FFT method to compute solution X-ray scattering curves

We present an efficient algorithm to compute X-ray intensities scattered by macromolecules in solution, from atomic positions found in crystal structures. The algorithm applied the FAst Fourier Transform to an electron density map created from the atomic coordinates and corrected for solvent density. We compute scattering curves for both allosteric forms of E. coli aspartate carbamoyltransferase. Calculated intensities are in agreement with the ones measured by Moddy et al. [1,2] which shows that the structures observed in solution in the presence or in the absence of a substrate analogue do correspond to those of two crystal forms analyzea by Lipscomb and collaborators [3,4,5].     

Amylose conformation in aqueous solution: a small-angle X-ray scattering study

An investigation of the small-angle X-ray scattering properties of aqueous solutions of an amylose derivative has been carried out. Experiments have been conducted in stable and fairly concentrated polymer solutions (up to 3.2%) by using a slightly substituted carboxymethylamylose having a degree of substitution of 0.08. Scattering intensities display a maximum in the low angle range which prevents extrapolation of the angular dependence to zero angle. Data obtained in the range of scattering vector 0.01<η<0.1Å^?1 yield 8 Å as the radius of gyration of the chain cross-section and 140 dalton Å^?1 as the mass per unit length. These results are analysed in terms of the current model of amylose solution conformation and compared with the theoretical calculations of the Debye scattering function of the isolated chain.     

Biologically active decorin is a monomer in solution

It has been reported that decorin and its protein core can have molecular masses nearly double the size of those previously published, suggesting a dimeric structure. In this study we tested whether biologically active decorin and its glycoprotein core would form dimers in solution. We used homo- and hetero-bifunctional chemical cross-linking reagents, BS3 and sulfo-SMPB, respectively, as well as glutaraldehyde and found no preferential dimer formation, whether chemical cross-linking was performed in the presence or absence of live cells. Under the same experimental conditions, we easily detected dimers of epidermal growth factor receptor and basic fibroblast growth factor, two glycoproteins known to dimerize. Only at very high cross-linker to decorin molar ratios (2000:1) were trimers and multimers observed, but performing the chemical cross-linking in the presence of a reducing agent abolished these. The elution of decorin protein core in Superose 6 gel chromatography gave masses compatible with monomeric proteins, both before and after denaturation with 2.5 M guanidine HCl. Matrix-assisted laser desorption ionization gave a mass of 44,077 Da for decorin protein core, without any evidence of dimers or oligomers. Extensive oligomerization of the decorin protein core was observed only after dialysis against water and freeze-drying. These oligomers were considered artifacts because they were independent of chemical cross-linking and were resistant to heat denaturation and disulfide-bond reduction. Oligomeric preparations showed markedly reduced biological activity in both phosphorylation and collagen fibrillogenesis assays. Thus, biologically active decorin is a monomer in solution and, as such, is a monovalent ligand for various extracellular matrix proteins, growth factors, and cell surface receptors.     

Reconstruction of protein form with X-ray solution scattering and a genetic algorithm

We have reconstructed, from experimental approximately 2 nm resolution X-ray solution scattering profiles, the corresponding shapes and sizes of myoglobin, troponin C, spermadhesin PSP-I/PSP-II, chymotrypsinogen A, superoxide dismutase, ovalbumin, tubulin, nitrite reductase, catalase, the structural change of troponin C upon dissociation of the two high affinity Ca(2+), and the solution model structure of a tandem pair of fibronectin type III cytoplasmic domains of integrin alpha6beta4 before determination of its crystal structure. To this purpose we have designed a new genetic algorithm which gradually explores a discrete search space and evolves convergent models made of several hundred beads (down to 0.3 nm radius) best fitting the scattering profile upon Debye calculation, without geometrical constraints or penalty for loose beads. This is a procedure of effective numerical transformation of the one-dimensional scattering profiles into three-dimensional model structures. The number of beads in models is correlated with the protein molecular mass (with one exception). The shape and approximate dimensions of each protein have been retrieved by a set of ten solution models, essentially superimposable with the available crystal structures.     

Experimental approaches for solution X-ray scattering and fiber diffraction

X-ray scattering and diffraction from non-crystalline systems have gained renewed interest in recent years, as focus shifts from the structural chemistry information gained by high-resolution studies to the context of structural physiology at larger length scales. Such techniques permit the study of isolated macromolecules as well as highly organized macromolecular assemblies as a whole under near-physiological conditions. Time-resolved approaches, made possible by advanced synchrotron instrumentation, add a crucial dimension to many of these investigations. This article reviews experimental approaches in non-crystalline X-ray scattering and diffraction that may be used to illuminate important scientific questions such as protein/nucleic acid folding and structure-function relationships in large macromolecular assemblies.     

