X-ray Scattering Studies of Protein Structural Dynamics

The Unique Role of the Second Coordination Sphere to Unlock and Control Catalysis in Nonheme Fe(II)/2-Oxoglutarate Histone Demethylase KDM2A

Nonheme Fe(II) and 2-oxoglutarate (2OG)-dependent histone lysine demethylases 2A (KDM2A) catalyze the demethylation of the mono- or dimethylated lysine 36 residue in the histone H3 peptide (H3K36me1/me2), which plays a crucial role in epigenetic regulation and can be involved in many cancers. Although the overall catalytic mechanism of KDMs has been studied, how KDM2 catalysis takes place in contrast to other KDMs remains unknown. Understanding such differences is vital for enzyme redesign and can help in enzyme-selective drug design. Herein, we employed molecular dynamics (MD) and combined quantum mechanics/molecular mechanics (QM/MM) to explore the complete catalytic mechanism of KDM2A, including dioxygen diffusion and binding, dioxygen activation, and substrate oxidation. Our study demonstrates that the catalysis of KDM2A is controlled by the conformational change of the second coordination sphere (SCS), specifically by a change in the orientation of Y222, which unlocks the 2OG rearrangement from off-line to in-line mode. The study demonstrates that the variant Y222A makes the 2OG rearrangement more favorable. Furthermore, the study reveals that it is the size of H3K36me3 that prevents the 2OG rearrangement, thus rendering the enzyme inactivity with trimethylated lysine. Calculations show that the SCS and long-range interacting residues that stabilize the HAT transition state in KDM2A differ from those in KDM4A, KDM7B, and KDM6A, thus providing the basics for the enzyme-selective redesign and modulation of KDM2A without influencing other KDMs.

Chirality Transfer of Glycopeptide across Scales Defined by the Continuity of Hydrogen Bonds

In nature, chirality transfer refines biomolecules across all size scales, bestowing them with a myriad of sophisticated functions. Despite recent advances in replicating chirality transfer with biotic or abiotic building blocks, a molecular understanding of the underlying mechanism of chirality transfer remains a daunting challenge. In this paper, the coassembly of two types of glycopeptide molecules differing in capability of forming intermolecular hydrogen bonds enabled the involvement of discontinuous hydrogen bond, which allowed for a nanoscale chirality transfer from glycopeptide molecules to chiral micelles, yet inhibited the micrometer scale chirality transfer toward helix formation, leading to an achiral transfer from chiral micelles to planar monolayer. Upon stacking the monolayer into a bilayer, the nonsuperimposable front and back faces of the chiral micelles involved in the monolayer ribbons lead to the opposite rotation of two layers toward increasing the continuity of H-bonds. The resultant continuity triggered the symmetry breaking of stacked bilayers and thus reactivated the micrometer-scale chirality transfer toward the final helix. This work delineates a promising step toward a better understanding and replicating the naturally occurring chirality transfer events and will be instructive to future chiral material design.

Steady-state and time-resolved fluorescent methodologies to characterize the conformational landscape of the selectivity filter of K+ channels

A variety of equilibrium and non-equilibrium methods have been used in a multidisciplinary approach to study the conformational landscape associated with the binding of different cations to the pore of potassium channels. These binding processes, and the conformational changes resulting therefrom, modulate the functional properties of such integral membrane properties, revealing these permeant and blocking cations as true effectors of such integral membrane proteins. KcsA, a prototypic K+ channel from Streptomyces lividans, has been extensively characterized in this regard. Here, we revise several fluorescence-based approaches to monitor cation binding under different experimental conditions in diluted samples, analyzing the advantages and disadvantages of each approach. These studies have contributed to explain the selectivity, conduction, and inactivation properties of K+ channels at the molecular level, together with the allosteric communication between the two gates that control the ion channel flux, and how they are modulated by lipids.

Single-Molecule Electrical Profiling of Peptides and Proteins

In recent decades, there has been a significant increase in the application of single-molecule electrical analysis platforms in studying proteins and peptides. These advanced analysis methods have the potential for deep investigation of enzymatic working mechanisms and accurate monitoring of dynamic changes in protein configurations, which are often challenging to achieve in ensemble measurements. In this work, the prominent research progress in peptide and protein-related studies are surveyed using electronic devices with single-molecule/single-event sensitivity, including single-molecule junctions, single-molecule field-effect transistors, and nanopores. In particular, the successful commercial application of nanopores in DNA sequencing has made it one of the most promising techniques in protein sequencing at the single-molecule level. From single peptides to protein complexes, the correlation between their electrical characteristics, structures, and biological functions is gradually being established. This enables to distinguish different molecular configurations of these biomacromolecules through real-time electrical monitoring of their life activities, significantly improving the understanding of the mechanisms underlying various life processes.

