A simple genetic algorithm for the optimization of multidomain protein homology models driven by NMR residual dipolar coupling and small angle <Emphasis Type="Italic">X</Emphasis>-ray scattering data

Most proteins comprise several domains and/or participate in functional complexes. Owing to ongoing structural genomic projects, it is likely that it will soon be possible to predict, with reasonable accuracy, the conserved regions of most structural domains. Under these circumstances, it will be important to have methods, based on simple-to-acquire experimental data, that allow to build and refine structures of multi-domain proteins or of protein complexes from homology models of the individual domains/proteins. It has been recently shown that small angle X-ray scattering (SAXS) and NMR residual dipolar coupling (RDC) data can be combined to determine the architecture of such objects when the X-ray structures of the domains are known and can be considered as rigid objects. We developed a simple genetic algorithm to achieve the same goal, but by using homology models of the domains considered as deformable objects. We applied it to two model systems, an S1KH bi-domain of the NusA protein and the γS-crystallin protein. Despite its simplicity our algorithm is able to generate good solutions when driven by SAXS and RDC data.     

Quaternary structure built from subunits combining NMR and small-angle x-ray scattering data

A new principle in constructing molecular complexes from the known high-resolution domain structures joining data from NMR and small-angle x-ray scattering (SAXS) measurements is described. Structure of calmodulin in complex with trifluoperazine was built from N- and C-terminal domains oriented based on residual dipolar couplings measured by NMR in a dilute liquid crystal, and the overall shape of the complex was derived from SAXS data. The residual dipolar coupling data serves to reduce angular degrees of freedom, and the small-angle scattering data serves to confine the translational degrees of freedom. The complex built by this method was found to be consistent with the known crystal structure. The study demonstrates how approximate tertiary structures of modular proteins or quaternary structures composed of subunits can be assembled from high-resolution structures of domains or subunits using mutually complementary NMR and SAXS data.     

Note on the Theory of X-Ray Diffraction by Spherical Shell Structures

An equation is derived, which connects two functions P(r) and g(x), the first being related to the scattering intensity by a simple transformation, the second to the elctron density distribution of a spherically symmetric structure. This relation seems to be a suitable starting point for an analysis of shell structures from diffraction patterns.     

A simple procedure to evaluate the efficiency of bio-macromolecular rigid-body refinement by small-angle scattering

A simple and rapid procedure is presented that enables evaluation and visualization of refinement efficiency for bio-macromolecular complexes consisting of two subunits in a given orientation by using small-angle scattering. Subunit orientations within a complex can be provided in practice by NMR residual dipolar couplings, an approach that has been combined with increasing success to complement small-angle data. The procedure is illustrated by applying it to several systems composed of two simple geometric bodies (ellipsoids) and to protein complexes from the protein data bank that vary in subunit size and anisometry. The effects of the experimental small-angle scattering range (Q-range) and data noise level on the refinement efficiency are investigated and discussed. The procedure can be used in two ways: (1) either as a quick preliminary test to probe the refinement capacity expected for a given bio-macromolecular complex prior to sophisticated and time-consuming experiments and data analysis, or (2) as an a posteriori check of the stability and accuracy of a refined model and for illustration of the residual degrees of freedom of the subunit positions that are in agreement with both small-angle data and restraints on subunit orientation (as provided, e.g., by NMR).     

Machine Learning Methods for X-Ray Scattering Data Analysis from Biomacromolecular Solutions

Small-angle x-ray scattering (SAXS) of biological macromolecules in solutions is a widely employed method in structural biology. SAXS patterns include information about the overall shape and low-resolution structure of dissolved particles. Here, we describe how to transform experimental SAXS patterns to feature vectors and how a simple k-nearest neighbor approach is able to retrieve information on overall particle shape and maximal diameter (D_max) as well as molecular mass directly from experimental scattering data. Based on this transformation, we develop a rapid multiclass shape-classification ranging from compact, extended, and flat categories to hollow and random-chain-like objects. This classification may be employed, e.g., as a decision block in automated data analysis pipelines. Further, we map protein structures from the Protein Data Bank into the classification space and, in a second step, use this mapping as a data source to obtain accurate estimates for the structural parameters (D_max, molecular mass) of the macromolecule under study based on the experimental scattering pattern alone, without inverse Fourier transform for D_max. All methods presented are implemented in a Fortran binary DATCLASS, part of the ATSAS data analysis suite, available on Linux, Mac, and Windows and free for academic use.     

