Accurate assessment of the strain energy in a protein-bound drug using QM/MM X-ray refinement and converged quantum chemistry

Feeling the Strain: Quantifying Ligand Deformation in Photosynthesis

Structural distortion of protein-bound ligands can play a critical role in enzyme function by tuning the electronic and chemical properties of the ligand molecule. However, quantifying these effects is difficult due to the limited resolution of protein structures and the difficulty of generating accurate structural restraints for nonprotein ligands. Here, we seek to quantify these effects through a statistical analysis of ligand distortion in chlorophyll proteins (CP), where ring deformation is thought to play a role in energy and electron transfer. To assess the accuracy of ring-deformation estimates from available structural data, we take advantage of the C2 symmetry of photosystem II (PSII), comparing ring-deformation estimates for equivalent sites both within and between 113 distinct X-ray and cryogenic electron microscopy PSII structures. Significantly, we find that several deformation modes exhibit considerable variability in predictions, even for equivalent monomers, down to a 2 Å resolution, to an extent that probably prevents their utilization in optical calculations. We further find that refinement restraints play a critical role in determining deformation values to resolution as low as 2 Å. However, for those modes that are well-resolved in the structural data, ring deformation in PSII is strongly conserved across all species tested from cyanobacteria to algae. These results highlight both the opportunities and limitations inherent in structure-based analyses of the bioenergetic and optical properties of CPs and other protein-ligand complexes.

Complex peptide macrocycle optimization: combining NMR restraints with conformational analysis to guide structure-based and ligand-based design

Systematic optimization of large macrocyclic peptide ligands is a serious challenge. Here, we describe an approach for lead-optimization using the PD-1/PD-L1 system as a retrospective example of moving from initial lead compound to clinical candidate. We show how conformational restraints can be derived by exploiting NMR data to identify low-energy solution ensembles of a lead compound. Such restraints can be used to focus conformational search for analogs in order to accurately predict bound ligand poses through molecular docking and thereby estimate ligand strain and protein-ligand intermolecular binding energy. We also describe an analogous ligand-based approach that employs molecular similarity optimization to predict bound poses. Both approaches are shown to be effective for prioritizing lead-compound analogs. Surprisingly, relatively small ligand modifications, which may have minimal effects on predicted bound pose or intermolecular interactions, often lead to large changes in estimated strain that have dominating effects on overall binding energy estimates. Effective macrocyclic conformational search is crucial, whether in the context of NMR-based restraints, X-ray ligand refinement, partial torsional restraint for docking/ligand-similarity calculations or agnostic search for nominal global minima. Lead optimization for peptidic macrocycles can be made more productive using a multi-disciplinary approach that combines biophysical data with practical and efficient computational methods.

A Distributional Model of Bound Ligand Conformational Strain: From Small Molecules up to Large Peptidic Macrocycles

The internal conformational strain incurred by ligands upon binding a target site has a critical impact on binding affinity, and expectations about the magnitude of ligand strain guide conformational search protocols. Estimates for bound ligand strain begin with modeled ligand atomic coordinates from X-ray co-crystal structures. By deriving low-energy conformational ensembles to fit X-ray diffraction data, calculated strain energies are substantially reduced compared with prior approaches. We show that the distribution of expected global strain energy values is dependent on molecular size in a superlinear manner. The distribution of strain energy follows a rectified normal distribution whose mean and variance are related to conformational complexity. The modeled strain distribution closely matches calculated strain values from experimental data comprising over 3000 protein-ligand complexes. The distributional model has direct implications for conformational search protocols as well as for directions in molecular design.

Small Molecules Promote Selective Denaturation and Degradation of Tubulin Heterodimers through a Low-Barrier Hydrogen Bond

Here, we report a novel mechanism to selectively degrade target proteins. 3-(3-Phenoxybenzyl)amino-β-carboline (PAC), a tubulin inhibitor, promotes selective degradation of αβ-tubulin heterodimers. Biochemical studies have revealed that PAC specifically denatures tubulin, making it prone to aggregation that predisposes it to ubiquitinylation and then degradation. The degradation is mediated by a single hydrogen bond formed between the pyridine nitrogen of PAC and βGlu198, which is identified as a low-barrier hydrogen bond (LBHB). In contrast, another two tubulin inhibitors that only form normal hydrogen bonds with βGlu198 exhibit no degradation effect. Thus, the LBHB accounts for the degradation. We then screened for compounds capable of forming an LBHB with βGlu198 and demonstrated that BML284, a Wnt signaling activator, also promotes tubulin heterodimer degradation through the LBHB. Our study provided a unique example of LBHB function and identified a novel approach to obtain tubulin degraders.

