Modeling protein conformational ensembles: from missing loops to equilibrium fluctuations

Characterizing protein flexibility is an important goal for understanding the physical-chemical principles governing biological function. This paper presents a Fragment Ensemble Method to capture the mobility of a protein fragment such as a missing loop and its extension into a Protein Ensemble Method to characterize the mobility of an entire protein at equilibrium. The underlying approach in both methods is to combine a geometric exploration of conformational space with a statistical mechanics formulation to generate an ensemble of physical conformations on which thermodynamic quantities can be measured as ensemble averages. The Fragment Ensemble Method is validated by applying it to characterize loop mobility in both instances of strongly stable and disordered loop fragments. In each instance, fluctuations measured over generated ensembles are consistent with data from experiment and simulation. The Protein Ensemble Method captures the mobility of an entire protein by generating and combining ensembles of conformations for consecutive overlapping fragments defined over the protein sequence. This method is validated by applying it to characterize flexibility in ubiquitin and protein G. Thermodynamic quantities measured over the ensembles generated for both proteins are fully consistent with available experimental data. On these proteins, the method recovers nontrivial data such as order parameters, residual dipolar couplings, and scalar couplings. Results presented in this work suggest that the proposed methods can provide insight into the interplay between protein flexibility and function.     

Superhelical DNA studied by solution scattering and computer models

We present here recent results on the structure of superhelical DNA and its changes with salt concentration between 0.01 and 1.5 M NaCl. Scattering curves of two different superhelical DNAs were determined by static light scattering. The measured radii of gyration do not change significantly with salt concentration. Small-angle neutron scattering, together with calculations from a Monte Carlo model, allows to determine the superhelix diameter. Measured and simulated scattering curves agreed almost quantitatively. Experimentally we find that the diameter decreases from 16.0±0.9 nm at 10 mM to 9.0±0.7 nm at 100 mM NaCl. The superhelix diameter from the simulated conformations decreased from 18.0±1.5 nm at 10 mM to 9.4±1.5 nm at 100 mM NaCl. At higher salt concentrations up to 1.5 M NaCl, the diameter stays constant at 9 nm.This revised version was published online in October 2005 with corrections to the Cover Date.     

Characterization of the solution structure of the M intermediate of photoactive yellow protein using high-angle solution x-ray scattering

It is widely accepted that PYP undergoes global structural changes during the formation of the biologically active intermediate PYP(M). High-angle solution x-ray scattering experiments were performed using PYP variants that lacked the N-terminal 6-, 15-, or 23-amino-acid residues (T6, T15, and T23, respectively) to clarify these structural changes. The scattering profile of the dark state of intact PYP exhibited two broad peaks in the high-angle region (0.3 A(-1) < Q < 0.8 A(-1)). The intensities and positions of the peaks were systematically changed as a result of the N-terminal truncations. These observations and the agreement between the observed scattering profiles and the calculated profiles based on the crystal structure confirm that the high-angle scattering profiles were caused by intramolecular interference and that the structure of the chromophore-binding domain was not affected by the N-terminal truncations. The profiles of the PYP(M) intermediates of the N-terminally truncated PYP variants were significantly different from the profiles of the dark states of these proteins, indicating that substantial conformational rearrangements occur within the chromophore-binding domain during the formation of PYP(M). By use of molecular fluctuation analysis, structural models of the chromophore-binding region of PYP(M) were constructed to reproduce the observed profile of T23. The structure obtained by averaging 51 potential models revealed the displacement of the loop connecting beta4 and beta5, and the deformation of the alpha4 helix. High-angle x-ray scattering with molecular fluctuation simulation allows us to derive the structural properties of the transient state of a protein in solution.     

Anomalous x-ray scattering from terbium-labeled parvalbumin in solution

We have used anomalous small-angle x-ray scattering as a structural probe for solutions of rabbit parvalbumin labeled with terbium. This technique makes use of the large changes in the terbium scattering factor that occur when the x-ray energy is tuned around an L3 absorption edge of this heavy-atom label. These changes in scattering result in changes in the small-angle scattering curve of the labeled protein as a whole, which can then be analyzed to derive structural information concerning the distribution of labels in the protein. Based on a Gaussian model for the protein electron density, the mean distance from the terbiums to the protein center of mass is determined to be 13.2 A and is consistent with crystallographic results. Our results demonstrate the usefulness of terbium as an anomalous scattering label and provide criteria to help establish anomalous scattering as a reliable structural technique for proteins in solution.     

CD and small-angle x-ray scattering of silk fibroin in solution

We investigated the structure of silk fibroin dissolved in water and in water-organic solvent mixtures by CD and small-angle x-ray scattering (SAXS). CD spectra indicated a disordered secondary structure in water and a beta-sheet conformation in aqueous organic solvents, such as methanol, dioxane, and trifluoroethanol (in trifluoroethanol a transient form evolving toward beta-sheet conformation was seen just after dissolution). The SAXS technique indicated the presence of fibroin particles of lamellar shape. The molecular weight was 188,000 daltons in water and 302,000 daltons in aqueous methanol.     

