Hydrodynamics of macromolecular complexes. III. Bacterial viruses

Impact of bacteria motility in the encounter rates with bacteriophage in mucus

Bacteriophages—or phages—are viruses that infect bacteria and are present in large concentrations in the mucosa that cover the internal organs of animals. Immunoglobulin (Ig) domains on the phage surface interact with mucin molecules, and this has been attributed to an increase in the encounter rates of phage with bacteria in mucus. However, the physical mechanism behind this phenomenon remains unclear. A continuous time random walk (CTRW) model simulating the diffusion due to mucin-T4 phage interactions was developed and calibrated to empirical data. A Langevin stochastic method for Escherichia coli (E. coli) run-and-tumble motility was combined with the phage CTRW model to describe phage-bacteria encounter rates in mucus for different mucus concentrations. Contrary to previous theoretical analyses, the emergent subdiffusion of T4 in mucus did not enhance the encounter rate of T4 against bacteria. Instead, for static E. coli, the diffusive T4 mutant lacking Ig domains outperformed the subdiffusive T4 wild type. E. coli’s motility dominated the encounter rates with both phage types in mucus. It is proposed, that the local fluid-flow generated by E. coli’s motility combined with T4 interacting with mucins may be the mechanism for increasing the encounter rates between the T4 phage and E. coli bacteria.

Distinguishing Between Monomeric scFv and Diabody in Solution Using Light and Small Angle X-ray Scattering

Depending on the linker length between the VH and the VL domain, single-chain Fv (scFv) antibody fragments form monomers, dimers (diabodies) or higher oligomers. We aimed at generating a diabody of the anti-MET antibody 3H3 to use it as crystallization chaperone to promote crystallization of the MET ectodomain through the introduction of a pre-formed twofold axis of symmetry. Size exclusion chromatography, however, suggested the protein to be monomeric. Hence, we used scattering techniques applied to solutions to further investigate its oligomerization state. The small angle X-ray scattering (SAXS) curve measured for our protein nicely fits to the scattering curve calculated from the known crystal structure of a diabody. In addition, concentration-dependent photon correlation spectroscopy (PCS) measurements revealed a hydrodynamic radius of 3.4 nm at infinite dilution and a negative interaction parameter kD, indicating attractive interactions that are beneficial for crystallization. Both SAXS and PCS measurements clearly suggest our antibody fragment to be a diabody in solution. Chemical cross-linking with glutaraldehyde and cell motility assays confirmed this conclusion.

Fluctuation-induced hydrodynamic coupling in an asymmetric, anisotropic dumbbell

We recently introduced a model of an asymmetric dumbbell made of two hydrodynamically coupled subunits as a minimal model for a macromolecular complex, in order to explain the observation of enhanced diffusion of catalytically active enzymes. It was shown that internal fluctuations lead to a negative contribution to the overall diffusion coefficient and that the fluctuation-induced contribution is controlled by the strength of the interactions between the subunits and their asymmetry. We develop the model by studying the effect of anisotropy on the diffusion properties of a modular structure. Using a moment expansion method we derive an analytic form for the long-time diffusion coefficient of an asymmetric, anisotropic dumbbell and show systematically its dependence on internal and external symmetry. The method provides a tractable, analytical route for studying the stochastic dynamics of dumbbell models. The present work opens the way to more detailed descriptions of the effect of hydrodynamic interactions on the diffusion and transport properties of biomolecules with complex structures.

Dense Layer of Bacteriophages Ordered in Alternating Electric Field and Immobilized by Surface Chemical Modification as Sensing Element for Bacteria Detection

Faster and more sensitive environmental monitoring should be developed to face the worldwide problem of bacterial infections. To remedy this issue, we demonstrate a bacteria-sensing element that utilizes dense and ordered layers of bacteriophages specific to the given bacteria strain. We combine (1) the chemical modification of a surface to increase the surface coverage of bacteriophages (2) with an alternating electric field to greatly increase the number of properly oriented bacteriophages at the surface. Usually, in sensing elements, a random orientation of bacteriophages results in steric hindrance, which results in no more than a few percent of all receptors being available. An increased number of properly ordered phages results in the optimal performance of phage receptors, manifesting in up to a 64-fold increase in sensitivity and a limit of detection as low as 100 CFU mL^-1. Our sensing elements can be applied for selective, sensitive, and fast (15 min) bacterial detection. A well-studied pair T4 bacteriophage-bacteria Escherichia coli, was used as a model; however, the method could be adapted to prepare bacteriophage-based sensors for detection of a variety of bacterial strains.

SDA 7: A modular and parallel implementation of the simulation of diffusional association software

The simulation of diffusional association (SDA) Brownian dynamics software package has been widely used in the study of biomacromolecular association. Initially developed to calculate bimolecular protein-protein association rate constants, it has since been extended to study electron transfer rates, to predict the structures of biomacromolecular complexes, to investigate the adsorption of proteins to inorganic surfaces, and to simulate the dynamics of large systems containing many biomacromolecular solutes, allowing the study of concentration-dependent effects. These extensions have led to a number of divergent versions of the software. In this article, we report the development of the latest version of the software (SDA 7). This release was developed to consolidate the existing codes into a single framework, while improving the parallelization of the code to better exploit modern multicore shared memory computer architectures. It is built using a modular object-oriented programming scheme, to allow for easy maintenance and extension of the software, and includes new features, such as adding flexible solute representations. We discuss a number of application examples, which describe some of the methods available in the release, and provide benchmarking data to demonstrate the parallel performance.

Many-particle Brownian and Langevin Dynamics Simulations with the Brownmove package

Background

Brownian Dynamics (BD) is a coarse-grained implicit-solvent simulation method that is routinely used to investigate binary protein association dynamics, but due to its efficiency in handling large simulation volumes and particle numbers it is well suited to also describe many-protein scenarios as they often occur in biological cells.

Results

Here we introduce our "brownmove" simulation package which was designed to handle many-particle problems with varying particle numbers and allows for a very flexible definition of rigid and flexible protein and polymer models. Both a Brownian and a Langevin dynamics (LD) propagation scheme can be used and hydrodynamic interactions are treated efficiently with our recently introduced TEA-HI ansatz [Geyer, Winter, JCP 130 (2009) 114905]. With simulations of constrained polymers and flexible models of spherical proteins we demonstrate that it is crucial to include hydrodynamics when multi-bead models are used in BD or LD simulations. Only then both the translational and the rotational diffusion coefficients and the timescales of the internal dynamics can be reproduced correctly. In the third example project we show how constant density boundary conditions [Geyer et al, JCP 120 (2004) 4573] can be used to set up a non-equilibrium simulation of diffusional transport across an array of fixed obstacles. Finally, we demonstrate how the agglomeration dynamics of multiple particles with attractive patches can be analysed conveniently with the help of a dynamic interaction network.

