Limits of Free Energy Computation for Protein-Ligand Interactions

MDFit: automated molecular simulations workflow enables high throughput assessment of ligands-protein dynamics

Molecular dynamics (MD) simulation is a powerful tool for characterizing ligand-protein conformational dynamics and offers significant advantages over docking and other rigid structure-based computational methods. However, setting up, running, and analyzing MD simulations continues to be a multi-step process making it cumbersome to assess a library of ligands in a protein binding pocket using MD. We present an automated workflow that streamlines setting up, running, and analyzing Desmond MD simulations for protein-ligand complexes using machine learning (ML) models. The workflow takes a library of pre-docked ligands and a prepared protein structure as input, sets up and runs MD with each protein-ligand complex, and generates simulation fingerprints for each ligand. Simulation fingerprints (SimFP) capture protein-ligand compatibility, including stability of different ligand-pocket interactions and other useful metrics that enable easy rank-ordering of the ligand library for pocket optimization. SimFPs from a ligand library are used to build & deploy ML models that predict binding assay outcomes and automatically infer important interactions. Unlike relative free-energy methods that are constrained to assess ligands with high chemical similarity, ML models based on SimFPs can accommodate diverse ligand sets. We present two case studies on how SimFP helps delineate structure-activity relationship (SAR) trends and explain potency differences across matched-molecular pairs of (1) cyclic peptides targeting PD-L1 and (2) small molecule inhibitors targeting CDK9.

Prediction of protein-ligand binding affinity via deep learning models

Accurately predicting the binding affinity between proteins and ligands is crucial in drug screening and optimization, but it is still a challenge in computer-aided drug design. The recent success of AlphaFold2 in predicting protein structures has brought new hope for deep learning (DL) models to accurately predict protein-ligand binding affinity. However, the current DL models still face limitations due to the low-quality database, inaccurate input representation and inappropriate model architecture. In this work, we review the computational methods, specifically DL-based models, used to predict protein-ligand binding affinity. We start with a brief introduction to protein-ligand binding affinity and the traditional computational methods used to calculate them. We then introduce the basic principles of DL models for predicting protein-ligand binding affinity. Next, we review the commonly used databases, input representations and DL models in this field. Finally, we discuss the potential challenges and future work in accurately predicting protein-ligand binding affinity via DL models.

Free Energy Calculations Using the Movable Type Method with Molecular Dynamics Driven Protein–Ligand Sampling

Fast and accurate biomolecular free energy estimation has been a significant interest for decades, and with recent advances in computer hardware, interest in new method development in this field has even grown. Thorough configurational state sampling using molecular dynamics (MD) simulations has long been applied to the estimation of the free energy change corresponding to the receptor-ligand complexing process. However, performing large-scale simulation is still a computational burden for the high-throughput hit screening. Among molecular modeling tools, docking and scoring methods are widely used during the early stages of the drug discovery process in that they can rapidly generate discrete receptor-ligand binding modes and their individual binding affinities. Unfortunately, the lack of thorough conformational sampling in docking and scoring protocols leads to difficulty discovering global minimum binding modes on a complicated energy landscape. The Movable Type (MT) method is a novel absolute binding free energy approach which has demonstrated itself to be robust across a wide range of targets and ligands. Traditionally, the MT method is used with protein-ligand binding modes generated with rigid-receptor or flexible-receptor (induced fit) docking protocols; however, these protocols are by their nature less likely to be effective with more highly flexible targets or with those situations in which binding involves multiple step pathways. In these situations, more thorough samplings are required to better explain the free energy of binding. Therefore, to explore the prediction capability and computational efficiency of the MT method when using more thorough protein-ligand conformational sampling protocols, in the present work, we introduced a series of binding mode modeling protocols ranging from conventional docking routines to single-trajectory conventional molecular dynamics (cMD) and parallel Monte Carlo molecular dynamics (MCMD). Through validation against several structurally and mechanistically diverse protein-ligand test sets, we explore the performance of the MT method as a virtual screening tool to work with the docking protocols and as an MD simulation-based binding free energy tool.

Computational methods for calculation of protein-ligand binding affinities in structure-based drug design

Drug design is an expensive and time-consuming process. Any method that allows reducing the time the costs of the drug development project can have great practical value for the pharmaceutical industry. In structure-based drug design, affinity prediction methods are of great importance. The majority of methods used to predict binding free energy in protein-ligand complexes use molecular mechanics methods. However, many limitations of these methods in describing interactions exist. An attempt to go beyond these limits is the application of quantum-mechanical description for all or only part of the analyzed system. However, the extensive use of quantum mechanical (QM) approaches in drug discovery is still a demanding challenge. This chapter briefly reviews selected methods used to calculate protein-ligand binding affinity applied in virtual screening (VS), rescoring of docked poses, and lead optimization stage, including QM methods based on molecular simulations.

Data Mining Meets Machine Learning: A Novel ANN-based Multi-Body Interaction Docking Scoring Function (MBI-Score) based on Utilizing Frequent Geometric and Chemical Patterns of Interfacial Atoms in Native Protein-Ligand Complexes

Accurate prediction of binding poses is crucial to structure-based drug design. We employ two powerful artificial intelligence (AI) approaches, data-mining and machine-learning, to design artificial neural network (ANN) based pose-scoring function. It is a simple machine-learning-based statistical function that employs frequent geometric and chemical patterns of interacting atoms at protein-ligand interfaces. The patterns are derived by mining interfaces of "native" protein-ligand complexes. Each interface is represented by a graph where nodes are atoms and edges connect protein-ligand interfacial atoms located within certain cutoff distance of each other. Applying frequent subgraph mining to these interfaces provides "native" frequent patterns of interacting atoms. Subsequently, given a pose for a protein-ligand complex of interest, the pose-scoring function (the information-processing unit or neuron) calculates the degree of matching between the interaction patterns present at the pose's interface and the native frequent patterns. The pose-scoring function takes into account the frequency of occurrence of the matching native patterns, the size of the match, and the degree of geometrical similarity between pose-specific and matching native frequent patterns. This novel "multi-body interaction" pose-scoring function (MBI-Score) was validated using two databases, PDBbind and Astex-85, and it outperformed seven commonly used commercial scoring functions. MBI-Score is available at www.khashanlab.org/mbi-score.