Improving protein template recognition by using small-angle x-ray scattering profiles

Small-angle x-ray scattering (SAXS) is able to extract low-resolution protein shape information without requiring a specific crystal formation. However, it has found little use in atomic-level protein structure determination due to the uncertainty of residue-level structural assignment. We developed a new algorithm, SAXSTER, to couple the raw SAXS data with protein-fold-recognition algorithms and thus improve template-based protein-structure predictions. We designed nine different matching scoring functions of template and experimental SAXS profiles. The logarithm of the integrated correlation score showed the best template recognition ability and had the highest correlation with the true template modeling (TM)-score of the target structures. We tested the method in large-scale protein-fold-recognition experiments and achieved significant improvements in prioritizing the best template structures. When SAXSTER was applied to the proteins of asymmetric SAXS profile distributions, the average TM-score of the top-ranking templates increased by 18% after homologous templates were excluded, which corresponds to a p-value < 10⁻⁹ in Student's t-test. These data demonstrate a promising use of SAXS data to facilitate computational protein structure modeling, which is expected to work most efficiently for proteins of irregular global shape and/or multiple-domain protein complexes.     

Small-angle x-ray scattering of bovine nasal cartilage proteoglycan in solution

The proteoglycan subunit (PGS) from bovine nasal cartilage was examined in water and in 0.15 N LiCl by small-angle x-ray scattering (SAXS). The molecular weight of 2.5 × 10⁶ and the radius of gyration, R_g = 493 Å, in 0.15 N LiCl, obtained by SAXS, are in good agreement with values reported by others for similar preparations. Values of the radius of gyration of the cross section, mass per unit length, and persistence length of the PGS are also reported. The low value of intrinsic viscosity ([η]) found in 0.15 N LiCl, and a comparison of the experimental distance distribution function to that of the theoretical distance distribution function for sphere, suggest that the PGS in salt solution approaches spherical symmetry. The much higher value of [η] in water suggests a prolate ellipsoid of low axial ratio.     

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.     

Diffuse x-ray wide-angle scattering of polyglutamic acid in solution]

The diffuse wide angle x-ray scattering (WAXS) of polyglutamic acid (PGA) in solution was studied using an x-ray diffractometer with small aperture of the primary beam. The scattering curve was recorded at an angular interval from (article: see text). The experimental scattering intensity of PGA with alpha-helical CD spectrum showed a maximum at 14.4 nm-1. Unordered PGA in solution yielded no maximum at this scattering angle. The studies have proved that the scattering theory can be applied to globular proteins in solution as well as to chain molecules in solution in this angular interval. The differences between the calculated scattering curves and the experimental curves indicate minor movements of the side chains of PGA in solutions and slight structuring of the solvent at the surface of the polypeptide chain.     

Small-angle x-ray scattering investigation of the solution structure of troponin C

X-ray crystallographic studies of troponin C (Herzberg, O., and James, M.N.G. (1985) Nature 313, 653-659; Sundaralingam, M., Bergstrom, R., Strasburg, G., Rao, S.T., and Roychowdhury, P. (1985a) Science 227, 945-948) have revealed a novel protein structure consisting of two globular domains, each containing two Ca2+-binding sites, connected via a nine-turn alpha-helix, three turns of which are fully exposed to solvent. Since the crystals were grown at pH approximately 5, it is of interest to determine whether this structure is applicable to the protein in solution under physiological conditions. We have used small-angle x-ray scattering to examine the solution structure of troponin C at pH 6.8 and the effect of Ca2+ on the structure. The scattering data are consistent with an elongated structure in solution with a radius of gyration of approximately 23.0 A, which is quite comparable to that computed for the crystal structure. The experimental scattering profile and the scattering profile computed from the crystal structure coordinates do, however, exhibit differences at the 40-A level. A weak Ca2+-facilitated dimerization of troponin C was observed. The data rule out large Ca2+-induced structural changes, indicating rather that the molecule with Ca2+ bound is only slightly more compact than the Ca2+-free molecule.     

Small-angle x-ray scattering by poly-L-alanine solutions

The radius of gyration and “persistence length” of poly-L -alanine, calculated from small-angle x-ray scattering data, have values of 56 Å and 44 Å, respectively, in dichloroacetic acid, and 78 Å and ～30 Å in a 1:1 v/v mixture of trifluoroacetic acid and trifluoroethanol. This can be interpreted to mean that poly-L -alanine exists in a relatively rigid, predominantly α-helical conformation in dichloroacetic acid and in an extended, more flexible form in the mixed solvent system.     

