The hydrodynamic and conformational properties of denatured proteins in dilute solutions

Published data on the characterization of unfolded proteins in dilute solutions in aqueous guanidine hydrochloride are analyzed to show that the data are not fit by either the random flight or wormlike chain models for linear chains. The analysis includes data on the intrinsic viscosity, root‐mean‐square radius of gyration, from small‐angle X‐ray scattering, and hydrodynamic radius, from the translational diffusion coefficient. It is concluded that residual structure consistent with that deduced from nuclear magnetic resonance on these solutions can explain the dilute solution results in a consistent manner through the presence of ring structures, which otherwise have an essentially flexible coil conformation. The ring structures could be in a state of continual flux and rearrangement. Calculation of the radius of gyration for the random‐flight model gives a similar reduction of this measure for chains joined at their endpoints, or those containing loop with two dangling ends, each one‐fourth the total length of the chain. This relative insensitivity to the details of the ring structure is taken to support the behavior observed across a range of proteins.     

Comparison of the three-dimensional molecular models of bovine submicellar caseins with small-angle X-ray scattering. Influence of protein hydration

To test the applicability of two energy-minimized, three-dimensional structures of the bovine casein submicelle, theoretical small-angle X-ray scattering curves in the presence and absence of water were compared to experimental data. The published method simulates molecular dynamics of proteins in solution by employing adjustable Debye-Waller temperature factors (B factors) for the protein, for the solvent, and for protein-bound water. The programs were first tested upon bovine pancreatic trypsin inhibitor beginning with its known X-ray crystal structure. To approximate the degree of protein hydration previously determined by NMR relaxation experiments (0.01 g water/g protein), 120 water molecules were docked into the large void of the-casein portion of the structure for both the symmetric and asymmetric casein submicelle models. To approximate hydrodynamic hydration (0.244 g water/g protein), 2703 water molecules were added to each of the above structures using the droplet algorithm in the Sybyl molecular modeling package. All structures were then energy-minimized and their solvation energies calculated. Theoretical small-angle X-ray scattering curves were calculated for all unhydrated and hydrated structures and compared with experimentally determined scattering profiles for submicellar casein. Best results were achieved with the 120-bound-water structure for both the symmetric and asymmetric submicelle models. Comparison of results for the protein submicelle models with those for the theoretical and literature values of bovine pancreatic trypsin inhibitor demonstrates the applicability of the methodology.Reference to a brand or firm name does not constitute endorsement by the U.S. Department of Agriculture over others of a similar nature not mentioned.     

Analytical ultracentrifugation combined with X-ray and neutron scattering: Experiment and modelling

Analytical ultracentrifugation and solution scattering provide different multi-parameter structural and compositional information on proteins. The joint application of the two methods supplements high resolution structural studies by crystallography and NMR. We summarise the procedures required to obtain equivalent ultracentrifugation and X-ray and neutron scattering data. The constrained modelling of ultracentrifugation and scattering data is important to confirm the experimental data analysis and yields families of best-fit molecular models for comparison with crystallography and NMR structures. This modelling of ultracentrifugation and scattering data is described in terms of starting models, their conformational randomisation in trial-and-error fits, and the identification of the final best-fit models. Seven applications of these methods are described to illustrate the current state-of-the-art. These include the determination of antibody solution structures (the human IgG4 subclass, and oligomeric forms of human IgA and its secretory component), the solution structures of the complement proteins of innate immunity (Factor H and C3/C3u) and their interactions with macromolecular ligands (C-reactive protein), and anionic polysaccharides (heparin). Complementary features of joint ultracentrifugation and scattering experiments facilitate an improved understanding of crystal structures (illustrated for C3/C3u, C-reactive protein and heparin). If a large protein or its complex cannot be crystallised, the joint ultracentrifugation-scattering approach provides a means to obtain an overall macromolecular structure.     

