X-ray free electron lasers (XFELs) are potentially revolutionary X-ray sources because of their very short pulse duration, extreme peak brilliance and high spatial coherence, features that distinguish them from today’s synchrotron sources. We review recent time-resolved Laue diffraction and time-resolved wide angle X-ray scattering (WAXS) studies at synchrotron sources, and initial static studies at XFELs. XFELs have the potential to transform the field of time-resolved structural biology, yet many challenges arise in devising and adapting hardware, experimental design and data analysis strategies to exploit their unusual properties. Despite these challenges, we are confident that XFEL sources are poised to shed new light on ultrafast protein reaction dynamics.
The effect of the X-ray dose on room-temperature time-resolved Laue data is discussed.
Protein X-ray structures are determined with ionizing radiation that damages the protein at high X-ray doses. As a result, diffraction patterns deteriorate with the increased absorbed dose. Several strategies such as sample freezing or scavenging of X-ray-generated free radicals are currently employed to minimize this damage. However, little is known about how the absorbed X-ray dose affects time-resolved Laue data collected at physiological temperatures where the protein is fully functional in the crystal, and how the kinetic analysis of such data depends on the absorbed dose. Here, direct evidence for the impact of radiation damage on the function of a protein is presented using time-resolved macromolecular crystallography. The effect of radiation damage on the kinetic analysis of time-resolved X-ray data is also explored.
radiation damage; X-ray dose; room temperature; time-resolved crystallography; Laue crystallography
We demonstrate tracking of protein structural changes with time-resolved wide-angle X-ray scattering (TR-WAXS) with nanosecond time resolution. We investigated the tertiary and quaternary conformational changes of human hemoglobin under nearly physiological conditions triggered by laser-induced ligand photolysis. We also report data on optically induced tertiary relaxations of myoglobin and refolding of cytochrome c to illustrate the wide applicability of the technique. By providing insights into the structural dynamics of proteins functioning in their natural environment, TR-WAXS complements and extends results obtained with time-resolved optical spectroscopy and X-ray crystallography.
In kinetic crystallography, the usually static method of X-ray diffraction is expanded to allow time-resolved analysis of conformational rearrangements in protein structures. To achieve this, reactions have to be triggered within the protein crystals of interest, and optical spectroscopy can be used to monitor the reaction state. For this approach, a modified form of H-Ras p21 was designed which allows reaction initiation and fluorescence readout of the initiated GTPase reaction within the crystalline state. Rearrangements within the crystallized protein due to the progressing reaction and associated heterogeneity in the protein conformations have to be considered in the subsequent refinement processes.
X-ray diffraction experiments on H-Ras p21 in different states along the reaction pathway provide detailed information about the kinetics and mechanism of the GTPase reaction. In addition, a very high data quality of up to 1.0 Å resolution allowed distinguishing two discrete subconformations of H-Ras p21, expanding the knowledge about the intrinsic flexibility of Ras-like proteins, which is important for their function. In a complex of H-Ras•GppNHp (guanosine-5'-(β,γ-imido)-triphosphate), a second Mg2+ ion was found to be coordinated to the γ-phosphate group of GppNHp, which positions the hydrolytically active water molecule very close to the attacked γ-phosphorous atom.
For the structural analysis of very high-resolution data we have used a new 'two-chain-isotropic-refinement' strategy. This refinement provides an alternative and easy to interpret strategy to reflect the conformational variability within crystal structures of biological macromolecules. The presented fluorescent form of H-Ras p21 will be advantageous for fluorescence studies on H-Ras p21 in which the use of fluorescent nucleotides is not feasible.
Microsecond (μs) time-resolved extended X-ray absorption fine structure spectroscopy (EXAFS) has been developed using an energy-dispersive EXAFS (EDE) setup equipped with a silicon Quantum Detector ULTRA. The feasibility was investigated with a prototypical thermally driven redox reaction, the thermal decomposition of (NH4)2[PtCl6]. EXAFS data were collected with snapshots every 60 μs during the course of the thermolysis reaction, then averaged for 100 times along the reaction to get better signal to noise ratio which reduces the time resolution to 6 millisecond (ms). Our results provide direct structural evidence of cis-PtCl2(NH3)2 as the intermediate, together with continuous electronic and geometric structure dynamics of the reactant, intermediate and final product during the course of the thermolysis of (NH4)2[PtCl6]. The thermal effect on EXAFS signals at high temperatures is considered in the data analysis, which is essential to follow the reaction process correctly. This method could also be applied to other reaction dynamics.
