Probing the Average Local Structure of Biomolecules Using Small-Angle Scattering and Scaling Laws

Small-angle neutron and x-ray scattering have become invaluable tools for probing the nanostructure of molecules in solution. It was recently shown that the definite integral of the scattering profile exhibits a scaling (power-law) behavior with respect to molecular mass. We derive the origin of this relationship, and discuss how the integrated scattering profile can be used to identify differing levels of disorder over local ≲30 Å length scales. We apply our analysis to globular and intrinsically disordered proteins.     

On the interpretation and prediction of X-ray scattering profiles of biomolecules in solution

If solution scattering curves can be accurately predicted from structural models, measurements can provide useful tests of predictions of secondary and tertiary structure. We have developed a computational technique for the prediction and interpretation of x-ray scattering profiles of biomolecules in solution. The method employs a Monte Carlo procedure for the generation of length distribution functions and provides predictions to moderate resolution (～5 Å). In addition to facilitating the assignment and interpretation of features in a solution scattering profile, the method also allows the elucidation of the role of protein motion in shaping the final scattering curve. The effect of protein motion on a scattering profile is investigated by generating scattering curves from several consecutive 0.147 ps atomic coordinate frames from a molecular dynamics simulation of the motion of bovine pancreatic trypsin inhibitor (BPTI) [McCammon, J. A. & Karplus, M. (1980) Annu. Rev. Phys. Chem. 31 , 29–45]. The theoretical approach is applied to chicken egg white lysozyme and BPTI, and the overall features in the resulting theoretical scattering profiles match well with the experimental solution scattering curves recorded on film. It is apparent from this study that the scattering profile prediction technique in conjunction with other experimental methods may have value in testing ideas of conformational change based on crystallographic studies; investigations of this type would include a comparison of predicted scattering curves generated from a variety of crystallographic models with an actual scattering profile of the biomolecule in solution.     

Structural Insights into Yeast DNA Polymerase δ by Small Angle X-ray Scattering

DNA polymerase δ (Polδ) is a multisubunit polymerase that plays an indispensable role in replication from yeast to humans. Polδ from Saccharomyces cerevisiae is composed of three subunits: Pol3, Pol31, and Pol32. Despite the elucidation of the structures and models of the individual subunits (or portions, thereof), the nature of their assembly remains unclear. We present here a small-angle X-ray scattering analysis of a yeast Polδ complex (Polδ_T) composed of Pol3, Pol31, and Pol32N (amino acids 1-103 of Pol32). From the small angle X-ray scattering global parameters and reconstructed envelopes, we show that Polδ_T adopts an elongated conformation with a radius of gyration (R_g) of ∼ 52 Å and a maximal dimension of ∼ 190 Å. We also propose an orientation for the accessory Pol31-Pol32N subunits relative to the Pol3 catalytic core that best agrees with the experimental scattering profile. The analysis also points to significant conformational variability that may allow Polδ to better coordinate its action with other proteins at the replication fork.     

Revisiting the bilayer structures of fluid phase phosphatidylglycerol lipids: Accounting for exchangeable hydrogens

We recently published two papers detailing the structures of fluid phase phosphatidylglycerol (PG) lipid bilayers (Ku?erka et al., 2012 J. Phys. Chem. B 116: 232–239; Pan et al., 2012 Biochim. Biophys. Acta Biomembr. 1818: 2135–2148), which were determined using the scattering density profile model. This hybrid experimental/computational technique utilizes molecular dynamics simulations to parse a lipid bilayer into components whose volume probabilities follow simple analytical functional forms. Given the appropriate scattering densities, these volume probabilities are then translated into neutron scattering length density (NSLD) and electron density (ED) profiles, which are used to jointly refine experimentally obtained small angle neutron and X-ray scattering data. However, accurate NSLD and ED profiles can only be obtained if the bilayer's chemical composition is known. Specifically, in the case of neutron scattering, the lipid's exchangeable hydrogens with aqueous D₂O must be accounted for, as they can have a measureable effect on the resultant lipid bilayer structures. This was not done in our above-mentioned papers. Here we report on the molecular structures of PG lipid bilayers by appropriately taking into account the exchangeable hydrogens. Analysis indicates that the temperature-averaged PG lipid areas decrease by 1.5 to 3.8 Å², depending on the lipid's acyl chain length and unsaturation, compared to PG areas when hydrogen exchange was not taken into account.     