The future of biomolecular simulation in the pharmaceutical industry: what we can learn from aerodynamics modelling and weather prediction. Part 1. understanding the physical and computational complexity of in silico drug design

The predictive power of simulation has become embedded in the infrastructure of modern economies. Computer-aided design is ubiquitous throughout industry. In aeronautical engineering, built infrastructure and materials manufacturing, simulations are routinely used to compute the performance of potential designs before construction. The ability to predict the behaviour of products is a driver of innovation by reducing the cost barrier to new designs, but also because radically novel ideas can be piloted with relatively little risk. Accurate weather forecasting is essential to guide domestic and military flight paths, and therefore the underpinning simulations are critical enough to have implications for national security. However, in the pharmaceutical and biotechnological industries, the application of computer simulations remains limited by the capabilities of the technology with respect to the complexity of molecular biology and human physiology. Over the last 30 years, molecular-modelling tools have gradually gained a degree of acceptance in the pharmaceutical industry. Drug discovery has begun to benefit from physics-based simulations. While such simulations have great potential for improved molecular design, much scepticism remains about their value. The motivations for such reservations in industry and areas where simulations show promise for efficiency gains in preclinical research are discussed. In this, the first of two complementary papers, the scientific and technical progress that needs to be made to improve the predictive power of biomolecular simulations, and how this might be achieved, is firstly discussed (Part 1). In Part 2, the status of computer simulations in pharma is contrasted with aerodynamics modelling and weather forecasting, and comments are made on the cultural changes needed for equivalent computational technologies to become integrated into life-science industries.

Locating ligand binding sites in G-protein coupled receptors using combined information from docking and sequence conservation

GPCRs (G-protein coupled receptors) are the largest family of drug targets and share a conserved structure. Binding sites are unknown for many important GPCR ligands due to the difficulties of GPCR recombinant expression, biochemistry, and crystallography. We describe our approach, ConDockSite, for predicting ligand binding sites in class A GPCRs using combined information from surface conservation and docking, starting from crystal structures or homology models. We demonstrate the effectiveness of ConDockSite on crystallized class A GPCRs such as the beta2 adrenergic and A2A adenosine receptors. We also demonstrate that ConDockSite successfully predicts ligand binding sites from high-quality homology models. Finally, we apply ConDockSite to predict the ligand binding sites on a structurally uncharacterized GPCR, GPER, the G-protein coupled estrogen receptor. Most of the sites predicted by ConDockSite match those found in other independent modeling studies. ConDockSite predicts that four ligands bind to a common location on GPER at a site deep in the receptor cleft. Incorporating sequence conservation information in ConDockSite overcomes errors introduced from physics-based scoring functions and homology modeling.

Evaluation of nine condensed-phase force fields of the GROMOS, CHARMM, OPLS, AMBER, and OpenFF families against experimental cross-solvation free energies

Experimental solvation free energies are nowadays commonly included as target properties in the validation of condensed-phase force fields, sometimes even in their calibration. In a previous article [Kashefolgheta et al., J. Chem. Theory. Comput., 2020, 16, 7556-7580], we showed how the involved comparison between experimental and simulation results could be made more systematic by considering a full matrix of cross-solvation free energies . For a set of N molecules that are all in the liquid state under ambient conditions, such a matrix encompasses N×N entries for considering each of the N molecules either as solute (A) or as solvent (B). In the quoted study, a cross-solvation matrix of 25 × 25 experimental value was introduced, considering 25 small molecules representative for alkanes, chloroalkanes, ethers, ketones, esters, alcohols, amines, and amides. This experimental data was used to compare the relative accuracies of four popular condensed-phase force fields, namely GROMOS-2016H66, OPLS-AA, AMBER-GAFF, and CHARMM-CGenFF. In the present work, the comparison is extended to five additional force fields, namely GROMOS-54A7, GROMOS-ATB, OPLS-LBCC, AMBER-GAFF2, and OpenFF. Considering these nine force fields, the correlation coefficients between experimental values and simulation results range from 0.76 to 0.88, the root-mean-square errors (RMSEs) from 2.9 to 4.8 kJ mol-1, and average errors (AVEEs) from -1.5 to +1.0 kJ mol-1. In terms of RMSEs, GROMOS-2016H66 and OPLS-AA present the best accuracy (2.9 kJ mol-1), followed by OPLS-LBCC, AMBER-GAFF2, AMBER-GAFF, and OpenFF (3.3 to 3.6 kJ mol-1), and then by GROMOS-54A7, CHARM-CGenFF, and GROMOS-ATB (4.0 to 4.8 kJ mol-1). These differences are statistically significant but not very pronounced, and are distributed rather heterogeneously over the set of compounds within the different force fields.

The critical role of QM/MM X-ray refinement and accurate tautomer/protomer determination in structure-based drug design

Conventional protein:ligand crystallographic refinement uses stereochemistry restraints coupled with a rudimentary energy functional to ensure the correct geometry of the model of the macromolecule-along with any bound ligand(s)-within the context of the experimental, X-ray density. These methods generally lack explicit terms for electrostatics, polarization, dispersion, hydrogen bonds, and other key interactions, and instead they use pre-determined parameters (e.g. bond lengths, angles, and torsions) to drive structural refinement. In order to address this deficiency and obtain a more complete and ultimately more accurate structure, we have developed an automated approach for macromolecular refinement based on a two layer, QM/MM (ONIOM) scheme as implemented within our DivCon Discovery Suite and "plugged in" to two mainstream crystallographic packages: PHENIX and BUSTER. This implementation is able to use one or more region layer(s), which is(are) characterized using linear-scaling, semi-empirical quantum mechanics, followed by a system layer which includes the balance of the model and which is described using a molecular mechanics functional. In this work, we applied our Phenix/DivCon refinement method-coupled with our XModeScore method for experimental tautomer/protomer state determination-to the characterization of structure sets relevant to structure-based drug design (SBDD). We then use these newly refined structures to show the impact of QM/MM X-ray refined structure on our understanding of function by exploring the influence of these improved structures on protein:ligand binding affinity prediction (and we likewise show how we use post-refinement scoring outliers to inform subsequent X-ray crystallographic efforts). Through this endeavor, we demonstrate a computational chemistry ↔ structural biology (X-ray crystallography) "feedback loop" which has utility in industrial and academic pharmaceutical research as well as other allied fields.

