SCT: a suite of programs for comparing atomistic models with small-angle scattering data

The SCR-17 and SCR-18 glycans in human complement factor H enhance its regulatory function

Human complement factor H (CFH) plays a central role in regulating activated C3b to protect host cells. CFH contain 20 short complement regulator (SCR) domains and eight N-glycosylation sites. The N-terminal SCR domains mediate C3b degradation while the C-terminal CFH domains bind to host cell surfaces to protect these. Our earlier study of Pichia-generated CFH fragments indicated a self-association site at SCR-17/18 that comprises a dimerization site for human factor H. Two N-linked glycans are located on SCR-17 and SCR-18. Here, when we expressed SCR-17/18 without glycans in an Escherichia coli system, analytical ultracentrifugation showed that no dimers were now formed. To investigate this novel finding, full-length CFH and its C-terminal fragments were purified from human plasma and Pichia pastoris respectively, and their glycans were enzymatically removed using PNGase F. Using size-exclusion chromatography, mass spectrometry, and analytical ultracentrifugation, SCR-17/18 from Pichia showed notably less dimer formation without its glycans, confirming that the glycans are necessary for the formation of SCR-17/18 dimers. By surface plasmon resonance, affinity analyses interaction showed decreased binding of deglycosylated full-length CFH to immobilized C3b, showing that CFH glycosylation enhances the key CFH regulation of C3b. We conclude that our study revealed a significant new aspect of CFH regulation based on its glycosylation and its resulting dimerization.

Using atomistic solution scattering modelling to elucidate the role of the Fc glycans in human IgG4

Human immunoglobulin G (IgG) exists as four subclasses IgG1-4, each of which has two Fab subunits joined by two hinges to a Fc subunit. IgG4 has the shortest hinge with 12 residues. The Fc subunit has two glycan chains, but the importance of glycosylation is not fully understood in IgG4. Here, to evaluate the stability and structure of non-glycosylated IgG4, we performed a multidisciplinary structural study of glycosylated and deglycosylated human IgG4 A33 for comparison with our similar study of human IgG1 A33. After deglycosylation, IgG4 was found to be monomeric by analytical ultracentrifugation; its sedimentation coefficient of 6.52 S was reduced by 0.27 S in reflection of its lower mass. X-ray and neutron solution scattering showed that the overall Guinier radius of gyration RG and its cross-sectional values after deglycosylation were almost unchanged. In the P(r) distance distribution curves, the two M1 and M2 peaks that monitor the two most common distances within IgG4 were unchanged following deglycosylation. Further insight from Monte Carlo simulations for glycosylated and deglycosylated IgG4 came from 111,382 and 117,135 possible structures respectively. Their comparison to the X-ray and neutron scattering curves identified several hundred best-fit models for both forms of IgG4. Principal component analyses showed that glycosylated and deglycosylated IgG4 exhibited different conformations from each other. Within the constraint of unchanged RG and M1-M2 values, the glycosylated IgG4 models showed more restricted Fc conformations compared to deglycosylated IgG4, but no other changes. Kratky plots supported this interpretation of greater disorder upon deglycosylation, also observed in IgG1. Overall, these more variable Fc conformations may demonstrate a generalisable impact of deglycosylation on Fc structures, but with no large conformational changes in IgG4 unlike those seen in IgG1.

Insight into structural biophysics from solution X-ray scattering

The current challenges of structural biophysics include determining the structure of large self-assembled complexes, resolving the structure of ensembles of complex structures and their mass fraction, and unraveling the dynamic pathways and mechanisms leading to the formation of complex structures from their subunits. Modern synchrotron solution X-ray scattering data enable simultaneous high-spatial and high-temporal structural data required to address the current challenges of structural biophysics. These data are complementary to crystallography, NMR, and cryo-TEM data. However, the analysis of solution scattering data is challenging; hence many different analysis tools, listed in the SAS Portal (http://smallangle.org/), were developed. In this review, we start by briefly summarizing classical X-ray scattering analyses providing insight into fundamental structural and interaction parameters. We then describe recent developments, integrating simulations, theory, and advanced X-ray scattering modeling, providing unique insights into the structure, energetics, and dynamics of self-assembled complexes. The structural information is essential for understanding the underlying physical chemistry principles leading to self-assembled supramolecular architectures and computational structural refinement.

