energy simulations with explicit solvent molecules were carried out. Relative to Gleevec, G6G forms highly favorable van der Waals dispersive interactions upon binding to the kinases via its triazine functional group, which is considerably larger than the corresponding pyridine moiety in Gleevec. Upon binding of G6G to c-Src, these interactions offset the unfavorable free energy cost of the DFG-out conformation. When binding to Abl, however, G6G experiences an unfavorable free energy penalty due to steric clashes with the phosphate-binding loop, yielding an overall binding affinity that is similar to that of Gleevec. Such steric clashes are absent when G6G binds to c-Src, due to the extended conformation of the phosphate-binding loop.

Computational analysis of the binding specificity of Gleevec to Abl, c-Kit, Lck, and c-Src tyrosine kinases

Gleevec, a well-known cancer therapeutic agent, is an effective inhibitor of several tyrosine kinases, including Abl and c-Kit, but displays less potency to inhibit closely homologous tyrosine kinases, such as Lck and c-Src. Because many structural features of the binding site are highly conserved in these homologous kinases, the molecular determinants responsible for the binding specificity of Gleevec remain poorly understood. To address this issue, free energy perturbation molecular dynamics (FEP/MD) simulations with explicit solvent was used to compute the binding affinity of Gleevec to Abl, c-Kit, Lck, and c-Src. The results of the FEP/MD calculations are in good agreement with experiments, enabling a detailed and quantitative dissection of the absolute binding free energy in terms of various thermodynamic contributions affecting the binding specificity of Gleevec to the kinases. Dominant binding free energy contributions arises from the van der Waals dispersive interaction, compensating about two-thirds of the unfavorable free energy penalty associated with the loss of translational, rotational, and conformational freedom of the ligand upon binding. In contrast, the contributions from electrostatic and repulsive interactions nearly cancel out due to solvent effects. Furthermore, the calculations show the importance of the conformation of the kinase activation loop. Among the kinases examined, Abl provides the most favorable binding environment for Gleevec via optimal protein-ligand interactions and a small free energy cost for loss of the translational, rotational, and conformational freedom upon ligand binding. The FEP/MD calculations additionally reveal that Lck and c-Src provide similar nonbinding interactions with the bound-Gleevec, but the former pays less entropic penalty for the ligand losing its translational, rotational, and conformational motions to bind, examining the empirically observed differential binding affinities of Gleevec between the two Src-family kinases.

Impact of ribosomal modification on the binding of the antibiotic telithromycin using a combined grand canonical monte carlo/molecular dynamics simulation approach

Resistance to macrolide antibiotics is conferred by mutation of A2058 to G or methylation by Erm methyltransferases of the exocyclic N6 of A2058 (E. coli numbering) that forms the macrolide binding site in the 50S subunit of the ribosome. Ketolides such as telithromycin mitigate A2058G resistance yet remain susceptible to Erm-based resistance. Molecular details associated with macrolide resistance due to the A2058G mutation and methylation at N6 of A2058 by Erm methyltransferases were investigated using empirical force field-based simulations. To address the buried nature of the macrolide binding site, the number of waters within the pocket was allowed to fluctuate via the use of a Grand Canonical Monte Carlo (GCMC) methodology. The GCMC water insertion/deletion steps were alternated with Molecular Dynamics (MD) simulations to allow for relaxation of the entire system. From this GCMC/MD approach information on the interactions between telithromycin and the 50S ribosome was obtained. In the wild-type (WT) ribosome, the 2'-OH to A2058 N1 hydrogen bond samples short distances with a higher probability, while the effectiveness of telithromycin against the A2058G mutation is explained by a rearrangement of the hydrogen bonding pattern of the 2'-OH to 2058 that maintains the overall antibiotic-ribosome interactions. In both the WT and A2058G mutation there is significant flexibility in telithromycin's imidazole-pyridine side chain (ARM), indicating that entropic effects contribute to the binding affinity. Methylated ribosomes show lower sampling of short 2'-OH to 2058 distances and also demonstrate enhanced G2057-A2058 stacking leading to disrupted A752-U2609 Watson-Crick (WC) interactions as well as hydrogen bonding between telithromycin's ARM and U2609. This information will be of utility in the rational design of novel macrolide analogs with improved activity against methylated A2058 ribosomes.

