Peptide crystal simulations reveal hidden dynamics

Functional protein dynamics in a crystal

Proteins are molecular machines and to understand how they work, we need to understand how they move. New pump-probe time-resolved X-ray diffraction methods open up ways to initiate and observe protein motions with atomistic detail in crystals on biologically relevant timescales. However, practical limitations of these experiments demands parallel development of effective molecular dynamics approaches to accelerate progress and extract meaning. Here, we establish robust and accurate methods for simulating dynamics in protein crystals, a nontrivial process requiring careful attention to equilibration, environmental composition, and choice of force fields. With more than seven milliseconds of sampling of a single chain, we identify critical factors controlling agreement between simulation and experiments and show that simulated motions recapitulate ligand-induced conformational changes. This work enables a virtuous cycle between simulation and experiments for visualizing and understanding the basic functional motions of proteins.

gmXtal: Cooking Crystals with GROMACS

Molecular dynamics (MD) simulations are routinely performed of biomolecules in solution, because this is their native environment. However, the structures used in such simulations are often obtained with X-ray crystallography, which provides the atomic coordinates of the biomolecule in a crystal environment. With the advent of free electron lasers and time-resolved techniques, X-ray crystallography can now also access metastable states that are intermediates in a biochemical process. Such experiments provide additional data, which can be used, for example, to optimize MD force fields. Doing so requires that the simulation of the biomolecule is also performed in the crystal environment. However, in contrast to simulations of biomolecules in solution, setting up a crystal is challenging. In particular, because not all solvent molecules are resolved in X-ray crystallography, adding a suitable number of solvent molecules, such that the properties of the crystallographic unit cell are preserved in the simulation, can be difficult and typically is a trial-and-error based procedure requiring manual interventions. Such interventions preclude high throughput applications. To overcome this bottleneck, we introduce gmXtal, a tool for setting up crystal simulations for MD simulations with GROMACS. With the information from the protein data bank (rcsb.org) gmXtal automatically (i) builds the crystallographic unit cell; (ii) sets the protonation of titratable residues; (iii) builds missing residues that were not resolved experimentally; and (iv) adds an appropriate number of solvent molecules to the system. gmXtal is available as a standalone tool https://gitlab.com/pbuslaev/gmxtal .

Functional Protein Dynamics in a Crystal

Proteins are molecular machines and to understand how they work, we need to understand how they move. New pump-probe time-resolved X-ray diffraction methods open up ways to initiate and observe protein motions with atomistic detail in crystals on biologically relevant timescales. However, practical limitations of these experiments demands parallel development of effective molecular dynamics approaches to accelerate progress and extract meaning. Here, we establish robust and accurate methods for simulating dynamics in protein crystals, a nontrivial process requiring careful attention to equilibration, environmental composition, and choice of force fields. With more than seven milliseconds of sampling of a single chain, we identify critical factors controlling agreement between simulation and experiments and show that simulated motions recapitulate ligand-induced conformational changes. This work enables a virtuous cycle between simulation and experiments for visualizing and understanding the basic functional motions of proteins.

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.

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.

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.

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.

Simulations of Amyloid-Forming Peptides in the Crystal State

There still is little treatment available for amyloid diseases, despite their significant impact on individuals and the social and economic implications for society. One reason for this is that the physical nature of amyloid formation is not understood sufficiently well. Therefore, fundamental research at the molecular level remains necessary to support the development of therapeutics. A few structures of short peptides from amyloid-forming proteins have been determined. These can in principle be used as scaffolds for designing aggregation inhibitors. Attempts to this end have often used the tools of computational chemistry, in particular molecular simulation. However, few simulation studies of these peptides in the crystal state have been presented so far. Hence, to validate the capability of common force fields (AMBER19SB, CHARMM36m, and OPLS-AA/M) to yield insight into the dynamics and structural stability of amyloid peptide aggregates, we have performed molecular dynamics simulations of twelve different peptide crystals at two different temperatures. From the simulations, we evaluate the hydrogen bonding patterns, the isotropic B-factors, the change in energy, the Ramachandran plots, and the unit cell parameters and compare the results with the crystal structures. Most crystals are stable in the simulations but for all force fields there is at least one that deviates from the experimental crystal, suggesting more work is needed on these models.