An Active Site Inhibitor Induces Conformational Penalties for ACE2 Recognition by the Spike Protein of SARS-CoV-2

The novel RNA virus, severe acute respiratory syndrome coronavirus II (SARS-CoV-2), is currently the leading cause of mortality in 2020, having led to over 1.6 million deaths and infecting over 75 million people worldwide by December 2020. While vaccination has started and several clinical trials for a number of vaccines are currently underway, there is a pressing need for a cure for those already infected with the virus. Of particular interest in the design of anti-SARS-CoV-2 therapeutics is the human protein angiotensin converting enzyme II (ACE2) to which this virus adheres before entry into the host cell. The SARS-CoV-2 virion binds to cell-surface bound ACE2 via interactions of the spike protein (s-protein) on the viral surface with ACE2. In this paper, we use all-atom molecular dynamics simulations and binding enthalpy calculations to determine the effect that a bound ACE2 active site inhibitor (MLN-4760) would have on the binding affinity of SARS-CoV-2 s-protein with ACE2. Our analysis indicates that the binding enthalpy could be reduced for s-protein adherence to the active site inhibitor-bound ACE2 protein by as much as 1.48-fold as an upper limit. This weakening of binding strength was observed to be due to the destabilization of the interactions between ACE2 residues Glu-35, Glu-37, Tyr-83, Lys-353, and Arg-393 and the SARS-CoV-2 s-protein receptor binding domain (RBD). The conformational changes were shown to lead to weakening of ACE2 interactions with SARS-CoV-2 s-protein, therefore reducing s-protein binding strength. Further, we observed increased conformational lability of the N-terminal helix and a conformational shift of a significant portion of the ACE2 motifs involved in s-protein binding, which may affect the kinetics of the s-protein binding when the small molecule inhibitor is bound to the ACE2 active site. These observations suggest potential new ways for interfering with the SARS-CoV-2 adhesion by modulating ACE2 conformation through distal active site inhibitor binding.

MovableType Software for Fast Free Energy-Based Virtual Screening: Protocol Development, Deployment, Validation, and Assessment

For decades, the complicated energy surfaces found in macromolecular protein:ligand structures, which require large amounts of computational time and resources for energy state sampling, have been an inherent obstacle to fast, routine free energy estimation in industrial drug discovery efforts. Beginning in 2013, the Merz research group addressed this cost with the introduction of a novel sampling methodology termed “Movable Type” (MT). Using numerical integration methods, the MT method reduces the computational expense for energy state sampling by independently calculating each atomic partition function from an initial molecular conformation in order to estimate the molecular free energy using ensembles of the atomic partition functions. In this work, we report a software package, the DivCon Discovery Suite with the MovableType module from QuantumBio Inc., that performs this MT free energy estimation protocol in a fast, fully encapsulated manner. We discuss the computational procedures and improvements to the original work, and we detail the corresponding settings for this software package. Finally, we introduce two validation benchmarks to evaluate the overall robustness of the method against a broad range of protein:ligand structural cases. With these publicly available benchmarks, we show that the method can use a variety of input types and parameters and exhibits comparable predictability whether the method is presented with “expensive” X-ray structures or “inexpensively docked” theoretical models. We also explore some next steps for the method. The MovableType software is available at http://www.quantumbioinc.com/

Multidimensional Global Optimization and Robustness Analysis in the Context of Protein-Ligand Binding

Accuracy of protein-ligand binding free energy calculations utilizing implicit solvent models is critically affected by parameters of the underlying dielectric boundary, specifically, the atomic and water probe radii. Here, a global multidimensional optimization pipeline is developed to find optimal atomic radii specifically for protein-ligand binding calculations in implicit solvent. The computational pipeline has these three key components: (1) a massively parallel implementation of a deterministic global optimization algorithm (VTDIRECT95), (2) an accurate yet reasonably fast generalized Born implicit solvent model (GBNSR6), and (3) a novel robustness metric that helps distinguish between nearly degenerate local minima via a postprocessing step of the optimization. A graph-based "kT-connectivity" approach to explore and visualize the multidimensional energy landscape is proposed: local minima that can be reached from the global minimum without exceeding a given energy threshold (kT) are considered to be connected. As an illustration of the capabilities of the optimization pipeline, we apply it to find a global optimum in the space of just five radii: four atomic (O, H, N, and C) radii and water probe radius. The optimized radii, ρW = 1.37 Å, ρC = 1.40 Å, ρH = 1.55 Å, ρN = 2.35 Å, and ρO = 1.28 Å, lead to a closer agreement of electrostatic binding free energies with the explicit solvent reference than two commonly used sets of radii previously optimized for small molecules. At the same time, the ability of the optimizer to find the global optimum reveals fundamental limits of the common two-dielectric implicit solvation model: the computed electrostatic binding free energies are still almost 4 kcal/mol away from the explicit solvent reference. The proposed computational approach opens the possibility to further improve the accuracy of practical computational protocols for binding free energy calculations.

Rigorous Free Energy Simulations in Virtual Screening

Virtual high throughput screening (vHTS) in drug discovery is a powerful approach to identify hits: when applied successfully, it can be much faster and cheaper than experimental high-throughput screening approaches. However, mainstream vHTS tools have significant limitations: ligand-based methods depend on knowledge of existing chemical matter, while structure-based tools such as docking involve significant approximations that limit their accuracy. Recent advances in scientific methods coupled with dramatic speedups in computational processing with GPUs make this an opportune time to consider the role of more rigorous methods that could improve the predictive power of vHTS workflows. In this Perspective, we assert that alchemical binding free energy methods using all-atom molecular dynamics simulations have matured to the point where they can be applied in virtual screening campaigns as a final scoring stage to prioritize the top molecules for experimental testing. Specifically, we propose that alchemical absolute binding free energy (ABFE) calculations offer the most direct and computationally efficient approach within a rigorous statistical thermodynamic framework for computing binding energies of diverse molecules, as is required for virtual screening. ABFE calculations are particularly attractive for drug discovery at this point in time, where the confluence of large-scale genomics data and insights from chemical biology have unveiled a large number of promising disease targets for which no small molecule binders are known, precluding ligand-based approaches, and where traditional docking approaches have foundered to find progressible chemical matter.

Quantum Mechanical Investigation of Three-Dimensional Activity Cliffs Using the Molecules-in-Molecules Fragmentation-Based Method

The concept of activity cliff (AC) (i.e., a small structural modification resulting in a substantial bioactivity change) is widely encountered in medicinal chemistry during compound design. Whereas the study of ACs is of high interest as it provides a wealth of opportunities for effective drug design, its practical application in the actual drug development process has been difficult because of significant computational challenges. To provide some understanding of the ACs, we have carried out a rigorous quantum-mechanical investigation of the electronic interactions of a wide range of ACs (205 cliffs formed by 261 protein-ligand complexes covering 37 different receptor types) using multilayer molecules-in-molecules (MIM) fragmentation-based methodology. The MIM methodology enables performing accurate high-level quantum mechanical (QM) calculations at a substantially lower computational cost, while allowing for a quantitative decomposition of the protein-ligand binding energy into the contributions from individual residues, solvation, and entropy. Our investigation in this study is mainly focused on whether the QM binding energy calculation can correctly identify the higher potency cliff partner for a given ligand pair having a sufficiently high activity difference. We have also analyzed the effect of including crystal water molecules as a part of the receptor as well as the impact of ligand desolvation energy on the correct identification of the more potent ligand in a cliff pair. Our analysis reveals that, in the majority of the cases, the AC prediction could be significantly improved by carefully identifying the critical crystal water molecules, whereas the contribution from the ligand desolvation also remains essential. Additionally, we have exploited the residue-specific interaction energies provided by MIM to identify the key residues and interaction hot-spots that are responsible for the experimentally observed drastic activity changes. The results show that our MIM fragmentation-based protocol provides comprehensive interaction energy profiles that can be employed to understand the distinctiveness of ligand modifications, for potential applications in structure-based drug design.