Conclusions

Combining BD and LD propagation, fast hydrodynamics, a flexible protein model, and interfaces for "open" simulation settings, our freely available "brownmove" simulation package constitutes a new platform for coarse-grained many-particle simulations of biologically relevant diffusion and transport processes.

Recent advances in macromolecular hydrodynamic modeling

The modern implementation of the boundary element method [23] has ushered unprecedented accuracy and precision for the solution of the Stokes equations of hydrodynamics with stick boundary conditions. This article begins by reviewing computations with the program BEST of smooth surface objects such as ellipsoids, the dumbbell, and cylinders that demonstrate that the numerical solution of the integral equation formulation of hydrodynamics yields very high precision and accuracy. When BEST is used for macromolecular computations, the limiting factor becomes the definition of the molecular hydrodynamic surface and the implied effective solvation of the molecular surface. Studies on 49 different proteins, ranging in molecular weight from 9 to over 400kDa, have shown that a model using a 1.1Å thick hydration layer describes all protein transport properties very well for the overwhelming majority of them. In addition, this data implies that the crystal structure is an excellent representation of the average solution structure for most of them. In order to investigate the origin of a handful of significant discrepancies in some multimeric proteins (about -20% observed in the intrinsic viscosity), the technique of Molecular Dynamics simulation (MD) has been incorporated into the research program. A preliminary study of dimeric α-chymotrypsin using approximate implicit water MD is presented. In addition I describe the successful validation of modern protein force fields, ff03 and ff99SB, for the accurate computation of solution structure in explicit water simulation by comparison of trajectory ensemble average computed transport properties with experimental measurements. This work includes small proteins such as lysozyme, ribonuclease and ubiquitin using trajectories around 10ns duration. We have also studied a 150kDa flexible monoclonal IgG antibody, Trastuzumab, with multiple independent trajectories encompassing over 320ns of simulation. The close agreement within experimental error of the computed and measured properties allows us to conclude that MD does produce structures typical of those in solution, and that flexible molecules can be properly described using the method of ensemble averaging over a trajectory. We review similar work on the study of a transfer RNA molecule and DNA oligomers that demonstrate that within 3% a simple uniform hydration model 1.1Å thick provides agreement with experiment for these nucleic acids. In the case of linear oligomers, the precision can be improved close to 1% by a non-uniform hydration model that hydrates mainly in the DNA grooves, in agreement with high resolution X-ray diffraction. We conclude with a vista on planned improvements for the BEST program to decrease its memory requirements and increase its speed without sacrificing accuracy.

Designing bioactive delivery systems for tissue regeneration

The direct infusion of macromolecules into defect sites generally does not impart adequate physiological responses. Without the protection of delivery systems, inductive molecules may likely redistribute away from their desired locale and are vulnerable to degradation. In order to achieve efficacy, large doses supplied at interval time periods are necessary, often at great expense and ensuing detrimental side effects. The selection of a delivery system plays an important role in the rate of re-growth and functionality of regenerating tissue: not only do the release kinetics of inductive molecules and their consequent bioactivities need to be considered, but also how the delivery system interacts and integrates with its surrounding host environment. In the current review, we describe the means of release of macromolecules from hydrogels, polymeric microspheres, and porous scaffolds along with the selection and utilization of bioactive delivery systems in a variety of tissue-engineering strategies.

X-ray and neutron scattering data and their constrained molecular modeling

X-ray and neutron solution scattering methods provide multiparameter structural and compositional information on proteins that complements high-resolution protein crystallography and NMR studies. We describe the procedures required to (1) obtain validated X-ray and neutron scattering data, (2) perform Guinier analyses of the scattering data to extract the radius of gyration R(G) and intensity parameters, and (3) calculate the distance distribution function P(r). Constrained modeling is important because this confirms the experimental data analysis and produces families of best-fit molecular models for comparison with crystallography and NMR structures. The modeling procedures are described in terms of (4) generating appropriate starting models, (5) randomizing these for trial-and-error scattering fits, (6) identifying the final best-fit models, and (7) applying analytical ultracentrifugation (AUC) data to validate the scattering modeling. These procedures and pitfalls in them will be illustrated using work performed in the authors' laboratory on antibodies and the complement proteins of the human immune defense system. Four different types of modeling procedures are distinguished, depending on the number and type of domains in the protein. Examples when comparisons with crystallography and NMR structures are important are described. For multidomain proteins, it is often found that scattering provides essential evidence to validate or disprove a crystal structure. If a large protein cannot be crystallized, scattering provides the only means to obtain a structure.

Extended and Flexible Domain Solution Structure of the Extracellular Matrix Protein Anosmin-1 by X-ray Scattering, Analytical Ultracentrifugation and Constrained Modelling

Kallmann's syndrome corresponds to a loss of sense of smell and hypogonadotrophic hypogonadism. Defects in anosmin-1 result in the X-linked inherited form of Kallmann's syndrome. Anosmin-1 is an extracellular matrix protein comprised of an N-terminal, cysteine-rich (Cys-box) domain and a whey acidic protein-like (WAP) domain, followed by four fibronectin type III (FnIII) domains. The solution structures of recombinant proteins containing the first three domains (PIWF1) and all six domains (PIWF4) were determined by X-ray scattering and analytical ultracentrifugation. Guinier analyses showed that PIWF1 and PIWF4 have different radii of gyration (R(G)) values of 3.1 nm and 6.7 nm, respectively, but similar cross-sectional radii of gyration (R(XS)) values of 1.5 nm and 1.9 nm, respectively. Distance distribution functions showed that the maximum lengths of PIWF1 and PIWF4 were 11 nm and 23 nm, respectively. Analytical ultracentrifugation gave sedimentation coefficients of 2.52 S and 3.55 S for PIWF1 and PIWF4, respectively. The interpretation of the scattering data by constrained modelling requires homology models for all six domains in anosmin-1. While models were already available for the WAP and FnIII domains, searches suggested the Cys-box domain may resemble the cysteine-rich region of the insulin-like growth factor receptor. Automated constrained molecular modelling based on joining the anosmin-1 domains with structurally randomised linkers resulted in 10,000 models for anosmin-1. A trial-and-error search showed that about 0.1-1.4% of these models fitted the X-ray data. The best models showed that the three domains and six domains in PIWF1 and PIWF4, respectively, were extended. The inter-domain linkers in anosmin-1 could not all be extended at the same time, and there was evidence for inter-domain flexibility. Models with folded-back domain arrangements do not fit the data. These solution structures account for the known biological function of anosmin-1, in particular its ability to interact with its three macromolecular ligands.