Large scale affinity calculations of cyclodextrin host-guest complexes: Understanding the role of reorganization in the molecular recognition process

Host-guest inclusion complexes are useful models for understanding the structural and energetic aspects of molecular recognition. Due to their small size relative to much larger protein-ligand complexes, converged results can be obtained rapidly for these systems thus offering the opportunity to more reliably study fundamental aspects of the thermodynamics of binding. In this work, we have performed a large scale binding affinity survey of 57 β-cyclodextrin (CD) host guest systems using the binding energy distribution analysis method (BEDAM) with implicit solvation (OPLS-AA/AGBNP2). Converged estimates of the standard binding free energies are obtained for these systems by employing techniques such as parallel Hamitionian replica exchange molecular dynamics, conformational reservoirs and multistate free energy estimators. Good agreement with experimental measurements is obtained in terms of both numerical accuracy and affinity rankings. Overall, average effective binding energies reproduce affinity rank ordering better than the calculated binding affinities, even though calculated binding free energies, which account for effects such as conformational strain and entropy loss upon binding, provide lower root mean square errors when compared to measurements. Interestingly, we find that binding free energies are superior rank order predictors for a large subset containing the most flexible guests. The results indicate that, while challenging, accurate modeling of reorganization effects can lead to ligand design models of superior predictive power for rank ordering relative to models based only on ligand-receptor interaction energies.

Protonation and pK changes in protein-ligand binding

Formation of protein-ligand complexes causes various changes in both the receptor and the ligand. This review focuses on changes in pK and protonation states of ionizable groups that accompany protein-ligand binding. Physical origins of these effects are outlined, followed by a brief overview of the computational methods to predict them and the associated corrections to receptor-ligand binding affinities. Statistical prevalence, magnitude and spatial distribution of the pK and protonation state changes in protein-ligand binding are discussed in detail, based on both experimental and theoretical studies. While there is no doubt that these changes occur, they do not occur all the time; the estimated prevalence varies, both between individual complexes and by method. The changes occur not only in the immediate vicinity of the interface but also sometimes far away. When receptor-ligand binding is associated with protonation state change at particular pH, the binding becomes pH dependent: we review the interplay between sub-cellular characteristic pH and optimum pH of receptor-ligand binding. It is pointed out that there is a tendency for protonation state changes upon binding to be minimal at physiologically relevant pH for each complex (no net proton uptake/release), suggesting that native receptor-ligand interactions have evolved to reduce the energy cost associated with ionization changes. As a result, previously reported statistical prevalence of these changes - typically computed at the same pH for all complexes - may be higher than what may be expected at optimum pH specific to each complex. We also discuss whether proper account of protonation state changes appears to improve practical docking and scoring outcomes relevant to structure-based drug design. An overview of some of the existing challenges in the field is provided in conclusion.

Charging free energy calculations using the Generalized Solvent Boundary Potential (GSBP) and periodic boundary condition: a comparative analysis using ion solvation and oxidation free energy in proteins

Free energy simulations using a finite sphere boundary condition rather than a periodic boundary condition (PBC) are attractive in the study of very large biomolecular systems. To understand the quantitative impact of various approximations in such simulations, we compare charging free energies in both solution and protein systems calculated in a linear response framework with the Generalized Solvent Boundary Potential (GSBP) and PBC simulations. For simple ions in solution, we find good agreements between GSBP and PBC charging free energies, once the relevant correction terms are taken into consideration. For PBC simulations with the particle-mesh-Ewald for long-range electrostatics, the contribution (ΔG(P-M)) due to the use of a particle rather than molecule based summation scheme in real space is found to be significant, as pointed out by Hünenberger and co-workers. For GSBP, when the inner region is close to be charge neutral, the key correction is the overpolarization of water molecules at the inner/outer dielectric boundary; the magnitude of the correction (ΔG(s-pol)), however, is relatively small. For charging (oxidation) free energy in proteins, the situation is more complex, although good agreement between GSBP and PBC can still be obtained when care is exercised. The smooth dielectric boundary approximation inherent to GSBP tends to make significant errors when the inner region is featured with a high net charge. However, the error can be corrected with Poisson-Boltzmann calculations using snapshots from GSBP simulations in a straightforward and robust manner. Because of the more complex charge and solvent distributions, the magnitudes of ΔG(P-M) and ΔG(s-pol) in protein simulations appear to be different from those derived for solution simulations, leading to uncertainty in directly comparing absolute charging free energies from PBC and GSBP simulations for protein systems. The relative charging/oxidation free energies, however, are robust. With the linear response approximation, for the specific protein system (CueR) studied, the effect of freezing the protein structure in the outer region is found to be small, unless a very small (8 Å) inner region is used; even in the latter case, the result is substantially improved when the nearby metal binding loop is allowed to respond to metal oxidation. The implications of these results to the applicability of GSBP to complex biomolecules and in ab initio QM/MM simulations are discussed.