Here it is demonstrated how five-dimensional crystallography can be used to determine a comprehensive chemical kinetic mechanism in concert with the atomic structures of transient intermediates that form and decay during the course of the reaction.
A method for determining a comprehensive chemical kinetic mechanism in macromolecular reactions is presented. The method is based on five-dimensional crystallography, where, in addition to space and time, temperature is also taken into consideration and an analysis based on singular value decomposition is applied. First results of such a time-resolved crystallographic study are presented. Temperature-dependent time-resolved X-ray diffraction measurements were conducted on the newly upgraded BioCARS 14-ID-B beamline at the Advanced Photon Source and aimed at elucidating a comprehensive kinetic mechanism of the photoactive yellow protein photocycle. Extensive time series of crystallographic data were collected at two temperatures, 293 K and 303 K. Relaxation times of the reaction extracted from these time series exhibit measurable differences for the two temperatures, hence demonstrating that five-dimensional crystallography is feasible.
time-resolved crystallography; chemical kinetics; protein structure; temperature dependence
Hydroxyl radical protein footprinting coupled to mass spectrometry has been developed over the last decade and has matured to a powerful method for analyzing protein structure and dynamics. It has been successfully applied in the analysis of protein structure, protein folding, protein dynamics, and protein-protein and protein-DNA interactions. Using synchrotron radiolysis, exposures of proteins to a “white” x-ray beam for milliseconds provide sufficient oxidative modifications to surface amino acid side chains that can be easily detected and quantified by mass spectrometry. Thus, conformational changes in proteins or protein complexes can be examined using a time-resolved approach, which would be a valuable method for the study of macromolecular dynamics. In this review, we describe a new application of hydroxyl radical protein footprinting to probe the time evolution of the calcium-dependent conformational changes of gelsolin on the millisecond timescale. The data suggest a cooperative transition as multiple sites in different molecular sub-domains have similar rates of conformational change. These findings demonstrate that time-resolved protein footprinting is suitable for studies of protein dynamics that occur over periods ranging from milliseconds to seconds. In this review we also show how the structural resolution and sensitivity of the technology can be improved as well. The hydroxyl radical varies in its reactivity to different side chains by over two orders of magnitude, thus oxidation of amino acid side chains of lower reactivity are more rarely observed in such experiments. Here we demonstrate that selected reaction monitoring (SRM)-based method can be utilized for quantification of oxidized species, improving the signal to noise ratio. This expansion of the set of oxidized residues of lower reactivity will improve the overall structural resolution of the technique. This approach is also suggested as a basis for developing hypothesis driven structural mass spectrometry experiments.
Kinetic studies of the early events in cytochrome c folding are reviewed with a focus on the evidence for folding intermediates on the submillisecond timescale. Evidence from time-resolved absorption, circular dichroism, magnetic circular dichroism, fluorescence energy and electron transfer, small-angle X-ray scattering and amide hydrogen exchange studies on the t ≤ 1 ms timescale reveals a picture of cytochrome c folding that starts with the ~ 1-μs conformational diffusion dynamics of the unfolded chains. A fractional population of the unfolded chains collapses on the 1 – 100 μs timescale to a compact intermediate IC containing some native-like secondary structure. Although the existence and nature of IC as a discrete folding intermediate remains controversial, there is extensive high time-resolution kinetic evidence for the rapid formation of IC as a true intermediate, i.e., a metastable state separated from the unfolded state by a discrete free energy barrier. Final folding to the native state takes place on millisecond and longer timescales, depending on the presence of kinetic traps such as heme misligation and proline mis-isomerization. The high folding rates observed in equilibrium molten globule models suggest that IC may be a productive folding intermediate. Whether it is an obligatory step on the pathway to the high free energy barrier associated with millisecond timescale folding to the native state, however, remains to be determined.