Dynamic correlations: exact and approximate methods for mutual information

MOTIVATION

Proteins are dynamic entities that undergo conformational changes critical for their functions. Understanding the communication pathways and information transfer within proteins is crucial for elucidating allosteric interactions in their mechanisms. This study utilizes mutual information (MI) analysis to probe dynamic allostery. Using two cases, Ubiquitin and PLpro, we have evaluated the accuracy and limitations of different approximations including the exact anisotropic and isotropic models, multivariate Gaussian model, isotropic Gaussian model, and the Gaussian Network Model (GNM) in revealing allosteric interactions.

RESULTS

Our findings emphasize the required trajectory length for capturing accurate mutual information profiles. Long molecular dynamics trajectories, 1 ms for Ubiquitin and 100 µs for PLpro are used as benchmarks, assuming they represent the ground truth. Trajectory lengths of approximately 5 µs for Ubiquitin and 1 µs for PLpro marked the onset of convergence, while the multivariate Gaussian model accurately captured mutual information with trajectories of 5 ns for Ubiquitin and 350 ns for PLpro. However, the isotropic Gaussian model is less successful in representing the anisotropic nature of protein dynamics, particularly in the case of PLpro, highlighting its limitations. The GNM, however, provides reasonable approximations of long-range information exchange as a minimalist network model based on a single crystal structure. Overall, the optimum trajectory lengths for effective Gaussian approximations of long-time dynamic behavior depend on the inherent dynamics within the protein's topology. The GNM, by showcasing dynamics across relatively diverse time scales, can be used either as a standalone method or to gauge the adequacy of MD simulation lengths.

AVAILABILITY AND IMPLEMENTATION

Mutual information codes are available at https://github.com/kemaldemirtas/prc-MI.git.

BioXTAS RAW 2: new developments for a free open-source program for small-angle scattering data reduction and analysis

BioXTAS RAW is a free open-source program for reduction, analysis and modelling of biological small-angle scattering data. Here, the new developments in RAW version 2 are described. These include improved data reduction using pyFAI; updated automated Guinier fitting and D max finding algorithms; automated series (e.g. size-exclusion chromatography coupled small-angle X-ray scattering or SEC-SAXS) buffer- and sample-region finding algorithms; linear and integral baseline correction for series; deconvolution of series data using regularized alternating least squares (REGALS); creation of electron-density reconstructions using electron density via solution scattering (DENSS); a comparison window showing residuals, ratios and statistical comparisons between profiles; and generation of PDF reports with summary plots and tables for all analysis. Furthermore, there is now a RAW API, which can be used without the graphical user interface (GUI), providing full access to all of the functionality found in the GUI. In addition to these new capabilities, RAW has undergone significant technical updates, such as adding Python 3 compatibility, and has entirely new documentation available both online and in the program.

BioXTAS RAW 2: new developments for a free open-source program for small angle scattering data reduction and analysis

BioXTAS RAW is a free, open-source program for reduction, analysis and modelling of biological small angle scattering data. Here, the new developments in RAW version 2 are described. These include: improved data reduction using pyFAI; updated automated Guinier fitting and Dmax finding algorithms; automated series (e.g. SEC-SAXS) buffer and sample region finding algorithms; linear and integral baseline correction for series; deconvolution of series data using REGALS; creation of electron density reconstructions via DENSS; a comparison window showing residuals, ratios, and statistical comparisons between profiles; and generation of PDF reports with summary plots and tables for all analysis. In addition, there is now a RAW API, which can be used without the GUI, providing full access to all of the functionality found in the GUI. In addition to these new capabilities, RAW has undergone significant technical updates, such as adding Python 3 compatibility, and has entirely new documentation available both online and in the program.

Intrinsic Flexibility beyond the Highly Ordered DNA Tetrahedron: An Integrative Spectroscopic and Molecular Dynamics Approach

Since the introduction of DNA-based architectures, in the past decade, DNA tetrahedrons have aroused great interest. Applications of such nanostructures require structural control, especially in the perspective of their possible functionalities. In this work, an integrated approach for structural characterization of a tetrahedron structure is proposed with a focus on the fundamental biophysical aspects driving the assembly process. To address such an issue, spin-labeled DNA sequences are chemically synthesized, self-assembled, and then analyzed by Continuous-Wave (CW) and pulsed Electron Paramagnetic Resonance (EPR) spectroscopy. Interspin distance measurements based on PELDOR/DEER techniques combined with molecular dynamics (MD) thus revealed unexpected dynamic heterogeneity and flexibility of the assembled structures. The observation of flexibility in these ordered 3D structures demonstrates the sensitivity of this approach and its effectiveness in accessing the main dynamic and structural features with unprecedented resolution.

Hydrogen atoms in supramolecular chemistry: a structural perspective. Where are they, and why does it matter?

Hydrogen bonding interactions are ubiquitous across the biochemical and chemical sciences, and are of particular interest to supramolecular chemists. They have been used to assemble hydrogen bonded polymers, cages and frameworks, and are the functional motif in many host-guest systems. Single crystal X-ray diffraction studies are often used as a key support for proposed structures, although this presents challenges as hydrogen atoms interact only weakly with X-rays. In this Tutorial Review, we discuss the information that can be gleaned about hydrogen bonding interactions through crystallographic experiments, key limitations of the data, and emerging techniques to overcome these limitations.