Explaining why Gleevec is a specific and potent inhibitor of Abl kinase

Tyrosine kinases present attractive drug targets for specific types of cancers. Gleevec, a well-known therapeutic agent against chronic myelogenous leukemia, is an effective inhibitor of Abl tyrosine kinase. However, Gleevec fails to inhibit closely homologous tyrosine kinases, such as c-Src. Because many structural features of the binding site are conserved, the molecular determinants responsible for binding specificity are not immediately apparent. Some have attributed the difference in binding specificity of Gleevec to subtle variations in ligand-protein interactions (binding affinity control), whereas others have proposed that it is the conformation of the DFG motif, in which ligand binding is only accessible to Abl and not to c-Src (conformational selection control). To address this issue, the absolute binding free energy was computed using all-atom molecular dynamics simulations with explicit solvent. The results of the free energy simulations are in good agreement with experiments, thereby enabling a meaningful decomposition of the binding free energy to elucidate the factors controlling Gleevec's binding specificity. The latter is shown to be controlled by a conformational selection mechanism and also by differences in key van der Waals interactions responsible for the stabilization of Gleevec in the binding pocket of Abl.

CHARMM-GUI Ligand Binder for absolute binding free energy calculations and its application

Advanced free energy perturbation molecular dynamics (FEP/MD) simulation methods are available to accurately calculate absolute binding free energies of protein-ligand complexes. However, these methods rely on several sophisticated command scripts implementing various biasing energy restraints to enhance the convergence of the FEP/MD calculations, which must all be handled properly to yield correct results. Here, we present a user-friendly Web interface, CHARMM-GUI Ligand Binder ( http://www.charmm-gui.org/input/gbinding ), to provide standardized CHARMM input files for calculations of absolute binding free energies using the FEP/MD simulations. A number of features are implemented to conveniently set up the FEP/MD simulations in highly customizable manners, thereby permitting an accelerated throughput of this important class of computations while decreasing the possibility of human errors. The interface and a series of input files generated by the interface are tested with illustrative calculations of absolute binding free energies of three nonpolar aromatic ligands to the L99A mutant of T4 lysozyme and three FK506-related ligands to FKBP12. Statistical errors within individual calculations are found to be small (~1 kcal/mol), and the calculated binding free energies generally agree well with the experimental measurements and the previous computational studies (within ~2 kcal/mol). Therefore, CHARMM-GUI Ligand Binder provides a convenient and reliable way to set up the ligand binding free energy calculations and can be applicable to pharmaceutically important protein-ligand systems.

Application of binding free energy calculations to prediction of binding modes and affinities of MDM2 and MDMX inhibitors

Molecular docking is widely used to obtain binding modes and binding affinities of a molecule to a given target protein. Despite considerable efforts, however, prediction of both properties by docking remains challenging mainly due to protein's structural flexibility and inaccuracy of scoring functions. Here, an integrated approach has been developed to improve the accuracy of binding mode and affinity prediction and tested for small molecule MDM2 and MDMX antagonists. In this approach, initial candidate models selected from docking are subjected to equilibration MD simulations to further filter the models. Free energy perturbation molecular dynamics (FEP/MD) simulations are then applied to the filtered ligand models to enhance the ability in predicting the near-native ligand conformation. The calculated binding free energies for MDM2 complexes are overestimated compared to experimental measurements mainly due to the difficulties in sampling highly flexible apo-MDM2. Nonetheless, the FEP/MD binding free energy calculations are more promising for discriminating binders from nonbinders than docking scores. In particular, the comparison between the MDM2 and MDMX results suggests that apo-MDMX has lower flexibility than apo-MDM2. In addition, the FEP/MD calculations provide detailed information on the different energetic contributions to ligand binding, leading to a better understanding of the sensitivity and specificity of protein-ligand interactions.