Hydrodynamic multibead modeling: problems, pitfalls, and solutions. 1. Ellipsoid models

The shape of macromolecules can be approximated by filling models, if both hydrodynamic and scattering properties should be predicted. Modeling of complex biological macromolecules, such as oligomeric proteins, or of molecule details calls for usage of many beads to preserve the original features. However, the calculation of precise values for structural and hydrodynamic parameters has to consider many problems and pitfalls. Among these, the huge number of beads required for modeling details and the choice of appropriate volume corrections for the calculation of intrinsic viscosities are pestering problems to date. As a first step to tackle these problems, various tests with multibead models (ellipsoids of different axial ratios) were performed. The agreement of the predicted molecular properties with those derived from whole-body approaches can be used as evaluation criteria. Modification of previously available versions of García de la Torre’s program HYDRO allows hydrodynamic modeling of macromolecules composed of a maximum of about 11,000 beads. Moreover, application of our recently suggested “reduced volume correction” enables a fast and efficient anticipation of intrinsic viscosities. Correct parameter predictions were obtained for all models analyzed. The data obtained were compared to the results of calculations based on HYDRO programs available to the public. The calculations revealed some unexpected results and allowed founded conclusions of general importance for precise calculations on multibead models (e.g., the requirement of calculations in the double-precision mode).     

Size and shape of the repetitive domain of high molecular weight wheat gluten proteins. II. Hydrodynamic studies

This study describes the hydrodynamic properties of the repetitive domain of high molecular weight (HMW) wheat proteins, which complement the small-angle scattering (SANS) experiments performed in the first paper of this series. The sedimentation coefficients, s(0), and diffusion coefficients, D(0), were obtained from the homologous HMW proteins dB1 and dB4 that were cloned from the gluten protein HMW Dx5, and expressed in Escherichia coli. Monodisperse conditions for accurate determination of s(0) and D(0), were obtained by screening a series of buffers using dynamic light scattering. For the first time, hydrodynamic parameters were obtained on monodisperse samples that enabled the determination of the monomeric size and shape. The hydrodynamic values determined on dB1 and dB4 were used to test the worm-like chain (WLC) model that was proposed in the SANS studies. The successful matching of two separately obtained hydrodynamic parameters of dB1 and dB4 using the WLC model provides further evidence for the WLC model. The small discrepancy between the hydrodynamic and scattering data, possibly coming from the excluded volume effect, was compensated by a solvation layer of 1-2 water molecules thick around the protein in the WLC model. The solvation of the central domain is much higher than those of the terminal domains of the HMW subunits. This difference emphasizes the dual role of HMW wheat gluten proteins in water-binding and aggregation.     

Hydrodynamic multibead modeling: problems, pitfalls, and solutions. 2. Proteins

The shape of macromolecules can be approximated by filling models, if both hydrodynamic and scattering properties should be predicted. Modeling of complex biological macromolecules, such as oligomeric proteins, or of molecule details calls for usage of many beads to preserve the original features. However, the calculation of precise values for structural and hydrodynamic parameters has to consider many problems and pitfalls. Among these, the huge number of beads required for modeling details and the choice of appropriate volume corrections for the calculation of intrinsic viscosities are pestering problems to date. As a first step to tackle these problems, various tests with multibead models (ellipsoids of different axial ratios) were performed. The agreement of the predicted molecular properties with those derived from whole-body approaches can be used as evaluation criteria. Modification of previously available versions of García de la Torre’s program HYDRO allows hydrodynamic modeling of macromolecules composed of a maximum of about 11,000 beads. Moreover, application of our recently suggested “reduced volume correction” enables a fast and efficient anticipation of intrinsic viscosities. Correct parameter predictions were obtained for all models analyzed. The data obtained were compared to the results of calculations based on HYDRO programs available to the public. The calculations revealed some unexpected results and allowed founded conclusions of general importance for precise calculations on multibead models (e.g., the requirement of calculations in the double-precision mode).     

Calculation of translational friction and intrinsic viscosity. II. Application to globular proteins.