Collapsed intermediate; secondary structure formation; disordered tertiary structure; conformational diffusion; unfolded chains; molten globule; heme misligation; time-resolved spectroscopy; far-UV circular dichroism; magnetic circular dichroism; Trp59 fluorescence; amide hydrogen exchange; small-angle X-ray scattering; thermophiles; three-state pathway
Small-angle x-ray scattering (SAXS) is a powerful method for obtaining quantitative structural information on the size and shape of proteins, and it is increasingly used in kinetic studies of folding and association reactions. In this mini-review, we discuss recent developments in using SAXS to obtain structural information on the unfolded ensemble and early folding intermediates of proteins using continuous-flow mixing devices. Interfacing of these micromachined devices to SAXS beamlines has allowed access to the microsecond time regime. The experimental constraints in implementation of turbulence and laminar flow based mixers with SAXS detection and a comparison of the two approaches are presented. Current improvements and future prospects of microsecond time-resolved SAXS and the synergy with ab initio structure prediction and molecular dynamics simulations are discussed.
A new method of time-resolved solution scattering utilizing X-ray multilayer optics is presented.
100 ps time-resolved X-ray solution-scattering capabilities have been developed using multilayer optics at the beamline NW14A, Photon Factory Advanced Ring, KEK. X-ray pulses with an energy bandwidth of ΔE/E = 1–5% are generated by reflecting X-ray pulses (ΔE/E = 15%) through multilayer optics, made of W/B4C or depth-graded Ru/C on silicon substrate. This tailor-made wide-bandwidth X-ray pulse provides high-quality solution-scattering data for obtaining photo-induced molecular reaction dynamics. The time-resolved solution scattering of CH2I2 in methanol is demonstrated as a typical example.
time-resolved solution scattering; photodissociation reaction; liquidography; multilayers
Myoglobin, a small globular heme protein that binds gaseous ligands such asO2, CO and NO reversibly at the heme iron, provides an excellent modelsystem for studying structural and dynamic aspects of protein reactions. Flashphotolysis experiments, performed over wide ranges in time and temperature, reveal a complex ligand binding reaction with multiple kinetic intermediates, resulting from protein relaxation and movements of the ligand within the protein. Our recent studies of carbonmonoxy-myoglobin (MbCO) mutant L29W, using time-resolved infrared spectroscopy in combination with x-ray crystallography, have correlated kinetic intermediates with photoproduct structures that are characterized by the CO residing in different internal protein cavities, so-called xenon holes. Here we have used Fourier transform infrared temperature derivative spectroscopy (FTIR-TDS) to further examine the role of internal cavities in the dynamics. Different cavities can be accessed by the CO ligands at different temperatures, and characteristic infrared absorption spectra have been obtained for the different locations of the CO ligand within the protein, enabling us to monitor ligand migration through the protein as well as conformational changes of the protein.
FTIR spectroscopy; ligand binding; myoglobin; temperature derivative spectroscopy
Third generation synchrotron sources such as the Advanced Photon Source at Argonne National Laboratory, Argonne, IL, are outstanding tools for X-ray diffraction and scattering studies of non-crystalline biological materials. However, these studies are hindered by the lack of adequate detectors that can provide multiple frames of detailed structural information on the required millisecond time scale at the extremely high count rates available at the APS. RMD is developing a cost effective detector for time-resolved small angle X-ray scattering, using a cooled, 512×512 pixel electron multiplying CCD (EMCCD). This paper describes the detector design, its efficacy for time-resolved SAXS studies, and its imaging performance with frame rates of 30 to 500 fps.
Synchrotron detector; EMCCD; SAXS; time resolved SAXS; Advanced Photon Source
A RATIO method for analysis of intensity changes in time-resolved pump–probe Laue diffraction experiments is described.
A RATIO method for analysis of intensity changes in time-resolved pump–probe Laue diffraction experiments is described. The method eliminates the need for scaling the data with a wavelength curve representing the spectral distribution of the source and removes the effect of possible anisotropic absorption. It does not require relative scaling of series of frames and removes errors due to all but very short term fluctuations in the synchrotron beam.
