Critical assessment of quantum mechanics based energy restraints in protein crystal structure refinement

Hotspot Identification and Drug Design of Protein-Protein Interaction Modulators Using the Fragment Molecular Orbital Method

Protein-protein interactions (PPIs) are essential for the function of many proteins. Aberrant PPIs have the potential to lead to disease, making PPIs promising targets for drug discovery. There are over 64,000 PPIs in the human interactome reference database; however, to date, very few PPI modulators have been approved for clinical use. Further development of PPI-specific therapeutics is highly dependent on the availability of structural data and the existence of reliable computational tools to explore the interface between two interacting proteins. The fragment molecular orbital (FMO) quantum mechanics method offers comprehensive and computationally inexpensive means of identifying the strength (in kcal/mol) and the chemical nature (electrostatic or hydrophobic) of the molecular interactions taking place at the protein-protein interface. We have integrated FMO and PPI exploration (FMO-PPI) to identify the residues that are critical for protein-protein binding (hotspots). To validate this approach, we have applied FMO-PPI to a dataset of protein-protein complexes representing several different protein subfamilies and obtained FMO-PPI results that are in agreement with published mutagenesis data. We observed that critical PPIs can be divided into three major categories: interactions between residues of two proteins (intermolecular), interactions between residues within the same protein (intramolecular), and interactions between residues of two proteins that are mediated by water molecules (water bridges). We extended our findings by demonstrating how this information obtained by FMO-PPI can be utilized to support the structure-based drug design of PPI modulators (SBDD-PPI).

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.

Guiding Medicinal Chemistry with Fragment Molecular Orbital (FMO) Method

The understanding of binding interactions between a protein and a small molecule plays a key role in the rationalization of potency and selectivity and in design of new ideas. However, even when a target of interest is structurally enabled, visual inspection and force field-based molecular mechanics calculations cannot always explain the full complexity of the molecular interactions that are critical in drug design. Quantum mechanical methods have the potential to address this shortcoming, but traditionally, computational expense has made the application of these calculations impractical. The fragment molecular orbital (FMO) method offers a solution that combines accuracy, speed, and the ability to characterize important interactions (i.e. its strength in kcal/mol and chemical nature: hydrophobic, electrostatic, etc) that would otherwise be hard to detect. In this chapter, we describe the FMO method and illustrate its application in the discovery of the benzothiazole (BZT) series as novel tyrosine kinase ITK inhibitors for treatment of allergic asthma.

Analyzing GPCR-Ligand Interactions with the Fragment Molecular Orbital (FMO) Method

G-protein-coupled receptors (GPCRs) have enormous physiological and biomedical importance, and therefore it is not surprising that they are the targets of many prescribed drugs. Further progress in GPCR drug discovery is highly dependent on the availability of protein structural information. However, the ability of X-ray crystallography to guide the drug discovery process for GPCR targets is limited by the availability of accurate tools to explore receptor-ligand interactions. Visual inspection and molecular mechanics approaches cannot explain the full complexity of molecular interactions. Quantum mechanics (QM) approaches are often too computationally expensive to be of practical use in time-sensitive situations, but the fragment molecular orbital (FMO) method offers an excellent solution that combines accuracy, speed, and the ability to reveal key interactions that would otherwise be hard to detect. Integration of GPCR crystallography or homology modelling with FMO reveals atomistic details of the individual contributions of each residue and water molecule toward ligand binding, including an analysis of their chemical nature. Such information is essential for an efficient structure-based drug design (SBDD) process. In this chapter, we describe how to use FMO in the characterization of GPCR-ligand interactions.

Characterizing Interhelical Interactions of G-Protein Coupled Receptors with the Fragment Molecular Orbital Method

G-protein coupled receptors (GPCRs) are the largest superfamily of membrane proteins, regulating almost every aspect of cellular activity and serving as key targets for drug discovery. We have identified an accurate and reliable computational method to characterize the strength and chemical nature of the interhelical interactions between the residues of transmembrane (TM) domains during different receptor activation states, something that cannot be characterized solely by visual inspection of structural information. Using the fragment molecular orbital (FMO) quantum mechanics method to analyze 35 crystal structures representing different branches of the class A GPCR family, we have identified 69 topologically equivalent TM residues that form a consensus network of 51 inter-TM interactions, providing novel results that are consistent with and help to rationalize experimental data. This discovery establishes a comprehensive picture of how defined molecular forces govern specific interhelical interactions which, in turn, support the structural stability, ligand binding, and activation of GPCRs.