PLUG (Pruning of Local Unrealistic Geometries) removes restrictions on biophysical modeling for protein design

Protein design algorithms must search an enormous conformational space to identify favorable conformations. As a result, those that perform this search with guarantees of accuracy generally start with a conformational pruning step, such as dead-end elimination (DEE). However, the mathematical assumptions of DEE-based pruning algorithms have up to now severely restricted the biophysical model that can feasibly be used in protein design. To lift these restrictions, I propose to prune local unrealistic geometries (PLUG) using a linear programming-based method. PLUG's biophysical model consists only of well-known lower bounds on interatomic distances. PLUG is intended as preprocessing for energy-based protein design calculations, whose biophysical model need not support DEE pruning. Based on 96 test cases, PLUG is at least as effective at pruning as DEE for larger protein designs-the type that most require pruning. When combined with the LUTE protein design algorithm, PLUG greatly facilitates designs that account for continuous entropy, large multistate designs with continuous flexibility, and designs with extensive continuous backbone flexibility and advanced nonpairwise energy functions. Many of these designs are tractable only with PLUG, either for empirical reasons (LUTE's machine learning step achieves an accurate fit only after PLUG pruning), or for theoretical reasons (many energy functions are fundamentally incompatible with DEE).

Accuracy Comparison of Generalized Born Models in the Calculation of Electrostatic Binding Free Energies

The need for accurate yet efficient representation of the aqueous environment in biomolecular modeling has led to the development of a variety of generalized Born (GB) implicit solvent models. While many studies have focused on the accuracy of available GB models in predicting solvation free energies, a systematic assessment of the quality of these models in binding free energy calculations, crucial for rational drug design, has not been undertaken. Here, we evaluate the accuracies of eight common GB flavors (GB-HCT, GB-OBC, GB-neck2, GBNSR6, GBSW, GBMV1, GBMV2, and GBMV3), available in major molecular dynamics packages, in predicting the electrostatic binding free energies ( ΔΔ G_el) for a diverse set of 60 biomolecular complexes belonging to four main classes: protein-protein, protein-drug, RNA-peptide, and small complexes. The GB flavors are examined in terms of their ability to reproduce the results from the Poisson-Boltzmann (PB) model, commonly used as accuracy reference in this context. We show that the agreement with the PB of ΔΔ G_el estimates varies widely between different GB models and also across different types of biomolecular complexes, with R² correlations ranging from 0.3772 to 0.9986. A surface-based "R6" GB model recently implemented in AMBER shows the closest overall agreement with reference PB ( R² = 0.9949, RMSD = 8.75 kcal/mol). The RNA-peptide and protein-drug complex sets appear to be most challenging for all but one model, as indicated by the large deviations from the PB in ΔΔ G_el. Small neutral complexes present the least challenge for most of the GB models tested. The quantitative demonstration of the strengths and weaknesses of the GB models across the diverse complex types provided here can be used as a guide for practical computations and future development efforts.

Activity-based classification circumvents affinity prediction problems for pyrrolidine carboxamide inhibitors of InhA

Developing reliable structure-based activity prediction models for a particular ligand series can be challenging if the target is flexible and the affinity range of the training compounds is narrow. For a data set of 44 pyrrolidine carboxamide inhibitors of the mycobacterial enoyl-ACP-reductase InhA this proved to be case, as scoring methods of various origin and complexity did not succeed in providing practically useful correlations with experimental inhibition data. In contrast, logistic regression models for activity-based classification trained with combinations of scoring functions led to good separation of the more active inhibitors from the weakest compounds. The approach is suggested as an alternative in cases where classical scoring and ranking procedures fail.

Relative Binding Free Energy Calculations in Drug Discovery: Recent Advances and Practical Considerations

Accurate in silico prediction of protein-ligand binding affinities has been a primary objective of structure-based drug design for decades due to the putative value it would bring to the drug discovery process. However, computational methods have historically failed to deliver value in real-world drug discovery applications due to a variety of scientific, technical, and practical challenges. Recently, a family of approaches commonly referred to as relative binding free energy (RBFE) calculations, which rely on physics-based molecular simulations and statistical mechanics, have shown promise in reliably generating accurate predictions in the context of drug discovery projects. This advance arises from accumulating developments in the underlying scientific methods (decades of research on force fields and sampling algorithms) coupled with vast increases in computational resources (graphics processing units and cloud infrastructures). Mounting evidence from retrospective validation studies, blind challenge predictions, and prospective applications suggests that RBFE simulations can now predict the affinity differences for congeneric ligands with sufficient accuracy and throughput to deliver considerable value in hit-to-lead and lead optimization efforts. Here, we present an overview of current RBFE implementations, highlighting recent advances and remaining challenges, along with examples that emphasize practical considerations for obtaining reliable RBFE results. We focus specifically on relative binding free energies because the calculations are less computationally intensive than absolute binding free energy (ABFE) calculations and map directly onto the hit-to-lead and lead optimization processes, where the prediction of relative binding energies between a reference molecule and new ideas (virtual molecules) can be used to prioritize molecules for synthesis. We describe the critical aspects of running RBFE calculations, from both theoretical and applied perspectives, using a combination of retrospective literature examples and prospective studies from drug discovery projects. This work is intended to provide a contemporary overview of the scientific, technical, and practical issues associated with running relative binding free energy simulations, with a focus on real-world drug discovery applications. We offer guidelines for improving the accuracy of RBFE simulations, especially for challenging cases, and emphasize unresolved issues that could be improved by further research in the field.

Structural Basis and Mechanism of Chiral Benzedrine Molecules Interacting With Third Dopamine Receptor

In order to investigate the chiral benzedrine molecules corresponding to their different characteristics in biochemical systems, we studied their interaction with D3 R using the docking method, molecular dynamic simulation, and quantum chemistry. The obtained results indicate that the active residues for R-benzedrine (RAT) bound with D3 R are Ala132, Asp133, and Tyr55, while Asn57, Asp133, Asp168, Cys172, Gly54, Trp24, and Vall136 act as the active residues for S-benzedrine (SAT). The different active pockets are observed for ART or SAT because they possess different active residues. The binding energies between RAT and SAT with D3 R were determined to be -44.0 kJ.mol(-1) and -71.2 kJ.mol(-1) , respectively. These results demonstrate that SAT within the studied pocket of D3 R has a stronger capability of binding with D3 R, while it is more feasible for RAT to leave from the interior positions of D3 R. In addition, the results suggest that the D3 R protein can recognize chiral benzedrine molecules and influence their different addictive and pharmacological effects in biochemical systems. Chirality 28:674-685, 2016. © 2016 Wiley Periodicals, Inc.