Simulating diffraction photographs based on molecular dynamics trajectories of a protein crystal: a new option to examine structure-solving strategies in protein crystallography

A molecular dynamics (MD)-based pipeline has been designed and implemented to emulate the entire process of collecting diffraction photographs and calculating crystallographic structures of proteins from them. Using a structure of lysozyme solved in-house, a supercell comprising 125 (5 × 5 × 5) crystal unit cells containing a total of 1000 protein molecules and explicit interstitial solvent was constructed. For this system, two 300 ns MD trajectories at 298 and 250 K were recorded. A series of snapshots from these trajectories were then used to simulate a fully realistic set of diffraction photographs, which were further fed into the standard pipeline for structure determination. The resulting structures show very good agreement with the underlying MD model not only in terms of coordinates but also in terms of B factors; they are also consistent with the original experimental structure. The developed methodology should find a range of applications, such as optimizing refinement protocols to solve crystal structures and extracting dynamics information from diffraction data or diffuse scattering.

Molecular dynamics simulation of the heart type fatty acid binding protein in a crystal environment

Crystallographic data comes from a space-time average over all the unit cells within the crystal, so dynamic phenomena do not contribute significantly to the diffraction data. Many efforts have been made to reconstitute the movement of the macromolecules and explore the microstates that the confined proteins can adopt in the crystalline network. We explored different strategies to simulate a heart fatty acid binding protein (H-FABP) crystal by means of Molecular Dynamics (MD) simulations. We evaluate the effect of introducing restraints according to experimental isotropic B-factors and we analyzed the H-FABP motions in the crystal using Principal Component Analysis (PCA), isotropic and anisotropic B-factors. We compared the behavior of the protein simulated in the crystal confinement versus in solution, and we observed the effect of that confinement in the mobility of the protein residues. Restraining one-third of Cα atoms based on experimental B-factors produce lower B-factors than simulations without restraints, showing that the position restraint of the atoms with the lowest experimental B-factor is a good strategy to maintain the geometry of the crystal with an obvious decrease in the degrees of motion of the protein. PCA shows that, as position restraint reduces the conformational space explored by the system, the motion of the crystal is better recovered, for an essential subspace of the same size, in the simulations without restraints. Restraining only one Cα seems to be a good balance between giving flexibility to the system and preserving its structure. Communicated by Ramaswamy H. Sarma.

Improved chemistry restraints for crystallographic refinement by integrating the Amber force field into Phenix

The refinement of biomolecular crystallographic models relies on geometric restraints to help to address the paucity of experimental data typical in these experiments. Limitations in these restraints can degrade the quality of the resulting atomic models. Here, an integration of the full all-atom Amber molecular-dynamics force field into Phenix crystallographic refinement is presented, which enables more complete modeling of biomolecular chemistry. The advantages of the force field include a carefully derived set of torsion-angle potentials, an extensive and flexible set of atom types, Lennard-Jones treatment of nonbonded interactions and a full treatment of crystalline electrostatics. The new combined method was tested against conventional geometry restraints for over 22 000 protein structures. Structures refined with the new method show substantially improved model quality. On average, Ramachandran and rotamer scores are somewhat better, clashscores and MolProbity scores are significantly improved, and the modeling of electrostatics leads to structures that exhibit more, and more correct, hydrogen bonds than those refined using traditional geometry restraints. In general it is found that model improvements are greatest at lower resolutions, prompting plans to add the Amber target function to real-space refinement for use in electron cryo-microscopy. This work opens the door to the future development of more advanced applications such as Amber-based ensemble refinement, quantum-mechanical representation of active sites and improved geometric restraints for simulated annealing.

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.

