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

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

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.

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

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

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.

XModeScore: a novel method for accurate protonation/tautomer-state determination using quantum-mechanically driven macromolecular X-ray crystallographic refinement

Gaining an understanding of the protein-ligand complex structure along with the proper protonation and explicit solvent effects can be important in obtaining meaningful results in structure-guided drug discovery and structure-based drug discovery. Unfortunately, protonation and tautomerism are difficult to establish with conventional methods because of difficulties in the experimental detection of H atoms owing to the well known limitations of X-ray crystallography. In the present work, it is demonstrated that semiempirical, quantum-mechanics-based macromolecular crystallographic refinement is sensitive to the choice of a protonation-state/tautomer form of ligands and residues, and can therefore be used to explore potential states. A novel scoring method, called XModeScore, is described which enumerates the possible protomeric/tautomeric modes, refines each mode against X-ray diffraction data with the semiempirical quantum-mechanics (PM6) Hamiltonian and scores each mode using a combination of energetic strain (or ligand strain) and rigorous statistical analysis of the difference electron-density distribution. It is shown that using XModeScore it is possible to consistently distinguish the correct bound protomeric/tautomeric modes based on routine X-ray data, even at lower resolutions of around 3 Å. These X-ray results are compared with the results obtained from much more expensive and laborious neutron diffraction studies for three different examples: tautomerism in the acetazolamide ligand of human carbonic anhydrase II (PDB entries 3hs4 and 4k0s), tautomerism in the 8HX ligand of urate oxidase (PDB entries 4n9s and 4n9m) and the protonation states of the catalytic aspartic acid found within the active site of an aspartic protease (PDB entry 2jjj). In each case, XModeScore applied to the X-ray diffraction data is able to determine the correct protonation state as defined by the neutron diffraction data. The impact of QM-based refinement versus conventional refinement on XModeScore is also discussed.

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.

Computational alanine scanning with linear scaling semiempirical quantum mechanical methods

Alanine scanning is a powerful experimental tool for understanding the key interactions in protein-protein interfaces. Linear scaling semiempirical quantum mechanical calculations are now sufficiently fast and robust to allow meaningful calculations on large systems such as proteins, RNA and DNA. In particular, they have proven useful in understanding protein-ligand interactions. Here we ask the question: can these linear scaling quantum mechanical methods developed for protein-ligand scoring be useful for computational alanine scanning? To answer this question, we assembled 15 protein-protein complexes with available crystal structures and sufficient alanine scanning data. In all, the data set contains Delta Delta Gs for 400 single point alanine mutations of these 15 complexes. We show that with only one adjusted parameter the quantum mechanics-based methods outperform both buried accessible surface area and a potential of mean force and compare favorably to a variety of published empirical methods. Finally, we closely examined the outliers in the data set and discuss some of the challenges that arise from this examination.

Quantum mechanical pairwise decomposition analysis of protein kinase B inhibitors: validating a new tool for guiding drug design

Quantum mechanical semiempirical comparative binding energy analysis calculations have been carried out for a series of protein kinase B (PKB) inhibitors derived from fragment- and structure-based drug design. These protein−ligand complexes were selected because they represent a consistent set of experimental data that includes both crystal structures and affinities. Seven scoring functions were evaluated based on both the PM3 and the AM1 Hamiltonians. The optimal models obtained by partial least-squares analysis of the aligned poses are predictive as measured by a number of standard statistical criteria and by validation with an external data set. An algorithm has been developed that provides residue-based contributions to the overall binding affinity. These residue-based binding contributions can be plotted in heat maps so as to highlight the most important residues for ligand binding. In the case of these PKB inhibitors, the maps show that Met166, Thr97, Gly43, Glu114, Ala116, and Val50, among other residues, play an important role in determining binding affinity. The interaction energy map makes it easy to identify the residues that have the largest absolute effect on ligand binding. The structure−activity relationship (SAR) map highlights residues that are most critical to discriminating between more and less potent ligands. Taken together the interaction energy and the SAR maps provide useful insights into drug design that would be difficult to garner in any other way.