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.

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.

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.

Combining temperature perturbations with X-ray crystallography to study dynamic macromolecules: A thorough discussion of experimental methods

Temperature is an important state variable that governs the behavior of microscopic systems, yet crystallographers rarely exploit temperature changes to study the structure and dynamics of biological macromolecules. In fact, approximately 90% of crystal structures in the Protein Data Bank were determined under cryogenic conditions, because sample cryocooling makes crystals robust to X-ray radiation damage and facilitates data collection. On the other hand, cryocooling can introduce artifacts into macromolecular structures, and can suppress conformational dynamics that are critical for function. Fortunately, recent advances in X-ray detector technology, X-ray sources, and computational data processing algorithms make non-cryogenic X-ray crystallography easier and more broadly applicable than ever before. Without the reliance on cryocooling, high-resolution crystallography can be combined with various temperature perturbations to gain deep insight into the conformational landscapes of macromolecules. This Chapter reviews the historical reasons for the prevalence of cryocooling in macromolecular crystallography, and discusses its potential drawbacks. Next, the Chapter summarizes technological developments and methodologies that facilitate non-cryogenic crystallography experiments. Finally, the chapter discusses the theoretical underpinnings and practical aspects of multi-temperature and temperature-jump crystallography experiments, which are powerful tools for understanding the relationship between the structure, dynamics, and function of proteins and other biological macromolecules.

Interpreting macromolecular diffraction through simulation

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

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.

Conformational switching and flexibility in cobalamin-dependent methionine synthase studied by small-angle X-ray scattering and cryoelectron microscopy

Cobalamin-dependent methionine synthase (MetH) catalyzes the synthesis of methionine from homocysteine and 5-methyltetrahydrofolate (CH3-H4folate) using the unique chemistry of its cofactor. In doing so, MetH links the cycling of S-adenosylmethionine with the folate cycle in one-carbon metabolism. Extensive biochemical and structural studies on Escherichia coli MetH have shown that this flexible, multidomain enzyme adopts two major conformations to prevent a futile cycle of methionine production and consumption. However, as MetH is highly dynamic as well as both a photosensitive and oxygen-sensitive metalloenzyme, it poses special challenges for structural studies, and existing structures have necessarily come from a "divide and conquer" approach. In this study, we investigate E. coli MetH and a thermophilic homolog from Thermus filiformis using small-angle X-ray scattering (SAXS), single-particle cryoelectron microscopy (cryo-EM), and extensive analysis of the AlphaFold2 database to present a structural description of the full-length MetH in its entirety. Using SAXS, we describe a common resting-state conformation shared by both active and inactive oxidation states of MetH and the roles of CH3-H4folate and flavodoxin in initiating turnover and reactivation. By combining SAXS with a 3.6-Å cryo-EM structure of the T. filiformis MetH, we show that the resting-state conformation consists of a stable arrangement of the catalytic domains that is linked to a highly mobile reactivation domain. Finally, by combining AlphaFold2-guided sequence analysis and our experimental findings, we propose a general model for functional switching in MetH.

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.

Conformational switching and flexibility in cobalamin-dependent methionine synthase studied by small-angle X-ray scattering and cryo-electron microscopy

Cobalamin-dependent methionine synthase (MetH) catalyzes the synthesis of methionine from homocysteine and 5-methyltetrahydrofolate (CH ₃ -H ₄ folate) using the unique chemistry of its cofactor. In doing so, MetH links the cycling of S -adenosylmethionine with the folate cycle in one-carbon metabolism. Extensive biochemical and structural studies on Escherichia coli MetH have shown that this flexible, multi-domain enzyme adopts two major conformations to prevent a futile cycle of methionine production and consumption. However, as MetH is highly dynamic as well as both a photosensitive and oxygen-sensitive metalloenzyme, it poses special challenges for structural studies, and existing structures have necessarily come from a "divide and conquer" approach. In this study, we investigate E. coli MetH and a thermophilic homolog from Thermus filiformis using small-angle X-ray scattering (SAXS), single-particle cryo-electron microscopy (cryo-EM), and extensive analysis of the AlphaFold2 database to present the first structural description of MetH in its entirety. Using SAXS, we describe a common resting-state conformation shared by both active and inactive oxidation states of MetH and the roles of CH ₃ -H ₄ folate and flavodoxin in initiating turnover and reactivation. By combining SAXS with a 3.6-Å cryo-EM structure of the T. filiformis MetH, we show that the resting-state conformation consists of a stable arrangement of the catalytic domains that is linked to a highly mobile reactivation domain. Finally, by combining AlphaFold2-guided sequence analysis and our experimental findings, we propose a general model for functional switching in MetH.