Analysis of self-associating proteins by singular value decomposition of solution scattering data

We describe a method by which a single experiment can reveal both association model (pathway and constants) and low-resolution structures of a self-associating system. Small-angle scattering data are collected from solutions at a range of concentrations. These scattering data curves are mass-weighted linear combinations of the scattering from each oligomer. Singular value decomposition of the data yields a set of basis vectors from which the scattering curve for each oligomer is reconstructed using coefficients that depend on the association model. A search identifies the association pathway and constants that provide the best agreement between reconstructed and observed data. Using simulated data with realistic noise, our method finds the correct pathway and association constants. Depending on the simulation parameters, reconstructed curves for each oligomer differ from the ideal by 0.05-0.99% in median absolute relative deviation. The reconstructed scattering curves are fundamental to further analysis, including interatomic distance distribution calculation and low-resolution ab initio shape reconstruction of each oligomer in solution. This method can be applied to x-ray or neutron scattering data from small angles to moderate (or higher) resolution. Data can be taken under physiological conditions, or particular conditions (e.g., temperature) can be varied to extract fundamental association parameters (ΔH_ass, ΔS_ass).     

Structural characterization of intramolecular Hg(2+) transfer between flexibly linked domains of mercuric ion reductase

The enzyme mercuric ion reductase MerA is the central component of bacterial mercury resistance encoded by the mer operon. Many MerA proteins possess metallochaperone-like N-terminal domains (NmerA) that can transfer Hg²⁺ to the catalytic core domain (Core) for reduction to Hg⁰. These domains are tethered to the homodimeric Core by ∼ 30-residue linkers that are susceptible to proteolysis, the latter of which has prevented characterization of the interactions of NmerA and the Core in the full-length protein. Here, we report purification of homogeneous full-length MerA from the Tn21 mer operon using a fusion protein construct and combine small-angle X-ray scattering and small-angle neutron scattering with molecular dynamics simulation to characterize the structures of full-length wild-type and mutant MerA proteins that mimic the system before and during handoff of Hg²⁺ from NmerA to the Core. The radii of gyration, distance distribution functions, and Kratky plots derived from the small-angle X-ray scattering data are consistent with full-length MerA adopting elongated conformations as a result of flexibility in the linkers to the NmerA domains. The scattering profiles are best reproduced using an ensemble of linker conformations. This flexible attachment of NmerA may facilitate fast and efficient removal of Hg²⁺ from diverse protein substrates. Using a specific mutant of MerA allowed the formation of a metal-mediated interaction between NmerA and the Core and the determination of the position and relative orientation of NmerA to the Core during Hg²⁺ handoff.     

Macromolecular docking restrained by a small angle X-ray scattering profile

While many structures of single protein components are becoming available, structural characterization of their complexes remains challenging. Methods for modeling assembly structures from individual components frequently suffer from large errors, due to protein flexibility and inaccurate scoring functions. However, when additional information is available, it may be possible to reduce the errors and compute near-native complex structures. One such type of information is a small angle X-ray scattering (SAXS) profile that can be collected in a high-throughput fashion from a small amount of sample in solution. Here, we present an efficient method for protein–protein docking with a SAXS profile (FoXSDock): generation of complex models by rigid global docking with PatchDock, filtering of the models based on the SAXS profile, clustering of the models, and refining the interface by flexible docking with FireDock. FoXSDock is benchmarked on 124 protein complexes with simulated SAXS profiles, as well as on 6 complexes with experimentally determined SAXS profiles. When induced fit is less than 1.5 Å interface C_α RMSD and the fraction residues of missing from the component structures is less than 3%, FoXSDock can find a model close to the native structure within the top 10 predictions in 77% of the cases; in comparison, docking alone succeeds in only 34% of the cases. Thus, the integrative approach significantly improves on molecular docking alone. The improvement arises from an increased resolution of rigid docking sampling and more accurate scoring.     

Assessing the Conformational Changes of pb5, the Receptor-binding Protein of Phage T5, upon Binding to Its Escherichia coli Receptor FhuA

Within tailed bacteriophages, interaction of the receptor-binding protein (RBP) with the target cell triggers viral DNA ejection into the host cytoplasm. In the case of phage T5, the RBP pb5 and the receptor FhuA, an outer membrane protein of Escherichia coli, have been identified. Here, we use small angle neutron scattering and electron microscopy to investigate the FhuA-pb5 complex. Specific deuteration of one of the partners allows the complete masking in small angle neutron scattering of the surfactant and unlabeled proteins when the complex is solubilized in the fluorinated surfactant F₆-DigluM. Thus, individual structures within a membrane protein complex can be described. The solution structure of FhuA agrees with its crystal structure; that of pb5 shows an elongated shape. Neither displays significant conformational changes upon interaction. The mechanism of signal transduction within phage T5 thus appears different from that of phages binding cell wall saccharides, for which structural information is available.     

