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

Scaling and merging macromolecular diffuse scattering with mdx2

Diffuse scattering is a promising method to gain additional insight into protein dynamics from macromolecular crystallography experiments. Bragg intensities yield the average electron density, while the diffuse scattering can be processed to obtain a three-dimensional reciprocal-space map that is further analyzed to determine correlated motion. To make diffuse scattering techniques more accessible, software for data processing called mdx2 has been created that is both convenient to use and simple to extend and modify. mdx2 is written in Python, and it interfaces with DIALS to implement self-contained data-reduction workflows. Data are stored in NeXus format for software interchange and convenient visualization. mdx2 can be run on the command line or imported as a package, for instance to encapsulate a complete workflow in a Jupyter notebook for reproducible computing and education. Here, mdx2 version 1.0 is described, a new release incorporating state-of-the-art techniques for data reduction. The implementation of a complete multi-crystal scaling and merging workflow is described, and the methods are tested using a high-redundancy data set from cubic insulin. It is shown that redundancy can be leveraged during scaling to correct systematic errors and obtain accurate and reproducible measurements of weak diffuse signals.

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.

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.

Modeling diffuse scattering with simple, physically interpretable models

Diffuse scattering has long been proposed to probe protein dynamics relevant for biological function, and more recently, as a tool to aid structure determination. Despite recent advances in measuring and modeling this signal, the field has not been able to routinely use experimental diffuse scattering for either application. A persistent challenge has been to devise models that are sophisticated enough to robustly reproduce experimental diffuse features but remain readily interpretable from the standpoint of structural biology. This chapter presents eryx, a suite of computational tools to evaluate the primary models of disorder that have been used to analyze protein diffuse scattering. By facilitating comparative modeling, eryx aims to provide insights into the physical origins of this signal and help identify the sources of disorder that are critical for reproducing experimental features. This framework also lays the groundwork for the development of more advanced models that integrate different types of disorder without loss of interpretability.

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.

Linking B-factor and temperature-induced conformational transition

The crystallographic B-factor, also called temperature factor or Debye-Waller factor, has long been used as a surrogate for local protein flexibility. However, the use of the absolute B-factor as a probe for protein motion requires reproducible validation against conformational changes against chemical and physical variables. Here we report the investigation of the thermal dependence of the crystallographic B-factor and its correlation with conformational changes of the protein. We obtained the crystal protein structure coordinates and B-factors at high resolution (1.5 Å) over a broad temperature range (100 K to 325 K). The exponential thermal dependence of B-factor as a function of temperature was equal for both the diffraction intensity data (Wilson B-factor) and for all modeled atoms of the system (protein and non-protein atoms), with a thermal diffusion constant of about 0.0045 K^-1, similar for all atoms. The extrapolated B-factor at zero Kelvin (or zero-point fluctuation) varies among the atoms, although with no apparent correlation with temperature-dependent protein conformational changes. These data suggest that the thermal vibration of the atom does not necessarily correlate with the conformational dynamics of the protein.

Robust total X-ray scattering workflow to study correlated motion of proteins in crystals

The breathing motions of proteins are thought to play a critical role in function. However, current techniques to study key collective motions are limited to spectroscopy and computation. We present a high-resolution experimental approach based on the total scattering from protein crystals at room temperature (TS/RT-MX) that captures both structure and collective motions. To reveal the scattering signal from protein motions, we present a general workflow that enables robust subtraction of lattice disorder. The workflow introduces two methods: GOODVIBES, a detailed and refinable lattice disorder model based on the rigid-body vibrations of a crystalline elastic network; and DISCOBALL, an independent method of validation that estimates the displacement covariance between proteins in the lattice in real space. Here, we demonstrate the robustness of this workflow and further demonstrate how it can be interfaced with MD simulations towards obtaining high-resolution insight into functionally important protein motions.