Solution structure of the complex between CR2 SCR 1-2 and C3d of human complement: an X-ray scattering and sedimentation modelling study

Complement receptor type 2 (CR2, CD21) forms a tight complex with C3d, a fragment of C3, the major complement component. Previous crystal structures of the C3d-CR2 SCR 1-2 complex and free CR2 SCR 1-2 showed that the two SCR domains of CR2 form contact with each other in a closed V-shaped structure. SCR 1 and SCR 2 are connected by an unusually long eight-residue linker peptide. Medium-resolution solution structures for CR2 SCR 1-2, C3d, and their complex were determined by X-ray scattering and analytical ultracentrifugation. CR2 SCR 1-2 is monomeric. For CR2 SCR 1-2, its radius of gyration R(G) of 2.12(+/-0.05) nm, its maximum length of 10nm and its sedimentation coefficient s20,w(o) of 1.40(+/-0.03) S do not agree with those calculated from the crystal structures, and instead suggest an open structure. Computer modelling of the CR2 SCR1-2 solution structure was based on the structural randomisation of the eight-residue linker peptide joining SCR 1 and SCR 2 to give 9950 trial models. Comparisons with the X-ray scattering curve indicated that the most favoured arrangements for the two SCR domains corresponded to an open V-shaped structure with no contacts between the SCR domains. For C3d, X-ray scattering and sedimentation velocity experiments showed that it exists as a monomer-dimer equilibrium with a dissociation constant of 40 microM. The X-ray scattering curve for monomeric C3d gave an R(G) value of 1.95 nm, and this together with its s20,w(o) value of 3.17 S gave good agreement with the monomeric C3d crystal structure. Modelling of the C3d dimer gave good agreements with its scattering and ultracentrifugation parameters. For the complex, scattering and ultracentrifugation experiments showed that there was no dimerisation, indicating that the C3d dimerisation site was located close to the CR2 SCR 1-2 binding site. The R(G) value of 2.44(+/-0.1) nm, its length of 9 nm and its s20,w(o) value of 3.45(+/-0.01) S showed that its structure was not much more elongated than that of C3d. Calculations with 9950 models of CR2 SCR 1-2 bound to C3d through SCR 2 showed that SCR 1 formed an open V-shaped structure with SCR 2 and was capable of interacting with the surface of C3d. We conclude that the open V-shaped structures formed by CR2 SCR 1-2, both when free and when bound to C3d, are optimal for the formation of a tight two-domain interaction with its ligand C3d.

The dimeric and trimeric solution structures of the multidomain complement protein properdin by X-ray scattering, analytical ultracentrifugation and constrained modelling

Properdin regulates the alternative pathway of the complement system of immune defence by stabilising the C3 convertase complex. It contains six thrombospondin repeat type I (TSR-1 to TSR-6) domains and an N-terminal domain. Properdin exists as either a dimer, trimer or tetramer. In order to determine the solution structure of multiple TSR domains, the molecular structures of dimeric and trimeric properdin were studied by X-ray scattering and analytical ultracentrifugation. Guinier analyses showed that the dimer and trimer have radii of gyration R(G) values of 7.5 nm and 10.3 nm, respectively, and cross-sectional radii of gyration R(XS) values of 1.3 nm and 1.5 nm, respectively. Distance distribution functions showed that the maximum lengths of the dimer and trimer were 25 nm and 30 nm, respectively. Analytical ultracentrifugation gave sedimentation coefficients of 5.1S and 5.2S for the dimer and trimer forms, respectively. Homology models for the TSR domains were constructed using the crystal structure of the TSP-2 and TSP-3 domains in human thrombospondin as templates. Properdin could be represented by seven TSR domains, not six as believed, since the crystal structure determined for TSP-2 and TSP-3 showed that the N-terminal domain (TSR-0) could be represented by a truncated TSR domain with the same six conserved Cys residues found in TSR-1 to TSR-6. Automated constrained molecular modelling revealed the solution conformations of multiple TSR domains in properdin at medium resolution. The comparison of 3125 systematically generated conformational models for the trimer with the X-ray data showed that good curve fits could be obtained by assuming that the linker between adjacent TSR domains possessed limited flexibility. Good trimer models correspond to partially collapsed triangular structures, and extended triangular shapes do not fit the data. The corresponding 3125 models for the dimer revealed a similar outcome in which a partially collapsed TSR structure gave good fits. The models account for the effect of mutations that cause properdin deficiencies, and suggest that the biologically active TSR-4, TSR-5 and TSR-6 domains are exposed for protein-protein interactions. The role of the other TSR domains in properdin may be to act as spacers to make TSR-4, TSR-5 and TSR-6 accessible for function.

Solution Structure Determination of Monomeric Human IgA2 by X-ray and Neutron Scattering, Analytical Ultracentrifugation and Constrained Modelling: A Comparison with Monomeric Human IgA1

Immunoglobulin A (IgA), the most abundant human immunoglobulin, mediates immune protection at mucosal surfaces as well as in plasma. It exists as two subclasses IgA1 and IgA2, and IgA2 is found in at least two allotypic forms, IgA2m(1) or IgA2m(2). Compared to IgA1, IgA2 has a much shorter hinge region, which joins the two Fab and one Fc fragments. In order to assess its solution structure, monomeric recombinant IgA2m(1) was studied by X-ray and neutron scattering. Its Guinier X-ray radius of gyration R(G) is 5.18 nm and its neutron R(G) is 5.03 nm, both of which are significantly smaller than those for monomeric IgA1 at 6.1-6.2 nm. The distance distribution function P(r)for IgA2m(1) showed a broad peak with a subpeak and gave a maximum dimension of 17 nm, in contrast to the P(r) curve for IgA1, which showed two distinct peaks and a maximum dimension of 21 nm. The sedimentation coefficients of IgA1 and IgA2m(1) were 6.2S and 6.4S, respectively. These data show that the solution structure of IgA2m(1) is significantly more compact than IgA1. The complete monomeric IgA2m(1) structure was modelled using molecular dynamics to generate random IgA2 hinge structures, to which homology models for the Fab and Fc fragments were connected to generate 10,000 full models. A total of 104 compact best-fit IgA2m(1) models gave good curve fits. These best-fit models were modified by linking the two Fab light chains with a disulphide bridge that is found in IgA2m(1), and subjecting these to energy refinement to optimise this linkage. The averaged solution structure of the arrangement of the Fab and Fc fragments in IgA2m(1) was found to be predominantly T-shaped and flexible, but also included Y-shaped structures. The IgA2 models show full steric access to the two FcalphaRI-binding sites at the Calpha2-Calpha3 interdomain region in the Fc fragment. Since previous scattering modelling had shown that IgA1 also possessed a flexible T-shaped solution structure, such a T-shape may be common to both IgA1 and IgA2. The final models suggest that the combination of the more compact IgA2m(1) and the more extended IgA1 structures will enable human IgA to access a broader range of antigens than either acting alone. The hinges of both IgA subclasses appear to show reduced flexibility when compared to their equivalents in IgG, and this may be important for maintaining an extended IgA structure.