Effects of macromolecular crowding on an intrinsically disordered protein characterized by small-angle neutron scattering with contrast matching

Small-angle neutron scattering was used to examine the effects of molecular crowding on an intrinsically disordered protein, the N protein of bacteriophage λ, in the presence of high concentrations of a small globular protein, bovine pancreatic trypsin inhibitor (BPTI). The N protein was labeled with deuterium, and the D₂O concentration of the solvent was adjusted to eliminate the scattering contrast between the solvent and unlabeled BPTI, leaving only the scattering signal from the unfolded protein. The scattering profile observed in the absence of BPTI closely matched that predicted for an ensemble of random conformations. With BPTI added to a concentration of 65 mg/mL, there was a clear change in the scattering profile representing an increase in the mass fractal dimension of the unfolded protein, from 1.7 to 1.9, as expected if crowding favors more compact conformations. The crowding protein also inhibited aggregation of the unfolded protein. At 130 mg/mL BPTI, however, the fractal dimension was not significantly different from that measured at the lower concentration, contrary to the predictions of models that treat the unfolded conformations as convex particles. These results are reminiscent of the behavior of polymers in concentrated melts, suggesting that these synthetic mixtures may provide useful insights into the properties of unfolded proteins under crowding conditions.     

Lateral packing of mineral crystals in bone collagen fibrils

Combined small-angle x-ray scattering and transmission electron microscopy studies of intramuscular fish bone (shad and herring) indicate that the lateral packing of nanoscale calcium-phosphate crystals in collagen fibrils can be represented by irregular stacks of platelet-shaped crystals, intercalated with organic layers of collagen molecules. The scattering intensity distribution in this system can be described by a modified Zernike-Prins model, taking preferred orientation effects into account. Using the model, the diffuse fan-shaped small-angle x-ray scattering intensity profile, dominating the equatorial region of the scattering pattern, could be quantitatively analyzed as a function of the degree of mineralization. The mineral platelets were found to be very thin (1.5 nm ∼ 2.0 nm), having a narrow thickness distribution. The thickness of the organic layers between adjacent mineral platelets within a stack is more broadly distributed with the average value varying from 6 nm to 10 nm, depending on the extent of mineralization. The two-dimensional analytical scheme also leads to quantitative information about the preferred orientation of mineral stacks and the average height of crystals along the crystallographic c axis.     

X-Ray Solution Scattering of Squid Heavy Meromyosin: Strengthening the Evidence for an Ancient Compact off State

The overall conformations of regulated myosins or heavy meromyosins from chicken/turkey, scallop, tarantula, limulus, and scorpion sources have been studied by a number of techniques, including electron microscopy, sedimentation, and pulsed electron paramagnetic resonance. These studies have indicated that the binding of regulatory ions changes the conformation of the molecule from a compact shape found in the “off” state of the muscle to extended relationships between the tail and independently mobile heads that predominate in the “on” state. Here we strengthen the argument for the generality of this conformational change by using small angle X-ray scattering on heavy meromyosin from squid. Small angle X-ray scattering allows the protein to be visualized in solution under mild and relatively physiological conditions, and squid differs from the other species studied by at least 500 million years of evolution. Analysis of the data indicates that upon addition of Ca²⁺ the radius of gyration increases. Differences in the squid “on” and “off” states are clearly distinguishable as bimodal and unimodal pair distance distribution functions respectively. These observations are consistent with a Ca²⁺-free squid heavy meromyosin that is compact, but which becomes extended when Ca²⁺ is bound. Further, the scattering profile derived from the current model of tarantula heavy meromyosin in the “off” state is in excellent agreement with the measured “off” state scattering profile for squid heavy meromyosin. The previous and current studies together provide significant evidence that regulated myosin''s compact off-state conformation is an ancient trait, inherited from a common ancestor during divergent evolution.     

