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.

Scaling and merging macromolecular diffuse scattering with mdx2.

Diffuse scattering is a promising method to gain additional insight into protein dynamics from macromolecular crystallography (MX) 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, we have created software for data processing called mdx2 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, we describe mdx2 version 1.0, a new release incorporating state-of-the-art techniques for data reduction. We describe the implementation of a complete multi-crystal scaling and merging workflow, and test the methods using a high-redundancy dataset from cubic insulin. We show that redundancy can be leveraged during scaling to correct systematic errors, and obtain accurate and reproducible measurements of weak diffuse signals.

Introduction to diffuse scattering and data collection.

A long-standing goal in X-ray crystallography has been to extract information about the collective motions of proteins from diffuse scattering: the weak, textured signal that is found in the background of diffraction images. In the past few years, the field of macromolecular diffuse scattering has seen dramatic progress, and many of the past challenges in measurement and interpretation are now considered tractable. However, the concept of diffuse scattering is still new to many researchers, and a general set of procedures needed to collect a high-quality dataset has never been described in detail. Here, we provide the first guidelines for performing diffuse scattering experiments, which can be performed at any macromolecular crystallography beamline that supports room-temperature studies with a direct detector. We begin with a brief introduction to the theory of diffuse scattering and then walk the reader through the decision-making processes involved in preparing for and conducting a successful diffuse scattering experiment. Finally, we define quality metrics and describe ways to assess data quality both at the beamline and at home. Data obtained in this way can be processed independently by crystallographic software and diffuse scattering software to produce both a crystal structure, which represents the average atomic coordinates, and a three-dimensional diffuse scattering map that can then be interpreted in terms of models for protein motions.

Processing macromolecular diffuse scattering data.

Diffuse scattering is a powerful technique to study disorder and dynamics of macromolecules at atomic resolution. Although diffuse scattering is always present in diffraction images from macromolecular crystals, the signal is weak compared with Bragg peaks and background, making it a challenge to visualize and measure accurately. Recently, this challenge has been addressed using the reciprocal space mapping technique, which leverages ideal properties of modern X-ray detectors to reconstruct the complete three-dimensional volume of continuous diffraction from diffraction images of a crystal (or crystals) in many different orientations. This chapter will review recent progress in reciprocal space mapping with a particular focus on the strategy implemented in the mdx-lib and mdx2 software packages. The chapter concludes with an introductory data processing tutorial using Python packages DIALS, NeXpy, and mdx2.

Processing macromolecular diffuse scattering data.

Diffuse scattering is a powerful technique to study disorder and dynamics of macromolecules at atomic resolution. Although diffuse scattering is always present in diffraction images from macromolecular crystals, the signal is weak compared with Bragg peaks and background, making it a challenge to visualize and measure accurately. Recently, this challenge has been addressed using the reciprocal space mapping technique, which leverages ideal properties of modern X-ray detectors to reconstruct the complete three-dimensional volume of continuous diffraction from diffraction images of a crystal (or crystals) in many different orientations. This chapter will review recent progress in reciprocal space mapping with a particular focus on the strategy implemented in the mdx-lib and mdx2 software packages. The chapter concludes with an introductory data processing tutorial using Python packages DIALS, NeXpy , and mdx2 .

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.

Correlated Motions in Structural Biology.

Correlated motions in proteins arising from the collective movements of residues have long been proposed to be fundamentally important to key properties of proteins, from allostery and catalysis to evolvability. Recent breakthroughs in structural biology have made it possible to capture proteins undergoing complex conformational changes, yet intrinsic correlated motions within a conformation remain one of the least understood facets of protein structure. For many decades, the analysis of total X-ray scattering held the promise of animating crystal structures with correlated motions. With recent advances in both X-ray detectors and data interpretation methods, this long-held promise can now be met. In this Perspective, we will introduce how correlated motions are captured in total scattering and provide guidelines for the collection, interpretation, and validation of data. As structural biology continues to push the boundaries, we see an opportunity to gain atomistic insight into correlated motions using total scattering as a bridge between theory and experiment.

REGALS: a general method to deconvolve X-ray scattering data from evolving mixtures.