Framework for Conducting and Analyzing Crystal Simulations of Nucleic Acids to Aid in Modern Force Field Evaluation

Crystal simulations provide useful tools, along with solution simulations, to test nucleic acid force fields, but should be interpreted with care owing to the difficulty of establishing the environmental conditions needed to reproduce experimental crystal packing. These challenges underscore the need to construct proper protocols for carrying out crystal simulations and analyzing results to identify the origin of deviations from crystallographic data. Toward this end, we introduce a novel framework for B-factor decomposition into additive intramolecular, rotational, and translational atomic fluctuation components and partitioning of each of these components into individual asymmetric unit and lattice contributions. We apply the framework to a benchmark set of A-DNA, Z-DNA, and B-DNA double helix systems of various chain lengths. Overall, the intramolecular deviations from the crystal were quite small (≤1.0 Å), suggesting high accuracy of the force field, whereas crystal packing was not well reproduced. The present work establishes a framework to conduct and analyze crystal simulations that ultimately take on issues of crystal packing and can provide insight into nucleic acid force fields.

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.

Cryo-Cooling Effect on DHFR Crystal Studied by Replica-Exchange Molecular Dynamics Simulations

Cryo-cooling is routinely performed before x-ray diffraction image collection to reduce the damage to crystals due to ionizing radiation. It has been suggested that although backbone structures are usually very similar between room temperature and cryo-temperature, cryo-cooling may hamper biologically relevant dynamics. In this study, the crystal of Escherichia coli dihydrofolate reductase is studied with replica-exchange molecular dynamics simulation, and the results are compared with the crystal structure determined at cryo-temperature and room temperature with the time-averaged ensemble method. Although temperature dependence of unit cell compaction and root mean-square fluctuation of Cα is found in accord with experiment, it is found that the protein structure at low temperature can be more heterogeneous than the ensemble of structures reported by using the time-averaged ensemble method, encouraging further development of the time-averaged ensemble method and indicating that data should be examined carefully to avoid overinterpretation of one average structure.

Fluorescence enhancement of a ligand-activated fluorescent protein induced by collective noncovalent interactions

Fluorescent proteins contain an internal chromophore constituted of amino acids or an external chromophore covalently bonded to the protein. To increase their fluorescence intensities, many research groups have attempted to mutate amino acids within or near the chromophore. Recently, a new type of fluorescent protein, called UnaG, in which the ligand binds to the protein through many noncovalent interactions was discovered. Later, a series of mutants of the UnaG protein were introduced, which include eUnaG with valine 2 mutated to leucine emitting significantly stronger fluorescence than the wild type and V2T mutant, in which valine 2 is mutated to threonine, emitting weaker fluorescence than the wild type. Interestingly, the single mutation sites of both eUnaG and V2T mutants are distant from the fluorophore, bilirubin, which renders the mechanism of such fluorescence enhancement or reduction unclear. To elucidate the origin of fluorescence intensity changes induced by the single mutations, we carried out extensive analyses on MD simulations for the original UnaG, eUnaG and V2T, and found that the bilirubin ligand bound to eUnaG is conformationally more rigid than the wild-type, particularly in the skeletal dihedral angles, possibly resulting in the increase of quantum yield through a reduction of non-radiative decay. On the other hand, the bilirubin bound to the V2T appears to be flexible than that in the UnaG. Furthermore, examining the structural correlations between the ligand and proteins, we found evidence that the bilirubin ligand is encapsulated in different environments composed of protein residues and water molecules that increase or decrease the stability of the ligand. The changed protein stability affects the mobility and confinement of water molecules captured between bilirubin and the protein. Since the flexible ligand contains multiple hydrogen bond (H-bond) donors and acceptors, the H-bonding structure and dynamics of bound water molecules are highly correlated with the rigidity of the bound ligand. Our results suggest that, to understand the fluorescence properties of protein mutants, especially the ones with noncovalently bound fluorophores with internal rotations, the interaction network among protein residues, ligand, and water molecules within the binding cavity should be investigated rather than focusing on the local structure near the fluorescing moiety. Our in-depth simulation study may offer a foundation for the design principles for engineering this new class of fluorescent proteins.