Property Map Collective Variable as a Useful Tool for a Force Field Correction

The accuracy of biomolecular simulations depends on the accuracy of an empirical molecular mechanics potential known as a force field: a set of parameters and expressions to estimate the potential from atomic coordinates. Accurate parametrization of force fields for small organic molecules is a challenge due to their high diversity. One of the possible approaches is to apply a correction to the existing force fields. Here, we propose an approach to estimate the density functional theory (DFT)-derived force field correction which is calculated during the run of molecular dynamics without significantly affecting its speed. Using the formula known as a property map collective variable, we approximate the force field correction by a weighted average of this force field correction calculated only for a small series of reference structures. To validate this method, we used seven AMBER force fields, and we show how it is possible to convert one force field to behave like the other one. We also present the force field correction for the important anticancer drug Imatinib as a use case example. Our method appears to be suitable for adjusting the force field for general drug-like molecules. We provide a pipeline that generates the correction; this pipeline is available at https://pmcvff-correction.cerit-sc.cz/.

The reorganization energy of compounds upon binding to proteins, from dynamic and solvated bound and unbound states

The intramolecular reorganization energy (ΔE_Reorg) of compounds upon binding to proteins is a component of the binding free energy, which has long received particular attention, for fundamental and practical reasons. Understanding ΔE_Reorg would benefit the science of molecular recognition and drug design. For instance, the tolerable strain energy of compounds upon binding has been elusive. Prior studies found some large ΔE_Reorg values (e.g. > 10 kcal/mol), received with skepticism since they imply excessive opposition to binding. Indeed, estimating ΔE_Reorg is technically difficult. Typically, ΔE_Reorg has been approached by taking two energy-minimized conformers representing the bound and unbound states, and subtracting their conformational energy. This is a drastic oversimplification, liable to conformational collapse of the unbound conformer. Instead, the present work applies extensive molecular dynamics (MD) and the modern OPLS3 force-field to simulate compounds bound and unbound states, in explicit solvent under physically relevant conditions. The thermalized unbound compounds populate multiple conformations, not reducible to one or a few energy-minimized conformers. The intramolecular energies in the bound and unbound states were averaged over pertinent conformational ensembles, and the reorganization enthalpy upon binding (ΔH_Reorg) deduced by subtraction. This was applied to 76 systems, including 43 approved drugs, carefully selected for i) the quality of the bioactive X-ray structures and ii) the diversity of the chemotypes, their properties and protein targets. It yielded comparatively low ΔH_Reorg values (median = 1.4 kcal/mol, mean = 3.0 kcal/mol). A new finding is the observation of negative ΔH_Reorg values. Indeed, reorganization energies do not have to oppose binding, e.g. when intramolecular interactions stabilize preferentially the bound state. Conversely, even with competing water molecules, intramolecular interactions can occur predominantly in the unbound compound, and be replaced by intermolecular counterparts upon protein binding. Such disruption of intramolecular interactions upon binding gives rise to occasional larger ΔH_Reorg values. Such counterintuitive larger ΔH_Reorg values may be rationalized as a redistribution of interactions upon binding, qualitatively compatible with binding.

Ligand Strain Energy in Large Library Docking

While small molecule internal strain is crucial to molecular docking, using it in evaluating ligand scores has remained elusive. Here, we investigate a technique that calculates strain using relative torsional populations in the Cambridge Structural Database, enabling fast precalculation of these energies. In retrospective studies of large docking screens of the dopamine D4 receptor and of AmpC β-lactamase, where close to 600 docking hits were tested experimentally, including such strain energies improved hit rates by preferentially reducing the ranks of strained high-scoring decoy molecules. In a 40-target subset of the DUD-E benchmark, we found two thresholds that usefully distinguished between ligands and decoys: one based on the total strain energy of the small molecules and another based on the maximum strain allowed for any given torsion within them. Using these criteria, about 75% of the benchmark targets had improved enrichment after strain filtering. Relying on precalculated population distributions, this approach is rapid, taking less than 0.04 s to evaluate a conformation on a standard core, making it pragmatic for precalculating strain in even ultralarge libraries. Since it is scoring function agnostic, it may be useful to multiple docking approaches; it is openly available at http://tldr.docking.org.