Numerical path integration technique for the calculation of transport properties of proteins

We present a new technique for the computation of both the translational diffusivity and the intrinsic viscosity of macromolecules, and apply it here to proteins. Traditional techniques employ finite element representations of the surface of the macromolecule, taking the surface to be a union of spheres or of polygons, and have computation times that are O(m(3)) where m is the number of finite elements. The new technique, a numerical path integration method, has computation times that are only O(m). We have applied the technique to approximately 1000 different protein structures. The computed translational diffusivities and intrinsic viscosities are, to lowest order, proportional respectively to N(-1/3)(R) and N(0)(R), where N(R) is the number of amino acid residues in the protein. Our calculations also show some correlation with the shape of the molecule, as represented by the ratio m(2)/m(3), where m(2) and m(3) are, respectively, the middle and the smallest of the three principal moments of inertia. Comparisons with a number of experimental results are also performed, with results generally consistent to within experimental error.

A precise boundary element method for macromolecular transport properties

A very precise boundary element numerical solution of the exact formulation of the hydrodynamic resistance problem with stick boundary conditions is presented. BEST, the Fortran 77 program developed for this purpose, computes the full transport tensors in the center of resistance or the center of diffusion for an arbitrarily shaped rigid body, including rotation-translation coupling. The input for this program is a triangulation of the solvent-defined surface of the molecule of interest, given by Connolly's MSROLL or other suitable triangulator. The triangulation is prepared for BEST by COALESCE, a program that allows user control over the quality and number of triangles to describe the surface. High numerical precision is assured by effectively exact integration of the Oseen tensor over triangular surface elements, and by scaling the hydrodynamic computation to the precise surface area of the molecule. Efficiency of computation is achieved by the use of public domain LAPACK routines that call BLAS Level 3 hardware-optimized subroutines available for most processors. A protein computation can be done in less than 10 min of CPU time in a modern Pentium IV processor. The present work includes a complete analysis of the sources of error in the numerical work and techniques to eliminate these errors. The operation of BEST is illustrated with applications to ellipsoids of revolution, and Lysozyme, a small protein. The typical numerical accuracy achieved is 0.05% compared to analytical theory. The numerical precision for a protein is better than 1%, much better than experimental errors in these quantities, and more than 10 times better than traditional bead-based methods.

Effect of DNA superhelicity and bound proteins on mechanistic aspects of the Hin-mediated and Fis-enhanced inversion

Using a recently developed inhomogeneous, macroscopic model for long DNA bound to proteins, we examine topological and geometric aspects of DNA/protein structures and dynamics on various stages of the Hin inversion pathway. This biological reaction involves exchange of DNA in a synaptic complex that brings together several DNA sites bound to Hin dimers as well as Fis enhancers. Brownian dynamics simulations in the millisecond timescale allow us to follow and analyze the DNA/protein dynamics trajectories and to examine the effects of DNA superhelicity and protein binding on various reaction steps. Analysis of the generated kinetic pathways helps explain mechanistic aspects regarding the process by which two or three protein-bound DNA sites come to close spatial proximity and show that how topological selectivity (two trapped supercoils), enhancer binding, and properties of supercoiled DNA play critical roles in regulating the inversion reaction. Specifically, a critical amount of DNA superhelicity (e.g., |sigma| > 0.02) leads to an optimal interplay for the first reaction step-two-site juxtaposition-between large-scale random rearrangements of Hin-bound DNA and local slithering within branches of plectonemes. The three-site juxtaposition, the second step, is significantly accelerated by the presence of an enhancer protein that, due to severe local bending, also alters juxtaposition mechanisms, especially for superhelical density magnitude greater than around 0.04.

Calculation of hydrodynamic properties of globular proteins from their atomic-level structure

The solution properties, including hydrodynamic quantities and the radius of gyration, of globular proteins are calculated from their detailed, atomic-level structure, using bead-modeling methodologies described in our previous article (, Biophys. J. 76:3044-3057). We review how this goal has been pursued by other authors in the past. Our procedure starts from a list of atomic coordinates, from which we build a primary hydrodynamic model by replacing nonhydrogen atoms with spherical elements of some fixed radius. The resulting particle, consisting of overlapping spheres, is in turn represented by a shell model treated as described in our previous work. We have applied this procedure to a set of 13 proteins. For each protein, the atomic element radius is adjusted, to fit all of the hydrodynamic properties, taking values close to 3 A, with deviations that fall within the error of experimental data. Some differences are found in the atomic element radius found for each protein, which can be explained in terms of protein hydration. A computational shortcut makes the procedure feasible, even in personal computers. All of the model-building and calculations are carried out with a HYDROPRO public-domain computer program.

Hydrodynamic properties of rigid particles: comparison of different modeling and computational procedures

The hydrodynamic properties of rigid particles are calculated from models composed of spherical elements (beads) using theories developed by Kirkwood, Bloomfield, and their coworkers. Bead models have usually been built in such a way that the beads fill the volume occupied by the particles. Sometimes the beads are few and of varying sizes (bead models in the strict sense), and other times there are many small beads (filling models). Because hydrodynamic friction takes place at the molecular surface, another possibility is to use shell models, as originally proposed by Bloomfield. In this work, we have developed procedures to build models of the various kinds, and we describe the theory and methods for calculating their hydrodynamic properties, including approximate methods that may be needed to treat models with a very large number of elements. By combining the various possibilities of model building and hydrodynamic calculation, several strategies can be designed. We have made a quantitative comparison of the performance of the various strategies by applying them to some test cases, for which the properties are known a priori. We provide guidelines and computational tools for bead modeling.