Computational Approaches to Designing Antiviral Drugs against COVID-19: A Comprehensive Review

The global impact of the COVID-19 pandemic caused by SARS-CoV-2 necessitates innovative strategies for the rapid development of effective treatments. Computational methodologies, such as molecular modelling, molecular dynamics simulations, and artificial intelligence, have emerged as indispensable tools in the drug discovery process. This review aimed to provide a comprehensive overview of these computational approaches and their application in the design of antiviral agents for COVID-19. Starting with an examination of ligand-based and structure-based drug discovery, the review has delved into the intricate ways through which molecular modelling can accelerate the identification of potential therapies. Additionally, the investigation extends to phytochemicals sourced from nature, which have shown promise as potential antiviral agents. Noteworthy compounds, including gallic acid, naringin, hesperidin, Tinospora cordifolia, curcumin, nimbin, azadironic acid, nimbionone, nimbionol, and nimocinol, have exhibited high affinity for COVID-19 Mpro and favourable binding energy profiles compared to current drugs. Although these compounds hold potential, their further validation through in vitro and in vivo experimentation is imperative. Throughout this exploration, the review has emphasized the pivotal role of computational biologists, bioinformaticians, and biotechnologists in driving rapid advancements in clinical research and therapeutic development. By combining state-of-the-art computational techniques with insights from structural and molecular biology, the search for potent antiviral agents has been accelerated. The collaboration between these disciplines holds immense promise in addressing the transmissibility and virulence of SARS-CoV-2.

Analysis of insertions and extensions in the functional evolution of the ribonucleotide reductase family

Ribonucleotide reductases (RNRs) are used by all free-living organisms and many viruses to catalyze an essential step in the de novo biosynthesis of DNA precursors. RNRs are remarkably diverse by primary sequence and cofactor requirement, while sharing a conserved fold and radical-based mechanism for nucleotide reduction. In this work, we expand on our recent phylogenetic inference of the entire RNR family and describe the evolutionarily relatedness of insertions and extensions around the structurally homologous catalytic barrel. Using evo-velocity and sequence similarity network (SSN) analyses, we show that the N-terminal regulatory motif known as the ATP-cone domain was likely inherited from an ancestral RNR. By combining SSN analysis with AlphaFold2 predictions, we also show that the C-terminal extensions of class II RNRs can contain folded domains that share homology with an Fe-S cluster assembly protein. Finally, using sequence analysis and AlphaFold2, we show that the sequence motif of a catalytically essential insertion known as the finger loop is tightly coupled to the catalytic mechanism. Based on these results, we propose an evolutionary model for the diversification of the RNR family.

Evolving Experimental Techniques for Structure-Based Drug Design

Structure-based drug design (SBDD) is a prominent method in rational drug development and has traditionally benefitted from the atomic models of protein targets obtained using X-ray crystallography at cryogenic temperatures. In this perspective, we highlight recent advances in the development of structural techniques that are capable of probing dynamic information about protein targets. First, we discuss advances in the field of X-ray crystallography including serial room-temperature crystallography as a method for obtaining high-resolution conformational dynamics of protein-inhibitor complexes. Next, we look at cryogenic electron microscopy (cryoEM), another high-resolution technique that has recently been used to study proteins and protein complexes that are too difficult to crystallize. Finally, we present small-angle X-ray scattering (SAXS) as a potential high-throughput screening tool to identify inhibitors that target protein complexes and protein oligomerization.

Comprehensive phylogenetic analysis of the ribonucleotide reductase family reveals an ancestral clade

Ribonucleotide reductases (RNRs) are used by all free-living organisms and many viruses to catalyze an essential step in the de novo biosynthesis of DNA precursors. RNRs are remarkably diverse by primary sequence and cofactor requirement, while sharing a conserved fold and radical-based mechanism for nucleotide reduction. Here, we structurally aligned the diverse RNR family by the conserved catalytic barrel to reconstruct the first large-scale phylogeny consisting of 6779 sequences that unites all extant classes of the RNR family and performed evo-velocity analysis to independently validate our evolutionary model. With a robust phylogeny in-hand, we uncovered a novel, phylogenetically distinct clade that is placed as ancestral to the classes I and II RNRs, which we have termed clade Ø. We employed small-angle X-ray scattering (SAXS), cryogenic-electron microscopy (cryo-EM), and AlphaFold2 to investigate a member of this clade from Synechococcus phage S-CBP4 and report the most minimal RNR architecture to-date. Based on our analyses, we propose an evolutionary model of diversification in the RNR family and delineate how our phylogeny can be used as a roadmap for targeted future study.

Billions of years ago, the Earth’s atmosphere had very little oxygen. It was only after some bacteria and early plants evolved to harness energy from sunlight that oxygen began to fill the Earth’s environment. Oxygen is highly reactive and can interfere with enzymes and other molecules that are essential to life. Organisms living at this point in history therefore had to adapt to survive in this new oxygen-rich world.