The translational friction coefficients and intrinsic viscosities of four proteins (ribonuclease A, lysozyme, myoglobin, and chymotrypsinogen A) are calculated using atomic-level structural details. Inclusion of a 0.9-A-thick hydration shell allows calculated results for both hydrodynamic properties of each protein to reproduce experimental data. The use of detailed protein structures is made possible by relating translational friction and intrinsic viscosity to capacitance and polarizability, which can be calculated easily. The 0.9-A hydration shell corresponds to a hydration level of 0.3-0.4 g water/g protein. Hydration levels within this narrow range are also found by a number of other techniques such as nuclear magnetic resonance spectroscopy, infrared spectroscopy, calorimetry, and computer simulation. The use of detailed protein structures in predicting hydrodynamic properties thus allows hydrodynamic measurement to join the other techniques in leading to a unified picture of protein hydration. In contrast, earlier interpretations of hydrodynamic data based on modeling proteins as ellipsoids gave hydration levels that varied widely from protein to protein and thus challenged the existence of a unified picture of protein hydration.     

Modeling the hydration of proteins: prediction of structural and hydrodynamic parameters from X-ray diffraction and scattering data

The implications of protein-water interactions are of importance for understanding the solution behavior of proteins and for analyzing the fine structure of proteins in aqueous solution. Starting from the atomic coordinates, by bead modeling the scattering and hydrodynamic properties of proteins can be predicted reliably (Debye modeling, program HYDRO). By advanced modeling techniques the hydration can be taken into account appropriately: by some kind of rescaling procedures, by modeling a water shell, by iterative comparisons to experimental scattering curves (ab initio modeling) or by special hydration algorithms. In the latter case, the surface topography of proteins is visualized in terms of dot surface points, and the normal vectors to these points are used to construct starting points for placing water molecules in definite positions on the protein envelope. Bead modeling may then be used for shaping the individual atomic or amino acid residues and also for individual water molecules. Among the tuning parameters, the choice of the scaling factor for amino acid hydration and of the molecular volume of bound water turned out to be crucial. The number and position of bound water molecules created by our hydration modeling program HYDCRYST were compared with those derived from X-ray crystallography, and the capability to predict hydration, structural and hydrodynamic parameters (hydrated volume, radius of gyration, translational diffusion and sedimentation coefficients) was compared with the findings generated by the water-shell approach CRYSOL. If the atomic coordinates are unknown, ab initio modeling approaches based on experimental scattering curves can provide model structures for hydrodynamic predictions.     

Isolation and physical characterization of an exocellular polysaccharide

The physical properties of a polysaccharide produced by the lactic acid bacterium Lactococcus lactis subsp. cremoris strain NIZO B40 were investigated. Separation of the polysaccharide from most low molar mass compounds in the culture broth was performed by filtration processes. Residual proteins and peptides were removed by washing with a mixture of formic acid, ethanol, and water. Gel permeation chromatography (GPC) was used to size fractionate the polysaccharide. Fractions were analyzed by multiangle static light scattering in aqueous 0.10 M NaNO3 solutions from which a number- (Mn) and weight-averaged (Mw) molar mass of (1.47 +/- 0.06).10(3) and (1.62 +/- 0.07).10(3) kg/mol, respectively, were calculated so that Mw/Mn approximately 1.13. The number-averaged radius of gyration was found to be 86 +/- 2 nm. From dynamic light scattering an apparent z-averaged diffusion coefficient was obtained. Upon correcting for the contributions from intramolecular modes by extrapolating to zero wave vector a hydrodynamic radius of 86 +/- 4 nm was calculated. Theoretical models for random coil polymers show that this z-averaged hydrodynamic radius is consistent with the z-averaged radius of gyration, 97 +/- 3 nm, as found with GPC.     

Determination of domain structure of proteins from X-ray solution scattering

An ab initio method for building structural models of proteins from x-ray solution scattering data is presented. Simulated annealing is employed to find a chain-compatible spatial distribution of dummy residues which fits the experimental scattering pattern up to a resolution of 0.5 nm. The efficiency of the method is illustrated by the ab initio reconstruction of models of several proteins, with known and unknown crystal structure, from experimental scattering data. The new method substantially improves the resolution and reliability of models derived from scattering data and makes solution scattering a useful technique in large-scale structural characterization of proteins.     