The solution structure of the heavy chain-only C5-Fc nanobody reveals exposed variable regions that are optimal for COVID-19 antigen interactions

Heavy chain-only antibodies can offer advantages of higher binding affinities, reduced sizes, and higher stabilities than conventional antibodies. To address the challenge of SARS-CoV-2 coronavirus, a llama-derived single-domain nanobody C5 was developed previously that has high COVID-19 virus neutralization potency. The fusion protein C5-Fc comprises two C5 domains attached to a glycosylated Fc region of a human IgG1 antibody and shows therapeutic efficacy in vivo. Here, we have characterized the solution arrangement of the molecule. Two 1443 Da N-linked glycans seen in the mass spectra of C5-Fc were removed and the glycosylated and deglycosylated structures were evaluated. Reduction of C5-Fc with 2-mercaptoethylamine indicated three interchain Cys-Cys disulfide bridges within the hinge. The X-ray and neutron Guinier RG values, which provide information about structural elongation, were similar at 4.1 to 4.2 nm for glycosylated and deglycosylated C5-Fc. To explain these RG values, atomistic scattering modeling based on Monte Carlo simulations resulted in 72,737 and 56,749 physically realistic trial X-ray and neutron structures, respectively. From these, the top 100 best-fit X-ray and neutron models were identified as representative asymmetric solution structures, similar to that of human IgG1, with good R-factors below 2.00%. Both C5 domains were solvent exposed, consistent with the functional effectiveness of C5-Fc. Greater disorder occurred in the Fc region after deglycosylation. Our results clarify the importance of variable and exposed C5 conformations in the therapeutic function of C5-Fc, while the glycans in the Fc region are key for conformational stability in C5-Fc.

The solution structure of the unbound IgG Fc receptor CD64 resembles its crystal structure: Implications for function

FcγRI (CD64) is the only high-affinity Fcγ receptor found on monocytes, macrophages, eosinophils, neutrophils and dendritic cells. It binds immunoglobulin G (IgG) antibody-antigen complexes at its Fc region to trigger key immune responses. CD64 contains three immunoglobulin-fold extracellular domains (D1, D2 and D3) and a membrane-spanning region. Despite the importance of CD64, no solution structure for this is known to date. To investigate this, we used analytical ultracentrifugation, small-angle X-ray scattering, and atomistic modelling. Analytical ultracentrifugation revealed that CD64 was monomeric with a sedimentation coefficient s020,w of 2.53 S, together with some dimer. Small-angle X-ray scattering showed that its radius of gyration RG was 3.3-3.4 nm and increased at higher concentrations to indicate low dimerization. Monte Carlo modelling implemented in the SASSIE-web package generated 279,162 physically-realistic trial CD64 structures. From these, the scattering best-fit models at the lowest measured concentrations that minimised dimers revealed that the D1, D2 and D3 domains were structurally similar to those seen in three CD64 crystal structures, but showed previously unreported flexibility between D1, D2 and D3. Despite the limitations of the scattering data, the superimposition of the CD64 solution structures onto crystal structures of the IgG Fc-CD64 complex showed that the CD64 domains do not sterically clash with the IgG Fc region, i.e. the solution structure of CD64 was sufficiently compact to allow IgG to bind to its high-affinity Fcγ receptor. This improved understanding may result in novel approaches to inhibit CD64 function, and opens the way for the solution study of the full-length CD64-IgG complex.

A solution structure analysis reveals a bent collagen triple helix in the complement activation recognition molecule mannan-binding lectin

Collagen triple helices are critical in the function of mannan-binding lectin (MBL), an oligomeric recognition molecule in complement activation. The MBL collagen regions form complexes with the serine proteases MASP-1 and MASP-2 in order to activate complement, and mutations lead to common immunodeficiencies. To evaluate their structure-function properties, we studied the solution structures of four MBL-like collagen peptides. The thermal stability of the MBL collagen region was much reduced by the presence of a GQG interruption in the typical (X-Y-Gly)n repeat compared to controls. Experimental solution structural data were collected using analytical ultracentrifugation and small angle X-ray and neutron scattering. As controls, we included two standard Pro-Hyp-Gly collagen peptides (POG)10-13, as well as three more peptides with diverse (X-Y-Gly)n sequences that represented other collagen features. These data were quantitatively compared with atomistic linear collagen models derived from crystal structures and 12,000 conformations obtained from molecular dynamics simulations. All four MBL peptides were bent to varying degrees up to 85o in the best-fit molecular dynamics models. The best-fit benchmark peptides (POG)n were more linear but exhibited a degree of conformational flexibility. The remaining three peptides showed mostly linear solution structures. In conclusion, the collagen helix is not strictly linear, the degree of flexibility in the triple helix depends on its sequence, and the triple helix with the GQG interruption showed a pronounced bend. The bend in MBL GQG peptides resembles the bend in the collagen of complement C1q and may be key for lectin pathway activation.

SGTools: a suite of tools for processing and analyzing large data sets from in situ X-ray scattering experiments

In situ synchrotron small-angle X-ray scattering (SAXS) is a powerful tool for studying dynamic processes during material preparation and application. The processing and analysis of large data sets generated from in situ X-ray scattering experiments are often tedious and time consuming. However, data processing software for in situ experiments is relatively rare, especially for grazing-incidence small-angle X-ray scattering (GISAXS). This article presents an open-source software suite (SGTools) to perform data processing and analysis for SAXS and GISAXS experiments. The processing modules in this software include (i) raw data calibration and background correction; (ii) data reduction by multiple methods; (iii) animation generation and intensity mapping for in situ X-ray scattering experiments; and (iv) further data analysis for the sample with an order degree and interface correlation. This article provides the main features and framework of SGTools. The workflow of the software is also elucidated to allow users to develop new features. Three examples are demonstrated to illustrate the use of SGTools for dealing with SAXS and GISAXS data. Finally, the limitations and future features of the software are also discussed.