An ancient family of enzymes known as ribonucleotide reductases are used by all free-living organisms and many viruses to repair and replicate their DNA. Because of their essential role in managing DNA, these enzymes have been around on Earth for billions of years. Understanding how they evolved could therefore shed light on how nature adapted to increasing oxygen levels and other environmental changes at the molecular level.

One approach to study how proteins evolved is to use computational analysis to construct a phylogenetic tree. This reveals how existing members of a family are related to one another based on the chain of molecules (known as amino acids) that make up each protein. Despite having similar structures and all having the same function, ribonucleotide reductases have remarkably diverse sequences of amino acids. This makes it computationally very demanding to build a phylogenetic tree.

To overcome this, Burnim, Spence, Xu et al. created a phylogenetic tree using structural information from a part of the enzyme that is relatively similar in many modern-day ribonucleotide reductases. The final result took seven continuous months on a supercomputer to generate, and includes over 6,000 members of the enzyme family.

The phylogenetic tree revealed a new distinct group of ribonucleotide reductases that may explain how one adaptation to increasing levels of oxygen emerged in some family members, while another adaptation emerged in others. The approach used in this work also opens up a new way to study how other highly diverse enzymes and other protein families evolved, potentially revealing new insights about our planet’s past.

Hinge disulfides in human IgG2 CD40 antibodies modulate receptor signaling by regulation of conformation and flexibility

Antibodies protect from infection, underpin successful vaccines and elicit therapeutic responses in otherwise untreatable cancers and autoimmune conditions. The human IgG2 isotype displays a unique capacity to undergo disulfide shuffling in the hinge region, leading to modulation of its ability to drive target receptor signaling (agonism) in a variety of important immune receptors, through hitherto unexplained molecular mechanisms. To address the underlying process and reveal how hinge disulfide orientation affects agonistic activity, we generated a series of cysteine to serine exchange variants in the hinge region of the clinically relevant monoclonal antibody ChiLob7/4, directed against the key immune receptor CD40. We report how agonistic activity varies with disulfide pattern and is afforded by the presence of a disulfide crossover between F(ab) arms in the agonistic forms, independently of epitope, as observed in the determined crystallographic structures. This structural "switch" affects directly on antibody conformation and flexibility. Small-angle x-ray scattering and ensemble modeling demonstrated that the least flexible variants adopt the fewest conformations and evoke the highest levels of receptor agonism. This covalent change may be amenable for broad implementation to modulate receptor signaling in an epitope-independent manner in future therapeutics.

Superstoichiometric Binding of the Anticancer Agent Titanocene Dichloride by Human Serum Transferrin and the Accompanying Lobe Closure

Titanocene dichloride (TDC) is an anticancer agent that delivers Ti(IV) into each of the two Fe(III) binding sites of bilobal human serum transferrin (Tf). This protein has been implicated in the selective transport of Ti(IV) to cells. How Ti(IV) might be released from the Tf Fe(III) binding site has remained a question, and crystal structures have raised issues about lobe occupancy and lobe closure in Ti(IV)-loaded Tf, compared with the Fe(III)-loaded form. Here, inductively coupled plasma optical emission spectroscopy reveals that Tf can stabilize toward hydrolytic precipitation more than 2 equiv of Ti, implying superstoichiometric binding beyond the two Fe(III) binding sites. Further studies support the inability of TDC to induce a complete lobe closure of Tf. Fluorescence data for TDC binding at low equivalents of TDC support an initial protein conformational change and lobe closure upon Ti binding, whereas data at higher equivalents support an open lobe configuration. Spectroscopic titration reveals less intense protein-metal electronic transitions as TDC equivalents are increased. Denaturing urea-PAGE gels and small angle X-ray scattering studies support an open lobe conformation. The concentrations of bicarbonate used in some earlier studies are demonstrated here to cause a pH change over time, which may contribute to variation in the apparent molar absorptivity associated with Ti(IV) binding in the Fe binding site. Finally, Fe(III)-bound holo-Tf still stabilizes TDC toward hydrolytic precipitation, a finding that underscores the importance of the interactions of Tf and TDC outside the Fe(III) binding site and suggests possible new pathways of Ti introduction to cells.

Structure-mechanics statistical learning uncovers mechanical relay in proteins

A protein's adaptive response to its substrates is one of the key questions driving molecular physics and physical chemistry. This work employs the recently developed structure-mechanics statistical learning method to establish a mechanical perspective. Specifically, by mapping all-atom molecular dynamics simulations onto the spring parameters of a backbone-side-chain elastic network model, the chemical moiety specific force constants (or mechanical rigidity) are used to assemble the rigidity graph, which is the matrix of inter-residue coupling strength. Using the S1A protease and the PDZ3 signaling domain as examples, chains of spatially contiguous residues are found to exhibit prominent changes in their mechanical rigidity upon substrate binding or dissociation. Such a mechanical-relay picture thus provides a mechanistic underpinning for conformational changes, long-range communication, and inter-domain allostery in both proteins, where the responsive mechanical hotspots are mostly residues having important biological functions or significant mutation sensitivity.