An Atomistic Statistically Effective Energy Function for Computational Protein Design

Shortcomings in the definition of effective free-energy surfaces of proteins are recognized to be a major contributory factor responsible for the low success rates of existing automated methods for computational protein design (CPD). The formulation of an atomistic statistically effective energy function (SEEF) suitable for a wide range of CPD applications and its derivation from structural data extracted from protein domains and protein-ligand complexes are described here. The proposed energy function comprises nonlocal atom-based and local residue-based SEEFs, which are coupled using a novel atom connectivity number factor to scale short-range, pairwise, nonbonded atomic interaction energies and a surface-area-dependent cavity energy term. This energy function was used to derive additional SEEFs describing the unfolded-state ensemble of any given residue sequence based on computed average energies for partially or fully solvent-exposed fragments in regions of irregular structure in native proteins. Relative thermal stabilities of 97 T4 bacteriophage lysozyme mutants were predicted from calculated energy differences for folded and unfolded states with an average unsigned error (AUE) of 0.84 kcal mol(-1) when compared to experiment. To demonstrate the utility of the energy function for CPD, further validation was carried out in tests of its capacity to recover cognate protein sequences and to discriminate native and near-native protein folds, loop conformers, and small-molecule ligand binding poses from non-native benchmark decoys. Experimental ligand binding free energies for a diverse set of 80 protein complexes could be predicted with an AUE of 2.4 kcal mol(-1) using an additional energy term to account for the loss in ligand configurational entropy upon binding. The atomistic SEEF is expected to improve the accuracy of residue-based coarse-grained SEEFs currently used in CPD and to extend the range of applications of extant atom-based protein statistical potentials.

Evaluating thermodynamic integration performance of the new amber molecular dynamics package and assess potential halogen bonds of enoyl-ACP reductase (FabI) benzimidazole inhibitors

Thermodynamic integration (TI) can provide accurate binding free energy insights in a lead optimization program, but its high computational expense has limited its usage. In the effort of developing an efficient and accurate TI protocol for FabI inhibitors lead optimization program, we carefully compared TI with different Amber molecular dynamics (MD) engines (sander and pmemd), MD simulation lengths, the number of intermediate states and transformation steps, and the Lennard-Jones and Coulomb Softcore potentials parameters in the one-step TI, using eleven benzimidazole inhibitors in complex with Francisella tularensis enoyl acyl reductase (FtFabI). To our knowledge, this is the first study to extensively test the new AMBER MD engine, pmemd, on TI and compare the parameters of the Softcore potentials in the one-step TI in a protein-ligand binding system. The best performing model, the one-step pmemd TI, using 6 intermediate states and 1 ns MD simulations, provides better agreement with experimental results (RMSD = 0.52 kcal/mol) than the best performing implicit solvent method, QM/MM-GBSA from our previous study (RMSD = 3.00 kcal/mol), while maintaining similar efficiency. Briefly, we show the optimized TI protocol to be highly accurate and affordable for the FtFabI system. This approach can be implemented in a larger scale benzimidazole scaffold lead optimization against FtFabI. Lastly, the TI results here also provide structure-activity relationship insights, and suggest the parahalogen in benzimidazole compounds might form a weak halogen bond with FabI, which is a well-known halogen bond favoring enzyme.

Protein-Ligand Electrostatic Binding Free Energies from Explicit and Implicit Solvation

Accurate yet efficient computational models of solvent environment are central for most calculations that rely on atomistic modeling, such as prediction of protein-ligand binding affinities. In this study, we evaluate the accuracy of a recently developed generalized Born implicit solvent model, GBNSR6 (Aguilar et al. J. Chem. Theory Comput. 2010, 6, 3613-3639), in estimating the electrostatic solvation free energies (ΔG(pol)) and binding free energies (ΔΔG(pol)) for small protein-ligand complexes. We also compare estimates based on three different explicit solvent models (TIP3P, TIP4PEw, and OPC). The two main findings are as follows. First, the deviation (RMSD = 7.04 kcal/mol) of GBNSR6 binding affinities from commonly used TIP3P reference values is comparable to the deviations between explicit models themselves, e.g. TIP4PEw vs TIP3P (RMSD = 5.30 kcal/mol). A simple uniform adjustment of the atomic radii by a single scaling factor reduces the RMS deviation of GBNSR6 from TIP3P to within the above "error margin" - differences between ΔΔG(pol) estimated by different common explicit solvent models. The simple radii scaling virtually eliminates the systematic deviation (ΔΔG(pol)) between GBNSR6 and two out of the three explicit water models and significantly reduces the deviation from the third explicit model. Second, the differences between electrostatic binding energy estimates from different explicit models is disturbingly large; for example, the deviation between TIP4PEw and TIP3P estimates of ΔΔG(pol) values can be up to ∼50% or ∼9 kcal/mol, which is significantly larger than the "chemical accuracy" goal of ∼1 kcal/mol. The absolute ΔG(pol) calculated with different explicit models could differ by tens of kcal/mol. These discrepancies point to unacceptably high sensitivity of binding affinity estimates to the choice of common explicit water models. The absence of a clear "gold standard" among these models strengthens the case for the use of accurate implicit solvation models for binding energetics, which may be orders of magnitude faster.

Binding affinities by alchemical perturbation using QM/MM with a large QM system and polarizable MM model

The most general way to improve the accuracy of binding-affinity calculations for protein-ligand systems is to use quantum-mechanical (QM) methods together with rigorous alchemical-perturbation (AP) methods. We explore this approach by calculating the relative binding free energy of two synthetic disaccharides binding to galectin-3 at a reasonably high QM level (dispersion-corrected density functional theory with a triple-zeta basis set) and with a sufficiently large QM system to include all short-range interactions with the ligand (744-748 atoms). The rest of the protein is treated as a collection of atomic multipoles (up to quadrupoles) and polarizabilities. Several methods for evaluating the binding free energy from the 3600 QM calculations are investigated in terms of stability and accuracy. In particular, methods using QM calculations only at the endpoints of the transformation are compared with the recently proposed non-Boltzmann Bennett acceptance ratio (NBB) method that uses QM calculations at several stages of the transformation. Unfortunately, none of the rigorous approaches give sufficient statistical precision. However, a novel approximate method, involving the direct use of QM energies in the Bennett acceptance ratio method, gives similar results as NBB but with better precision, ∼3 kJ/mol. The statistical error can be further reduced by performing a greater number of QM calculations.