A study of apo- and holo-forms of horse liver alcohol dehydrogenase in solution by diffuse x-ray scattering

Apo- and holo-forms of horse liver alcohol dehydrogenase (LADH) in solution were studied by diffuse x-ray scattering. Experimental scattering curves for apo- and holo-forms coincide both with the curves calculated from the crystal structures of apo- and holo-enzymes, and with each other. Thus the “sliding” of catalytical domains in LADH upon substrate binding, which has been shown by x-ray analysis, cannot be detected by diffuse x-ray scattering. Sensitivity of the scattering curves to the domain displacements of sliding and “locking” types has been investigated. It has been shown that the scattering curves of LADH are rather sensitive to the domain “unlocking.” However, these curves change only slightly upon sliding of domains, including the sliding of domains observed in LADH by x-ray analysis.     

Structure of an integrin-ligand complex deduced from solution x-ray scattering and site-directed mutagenesis

The structural basis of the interaction of integrin heterodimers with their physiological ligands is poorly understood. We have used solution x-ray scattering to visualize the head region of integrin alpha 5 beta 1 in an inactive (Ca2+-occupied) state, and in complex with a fragment of fibronectin containing the RGD and synergy recognition sequences. Shape reconstructions of the data have been interpreted in terms of appropriate molecular models. The scattering data suggest that the head region undergoes no gross conformational changes upon ligand binding but do lend support to a proposed outward movement of the hybrid domain in the beta subunit. Fibronectin is observed to bind across the top of the head region, which contains an alpha subunit beta-propeller and a beta subunit vWF type A domain. The model of the complex indicates that the synergy region binds on the side of the beta-propeller domain. In support of this suggestion, mutagenesis of a prominent loop region on the side of the propeller identifies two residues (Tyr208 and Ile210) involved in recognition of the synergy region. Our data provide the first view of a complex between an integrin and a macromolecular ligand in solution, at a nominal resolution of approximately 10 A.     

Determination of three-dimensional low-resolution viral structure from solution x-ray scattering data.

The capsid is modeled as a region of constant electron density located between inner and outer envelopes that exhibit icosahedral symmetry. For computational purposes the envelopes are represented as truncated sums of weighted icosahedral harmonics. Methods are described for estimating the weights from x-ray solution scattering patterns based on nonlinear least squares, and two examples of the procedure, for viruses with known atomic-resolution structures, are given.     

On the interpretation of small-angle x-ray solution scattering from spherical viruses.

The intermediates in the ribosome assembly in exponentially growing Escherichia coli have been identified by centrifuging a crude lysate, pulse-labeled with a radioactive RNA base, through a sucrose gradient and analyzing for precursor rRNA in the gradient fractions by gel electrophoresis. The major intermediate in the assembly of the 50 S subunit cosediments with the mature subunit, whereas two minor precursor species sediment between the 30 S and 50 S peaks. The assembly of the 30 S subunit proceeds via a minor intermediate sedimenting slightly behind the mature subunit and a major precursor particle that cosediments with the mature 30 S subunit.The fraction of the rRNA contained in these precursor particles was determined by direct determination of the amount of rRNA in the precursor particles, and from the labeling kinetics of their rRNA. The direct estimation indicated that about 2% of the total 23 S type RNA, and 3 to 5% of the total 16 S type RNA is harboured in precursor particles. In the kinetic experiments the specific activity of the nucleoside triphosphates and of the different ribosomal particles was followed after addition of a radioactive RNA precursor to the growth medium. The results were compared with a digital simulation of the flow of isotopes through the assembly pathways. This method indicated that approximately 2% of the total 23 S type RNA, as well as 2% of the total 16 S type RNA, is contained in the precursor particles.     

Domain conformation of tau protein studied by solution small-angle X-ray scattering

Tau is one of the two main proteins involved in the pathology of Alzheimer's disease via formation of beta-sheet rich intracellular aggregates named paired helical filaments (PHFs). Given that tau is a natively unfolded protein with no folded core (even upon binding to physiological partners such as microtubules), its structural analysis by high-resolution techniques has been difficult. In this study, employing solution small-angle X-ray scattering from the full length isoforms and from a variety of deletion and point mutants the conformation of tau in solution is structurally characterized. A recently developed ensemble optimization method was employed to generate pools of random models and to select ensembles of coexisting conformations, which fitted simultaneously the scattering data from the full length protein and deletion mutants. The analysis of the structural properties of these selected ensembles allowed us to extract information about residual structure in different domains of the native protein. The short deletion mutants containing the repeat domain (considered the core constituent of the PHFs) are significantly more extended than random coils, suggesting an extended conformation of the repeat domain. The longer tau constructs are comparable in size with the random coils, pointing to long-range contacts between the N- and C-termini compensating for the extension of the repeat domain. Moreover, most of the aggregation-promoting mutants did not show major differences in structure from their wild-type counterparts, indicating that their increased pathological effect is triggered only after an aggregation core has been formed.