Hybrid programming-model strategies for GPU offloading of electronic structure calculation kernels.

To address the challenge of performance portability and facilitate the implementation of electronic structure solvers, we developed the basic matrix library (BML) and Parallel, Rapid O(N), and Graph-based Recursive Electronic Structure Solver (PROGRESS) library. The BML implements linear algebra operations necessary for electronic structure kernels using a unified user interface for various matrix formats (dense and sparse) and architectures (CPUs and GPUs). Focusing on density functional theory and tight-binding models, PROGRESS implements several solvers for computing the single-particle density matrix and relies on BML. In this paper, we describe the general strategies used for these implementations on various computer architectures, using OpenMP target functionalities on GPUs, in conjunction with third-party libraries to handle performance critical numerical kernels. We demonstrate the portability of this approach and its performance in benchmark problems.

Changes in an enzyme ensemble during catalysis observed by high-resolution XFEL crystallography.

Enzymes populate ensembles of structures necessary for catalysis that are difficult to experimentally characterize. We use time-resolved mix-and-inject serial crystallography at an x-ray free electron laser to observe catalysis in a designed mutant isocyanide hydratase (ICH) enzyme that enhances sampling of important minor conformations. The active site exists in a mixture of conformations, and formation of the thioimidate intermediate selects for catalytically competent substates. The influence of cysteine ionization on the ICH ensemble is validated by determining structures of the enzyme at multiple pH values. Large molecular dynamics simulations in crystallo and time-resolved electron density maps show that Asp17 ionizes during catalysis and causes conformational changes that propagate across the dimer, permitting water to enter the active site for intermediate hydrolysis. ICH exhibits a tight coupling between ionization of active site residues and catalysis-activated protein motions, exemplifying a mechanism of electrostatic control of enzyme dynamics.

Molecular-dynamics simulations of macromolecular diffraction, part II: Analysis of protein crystal simulations.

Molecular-dynamics (MD) simulations have contributed substantially to our understanding of protein structure and dynamics, yielding insights into many biological processes including protein folding, drug binding, and mechanisms of protein-protein interactions. Much of what is known about protein structure comes from macromolecular crystallography (MX) experiments. MD simulations of protein crystals are useful in the study of MX because the simulations can be analyzed to calculate almost any crystallographic observable of interest, from atomic coordinates to structure factors and densities, B-factors, multiple conformations and their populations/occupancies, and diffuse scattering intensities. Computing resources and software to support crystalline MD simulations are now readily available to many researchers studying protein structure and dynamics and who may be interested in advanced interpretation of MX data, including diffuse scattering. In this work, we outline methods of analyzing MD simulations of protein crystals and provide accompanying Jupyter notebooks as practical resources for researchers wishing to perform similar analyses on their own systems of interest.

Interpreting macromolecular diffraction through simulation.

This chapter discusses the use of diffraction simulators to improve experimental outcomes in macromolecular crystallography, in particular for future experiments aimed at diffuse scattering. Consequential decisions for upcoming data collection include the selection of either a synchrotron or free electron laser X-ray source, rotation geometry or serial crystallography, and fiber-coupled area detector technology vs. pixel-array detectors. The hope is that simulators will provide insights to make these choices with greater confidence. Simulation software, especially those packages focused on physics-based calculation of the diffraction, can help to predict the location, size, shape, and profile of Bragg spots and diffuse patterns in terms of an underlying physical model, including assumptions about the crystal's mosaic structure, and therefore can point to potential issues with data analysis in the early planning stages. Also, once the data are collected, simulation may offer a pathway to improve the measurement of diffraction, especially with weak data, and might help to treat problematic cases such as overlapping patterns.

Molecular-dynamics simulations of macromolecular diffraction, part I: Preparation of protein crystal simulations.

Molecular-dynamics (MD) simulations of protein crystals enable the prediction of structural and dynamical features of both the protein and the solvent components of macromolecular crystals, which can be validated against diffraction data from X-ray crystallographic experiments. The simulations have been useful for studying and predicting both Bragg and diffuse scattering in protein crystallography; however, the preparation is not yet automated and includes choices and tradeoffs that can impact the results. Here we examine some of the intricacies and consequences of the choices involved in setting up MD simulations of protein crystals for the study of diffraction data, and provide a recipe for preparing the simulations, packaged in an accompanying Jupyter notebook. This article and the accompanying notebook are intended to serve as practical resources for researchers wishing to put these models to work.

Changes in an Enzyme Ensemble During Catalysis Observed by High Resolution XFEL Crystallography.