Ligand-dependent conformations and dynamics of the serotonin 5-HT(2A) receptor determine its activation and membrane-driven oligomerization properties

From computational simulations of a serotonin 2A receptor (5-HT_2AR) model complexed with pharmacologically and structurally diverse ligands we identify different conformational states and dynamics adopted by the receptor bound to the full agonist 5-HT, the partial agonist LSD, and the inverse agonist Ketanserin. The results from the unbiased all-atom molecular dynamics (MD) simulations show that the three ligands affect differently the known GPCR activation elements including the toggle switch at W6.48, the changes in the ionic lock between E6.30 and R3.50 of the DRY motif in TM3, and the dynamics of the NPxxY motif in TM7. The computational results uncover a sequence of steps connecting these experimentally-identified elements of GPCR activation. The differences among the properties of the receptor molecule interacting with the ligands correlate with their distinct pharmacological properties. Combining these results with quantitative analysis of membrane deformation obtained with our new method (Mondal et al, Biophysical Journal 2011), we show that distinct conformational rearrangements produced by the three ligands also elicit different responses in the surrounding membrane. The differential reorganization of the receptor environment is reflected in (i)-the involvement of cholesterol in the activation of the 5-HT_2AR, and (ii)-different extents and patterns of membrane deformations. These findings are discussed in the context of their likely functional consequences and a predicted mechanism of ligand-specific GPCR oligomerization.

The 5-HT_2A receptor for the neurotransmitter serotonin (5-HT) belongs to family A (rhodopsin-like) G-protein coupled receptors (GPCRs), one of the most important classes of membrane proteins that are targeted by an extensive and diverse collection of external stimuli. Recently we learned that different ligands targeting the same GPCR can elicit different biological responses, but the mechanisms remain unknown. We address this fundamental question for the serotonin 5-HT_2A receptor, because it is known to respond to the binding of structurally diverse ligands by producing similar stimuli in the cell, and to the binding of quite similar ligands with dramatically different responses. Molecular dynamics simulations of molecular models of the serotonin 5-HT_2A receptor in complex with pharmacologically distinct ligands show the dynamic rearrangements of the receptor molecule to be different for these ligands, and the nature and extents of the rearrangements reflect the known pharmacological properties of the ligands as full, partial or inverse activators of the receptor. The different rearrangements of the receptor molecule are shown to produce different rearrangements of the surrounding membrane, a remodeling of the environment that can have differential ligand-determined effects on receptor function and association in the cell's membrane.

Computational studies of molecular machines: the ribosome

The past decade has produced an avalanche of experimental data on the structure and dynamics of the ribosome. Groundbreaking studies in structural biology and kinetics have placed important constraints on ribosome structural dynamics. However, a gulf remains between static structures and time dependent data. In particular, X-ray crystallography and cryo-EM studies produce static models of the ribosome in various states, but lack dynamic information. Single molecule studies produce information on the rates of transitions between these states but do not have high-resolution spatial information. Computational studies have aided in bridging this gap by providing atomic resolution simulations of structural fluctuations and transitions between configurations.

Conformational Transitions and Convergence of Absolute Binding Free Energy Calculations

The Binding Energy Distribution Analysis Method (BEDAM) is employed to compute the standard binding free energies of a series of ligands to a FK506 binding protein (FKBP12) with implicit solvation. Binding free energy estimates are in reasonably good agreement with experimental affinities. The conformations of the complexes identified by the simulations are in good agreement with crystallographic data, which was not used to restrain ligand orientations. The BEDAM method is based on λ -hopping Hamiltonian parallel Replica Exchange (HREM) molecular dynamics conformational sampling, the OPLS-AA/AGBNP2 effective potential, and multi-state free energy estimators (MBAR). Achieving converged and accurate results depends on all of these elements of the calculation. Convergence of the binding free energy is tied to the level of convergence of binding energy distributions at critical intermediate states where bound and unbound states are at equilibrium, and where the rate of binding/unbinding conformational transitions is maximal. This finding mirrors similar observations in the context of order/disorder transitions as for example in protein folding. Insights concerning the physical mechanism of ligand binding and unbinding are obtained. Convergence for the largest FK506 ligand is achieved only after imposing strict conformational restraints, which however require accurate prior structural knowledge of the structure of the complex. The analytical AGBNP2 model is found to underestimate the magnitude of the hydrophobic driving force towards binding in these systems characterized by loosely packed protein-ligand binding interfaces. Rescoring of the binding energies using a numerical surface area model corrects this deficiency. This study illustrates the complex interplay between energy models, exploration of conformational space, and free energy estimators needed to obtain robust estimates from binding free energy calculations.