A critical assessment of the performance of protein-ligand scoring functions based on NMR chemical shift perturbations

We have generated docking poses for the FKBP-GPI complex using eight docking programs, and compared their scoring functions with scoring based on NMR chemical shift perturbations (NMRScore). Because the chemical shift perturbation (CSP) is exquisitely sensitive on the orientation of the ligand inside the binding pocket, NMRScore offers an accurate and straightforward approach to score different poses. All scoring functions were inspected by their abilities to highly rank the native-like structures and separate them from decoy poses generated for a protein-ligand complex. The overall performance of NMRScore is much better than that of energy-based scoring functions associated with docking programs in both aspects. In summary, we find that the combination of docking programs with NMRScore results in an approach that can robustly determine the binding site structure for a protein-ligand complex, thereby providing a new tool facilitating the structure-based drug discovery process.

The role of quantum mechanics in structure-based drug design

Herein we will focus on the use of quantum mechanics (QM) in drug design (DD) to solve disparate problems from scoring protein-ligand poses to building QM QSAR models. Through the variational principle of QM we know that we can obtain a more accurate representation of molecular systems than classical models, and while this is not a matter of debate, it still has not been shown that the expense of QM approaches is offset by improved accuracy in DD applications. Objectively validating the improved applicability and performance of QM over classical-based models in DD will be the focus of research in the coming years along with research on the conformational sampling problem as it relates to protein-ligand complexes.

Quantum mechanical description of the interactions between DNA and water

In recent years, a lot of attention has been focused on the electronic properties of DNA. With recent advances in linear scaling quantum mechanics there are now new tools available to enhance our understanding of the electronic properties of DNA among other biomolecules. Using both explicit solvent models and implicit (continuum) solvent models, the electronic characteristics of a dodecamer duplex DNA have been fully studied using both divide and conquer (D&C), semi-empirical quantum mechanics and non-D&C semi-empirical quantum mechanics. According to the AM1 Hamiltonian, approximately 3.5 electrons (approximately 0.3 electron/base pair) are transferred from the duplex to the solvent. According to the density of state (DOS) analysis, in vacuo DNA has a band gap of approximately 1 eV showing that in the absence of solvent, the DNA may exhibit similar properties to those of a semiconductor. Upon increasing solvation (2.5-5.5 A), the band gap ranges from approximately 3 eV to approximately 6 eV. For the implicit solvent model, the band gap continues this widening trend to approximately 7 eV. Therefore, upon solvation and in the absence of dopants, the DNA should begin to loose its conductive properties. Finally, when one considers the energy and localization of the frontier orbitals (HOMO and LUMO), solvent has a stabilizing effect on the DNA system. The energy of the HOMO drops from approximately 15 eV in vacuo to approximately 2 eV for 5.5 A of water to approximately -8 eV for the implicit solvent model. Similarly, the LUMO drops from approximately 16 eV for in vacuo to approximately 9 eV for 5.5 A of water to approximately -1 eV for the implicit model. Beyond the importance of the computed results on the materials properties of DNA, the present work also shows that the behavior of intercalators will be affected by the electronic properties of DNA. This could have an impact on our understanding of how DNA based drugs interact with DNA and on the design of new DNA based small molecule drugs.

Pairwise decomposition of residue interaction energies using semiempirical quantum mechanical methods in studies of protein-ligand interaction

Pairwise decomposition of the interaction energy between molecules is shown to be a powerful tool that can increase our understanding of macromolecular recognition processes. Herein we calculate the pairwise decomposition of the interaction energy between the protein human carbonic anhydrase II (HCAII) and the fluorine-substituted ligand N-(4-sulfamylbenzoyl)benzylamine (SBB) using semiempirical quantum mechanics based methods. We dissect the interaction between the ligand and the protein by dividing the ligand and the protein into subsystems to understand the structure-activity relationships as a result of fluorine substitution. In particular, the off-diagonal elements of the Fock matrix that is composed of the interaction between the ionic core and the valence electrons and the exchange energy between the subsystems or atoms of interest is examined in detail. Our analysis reveals that the fluorine-substituted benzylamine group of SBB does not directly affect the binding energy. Rather, we find that the strength of the interaction between Thr199 of HCAII and the sulfamylbenzoyl group of SBB affects the binding affinity between the protein and the ligand. These observations underline the importance of the sulfonamide group in binding affinity as shown by previous experiments (Maren, T. H.; Wiley: C. E. J. Med. Chem. 1968, 11, 228-232). Moreover, our calculations qualitatively agree with the structural aspects of these protein-ligand complexes as determined by X-ray crystallography.