Enzymes populate ensembles of structures with intrinsically different catalytic proficiencies that are difficult to experimentally characterize. We use time-resolved mix-and-inject serial crystallography (MISC) at an X-ray free electron laser (XFEL) to observe catalysis in a designed mutant (G150T) isocyanide hydratase (ICH) enzyme that enhances sampling of important minor conformations. The active site exists in a mixture of conformations and formation of the thioimidate catalytic intermediate selects for catalytically competent substates. A prior proposal for active site cysteine charge-coupled conformational changes in ICH is validated by determining structures of the enzyme over a range of pH values. A combination of large molecular dynamics simulations of the enzyme in crystallo and time-resolved electron density maps shows that ionization of the general acid Asp17 during catalysis causes additional conformational changes that propagate across the dimer interface, connecting the two active sites. These ionization-linked changes in the ICH conformational ensemble permit water to enter the active site in a location that is poised for intermediate hydrolysis. ICH exhibits a tight coupling between ionization of active site residues and catalysis-activated protein motions, exemplifying a mechanism of electrostatic control of enzyme dynamics.

Water Networks in Photosystem II Using Crystalline Molecular Dynamics Simulations and Room-Temperature XFEL Serial Crystallography.

Structural dynamics of water and its hydrogen-bonding networks play an important role in enzyme function via the transport of protons, ions, and substrates. To gain insights into these mechanisms in the water oxidation reaction in Photosystem II (PS II), we have performed crystalline molecular dynamics (MD) simulations of the dark-stable S1 state. Our MD model consists of a full unit cell with 8 PS II monomers in explicit solvent (861 894 atoms), enabling us to compute the simulated crystalline electron density and to compare it directly with the experimental density from serial femtosecond X-ray crystallography under physiological temperature collected at X-ray free electron lasers (XFELs). The MD density reproduced the experimental density and water positions with high fidelity. The detailed dynamics in the simulations provided insights into the mobility of water molecules in the channels beyond what can be interpreted from experimental B-factors and electron densities alone. In particular, the simulations revealed fast, coordinated exchange of waters at sites where the density is strong, and water transport across the bottleneck region of the channels where the density is weak. By computing MD hydrogen and oxygen maps separately, we developed a novel Map-based Acceptor-Donor Identification (MADI) technique that yields information which helps to infer hydrogen-bond directionality and strength. The MADI analysis revealed a series of hydrogen-bond wires emanating from the Mn cluster through the Cl1 and O4 channels; such wires might provide pathways for proton transfer during the reaction cycle of PS II. Our simulations provide an atomistic picture of the dynamics of water and hydrogen-bonding networks in PS II, with implications for the specific role of each channel in the water oxidation reaction.

Graph-based quantum response theory and shadow Born-Oppenheimer molecular dynamics.

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born-Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. The proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.

Molecular-dynamics simulation methods for macromolecular crystallography.

It is investigated whether molecular-dynamics (MD) simulations can be used to enhance macromolecular crystallography (MX) studies. Historically, protein crystal structures have been described using a single set of atomic coordinates. Because conformational variation is important for protein function, researchers now often build models that contain multiple structures. Methods for building such models can fail, however, in regions where the crystallographic density is difficult to interpret, for example at the protein-solvent interface. To address this limitation, a set of MD-MX methods that combine MD simulations of protein crystals with conventional modeling and refinement tools have been developed. In an application to a cyclic adenosine monophosphate-dependent protein kinase at room temperature, the procedure improved the interpretation of ambiguous density, yielding an alternative water model and a revised protein model including multiple conformations. The revised model provides mechanistic insights into the catalytic and regulatory interactions of the enzyme. The same methods may be used in other MX studies to seek mechanistic insights.

Enhancing Sampling of Water Rehydration on Ligand Binding: A Comparison of Techniques.

Water often plays a key role in protein structure, molecular recognition, and mediating protein-ligand interactions. Thus, free energy calculations must adequately sample water motions, which often proves challenging in typical MD simulation time scales. Thus, the accuracy of methods relying on MD simulations ends up limited by slow water sampling. Particularly, as a ligand is removed or modified, bulk water may not have time to fill or rearrange in the binding site. In this work, we focus on several molecular dynamics (MD) simulation-based methods attempting to help rehydrate buried water sites: BLUES, using nonequilibrium candidate Monte Carlo (NCMC); grand, using grand canonical Monte Carlo (GCMC); and normal MD. We assess the accuracy and efficiency of these methods in rehydrating target water sites. We selected a range of systems with varying numbers of waters in the binding site, as well as those where water occupancy is coupled to the identity or binding mode of the ligand. We analyzed the rehydration of buried water sites in binding pockets using both clustering of trajectories and direct analysis of electron density maps. Our results suggest both BLUES and grand enhance water sampling relative to normal MD and grand is more robust than BLUES, but also that water sampling remains a major challenge for all of the methods tested. The lessons we learned for these methods and systems are discussed.

Reproducibility of protein x-ray diffuse scattering and potential utility for modeling atomic displacement parameters.