Combining crystallography with quantum mechanics

In standard crystallographic refinement of biomacromolecules, the crystallographic raw data are supplemented by empirical restraints that ensure that the structure makes chemical sense. These restraints are typically accurate for amino acids and nucleic acids, but less so for cofactors, substrates, inhibitors, ligands and metal sites. In quantum refinement, this potential is replaced by more accurate quantum mechanical (QM) calculations. Several implementations have been presented, differing in the level of QM and whether it is used for the entire structure or only for a site of particular interest. It has been shown that the method can improve and correct errors in crystal structures and that it can be used to determine protonation and tautomeric states of various ligands and to decide what is really seen in the structure by refining different interpretations and using standard crystallographic and QM quality measures to decide which fits the structure best.

Multiscale Quantum Refinement Approaches for Metalloproteins

Biomolecules with metal ion(s) (e.g., metalloproteins) play many important biological roles. However, accurate structural determination of metalloproteins, particularly those containing transition metal ion(s), is challenging due to their complicated electronic structure, complex bonding of metal ions, and high number of conformations in biomolecules. Quantum refinement, which was proposed to combine crystallographic data with computational chemistry methods by several groups, can improve the local structures of some proteins. In this study, a quantum refinement method combining several multiscale computational schemes with experimental (X-ray diffraction) information was developed for metalloproteins. Various quantum refinement approaches using different ONIOM (our own N-layered integrated molecular orbital and molecular mechanics) combinations of quantum mechanics (QM), semiempirical (SE), and molecular mechanics (MM) methods were conducted to assess the performance and reliability on the refined local structure in two metalloproteins. The structures for two (Cu- or Zn-containing) metalloproteins were refined by combining two-layer ONIOM2(QM1/QM2) and ONIOM2(QM/MM) and three-layer ONIOM3(QM1/QM2/MM) schemes with experimental data. The accuracy of the quantum-refined metal binding sites was also examined and compared in these multiscale quantum refinement calculations. ONIOM3(QM/SE/MM) schemes were found to give good results with lower computational costs and were proposed to be a good choice for the multiscale computational scheme for quantum refinement calculations of metal binding site(s) in metalloproteins with high efficiency. Additionally, a two-center ONIOM approach was employed to speed up the quantum refinement calculations for the Zn metalloprotein with two remote active sites/ligands. Moreover, a recent quantum-embedding wavefunction-in-density functional theory (WF-in-DFT) method was also adopted as the high-level method in unprecedented ONIOM2(CCSD-in-B3LYP/MM) and ONIOM3(CCSD-in-B3LYP/SE/MM) calculations, which can be regarded as novel pseudo-three- and pseudo-four-layer ONIOM methods, respectively, to refine the key Zn binding site at the coupled-cluster singles and doubles (CCSD) level. These refined results indicate that multiscale quantum refinement schemes can be used to improve the structural accuracy obtained for local metal binding site(s) in metalloproteins with high efficiency.

The Good, the Bad, and the Twisted Revisited: An Analysis of Ligand Geometry in Highly Resolved Protein-Ligand X-ray Structures

An analysis of the rotatable bond geometry of drug-like ligand models is reported for high-resolution (<1.1 Å) crystallographic protein-ligand complexes. In cases where the ligand fit to the electron density is very good, unusual torsional geometry is rare and, most often, though not exclusively, associated with strong polar, metal, or covalent ligand-protein interactions. It is rarely associated with a torsional strain of greater than 2 kcal mol^-1 by calculation. An unusual torsional geometry is more prevalent where the fit to electron density is not perfect. Multiple low-strain conformer bindings were observed in 21% of the set and, it is suggested, may also lie behind many of the 35% of single-occupancy cases, where a poor fit to the e-density was found. It is concluded that multiple conformer ligand binding is an under-recognized phenomenon in structure-based drug design and that there is a need for more robust crystallographic refinement methods to better handle such cases.