Characterizing Protein-Protein Interactions with the Fragment Molecular Orbital Method

Proteins are vital components of living systems, serving as building blocks, molecular machines, enzymes, receptors, ion channels, sensors, and transporters. Protein-protein interactions (PPIs) are a key part of their function. There are more than 645,000 reported disease-relevant PPIs in the human interactome, but drugs have been developed for only 2% of these targets. The advances in PPI-focused drug discovery are highly dependent on the availability of structural data and accurate computational tools for analysis of this data. Quantum mechanical approaches are often too expensive computationally, but the fragment molecular orbital (FMO) method offers an excellent solution that combines accuracy, speed and the ability to reveal key interactions that would otherwise be hard to detect. FMO provides essential information for PPI drug discovery, namely, identification of key interactions formed between residues of two proteins, including their strength (in kcal/mol) and their chemical nature (electrostatic or hydrophobic). In this chapter, we have demonstrated how three different FMO-based approaches (pair interaction energy analysis (PIE analysis), subsystem analysis (SA) and analysis of protein residue networks (PRNs)) have been applied to study PPI in three protein-protein complexes.

Including crystallographic symmetry in quantum-based refinement: Q|R#2

Three-dimensional structure models refined using low-resolution data from crystallographic or electron cryo-microscopy experiments can benefit from high-quality restraints derived from quantum-chemical methods. However, nonperiodic atom-centered quantum-chemistry codes do not inherently account for nearest-neighbor interactions of crystallographic symmetry-related copies in a satisfactory way. Here, these nearest-neighbor effects have been included in the model by expanding to a super-cell and then truncating the super-cell to only include residues from neighboring cells that are interacting with the asymmetric unit. In this way, the fragmentation approach can adequately and efficiently include nearest-neighbor effects. It has previously been shown that a moderately sized X-ray structure can be treated using quantum methods if a fragmentation approach is applied. In this study, a target protein (PDB entry 4gif) was partitioned into a number of large fragments. The use of large fragments (typically hundreds of atoms) is tractable when a GPU-based package such as TeraChem is employed or cheaper (semi-empirical) methods are used. The QM calculations were run at the HF-D3/6-31G level. The models refined using a recently developed semi-empirical method (GFN2-xTB) were compared and contrasted. To validate the refinement procedure for a non-P1 structure, a standard set of crystallographic metrics were used. The robustness of the implementation is shown by refining 13 additional protein models across multiple space groups and a summary of the refinement metrics is presented.

Conformational Searching with Quantum Mechanics

Estimating the range of three-dimensional structures (conformations) that are available to a molecule is a key component of computer-aided drug design. Quantum mechanical simulation offers improved accuracy over forcefield methods, but at a high computational cost. The question is whether this increased cost can be justified in a context in which high-throughput analysis of large numbers of molecules is often key. This chapter discusses the application of quantum mechanics to conformational searching, with a focus on three key challenges: (1) the generation of ensembles that include a good approximation to a molecule's bioactive conformation at as prominent a ranking as possible; (2) rational analysis and modification of a pre-established bioactive conformation in terms of its energetics; and (3) approximation of real solution-phase conformational ensembles in tandem with NMR data. The impact of QM on the high-throughput application (1) is debatable, meaning that for the moment its primary application is still lower-throughput applications such as (2) and (3). The optimal choice of QM method is also discussed. Rigorous benchmarking suggests that DFT methods are only acceptable when used with large basis sets, but a trickle of papers continue to obtain useful results with relatively low-cost methods, leading to a dilemma that the literature has yet to fully resolve.

Characterising GPCR-ligand interactions using a fragment molecular orbital-based approach

There has been fantastic progress in solving GPCR crystal structures. However, the ability of X-ray crystallography to guide the drug discovery process for GPCR targets is limited by the availability of accurate tools to explore receptor-ligand interactions. Visual inspection and molecular mechanics approaches cannot explain the full complexity of molecular interactions. Quantum mechanical approaches (QM) are often too computationally expensive, but the fragment molecular orbital (FMO) method offers an excellent solution that combines accuracy, speed and the ability to reveal key interactions that would otherwise be hard to detect. Integration of GPCR crystallography or homology modelling with FMO reveals atomistic details of the individual contributions of each residue and water molecule towards ligand binding, including an analysis of their chemical nature.