Prediction of hydrodynamic and other solution properties of rigid proteins from atomic- and residue-level models

Here we extend the ability to predict hydrodynamic coefficients and other solution properties of rigid macromolecular structures from atomic-level structures, implemented in the computer program HYDROPRO, to models with lower, residue-level resolution. Whereas in the former case there is one bead per nonhydrogen atom, the latter contains one bead per amino acid (or nucleotide) residue, thus allowing calculations when atomic resolution is not available or coarse-grained models are preferred. We parameterized the effective hydrodynamic radius of the elements in the atomic- and residue-level models using a very large set of experimental data for translational and rotational coefficients (intrinsic viscosity and radius of gyration) for >50 proteins. We also extended the calculations to very large proteins and macromolecular complexes, such as the whole 70S ribosome. We show that with proper parameterization, the two levels of resolution yield similar and rather good agreement with experimental data. The new version of HYDROPRO, in addition to considering various computational and modeling schemes, is far more efficient computationally and can be handled with the use of a graphical interface.     

Trifluoroethanol-induced conformational transitions of proteins: insights gained from the differences between alpha-lactalbumin and ribonuclease A

The trifluoroethanol (TFE)-induced structural changes of two proteins widely used in folding experiments, bovine alpha-lactalbumin, and bovine pancreatic ribonuclease A, have been investigated. The experiments were performed using circular dichroism spectroscopy in the far- and near-UV region to monitor changes in the secondary and tertiary structures, respectively, and dynamic light scattering to measure the hydrodynamic dimensions and the intermolecular interactions of the proteins in different conformational states. Both proteins behave rather differently under the influence of TFE: alpha-lactalbumin exhibits a molten globule state at low TFE concentrations before it reaches the so-called TFE state, whereas ribonuclease A is directly transformed into the TFE state at TFE concentrations above 40% (v/v). The properties of the TFE-induced states are compared with those of equilibrium and kinetic intermediate states known from previous work to rationalize the use of TFE in yielding information about the folding of proteins. Additionally, we report on the properties of TFE/water and TFE/buffer mixtures derived from dynamic light scattering investigations under conditions used in our experiments.     

The polyprotein and FAR lipid binding proteins of nematodes: shape and monomer/dimer states in ligand-free and bound forms

Nematodes produce two classes of small, helix-rich fatty acid- and retinol-binding proteins whose structures and in vivo functions remain to be elucidated. These are the polyprotein allergens (NPA) and the FAR proteins. The solution properties of recombinant forms of these proteins from parasitic [Ascaris suum (As) and Onchocerca volvulus (Ov)] and free-living [Caenorhabditis elegans (Ce)] nematodes have been examined. Analytical ultracentrifugation (AUC) showed that, contrary to previous findings, the rAs-NPA-1A polyprotein unit (approximately 15 kDa) is a monomer, and this stoichiometry is unaltered by ligand (oleic acid) binding. The rOv-FAR-1 and rCe-FAR-5 proteins differ in that the former forms a tight dimer and the latter a monomer, and these oligomeric states are also unaffected by ligand binding or protein concentration. Sedimentation equilibrium experiments showed that the partial specific volume v of the unliganded proteins agree well with the value calculated from amino acid composition extrapolated to experimental temperature, and was unaffected upon ligand binding. Data from small-angle X-ray scattering (SAXS) indicated that both of the monomeric proteins rAs-NPA-1A and rCe-FAR-5 are globular, although slightly elongated and flattened. These data are in good agreement with shapes predicted from sedimentation velocity experiments and hydrodynamic bead modelling. On the basis of functional and secondary structural homology with the ligand-binding domain of the retinoic acid receptor RXRalpha, de novo atomic resolution structures for rAs-NPA-1A and rCe-FAR-5 have been constructed which are consistent with the SAXS and hydrodynamic data.     

Molecular modeling of the domain structure of C9 of human complement by neutron and X-ray solution scattering.