Theoretical Insight into the Library Screening Approach for Binding of Intermolecular G-Quadruplex RNA and Small Molecules through Docking and Molecular Dynamics Simulation Studies

The interactions of intermolecular G-quadruplex RNA and small molecules have been investigated by computational studies. Various anthraquinone, bisbenzimidazole, and carbazole-benzimidazole based ligands have shown a distinct preference to G-quadruplex structures as opposed to the corresponding duplex forms of DNA that were docked with telomeric G-quadruplex RNA. The comparative binding study of such ligands with G-quadruplex (G4) RNA showed higher binding affinities toward carbazole-benzimidazole ligands than those of the anthraquinone and bisbenzimidazole based ligands. A molecular dynamics simulation study was used to examine quadruplex-ligand interactions. Analysis of the binding free energy indicated the formation of the thermodynamically favorable RNA-ligand complex. The formation of several H-bonding interactions and the change of the solvent accessible surface area (SASA) also support the effective binding of the carbazole-benzimidazole ligands with G4 RNA structures. Thus, the library screening approach has assisted in getting a structure-activity relationship for the selected small molecules toward the G-quadruplex RNA binding, which can be applied in the targeting of G-quadruplex RNA medicated anticancer therapeutics.

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.

Metabolite Structure Assignment Using In Silico NMR Techniques

A major challenge for metabolomic analysis is to obtain an unambiguous identification of the metabolites detected in a sample. Among metabolomics techniques, NMR spectroscopy is a sophisticated, powerful, and generally applicable spectroscopic tool that can be used to ascertain the correct structure of newly isolated biogenic molecules. However, accurate structure prediction using computational NMR techniques depends on how much of the relevant conformational space of a particular compound is considered. It is intrinsically challenging to calculate NMR chemical shifts using high-level DFT when the conformational space of a metabolite is extensive. In this work, we developed NMR chemical shift calculation protocols using a machine learning model in conjunction with standard DFT methods. The pipeline encompasses the following steps: (1) conformation generation using a force field (FF)-based method, (2) filtering the FF generated conformations using the ASE-ANI machine learning model, (3) clustering of the optimized conformations based on structural similarity to identify chemically unique conformations, (4) DFT structural optimization of the unique conformations, and (5) DFT NMR chemical shift calculation. This protocol can calculate the NMR chemical shifts of a set of molecules using any available combination of DFT theory, solvent model, and NMR-active nuclei, using both user-selected reference compounds and/or linear regression methods. Our protocol reduces the overall computational time by 2 orders of magnitude over methods that optimize the conformations using fully ab initio methods, while still producing good agreement with experimental observations. The complete protocol is designed in such a manner that makes the computation of chemical shifts tractable for a large number of conformationally flexible metabolites.

Flexible Fitting of Small Molecules into Electron Microscopy Maps Using Molecular Dynamics Simulations with Neural Network Potentials

Despite significant advances in resolution, the potential for cryo-electron microscopy (EM) to be used in determining the structures of protein-drug complexes remains unrealized. Determination of accurate structures and coordination of bound ligands necessitates simultaneous fitting of the models into the density envelopes, exhaustive sampling of the ligand geometries, and, most importantly, concomitant rearrangements in the side chains to optimize the binding energy changes. In this article, we present a flexible-fitting pipeline where molecular dynamics flexible fitting (MDFF) is used to refine structures of protein-ligand complexes from 3 to 5 Å electron density data. Enhanced sampling is employed to explore the binding pocket rearrangements. To provide a model that can accurately describe the conformational dynamics of the chemically diverse set of small-molecule drugs inside MDFF, we use QM/MM and neural-network potential (NNP)/MM models of protein-ligand complexes, where the ligand is represented using the QM or NNP model, and the protein is represented using established molecular mechanical force fields (e.g., CHARMM). This pipeline offers structures commensurate to or better than recently submitted high-resolution cryo-EM or X-ray models, even when given medium to low-resolution data as input. The use of the NNPs makes the algorithm more robust to the choice of search models, offering a radius of convergence of 6.5 Å for ligand structure determination. The quality of the predicted structures was also judged by density functional theory calculations of ligand strain energy. This strain potential energy is found to systematically decrease with better fitting to density and improved ligand coordination, indicating correct binding interactions. A computationally inexpensive protocol for computing strain energy is reported as part of the model analysis protocol that monitors both the ligand fit as well as model quality.