The Fab and Fc fragments of IgA1 exhibit a different arrangement from that in IgG: a study by X-ray and neutron solution scattering and homology modelling

Human immunoglobulin A (IgA) is an abundant antibody that mediates immune protection at mucosal surfaces as well as in plasma. The IgA1 isotype contains two four-domain Fab fragments and a four-domain Fc fragment analogous to that in immunoglobulin G (IgG), linked by a glycosylated hinge region made up of 23 amino acid residues from each of the heavy chains. IgA1 also has two 18 residue tailpieces at the C terminus of each heavy chain in the Fc fragment. X-ray scattering using H2O buffers and neutron scattering using 100 % 2H2O buffers were performed on monomeric IgA1 and a recombinant IgA1 that lacks the tailpiece (PTerm455). The radii of gyration RG from Guinier analyses were similar at 6.11-6.20 nm for IgA1 and 5.84-6.16 nm for PTerm455, and their cross-sectional radii of gyration RXS were also similar. The similarity of the RG and RXS values suggests that the tailpiece of IgA1 is not extended outwards in solution. The IgA1 RG values are higher than those for IgG, and the distance distribution function P(r) showed two distinct peaks, whereas a single peak was observed for IgG. Both results show that the hinge of IgA1 results in an extended Fab and Fc arrangement that is different from that in IgG. Automated curve-fit searches constrained by homology models for the Fab and Fc fragments were used to model the experimental IgA1 scattering curves. A translational search to optimise the relative arrangement of the Fab and Fc fragments held in a fixed orientation resembling that in IgG was not successful in fitting the scattering data. A new molecular dynamics curve-fit search method generated IgA1 hinge structures to which the Fab and Fc fragments could be connected in any orientation. A search based on these identified a limited family of IgA1 structures that gave good curve fits to the experimental data. These contained extended hinges of length about 7 nm that positioned the Fab-to-Fab centre-to-centre separation 17 nm apart while keeping the corresponding Fab-to-Fc separation at 9 nm. The resulting extended T-shaped IgA1 structures are distinct from IgG structures previously determined by scattering and crystallography which have Fab-to-Fab and Fab-to-Fc centre-to-centre separations of 7-9 nm and 6-8 nm, respectively. It was concluded that the IgA1 hinge is structurally distinct from that in IgG, and this results in a markedly different antibody structure that may account for a unique immune role of monomeric IgA1 in plasma and mucosa.

On the hydrodynamic analysis of macromolecular conformation

Hydrodynamics provides a powerful complementary role to the traditional "high resolution" techniques for the investigation of macromolecular conformation, especially in dilute solution, conditions which are generally inaccessible to other structural techniques. This paper describes the state of art of hydrodynamic representations for macromolecular conformation, in terms of (1) simple but straightforward ellipsoid of revolution modelling; (2) general triaxial ellipsoid modelling; (3) hydrodynamic bead modelling; (4) the ability, especially for polydisperse macromolecular systems, to distinguish between various conformation types; (5) analysis of macromolecular flexibility.

Hydrodynamic studies of a complex between the Fc fragment of human IgE and a soluble fragment of the Fc epsilon RI alpha chain

The interaction between immunoglobulin E (IgE) and its high-affinity receptor Fc epsilon RI is central to allergic disease. The binding site for Fc epsilon RI lies in the third constant region domain of the epsilon heavy chain of IgE (C epsilon 3). Identical epitopes on the two C epsilon 3 domains in the IgE-Fc are predicted to be on opposite sides of the structure, and therefore each could bind independently to a receptor molecule. Titrations, however, reveal that the IgE-Fc forms an equimolar complex with a soluble fragment of the Fc epsilon RI alpha chain (sFc epsilon RI alpha), and the molecular weight of the complex, as determined by sedimentation equilibrium, confirms this stoichiometry. The measured sedimentation coefficients of the two ligands are in good agreement with computed values for a compact IgE-Fc and an elongated sFc epsilon RI alpha structure. The calculated sedimentation coefficients for possible models of a 1:1 complex lead to exclusion of all highly extended geometries for the complex. Possible explanations for the paradoxical stoichiometry of the IgE-Fc/sFc epsilon RI alpha complex, in terms of the curved shape of IgE, a conformational change in IgE when the receptor binds, and steric interference between two molecules of Fc epsilon RI binding to identical sites, are discussed.

Modelling of the serine-proteinase fold by X-ray and neutron scattering and sedimentation analyses: occurrence of the fold in factor D of the complement system

Solution scattering is a powerful means of determining the overall arrangement of domains in the multidomain proteins of complement. the serine-proteinase domain is central to all proteolytic events during complement activation. As models of this domain, bovine beta-trypsin, trypsinogen, alpha-chymotrypsin and chymotrypsinogen A were studied by neutron and X-ray synchrotron solution scattering. At pH 7, all the X-ray and neutron M(r) values corresponded to monomeric proteins. The X-ray radii of gyration, RG, of beta-trypsin, trypsinogen, alpha-chymotrypsin and chymotrypsinogen A (measured in positive solute-solvent contrasts) were 1.59 nm, 1.78 nm, 1.71 nm and 1.76 nm (+/- 0.05-0.11 nm) in that order. Neutron contrast variation showed that the RG at infinite contrast, RC, for these four proteins were 1.57 nm, 1.70 nm, 1.67 nm and 1.78 nm (+/- 0.03 nm) in that same order. The radial inhomogeneity of neutron-scattering density, alpha, was positive at (5-13) x 10(-5), and corresponds to the preponderance of hydrophilic residues near the protein surface. On trypsinogen activation, a small reduction in the RG value of 0.13 +/- 0.07 nm was just detectable, while the RG of chymotrypsinogen A was unchanged after activation. The RC and alpha values of the four proteins can be calculated by using crystallographic co-ordinates. The reduced RG of beta-trypsin relative to trypsinogen was explained in terms of the removal of the extended N-terminal hexapeptide of trypsinogen. The full X-ray and neutron-scattering curves in positive and negative contrasts agreed well with scattering curves calculated from crystallographic coordinates to a nominal structural resolution of 4.5 nm, provided that the internal structure was considered in neutron modelling, and that the hydration was considered in X-ray modelling. Sedimentation-coefficient data also provide information on the disposition of domains in multidomain proteins. It was found that the hydrated X-ray sphere model could be directly utilized to calculate sedimentation coefficients. X-ray scattering on factor D showed from its RG of 1.78 nm that this is monomeric and very similar in structure to beta-trypsin. The X-ray-scattering curve of factor D was readily modelled using the beta-trypsin crystal structure after allowance for sequence changes. The success of these modellings provides a basis for the constrained modelling of solution scattering data for the multidomain proteins of complement.