Mixtures of biological macromolecules are inherently difficult to study using structural methods, as increasing complexity presents new challenges for data analysis. Recently, there has been growing interest in studying evolving mixtures using small-angle X-ray scattering (SAXS) in conjunction with time-resolved, high-throughput or chromatography-coupled setups. Deconvolution and interpretation of the resulting datasets, however, are nontrivial when neither the scattering components nor the way in which they evolve are known a priori. To address this issue, the REGALS method (regularized alternating least squares) is introduced, which incorporates simple expectations about the data as prior knowledge, and utilizes parameterization and regularization to provide robust deconvolution solutions. The restraints used by REGALS are general properties such as smoothness of profiles and maximum dimensions of species, making it well suited for exploring datasets with unknown species. Here, REGALS is applied to the analysis of experimental data from four types of SAXS experiment: anion-exchange (AEX) coupled SAXS, ligand titration, time-resolved mixing and time-resolved temperature jump. Based on its performance with these challenging datasets, it is anticipated that REGALS will be a valuable addition to the SAXS analysis toolkit and enable new experiments. The software is implemented in both MATLAB and Python and is available freely as an open-source software package.

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.

The phenylketonuria-associated substitution R68S converts phenylalanine hydroxylase to a constitutively active enzyme but reduces its stability.

The naturally occurring R68S substitution of phenylalanine hydroxylase (PheH) causes phenylketonuria (PKU). However, the molecular basis for how the R68S variant leads to PKU remains unclear. Kinetic characterization of R68S PheH establishes that the enzyme is fully active in the absence of allosteric binding of phenylalanine, in contrast to the WT enzyme. Analytical ultracentrifugation establishes that the isolated regulatory domain of R68S PheH is predominantly monomeric in the absence of phenylalanine and dimerizes in its presence, similar to the regulatory domain of the WT enzyme. Fluorescence and small-angle X-ray scattering analyses establish that the overall conformation of the resting form of R68S PheH is different from that of the WT enzyme. The data are consistent with the substitution disrupting the interface between the catalytic and regulatory domains of the enzyme, shifting the equilibrium between the resting and activated forms ∼200-fold, so that the resting form of R68S PheH is ∼70% in the activated conformation. However, R68S PheH loses activity 2 orders of magnitude more rapidly than the WT enzyme at 37 °C and is significantly more sensitive to proteolysis. We propose that, even though this substitution converts the enzyme to a constitutively active enzyme, it results in PKU because of the decrease in protein stability.

An endogenous dAMP ligand in Bacillus subtilis class Ib RNR promotes assembly of a noncanonical dimer for regulation by dATP.

The high fidelity of DNA replication and repair is attributable, in part, to the allosteric regulation of ribonucleotide reductases (RNRs) that maintains proper deoxynucleotide pool sizes and ratios in vivo. In class Ia RNRs, ATP (stimulatory) and dATP (inhibitory) regulate activity by binding to the ATP-cone domain at the N terminus of the large α subunit and altering the enzyme's quaternary structure. Class Ib RNRs, in contrast, have a partial cone domain and have generally been found to be insensitive to dATP inhibition. An exception is the Bacillus subtilis Ib RNR, which we recently reported to be inhibited by physiological concentrations of dATP. Here, we demonstrate that the α subunit of this RNR contains tightly bound deoxyadenosine 5'-monophosphate (dAMP) in its N-terminal domain and that dATP inhibition of CDP reduction is enhanced by its presence. X-ray crystallography reveals a previously unobserved (noncanonical) α2 dimer with its entire interface composed of the partial N-terminal cone domains, each binding a dAMP molecule. Using small-angle X-ray scattering (SAXS), we show that this noncanonical α2 dimer is the predominant form of the dAMP-bound α in solution and further show that addition of dATP leads to the formation of larger oligomers. Based on this information, we propose a model to describe the mechanism by which the noncanonical α2 inhibits the activity of the B. subtilis Ib RNR in a dATP- and dAMP-dependent manner.

Correlated Motions from Crystallography beyond Diffraction.

Over the past century, X-ray crystallography has been defined by a pursuit for perfection and high resolution. The next Holy Grail of crystallography is to embrace imperfection toward a dynamic picture of enzymes.

X-ray Scattering Studies of Protein Structural Dynamics.