Simulating protein-ligand binding with neural network potentials

Drug molecules adopt a range of conformations both in solution and in their protein-bound state. The strain and reduced flexibility of bound drugs can partially counter the intermolecular interactions that drive protein-ligand binding. To make accurate computational predictions of drug binding affinities, computational chemists have attempted to develop efficient empirical models of these interactions, although these methods are not always reliable. Machine learning has allowed the development of highly-accurate neural-network potentials (NNPs), which are capable of predicting the stability of molecular conformations with accuracy comparable to state-of-the-art quantum chemical calculations but at a billionth of the computational cost. Here, we demonstrate that these methods can be used to represent the intramolecular forces of protein-bound drugs within molecular dynamics simulations. These simulations are shown to be capable of predicting the protein-ligand binding pose and conformational component of the absolute Gibbs energy of binding for a set of drug molecules. Notably, the conformational energy for anti-cancer drug erlotinib binding to its target was found to be considerably overestimated by a molecular mechanical model, while the NNP predicts a more moderate value. Although the ANI-1ccX NNP was not trained to describe ionic molecules, reasonable binding poses are predicted for charged ligands, but this method is not suitable for modeling charged ligands in solution.

High-throughput quantum-mechanics/molecular-mechanics (ONIOM) macromolecular crystallographic refinement with PHENIX/DivCon: the impact of mixed Hamiltonian methods on ligand and protein structure

Conventional macromolecular crystallographic refinement relies on often dubious stereochemical restraints, the preparation of which often requires human validation for unusual species, and on rudimentary energy functionals that are devoid of nonbonding effects owing to electrostatics, polarization, charge transfer or even hydrogen bonding. While this approach has served the crystallographic community for decades, as structure-based drug design/discovery (SBDD) has grown in prominence it has become clear that these conventional methods are less rigorous than they need to be in order to produce properly predictive protein-ligand models, and that the human intervention that is required to successfully treat ligands and other unusual chemistries found in SBDD often precludes high-throughput, automated refinement. Recently, plugins to the Python-based Hierarchical ENvironment for Integrated Xtallography (PHENIX) crystallographic platform have been developed to augment conventional methods with the in situ use of quantum mechanics (QM) applied to ligand(s) along with the surrounding active site(s) at each step of refinement [Borbulevych et al. (2014), Acta Cryst D70, 1233-1247]. This method (Region-QM) significantly increases the accuracy of the X-ray refinement process, and this approach is now used, coupled with experimental density, to accurately determine protonation states, binding modes, ring-flip states, water positions and so on. In the present work, this approach is expanded to include a more rigorous treatment of the entire structure, including the ligand(s), the associated active site(s) and the entire protein, using a fully automated, mixed quantum-mechanics/molecular-mechanics (QM/MM) Hamiltonian recently implemented in the DivCon package. This approach was validated through the automatic treatment of a population of 80 protein-ligand structures chosen from the Astex Diverse Set. Across the entire population, this method results in an average 3.5-fold reduction in ligand strain and a 4.5-fold improvement in MolProbity clashscore, as well as improvements in Ramachandran and rotamer outlier analyses. Overall, these results demonstrate that the use of a structure-wide QM/MM Hamiltonian exhibits improvements in the local structural chemistry of the ligand similar to Region-QM refinement but with significant improvements in the overall structure beyond the active site.

Conformational investigation of the structure-activity relationship of GdFFD and its analogues on an achatin-like neuropeptide receptor of Aplysia californica involved in the feeding circuit

Proteins and peptides in nature are almost exclusively made from l-amino acids, and this is even more absolute in the metazoan. With the advent of modern bioanalytical techniques, however, previously unappreciated roles for d-amino acids in biological processes have been revealed. Over 30 d-amino acid containing peptides (DAACPs) have been discovered in animals where at least one l-residue has been isomerized to the d-form via an enzyme-catalyzed process. In Aplysia californica, GdFFD and GdYFD (the lower-case letter "d" indicates a d-amino acid residue) modulate the feeding behavior by activating the Aplysia achatin-like neuropeptide receptor (apALNR). However, little is known about how the three-dimensional conformation of DAACPs influences activity at the receptor, and the role that d-residues play in these peptide conformations. Here, we use a combination of computational modeling, drift-tube ion-mobility mass spectrometry, and receptor activation assays to create a simple model that predicts bioactivities for a series of GdFFD analogs. Our results suggest that the active conformations of GdFFD and GdYFD are similar to their lowest energy conformations in solution. Our model helps connect the predicted structures of GdFFD analogs to their activities, and highlights a steric effect on peptide activity at position 1 on the GdFFD receptor apALNR. Overall, these methods allow us to understand ligand-receptor interactions in the absence of high-resolution structural data.