Molecular Dynamics Simulations of Macromolecular Crystals

The structures of biological macromolecules would not be known to their present extent without X-ray crystallography. Most simulations of globular proteins in solution begin by surrounding the crystal structure of the monomer in a bath of water molecules, but the standard simulation employing periodic boundary conditions is already close to a crystal lattice environment. With simple protocols, the same software and molecular models can perform simulations of the crystal lattice, including all asymmetric units and solvent to fill the box. Throughout the history of molecular dynamics, studies of crystal lattices have served to investigate the quality of the underlying force fields, correlate the simulated ensembles to experimental structure factors, and extrapolate the behavior in lattices to behavior in solution. Powerful new computers are enabling molecular simulations with greater realism and statistical convergence. Meanwhile, the advent of exciting new methods in crystallography, including femtosecond free-electron lasers and image reconstruction for time-resolved crystallography on slurries of small crystals, is expanding the range of structures accessible to X-ray diffraction. We review past fusions of simulations and crystallography, then look ahead to the ways that simulations of crystal structures will enhance structural biology in the future.

Role of Computational Methods in Going beyond X-ray Crystallography to Explore Protein Structure and Dynamics

Protein structural biology came a long way since the determination of the first three-dimensional structure of myoglobin about six decades ago. Across this period, X-ray crystallography was the most important experimental method for gaining atomic-resolution insight into protein structures. However, as the role of dynamics gained importance in the function of proteins, the limitations of X-ray crystallography in not being able to capture dynamics came to the forefront. Computational methods proved to be immensely successful in understanding protein dynamics in solution, and they continue to improve in terms of both the scale and the types of systems that can be studied. In this review, we briefly discuss the limitations of X-ray crystallography in studying protein dynamics, and then provide an overview of different computational methods that are instrumental in understanding the dynamics of proteins and biomacromolecular complexes.

Protein-protein interactions within photosystem II under photoprotection: the synergy between CP29 minor antenna, subunit S (PsbS) and zeaxanthin at all-atom resolution

The assembly and disassembly of protein complexes within cells are crucial life-sustaining processes. In photosystem II (PSII) of higher plants, there is a delicate yet obscure balance between light harvesting and photo-protection under fluctuating light conditions, that involves protein-protein complexes. Recent breakthroughs in molecular dynamics (MD) simulations are combined with new approaches herein to provide structural and energetic insight into such a complex between the CP29 minor antenna and the PSII subunit S (PsbS). The microscopic model involves extensive sampling of bound and dissociated states at atomic resolution in the presence of photo-protective zeaxanthin (Zea), and reveals well defined protein-protein cross-sections. The complex is placed within PSII, and macroscopic connections are emerging (PsbS-CP29-CP24-CP47) along the energy transfer pathways from the antenna to the PSII core. These connections explain macroscopic observations in the literature, while the previously obscured atomic scale details are now revealed. The implications of these findings are discussed in the context of the Non-Photochemical Quenching (NPQ) of chlorophyll fluorescence, the down-regulatory mechanism of photosynthesis, that enables the protection of PSII against excess excitation load. Zea is found at the PsbS-CP29 cross-section and a pH-dependent equilibrium between PsbS dimer/monomers and the PsbS-CP29 dissociation/association is identified as the target for engineering tolerant plants with increased crop and biomass yields. Finally, the new MD based approaches can be used to probe protein-protein interactions in general, and the PSII structure provided can initiate large scale molecular simulations of the photosynthetic apparatus, under NPQ conditions.

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.

Changes in the free-energy landscape of p38α MAP kinase through its canonical activation and binding events as studied by enhanced molecular dynamics simulations

p38α is a Ser/Thr protein kinase involved in a variety of cellular processes and pathological conditions, which makes it a promising pharmacological target. Although the activity of the enzyme is highly regulated, its molecular mechanism of activation remains largely unexplained, even after decades of research. By using state-of-the-art molecular dynamics simulations, we decipher the key elements of the complex molecular mechanism refined by evolution to allow for a fine tuning of p38α kinase activity. Our study describes for the first time the molecular effects of different regulators of the enzymatic activity, and provides an integrative picture of the activation mechanism that explains the seemingly contradictory X-ray and NMR data.