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.     

The structure of psi DNA

In concentrated solutions of neutral or anionic polymers (and an adequate cation concentration), DNA condenses into a compact state, which is of interest for its possible relevance to chromosome structure and the packing of DNA in viruses. The X-ray scattering of DNA condensed in this way has been examined with respect to the secondary structure of the helix and the tertiary structure of the compact state. Measurements have also been made with dense aqueous gels of DNA in the absence of poly(ethylene oxide) at ordinary salt concentrations and in 6·0 M-LiCl. All preparations exhibit a well-defined interhelical spacing, implying substantial parallelism, but no lattice spacings higher than first order are observed. Comparison with calculated scattering curves for disoriented helical segments indicates that a structure very close to the B fiber structure prevails in all preparations. No significant contribution from the A or C fiber structures can be detected in either the condensed preparations or the LiCl solutions. Thus there is no basis for attributing the origin of the strongly anomalous circular dichroism spectra to a secondary structure significantly different from that in dilute solution. The decrease in interhelix spacing with increasing polymer concentration is in reasonable accord with expectation on the basis of excluded volume interactions. There is improved short-range order in the polymer-induced compact state as compared with the simple solution having the same interhelix spacing.The results are in reasonably good agreement with expectation for a folded chain structure of the compact state, similar to the usual mode of crystallization of simple linear polymers. There is no evidence for supercoiling.     

Structure of the scaffold in bacteriophage lambda preheads removal of the scaffold leads to a change of the prehead shell

Small angle X-ray scattering was performed on unprocessed and processed preheads, intermediates in the morphogenesis of bacteriophage λ heads. Unprocessed preheads possess an internal structure (scaffold), necessary for efficient assembly of closed shells. Processed preheads, formed after removal of the scaffold, are able to pack and cut the viral DNA in vitro. Our data show that the scaffold fills out the inside of the shell in an almost (but not completely) homogeneous fashion; structures of the scaffold with the bulk of the mass in a small core inside the shell can be excluded. Unprocessed preheads are larger than processed ones. A change in shell architecture takes place upon transition from unprocessed to processed prehead; the shell becomes roughened up. Shrinking of the shell as well as roughening up can be triggered by accidental partial degradation of the scaffold. The lattice constant of type A polyheads is in agreement with the lattice constant derived from our icosahedral models of the shell, indicating a close relationship between processed preheads and type A polyheads. This observation, together with the type of subunit clustering found, leads us to propose a simple model for the interaction of prehead shell and protein pD, which stabilizes phage DNA after packaging.     

Determination of protein oligomeric structure from small‐angle X‐ray scattering

Small‐angle X‐ray scattering (SAXS) is useful for determining the oligomeric states and quaternary structures of proteins in solution. The average molecular mass in solution can be calculated directly from a single SAXS curve collected on an arbitrary scale from a sample of unknown protein concentration without the need for beamline calibration or protein standards. The quaternary structure in solution can be deduced by comparing the experimental SAXS curve to theoretical curves calculated from proposed models of the oligomer. This approach is especially robust when the crystal structure of the target protein is known, and the candidate oligomer models are derived from the crystal lattice. When SAXS data are obtained at multiple protein concentrations, this analysis can provide insight into dynamic self‐association equilibria. Herein, we summarize the computational methods that are used to determine protein molecular mass and quaternary structure from SAXS data. These methods are organized into a workflow and demonstrated with four case studies using experimental SAXS data from the published literature.     

Propensities,probabilities, and the Boltzmann hypothesis

The relative strengths of interactions involving polypeptide chains can be estimated with reasonable accuracy with statistical potentials, free-energy functions derived from the frequency of occurrence of structural arrangements of residues or atoms in collections of protein structures. Recent published work has shown that the energetics of side-chain/backbone interactions can be modeled by the phi/psi propensities of the 20 amino acids. In this report, the more commonly used phi/psi probabilities are demonstrated to fail in evaluating the free energies of protein conformations because of an overriding preference for all helical structures. Comparison of the hypothetical reactions implied by these two different statistics-propensities versus probabilities-leads to the conclusion that the Boltzmann hypothesis may only be applicable for the calculation of statistical potentials after the starting conformation has been specified. This conclusion supports a simple conjecture: The surprising success of the Boltzmann hypothesis in explaining the energetics of protein structures is a direct consequence of a real equilibrium, one extending over evolutionary time that has maintained the stability of each protein within a narrow range of values.     