Protein residues exhibit specific routes of mechanical relay as the adaptive responses to substrate binding or dissociation. On such physically contiguous connections, residues experience prominent changes in their coupling strengths.

Supramolecular Copolymers of Peptides and Lipidated Peptides and Their Therapeutic Potential

Supramolecular peptide chemistry offers a versatile strategy to create chemical systems useful as new biomaterials with potential to deliver nearly 1000 known candidate peptide therapeutics or integrate other types of bioactivity. We report here on the co-assembly of lipidated β-sheet-forming peptides with soluble short peptides, yielding supramolecular copolymers with various degrees of internal order. At low peptide concentrations, the co-monomer is protected by lodging within internal aqueous compartments and stabilizing internal β-sheets formed by the lipidated peptides. At higher concentrations, the peptide copolymerizes with the lipidated peptide and disrupts the β-sheet secondary structure. The thermodynamic metastability of the co-assembly in turn leads to the spontaneous release of peptide monomers and thus serves as a potential mechanism for drug delivery. We demonstrated the function of these supramolecular systems using a drug candidate for Alzheimer's disease and found that the copolymers enhance neuronal cell viability when the soluble peptide is released from the assemblies.

Computational anti-COVID-19 drug design: progress and challenges

Vaccines have made gratifying progress in preventing the 2019 coronavirus disease (COVID-19) pandemic. However, the emergence of variants, especially the latest delta variant, has brought considerable challenges to human health. Hence, the development of robust therapeutic approaches, such as anti-COVID-19 drug design, could aid in managing the pandemic more efficiently. Some drug design strategies have been successfully applied during the COVID-19 pandemic to create and validate related lead drugs. The computational drug design methods used for COVID-19 can be roughly divided into (i) structure-based approaches and (ii) artificial intelligence (AI)-based approaches. Structure-based approaches investigate different molecular fragments and functional groups through lead drugs and apply relevant tools to produce antiviral drugs. AI-based approaches usually use end-to-end learning to explore a larger biochemical space to design antiviral drugs. This review provides an overview of the two design strategies of anti-COVID-19 drugs, the advantages and disadvantages of these strategies and discussions of future developments.

Open-Bundle Structure as the Unfolding Intermediate of Cytochrome c' Revealed by Small Angle Neutron Scattering

The dynamic structure changes, including the unfolding, dimerization, and transition from the compact to the open-bundle unfolding intermediate structure of Cyt c', were detected by a small-angle neutron scattering experiment (SANS). The structure of Cyt c' was changed into an unstructured random coil at pD = 1.7 (Rg = 25 Å for the Cyt c' monomer). The four-α-helix bundle structure of Cyt c' at neutral pH was transitioned to an open-bundle structure (at pD ~13), which is given by a numerical partial scattering function analysis as a joint-clubs model consisting of four clubs (α-helices) connected by short loops. The compactly folded structure of Cyt c' (radius of gyration, Rg = 18 Å for the Cyt c' dimer) at neutral or mildly alkaline pD transited to a remarkably larger open-bundle structure at pD ~13 (Rg = 25 Å for the Cyt c' monomer). The open-bundle structure was also supported by ab initio modeling.

Refining conformational ensembles of flexible proteins against small-angle x-ray scattering data

Intrinsically disordered proteins and flexible regions in multidomain proteins display substantial conformational heterogeneity. Characterizing the conformational ensembles of these proteins in solution typically requires combining one or more biophysical techniques with computational modeling or simulations. Experimental data can either be used to assess the accuracy of a computational model or to refine the computational model to get a better agreement with the experimental data. In both cases, one generally needs a so-called forward model (i.e., an algorithm to calculate experimental observables from individual conformations or ensembles). In many cases, this involves one or more parameters that need to be set, and it is not always trivial to determine the optimal values or to understand the impact on the choice of parameters. For example, in the case of small-angle x-ray scattering (SAXS) experiments, many forward models include parameters that describe the contribution of the hydration layer and displaced solvent to the background-subtracted experimental data. Often, one also needs to fit a scale factor and a constant background for the SAXS data but across the entire ensemble. Here, we present a protocol to dissect the effect of the free parameters on the calculated SAXS intensities and to identify a reliable set of values. We have implemented this procedure in our Bayesian/maximum entropy framework for ensemble refinement and demonstrate the results on four intrinsically disordered proteins and a protein with three domains connected by flexible linkers. Our results show that the resulting ensembles can depend on the parameters used for solvent effects and suggest that these should be chosen carefully. We also find a set of parameters that work robustly across all proteins.