A coarse graining approach to determine nucleic acid structures from small angle neutron scattering profiles in solution

We present a theoretical method to calculate the small angle neutron scattering profile of nucleic acid structures in solution. Our approach is sensitive to the sequence and the structure of the nucleic acid. In order to test our approach, we apply this method to the calculation of the experimental scattered intensity of the decamer d(CCAACGTTGG)₂ in H₂O. This sequence was specifically chosen for this study as it is believed to adopt a canonical B-form structure in 0.3 M NaCl. We find that not only will our methodology reproduce the experimental scattered intensity for this sequence, but our method will also discriminate between B-, A- and Z-form DNA. By studying the scattering profile of this structure in 0.5 and 1.0 M NaCl, we are also able to identify tetraplex and other similar oligomers formation and to model the complex using the experimental scattering data in conjunction with our methodology.     

Contrast variation studies of clathrin coated vesicles by small-angle neutron scattering

Structural information on clathrin coated vesicles has been obtained by small angle neutron scattering using contrast variation. A characteristic peak in the neutron scattering profile, which is apparent in 75 % D₂O, as well as in H₂O, disappears when contrast matching the protein component of the coated vesicles in 42% D₂O. Neutron, as well as dynamic, light scattering give a coated vesicle size of about 900 Å in H₂O and D₂O, but for neutron scattering the diameter decreases when matching out the protein coat of the clathrin coated vesicles. From the match point for the clathrin coated vesicles it is demonstrated that the clathrin cages do contain internal membrane. The mass of 34 MD and composition of 75% protein and 25% lipid found from the analysis of the small-angle scattering data are both in good agreement with the values reported in the literature. Electron microscopy gives an average outer diameter of 880 Å for the coated vesicles and an average diameter of 460 Å for the vesicle itself. Offprint requests to: Correspondence to: R. Bauer     

A non-invasive laser technique for characterisation of hybridoma suspensions in stirred vessels

Summary A novel optical method based on the analysis of the radial light intensity profile from a Laser source (HeNe 632.8 nm) is proposed and its use with hybridoma cells in suspension described. The technique enables direct determination of extinction (α) and scattering coefficient at 90 degrees (β) of the suspension, which are shown to vary during a batch culture and under different agitation conditions.     

Disposition of ceramide in model lipid membranes determined by neutron diffraction

The lipid matrix present in the uppermost layer of the skin, the stratum corneum, plays a crucial role in the skin barrier function. The lipids are organized into two lamellar phases. To gain more insight into the molecular organization of one of these lamellar phases, we performed neutron diffraction studies. In the diffraction pattern, five diffraction orders were observed attributed to a lamellar phase with a repeat distance of 5.4 nm. Using contrast variation, the scattering length density profile could be calculated showing a typical bilayer arrangement. To obtain information on the arrangement of ceramides in the unit cell, a mixture that included a partly deuterated ceramide was also examined. The scattering length density profile of the 5.4-nm phase containing this deuterated ceramide demonstrated a symmetric arrangement of the ceramides with interdigitating acyl chains in the center of the unit cell.     