Solution structures of human myeloma IgG3 antibody reveal extended Fab and Fc regions relative to the other IgG subclasses

Human immunoglobulin G subclass 3 (IgG3) possesses a uniquely long hinge region that separates its Fab antigen-binding and Fc receptor-binding regions. Owing to this hinge length, the molecular structure of full-length IgG3 remains elusive, and the role of the two conserved Fc glycosylation sites are unknown. To address these issues, we subjected glycosylated and deglycosylated human myeloma IgG3 to multidisciplinary solution structure studies. Using analytical ultracentrifugation, the elongated structure of IgG3 was determined from the reduced sedimentation coefficients s020,w of 5.82 to 6.29 S for both glycosylated and deglycosylated IgG3. X-ray and neutron scattering showed that the Guinier RG values were 6.95 nm for glycosylated IgG3 and were unchanged after deglycosylation, again indicating an elongated structure. The distance distribution function P(r) showed a maximum length of 25 to 28 nm and three distinct maxima. The molecular structure of IgG3 was determined using atomistic modeling based on molecular dynamics simulations of the IgG3 hinge and Monte Carlo simulations to identify physically realistic arrangements of the Fab and Fc regions. This resulted in libraries containing 135,135 and 73,905 glycosylated and deglycosylated IgG3 structures, respectively. Comparisons with the X-ray and neutron scattering curves gave 100 best-fit models for each form of IgG3 that accounted for the experimental scattering curves. These models revealed the first molecular structures for full-length IgG3. The structures exhibited relatively restricted Fab and Fc conformations joined by an extended semirigid hinge, which explains the potent effector functions of IgG3 relative to the other subclasses IgG1, IgG2, and IgG4.

Solution structure of deglycosylated human IgG1 shows the role of CH2 glycans in its conformation

The human immunoglobulin G (IgG) class is the most prevalent antibody in serum, with the IgG1 subclass being the most abundant. IgG1 is composed of two Fab regions connected to a Fc region through a 15-residue hinge peptide. Two glycan chains are conserved in the Fc region in IgG; however, their importance for the structure of intact IgG1 has remained unclear. Here, we subjected glycosylated and deglycosylated monoclonal human IgG1 (designated as A33) to a comparative multidisciplinary structural study of both forms. After deglycosylation using peptide:N-glycosidase F, analytical ultracentrifugation showed that IgG1 remained monomeric and the sedimentation coefficients s⁰_20,w of IgG1 decreased from 6.45 S by 0.16-0.27 S. This change was attributed to the reduction in mass after glycan removal. X-ray and neutron scattering revealed changes in the Guinier structural parameters after deglycosylation. Although the radius of gyration (R_G) was unchanged, the cross-sectional radius of gyration (R_XS-1) increased by 0.1 nm, and the commonly occurring distance peak M2 of the distance distribution curve P(r) increased by 0.4 nm. These changes revealed that the Fab-Fc separation in IgG1 was perturbed after deglycosylation. To explain these changes, atomistic scattering modeling based on Monte Carlo simulations resulted in 123,284 and 119,191 trial structures for glycosylated and deglycosylated IgG1 respectively. From these, 100 x-ray and neutron best-fit models were determined. For these, principal component analyses identified five groups of structural conformations that were different for glycosylated and deglycosylated IgG1. The Fc region in glycosylated IgG1 showed a restricted range of conformations relative to the Fab regions, whereas the Fc region in deglycosylated IgG1 showed a broader conformational spectrum. These more variable Fc conformations account for the loss of binding to the Fcγ receptor in deglycosylated IgG1.

A Dimerization Site at SCR-17/18 in Factor H Clarifies a New Mechanism for Complement Regulatory Control

Complement Factor H (CFH), with 20 short complement regulator (SCR) domains, regulates the alternative pathway of complement in part through the interaction of its C-terminal SCR-19 and SCR-20 domains with host cell-bound C3b and anionic oligosaccharides. In solution, CFH forms small amounts of oligomers, with one of its self-association sites being in the SCR-16/20 domains. In order to correlate CFH function with dimer formation and the occurrence of rare disease-associated variants in SCR-16/20, we identified the dimerization site in SCR-16/20. For this, we expressed, in Pichia pastoris, the five domains in SCR-16/20 and six fragments of this with one-three domains (SCR-19/20, SCR-18/20, SCR-17/18, SCR-16/18, SCR-17 and SCR-18). Size-exclusion chromatography suggested that SCR dimer formation occurred in several fragments. Dimer formation was clarified using analytical ultracentrifugation, where quantitative c(s) size distribution analyses showed that SCR-19/20 was monomeric, SCR-18/20 was slightly dimeric, SCR-16/20, SCR-16/18 and SCR-18 showed more dimer formation, and SCR-17 and SCR-17/18 were primarily dimeric with dissociation constants of ~5 µM. The combination of these results located the SCR-16/20 dimerization site at SCR-17 and SCR-18. X-ray solution scattering experiments and molecular modelling fits confirmed the dimer site to be at SCR-17/18, this dimer being a side-by-side association of the two domains. We propose that the self-association of CFH at SCR-17/18 enables higher concentrations of CFH to be achieved when SCR-19/20 are bound to host cell surfaces in order to protect these better during inflammation. Dimer formation at SCR-17/18 clarified the association of genetic variants throughout SCR-16/20 with renal disease.