Conformational energy range of ligands in protein crystal structures: The difficult quest for accurate understanding

In this review, we address a fundamental question: What is the range of conformational energies seen in ligands in protein-ligand crystal structures? This value is important biophysically, for better understanding the protein-ligand binding process; and practically, for providing a parameter to be used in many computational drug design methods such as docking and pharmacophore searches. We synthesize a selection of previously reported conflicting results from computational studies of this issue and conclude that high ligand conformational energies really are present in some crystal structures. The main source of disagreement between different analyses appears to be due to divergent treatments of electrostatics and solvation. At the same time, however, for many ligands, a high conformational energy is in error, due to either crystal structure inaccuracies or incorrect determination of the reference state. Aside from simple chemistry mistakes, we argue that crystal structure error may mainly be because of the heuristic weighting of ligand stereochemical restraints relative to the fit of the structure to the electron density. This problem cannot be fixed with improvements to electron density fitting or with simple ligand geometry checks, though better metrics are needed for evaluating ligand and binding site chemistry in addition to geometry during structure refinement. The ultimate solution for accurately determining ligand conformational energies lies in ultrahigh-resolution crystal structures that can be refined without restraints.

Conformation Generation: The State of the Art

The generation of conformations for small molecules is a problem of continuing interest in cheminformatics and computational drug discovery. This review will present an overview of methods used to sample conformational space, focusing on those methods designed for organic molecules commonly of interest in drug discovery. Different approaches to both the sampling of conformational space and the scoring of conformational stability will be compared and contrasted, with an emphasis on those methods suitable for conformer sampling of large numbers of drug-like molecules. Particular attention will be devoted to the appropriate utilization of information from experimental solid-state structures in validating and evaluating the performance of these tools. The review will conclude with some areas worthy of further investigation.

Improved ligand geometries in crystallographic refinement using AFITT in PHENIX

Modern crystal structure refinement programs rely on geometry restraints to overcome the challenge of a low data-to-parameter ratio. While the classical Engh and Huber restraints work well for standard amino-acid residues, the chemical complexity of small-molecule ligands presents a particular challenge. Most current approaches either limit ligand restraints to those that can be readily described in the Crystallographic Information File (CIF) format, thus sacrificing chemical flexibility and energetic accuracy, or they employ protocols that substantially lengthen the refinement time, potentially hindering rapid automated refinement workflows. PHENIX-AFITT refinement uses a full molecular-mechanics force field for user-selected small-molecule ligands during refinement, eliminating the potentially difficult problem of finding or generating high-quality geometry restraints. It is fully integrated with a standard refinement protocol and requires practically no additional steps from the user, making it ideal for high-throughput workflows. PHENIX-AFITT refinements also handle multiple ligands in a single model, alternate conformations and covalently bound ligands. Here, the results of combining AFITT and the PHENIX software suite on a data set of 189 protein-ligand PDB structures are presented. Refinements using PHENIX-AFITT significantly reduce ligand conformational energy and lead to improved geometries without detriment to the fit to the experimental data. For the data presented, PHENIX-AFITT refinements result in more chemically accurate models for small-molecule ligands.

Free Energy-Based Conformational Search Algorithm Using the Movable Type Sampling Method

In this article, we extend the movable type (MT) sampling method to molecular conformational searches (MT-CS) on the free energy surface of the molecule in question. Differing from traditional systematic and stochastic searching algorithms, this method uses Boltzmann energy information to facilitate the selection of the best conformations. The generated ensembles provided good coverage of the available conformational space including available crystal structures. Furthermore, our approach directly provides the solvation free energies and the relative gas and aqueous phase free energies for all generated conformers. The method is validated by a thorough analysis of thrombin ligands as well as against structures extracted from both the Protein Data Bank (PDB) and the Cambridge Structural Database (CSD). An in-depth comparison between OMEGA and MT-CS is presented to illustrate the differences between the two conformational searching strategies, i.e., energy-based versus free energy-based searching. These studies demonstrate that our MT-based ligand conformational search algorithm is a powerful approach to delineate the conformational ensembles of molecular species on free energy surfaces.

The shape of ibuprofen in the gas phase

Broadband rotational spectroscopy reveals a striking conformational flexibility of ibuprofen – the famous painkiller – in the gas phase.

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.