Chiral Plasmonic Triangular Nanorings with SERS Activity for Ultrasensitive Detection of Amyloid Proteins in Alzheimer's Disease

Chiral plasmonic nanomaterials have attracted unprecedented attention due to their broad applications in biomedicine, negative refractive index, and chiral sensing. Here, using a wet-chemistry process, chiral triangular Au nanorings are fabricated with a platinum (Pt) framework (l/d-Pt@Au triangular nanorings, named l/d-Pt@Au TNRs). The l/d-Pt@Au TNRs exhibit strong optical activity with a g-factor of 0.023 and can be used effectively for the discrimination of enantiomers due to selective resonance coupling between the induced electric and magnetic dipoles associated with enantiomers and the chiral plasmonic TNRs, also known as the surface-enhanced Raman scattering-chiral anisotropy (SERS-ChA) effect. The chiral d-Pt@Au TNRs represent a label-free SERS platform that can be applied to detect Aβ monomers and fibrils, the hallmarks of Alzheimer's disease (AD), achieving a limit of detection (LOD) down to 0.045 × 10^-12 m and 4 × 10^-15 m for 42-residue-long amyloid-β (Aβ₄₂ ) monomer and fibrils, respectively. Furthermore, chiral d-Pt@Au TNRs can also be successfully carried out to detect Aβ₄₂ proteins in AD patients with ultrahigh levels of sensitivity, thus allowing picogram quantities of Aβ₄₂ proteins to be identified. This research opens up an avenue for the use of chiral plasmonic nanomaterials as ultrasensitive SERS substrates to early diagnosis of protein-misfolding diseases.

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.

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

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

Small-Angle X-ray Scattering Signatures of Conformational Heterogeneity and Homogeneity of Disordered Protein Ensembles

An accurate account of disordered protein conformations is of central importance to deciphering the physicochemical basis of biological functions of intrinsically disordered proteins and the folding-unfolding energetics of globular proteins. Physically, disordered ensembles of nonhomopolymeric polypeptides are expected to be heterogeneous, i.e., they should differ from those homogeneous ensembles of homopolymers that harbor an essentially unique relationship between average values of end-to-end distance R_EE and radius of gyration R_g. It was posited recently, however, that small-angle X-ray scattering (SAXS) data on conformational dimensions of disordered proteins can be rationalized almost exclusively by homopolymer ensembles. Assessing this perspective, chain-model simulations are used to evaluate the discriminatory power of SAXS-determined molecular form factors (MFFs) with regard to homogeneous versus heterogeneous ensembles. The general approach adopted here is not bound by any assumption about ensemble encodability, in that the postulated heterogeneous ensembles we evaluated are not restricted to those entailed by simple interaction schemes. Our analysis of MFFs for certain heterogeneous ensembles with more narrowly distributed R_EE and R_g indicates that while they deviate from MFFs of homogeneous ensembles, the differences can be rather small. Remarkably, some heterogeneous ensembles with asphericity and R_EE drastically different from those of homogeneous ensembles can nonetheless exhibit practically identical MFFs, demonstrating that SAXS MFFs do not afford unique characterizations of basic properties of conformational ensembles in general. In other words, the ensemble to MFF mapping is practically many-to-one and likely nonsmooth. Heteropolymeric variations of the R_EE-R_g relationship were further showcased using an analytical perturbation theory developed here for flexible heteropolymers. Ramifications of our findings for interpretation of experimental data are discussed.

Structural Perspectives on the Mechanism of Soluble Guanylate Cyclase Activation

The enzyme soluble guanylate cyclase (sGC) is the prototypical nitric oxide (NO) receptor in humans and other higher eukaryotes and is responsible for transducing the initial NO signal to the secondary messenger cyclic guanosine monophosphate (cGMP). Generation of cGMP in turn leads to diverse physiological effects in the cardiopulmonary, vascular, and neurological systems. Given these important downstream effects, sGC has been biochemically characterized in great detail in the four decades since its discovery. Structures of full-length sGC, however, have proven elusive until very recently. In 2019, advances in single particle cryo–electron microscopy (cryo-EM) enabled visualization of full-length sGC for the first time. This review will summarize insights revealed by the structures of sGC in the unactivated and activated states and discuss their implications in the mechanism of sGC activation.

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.

Macromolecular room temperature crystallography

X-ray crystallography enables detailed structural studies of proteins to understand and modulate their function. Conducting crystallographic experiments at cryogenic temperatures has practical benefits but potentially limits the identification of functionally important alternative protein conformations that can be revealed only at room temperature (RT). This review discusses practical aspects of preparing, acquiring, and analyzing X-ray crystallography data at RT to demystify preconceived impracticalities that freeze progress of routine RT data collection at synchrotron sources. Examples are presented as conceptual and experimental templates to enable the design of RT-inspired studies; they illustrate the diversity and utility of gaining novel insights into protein conformational landscapes. An integrative view of protein conformational dynamics enables opportunities to advance basic and biomedical research.

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.