Molecular modelling of the domain structure of factor I of human complement by X-ray and neutron solution scattering

Factor I is a typical multidomain protein of the complement system. It regulates complement activation by proteolytic degradation of C3b or C4b in the presence of factor H, complement receptor type 1, membrane cofactor protein or C4b-binding protein as cofactor. It is constructed from five presumed independently folded domains, namely a factor I module, a CD5-like domain, two low-density-lipoprotein receptor type A domains and a serine-proteinase domain. X-ray and neutron solution scattering was used to study the arrangement of these domains in factor I. Factor I was determined to be monomeric in solution, with an A280(1%,1cm) of 12.3-14.1. Its radius of gyration (RG) was 3.96 nm by X-rays in a high positive solute-solvent contrast, and 3.84 nm by neutrons at infinite solute-solvent contrast. The cross-sectional radius of gyration (RXS) was likewise found to be 1.64 nm by X-rays and 1.55 nm by neutrons. The RG data were not noticeably dependent on the solute-solvent contrast, whereas the RXS data showed a small dependence. The maximum dimension of factor I was determined to be 12.8 nm from the RG and RXS data, and 14-15 nm from the X-ray and neutron distance distribution functions. This length is too short to account for a linear arrangement of the domains in factor I. Small sphere models were developed for factor I in which the largest domain was modelled from the crystal structure for beta-trypsin. The attachment of either an elliptical cylinder or a two-armed V-shaped structure to this domain to represent the remaining four small domains gave good scattering curve-fits for factor I, and were compatible with experimental sedimentation coefficients. The non-extended domain models for factor I imply that the steric accessibility of each domain will be reduced, and this may be important for its functional activity.

Effect of thermoinduced changes in T4 bacteriophage structure on the process of molecular recognition of 'host' cells

By means of high-precision acoustic measurements and by methods of fluorescent and electron microscopy, investigations have been performed of thermoinduced conformational changes in T4 bacteriophage and its thermolabile mutants altered in baseplate proteins (gene products 7, 8, 10). A relationship was found between the conformational changes in T4 bacteriophage structure in the temperature range of 33-45 degrees C and the efficiency of bacteriophage adsorption and the changes in the orientation of long tail fibers. The possibility of heat regulation of 'recognition' of 'host' cells by bacterial viruses is suggested.

Molecular modeling of the multidomain structures of the proteoglycan binding region and the link protein of cartilage by neutron and synchrotron X-ray scattering

The interaction of proteoglycan monomers with hyaluronate in cartilage is mediated by a globular binding region at the N-terminus of the proteoglycan monomer; this interaction is stabilized by link protein. Sequences show that both the binding region (27% carbohydrate) and the link protein (6% carbohydrate) contain an immunoglobulin (Ig) fold domain and two proteoglycan tandem repeat (PTR) domains. Both proteins were investigated by neutron and synchrotron X-ray solution scattering, in which nonspecific aggregate formation was reduced by the use of citraconylation to modify surface lysine residues. The neutron and X-ray radius of gyration RG of native and citraconylated binding region is 5.1 nm, and the cross-sectional RG (RXS) is 1.9-2.0 nm. No neutron contrast dependence of the RG values was observed; however, a large contrast dependence was seen for the RXS values which is attributed to the high carbohydrate content of the binding region. The neutron RG for citraconylated link protein is 2.9 nm, its RXS is 0.8 nm, and these data are also independent of the neutron contrast. The scattering curves of binding region and link protein were modeled using small spheres. Both protein structures were defined initially by the representation of one domain by a crystal structure for a variable Ig fold and a fixed volume for the two PTR domains calculated from sequence data. The final models showed that the different dimensions and neutron contrast properties of binding region compared to link protein could be attributed to an extended glycosylated C-terminal peptide with extended carbohydrate structures in the binding region.(ABSTRACT TRUNCATED AT 250 WORDS)

Solution structure of human and mouse immunoglobulin M by synchrotron X-ray scattering and molecular graphics modelling. A possible mechanism for complement activation

The pentameric 71-domain structure of human and mouse immunoglobulin M (IgM) was investigated by synchrotron X-ray solution scattering and molecular graphics modelling. The radii of gyration RG of human IgM Quaife and its Fc5, IgM-S, Fab'2 and Fab fragments were determined as 12.2 nm, 6.1 nm, 6.1 nm, 4.9 nm and 2.9 nm in that order. The RG values were similar for mouse IgM P8 and its Fab'2 and Fab fragments, despite the presence of an additional carbohydrate site. The IgM scattering curves, to a nominal resolution of 5 nm, were compared with molecular graphics models based on published crystallographic alpha-carbon co-ordinates for the Fab and Fc structures of IgG. Good curve fits for Fab were obtained based on the crystal structure of Fab from IgG. A good curve fit was obtained for Fab'2, if the two Fab arms were positioned close together at their contact with the C mu 2 domains. The addition of the Fc fragment close to the C mu 2 domains of this Fab'2 model, to give a planar structure, accounted for the scattering curve of IgM-S. The Fc5 fragment was best modelled by a ring of five Fc monomers, constrained by packing considerations and disulphide bridge formation. A position for the J chain between two C mu 4 domains rather than at the centre of Fc5 was preferred. The intact IgM structure was best modelled using a planar arrangement of these Fab'2 and Fc5 models, with the side-to-side displacement of the Fab'2 arms in the plane of the IgM structure. All these models were consistent with hydrodynamic simulations of sedimentation data. The solution structure of IgM can therefore be reproduced quantitatively in terms of crystallographic structures for the fragments of IgG. Putative Clq binding sites have been identified on the C mu 3 domain. These would become accessible for interaction with Clq when the Fab'2 arms move out of the plane of the Fc5 disc in IgM, that is, a steric mechanism exposing pre-existing Clq sites. Comparison with a solution structure for Clq by neutron scattering shows that two or more of the six globular Clq heads in the hexameric head-and-stalk structure are readily able to make contacts with the putative Clq sites in the C mu 3 domains of free IgM if if the Clq arm-axis angle in solution is reduced from 40 degrees-45 degrees to 28 degrees. This could be the trigger for Cl activation.

Neutron and X-ray scattering studies on the human complement protein properdin provide an analysis of the thrombospondin repeat

Properdin is a regulatory glycoprotein of the alternative pathway of the complement system of immune defense. It is responsible for the stabilization of the C3 convertase complex formed between C3b and the Bb fragment of factor B. Neutron and X-ray solution scattering experiments were performed on the dimeric and trimeric forms of properdin. These have RG values of 9.1 and 10.7 nm, respectively. The scattering curves were compared with Debye sphere modeling simulations for properdin. Good agreements were obtained for models similar to published electron micrographs showing that the properdin trimer has a triangular structure with sides of 26 nm. Such a structure also accounted for sedimentation coefficient data on properdin. Primary structure analyses for mouse and human properdin have shown that this contains six homologous motifs known as the thrombospondin repeat (TSR), which is the second most abundant domain type found in the complement proteins. Sequences for these 12 TSRs were aligned with 19 others found in thrombospondin and the late complement components. Three distinct groups of TSRs were identified, namely, the TSRs found in thrombospondin and properdin, the TSRs mostly found at the N-terminus of the late complement components, and the TSRs found at the C-terminus of the late components. Averaged secondary structure predictions suggested that all three groups contain similar backbone structures with two amphipathic turn regions and one hydrophilic beta-strand region. The mean dimensions of the TSRs of properdin in solution were determined to be approximately 4 nm X 1.7 nm X 1.7 nm, showing that these are elongated in structure.