Joint use of small-angle X-ray and neutron scattering to study biological macromolecules in solution

Novel techniques for simultaneous analysis of X-ray and neutron scattering patterns from macromolecular complexes in solution are presented. They include ab initio shape and internal structure determination of multicomponent particles and more detailed rigid body modeling of complexes using high resolution structures of subunits. The methods fit simultaneously X-ray and neutron scattering curves including contrast variation data sets from selectively deuterated complexes. Biochemically sound interconnected models without steric clashes between the components displaying a pre-defined symmetry are generated. For rigid body modeling, distance restraints between specified residues/nucleotides or their ranges are taken into account. The efficiency of the methods is demonstrated in model examples, and potential sources of ambiguity are discussed.     

Contribution of solvent water to the solution X-ray scattering profile of proteins

A theoretical framework is presented to analyze how solvent water contributes to the X-ray scattering profile of protein solution. Molecular dynamics simulations were carried out on pure water and an aqueous solution of myoglobin to determine the spatial distribution of water molecules in each of them. Their solution X-ray scattering (SXS) profiles were numerically evaluated with obtained atomic-coordinate data. It is shown that two kinds of contributions from solvent water must be considered to predict the SXS profile of a solution accurately. One is the excluded solvent scattering originating in exclusion of water molecules from the space occupied by solutes. The other is the hydration effect resulting from formation of a specific distribution of water around solutes. Explicit consideration of only two molecular layers of water is practically enough to incorporate the hydration effect. Care should be given to using an approximation in which an averaged electron density distribution is assumed for the structure factor because it may predict profiles considerably deviating from the correct profile at large K.     

X-ray solution scattering studies of the structural diversity intrinsic to protein ensembles

It is becoming increasingly clear that characterization of the protein ensemble-the collection of all conformations of which the protein is capable-will be a critical step in developing a full understanding of the linkage between structure, dynamics, and function. X-ray solution scattering in the small angle (SAXS) and wide-angle (WAXS) regimes represents an important new window to exploring the behavior of ensembles. The characteristics of the ensemble express themselves in X-ray solution scattering data in predictable ways. Here we present an overview of the effect that structural diversity intrinsic to protein ensembles has on scattering data. We then demonstrate the observation of these effects in scattering from four molecular systems; myoglobin; ubiquitin; alcohol dehydrogenase; and HIV protease; and demonstrate the modulation of these ensembles by ligand binding, mutation, and environmental factors. The observations are analyzed quantitatively in terms of the average spatial extent of structural fluctuations occurring within these proteins under different experimental conditions. The insights which these analyses support are discussed in terms of the function of the various proteins.     

Transient dimer in the refolding kinetics of cytochrome c characterized by small-angle X-ray scattering

The equilibrium unfolding and the kinetic refolding of cytochrome c (Cyt c) in the presence of imidazole were studied with small-angle X-ray scattering (SAXS). The equilibrium unfolding experiments showed the radius of gyration, R(g), of native Cyt c to swell approximately 1 A with the addition of imidazole. The thermodynamic parameter m also reflects an expansion of the protein as its lower value demonstrates an increase in solvent-accessible surface area over that of native Cyt c in the absence of imidazole. Refolding was studied in the presence of imidazole as it prevents misligated intermediate states from forming during the refolding process, simplifying the kinetics, and making them easier to resolve. Time-resolved decreases in the forward scattering amplitude, I(0), demonstrated the transient formation of an aggregated intermediate. Final protein and denaturant concentrations were varied in the refolding kinetics, and the singular value decomposition (SVD) method was employed to characterize the associated state. This state was determined to be a dimer, with properties consistent with a molten globule.     

Characterization of protein fold by wide-angle X-ray solution scattering

Wide-angle X-ray solution scattering (WAXS) patterns contain substantial information about the three-dimensional structure of a protein. Although WAXS data have far less information than is required for determination of a full three-dimensional structure, the actual amount of information contained in a WAXS pattern has not been carefully quantified. Here we carry out an analysis of the amount of information that can be extracted from a WAXS pattern and demonstrate that it is adequate to estimate the secondary-structure content of a protein and to strongly limit its possible tertiary structures. WAXS patterns computed from the atomic coordinates of a set of 498 protein domains representing all of known fold space were used as the basis for constructing a multidimensional space of all corresponding WAXS patterns (‘WAXS space’). Within WAXS space, each scattering pattern is represented by a single vector. A principal components analysis was carried out to identify those directions in WAXS space that provide the greatest discrimination among patterns. The number of dimensions that provide significant discrimination among protein folds agrees well with the number of independent parameters estimated from a naïve Shannon sampling theorem approach. Estimates of the relative abundances of secondary structures were made using training/test sets derived from this data set. The average error in the estimate of α-helical content was 11%, and of β-sheet content was 9%. The distribution of proteins that are members of the four structure classes, α, β, α/β and α+β, are well separated in WAXS space when data extending to a spacing of 2.2 Å are used. Quantification of the information embedded within a WAXS pattern indicates that these data can be used as a powerful constraint in homology modeling of protein structures.     

Light scattering measurements supporting helical structures for chromatin in solution.