Enhanced semiempirical QM methods for biomolecular interactions

Recent successes and failures of the application of 'enhanced' semiempirical QM (SQM) methods are reviewed in the light of the benefits and backdraws of adding dispersion (D) and hydrogen-bond (H) correction terms. We find that the accuracy of SQM-DH methods for non-covalent interactions is very often reported to be comparable to dispersion-corrected density functional theory (DFT-D), while computation times are about three orders of magnitude lower. SQM-DH methods thus open up a possibility to simulate realistically large model systems for problems both in life and materials science with comparably high accuracy.

Theoretical insight into the structural mechanism for the binding of vinblastine with tubulin

Vinblastine (VLB) is one of vinca alkaloids with high cytotoxicity toward cancer cells approved for clinical use. However, because of drug resistance, toxicity, and other side effects caused from the use of VLB, new vinca alkaloids with higher cytotoxicity toward cancer cells and other good qualities need to develop. One strategy is to further study and better understand the essence why VLB possesses the high cytotoxicity toward cancer cells. In present work, by using molecular simulation, molecular docking, density functional calculation, and the crystal structure of α,β-tubulin complex, we find two modes labeled in catharanthine moiety (CM) and vindoline moiety (VM) modes of VLB bound with the interface of α,β-tubulin to probe the essence why VLB has the high cytotoxicity toward cancer cells. In the CM mode, nine key residues B-Ser178, B-Asp179, B-Glu183, B-Tyr210, B-Asp226, C-Lys326, C-Asp327, C-Lys336, and C-Lys352 from the α,β-tubulin complex are determined as the active sites for the interaction of VLB with α,β-tubulin. Some of them such as B-Ser178, B-Glu183, B-Tyr210, B-Asp226, C-Lys326, C-Asp327, and C-Lys336 are newly identified as the active sites in present work. The affinity between VLB and the active pocket within the interface of α,β-tubulin is -60.8 kJ mol(-1) in the CM mode. In the VM mode, that is a new mode established in present paper, nine similar key residues B-Lys176, B-Ser178, B-Asp179, B-Glu183, B-Tyr210, B-Asp226, C-Lys326, C-Asp327, and C-Lys336 from the α,β-tubulin complex are found as the active sites for the interaction with VLB. The difference is from one key residue C-Lys352 in the CM mode changed to the key residue B-Lys176 in the VM mode. The affinity between VLB and the active pocket within the interface of α,β-tubulin is -96.3 kJ mol(-1) in the VM mode. Based on the results obtained in present work, and because VLB looks like two faces, composed of CM and VM both to have similar polar active groups, to interact with the active sites, we suggest double-faces sticking mechanism for the binding of VLB to the interface of α,β-tubulin. The double-faces sticking mechanism can be used to qualitatively explain high cytotoxicity toward cancer cells of vinca alkaloids including vinblastine, vincristine, vindestine, and vinorelbine approved for clinical use and vinflunine still in a phase III clinical trial. Furthermore, this mechanism will be applied to develop novel vinca alkaloids with much higher cytotoxicity toward cancer cells.

Molecular modeling of peptides

This article presents a review of the field of molecular modeling of peptides. The main focus is on atomistic modeling with molecular mechanics potentials. The description of peptide conformations and solvation through potentials is discussed. Several important computer simulation methods are briefly introduced, including molecular dynamics, accelerated sampling approaches such as replica-exchange and metadynamics, free energy simulations and kinetic network models like Milestoning. Examples of recent applications for predictions of structure, kinetics, and interactions of peptides with complex environments are described. The reliability of current simulation methods is analyzed by comparison of computational predictions obtained using different models with each other and with experimental data. A brief discussion of coarse-grained modeling and future directions is also presented.

Using quantum mechanical approaches to study biological systems

Conspectus Quantum mechanics (QM) has revolutionized our understanding of the structure and reactivity of small molecular systems. Given the tremendous impact of QM in this research area, it is attractive to believe that this could also be brought into the biological realm where systems of a few thousand atoms and beyond are routine. Applying QM methods to biological problems brings an improved representation to these systems by the direct inclusion of inherently QM effects such as polarization and charge transfer. Because of the improved representation, novel insights can be gleaned from the application of QM tools to biomacromolecules in aqueous solution. To achieve this goal, the computational bottlenecks of QM methods had to be addressed. In semiempirical theory, matrix diagonalization is rate limiting, while in density functional theory or Hartree-Fock theory electron repulsion integral computation is rate-limiting. In this Account, we primarily focus on semiempirical models where the divide and conquer (D&C) approach linearizes the matrix diagonalization step with respect to the system size. Through the D&C approach, a number of applications to biological problems became tractable. Herein, we provide examples of QM studies on biological systems that focus on protein solvation as viewed by QM, QM enabled structure-based drug design, and NMR and X-ray biological structure refinement using QM derived restraints. Through the examples chosen, we show the power of QM to provide novel insights into biological systems, while also impacting practical applications such as structure refinement. While these methods can be more expensive than classical approaches, they make up for this deficiency by the more realistic modeling of the electronic nature of biological systems and in their ability to be broadly applied. Of the tools and applications discussed in this Account, X-ray structure refinement using QM models is now generally available to the community in the refinement package Phenix. While the power of this approach is manifest, challenges still remain. In particular, QM models are generally applied to static structures, so ways in which to include sampling is an ongoing challenge. Car-Parrinello or Born-Oppenheimer molecular dynamics approaches address the short time scale sampling issue, but how to effectively use QM to study phenomenon covering longer time scales will be the focus of future research. Finally, how to accurately and efficiently include electron correlation effects to facilitate the modeling of, for example, dispersive interactions, is also a major hurdle that a broad range of groups are addressing The use of QM models in biology is in its infancy, leading to the expectation that the most significant use of these tools to address biological problems will be seen in the coming years. It is hoped that while this Account summarizes where we have been, it will also help set the stage for future research directions at the interface of quantum mechanics and biology.

From molecular dynamics to Brownian dynamics

Three coarse-grained molecular dynamics (MD) models are investigated with the aim of developing and analysing multi-scale methods which use MD simulations in parts of the computational domain and (less detailed) Brownian dynamics (BD) simulations in the remainder of the domain. The first MD model is formulated in one spatial dimension. It is based on elastic collisions of heavy molecules (e.g. proteins) with light point particles (e.g. water molecules). Two three-dimensional MD models are then investigated. The obtained results are applied to a simplified model of protein binding to receptors on the cellular membrane. It is shown that modern BD simulators of intracellular processes can be used in the bulk and accurately coupled with a (more detailed) MD model of protein binding which is used close to the membrane.

Fragment-based error estimation in biomolecular modeling

Computer simulations are becoming an increasingly more important component of drug discovery. Computational models are now often able to reproduce and sometimes even predict outcomes of experiments. Still, potential energy models such as force fields contain significant amounts of bias and imprecision. We have shown how even small uncertainties in potential energy models can propagate to yield large errors, and have devised some general error-handling protocols for biomolecular modeling with imprecise energy functions. Herein we discuss those protocols within the contexts of protein-ligand binding and protein folding.