Laue diffraction; time-resolved diffraction; ratio method; data reduction
DNA repair enzymes are essential for maintaining the integrity of the DNA sequence. Unfortunately, very little is known about how these enzymes recognize damaged regions along the helix. Structural analysis of cellular repair enzymes bound to DNA reveals that these enzymes are able to recognize DNA in a variety of conformations. However, the prevalence of these deformations in the absence of enzymes remains unclear, as small populations of DNA conformations are often difficult to detect by NMR and X-ray crystallography. Here, we used time-resolved fluorescence spectroscopy to examine the conformational dynamics of linear, nicked, gapped, and bulged DNA in the absence of protein enzymes. This analysis reveals that damaged DNA is polymorphic in nature and able to adopt multiple individual conformations. We show that DNA repair intermediates that contain a one-nucleotide gap and bulge have a significant propensity to adopt conformations in which the orphan base resides outside the DNA helix, while DNA structures damaged by a nick or two-nucleotide gap favor intrahelical conformations. Because changes in DNA conformation appear to guide the recognition of DNA repair enzymes, we suggest that the current approach could be used to study the mechanism of DNA repair.
A modified Laue technique suitable for time-resolved diffraction is described in which profile-independent integration is used, the RATIO method is applied and multi-crystal data are normalized to a common scale. The method is applied in single-pulse pump–probe studies of a binuclear Rh complex, showing Rh—Rh bond shortening of 0.136 (8) Å on excitation.
A modified Laue method is shown to produce excited-state structures at atomic resolution of a quality competitive with those from monochromatic experiments. The much faster data collection allows the use of only one or a few X-ray pulses per data frame, which minimizes crystal damage caused by laser exposure of the samples and optimizes the attainable time resolution. The method has been applied to crystals of the α-modification of Rh2(μ-PNP)2(PNP)2 (BPh4)2 [PNP = CH3N(P(OCH3)2)2, Ph = phenyl]. The experimental results show a shortening of the Rh—Rh distance in the organometallic complex of 0.136 (8) Å on excitation and are quantitatively supported by quantum-mechanical (QM)/molecular-mechanics (MM) theoretical calculations which take into account the confining effect of the crystal environment, but not by theoretical results on the isolated complex, demonstrating the defining effect of the crystal matrix.
Laue techniques; single-pulse diffraction; quantum-mechanical/molecular-mechanics calculations; QM/MM calculations; time-resolved X-ray crystallography
The three-dimensional reconstruction program DAMMIN has been applied to time-resolved small-angle X-ray scattering data. The results are presented and their success in representing the molecules is assessed.
Modern computing power has made it possible to reconstruct low-resolution, three-dimensional shapes from solution small-angle X-ray scattering (SAXS) data on biomolecules without a priori knowledge of the structure. In conjunction with rapid mixing techniques, SAXS has been applied to time resolve conformational changes accompanying important biological processes, such as biomolecular folding. In response to the widespread interest in SAXS reconstructions, their value in conjunction with such time-resolved data has been examined. The group I intron from Tetrahymena thermophila and its P4–P6 subdomain are ideal model systems for investigation owing to extensive previous studies, including crystal structures. The goal of this paper is to assay the quality of reconstructions from time-resolved data given the sacrifice in signal-to-noise required to obtain sharp time resolution.
time resolution; small-angle X-ray scattering (SAXS); shape reconstruction; biomolecules; biomolecular folding
The hexameric Escherichia coli RNA chaperone Hfq (HfqEc) is involved in riboregulation of target mRNAs by small trans-encoded RNAs. Hfq proteins of different bacteria comprise an evolutionarily conserved core, whereas the C-terminus is variable in length. Although the structure of the conserved core has been elucidated for several Hfq proteins, no structural information has yet been obtained for the C-terminus. Using bioinformatics, nuclear magnetic resonance spectroscopy, synchrotron radiation circular dichroism (SRCD) spectroscopy and small angle X-ray scattering we provide for the first time insights into the conformation and dynamic properties of the C-terminal extension of HfqEc. These studies indicate that the C-termini are flexible and extend laterally away from the hexameric core, displaying in this way features typical of intrinsically disordered proteins that facilitate intermolecular interactions. We identified a minimal, intrinsically disordered region of the C-terminus supporting the interactions with longer RNA fragments. This minimal region together with rest of the C-terminal extension provides a flexible moiety capable of tethering long and structurally diverse RNA molecules. Furthermore, SRCD spectroscopy supported the hypothesis that RNA fragments exceeding a certain length interact with the C-termini of HfqEc.
A 2.0 Å resolution neutron diffraction data set has been collected from a D2O-soaked γ-chymotrypsin crystal at low pH on the Institute Laue–Langevin LADI-III beamline.