Effect of Oxidation on the Structure of Human Low- and High-Density Lipoproteins

This work presents a controlled study of low-density lipoprotein (LDL) and high-density lipoprotein (HDL) structural changes due to in vitro oxidation with copper ions. The changes were studied by small-angle x-ray scattering (SAXS) and dynamic light scattering (DLS) techniques in the case of LDL and by SAXS, DLS, and Z-scan (ZS) techniques in the case of HDL. SAXS data were analyzed with a to our knowledge new deconvolution method. This method provides the electron density profile of the samples directly from the intensity scattering of the monomers. Results show that LDL particles oxidized for 18 h show significant structural changes when compared to nonoxidized particles. Changes were observed in the electrical density profile, in size polydispersity, and in the degree of flexibility of the APO-B protein on the particle. HDL optical results obtained with the ZS technique showed a decrease of the amplitude of the nonlinear optical signal as a function of oxidation time. In contrast to LDL results reported in the literature, the HDL ZS signal does not lead to a complete loss of nonlinear optical signal after 18 h of copper oxidation. Also, the SAXS results did not indicate significant structural changes due to oxidation of HDL particles, and DLS results showed that a small number of oligomers formed in the sample oxidized for 18 h. All experimental results for the HDL samples indicate that this lipoprotein is more resistant to the oxidation process than are LDL particles.     

The influence of the blood vessel diameter on the full scattering profile from cylindrical tissues: experimental evidence for the shielding effect

Optical methods for detecting physiological state based on light–tissue interaction are noninvasive, inexpensive, simplistic, and thus very useful. The blood vessels in human tissue are the main cause of light absorbing and scattering. Therefore, the effect of blood vessels on light–tissue interactions is essential for optically detecting physiological tissue state, such as oxygen saturation, blood perfusion and blood pressure. We have previously suggested a new theoretical and experimental method for measuring the full scattering profile, which is the angular distribution of light intensity, of cylindrical tissues. In this work we will present experimental measurements of the full scattering profile of heterogenic cylindrical phantoms that include blood vessels. We show, for the first time that the vessel diameter influences the full scattering profile, and found higher reflection intensity for larger vessel diameters accordance to the shielding effect. For an increase of 60% in the vessel diameter the light intensity in the full scattering profile above 90° is between 9% to 40% higher, depending on the angle. By these results we claim that during respiration, when the blood‐vessel diameter changes, it is essential to consider the blood‐vessel diameter distribution in order to determine the optical path in tissues.

A CT scan of the measured silicon‐based phantoms. The phantoms contain the same blood volume in different blood‐vessel diameters.     

BCL::SAXS: GPU accelerated Debye method for computation of small angle X‐ray scattering profiles

Small angle X‐ray scattering (SAXS) is an experimental technique used for structural characterization of macromolecules in solution. Here, we introduce BCL::SAXS—an algorithm designed to replicate SAXS profiles from rigid protein models at different levels of detail. We first show our derivation of BCL::SAXS and compare our results with the experimental scattering profile of hen egg white lysozyme. Using this protein we show how to generate SAXS profiles representing: (1) complete models, (2) models with approximated side chain coordinates, and (3) models with approximated side chain and loop region coordinates. We evaluated the ability of SAXS profiles to identify a correct protein topology from a non‐redundant benchmark set of proteins. We find that complete SAXS profiles can be used to identify the correct protein by receiver operating characteristic (ROC) analysis with an area under the curve (AUC) > 99%. We show how our approximation of loop coordinates between secondary structure elements improves protein recognition by SAχS for protein models without loop regions and side chains. Agreement with SAXS data is a necessary but not sufficient condition for structure determination. We conclude that experimental SAXS data can be used as a filter to exclude protein models with large structural differences from the native. Proteins 2015; 83:1500–1512. © 2015 Wiley Periodicals, Inc.     