The solution structure of the complement deregulator FHR5 reveals a compact dimer and provides new insights into CFHR5 nephropathy

The human complement Factor H-related 5 protein (FHR5) antagonizes the main circulating complement regulator Factor H, resulting in the deregulation of complement activation. FHR5 normally contains nine short complement regulator (SCR) domains, but a FHR5 mutant has been identified with a duplicated N-terminal SCR-1/2 domain pair that causes CFHR5 nephropathy. To understand how this duplication causes disease, we characterized the solution structure of native FHR5 by analytical ultracentrifugation and small-angle X-ray scattering. Sedimentation velocity and X-ray scattering indicated that FHR5 was dimeric, with a radius of gyration (Rg ) of 5.5 ± 0.2 nm and a maximum protein length of 20 nm for its 18 domains. This result indicated that FHR5 was even more compact than the main regulator Factor H, which showed an overall length of 26-29 nm for its 20 SCR domains. Atomistic modeling for FHR5 generated a library of 250,000 physically realistic trial arrangements of SCR domains for scattering curve fits. Only compact domain structures in this library fit well to the scattering data, and these structures readily accommodated the extra SCR-1/2 domain pair present in CFHR5 nephropathy. This model indicated that mutant FHR5 can form oligomers that possess additional binding sites for C3b in FHR5. We conclude that the deregulation of complement regulation by the FHR5 mutant can be rationalized by the enhanced binding of FHR5 oligomers to C3b deposited on host cell surfaces. Our FHR5 structures thus explained key features of the mechanism and pathology of CFHR5 nephropathy.

Obtaining Tertiary Protein Structures by the ab Initio Interpretation of Small Angle X-ray Scattering Data

Small angle X-ray scattering (SAXS) is an important tool for investigating the structure of proteins in solution. We present a novel ab initio method representing polypeptide chains as discrete curves used to derive a meaningful three-dimensional model from only the primary sequence and SAXS data. High resolution structures were used to generate probability density functions for each common secondary structural element found in proteins, which are used to place realistic restraints on the model curve’s geometry. This is coupled with a novel explicit hydration shell model in order to derive physically meaningful three-dimensional models by optimizing against experimental SAXS data. The efficacy of this model is verified on an established benchmark protein set, and then it is used to predict the lysozyme structure using only its primary sequence and SAXS data. The method is used to generate a biologically plausible model of the coiled-coil component of the human synaptonemal complex central element protein.

Atomistic Modeling of Scattering Curves for Human IgG1/4 Reveals New Structure-Function Insights

Small angle x-ray and neutron scattering are techniques that give solution structures for large macromolecules. The creation of physically realistic atomistic models from known high-resolution structures to determine joint x-ray and neutron scattering best-fit structures offers a, to our knowledge, new method that significantly enhances the utility of scattering. To validate this approach, we determined scattering curves for two human antibody subclasses, immunoglobulin G (IgG) 1 and IgG4, on five different x-ray and neutron instruments to show that these were reproducible, then we modeled these by Monte Carlo simulations. The two antibodies have different hinge lengths that connect their antigen-binding Fab and effector-binding Fc regions. Starting from 231,492 and 190,437 acceptable conformations for IgG1 and IgG4, respectively, joint x-ray and neutron scattering curve fits gave low goodness-of-fit R factors for 28 IgG1 and 2748 IgG4 structures that satisfied the disulphide connectivity in their hinges. These joint best-fit structures showed that the best-fit IgG1 models had a greater separation between the centers of their Fab regions than those for IgG4, in agreement with their hinge lengths of 15 and 12 residues, respectively. The resulting asymmetric IgG1 solution structures resembled its crystal structure. Both symmetric and asymmetric solution structures were determined for IgG4. Docking simulations with our best-fit IgG4 structures showed greater steric clashes with its receptor to explain its weaker FcγRI receptor binding compared to our best-fit IgG1 structures with fewer clashes and stronger receptor binding. Compared to earlier approaches for fitting molecular antibody structures by solution scattering, we conclude that this joint fit approach based on x-ray and neutron scattering data, combined with Monte Carlo simulations, significantly improved our understanding of antibody solution structures. The atomistic nature of the output extended our understanding of known functional differences in Fc receptor binding between IgG1 and IgG4.