DOI:http://dx.doi.org/10.7554/eLife.22175.001

Crystal Structure of the DFNKF Segment of Human Calcitonin Unveils Aromatic Interactions between Phenylalanines

Although intensively studied, the high-resolution crystal structure of the peptide DFNKF, the core-segment of human calcitonin, has never been described. Here we report how the use of iodination as a strategy to promote crystallisation and facilitate phase determination, allowed us to solve, for the first time, the single-crystal X-ray structure of a DFNKF derivative. Computational studies suggest that both the iodinated and the wild-type peptides populate very similar conformations. Furthermore, the conformer found in the solid-state structure is one of the most populated in solution, making the crystal structure a reliable model for the peptide in solution. The crystal structure of DFNKF(I) confirms the overall features of the amyloid cross-β spine and highlights how aromatic-aromatic interactions are important structural factors in the self-assembly of this peptide. A detailed analysis of such interactions is reported.

Identifying and Visualizing Macromolecular Flexibility in Structural Biology

Structural biology comprises a variety of tools to obtain atomic resolution data for the investigation of macromolecules. Conventional structural methodologies including crystallography, NMR and electron microscopy often do not provide sufficient details concerning flexibility and dynamics, even though these aspects are critical for the physiological functions of the systems under investigation. However, the increasing complexity of the molecules studied by structural biology (including large macromolecular assemblies, integral membrane proteins, intrinsically disordered systems, and folding intermediates) continuously demands in-depth analyses of the roles of flexibility and conformational specificity involved in interactions with ligands and inhibitors. The intrinsic difficulties in capturing often subtle but critical molecular motions in biological systems have restrained the investigation of flexible molecules into a small niche of structural biology. Introduction of massive technological developments over the recent years, which include time-resolved studies, solution X-ray scattering, and new detectors for cryo-electron microscopy, have pushed the limits of structural investigation of flexible systems far beyond traditional approaches of NMR analysis. By integrating these modern methods with powerful biophysical and computational approaches such as generation of ensembles of molecular models and selective particle picking in electron microscopy, more feasible investigations of dynamic systems are now possible. Using some prominent examples from recent literature, we review how current structural biology methods can contribute useful data to accurately visualize flexibility in macromolecular structures and understand its important roles in regulation of biological processes.

Measuring and modeling diffuse scattering in protein X-ray crystallography

X-ray diffraction has the potential to provide rich information about the structural dynamics of macromolecules. To realize this potential, both Bragg scattering, which is currently used to derive macromolecular structures, and diffuse scattering, which reports on correlations in charge density variations, must be measured. Until now, measurement of diffuse scattering from protein crystals has been scarce because of the extra effort of collecting diffuse data. Here, we present 3D measurements of diffuse intensity collected from crystals of the enzymes cyclophilin A and trypsin. The measurements were obtained from the same X-ray diffraction images as the Bragg data, using best practices for standard data collection. To model the underlying dynamics in a practical way that could be used during structure refinement, we tested translation-libration-screw (TLS), liquid-like motions (LLM), and coarse-grained normal-modes (NM) models of protein motions. The LLM model provides a global picture of motions and was refined against the diffuse data, whereas the TLS and NM models provide more detailed and distinct descriptions of atom displacements, and only used information from the Bragg data. Whereas different TLS groupings yielded similar Bragg intensities, they yielded different diffuse intensities, none of which agreed well with the data. In contrast, both the LLM and NM models agreed substantially with the diffuse data. These results demonstrate a realistic path to increase the number of diffuse datasets available to the wider biosciences community and indicate that dynamics-inspired NM structural models can simultaneously agree with both Bragg and diffuse scattering.