C9 is the most abundant component of the membrane attack complex of the complement system of immune defense. This is a typical mosaic protein with thrombospondin (TSR) and low density lipoprotein receptor (LDLr) domains at its N-terminus and an epidermal growth factor-like (EGF) domain at its C-terminus. Between these lies a perforin-like sequence. In order to define the arrangement in solution of these four moieties in C9, high-flux neutron and synchrotron X-ray solution scattering studies were carried out. The neutron radius of gyration RG at infinite contrast is 3.33 nm, and its cross-sectional RG (RXS) is 1.66 nm. Similar values were obtained by synchrotron X-ray scattering after allowance for radiation effects. Stuhrmann analyses showed that the neutron radial inhomogeneity of scattering density alpha is 35 X 10(-5) from the RG data and 16 X 10(-5) from the RXS data. These values are typical for soluble glycoproteins and show no evidence for the existence of any large hydrophobic surface patches on free C9 that might form contacts with lipids. Indirect transformation of the neutron and X-ray scattering curves into real space showed that C9 had a maximum dimension estimated at 12 +/- 2 nm, and this suggests that the lengths of 7-8 nm deduced from previous electron microscopy studies in vacuo are underestimated. Molecular modeling of the C9 scattering curves utilized small spheres in the Debye equation, in which the analyses were constrained by the known volumes of the four moieties of C9 and the known sizes of the TSR and EGF-like domains. The most likely models for C9 suggest that these four regions of C9 are arranged in a V-shaped structure, with an angle of 10 degrees between the two arms, each of length 11.1 nm. This structure has a more hydrophobic character between the two arms. The scattering model is fully consistent with hydrodynamic sedimentation data on C9. Similar V-shaped hydrodynamic models could be developed for C6, C7, C8, and C9 of complement. Such a compact structure is atypical of other multidomain complement proteins so far studied by solution scattering and is fully compatible with mechanisms in which C9 is postulated, on activation, to undergo a drastic unfolding of its domain structure and to expose a more hydrophobic surface which can be embedded into lipid bilayers.     

Global rigid body modeling of macromolecular complexes against small-angle scattering data

New methods to automatically build models of macromolecular complexes from high-resolution structures or homology models of their subunits or domains against x-ray or neutron small-angle scattering data are presented. Depending on the complexity of the object, different approaches are employed for the global search of the optimum configuration of subunits fitting the experimental data. An exhaustive grid search is used for hetero- and homodimeric particles and for symmetric oligomers formed by identical subunits. For the assemblies or multidomain proteins containing more then one subunit/domain per asymmetric unit, heuristic algorithms based on simulated annealing are used. Fast computational algorithms based on spherical harmonics representation of scattering amplitudes are employed. The methods allow one to construct interconnected models without steric clashes, to account for the particle symmetry and to incorporate information from other methods, on distances between specific residues or nucleotides. For multidomain proteins, addition of missing linkers between the domains is possible. Simultaneous fitting of multiple scattering patterns from subcomplexes or deletion mutants is incorporated. The efficiency of the methods is illustrated by their application to complexes of different types in several simulated and practical examples. Limitations and possible ambiguity of rigid body modeling are discussed and simplified docking criteria are provided to rank multiple models. The methods described are implemented in publicly available computer programs running on major hardware platforms.     

Size and structure of antigen-antibody complexes. Electron microscopy and light scattering studies

Size parameters of model antigen-antibody (Ag-Ab) complexes formed by the interaction of bovine serum albumin (BSA) and pairs of monoclonal anti-BSA antibodies (mAb) were evaluated by quasielastic light scattering, classical light scattering, and electron microscopy (EM). Mean values for the hydrodynamic radius, radius of gyration, and molecular weight were determined by light scattering. Detailed information regarding the molecular weight distribution and the presence of cycles or open chains was obtained with EM. Average molecular weights were calculated from the EM data, and the Porod-Kratky wormlike chain theory was used to model the conformational behavior of the Ag-mAb complexes. Ag-mAb complexes prepared from three different mAb pairs displayed significantly different properties as assessed by each of the techniques employed. Observations and size parameter calculations from EM photomicrographs were consistent with the results from light scattering. The differences observed between the mab pairs would not have been predicted by idealized thermodynamic models. These results suggest that the geometric constraints imposed by the individual epitope environment and/or the relative epitope location are important in determining the average size of complexes and the ratio of linear to cyclic complexes.     