Effect of Oxidation on the Structure of Human Low- and High-Density Lipoproteins

This work presents a controlled study of low-density lipoprotein (LDL) and high-density lipoprotein (HDL) structural changes due to in vitro oxidation with copper ions. The changes were studied by small-angle x-ray scattering (SAXS) and dynamic light scattering (DLS) techniques in the case of LDL and by SAXS, DLS, and Z-scan (ZS) techniques in the case of HDL. SAXS data were analyzed with a to our knowledge new deconvolution method. This method provides the electron density profile of the samples directly from the intensity scattering of the monomers. Results show that LDL particles oxidized for 18 h show significant structural changes when compared to nonoxidized particles. Changes were observed in the electrical density profile, in size polydispersity, and in the degree of flexibility of the APO-B protein on the particle. HDL optical results obtained with the ZS technique showed a decrease of the amplitude of the nonlinear optical signal as a function of oxidation time. In contrast to LDL results reported in the literature, the HDL ZS signal does not lead to a complete loss of nonlinear optical signal after 18 h of copper oxidation. Also, the SAXS results did not indicate significant structural changes due to oxidation of HDL particles, and DLS results showed that a small number of oligomers formed in the sample oxidized for 18 h. All experimental results for the HDL samples indicate that this lipoprotein is more resistant to the oxidation process than are LDL particles.     

How random is a highly denatured protein?

There has been renewed interest in determining the physicochemical properties of denatured states of proteins. In many denatured states there is evidence for the existence of nonrandom configurational distributions. Here we examine the small-angle neutron scattering profile of yeast phosphoglycerate kinase in the native state and in highly denaturing conditions. We show that the denatured protein scattering profile can be interpreted using a model developed for synthetic polymers in which the chain behaves as a random coil in a good solvent, i.e. with excluded volume interactions. The implications of this result for our appreciation of the protein folding process are discussed.     

Zirconium Nitride for Plasmonic Cloaking of Visible Nanowire Photodetectors

Light scattered by a photodetector disturbs the probing field, resulting in noise. Cloaking is an effective method to reduce this noise. Here we investigate theoretically an emerging plasmonic material, zirconium nitride (ZrN), as a plasmonic cloak for silicon (Si) nanowire-based photodetectors and compare it with a traditional plasmonic material, gold (Au). Using Mie formalism, we have obtained the scattering cancelation across the visible spectrum. We found that ZrN cloaks produce a significant decrease in the scattering from bare Si nanowires, which is 40% greater than that obtained with Au cloaks in the wavelength region of 400–500 nm. The scattering cancelations become comparable at 550 nm, with Au providing a better scattering cancelation compared to ZrN over the wavelength region of 600–700 nm. To include the absorption and provide a measure of overall performance on noise reduction, a figure of merit (FOM), defined as the ratio of the absorption efficiency and the scattering efficiency of the cloaked nanowire to that of the bare Si nanowire, was calculated. We show that the optimized ZrN cloak provides up to 3 times enhancement of the FOM over a bare Si NW and a 60% improvement over an optimized Au-cloaked NW, in the wavelength region of 400–500 nm. An optimized Au-cloaked NW shows up to 17.69 times improvement in the wavelength region of 600–700 nm over a bare Si NW and up to a 2.7 times improvement over an optimized ZrN-cloaked NW. We also predicted the optimal dimensions for the cloaked NWs with respect to the largest FOM at various wavelengths between 400 and 650 nm.

     

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.     

Clathrin triskelia show evidence of molecular flexibility

The clathrin triskelion, which is a three-legged pinwheel-shaped heteropolymer, is a major component in the protein coats of certain post-Golgi and endocytic vesicles. At low pH, or at physiological pH in the presence of assembly proteins, triskelia will self-assemble to form a closed clathrin cage, or “basket”. Recent static light scattering and dynamic light scattering studies of triskelia in solution showed that an individual triskelion has an intrinsic pucker similar to, but differing from, that inferred from a high resolution cryoEM structure of a triskelion in a clathrin basket. We extend the earlier solution studies by performing small-angle neutron scattering (SANS) experiments on isolated triskelia, allowing us to examine a higher q range than that probed by static light scattering. Results of the SANS measurements are consistent with the light scattering measurements, but show a shoulder in the scattering function at intermediate q values (0.016 Å⁻¹), just beyond the Guinier regime. This feature can be accounted for by Brownian dynamics simulations based on flexible bead-spring models of a triskelion, which generate time-averaged scattering functions. Calculated scattering profiles are in good agreement with the experimental SANS profiles when the persistence length of the assumed semiflexible triskelion is close to that previously estimated from the analysis of electron micrographs.