Quantum Crystallography: Current Developments and Future Perspectives

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

Exploring GPCR-Ligand Interactions with the Fragment Molecular Orbital (FMO) Method

The understanding of binding interactions between any protein and a small molecule plays a key role in the rationalization of affinity and selectivity. It is essential for an efficient structure-based drug design (SBDD) process. FMO enables ab initio approaches to be applied to systems that conventional quantum-mechanical (QM) methods would find challenging. The key advantage of the Fragment Molecular Orbital Method (FMO) is that it can reveal atomistic details about the individual contributions and chemical nature of each residue and water molecule toward ligand binding which would otherwise be difficult to detect without using QM methods. In this chapter, we demonstrate the typical use of FMO to analyze 19 crystal structures of β1 and β2 adrenergic receptors with their corresponding agonists and antagonists.

Solving the scalability issue in quantum-based refinement: Q|R#1

Accurately refining biomacromolecules using a quantum-chemical method is challenging because the cost of a quantum-chemical calculation scales approximately as nm, where n is the number of atoms and m (≥3) is based on the quantum method of choice. This fundamental problem means that quantum-chemical calculations become intractable when the size of the system requires more computational resources than are available. In the development of the software package called Q|R, this issue is referred to as Q|R#1. A divide-and-conquer approach has been developed that fragments the atomic model into small manageable pieces in order to solve Q|R#1. Firstly, the atomic model of a crystal structure is analyzed to detect noncovalent interactions between residues, and the results of the analysis are represented as an interaction graph. Secondly, a graph-clustering algorithm is used to partition the interaction graph into a set of clusters in such a way as to minimize disruption to the noncovalent interaction network. Thirdly, the environment surrounding each individual cluster is analyzed and any residue that is interacting with a particular cluster is assigned to the buffer region of that particular cluster. A fragment is defined as a cluster plus its buffer region. The gradients for all atoms from each of the fragments are computed, and only the gradients from each cluster are combined to create the total gradients. A quantum-based refinement is carried out using the total gradients as chemical restraints. In order to validate this interaction graph-based fragmentation approach in Q|R, the entire atomic model of an amyloid cross-β spine crystal structure (PDB entry 2oNA) was refined.

Quantum crystallography

Approximate wavefunctions can be improved by constraining them to reproduce observations derived from diffraction and scattering experiments. Conversely, charge density models, incorporating electron-density distributions, atomic positions and atomic motion, can be improved by supplementing diffraction experiments with quantum chemically calculated, tailor-made electron densities (form factors). In both cases quantum chemistry and diffraction/scattering experiments are combined into a single, integrated tool. The development of quantum crystallographic research is reviewed. Some results obtained by quantum crystallography illustrate the potential and limitations of this field.

Q|R: quantum-based refinement

Quantum-based refinement utilizes chemical restraints derived from quantum-chemical methods instead of the standard parameterized library-based restraints used in refinement packages. The motivation is twofold: firstly, the restraints have the potential to be more accurate, and secondly, the restraints can be more easily applied to new molecules such as drugs or novel cofactors. Here, a new project called Q|R aimed at developing quantum-based refinement of biomacromolecules is under active development by researchers at Shanghai University together with PHENIX developers. The central focus of this long-term project is to develop software that is built on top of open-source components. A development version of Q|R was used to compare quantum-based refinements with standard refinement using a small model system.

Using the fragment molecular orbital method to investigate agonist-orexin-2 receptor interactions

The understanding of binding interactions between any protein and a small molecule plays a key role in the rationalization of affinity and selectivity and is essential for an efficient structure-based drug discovery (SBDD) process. Clearly, to begin SBDD, a structure is needed, and although there has been fantastic progress in solving G-protein-coupled receptor (GPCR) crystal structures, the process remains quite slow and is not currently feasible for every GPCR or GPCR-ligand complex. This situation significantly limits the ability of X-ray crystallography to impact the drug discovery process for GPCR targets in 'real-time' and hence there is still a need for other practical and cost-efficient alternatives. We present here an approach that integrates our previously described hierarchical GPCR modelling protocol (HGMP) and the fragment molecular orbital (FMO) quantum mechanics (QM) method to explore the interactions and selectivity of the human orexin-2 receptor (OX2R) and its recently discovered nonpeptidic agonists. HGMP generates a 3D model of GPCR structures and its complexes with small molecules by applying a set of computational methods. FMO allowsab initioapproaches to be applied to systems that conventional QM methods would find challenging. The key advantage of FMO is that it can reveal information on the individual contribution and chemical nature of each residue and water molecule to the ligand binding that normally would be difficult to detect without QM. We illustrate how the combination of both techniques provides a practical and efficient approach that can be used to analyse the existing structure-function relationships (SAR) and to drive forward SBDD in a real-world example for which there is no crystal structure of the complex available.