Experimental versus predicted affinities for ligand binding to estrogen receptor: iterative selection and rescoring of docked poses systematically improves the correlation

The computational determination of binding modes for a ligand into a protein receptor is much more successful than the prediction of relative binding affinities (RBAs) for a set of ligands. Here we consider the binding of a set of 26 synthetic A-CD ligands into the estrogen receptor ERα. We show that the MOE default scoring function (London dG) used to rank the docked poses leads to a negligible correlation with experimental RBAs. However, switching to an energy-based scoring function, using a multiple linear regression to fit experimental RBAs, selecting top-ranked poses and then iteratively repeating this process leads to exponential convergence in 4-7 iterations and a very strong correlation. The method is robust, as shown by various validation tests. This approach may be of general use in improving the quality of predicted binding affinities.

Absolute hydration free energies of blocked amino acids: implications for protein solvation and stability

Most proteins perform their function in aqueous solution. The interactions with water determine the stability of proteins and the desolvation costs of ligand binding or membrane insertion. However, because of experimental restrictions, absolute solvation free energies of proteins or amino acids are not available. Instead, solvation free energies are estimated based on side chain analog data. This approach implies that the contributions to free energy differences are additive, and it has often been employed for estimating folding or binding free energies. However, it is not clear how much the additivity assumption affects the reliability of the resulting data. Here, we use molecular dynamics-based free energy simulations to calculate absolute hydration free energies for 15 N-acetyl-methylamide amino acids with neutral side chains. By comparing our results with solvation free energies for side chain analogs, we demonstrate that estimates of solvation free energies of full amino acids based on group-additive methods are systematically too negative and completely overestimate the hydrophobicity of glycine. The largest deviation of additive protocols using side chain analog data was 6.7 kcal/mol; on average, the deviation was 4 kcal/mol. We briefly discuss a simple way to alleviate the errors incurred by using side chain analog data and point out the implications of our findings for the field of biophysics and implicit solvent models. To support our results and conclusions, we calculate relative protein stabilities for selected point mutations, yielding a root-mean-square deviation from experimental results of 0.8 kcal/mol.

One Size Does Not Fit All: The Limits of Structure-Based Models in Drug Discovery

A major goal in computational chemistry has been to discover the set of rules that can accurately predict the binding affinity of any protein-drug complex, using only a single snapshot of its three-dimensional structure. Despite the continual development of structure-based models, predictive accuracy remains low, and the fundamental factors that inhibit the inference of all-encompassing rules have yet to be fully explored. Using statistical learning theory and information theory, here we prove that even the very best generalized structure-based model is inherently limited in its accuracy, and protein-specific models are always likely to be better. Our results refute the prevailing assumption that large data sets and advanced machine learning techniques will yield accurate, universally applicable models. We anticipate that the results will aid the development of more robust virtual screening strategies and scoring function error estimations.

Calculating the sensitivity and robustness of binding free energy calculations to force field parameters

Binding free energy calculations offer a thermodynamically rigorous method to compute protein-ligand binding, and they depend on empirical force fields with hundreds of parameters. We examined the sensitivity of computed binding free energies to the ligand's electrostatic and van der Waals parameters. Dielectric screening and cancellation of effects between ligand-protein and ligand-solvent interactions reduce the parameter sensitivity of binding affinity by 65%, compared with interaction strengths computed in the gas-phase. However, multiple changes to parameters combine additively on average, which can lead to large changes in overall affinity from many small changes to parameters. Using these results, we estimate that random, uncorrelated errors in force field nonbonded parameters must be smaller than 0.02 e per charge, 0.06 Å per radius, and 0.01 kcal/mol per well depth in order to obtain 68% (one standard deviation) confidence that a computed affinity for a moderately-sized lead compound will fall within 1 kcal/mol of the true affinity, if these are the only sources of error considered.

Quantum Mechanics Approaches to Drug Research in the Era of Structural Chemogenomics

The rapid growth of the available crystallographic information about proteins and binding pockets creates remarkable opportunities for enriching the drug research pipelines with computational prediction of novel protein-ligand interactions. While ab initio quantum mechanical approaches are known to provide unprecedented accuracy in structure-based binding energy calculations, they are limited to only small systems of dozens of atoms. In the structural chemogenomics era, it is critical that new approaches are developed that enable application of QM methodologies to non-covalent interactions in systems as large as protein-ligand complexes and conformational ensembles. This perspective highlights recent advances towards bridging the gap between high accuracy and high volume computations in drug research.

Correlating protein hot spot surface analysis using ProBiS with simulated free energies of protein-protein interfacial residues

A protocol was developed for the computational determination of the contribution of interfacial amino acid residues to the free energy of protein-protein binding. Thermodynamic integration, based on molecular dynamics simulation in CHARMM, was used to determine the free energy associated with single point mutations to glycine in a protein-protein interface. The hot spot amino acids found in this way were then correlated to structural similarity scores detected by the ProBiS algorithm for local structural alignment. We find that amino acids with high structural similarity scores contribute on average -3.19 kcal/mol to the free energy of protein-protein binding and are thus correlated with hot spot residues, while residues with low similarity scores contribute on average only -0.43 kcal/mol. This suggests that the local structural alignment method provides a good approximation of the contribution of a residue to the free energy of binding and is particularly useful for detection of hot spots in proteins with known structures but undetermined protein-protein complexes.

Enhanced Sampling in Free Energy Calculations: Combining SGLD with the Bennett's Acceptance Ratio and Enveloping Distribution Sampling Methods

One of the key requirements for the accurate calculation of free energy differences is proper sampling of conformational space. Especially in biological applications, molecular dynamics simulations are often confronted with rugged energy surfaces and high energy barriers, leading to insufficient sampling and, in turn, poor convergence of the free energy results. In this work, we address this problem by employing enhanced sampling methods. We explore the possibility of using self-guided Langevin dynamics (SGLD) to speed up the exploration process in free energy simulations. To obtain improved free energy differences from such simulations, it is necessary to account for the effects of the bias due to the guiding forces. We demonstrate how this can be accomplished for the Bennett's acceptance ratio (BAR) and the enveloping distribution sampling (EDS) methods. While BAR is considered among the most efficient methods available for free energy calculations, the EDS method developed by Christ and van Gunsteren is a promising development that reduces the computational costs of free energy calculations by simulating a single reference state. To evaluate the accuracy of both approaches in connection with enhanced sampling, EDS was implemented in CHARMM. For testing, we employ benchmark systems with analytical reference results and the mutation of alanine to serine. We find that SGLD with reweighting can provide accurate results for BAR and EDS where conventional molecular dynamics simulations fail. In addition, we compare the performance of EDS with other free energy methods. We briefly discuss the implications of our results and provide practical guidelines for conducting free energy simulations with SGLD.