The solution structure of the human IgG2 subclass is distinct from those for human IgG1 and IgG4 providing an explanation for their discrete functions

Human IgG2 antibody displays distinct therapeutically-useful properties compared with the IgG1, IgG3, and IgG4 antibody subclasses. IgG2 is the second most abundant IgG subclass, being able to bind human FcγRII/FcγRIII but not to FcγRI or complement C1q. Structural information on IgG2 is limited by the absence of a full-length crystal structure for this. To this end, we determined the solution structure of human myeloma IgG2 by atomistic X-ray and neutron-scattering modeling. Analytical ultracentrifugation disclosed that IgG2 is monomeric with a sedimentation coefficient (s20, w0) of 7.2 S. IgG2 dimer formation was ≤5% and independent of the buffer conditions. Small-angle X-ray scattering in a range of NaCl concentrations and in light and heavy water revealed that the X-ray radius of gyration (Rg ) is 5.2-5.4 nm, after allowing for radiation damage at higher concentrations, and that the neutron Rg value of 5.0 nm remained unchanged in all conditions. The X-ray and neutron distance distribution curves (P(r)) revealed two peaks, M1 and M2, that were unchanged in different buffers. The creation of >123,000 physically-realistic atomistic models by Monte Carlo simulations for joint X-ray and neutron-scattering curve fits, constrained by the requirement of correct disulfide bridges in the hinge, resulted in the determination of symmetric Y-shaped IgG2 structures. These molecular structures were distinct from those for asymmetric IgG1 and asymmetric and symmetric IgG4 and were attributable to the four hinge disulfides. Our IgG2 structures rationalize the existence of the human IgG1, IgG2, and IgG4 subclasses and explain the receptor-binding functions of IgG2.

An Expanded Conformation of an Antibody Fab Region by X-Ray Scattering, Molecular Dynamics, and smFRET Identifies an Aggregation Mechanism

Protein aggregation is the underlying cause of many diseases, and also limits the usefulness of many natural and engineered proteins in biotechnology. Better mechanistic understanding and characterization of aggregation-prone states is needed to guide protein engineering, formulation, and drug-targeting strategies that prevent aggregation. While several final aggregated states-notably amyloids-have been characterized structurally, very little is known about the native structural conformers that initiate aggregation. We used a novel combination of small-angle x-ray scattering (SAXS), atomistic molecular dynamic simulations, single-molecule Förster resonance energy transfer, and aggregation-prone region predictions, to characterize structural changes in a native humanized Fab A33 antibody fragment, that correlated with the experimental aggregation kinetics. SAXS revealed increases in the native state radius of gyration, R_g, of 2.2% to 4.1%, at pH 5.5 and below, concomitant with accelerated aggregation. In a cutting-edge approach, we fitted the SAXS data to full MD simulations from the same conditions and located the conformational changes in the native state to the constant domain of the light chain (C_L). This C_L displacement was independently confirmed using single-molecule Förster resonance energy transfer measurements with two dual-labeled Fabs. These conformational changes were also found to increase the solvent exposure of a predicted APR, suggesting a likely mechanism through which they promote aggregation. Our findings provide a means by which aggregation-prone conformational states can be readily determined experimentally, and thus potentially used to guide protein engineering, or ligand binding strategies, with the aim of stabilizing the protein against aggregation.

D+: software for high-resolution hierarchical modeling of solution X-ray scattering from complex structures

This paper presents the computer program D+ (https://scholars.huji.ac.il/uriraviv/book/d-0), where the reciprocal-grid (RG) algorithm is implemented. D+ efficiently computes, at high-resolution, the X-ray scattering curves from complex structures that are isotropically distributed in random orientations in solution. Structures are defined in hierarchical trees in which subunits can be represented by geometric or atomic models. Repeating subunits can be docked into their assembly symmetries, describing their locations and orientations in space. The scattering amplitude of the entire structure can be calculated by computing the amplitudes of the basic subunits on 3D reciprocal-space grids, moving up in the hierarchy, calculating the RGs of the larger structures, and repeating this process for all the leaves and nodes of the tree. For very large structures (containing over 100 protein subunits), a hybrid method can be used to avoid numerical artifacts. In the hybrid method, only grids of smaller subunits are summed and used as subunits in a direct computation of the scattering amplitude. D+ can accurately analyze both small- and wide-angle solution X-ray scattering data. This article describes how D+ applies the RG algorithm, accounts for rotations and translations of subunits, processes atomic models, accounts for the contribution of the solvent as well as the solvation layer of complex structures in a scalable manner, writes and accesses RGs, interpolates between grid points, computes numerical integrals, enables the use of scripts to define complicated structures, applies fitting algorithms, accounts for several coexisting uncorrelated populations, and accelerates computations using GPUs. D+ may also account for different X-ray energies to analyze anomalous solution X-ray scattering data. An accessory tool that can identify repeating subunits in a Protein Data Bank file of a complex structure is provided. The tool can compute the orientation and translation of repeating subunits needed for exploiting the advantages of the RG algorithm in D+. A Python wrapper (https://scholars.huji.ac.il/uriraviv/book/python-api) is also available, enabling more advanced computations and integration of D+ with other computational tools. Finally, a large number of tests are presented. The results of D+ are compared with those of other programs when possible, and the use of D+ to analyze solution scattering data from dynamic microtubule structures with different protofilament number is demonstrated. D+ and its source code are freely available for academic users and developers (https://bitbucket.org/uriraviv/public-dplus/src/master/).