Ribozyme Catalysis with a Twist: Active State of the Twister Ribozyme in Solution Predicted from Molecular Simulation

We present results from molecular dynamics simulations and free energy calculations of the twister ribozyme at different stages along the reaction path to gain insight into its mechanism. The results, together with recent biochemical experiments, provide support for a mechanism involving general-acid catalysis by a conserved adenine residue in the active site. Although adenine has been previously implicated as a general acid acting through the N1 position in other ribozymes such as the hairpin and VS ribozymes, in the twister ribozyme there may be a twist. Biochemical experiments suggest that general acid catalysis may occur through the N3 position, which has never before been implicated in this role; however, currently, there is a lack of a detailed structural model for the active state of the twister ribozyme in solution that is consistent with these and other experiments. Simulations in a crystalline environment reported here are consistent with X-ray crystallographic data, and suggest that crystal packing contacts trap the RNA in an inactive conformation with U-1 in an extruded state that is incompatible with an in-line attack to the scissile phosphate. Simulations in solution, on the other hand, reveal this region to be dynamic and able to adopt a conformation where U-1 is stacked with G33. In this state, the nucleophile is in line with the scissile phosphate, and the N1 position of G33 and N3 position of A1 are poised to act as a general base and acid, respectively, as supported by mutational experiments. Free energy calculations further predict the electrostatic environment causes a shift of the microscopic pKa at the N3 position of A1 toward neutrality by approximately 5 pKa units. These results offer a unified interpretation of a broad range of currently available experimental data that points to a novel mode of general acid catalysis through the N3 position of an adenine nucleobase, thus expanding the repertoire of known mechanistic strategies employed by small nucleolytic ribozymes.

X-ray refinement significantly underestimates the level of microscopic heterogeneity in biomolecular crystals

Biomolecular X-ray structures typically provide a static, time- and ensemble-averaged view of molecular ensembles in crystals. In the absence of rigid-body motions and lattice defects, B-factors are thought to accurately reflect the structural heterogeneity of such ensembles. In order to study the effects of averaging on B-factors, we employ molecular dynamics simulations to controllably manipulate microscopic heterogeneity of a crystal containing 216 copies of villin headpiece. Using average structure factors derived from simulation, we analyse how well this heterogeneity is captured by high-resolution molecular-replacement-based model refinement. We find that both isotropic and anisotropic refined B-factors often significantly deviate from their actual values known from simulation: even at high 1.0 Å resolution and Rfree of 5.9%, B-factors of some well-resolved atoms underestimate their actual values even sixfold. Our results suggest that conformational averaging and inadequate treatment of correlated motion considerably influence estimation of microscopic heterogeneity via B-factors, and invite caution in their interpretation.

Predicting X-ray diffuse scattering from translation-libration-screw structural ensembles

Identifying the intramolecular motions of proteins and nucleic acids is a major challenge in macromolecular X-ray crystallography. Because Bragg diffraction describes the average positional distribution of crystalline atoms with imperfect precision, the resulting electron density can be compatible with multiple models of motion. Diffuse X-ray scattering can reduce this degeneracy by reporting on correlated atomic displacements. Although recent technological advances are increasing the potential to accurately measure diffuse scattering, computational modeling and validation tools are still needed to quantify the agreement between experimental data and different parameterizations of crystalline disorder. A new tool, phenix.diffuse, addresses this need by employing Guinier's equation to calculate diffuse scattering from Protein Data Bank (PDB)-formatted structural ensembles. As an example case, phenix.diffuse is applied to translation-libration-screw (TLS) refinement, which models rigid-body displacement for segments of the macromolecule. To enable the calculation of diffuse scattering from TLS-refined structures, phenix.tls_as_xyz builds multi-model PDB files that sample the underlying T, L and S tensors. In the glycerophosphodiesterase GpdQ, alternative TLS-group partitioning and different motional correlations between groups yield markedly dissimilar diffuse scattering maps with distinct implications for molecular mechanism and allostery. These methods demonstrate how, in principle, X-ray diffuse scattering could extend macromolecular structural refinement, validation and analysis.