Differences in spatial structures of the influenza virus M1 protein in crystal, solution and virion

Spatial structure of the influenza virus A/Puerto Rico/8/34 (PR8, subtype H1N1) M1 protein in a solution and composition of the virion was studied by tritium planigraphy technique. The special algorithm for modeling of the spatial structure is used to simulate the experiment, as well as a set of algorithms predicting secondary structure and disordered regions in proteins. Tertiary structures were refined using the program Rosetta. To compare the structures in solution and in virion, also used the X-ray diffraction data for NM-domain. The main difference between protein structure in solution and crystal is observed in the contact region of N- and M-domains, which are more densely packed in the crystalline state. Locations include the maximum label is almost identical to the unstructured regions of proteins predicted by bioinformatics analysis. These areas are concentrated in the C-domain and in the loop regions between the M-, N-, and C-domains. Analytical centrifugation and dynamic laser light scattering confirm data of tritium planigraphy. Anomalous hydrodynamic size, and low structuring of the M1 protein in solution were found. The multifunctionality of protein in the cell appears to be associated with its plastic tertiary structure, which provides at the expense of unstructured regions of contact with various molecules-partners.     

Hydrodynamic radii of native and denatured proteins measured by pulse field gradient NMR techniques

Pulse field gradient NMR methods have been used to determine the effective hydrodynamic radii of a range of native and nonnative protein conformations. From these experimental data, empirical relationships between the measured hydrodynamic radius (R(h)) and the number of residues in the polypeptide chain (N) have been established; for native folded proteins R(h) = 4.75N (0.29)A and for highly denatured states R(h) = 2.21N (0.57)A. Predictions from these equations agree well with experimental data from dynamic light scattering and small-angle X-ray or neutron scattering studies reported in the literature for proteins ranging in size from 58 to 760 amino acid residues. The predicted values of the hydrodynamic radii provide a framework that can be used to analyze the conformational properties of a range of nonnative states of proteins. Several examples are given here to illustrate this approach including data for partially structured molten globule states and for proteins that are unfolded but biologically active under physiological conditions. These reveal evidence for significant coupling between local and global features of the conformational ensembles adopted in such states. In particular, the effective dimensions of the polypeptide chain are found to depend significantly on the level of persistence of regions of secondary structure or features such as hydrophobic clusters within a conformational ensemble.     

Integration of small-angle X-ray scattering data into structural modeling of proteins and their assemblies

A major challenge in structural biology is to determine the configuration of domains and proteins in multidomain proteins and assemblies, respectively. All available data should be considered to maximize the accuracy and precision of these models. Small-angle X-ray scattering (SAXS) efficiently provides low-resolution experimental data about the shapes of proteins and their assemblies. Thus, we integrated SAXS profiles into our software for modeling proteins and their assemblies by satisfaction of spatial restraints. Specifically, we modeled the quaternary structures of multidomain proteins with structurally defined rigid domains as well as quaternary structures of binary complexes of structurally defined rigid proteins. In addition to SAXS profiles and the component structures, we used stereochemical restraints and an atomic distance-dependent statistical potential. The scoring function is optimized by a biased Monte Carlo protocol, including quasi-Newton and simulated annealing schemes. The final prediction corresponds to the best scoring solution in the largest cluster of many independently calculated solutions. To quantify how well the quaternary structures are determined based on their SAXS profiles, we used a benchmark of 12 simulated examples as well as an experimental SAXS profile of the homotetramer d-xylose isomerase. Optimization of the SAXS-dependent scoring function generally results in accurate models if sufficiently precise approximations for the constituent rigid bodies are available; otherwise, the best scoring models can have significant errors. Thus, SAXS profiles can play a useful role in the structural characterization of proteins and assemblies if they are combined with additional data and used judiciously. Our integration of a SAXS profile into modeling by satisfaction of spatial restraints will facilitate further integration of different kinds of data for structure determination of proteins and their assemblies.