D+: software for high-resolution hierarchical modeling of solution X-ray scattering from complex structures

This paper presents the computer program D+ (https://scholars.huji.ac.il/uriraviv/book/d-0), where the reciprocal-grid (RG) algorithm is implemented. D+ efficiently computes, at high-resolution, the X-ray scattering curves from complex structures that are isotropically distributed in random orientations in solution. Structures are defined in hierarchical trees in which subunits can be represented by geometric or atomic models. Repeating subunits can be docked into their assembly symmetries, describing their locations and orientations in space. The scattering amplitude of the entire structure can be calculated by computing the amplitudes of the basic subunits on 3D reciprocal-space grids, moving up in the hierarchy, calculating the RGs of the larger structures, and repeating this process for all the leaves and nodes of the tree. For very large structures (containing over 100 protein subunits), a hybrid method can be used to avoid numerical artifacts. In the hybrid method, only grids of smaller subunits are summed and used as subunits in a direct computation of the scattering amplitude. D+ can accurately analyze both small- and wide-angle solution X-ray scattering data. This article describes how D+ applies the RG algorithm, accounts for rotations and translations of subunits, processes atomic models, accounts for the contribution of the solvent as well as the solvation layer of complex structures in a scalable manner, writes and accesses RGs, interpolates between grid points, computes numerical integrals, enables the use of scripts to define complicated structures, applies fitting algorithms, accounts for several coexisting uncorrelated populations, and accelerates computations using GPUs. D+ may also account for different X-ray energies to analyze anomalous solution X-ray scattering data. An accessory tool that can identify repeating subunits in a Protein Data Bank file of a complex structure is provided. The tool can compute the orientation and translation of repeating subunits needed for exploiting the advantages of the RG algorithm in D+. A Python wrapper (https://scholars.huji.ac.il/uriraviv/book/python-api) is also available, enabling more advanced computations and integration of D+ with other computational tools. Finally, a large number of tests are presented. The results of D+ are compared with those of other programs when possible, and the use of D+ to analyze solution scattering data from dynamic microtubule structures with different protofilament number is demonstrated. D+ and its source code are freely available for academic users and developers (https://bitbucket.org/uriraviv/public-dplus/src/master/).

Two distinct conformations of factor H regulate discrete complement-binding functions in the fluid phase and at cell surfaces

Factor H (FH) is the major regulator of C3b in the alternative pathway of the complement system in immunity. FH comprises 20 short complement regulator (SCR) domains, including eight glycans, and its Y402H polymorphism predisposes those who carry it to age-related macular degeneration. To better understand FH complement binding and self-association, we have studied the solution structures of both the His-402 and Tyr-402 FH allotypes. Analytical ultracentrifugation revealed that up to 12% of both FH allotypes self-associate, and this was confirmed by small-angle X-ray scattering (SAXS), MS, and surface plasmon resonance analyses. SAXS showed that monomeric FH has a radius of gyration (Rg ) of 7.2-7.8 nm and a length of 25 nm. Starting from known structures for the SCR domains and glycans, the SAXS data were fitted using Monte Carlo methods to determine atomistic structures of monomeric FH. The analysis of 29,715 physically realistic but randomized FH conformations resulted in 100 similar best-fit FH structures for each allotype. Two distinct molecular structures resulted that showed either an extended N-terminal domain arrangement with a folded-back C terminus or an extended C terminus and a folded-back N terminus. These two structures are the most accurate to date for glycosylated full-length FH. To clarify FH functional roles in host protection, crystal structures for the FH complexes with C3b and C3dg revealed that the extended N-terminal conformation accounted for C3b fluid-phase regulation, the extended C-terminal conformation accounted for C3d binding, and both conformations accounted for bivalent FH binding to glycosaminoglycans on the target cell surface.

Non-linearity of the collagen triple helix in solution and implications for collagen function

Collagen adopts a characteristic supercoiled triple helical conformation which requires a repeating (Xaa-Yaa-Gly)_n sequence. Despite the abundance of collagen, a combined experimental and atomistic modelling approach has not so far quantitated the degree of flexibility seen experimentally in the solution structures of collagen triple helices. To address this question, we report an experimental study on the flexibility of varying lengths of collagen triple helical peptides, composed of six, eight, ten and twelve repeats of the most stable Pro-Hyp-Gly (POG) units. In addition, one unblocked peptide, (POG)_10unblocked, was compared with the blocked (POG)₁₀ as a control for the significance of end effects. Complementary analytical ultracentrifugation and synchrotron small angle X-ray scattering data showed that the conformations of the longer triple helical peptides were not well explained by a linear structure derived from crystallography. To interpret these data, molecular dynamics simulations were used to generate 50 000 physically realistic collagen structures for each of the helices. These structures were fitted against their respective scattering data to reveal the best fitting structures from this large ensemble of possible helix structures. This curve fitting confirmed a small degree of non-linearity to exist in these best fit triple helices, with the degree of bending approximated as 4–17° from linearity. Our results open the way for further studies of other collagen triple helices with different sequences and stabilities in order to clarify the role of molecular rigidity and flexibility in collagen extracellular and immune function and disease.