Studying allosteric regulation in metal sensor proteins using computational methods

In this chapter, we describe advances made in understanding the mechanism of allosteric regulation of DNA operator binding in the ArsR/SmtB family of metal-sensing proteins using computational methods. The paradigm, zinc-sensing transcriptional repressor Staphylococcus aureus CzrA represents an excellent model system to understand how metal sensor proteins maintain cellular metal homeostasis. Here, we discuss studies that helped to characterize a metal ion-mediated hydrogen-bonding pathway (HBP) that plays a dominant role in the allosteric mechanism of DNA operator binding in these proteins. The chapter discusses computational methods used to provide a molecular basis for the large conformational motions and allosteric coupling free energy (~6kcal/mol) associated with Zn(II) binding in CzrA. We present an accurate and convenient means by which to include metal ions in the nuclear magnetic resonance (NMR) structure determination process using molecular dynamics (MD) constrained by NMR-derived data. The method provides a realistic and physically viable description of the metal-binding site(s) and has potentially broad applicability in the structure determination of metal ion-bound proteins, protein folding, and metal template protein-design studies. Finally, our simulations provide strong support for a proposed HBP that physically connects the metal-binding residue, His97, to the DNA-binding interface through the αR helix that is present only in the Zn(II)-bound state. We find the interprotomer hydrogen bond interaction to be significantly stronger (~8kcal/mol) at functional allosteric metal-binding sites compared to the apo proteins. This interaction works to overcome the considerable disorder at these hydrogen-bonding sites in apo protein and functions as a "switch" to lock in a weak DNA-binding conformation once metal is bound. This interaction is found to be considerably weaker in nonresponsive metal-binding sites. These findings suggest a conserved functional role of metal-mediated second-shell coordination hydrogen bonds at allosterically responsive sites in zinc-sensing transcription regulators.

Accurate macromolecular crystallographic refinement: incorporation of the linear scaling, semiempirical quantum-mechanics program DivCon into the PHENIX refinement package

Macromolecular crystallographic refinement relies on sometimes dubious stereochemical restraints and rudimentary energy functionals to ensure the correct geometry of the model of the macromolecule and any covalently bound ligand(s). The ligand stereochemical restraint file (CIF) requires a priori understanding of the ligand geometry within the active site, and creation of the CIF is often an error-prone process owing to the great variety of potential ligand chemistry and structure. Stereochemical restraints have been replaced with more robust functionals through the integration of the linear-scaling, semiempirical quantum-mechanics (SE-QM) program DivCon with the PHENIX X-ray refinement engine. The PHENIX/DivCon package has been thoroughly validated on a population of 50 protein-ligand Protein Data Bank (PDB) structures with a range of resolutions and chemistry. The PDB structures used for the validation were originally refined utilizing various refinement packages and were published within the past five years. PHENIX/DivCon does not utilize CIF(s), link restraints and other parameters for refinement and hence it does not make as many a priori assumptions about the model. Across the entire population, the method results in reasonable ligand geometries and low ligand strains, even when the original refinement exhibited difficulties, indicating that PHENIX/DivCon is applicable to both single-structure and high-throughput crystallography.

Conformational analysis and parallel QM/MM X-ray refinement of protein bound anti-Alzheimer drug donepezil

The recognition and association of donepezil with acetylcholinesterase (AChE) has been extensively studied in the past several decades because of the former's use as a palliative treatment for mild Alzheimer disease. Herein we examine the conformational properties of donepezil and we re-examine the donepezil-AChE crystal structure using combined quantum mechanical/molecular mechanical (QM/MM) X-ray refinement tools. Donepezil's conformational energy surface was explored using the M06 suite of density functionals and with the MP2/complete basis set (CBS) method using the aug-cc-pVXZ (X = D and T) basis sets. The donepezil-AChE complex (PDB 1EVE) was also re-refined through a parallel QM/MM X-ray refinement approach based on an in-house ab initio code QUICK, which uses the message passing interface (MPI) in a distributed SCF algorithm to accelerate the calculation via parallelization. In the QM/MM re-refined donepezil structure, coordinate errors that previously existed in the PDB deposited geometry were improved leading to an improvement of the modeling of the interaction between donepezil and the aromatic side chains located in the AChE active site gorge. As a result of the re-refinement there was a 93% reduction in the donepezil conformational strain energy versus the original PDB structure. The results of the present effort offer further detailed structural and biochemical inhibitor-AChE information for the continued development of more effective and palliative treatments of Alzheimer disease.

Multiscale Multiphysics and Multidomain Models I: Basic Theory

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.