Molecular dynamics simulation of triclinic lysozyme in a crystal lattice

Molecular dynamics simulations of crystals can enlighten interpretation of experimental X-ray crystallography data and elucidate structural dynamics and heterogeneity in biomolecular crystals. Furthermore, because of the direct comparison against experimental data, they can inform assessment of molecular dynamics methods and force fields. We present microsecond scale results for triclinic hen egg-white lysozyme in a supercell consisting of 12 independent unit cells using four contemporary force fields (Amber ff99SB, ff14ipq, ff14SB, and CHARMM 36) in crystalline and solvated states (for ff14SB only). We find the crystal simulations consistent across multiple runs of the same force field and robust to various solvent equilibration schemes. However, convergence is slow compared with solvent simulations. All the tested force fields reproduce experimental structural and dynamic properties well, but Amber ff14SB maintains structure and reproduces fluctuations closest to the experimental model: its average backbone structure differs from the deposited structure by 0.37Å; by contrast, the average backbone structure in solution differs from the deposited by 0.65Å. All the simulations are affected by a small progressive deterioration of the crystal lattice, presumably due to imperfect modeling of hydrogen bonding and other crystal contact interactions; this artifact is smallest in ff14SB, with average lattice positions deviating by 0.20Å from ideal. Side-chain disorder is surprisingly low with fewer than 30% of the nonglycine or alanine residues exhibiting significantly populated alternate rotamers. Our results provide helpful insight into the methodology of biomolecular crystal simulations and indicate directions for future work to obtain more accurate energy models for molecular dynamics.

Conformational dynamics of a crystalline protein from microsecond-scale molecular dynamics simulations and diffuse X-ray scattering

X-ray diffraction from protein crystals includes both sharply peaked Bragg reflections and diffuse intensity between the peaks. The information in Bragg scattering is limited to what is available in the mean electron density. The diffuse scattering arises from correlations in the electron density variations and therefore contains information about collective motions in proteins. Previous studies using molecular-dynamics (MD) simulations to model diffuse scattering have been hindered by insufficient sampling of the conformational ensemble. To overcome this issue, we have performed a 1.1-μs MD simulation of crystalline staphylococcal nuclease, providing 100-fold more sampling than previous studies. This simulation enables reproducible calculations of the diffuse intensity and predicts functionally important motions, including transitions among at least eight metastable states with different active-site geometries. The total diffuse intensity calculated using the MD model is highly correlated with the experimental data. In particular, there is excellent agreement for the isotropic component of the diffuse intensity, and substantial but weaker agreement for the anisotropic component. Decomposition of the MD model into protein and solvent components indicates that protein-solvent interactions contribute substantially to the overall diffuse intensity. We conclude that diffuse scattering can be used to validate predictions from MD simulations and can provide information to improve MD models of protein motions.

Molecular dynamics simulation of protein crystal with polarized protein-specific force field

Two 250 ns molecular simulations have been carried out to study the structure and dynamics of crystal toxin protein II from the scorpion Androctonus australis Hector employing the polarized protein-specific charge (PPC), as well as the standard AMBER99SB force field, to investigate the electrostatic polarization on the simulated crystal stability. Results show that under PPC, the monomers in unit cell as well as the lattice in supercell are more stable with smaller root-mean-square deviations and more accurate lattice atomic fluctuations compared with the crystallographic B-factors than under AMBER99SB force field. Most of the interactions at interfaces in the X-ray structure are quite well-preserved, underscoring the important effect of polarization on maintaining the crystal stability. However, the results also show that the hydrogen bond between Asp53 and Gln37 and the cation-π interaction between Arg56 and His64 are not stable, indicating that further optimization of force field, especially the van der Waals interaction parameters, is desired.

All-atom crystal simulations of DNA and RNA duplexes

BACKGROUND

Molecular dynamics simulations can complement experimental measures of structure and dynamics of biomolecules. The quality of such simulations can be tested by comparisons to models refined against experimental crystallographic data.

METHODS

We report simulations of DNA and RNA duplexes in their crystalline environment. The calculations mimic the conditions for PDB entries 1D23 [d(CGATCGATCG)2] and 1RNA [(UUAUAUAUAUAUAA)2], and contain 8 unit cells, each with 4 copies of the Watson-Crick duplex; this yields in aggregate 64μs of duplex sampling for DNA and 16μs for RNA.