Flexibility in Mannan-Binding Lectin-Associated Serine Proteases-1 and -2 Provides Insight on Lectin Pathway Activation

The lectin pathway of complement is activated by complexes comprising a recognition component (mannose-binding lectin, serum ficolins, collectin-LK or collectin-K1) and a serine protease (MASP-1 or MASP-2). MASP-1 activates MASP-2, and MASP-2 cleaves C4 and C4b-bound C2. To clarify activation, new crystal structures of Ca²⁺-bound MASP dimers were determined, together with their solution structures from X-ray scattering, analytical ultracentrifugation, and atomistic modeling. Solution structures of the CUB1-EGF-CUB2 dimer of each MASP indicate that the two CUB2 domains were tilted by as much as 90° compared with the crystal structures, indicating considerable flexibility at the EGF-CUB2 junction. Solution structures of the full-length MASP dimers in their zymogen and activated forms revealed similar structures that were much more bent than anticipated from crystal structures. We conclude that MASP-1 and MASP-2 are flexible at multiple sites and that this flexibility may permit both intra- and inter-complex activation.

Atomistic modelling of scattering data in the Collaborative Computational Project for Small Angle Scattering (CCP-SAS)

The capabilities of current computer simulations provide a unique opportunity to model small-angle scattering (SAS) data at the atomistic level, and to include other structural constraints ranging from molecular and atomistic energetics to crystallography, electron microscopy and NMR. This extends the capabilities of solution scattering and provides deeper insights into the physics and chemistry of the systems studied. Realizing this potential, however, requires integrating the experimental data with a new generation of modelling software. To achieve this, the CCP-SAS collaboration (http://www.ccpsas.org/) is developing open-source, high-throughput and user-friendly software for the atomistic and coarse-grained molecular modelling of scattering data. Robust state-of-the-art molecular simulation engines and molecular dynamics and Monte Carlo force fields provide constraints to the solution structure inferred from the small-angle scattering data, which incorporates the known physical chemistry of the system. The implementation of this software suite involves a tiered approach in which GenApp provides the deployment infrastructure for running applications on both standard and high-performance computing hardware, and SASSIE provides a workflow framework into which modules can be plugged to prepare structures, carry out simulations, calculate theoretical scattering data and compare results with experimental data. GenApp produces the accessible web-based front end termed SASSIE-web, and GenApp and SASSIE also make community SAS codes available. Applications are illustrated by case studies: (i) inter-domain flexibility in two- to six-domain proteins as exemplified by HIV-1 Gag, MASP and ubiquitin; (ii) the hinge conformation in human IgG2 and IgA1 antibodies; (iii) the complex formed between a hexameric protein Hfq and mRNA; and (iv) synthetic 'bottlebrush' polymers.

Domain structure of human complement C4b extends with increasing NaCl concentration: implications for its regulatory mechanism

During the activation of complement C4 to C4b, the exposure of its thioester domain (TED) is crucial for the attachment of C4b to activator surfaces. In the C4b crystal structure, TED forms an Arg¹⁰⁴-Glu¹⁰³² salt bridge to tether its neighbouring macroglobulin (MG1) domain. Here, we examined the C4b domain structure to test whether this salt bridge affects its conformation. Dual polarisation interferometry of C4b immobilised at a sensor surface showed that the maximum thickness of C4b increased by 0.46 nm with an increase in NaCl concentration from 50 to 175 mM NaCl. Analytical ultracentrifugation showed that the sedimentation coefficient s_20,w of monomeric C4b of 8.41 S in 50 mM NaCl buffer decreased to 7.98 S in 137 mM NaCl buffer, indicating that C4b became more extended. Small angle X-ray scattering reported similar R_G values of 4.89-4.90 nm for C4b in 137-250 mM NaCl. Atomistic scattering modelling of the C4b conformation showed that TED and the MG1 domain were separated by 4.7 nm in 137-250 mM NaCl and this is greater than that of 4.0 nm in the C4b crystal structure. Our data reveal that in low NaCl concentrations, both at surfaces and in solution, C4b forms compact TED-MG1 structures. In solution, physiologically relevant NaCl concentrations lead to the separation of the TED and MG1 domain, making C4b less capable of binding to its complement regulators. These conformational changes are similar to those seen previously for complement C3b, confirming the importance of this salt bridge for regulating both C4b and C3b.