Oligomeric domain structure of human complement factor H by X-ray and neutron solution scattering

Factor H is a regulatory component of the complement system. It has a monomer Mr of 150,000. Primary structure analysis shows that the polypeptide is divided into 20 homologous regions, each 60 amino acid residues long. These are independently folding domains and are termed "short consensus repeats" (SCRs) or "complement control protein" (CCP) repeats. High-flux synchrotron X-ray and neutron scattering studies were performed in order to define its solution structure in conditions close to physiological. The Mr of factor H was determined as 250,000-320,000 to show that factor H is dimeric. This structure is maintained at concentrations between 1 and 11 mg/mL in the pH range 5-9. Zn2+ ions are an inhibitor of C3b cleavage by factor I, a reaction in which factor H acts as a cofactor. Additions of Zn2+ to factor H caused it to form oligomers containing 4-10 monomers. The radius of gyration RG of native factor H by X-rays or by neutrons in 0% or 100% 2H2O buffers is not measurable but is greater than 12.5 nm. Two cross-sectional radii of gyration RXS-1 and RXS-2 were determined as 3.0-3.1 and 1.8 nm, respectively. Analyses of the cross-sectional intensities show that factor H is composed of two distinct subunits. The RXS-1 corresponds to the cross-sectional properties of both subunits and exhibits an unusual radiation dependence on the X-ray flux. Since RXS-2 is close to the corresponding RXS of C4b binding protein (91% of which is formed from SCR/CCP domains), it is inferred that the SCR/CCP domains of factor H and C4b binding protein have similar solution structures. The use of hydrodynamic spheres to reproduce literature sedimentation coefficients of 5.5-5.6 S showed that these were compatible with a V-shaped arrangement of two rods (36 spheres each, length 87 +/- 5 nm) joined at an angle of 5 degrees. The use of a similar arrangement of 244 spheres arranged in two rods (length 77 nm) to fit the experimental X-ray and neutron scattering curves showed that the two rods are joined at an angle of 5 degrees. This model corresponds to an actual RG of 21-23 nm. The separation between each SCR/CCP in factor H is close to 4 nm. In the solution structure of factor H, the SCR/CCP domains are in a highly extended conformation.

Hydrodynamic data show that C1- inhibitor of complement forms compact complexes with C1-r and C1-s

The C1- inhibitor of the complement cascade forms stoichiometric complexes with C1-r and C1-s and controls the activation of first component C1 of complement. Literature sedimentation coefficients s degrees 20,w for the complexes formed between C1- inhibitor, C1-r and C1-s were analysed using frictional ratios and the hydrodynamic sphere approach. A head-and-tail two-domain model for C1- inhibitor was combined with cylindrical hydrodynamic models for the six-domain structures of C1-r and C1-s. The hydrodynamic data show that the heavily glycosylated N-terminal domain of C1- inhibitor is positioned close to the two complement 'short consensus repeat' domains found in the centre of C1-r and C1-s.

Two-domain structure of the native and reactive centre cleaved forms of C1 inhibitor of human complement by neutron scattering

The C1 inhibitor component of human complement is a member of the serpin superfamily, and controls C1 activation. Carbohydrate analyses showed that there are seven O-linked oligosaccharides in C1 inhibitor. Together with six N-linked complex-type oligosaccharides, the carbohydrate content is therefore 26% by weight and the molecular weight (Mr) is calculated as 71,100. Neutron scattering gives an Mr of 76,000 (+/- 4000) and a matchpoint of 41.8 to 42.3% 2H2O, in agreement with this carbohydrate and amino acid composition. Guinier plots to determine the radius of gyration RG were biphasic. Neutron contrast variation of C1 inhibitor in H2O-2H2O mixtures gave an overall radius of gyration RG at infinite contrast of 4.85 nm, from analyses at low Q, and a cross-sectional RG of 1.43 nm. The reactive centre cleaved form of C1 inhibitor has the same Mr and structure as the native molecule. The length of C1 inhibitor, 16 to 19 nm, is far greater than that of the putative serpin domain. This is attributed to an elongated structure for the carbohydrate-rich 113-residue N-terminal domain. The radial inhomogeneity of scattering density, alpha, is large at 59 x 10(-5) from the RG data and 28 x 10(-5) from the cross-sectional analysis, and this is accounted for by the high oligosaccharide content of C1 inhibitor. The scattering data were modelled using small spheres. A two-domain structure of length 18 nm based on two distinct scattering densities accounted for all the contrast variation data. One domain is based on the crystal structure of alpha 1 antitrypsin (7 nm x 3 nm x 3 nm). The other corresponds to an extended heavily glycosylated N-terminal domain of length 15 nm, whose long axis is close to the longest axis of the serpin domain. Calculation of the sedimentation coefficient s0(20),w for C1 inhibitor using the hydrodynamic sphere approach showed that a two-domain head-and-tail structure with an Mr of 71,000 and longest axis of 16 to 19 nm successfully reproduced the s0(20),w of 3.7 S. Possible roles of the N-terminal domain in the function of C1 inhibitor are discussed.

Structural comparisons of the native and reactive-centre-cleaved forms of alpha 1-antitrypsin by neutron- and X-ray-scattering in solution

alpha 1-Antitrypsin is the best-characterized member of the serpin (serine-proteinase inhibitor) superfamily. Its solution structure was studied by high-flux neutron-scattering and synchrotron X-ray-scattering. Neutron data show that its absorption coefficient A1% 280,1cm is 5.4. The neutron radius of gyration RG at infinite contrast for native alpha 1-antitrypsin is 2.61 nm, characteristic of a moderately elongated structure, and its cross-sectional RG is 1.34 nm. The internal inhomogeneity of scattering densities within alpha 1-antitrypsin is high at 29 x 10(-5). The X-ray RG is 2.91 nm, in good agreement with the neutron RG of 2.82 nm in 1H2O. This RG is unchanged in reactive-centre-cleaved alpha 1-antitrypsin. These parameters are also unchanged at pH 8 in sodium/potassium phosphate buffers up to 0.6 M. The neutron and X-ray curves for native alpha 1-antitrypsin were compared with Debye simulation based on the crystal structure of reactive-centre-cleaved (papain) alpha 1-antitrypsin. After allowance for residues not visible in the crystallographic electron-density map, and rejoining the proteolysed site between Met-358 and Ser-359 by means of a relatively minor conformational re-arrangement, good agreement to a structural resolution of 4 nm is obtained with the neutron data in two contrasts and with the X-ray data. The structures of the native and cleaved forms of alpha 1-antitrypsin are thus similar within the resolution of solution scattering. This places an upper limit on the magnitude of the presumed conformational changes that occur in alpha 1-antitrypsin on reactive-centre cleavage, as indicated in earlier spectroscopic investigations of the Met-358-Ser-359 peptide-bond cleavage. Methods for scattering-curve simulations from crystal structures are critically assessed. The RG data lead to dimensions of 7.8 nm x 4.9 nm x 2.2 nm for native alpha 1-antitrypsin. The high internal inhomogeneity and the asymmetric shorter semi-axes of 4.9 nm and 2.2 nm suggest that the three oligosaccharide chains of alpha 1-antitrypsin are essentially freely extended into solvent in physiological conditions. This conclusion is also supported by the Debye simulations, and by modelling based on hydrodynamic parameters.