The crystal preparation and preliminary neutron diffraction analysis of γ-chymotrypsin are presented. Large hydrogenated crystals of γ-chymotrypsin were exchanged into deuterated buffer via vapor diffusion in a capillary and neutron Laue diffraction data were collected from the resulting crystal to 2.0 Å resolution on the LADI-III diffractometer at the Institut Laue–Langevin (ILL) at room temperature. The neutron structure of a well studied protein such as γ-chymotrypsin, which is also amenable to ultrahigh-resolution X-ray crystallography, represents the first step in developing a model system for the study of H atoms in protein crystals.
γ-chymotrypsin; neutron diffraction
We demonstrate the use of an X-ray free electron laser synchronized with an optical pump laser to obtain X-ray diffraction snapshots from the photoactivated states of large membrane protein complexes in the form of nanocrystals flowing in a liquid jet. Light-induced changes of Photosystem I-Ferredoxin co-crystals were observed at time delays of 5 to 10 μs after excitation. The result correlates with the microsecond kinetics of electron transfer from Photosystem I to ferredoxin. The undocking process that follows the electron transfer leads to large rearrangements in the crystals that will terminally lead to the disintegration of the crystals. We describe the experimental setup and obtain the first time-resolved femtosecond serial X-ray crystallography results from an irreversible photo-chemical reaction at the Linac Coherent Light Source. This technique opens the door to time-resolved structural studies of reaction dynamics in biological systems.
We demonstrate the use of an X-ray free electron laser synchronized with an optical pump laser to obtain X-ray diffraction snapshots from the photoactivated states of large membrane protein complexes in the form of nanocrystals flowing in a liquid jet. Light-induced changes of Photosystem I-Ferredoxin co-crystals were observed at time delays of 5 to 10 µs after excitation. The result correlates with the microsecond kinetics of electron transfer from Photosystem I to ferredoxin. The undocking process that follows the electron transfer leads to large rearrangements in the crystals that will terminally lead to the disintegration of the crystals. We describe the experimental setup and obtain the first time-resolved femtosecond serial X-ray crystallography results from an irreversible photo-chemical reaction at the Linac Coherent Light Source. This technique opens the door to time-resolved structural studies of reaction dynamics in biological systems.
(170.7160) Ultrafast technology; (170.7440) X-ray imaging; (140.3450) Laser-induced chemistry; (140.7090) Ultrafast lasers; (170.0170) Medical optics and biotechnology
Motivation: To efficiently analyze the ‘native ensemble of conformations’ accessible to proteins near their folded state and to extract essential information from observed distributions of conformations, reliable mathematical methods and computational tools are needed.
Result: Examination of 24 pairs of structures determined by both NMR and X-ray reveals that the differences in the dynamics of the same protein resolved by the two techniques can be tracked to the most robust low frequency modes elucidated by principal component analysis (PCA) of NMR models. The active sites of enzymes are found to be highly constrained in these PCA modes. Furthermore, the residues predicted to be highly immobile are shown to be evolutionarily conserved, lending support to a PCA-based identification of potential functional sites. An online tool, PCA_NEST, is designed to derive the principal modes of conformational changes from structural ensembles resolved by experiments or generated by computations.
Supplementary information: Supplementary data are available at Bioinformatics online.
The PAS-LOV domain is a signal transducing component found in a large variety of proteins that is responsible for sensing different stimuli such as light, oxygen and voltage. The LOV protein VVD regulates blue-light responses in the filamentous fungi Neurospora crassa. Using photocoupled, time-resolved small angle x-ray scattering, we extract the solution protein structure in both dark-adapted and light-activated states. Two distinct dark-adapted conformations are detected in the wild type protein: a compact structure that corresponds to the crystal structure of the dark-state monomer as well as an extended structure that is well modeled by introducing conformational disorder at the N-terminus of the protein. These conformations are accentuated in carefully selected variants, in which a key residue for propagating structural transitions, Cys71, has been mutated or oxidized. Despite different dark state conformations, all proteins form a common dimer in response to illumination. Taken together, these data support a reaction scheme that describes the mechanism for light-induced dimerization of VVD. Envelope reconstructions of the transient light-state dimer reveal structures that are best described by a parallel arrangement of subunits that have significantly changed conformation compared to the crystal structure.
LOV domain proteins; blue light activated proteins; VVD; photocoupled small angle x-ray scattering
A soft X-ray angle-resolved photoemission system applicable to 100 µm crystals has been developed.