Laser light scattering measurements have been made on a series of polynucleosomes containing from 50 to 150 nucleosomes. Radii of gyration have been determined as a function of polynucleosome length for different ionic strength solutions. The results suggest that at low ionic strength the chromatin adopts a loosely helical structure rather than a random coil. The helix becomes more regular on increasing the ionic strength, the dimension resembling those proposed by Finch and Klug for their solenoid model.     

Architecture of a full-length retroviral integrase monomer and dimer, revealed by small angle X-ray scattering and chemical cross-linking

We determined the size and shape of full-length avian sarcoma virus (ASV) integrase (IN) monomers and dimers in solution using small angle x-ray scattering. The low resolution data obtained establish constraints for the relative arrangements of the three component domains in both forms. Domain organization within the small angle x-ray envelopes was determined by combining available atomic resolution data for individual domains with results from cross-linking coupled with mass spectrometry. The full-length dimer architecture so revealed is unequivocally different from that proposed from x-ray crystallographic analyses of two-domain fragments, in which interactions between the catalytic core domains play a prominent role. Core-core interactions are detected only in cross-linked IN tetramers and are required for concerted integration. The solution dimer is stabilized by C-terminal domain (CTD-CTD) interactions and by interactions of the N-terminal domain in one subunit with the core and CTD in the second subunit. These results suggest a pathway for formation of functional IN-DNA complexes that has not previously been considered and possible strategies for preventing such assembly.     

The complete VS ribozyme in solution studied by small-angle X-ray scattering

We have used small-angle X-ray solution scattering to obtain ab initio shape reconstructions of the complete VS ribozyme. The ribozyme occupies an electron density envelope with an irregular shape, into which helical sections have been fitted. The ribozyme is built around a core comprising a near-coaxial stack of three helices, organized by two three-way helical junctions. An additional three-way junction formed by an auxiliary helix directs the substrate stem-loop, juxtaposing the cleavage site with an internal loop to create the active complex. This is consistent with the current view of the probable mechanism of trans-esterification in which adenine and guanine nucleobases contributed by the interacting loops combine in general acid-base catalysis.     

Small angle X-ray scattering of dimeric yeast hexokinase in solution.

Small angle x-ray scattering measurements on dimeric yeast hexokinase B at pH 5.5 in acetate buffer yield a radius of gyration of 31.28 +/- 0.23 angstrom. This measured value is comparable to the radius of gyration of 31.5 angstrom calculated from the refined coordinates of the dimer in the BII crystal form. The hexokinase dimer found in the BI crystal form has a radius of gyration of 42 angstrom calculated from the atomic coordinates. Thus, the measured radius of gyration is consistent with the BII dimer being the predominant species in solution and rules out the existence of the BI dimer as a major species under these conditions.     

Interactions of hydrophobin proteins in solution studied by small-angle X-ray scattering

Hydrophobins are a group of very surface-active, fungal proteins known to self-assemble on various hydrophobic/hydrophilic interfaces. The self-assembled films coat fungal structures and mediate their attachment to surfaces. Hydrophobins are also soluble in water. Here, the association of hydrophobins HFBI and HFBII from Trichoderma reesei in aqueous solution was studied using small-angle x-ray scattering. Both HFBI and HFBII exist mainly as tetramers in solution in the concentration range 0.5-10 mg/ml. The assemblies of HFBII dissociate more easily than those of HFBI, which can tolerate changes of pH from 3 to 9 and temperatures in the range 5°C-60°C. The self-association of HFBI and HFBII is mainly driven by the hydrophobic effect, and addition of salts along the Hofmeister series promotes the formation of larger assemblies, whereas ethanol breaks the tetramers into monomers. The possibility that the oligomers in solution form the building blocks of the self-assembled film at the air/water interface is discussed.     

Denaturation and reassembly of chaperonin GroEL studied by solution X-ray scattering

We measured the denaturation and reassembly of Escherichia coli chaperonin GroEL using small-angle solution X-ray scattering, which is a powerful technique for studying the overall structure and assembly of a protein in solution. The results of the urea-induced unfolding transition show that GroEL partially dissociates in the presence of more than 2 M urea, cooperatively unfolds at around 3 M urea, and is in a monomeric random coil-like unfolded structure at more than 3.2 M urea. Attempted refolding of the unfolded GroEL monomer by a simple dilution procedure is not successful, leading to formation of aggregates. However, the presence of ammonium sulfate and MgADP allows the fully unfolded GroEL to refold into a structure with the same hydrodynamic dimension, within experimental error, as that of the native GroEL. Moreover, the X-ray scattering profiles of the GroEL thus refolded and the native GroEL are coincident with each other, showing that the refolded GroEL has the same structure and the molecular mass as the native GroEL. These results demonstrate that the fully unfolded GroEL monomer can refold and reassemble into the native tetradecameric structure in the presence of ammonium sulfate and MgADP without ATP hydrolysis and preexisting chaperones. Therefore, GroEL can, in principle, fold and assemble into the native structure according to the intrinsic characteristic of its polypeptide chain, although preexisting GroEL would be important when the GroEL folding takes place under in vivo conditions, in order to avoid misfolding and aggregation.