Fragment Molecular Orbital Method Applied to Lead Optimization of Novel Interleukin-2 Inducible T-Cell Kinase (ITK) Inhibitors

Inhibition of inducible T-cell kinase (ITK), a nonreceptor tyrosine kinase, may represent a novel treatment for allergic asthma. In our previous reports, we described the discovery of sulfonylpyridine (SAP), benzothiazole (BZT), indazole (IND), and tetrahydroindazole (THI) series as novel ITK inhibitors and how computational tools such as dihedral scans and docking were used to support this process. X-ray crystallography and modeling were applied to provide essential insight into ITK-ligand interactions. However, "visual inspection" traditionally used for the rationalization of protein-ligand affinity cannot always explain the full complexity of the molecular interactions. The fragment molecular orbital (FMO) quantum-mechanical (QM) method provides a complete list of the interactions formed between the ligand and protein that are often omitted from traditional structure-based descriptions. FMO methodology was successfully used as part of a rational structure-based drug design effort to improve the ITK potency of high-throughput screening hits, ultimately delivering ligands with potency in the subnanomolar range.

The Fragment Molecular Orbital Method Reveals New Insight into the Chemical Nature of GPCR–Ligand Interactions

Our interpretation of ligand-protein interactions is often informed by high-resolution structures, which represent the cornerstone of structure-based drug design. However, visual inspection and molecular mechanics approaches cannot explain the full complexity of molecular interactions. Quantum Mechanics approaches are often too computationally expensive, but one method, Fragment Molecular Orbital (FMO), offers an excellent compromise and has the potential to reveal key interactions that would otherwise be hard to detect. To illustrate this, we have applied the FMO method to 18 Class A GPCR-ligand crystal structures, representing different branches of the GPCR genome. Our work reveals key interactions that are often omitted from structure-based descriptions, including hydrophobic interactions, nonclassical hydrogen bonds, and the involvement of backbone atoms. This approach provides a more comprehensive picture of receptor-ligand interactions than is currently used and should prove useful for evaluation of the chemical nature of ligand binding and to support structure-based drug design.

New insights into the enzymatic mechanism of human chitotriosidase (CHIT1) catalytic domain by atomic resolution X-ray diffraction and hybrid QM/MM

Chitotriosidase (CHIT1) is a human chitinase belonging to the highly conserved glycosyl hydrolase family 18 (GH18). GH18 enzymes hydrolyze chitin, an N-acetylglucosamine polymer synthesized by lower organisms for structural purposes. Recently, CHIT1 has attracted attention owing to its upregulation in immune-system disorders and as a marker of Gaucher disease. The 39 kDa catalytic domain shows a conserved cluster of three acidic residues, Glu140, Asp138 and Asp136, involved in the hydrolysis reaction. Under an excess concentration of substrate, CHIT1 and other homologues perform an additional activity, transglycosylation. To understand the catalytic mechanism of GH18 chitinases and the dual enzymatic activity, the structure and mechanism of CHIT1 were analyzed in detail. The resolution of the crystals of the catalytic domain was improved from 1.65 Å (PDB entry 1waw) to 0.95-1.10 Å for the apo and pseudo-apo forms and the complex with chitobiose, allowing the determination of the protonation states within the active site. This information was extended by hybrid quantum mechanics/molecular mechanics (QM/MM) calculations. The results suggest a new mechanism involving changes in the conformation and protonation state of the catalytic triad, as well as a new role for Tyr27, providing new insights into the hydrolysis and transglycosylation activities.

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.

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.

QM and QM/MM simulations of proteins

Molecular dynamics simulations of biomolecules have matured into powerful tools of structural biology. In addition to the commonly used empirical force field potentials, quantum mechanical descriptions are gaining popularity for structure optimization and dynamic simulations of peptides and proteins. In this chapter, we introduce methodological developments such as the QM/MM framework and linear-scaling QM that make efficient calculations on large biomolecules possible. We identify the most common scenarios in which quantum descriptions of peptides and proteins are employed, such as structural refinement, force field development, treatment of unusual residues, and predicting spectroscopic and exited state properties. The benefits and shortcomings of QM potentials, in comparison to classical force fields, are discussed, with special emphasis on the sampling problems of protein conformational space. Finally, recent examples of QM/MM calculations in light-sensitive membrane proteins illustrate typical applications of the reviewed methods.