X-ray scattering is uniquely suited to the study of disordered systems and thus has the potential to provide insight into dynamic processes where diffraction methods fail. In particular, while X-ray crystallography has been a staple of structural biology for more than half a century and will continue to remain so, a major limitation of this technique has been the lack of dynamic information. Solution X-ray scattering has become an invaluable tool in structural and mechanistic studies of biological macromolecules where large conformational changes are involved. Such systems include allosteric enzymes that play key roles in directing metabolic fluxes of biochemical pathways, as well as large, assembly-line type enzymes that synthesize secondary metabolites with pharmaceutical applications. Furthermore, crystallography has the potential to provide information on protein dynamics via the diffuse scattering patterns that are overlaid with Bragg diffraction. Historically, these patterns have been very difficult to interpret, but recent advances in X-ray detection have led to a renewed interest in diffuse scattering analysis as a way to probe correlated motions. Here, we will review X-ray scattering theory and highlight recent advances in scattering-based investigations of protein solutions and crystals, with a particular focus on complex enzymes.

The impact of base stacking on the conformations and electrostatics of single-stranded DNA.

Single-stranded DNA (ssDNA) is notable for its interactions with ssDNA binding proteins (SSBs) during fundamentally important biological processes including DNA repair and replication. Previous work has begun to characterize the conformational and electrostatic properties of ssDNA in association with SSBs. However, the conformational distributions of free ssDNA have been difficult to determine. To capture the vast array of ssDNA conformations in solution, we pair small angle X-ray scattering with novel ensemble fitting methods, obtaining key parameters such as the size, shape and stacking character of strands with different sequences. Complementary ion counting measurements using inductively coupled plasma atomic emission spectroscopy are employed to determine the composition of the ion atmosphere at physiological ionic strength. Applying this combined approach to poly dA and poly dT, we find that the global properties of these sequences are very similar, despite having vastly different propensities for single-stranded helical stacking. These results suggest that a relatively simple mechanism for the binding of ssDNA to non-specific SSBs may be at play, which explains the disparity in binding affinities observed for these systems.

Asymmetric unwrapping of nucleosomal DNA propagates asymmetric opening and dissociation of the histone core.

The nucleosome core particle (NCP) is the basic structural unit for genome packaging in eukaryotic cells and consists of DNA wound around a core of eight histone proteins. DNA access is modulated through dynamic processes of NCP disassembly. Partly disassembled structures, such as the hexasome (containing six histones) and the tetrasome (four histones), are important for transcription regulation in vivo. However, the pathways for their formation have been difficult to characterize. We combine time-resolved (TR) small-angle X-ray scattering and TR-FRET to correlate changes in the DNA conformations with composition of the histone core during salt-induced disassembly of canonical NCPs. We find that H2A-H2B histone dimers are released sequentially, with the first dimer being released after the DNA has formed an asymmetrically unwrapped, teardrop-shape DNA structure. This finding suggests that the octasome-to-hexasome transition is guided by the asymmetric unwrapping of the DNA. The link between DNA structure and histone composition suggests a potential mechanism for the action of proteins that alter nucleosome configurations such as histone chaperones and chromatin remodeling complexes.

Visualizing single-stranded nucleic acids in solution.

Single-stranded nucleic acids (ssNAs) are ubiquitous in many key cellular functions. Their flexibility limits both the number of high-resolution structures available, leaving only a small number of protein-ssNA crystal structures, while forcing solution investigations to report ensemble averages. A description of the conformational distributions of ssNAs is essential to more fully characterize biologically relevant interactions. We combine small angle X-ray scattering (SAXS) with ensemble-optimization methods (EOM) to dynamically build and refine sets of ssNA structures. By constructing candidate chains in representative dinucleotide steps and refining the models against SAXS data, a broad array of structures can be obtained to match varying solution conditions and strand sequences. In addition to the distribution of large scale structural parameters, this approach reveals, for the first time, intricate details of the phosphate backbone and underlying strand conformations. Such information on unperturbed strands will critically inform a detailed understanding of an array of problems including protein-ssNA binding, RNA folding and the polymer nature of NAs. In addition, this scheme, which couples EOM selection with an iteratively refining pool to give confidence in the underlying structures, is likely extendable to the study of other flexible systems.

Full-length model of the human galectin-4 and insights into dynamics of inter-domain communication.