Molecular Docking and Site-Directed Mutagenesis of GH49 Family Dextranase for the Preparation of High-Degree Polymerization Isomaltooligosaccharide

The high-degree polymerization of isomaltooligosaccharide (IMO) not only effectively promotes the growth and reproduction of Bifidobacterium in the human body but also renders it resistant to rapid degradation by gastric acid and can stimulate insulin secretion. In this study, we chose the engineered strain expressed dextranase (PsDex1711) as the research model and used the AutoDock vina molecular docking technique to dock IMO4, IMO5, and IMO6 with it to obtain mutation sites, and then studied the potential effect of key amino acids in this enzyme on its hydrolysate composition and enzymatic properties by site-directed mutagenesis method. It was found that the yield of IMO4 increased significantly to 62.32% by the mutant enzyme H373A. Saturation mutation depicted that the yield of IMO4 increased to 69.81% by the mutant enzyme H373R, and its neighboring site S374R IMO4 yield was augmented to 64.31%. Analysis of the enzymatic properties of the mutant enzyme revealed that the optimum temperature of H373R decreased from 30 °C to 20 °C, and more than 70% of the enzyme activity was maintained under alkaline conditions. The double-site saturation mutation results showed that the mutant enzyme H373R/N445Y IMO4 yield increased to 68.57%. The results suggest that the 373 sites with basic non-polar amino acids, such as arginine and histidine, affect the catalytic properties of the enzyme. The findings provide an important theoretical basis for the future marketable production of IMO4 and analysis of the structure of dextranase.

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.

Advances in methods for atomic resolution macromolecular structure determination

Recent technical advances have dramatically increased the power and scope of structural biology. New developments in high-resolution cryo-electron microscopy, serial X-ray crystallography, and electron diffraction have been especially transformative. Here we highlight some of the latest advances and current challenges at the frontiers of atomic resolution methods for elucidating the structures and dynamical properties of macromolecules and their complexes.

Diffuse X-ray scattering from correlated motions in a protein crystal

Protein dynamics are integral to biological function, yet few techniques are sensitive to collective atomic motions. A long-standing goal of X-ray crystallography has been to combine structural information from Bragg diffraction with dynamic information contained in the diffuse scattering background. However, the origin of macromolecular diffuse scattering has been poorly understood, limiting its applicability. We present a finely sampled diffuse scattering map from triclinic lysozyme with unprecedented accuracy and detail, clearly resolving both the inter- and intramolecular correlations. These correlations are studied theoretically using both all-atom molecular dynamics and simple vibrational models. Although lattice dynamics reproduce most of the diffuse pattern, protein internal dynamics, which include hinge-bending motions, are needed to explain the short-ranged correlations revealed by Patterson analysis. These insights lay the groundwork for animating crystal structures with biochemically relevant motions.

Protein motion in crystals causes diffuse X-ray scattering, which so far has been very challenging to measure and interpret. Here the authors present a finely sampled diffuse scattering map from triclinic lysozyme, which allows them to resolve inter- and intramolecular correlations and they further analyze the maps using all-atom molecular dynamics simulations and simple vibrational models, revealing the contribution of internal protein motion.

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.

An introduction to classical molecular dynamics simulation for experimental scattering users

Classical molecular dynamics simulations are a common component of multi-modal analyses of scattering measurements, such as small-angle scattering and diffraction. Users of these experimental techniques often have no formal training in the theory and practice of molecular dynamics simulation, leading to the possibility of these simulations being treated as a 'black box' analysis technique. This article describes an open educational resource (OER) designed to introduce classical molecular dynamics to users of scattering methods. This resource is available as a series of interactive web pages, which can be easily accessed by students, and as an open-source software repository, which can be freely copied, modified and redistributed by educators. The topics covered in this OER include classical atomistic modelling, parameterizing interatomic potentials, molecular dynamics simulations, typical sources of error and some of the approaches to using simulations in the analysis of scattering data.

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.

Rigid-body motion is the main source of diffuse scattering in protein crystallography

The origin of diffuse X-ray scattering from protein crystals has been the subject of debate over the past three decades regarding whether it arises from correlated atomic motions within the molecule or from rigid-body disorder. Here, a supercell approach to modelling diffuse scattering is presented that uses ensembles of molecular models representing rigid-body motions as well as internal motions as obtained from ensemble refinement. This approach allows oversampling of Miller indices and comparison with equally oversampled diffuse data, thus allowing the maximum information to be extracted from experiments. It is found that most of the diffuse scattering comes from correlated motions within the unit cell, with only a minor contribution from longer-range correlated displacements. Rigid-body motions, and in particular rigid-body translations, make by far the most dominant contribution to the diffuse scattering, and internal motions give only a modest addition. This suggests that modelling biologically relevant protein dynamics from diffuse scattering may present an even larger challenge than was thought.

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.

Interactions that know no boundaries

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

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.