PDB ligand conformational energies calculated quantum-mechanically

We present here a greatly updated version of an earlier study on the conformational energies of protein-ligand complexes in the Protein Data Bank (PDB) [Nicklaus et al. Bioorg. Med. Chem. 1995, 3, 411-428], with the goal of improving on all possible aspects such as number and selection of ligand instances, energy calculations performed, and additional analyses conducted. Starting from about 357,000 ligand instances deposited in the 2008 version of the Ligand Expo database of the experimental 3D coordinates of all small-molecule instances in the PDB, we created a "high-quality" subset of ligand instances by various filtering steps including application of crystallographic quality criteria and structural unambiguousness. Submission of 640 Gaussian 03 jobs yielded a set of about 415 successfully concluded runs. We used a stepwise optimization of internal degrees of freedom at the DFT level of theory with the B3LYP/6-31G(d) basis set and a single-point energy calculation at B3LYP/6-311++G(3df,2p) after each round of (partial) optimization to separate energy changes due to bond length stretches vs bond angle changes vs torsion changes. Even for the most "conservative" choice of all the possible conformational energies-the energy difference between the conformation in which all internal degrees of freedom except torsions have been optimized and the fully optimized conformer-significant energy values were found. The range of 0 to ~25 kcal/mol was populated quite evenly and independently of the crystallographic resolution. A smaller number of "outliers" of yet higher energies were seen only at resolutions above 1.3 Å. The energies showed some correlation with molecular size and flexibility but not with crystallographic quality metrics such as the Cruickshank diffraction-component precision index (DPI) and R(free)-R, or with the ligand instance-specific metrics such as occupancy-weighted B-factor (OWAB), real-space R factor (RSR), and real-space correlation coefficient (RSCC). We repeated these calculations with the solvent model IEFPCM, which yielded energy differences that were generally somewhat lower than the corresponding vacuum results but did not produce a qualitatively different picture. Torsional sampling around the crystal conformation at the molecular mechanics level using the MMFF94s force field typically led to an increase in energy.

Structure refinement of protein low resolution models using the GNEIMO constrained dynamics method

The challenge in protein structure prediction using homology modeling is the lack of reliable methods to refine the low resolution homology models. Unconstrained all-atom molecular dynamics (MD) does not serve well for structure refinement due to its limited conformational search. We have developed and tested the constrained MD method, based on the generalized Newton-Euler inverse mass operator (GNEIMO) algorithm for protein structure refinement. In this method, the high-frequency degrees of freedom are replaced with hard holonomic constraints and a protein is modeled as a collection of rigid body clusters connected by flexible torsional hinges. This allows larger integration time steps and enhances the conformational search space. In this work, we have demonstrated the use of torsional GNEIMO method without using any experimental data as constraints, for protein structure refinement starting from low-resolution decoy sets derived from homology methods. In the eight proteins with three decoys for each, we observed an improvement of ~2 Å in the rmsd in coordinates to the known experimental structures of these proteins. The GNEIMO trajectories also showed enrichment in the population density of native-like conformations. In addition, we demonstrated structural refinement using a "freeze and thaw" clustering scheme with the GNEIMO framework as a viable tool for enhancing localized conformational search. We have derived a robust protocol based on the GNEIMO replica exchange method for protein structure refinement that can be readily extended to other proteins and possibly applicable for high throughput protein structure refinement.

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.

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.

Polarizable Atomic Multipole X-Ray Refinement: Particle Mesh Ewald Electrostatics for Macromolecular Crystals

Refinement of macromolecular models from X-ray crystallography experiments benefits from prior chemical knowledge at all resolutions. As the quality of the prior chemical knowledge from quantum or classical molecular physics improves, in principle so will resulting structural models. Due to limitations in computer performance and electrostatic algorithms, commonly used macromolecules X-ray crystallography refinement protocols have had limited support for rigorous molecular physics in the past. For example, electrostatics is often neglected in favor of nonbonded interactions based on a purely repulsive van der Waals potential. In this work we present advanced algorithms for desktop workstations that open the door to X-ray refinement of even the most challenging macromolecular data sets using state-of-the-art classical molecular physics. First we describe theory for particle mesh Ewald (PME) summation that consistently handles the symmetry of all 230 space groups, replicates of the unit cell such that the minimum image convention can be used with a real space cutoff of any size and the combination of space group symmetry with replicates. An implementation of symmetry accelerated PME for the polarizable atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field is presented. Relative to a single CPU core performing calculations on a P1 unit cell, our AMOEBA engine called Force Field X (FFX) accelerates energy evaluations by more than a factor of 24 on an 8-core workstation with a Tesla GPU coprocessor for 30 structures that contain 240 000 atoms on average in the unit cell. The benefit of AMOEBA electrostatics evaluated with PME for macromolecular X-ray crystallography refinement is demonstrated via rerefinement of 10 crystallographic data sets that range in resolution from 1.7 to 4.5 Å. Beginning from structures obtained by local optimization without electrostatics, further optimization using AMOEBA with PME electrostatics improved agreement of the model with the data (Rfree was lowered by 0.5%), improved geometric features such as favorable (ϕ, ψ) backbone conformations, and lowered the average potential energy per residue by over 10 kcal/mol. Furthermore, the MolProbity structure validation tool indicates that the geometry of these rerefined structures is consistent with X-ray crystallographic data collected up to 2.2 Å, which is 0.9 Å better than the actual mean quality (3.1 Å). We conclude that polarizable AMOEBA-assisted X-ray refinement offers advantages to methods that neglect electrostatics and is now efficient enough for routine use.