Consistent picture of the reversible thermal unfolding of hen egg-white lysozyme from experiment and molecular dynamics

Synchrotron radiation circular dichroism, Fourier transform infrared, and nuclear magnetic resonance spectroscopies, and small-angle x-ray scattering were used to monitor the reversible thermal unfolding of hen egg white lysozyme. The results were compared with crystal structures and high- and low-temperature structures derived from molecular-dynamics calculations. The results of both experimental and computational methods indicate that the unfolding process starts with the loss of β-structures followed by the reversible loss of helix content from ∼40% at 20°C to 27% at 70°C and ∼20% at 77°C, beyond which unfolding becomes irreversible. Concomitantly there is a reversible increase in the radius of gyration of the protein from 15 Å to 18 Å. The reversible decrease in forward x-ray scattering demonstrates a lack of aggregation upon unfolding, suggesting the change is due to a larger dilation of hydration water than of bulk water. Molecular-dynamics simulations suggest a similar sequence of events and are in good agreement with the ¹H^N chemical shift differences in nuclear magnetic resonance. This study demonstrates the power of complementary methods for elucidating unfolding/refolding processes and the nature of both the unfolded structure, for which there is no crystallographic data, and the partially unfolded forms of the protein that can lead to fibril formation and disease.     

Application of Dirichlet process mixture model to the identification of spin systems in protein NMR spectra

Protein structure determination using NMR is dependent on experimentally acquired distance restraints. Often, however, an insufficient number of these restraints are available for determining a protein’s correct fold, much less its detailed three-dimensional structure. In consideration of this problem, we propose a simple means to acquire supplemental structural restraints from protein surface accessibilities using solvent saturation transfer to proteins (SSTP), based on the principles of paramagnetic chemical-exchange saturation transfer. Here, we demonstrate the utility of SSTP in structure calculations of two proteins, TSG101 and ubiquitin. The observed SSTP was found to be directly proportional to solvent accessibility. Since SSTP does not involve the direct excitation of water, which compromises the analysis of protein protons entangled in the breadth of the water resonance, it has an advantage over conventional water-based magnetization transfers. Inclusion of structural restraints derived from SSTP improved both the precision and accuracy of the final protein structures in comparison to those determined by traditional approaches, when using minimal amounts of additional structural data. Furthermore, we show that SSTP can detect weak protein–protein interactions which are unobservable by chemical shift perturbations.     

Architectures of Whole-Module and Bimodular Proteins from the 6-Deoxyerythronolide B Synthase

The 6-deoxyerythronolide B synthase (DEBS) is a prototypical assembly line polyketide synthase produced by the actinomycete Saccharopolyspora erythraea that synthesizes the macrocyclic core of the antibiotic erythromycin 6-deoxyerythronolide B. The megasynthase is a 2-MDa trimeric complex composed of three unique homodimers assembled from the gene products DEBS1, DEBS2, and DEBS3, which are housed within the erythromycin biosynthetic gene cluster. Each homodimer contains two clusters of catalytically independent enzymatic domains, each referred to as a module, which catalyzes one round of polyketide chain extension and modification. Modules are named sequentially to indicate the order in which they are utilized during synthesis of 6-deoxyerythronolide B. We report small-angle X-ray scattering (SAXS) analyses of a whole module and a bimodule from DEBS, as well as a set of domains for which high-resolution structures are available. In all cases, the solution state was probed under previously established conditions ensuring that each protein is catalytically active. SAXS data are consistent with atomic-resolution structures of DEBS fragments. Therefore, we used the available high-resolution structures of DEBS domains to model the architectures of the larger protein assemblies using rigid-body refinement. Our data support a model in which the third module of DEBS forms a disc-shaped structure capable of caging the acyl carrier protein domain proximal to each active site. The molecular envelope of DEBS3 is a thin elongated ellipsoid, and the results of rigid-body modeling suggest that modules 5 and 6 stack collinearly along the 2-fold axis of symmetry.