Energetics of zinc-mediated interactions in the allosteric pathways of metal sensor proteins

A metal-mediated interprotomer hydrogen bond has been implicated in the allosteric mechanism of DNA operator binding in several metal-sensing proteins. Using computational methods, we investigate the energetics of such zinc-mediated interactions in members of the ArsR/SmtB family of proteins (CzrA, SmtB, CadC, and NmtR) and the MarR family zinc-uptake repressor AdcR, which feature similar interactions, but in sites that differ widely in their allosteric responsiveness. We provide novel structural insight into previously uncharacterized allosteric forms of these proteins using computational methodologies. We find this metal-mediated interaction to be significantly stronger (∼8 kcal/mol) at functional allosteric metal binding sites compared to a nonresponsive site (CadC) and the apo-proteins. Simulations of the apo-proteins further reveal that the high interaction energy works to overcome the considerable disorder at these hydrogen-bonding sites and functions as a "switch" to lock in a weak DNA-binding conformation once metal is bound. These findings suggest a conserved functional role of metal-mediated second coordination shell hydrogen bonds at allosterically responsive sites in zinc-sensing transcription regulators.

Conformational Analysis of Free and Bound Retinoic Acid

The conformational profiles of unbound all-trans and 9-cis retinoic acid (RA) have been determined using classical and quantum mechanical calculations. Sixty-six all-trans-RA (ATRA) and forty-eight 9-cis-RA energy minimum conformers were identified via HF/6-31G* geometry optimizations in vacuo. Their relative conformational energies were estimated utilizing the M06, M06-2x and MP2 methods combined with the 6-311+G(d,p), aug-cc-pVDZ and aug-cc-pVTZ basis sets, as well as complete basis set MP2 extrapolations using the latter two basis sets. Single-point energy calculations performed with the M06-2x density functional were found to yield similar results to MP2/CBS for the low-energy retinoic acid conformations. Not unexpectedly, the conformational propensities of retinoic acid were governed by the orientation and arrangement of the torsion angles associated with the polyene tail. We also used previously reported QM/MM X-ray refinement results on four ATRA-protein crystal structures plus one newly refined 9-cis-RA complex (PDB ID 1XDK) in order to investigate the conformational preferences of bound retinoic acid. In the re-refined RA conformers the conjugated double bonds are nearly coplanar, which is consistent with the global minimum identified by the Omega/QM method rather than the corresponding crystallographically determined conformations given in the PDB. Consequently, a 91.3% average reduction of the local strain energy in the gas phase, as well as 92.1% in PCM solvent, was observed using the QM/MM refined structures versus the PDB deposited RA conformations. These results thus demonstrate that our QM/MM X-ray refinement approach can significantly enhance the quality of X-ray crystal structures refined by conventional refinement protocols, thereby providing reliable drug-target structural information for use in structure-based drug discovery applications.

The good, the bad and the twisted: a survey of ligand geometry in protein crystal structures

The protein databank now contains the structures of over 11,000 ligands bound to proteins. These structures are invaluable in applied areas such as structure-based drug design, but are also the substrate for understanding the energetics of intermolecular interactions with proteins. Despite their obvious importance, the careful analysis of ligands bound to protein structures lags behind the analysis of the protein structures themselves. We present an analysis of the geometry of ligands bound to proteins and highlight the role of small molecule crystal structures in enabling molecular modellers to critically evaluate a ligand model's quality and investigate protein-induced strain.

QM/MM refinement and analysis of protein bound retinoic acid

Retinoic acid (RA) is a vitamin A derivative, which modifies the appearance of fine wrinkles and roughness of facial skin and treats acne and activates gene transcription by binding to heterodimers of the retinoic acid receptor (RAR) and the retinoic X receptor (RXR). There are series of protein bound RA complexes available in the protein databank (PDB), which provides a broad range of information about the different bioactive conformations of RA. To gain further insights into the observed bioactive RA conformations we applied quantum mechanic (QM)/molecular mechanic (MM) approaches to re-refine the available RA protein-ligand complexes. MP2 complete basis set (CBS) extrapolations single energy calculations are also carried out for both the experimental conformations and QM optimized geometries of RA in the gas as well as solution phase. The results demonstrate that the re-refined structures show better geometries for RA than seen in the originally deposited PDB structures through the use of QMs for the ligand in the X-ray refinement procedure. QM/MM re-refined conformations also reduced the computed strain energies found in the deposited crystal conformations for RA. Finally, the dependence of ligand strain on resolution is analyzed. It is shown that ligand strain is not converged in our calculations and is likely an artifact of the typical resolutions employed to study protein-ligand complexes.