Molecular dynamics simulations and drug discovery

This review discusses the many roles atomistic computer simulations of macromolecular (for example, protein) receptors and their associated small-molecule ligands can play in drug discovery, including the identification of cryptic or allosteric binding sites, the enhancement of traditional virtual-screening methodologies, and the direct prediction of small-molecule binding energies. The limitations of current simulation methodologies, including the high computational costs and approximations of molecular forces required, are also discussed. With constant improvements in both computer power and algorithm design, the future of computer-aided drug design is promising; molecular dynamics simulations are likely to play an increasingly important role.

A molecular mechanics approach to modeling protein-ligand interactions: relative binding affinities in congeneric series

We introduce the "Prime-ligand" method for ranking ligands in congeneric series. The method employs a single scoring function, the OPLS-AA/GBSA molecular mechanics/implicit solvent model, for all stages of sampling and scoring. We evaluate the method using 12 test sets of congeneric series for which experimental binding data is available in the literature, as well as the structure of one member of the series bound to the protein. Ligands are "docked" by superimposing a common stem fragment among the compounds in the series using a crystal complex from the Protein Data Bank and sampling the conformational space of the variable region. Our results show good correlation between our predicted rankings and the experimental data for cases in which binding affinities differ by at least 1 order of magnitude. For 11 out of 12 cases, >90% of such ligand pairs could be correctly ranked, while for the remaining case, Factor Xa, 76% of such pairs were correctly ranked. A small number of compounds could not be docked using the current protocol because of the large size of functional groups that could not be accommodated by a rigid receptor. CPU requirements for the method, involving CPU minutes per ligand, are modest compared with more rigorous methods that use similar force fields, such as free energy perturbation. We also benchmark the scoring function using series of ligands bound to the same protein within the CSAR data set. We demonstrate that energy minimization of ligands in the crystal structures is critical to obtain any correlation with experimentally determined binding affinities.

Alchemical free energy methods for drug discovery: progress and challenges

Improved rational drug design methods are needed to lower the cost and increase the success rate of drug discovery and development. Alchemical binding free energy calculations, one potential tool for rational design, have progressed rapidly over the past decade, but still fall short of providing robust tools for pharmaceutical engineering. Recent studies, especially on model receptor systems, have clarified many of the challenges that must be overcome for robust predictions of binding affinity to be useful in rational design. In this review, inspired by a recent joint academic/industry meeting organized by the authors, we discuss these challenges and suggest a number of promising approaches for overcoming them.

Advances in all atom sampling methods for modeling protein-ligand binding affinities

Conformational dynamics plays a fundamental role in the regulation of molecular recognition processes. Conformational heterogeneity and entropy variations upon binding, although not always evident from the analysis of structural data, can substantially affect affinity and specificity. Computer modeling is able to provide some of the most direct insights into these aspects of molecular recognition. We review recent physics-based computational studies that employ advanced conformational sampling algorithms and effective potentials to model the three main classes of degrees of freedom relevant to the binding process: ligand positioning relative to the receptor, ligand and receptor internal reorganization, and hydration. Collectively these studies show that all of these elements are important for proper modeling of protein-ligand interactions.

Recent theoretical and computational advances for modeling protein-ligand binding affinities

We review recent theoretical and algorithmic advances for the modeling of protein ligand binding free energies. We first describe a statistical mechanics theory of noncovalent association, with particular focus on deriving the fundamental formulas on which computational methods are based. The second part reviews the main computational models and algorithms in current use or development, pointing out the relations with each other and with the theory developed in the first part. Particular emphasis is given to the modeling of conformational reorganization and entropic effect. The methods reviewed are free energy perturbation, double decoupling, the Binding Energy Distribution Analysis Method, the potential of mean force method, mining minima and MM/PBSA. These models have different features and limitations, and their ranges of applicability vary correspondingly. Yet their origins can all be traced back to a single fundamental theory.