Protein structure and dynamics can be probed using x-ray crystallography. Whereas the Bragg peaks are only sensitive to the average unit-cell electron density, the signal between the Bragg peaks-diffuse scattering-is sensitive to spatial correlations in electron-density variations. Although diffuse scattering contains valuable information about protein dynamics, the diffuse signal is more difficult to isolate from the background compared to the Bragg signal, and the reproducibility of diffuse signal is not yet well understood. We present a systematic study of the reproducibility of diffuse scattering from isocyanide hydratase in three different protein forms. Both replicate diffuse datasets and datasets obtained from different mutants were similar in pairwise comparisons (Pearson correlation coefficient ≥0.8). The data were processed in a manner inspired by previously published methods using custom software with modular design, enabling us to perform an analysis of various data processing choices to determine how to obtain the highest quality data as assessed using unbiased measures of symmetry and reproducibility. The diffuse data were then used to characterize atomic mobility using a liquid-like motions (LLM) model. This characterization was able to discriminate between distinct anisotropic atomic displacement parameter (ADP) models arising from different anisotropic scaling choices that agreed comparably with the Bragg data. Our results emphasize the importance of data reproducibility as a model-free measure of diffuse data quality, illustrate the ability of LLM analysis of diffuse scattering to select among alternative ADP models, and offer insights into the design of successful diffuse scattering experiments.

Liquid-like and rigid-body motions in molecular-dynamics simulations of a crystalline protein.

To gain insight into crystalline protein dynamics, we performed molecular-dynamics (MD) simulations of a periodic 2 × 2 × 2 supercell of staphylococcal nuclease. We used the resulting MD trajectories to simulate X-ray diffraction and to study collective motions. The agreement of simulated X-ray diffraction with the data is comparable to previous MD simulation studies. We studied collective motions by analyzing statistically the covariance of alpha-carbon position displacements. The covariance decreases exponentially with the distance between atoms, which is consistent with a liquidlike motions (LLM) model, in which the protein behaves like a soft material. To gain finer insight into the collective motions, we examined the covariance behavior within a protein molecule (intraprotein) and between different protein molecules (interprotein). The interprotein atom pairs, which dominate the overall statistics, exhibit LLM behavior; however, the intraprotein pairs exhibit behavior that is consistent with a superposition of LLM and rigid-body motions (RBM). Our results indicate that LLM behavior of global dynamics is present in MD simulations of a protein crystal. They also show that RBM behavior is detectable in the simulations but that it is subsumed by the LLM behavior. Finally, the results provide clues about how correlated motions of atom pairs both within and across proteins might manifest in diffraction data. Overall, our findings increase our understanding of the connection between molecular motions and diffraction data and therefore advance efforts to extract information about functionally important motions from crystallography experiments.

Mix-and-inject XFEL crystallography reveals gated conformational dynamics during enzyme catalysis.

How changes in enzyme structure and dynamics facilitate passage along the reaction coordinate is a fundamental unanswered question. Here, we use time-resolved mix-and-inject serial crystallography (MISC) at an X-ray free electron laser (XFEL), ambient-temperature X-ray crystallography, computer simulations, and enzyme kinetics to characterize how covalent catalysis modulates isocyanide hydratase (ICH) conformational dynamics throughout its catalytic cycle. We visualize this previously hypothetical reaction mechanism, directly observing formation of a thioimidate covalent intermediate in ICH microcrystals during catalysis. ICH exhibits a concerted helical displacement upon active-site cysteine modification that is gated by changes in hydrogen bond strength between the cysteine thiolate and the backbone amide of the highly strained Ile152 residue. These catalysis-activated motions permit water entry into the ICH active site for intermediate hydrolysis. Mutations at a Gly residue (Gly150) that modulate helical mobility reduce ICH catalytic turnover and alter its pre-steady-state kinetic behavior, establishing that helical mobility is important for ICH catalytic efficiency. These results demonstrate that MISC can capture otherwise elusive aspects of enzyme mechanism and dynamics in microcrystalline samples, resolving long-standing questions about the connection between nonequilibrium protein motions and enzyme catalysis.

Biomolecular Solvation Structure Revealed by Molecular Dynamics Simulations.