Trends in template/fragment-free protein structure prediction

Predicting the structure of a protein from its amino acid sequence is a long-standing unsolved problem in computational biology. Its solution would be of both fundamental and practical importance as the gap between the number of known sequences and the number of experimentally solved structures widens rapidly. Currently, the most successful approaches are based on fragment/template reassembly. Lacking progress in template-free structure prediction calls for novel ideas and approaches. This article reviews trends in the development of physical and specific knowledge-based energy functions as well as sampling techniques for fragment-free structure prediction. Recent physical- and knowledge-based studies demonstrated that it is possible to sample and predict highly accurate protein structures without borrowing native fragments from known protein structures. These emerging approaches with fully flexible sampling have the potential to move the field forward.

Challenges in the determination of the binding modes of non-standard ligands in X-ray crystal complexes

Despite its central role in structure based drug design the determination of the binding mode (position, orientation and conformation in addition to protonation and tautomeric states) of small heteromolecular ligands in protein:ligand complexes based on medium resolution X-ray diffraction data is highly challenging. In this perspective we demonstrate how a combination of molecular dynamics simulations and free energy (FE) calculations can be used to correct and identify thermodynamically stable binding modes of ligands in X-ray crystal complexes. The consequences of inappropriate ligand structure, force field and the absence of electrostatics during X-ray refinement are highlighted. The implications of such uncertainties and errors for the validation of virtual screening and fragment-based drug design based on high throughput X-ray crystallography are discussed with possible solutions and guidelines.

QM/MM X-ray refinement of zinc metalloenzymes

Zinc metalloenzymes play an important role in biology. However, due to the limitation of molecular force field energy restraints used in X-ray refinement at medium or low resolutions, the precise geometry of the zinc coordination environment can be difficult to distinguish from ambiguous electron density maps. Due to the difficulties involved in defining accurate force fields for metal ions, the QM/MM (quantum-mechanical/molecular-mechanical) method provides an attractive and more general alternative for the study and refinement of metalloprotein active sites. Herein we present three examples that indicate that QM/MM based refinement yields a superior description of the crystal structure based on R and R(free) values and on the inspection of the zinc coordination environment. It is concluded that QM/MM refinement is an useful general tool for the improvement of the metal coordination sphere in metalloenzyme active sites.

Conformational variability of benzamidinium-based inhibitors

Determining the structure of a small molecule bound to a biological receptor (e.g., a protein implicated in a disease state) is a necessary step in structure-based drug design. The preferred conformation of a small molecule can change when bound to a protein, and a detailed knowledge of the preferred conformation(s) of a bound ligand can help in optimizing the affinity of a molecule for its receptor. However, the quality of a protein/ligand complex determined using X-ray crystallography is dependent on the size of the protein, the crystal quality, and the realized resolution. The energy restraints used in traditional X-ray refinement procedures typically use "reduced" (i.e., neglect of electrostatics and dispersion interactions) Engh and Huber force field models that, while quite suitable for modeling proteins, often are less suitable for small molecule structures due to a lack of validated parameters. Through the use of ab initio QM/MM-based X-ray refinement procedures, this shortcoming can be overcome especially in the active site or binding site of a small-molecule inhibitor. Herein, we demonstrate that ab initio QM/MM refinement of an inhibitor/protein complex provides insights into the binding of small molecules beyond what is available using more traditional refinement protocols. In particular, QM/MM refinement studies of benzamidinium derivatives show variable conformational preferences depending on the refinement protocol used and the nature of the active-site region.