Accurate optimization of amino acid form factors for computing small-angle X-ray scattering intensity of atomistic protein structures

Structure modelling via small-angle X-ray scattering (SAXS) data generally requires intensive computations of scattering intensity from any given biomolecular structure, where the accurate evaluation of SAXS profiles using coarse-grained (CG) methods is vital to improve computational efficiency. To date, most CG SAXS computing methods have been based on a single-bead-per-residue approximation but have neglected structural correlations between amino acids. To improve the accuracy of scattering calculations, accurate CG form factors of amino acids are now derived using a rigorous optimization strategy, termed electron-density matching (EDM), to best fit electron-density distributions of protein structures. This EDM method is compared with and tested against other CG SAXS computing methods, and the resulting CG SAXS profiles from EDM agree better with all-atom theoretical SAXS data. By including the protein hydration shell represented by explicit CG water molecules and the correction of protein excluded volume, the developed CG form factors also reproduce the selected experimental SAXS profiles with very small deviations. Taken together, these EDM-derived CG form factors present an accurate and efficient computational approach for SAXS computing, especially when higher molecular details (represented by the q range of the SAXS data) become necessary for effective structure modelling.

Zinc-induced oligomerization of zinc α2 glycoprotein reveals multiple fatty acid-binding sites

Zinc α2 glycoprotein (ZAG) is an adipokine with a class I MHC protein fold and is associated with obesity and diabetes. Although its intrinsic ligand remains unknown, ZAG binds the dansylated C11 fatty acid 11-(dansylamino)undecanoic acid (DAUDA) in the groove between the α1 and α2 domains. The surface of ZAG has approximately 15 weak zinc-binding sites deemed responsible for precipitation from human plasma. In the present study the functional significance of these metal sites was investigated. Analytical ultracentrifugation (AUC) and CD showed that zinc, but not other divalent metals, causes ZAG to oligomerize in solution. Thus ZAG dimers and trimers were observed in the presence of 1 and 2 mM zinc. Molecular modelling of X-ray scattering curves and sedimentation coefficients indicated a progressive stacking of ZAG monomers, suggesting that the ZAG groove may be occluded in these. Using fluorescence-detected sedimentation velocity, these ZAG-zinc oligomers were again observed in the presence of the fluorescent boron dipyrromethene fatty acid C16-BODIPY (4,4-difluoro-5,7-dimethyl-4-bora-3a,4a-diaza-s-indacene-3-hexadecanoic acid). Fluorescence spectroscopy confirmed that ZAG binds C16-BODIPY. ZAG binding to C16-BODIPY, but not to DAUDA, was reduced by increased zinc concentrations. We conclude that the lipid-binding groove in ZAG contains at least two distinct fatty acid-binding sites for DAUDA and C16-BODIPY, similar to the multiple lipid binding seen in the structurally related immune protein CD1c. In addition, because high concentrations of zinc occur in the pancreas, the perturbation of these multiple lipid-binding sites by zinc may be significant in Type 2 diabetes where dysregulation of ZAG and zinc homoeostasis occurs.

The solution structures of native and patient monomeric human IgA1 reveal asymmetric extended structures: implications for function and IgAN disease

Detailed analytical ultracentrifugation and X-ray/neutron scattering data and a new atomistic modelling approach revealed asymmetric extended solution structures for human IgA1 that account for its receptor-binding function. IgA1 with different hinge O-galactosylation patterns showed similar structures.

Native IgA1, for which no crystal structure is known, contains an O-galactosylated 23-residue hinge region that joins its Fab and Fc regions. IgA nephropathy (IgAN) is a leading cause of chronic kidney disease in developed countries. Because IgA1 in IgAN often has a poorly O-galactosylated hinge region, the solution structures of monomeric IgA1 from a healthy subject and three IgAN patients with four different O-galactosylation levels were studied. Analytical ultracentrifugation showed that all four IgA1 samples were monomeric with similar sedimentation coefficients, s⁰_20,w. X-ray scattering showed that the radius of gyration (R_g) slightly increased with IgA1 concentration, indicating self-association, although their distance distribution curves, P(r), were unchanged with concentration. Neutron scattering indicated similar R_g values and P(r) curves, although IgA1 showed a propensity to aggregate in heavy water buffer. A new atomistic modelling procedure based on comparisons with 177000 conformationally-randomized IgA1 structures with the individual experimental scattering curves revealed similar extended Y-shaped solution structures for all four differentially-glycosylated IgA1 molecules. The final models indicated that the N-glycans at Asn²⁶³ were folded back against the Fc surface, the C-terminal tailpiece conformations were undefined and hinge O-galactosylation had little effect on the solution structure. The solution structures for full-length IgA1 showed extended hinges and the Fab and Fc regions were positioned asymmetrically to provide ample space for the functionally-important binding of two FcαR receptors to its Fc region. Whereas no link between O-galactosylation and the IgA1 solution structure was detected, an increase in IgA1 aggregation with reduced O-galactosylation may relate to IgAN.