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

MD simulations of macromolecular crystals: Implications for the analysis of Bragg and diffuse scattering

Some of our most detailed information about structure and dynamics of macromolecules comes from X-ray-diffraction studies in crystalline environments. More than 170,000 atomic models have been deposited in the Protein Data Bank, and the number of observations (typically of intensities of Bragg diffraction peaks) is generally quite large, when compared to other experimental methods. Nevertheless, the general agreement between calculated and observed intensities is far outside the experimental precision, and the majority of scattered photons fall between the sharp Bragg peaks, and are rarely taken into account. This chapter considers how molecular dynamics simulations can be used to explore the connections between microscopic behavior in a crystalline lattice and observed scattering intensities, and point the way to new atomic models that could more faithfully recapitulate Bragg intensities and extract useful information from the diffuse scattering that lies between those peaks.

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.

Refinement of RNA Structures Using Amber Force Fields

Atomic models for nucleic acids derived from X-ray diffraction data at low resolution provide much useful information, but the observed scattering intensities can be fit with models that can differ in structural detail. Tradtional geometric restraints favor models that have bond length and angle terms derived from small molecule crystal structures. Here we explore replacing these restraints with energy gradients derived from force fields, including recently developed integral equation models to account for the effects of water molecules and ions that are not part of the explicit model. We compare conventional and force-field based refinements for 22 RNA crystals, ranging in resolution from 1.1 to 3.6 Å. As expected, it can be important to account for solvent screening of charge–charge interactions, especially in the crowded environment of a nucleic acid crystal. The newly refined models can show improvements in torsion angles and hydrogen-bonding interactions, and can significantly reduce unfavorable atomic clashes, while maintaining or improving agreement with observed scattering intensities.

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.

Macromolecular refinement of X-ray and cryoelectron microscopy structures with Phenix/OPLS3e for improved structure and ligand quality

With the advent of the resolution revolution in cryoelectron microscopy (cryo-EM), low-resolution refinement is common, and likewise increases the need for a reliable force field. Here, we report on the incorporation of the OPLS3e force field with the VSGB2.1 solvation model in the structure determination package Phenix. Our results show significantly improved structure quality and reduced ligand strain at lower resolution for X-ray refinement. For refinement of cryo-EM-based structures, we find comparable quality structures, goodness-of-fit, and reduced ligand strain. We also show how structure quality and ligand strain are related to the map-model cross-correlation as a function of data weight, and how that can detect overfitting. Signs of overfitting are found in over half of our cryo-EM dataset, which can be remedied by a re-refinement at a lower data weight. Finally, a start-to-end script for refining structures with Phenix/OPLS3e is available in the Schrödinger 2020-3 distribution.

Large-Scale Analysis of Bioactive Ligand Conformational Strain Energy by Ab Initio Calculation

Ligand conformational strain energy (LCSE) plays an important role in virtual screening and lead optimization. While various studies have provided insights into LCSE for small-molecule ligands in the Protein Data Bank (PDB), conclusions are inconsistent mainly due to small datasets, poor quality control of crystal structures, and molecular mechanics (MM) or low-level quantum mechanics (QM) calculations. Here, we built a high-quality dataset (LigBoundConf) of 8145 ligand-bound conformations from PDB crystal structures and calculated LCSE at the M062X-D3/ma-TZVPP (SMD)//M062X-D3/def2-SVP(SMD) level for each case in the dataset. The mean/median LCSE is 4.6/3.7 kcal/mol for 6672 successfully calculated cases, which is significantly lower than the estimates based on molecular mechanics in many previous analyses. Especially, when removing ligands with nonaromatic ring(s) that are prone to have large LCSEs due to electron density overfitting, the mean/median LCSE was reduced to 3.3/2.5 kcal/mol. We further reveal that LCSE is correlated with several ligand properties, including formal atomic charge, molecular weight, number of rotatable bonds, and number of hydrogen-bond donors and acceptors. In addition, our results show that although summation of torsion strains is a good approximation of LCSE for most cases, for a small fraction (about 6%) of our dataset, it underestimates LCSEs if ligands could form nonlocal intramolecular interactions in the unbound state. Taken together, our work provides a comprehensive profile of LCSE for ligands in PDB, which could help ligand conformation generation, ligand docking pose evaluation, and lead optimization.

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/

User-Friendly Quantum Mechanics: Applications for Drug Discovery

Quantum mechanics (QM) methods provide a fine description of receptor-ligand interactions and of chemical reactions. Their use in drug design and drug discovery is increasing, especially for complex systems including metal ions in the binding sites, for the design of highly selective inhibitors, for the optimization of bi-specific compounds, to understand enzymatic reactions, and for the study of covalent ligands and prodrugs. They are also used for generating molecular descriptors for predictive QSAR/QSPR models and for the parameterization of force fields. Thanks to the continuous increase of computational power offered by GPUs and to the development of sophisticated algorithms, QM methods are becoming part of the standard tools used in computer-aided drug design (CADD). We present the most used QM methods and software packages, and we discuss recent representative applications in drug design and drug discovery.

The upcoming subatomic resolution revolution

Subatomic resolution macromolecular crystallography has been revealing the most fascinating details of macromolecular structures for many years. This most extreme form of macromolecular crystallography is going through rapid changes. A new generation of superbrilliant X-ray sources and detectors is facilitating the rapid acquisition of high-quality datasets. Equally important, a new breed of methods and highly integrated advanced computational tools for structure refinement and analysis is poised to change the way we use subatomic resolution data and reposition high-resolution macromolecular crystallography in medicinal chemistry studies. Subatomic resolution macromolecular crystallography may soon be a routine source of detailed molecular information besides precise geometries, including binding energies and other chemical descriptors, opening new possibilities of application.