Prediction of SAMPL3 host-guest binding affinities: evaluating the accuracy of generalized force-fields

We used the second-generation mining minima method (M2) to compute the binding affinities of the novel host-guest complexes in the SAMPL3 blind prediction challenge. The predictions were in poor agreement with experiment, and we conjectured that much of the error might derive from the force field, CHARMm with Vcharge charges. Repeating the calculations with other generalized force-fields led to no significant improvement, and we observed that the predicted affinities were highly sensitive to the choice of force-field. We therefore embarked on a systematic evaluation of a set of generalized force fields, based upon comparisons with PM6-DH2, a fast yet accurate semi-empirical quantum mechanics method. In particular, we compared gas-phase interaction energies and entropies for the host-guest complexes themselves, as well as for smaller chemical fragments derived from the same molecules. The mean deviations of the force field interaction energies from the quantum results were greater than 3 kcal/mol and 9 kcal/mol, for the fragments and host-guest systems respectively. We further evaluated the accuracy of force-fields for computing the vibrational entropies and found the mean errors to be greater than 4 kcal/mol. Given these errors in energy and entropy, it is not surprising in retrospect that the predicted binding affinities deviated from the experiment by several kcal/mol. These results emphasize the need for improvements in generalized force-fields and also highlight the importance of systematic evaluation of force-field parameters prior to evaluating different free-energy methods.

Prediction of trypsin/molecular fragment binding affinities by free energy decomposition and empirical scores

Two families of binding affinity estimation methodologies are described which were utilized in the SAMPL3 trypsin/fragment binding affinity challenge. The first is a free energy decomposition scheme based on a thermodynamic cycle, which included separate contributions from enthalpy and entropy of binding as well as a solvent contribution. Enthalpic contributions were estimated with PM6-DH2 semiempirical quantum mechanical interaction energies, which were modified with a statistical error correction procedure. Entropic contributions were estimated with the rigid-rotor harmonic approximation, and solvent contributions to the free energy were estimated with several different methods. The second general methodology is the empirical score LISA, which contains several physics-based terms trained with the large PDBBind database of protein/ligand complexes. Here we also introduce LISA+, an updated version of LISA which, prior to scoring, classifies systems into one of four classes based on a ligand's hydrophobicity and molecular weight. Each version of the two methodologies (a total of 11 methods) was trained against a compiled set of known trypsin binders available in the Protein Data Bank to yield scaling parameters for linear regression models. Both raw and scaled scores were submitted to SAMPL3. Variants of LISA showed relatively low absolute errors but also low correlation with experiment, while the free energy decomposition methods had modest success when scaling factors were included. Nonetheless, re-scaled LISA yielded the best predictions in the challenge in terms of RMS error, and six of these models placed in the top ten best predictions by RMS error. This work highlights some of the difficulties of predicting binding affinities of small molecular fragments to protein receptors as well as the benefit of using training data.

The Effects of Computational Modeling Errors on the Estimation of Statistical Mechanical Variables

Computational models used in the estimation of thermodynamic quantities of large chemical systems often require approximate energy models that rely on parameterization and cancellation of errors to yield agreement with experimental measurements. In this work, we show how energy function errors propagate when computing statistical mechanics-derived thermodynamic quantities. Assuming that each microstate included in a statistical ensemble has a measurable amount of error in its calculated energy, we derive low-order expressions for the propagation of these errors in free energy, average energy, and entropy. Through gedanken experiments we show the expected behavior of these error propagation formulas on hypothetical energy surfaces. For very large microstate energy errors, these low-order formulas disagree with estimates from Monte Carlo simulations of error propagation. Hence, such simulations of error propagation may be required when using poor potential energy functions. Propagated systematic errors predicted by these methods can be removed from computed quantities, while propagated random errors yield uncertainty estimates. Importantly, we find that end-point free energy methods maximize random errors and that local sampling of potential energy wells decreases random error significantly. Hence, end-point methods should be avoided in energy computations and should be replaced by methods that incorporate local sampling. The techniques described herein will be used in future work involving the calculation of free energies of biomolecular processes, where error corrections are expected to yield improved agreement with experiment.

Searching the "biologically relevant"conformation of dopamine: a computational approach

We report here an exhaustive and complete conformational study on the conformational potential energy hypersurface (PEHS) of dopamine (DA) interacting with the dopamine D2 receptor (D2-DR). A reduced 3D model for the binding pocket of the human D2-DR was constructed on the basis of the theoretical model structure of bacteriorhodopsin. In our reduced model system, only 13 amino acids were included to perform the quantum mechanics calculations. To obtain the different complexes of DA/D2-DR, we combined semiempirical (PM6), DFT (B3LYP/6-31G(d)), and QTAIM calculations. The molecular flexibility of DA interacting with the D2-DR was evaluated from potential energy surfaces and potential energy curves. A comparative study between the molecular flexibility of DA in the gas phase and at D2-DR was carried out. In addition, several molecular dynamics simulations were carried out to evaluate the molecular flexibility of the different complexes obtained. Our results allow us to postulate the complexes of type A as the "biologically relevant conformations" of DA. In addition, the theoretical calculations reported here suggested that a mechanistic stepwise process takes place for DA in which the protonated nitrogen group (in any conformation) acts as the anchoring portion, and this process is followed by a rapid rearrangement of the conformation allowing the interaction of the catecholic OH groups.

Predicting binding affinities of host-guest systems in the SAMPL3 blind challenge: the performance of relative free energy calculations

Relative free energy calculations based on molecular dynamics simulations are combined with available experimental binding free energies to predict unknown binding affinities of acyclic Cucurbituril complexes in the blind SAMPL3 competition. The predictions yield root mean square errors between 2.6 and 3.2 kcal/mol for seven host-guest systems. Those deviations are comparable to results for solvation free energies of small organic molecules. However, the standard deviations found in our simulations range from 0.4 to 2.4 kcal/mol, which indicates the need for better sampling. Three different approaches are compared. Bennett's Acceptance Ratio Method and thermodynamic integration based on the trapezoidal rule with 12 λ-points exhibit a root mean square error of 2.6 kcal/mol, while thermodynamic integration with Simpson's rule and 11 λ-points leads to a root mean square error of 3.2 kcal/mol. In terms of absolute median errors, Bennett's Acceptance Ratio Method performs better than thermodynamic integration with the trapezoidal rule (1.7 vs. 2.9 kcal/mol). Simulations of the deprotonated forms of the guest molecules exhibit a poorer correspondence to experimental results with a root mean square error of 5.2 kcal/mol. In addition, a decrease of the buffer concentration by approximately 20 mM in the simulations raises the root mean square error to 3.8 kcal/mol.