To compare ordered water positions from experiment with those from molecular dynamics (MD) simulations, a number of MD models of water structure in crystalline endoglucanase were calculated. The starting MD model was derived from a joint X-ray and neutron diffraction crystal structure, enabling the use of experimentally assigned protonation states. Simulations were performed in the crystalline state, using a periodic 2 × 2 × 2 supercell with explicit solvent. Water X-ray and neutron scattering density maps were computed from MD trajectories using standard macromolecular crystallography methods. In one set of simulations, harmonic restraints were applied to bias the protein structure toward the crystal structure. For these simulations, the recall of crystallographic waters using strong peaks in the MD water electron density was very good, and there also was substantial visual agreement between the boomerang-like wings of the neutron scattering density and the crystalline water hydrogen positions. An unrestrained simulation also was performed. For this simulation, the recall of crystallographic waters was much lower. For both restrained and unrestrained simulations, the strongest water density peaks were associated with crystallographic waters. The results demonstrate that it is now possible to recover crystallographic water structure using restrained MD simulations but that it is not yet reasonable to expect unrestrained MD simulations to do the same. Further development and generalization of MD water models for force-field development, macromolecular crystallography, and medicinal chemistry applications is now warranted. In particular, the combination of room-temperature crystallography, neutron diffraction, and crystalline MD simulations promises to substantially advance modeling of biomolecular solvation.

Interactions that know no boundaries.

Diffuse scattering provides evidence that variations are correlated across molecular boundaries in macromolecular crystals.

Internal protein motions in molecular-dynamics simulations of Bragg and diffuse X-ray scattering.

Molecular-dynamics (MD) simulations of Bragg and diffuse X-ray scattering provide a means of obtaining experimentally validated models of protein conformational ensembles. This paper shows that compared with a single periodic unit-cell model, the accuracy of simulating diffuse scattering is increased when the crystal is modeled as a periodic supercell consisting of a 2 × 2 × 2 layout of eight unit cells. The MD simulations capture the general dependence of correlations on the separation of atoms. There is substantial agreement between the simulated Bragg reflections and the crystal structure; there are local deviations, however, indicating both the limitation of using a single structure to model disordered regions of the protein and local deviations of the average structure away from the crystal structure. Although it was anticipated that a simulation of longer duration might be required to achieve maximal agreement of the diffuse scattering calculation with the data using the supercell model, only a microsecond is required, the same as for the unit cell. Rigid protein motions only account for a minority fraction of the variation in atom positions from the simulation. The results indicate that protein crystal dynamics may be dominated by internal motions rather than packing interactions, and that MD simulations can be combined with Bragg and diffuse X-ray scattering to model the protein conformational ensemble.

Bringing diffuse X-ray scattering into focus.

X-ray crystallography is experiencing a renaissance as a method for probing the protein conformational ensemble. The inherent limitations of Bragg analysis, however, which only reveals the mean structure, have given way to a surge in interest in diffuse scattering, which is caused by structure variations. Diffuse scattering is present in all macromolecular crystallography experiments. Recent studies are shedding light on the origins of diffuse scattering in protein crystallography, and provide clues for leveraging diffuse scattering to model protein motions with atomic detail.

Dynamical Model of Drug Accumulation in Bacteria: Sensitivity Analysis and Experimentally Testable Predictions.

We present a dynamical model of drug accumulation in bacteria. The model captures key features in experimental time courses on ofloxacin accumulation: initial uptake; two-phase response; and long-term acclimation. In combination with experimental data, the model provides estimates of import and export rates in each phase, the time of entry into the second phase, and the decrease of internal drug during acclimation. Global sensitivity analysis, local sensitivity analysis, and Bayesian sensitivity analysis of the model provide information about the robustness of these estimates, and about the relative importance of different parameters in determining the features of the accumulation time courses in three different bacterial species: Escherichia coli, Staphylococcus aureus, and Pseudomonas aeruginosa. The results lead to experimentally testable predictions of the effects of membrane permeability, drug efflux and trapping (e.g., by DNA binding) on drug accumulation. A key prediction is that a sudden increase in ofloxacin accumulation in both E. coli and S. aureus is accompanied by a decrease in membrane permeability.

Quantum crystallographic charge density of urea.

Standard X-ray crystallography methods use free-atom models to calculate mean unit-cell charge densities. Real molecules, however, have shared charge that is not captured accurately using free-atom models. To address this limitation, a charge density model of crystalline urea was calculated using high-level quantum theory and was refined against publicly available ultra-high-resolution experimental Bragg data, including the effects of atomic displacement parameters. The resulting quantum crystallographic model was compared with models obtained using spherical atom or multipole methods. Despite using only the same number of free parameters as the spherical atom model, the agreement of the quantum model with the data is comparable to the multipole model. The static, theoretical crystalline charge density of the quantum model is distinct from the multipole model, indicating the quantum model provides substantially new information. Hydrogen thermal ellipsoids in the quantum model were very similar to those obtained using neutron crystallography, indicating that quantum crystallography can increase the accuracy of the X-ray crystallographic atomic displacement parameters. The results demonstrate the feasibility and benefits of integrating fully periodic quantum charge density calculations into ultra-high-resolution X-ray crystallographic model building and refinement.

Graph-based linear scaling electronic structure theory.

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.