A system for angle-resolved photoemission spectroscopy (ARPES) of small single crystals with sizes down to 100 µm has been developed. Soft X-ray synchrotron radiation with a spot size of ∼40 µm × 65 µm at the sample position is used for the excitation. Using this system an ARPES measurement has been performed on a Si crystal of size 120 µm × 100 µm × 80 µm. The crystal was properly oriented on a sample stage by measuring the Laue spots. The crystal was cleaved in situ with a microcleaver at 100 K. The cleaved surface was adjusted to the beam spot using an optical microscope. Consequently, clear band dispersions along the Γ–X direction reflecting the bulk electronic states were observed with a photon energy of 879 eV.
angle-resolved photoemission spectroscopy (ARPES); soft X-ray; small crystal; microcleaving; micropositioning
Lymphotactin/XCL1, the defining member of the C class of chemokines, undergoes a conformational change that involves the complete restructuring of all stabilizing interactions. Other chemokines are restricted to a single conformation by a pair of conserved disulfide crosslinks, one of which is absent in lymphotactin. This structural interconversion is entirely reversible, and the two-state equilibrium is sensitive to changes in temperature and ionic strength. One species adopts the conserved chemokine fold as a monomer and functions as an agonist for XCR1, the specific G protein-coupled receptor for lymphotactin. Rearrangement to the other conformation produces a novel four-stranded sheet that dimerizes to form a beta sandwich with high affinity for cell-surface glycosaminoglycans. We developed methods for resolving the two species, and investigated the dynamics of human lymphotactin structural interconversion using NMR spectroscopy, heparin affinity chromatography, and time-resolved fluorescence on the wild-type protein and a panel of amino acid substituted lymphotactin variants. Our results show that the lymphotactin structural rearrangement occurs at a rate of ~1/s, and that mutation of residues required for glycosaminoglycan binding shifts the conformational equilibrium toward the chemokine-like fold. We speculate that charge repulsion between arginines 23 and 43 destabilizes the chemokine fold and promotes conversion to the novel lymphotactin dimer, while binding of chloride or another anion stabilizes the chemokine fold by neutralizing the repulsive effect.
Modeling of the tetrahedral intermediate within the active site of Escherichia coli aspartate transcarbamoylase revealed a specific interaction with the side chain of Gln137, an interaction not previously observed in the structure of the X-ray enzyme in the presence of N-phosphonacetyl-L-aspartate (PALA). Previous site-specific mutagenesis experiments showed that when Gln137 was replaced by alanine, the resulting mutant enzyme (Q137A) exhibited approximately 50-fold less activity than the wild-type enzyme, exhibited no homotropic cooperativity, and the binding of both carbamoyl phosphate and aspartate were extremely compromised. To elucidate the structural alterations in the mutant enzyme that might lead to such pronounced changes in kinetic and binding properties, the Q137A enzyme was studied by time-resolved small-angle X-ray scattering and its structure was determined in the presence of PALA to 2.7Å resolution. Time-resolved small-angle X-ray scattering established that the natural substrates, carbamoyl phosphate and L-aspartate, do not induce in the Q137A enzyme the same conformational changes as observed for the wild-type enzyme, although the scattering pattern of the Q137A and wild-type enzymes in the presence of PALA were identical. The overall structure of the Q137A enzyme is similar to that of the R-state structure of wild-type enzyme with PALA bound. However, there are differences in the manner by which the Q137A enzyme coordinates PALA, especially in the side chain positions of Arg105 and His134. The replacement of Gln137 by Ala also has a dramatic effect on the electrostatics of the active site. These data taken together suggest that the side chain of Gln137 in the wild-type enzyme is required for the binding of carbamoyl phosphate in the proper orientation so as to induce conformational changes required for the creation of the high-affinity aspartate binding site. The inability of carbamoyl phosphate to create the high-affinity binding site in the Q137A enzyme results in an enzyme locked in the low activity low affinity T state. These results emphasize the absolute requirement of the binding of carbamoyl phosphate for the creation of the high-affinity aspartate binding site and for inducing the homotropic cooperativity in aspartate transcarbamoylase.
allosteric enzyme; polar contacts; electrostatics; Poisson-Boltzmann equation; small-angle X-ray scattering; domain closure; allosteric transition; intersubunit interactions