RESULTS

The duplex structures conform much more closely to the average structure seen in the crystal than do structures extracted from a solution simulation with the same force field. Sequence-dependent variations in helical parameters, and in groove widths, are largely maintained in the crystal structure, but are smoothed out in solution. However, the integrity of the crystal lattice is slowly degraded in both simulations, with the result that the interfaces between chains become heterogeneous. This problem is more severe for the DNA crystal, which has fewer inter-chain hydrogen bond contacts than does the RNA crystal.

CONCLUSIONS

Crystal simulations using current force fields reproduce many features of observed crystal structures, but suffer from a gradual degradation of the integrity of the crystal lattice.

GENERAL SIGNIFICANCE

The results offer insights into force-field simulations that test their ability to preserve weak interactions between chains, which will be of importance also in non-crystalline applications that involve binding and recognition. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

The R-factor gap in macromolecular crystallography: an untapped potential for insights on accurate structures

In macromolecular crystallography, the agreement between observed and predicted structure factors (R_cryst and R_free) is seldom better than 20%. This is much larger than the estimate of experimental error (R_merge). The difference between R_cryst and R_merge is the R-factor gap. There is no such gap in small-molecule crystallography, for which calculated structure factors are generally considered more accurate than the experimental measurements. Perhaps the true noise level of macromolecular data is higher than expected? Or is the gap caused by inaccurate phases that trap refined models in local minima? By generating simulated diffraction patterns using the program MLFSOM, and including every conceivable source of experimental error, we show that neither is the case. Processing our simulated data yielded values that were indistinguishable from those of real data for all crystallographic statistics except the final R_cryst and R_free. These values decreased to 3.8% and 5.5% for simulated data, suggesting that the reason for high R-factors in macromolecular crystallography is neither experimental error nor phase bias, but rather an underlying inadequacy in the models used to explain our observations. The present inability to accurately represent the entire macromolecule with both its flexibility and its protein-solvent interface may be improved by synergies between small-angle X-ray scattering, computational chemistry and crystallography. The exciting implication of our finding is that macromolecular data contain substantial hidden and untapped potential to resolve ambiguities in the true nature of the nanoscale, a task that the second century of crystallography promises to fulfill.

Current and emerging opportunities for molecular simulations in structure-based drug design

An overview of the current capabilities and limitations of molecular simulation of biomolecular complexes in the context of computer-aided drug design is provided. Steady improvements in computer hardware coupled with more refined representations of energetics are leading to a new appreciation of the driving forces of molecular recognition. Molecular simulations are poised to more frequently guide the interpretation of biophysical measurements of biomolecular complexes. Ligand design strategies emerge from detailed analyses of computed structural ensembles. The feasibility of routine applications to ligand optimization problems hinges upon successful extensive large scale validation studies and the development of protocols to intelligently automate computations.

Packing interface energetics in different crystal forms of the λ Cro dimer

Variation among crystal structures of the λ Cro dimer highlights conformational flexibility. The structures range from a wild type closed to a mutant fully open conformation, but it is unclear if each represents a stable solution state or if one may be the result of crystal packing. Here we use molecular dynamics (MD) simulation to investigate the energetics of crystal packing interfaces and the influence of site-directed mutagenesis on them in order to examine the effect of crystal packing on wild type and mutant Cro dimer conformation. Replica exchange MD of mutant Cro in solution shows that the observed conformational differences between the wild type and mutant protein are not the direct consequence of mutation. Instead, simulation of Cro in different crystal environments reveals that mutation affects the stability of crystal forms. Molecular Mechanics Poisson-Boltzmann Surface Area binding energy calculations reveal the detailed energetics of packing interfaces. Packing interfaces can have diverse properties in strength, energetic components, and some are stronger than the biological dimer interface. Further analysis shows that mutation can strengthen packing interfaces by as much as ∼5 kcal/mol in either crystal environment. Thus, in the case of Cro, mutation provides an additional energetic contribution during crystal formation that may stabilize a fully open higher energy state. Moreover, the effect of mutation in the lattice can extend to packing interfaces not involving mutation sites. Our results provide insight into possible models for the effect of crystallization on Cro conformational dynamics and emphasize careful consideration of protein crystal structures.