Galectins are proteins involved in diverse cellular contexts due to their capacity to decipher and respond to the information encoded by ß-galactoside sugars. In particular, human galectin-4, normally expressed in the healthy gastrointestinal tract, displays differential expression in cancerous tissues and is considered a potential drug target for liver and lung cancer. Galectin-4 is a tandem-repeat galectin characterized by two carbohydrate recognition domains connected by a linker-peptide. Despite their relevance to cell function and pathogenesis, structural characterization of full-length tandem-repeat galectins has remained elusive. Here, we investigate galectin-4 using X-ray crystallography, small- and wide-angle X-ray scattering, molecular modelling, molecular dynamics simulations, and differential scanning fluorimetry assays and describe for the first time a structural model for human galectin-4. Our results provide insight into the structural role of the linker-peptide and shed light on the dynamic characteristics of the mechanism of carbohydrate recognition among tandem-repeat galectins.

Domain Movements upon Activation of Phenylalanine Hydroxylase Characterized by Crystallography and Chromatography-Coupled Small-Angle X-ray Scattering.

Mammalian phenylalanine hydroxylase (PheH) is an allosteric enzyme that catalyzes the first step in the catabolism of the amino acid phenylalanine. Following allosteric activation by high phenylalanine levels, the enzyme catalyzes the pterin-dependent conversion of phenylalanine to tyrosine. Inability to control elevated phenylalanine levels in the blood leads to increased risk of mental disabilities commonly associated with the inherited metabolic disorder, phenylketonuria. Although extensively studied, structural changes associated with allosteric activation in mammalian PheH have been elusive. Here, we examine the complex allosteric mechanisms of rat PheH using X-ray crystallography, isothermal titration calorimetry (ITC), and small-angle X-ray scattering (SAXS). We describe crystal structures of the preactivated state of the PheH tetramer depicting the regulatory domains docked against the catalytic domains and preventing substrate binding. Using SAXS, we further describe the domain movements involved in allosteric activation of PheH in solution and present the first demonstration of chromatography-coupled SAXS with Evolving Factor Analysis (EFA), a powerful method for separating scattering components in a model-independent way. Together, these results support a model for allostery in PheH in which phenylalanine stabilizes the dimerization of the regulatory domains and exposes the active site for substrate binding and other structural changes needed for activity.

A microfabricated fixed path length silicon sample holder improves background subtraction for cryoSAXS.

The application of small-angle X-ray scattering (SAXS) for high-throughput characterization of biological macromolecules in solution is limited by radiation damage. By cryocooling samples, radiation damage and required sample volumes can be reduced by orders of magnitude. However, the challenges of reproducibly creating the identically sized vitrified samples necessary for conventional background subtraction limit the widespread adoption of this method. Fixed path length silicon sample holders for cryoSAXS have been microfabricated to address these challenges. They have low background scattering and X-ray absorption, require only 640 nl of sample, and allow reproducible sample cooling. Data collected in the sample holders from a nominal illuminated sample volume of 2.5 nl are reproducible down to q ≃ 0.02 Å-1, agree with previous cryoSAXS work and are of sufficient quality for reconstructions that match measured crystal structures. These sample holders thus allow faster, more routine cryoSAXS data collection. Additional development is required to reduce sample fracturing and improve data quality at low q.

Determining the Locations of Ions and Water around DNA from X-Ray Scattering Measurements.

Nucleic acids carry a negative charge, attracting salt ions and water. Interactions with these components of the solvent drive DNA to condense, RNA to fold, and proteins to bind. To understand these biological processes, knowledge of solvent structure around the nucleic acids is critical. Yet, because they are often disordered, ions and water evade detection by x-ray crystallography and other high-resolution methods. Small-angle x-ray scattering (SAXS) is uniquely sensitive to the spatial correlations between solutes and the surrounding solvent. Thus, SAXS provides an experimental constraint to guide or test emerging solvation theories. However, the interpretation of SAXS profiles is nontrivial because of the difficulty in separating the scattering signals of each component: the macromolecule, ions, and hydration water. Here, we demonstrate methods for robustly deconvoluting these signals, facilitating a more straightforward comparison with theory. Using SAXS data collected on an absolute intensity scale for short DNA duplexes in solution with Na(+), K(+), Rb(+), or Cs(+) counterions, we mathematically decompose the scattering profiles into components (DNA, water, and ions) and validate the decomposition using anomalous scattering measurements. In addition, we generate a library of physically motivated ion atmosphere models and rank them by agreement with the scattering data. The best-fit models have relatively compact ion atmospheres when compared to predictions from the mean-field Poisson-Boltzmann theory of electrostatics. Thus, the x-ray scattering methods presented here provide a valuable measurement of the global structure of the ion atmosphere that can be used to test electrostatics theories that go beyond the mean-field approximation.