Visualizing Disordered Single-Stranded RNA: Connecting Sequence, Structure, and Electrostatics

Disordered homopolymeric regions of single-stranded RNA, such as U or A tracts, are found within functional RNAs where they play distinct roles in defining molecular structure and facilitating recognition by partners. Despite this prominence, details of conformational and biophysical properties of these regions have not yet been resolved. We apply a number of experimental techniques to investigate the conformations of these biologically important motifs and provide quantitative measurements of their ion atmospheres. Single strands of RNA display pronounced sequence-dependent conformations that relate to the unique ion atmospheres each attracts. Chains of rU bases are relatively unstructured under all conditions, while chains of rA bases display distinct ordering through stacking or clustering motifs, depending on the composition of the surrounding solution. These dramatic structural differences are consistent with the measured disparity in ion composition and atmospheres around each homopolymer, revealing a complex interplay of base, ion, and single-strand ordering. The unique structural and ionic signatures of homopolymer ssRNAs explains their role(s) in folding structured RNAs and may explain their distinct recognition by protein partners.

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.

Convergent allostery in ribonucleotide reductase

Ribonucleotide reductases (RNRs) use a conserved radical-based mechanism to catalyze the conversion of ribonucleotides to deoxyribonucleotides. Within the RNR family, class Ib RNRs are notable for being largely restricted to bacteria, including many pathogens, and for lacking an evolutionarily mobile ATP-cone domain that allosterically controls overall activity. In this study, we report the emergence of a distinct and unexpected mechanism of activity regulation in the sole RNR of the model organism Bacillus subtilis. Using a hypothesis-driven structural approach that combines the strengths of small-angle X-ray scattering (SAXS), crystallography, and cryo-electron microscopy (cryo-EM), we describe the reversible interconversion of six unique structures, including a flexible active tetramer and two inhibited helical filaments. These structures reveal the conformational gymnastics necessary for RNR activity and the molecular basis for its control via an evolutionarily convergent form of allostery.

Ribonucleotide reductase (RNR) catalyzes the conversion of ribonucleotides to deoxyribonucleotides, which is an essential step in DNA synthesis. Here the authors use small-angle X-ray scattering, X-ray crystallography, and cryo-electron microscopy to capture active and inactive forms of the Bacillus subtilis RNR and provide mechanistic insights into a convergent form of allosteric regulation.

Structures of Class Id Ribonucleotide Reductase Catalytic Subunits Reveal a Minimal Architecture for Deoxynucleotide Biosynthesis

Class I ribonucleotide reductases (RNRs) share a common mechanism of nucleotide reduction in a catalytic α subunit. All RNRs initiate catalysis with a thiyl radical, generated in class I enzymes by a metallocofactor in a separate β subunit. Class Id RNRs use a simple mechanism of cofactor activation involving oxidation of a MnII2 cluster by free superoxide to yield a metal-based MnIIIMnIV oxidant. This simple cofactor assembly pathway suggests that class Id RNRs may be representative of the evolutionary precursors to more complex class Ia-c enzymes. X-ray crystal structures of two class Id α proteins from Flavobacterium johnsoniae ( Fj) and Actinobacillus ureae ( Au) reveal that this subunit is distinctly small. The enzyme completely lacks common N-terminal ATP-cone allosteric motifs that regulate overall activity, a process that normally occurs by dATP-induced formation of inhibitory quaternary structures to prevent productive β subunit association. Class Id RNR activity is insensitive to dATP in the Fj and Au enzymes evaluated here, as expected. However, the class Id α protein from Fj adopts higher-order structures, detected crystallographically and in solution. The Au enzyme does not exhibit these quaternary forms. Our study reveals structural similarity between bacterial class Id and eukaryotic class Ia α subunits in conservation of an internal auxiliary domain. Our findings with the Fj enzyme illustrate that nucleotide-independent higher-order quaternary structures can form in simple RNRs with truncated or missing allosteric motifs.

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.

Folded alkane chains and the emergence of the lamellar crystal

The competition between chain stiffness and chain collapse gives rise to complex low temperature morphologies of single polymer chains, in our case alkanes. These structures are characterized by specific sequences of dihedral angles along the chain, i.e., dihedral angle correlations extending beyond local steric effects. To describe and classify these morphologies, one can transfer concepts from protein science, where this creation of dihedral angle correlations underlies the formation of α-helices and β-sheets. We show here by means of flat-histogram Monte Carlo simulations that, although lacking in primary structure being simple homopolymers, short alkane chains fold into non-trivial ground states (tertiary structure) consisting of chain segments of defined secondary structures. The folded lamellar crystal typical for polyethylene chains requires a minimum chain length to occur as the ground state folded structure, which we identify to be around 150 repeat units.

Imaging electron-density fluctuations by multidimensional X-ray photon-coincidence diffraction

The ultrafast spontaneous electron-density fluctuation dynamics in molecules is studied theoretically by off-resonant multiple X-ray diffraction events. The time- and wavevector-resolved photon-coincidence signals give an image of electron-density fluctuations expressed through the four-point correlation function of the charge density in momentum space. A Fourier transform of the signal provides a real-space image of the multipoint charge-density correlation functions, which reveal snapshots of the evolving electron density in between the diffraction events. The proposed technique is illustrated by ab initio simulations of the momentum- and real-space inelastic scattering signals from a linear cyanotetracetylene molecule.