The quaternary structure in solution of human complement subcomponent C1r2C1s2

C1r2C1s2 is a subcomponent of first component C1 of the complement cascade. Previously two distinct models for its structure have been described, in which C1r2C1s2 is either a linear rod-like assembly of the globular domains found in each of C1s and C1r, or these domains are arranged to form an asymmetric X-shaped structure. These two models were evaluated by using hydrodynamic simulations and neutron scattering. The data on C1s, C1s2 and C1r are readily represented by straight hydrodynamic cylinders, but not C1r2 or C1r2C1s2. Tests of the X-structure for C1r2 and C1r2C1s2 successfully predicted the experimental sedimentation coefficients, thus supporting this model. Neutron scattering analyses on C1s and C1r2 are consistent with a linear structure for C1s, but not for C1r2. An X-shaped structure for C1r2 was found to give a good account of the neutron data at large scattering angles. The total length of the C1s and C1r monomers was determined as 17-20 nm, which is compatible with electron microscopy. On the basis of the known sequences of C1r and C1s, this length is accounted for by a linear arrangement of a serine-proteinase domain (length 4 nm), two short consensus repeat domains (2 x 4 nm), and a globular entity containing the I, II and III domains (4-7 nm).

Molecular modelling of human complement component C3 and its fragments by solution scattering

Solution scattering experiments using both X-rays and neutrons are reported for human complement component C3 and up to six other glycoprotein fragments that are derived from C3. The X-ray and neutron molecular masses and neutron matchpoints are in agreement with the known primary sequence of C3. The X-ray radius of gyration RG of C3 is 5.2 nm and is similar for the related forms C3u, C3(a + b) and C3b. The X-ray cross-sectional radius of gyration RXS of C3b is however less than that of C3, C3u and C3(a + b). The major fragments of C3b, namely C3c and C3dg, were studied. The RG of C3c is 4.7 nm and for C3dg is 2.9 nm. C3c and C3dg do not interact when they coexist in solution in equimolar amounts. When C3u is cleaved into iC3u, the RG of iC3u increases to 5.9 nm and its RXS decreases, showing that C3c and C3dg behave as independent entities within the parent glycoprotein. Analyses of the neutron RG and RXS values by contrast variation techniques confirm the X-ray analyses, and show no evidence for significant hydrophobic or hydrophilic domains within C3 or any of its fragments. Shape analyses show that C3, C3c and C3dg are elongated particles. Debye models were developed using the scattering curve out to Q = 1.6 nm-1. These show that C3 and C3c resemble oblate ellipsoids while C3dg resembles a prolate ellipsoid. C3dg lies on the long edge of C3c within C3. The dimensions of the models are 18 nm X 2 nm X 10 nm for C3, 18 nm X 2 nm X 7 nm for C3c and 10 nm X 2 nm X 3 nm for C3dg. These models are compatible with analyses of the scattering curve RG and RXS values, data from sedimentation coefficients, and images of C3 and C3c seen by electron microscopy.

Unusual ultrastructure of complement-component-C4b-binding protein of human complement by synchrotron X-ray scattering and hydrodynamic analysis

Solution X-ray-scattering experiments with the use of synchrotron radiation on the human complement-component-C4b-binding protein showed that its RG is 13 nm and that its Mr is 550,000. From the known primary amino acid sequence and estimated carbohydrate content, C4b-binding protein is inferred to have a total of 7.4 +/- 1 subunits. Heptameric computer models for C4b-binding protein were based on the X-ray-scattering curve to a resolution of 6.4 nm, and literature values for sedimentation coefficients and electron-microscopy images. The macromolecule was represented by a bundle of seven arms held together at the C-terminal end and spaced out by a base containing 23% of C4b-binding protein by volume. If the overall length of each arm is assumed to be 33 nm as seen in electron microscopy, the solution data indicate an average arm-axis angle of 5-10 degrees. The seven arms of C4b-binding protein are found to be close together, in distinction to the splayed-out images seen in electron micrographs.

Molecular modelling of human complement subcomponent C1q and its complex with C1r2C1s2 derived from neutron-scattering curves and hydrodynamic properties

Models for the structures of subcomponent C1q of first component C1 of human complement and its complex with subunit C1r2C1s2 are compared with experimental neutron-scattering curves. The length of the C1q collagenous arm is closer to 14.5 nm than to 11.5 nm proposed from electron microscopy, and this is consistent with the primary sequence of C1q. The mean C1q base-arm angle is 40-45 degrees and C1q is found to be flexible: the base-arm angle can vary up to 30 degrees from equilibrium at any moment. The complex of C1r2C1s2 and C1q requires a large shape change in C1r2C1s2. Ring-like models for C1r2C1s2 are not as successful at rationalizing the scattering data as are models that involve C1r2C1s2 binding to one side of C1q. Hydrodynamic calculations of the sedimentation coefficients for C1q and C1 are generally consistent with these neutron models.

The shapes of biantennary and tri/tetraantennary alpha 1 acid glycoprotein by small-angle neutron and X-ray scattering

Two forms of alpha 1 acid glycoprotein (orosomucoid) have been studied using small-angle neutron and X-ray scattering techniques; in one form all the five glycan chains were biantennary, while in the other they were either triantennary or tetraantennary. The radius of gyration RG was found to be sensitive to salt for the biantennary form, but to be unchanged up to an ionic strength of 3 M for the triantennary and tetraantennary forms. Conformational heterogeneity is thus associated with carbohydrate heterogeneity. Hydrodynamic frictional coefficients <f> confirm these findings. Simple models of alpha 1 acid glycoprotein were developed to account for the RG and <f> values. These show that the compact conformation is slightly more elongated than a globular protein and that the expanded biantennary conformation has a most extended carbohydrate structure. Up to half of the surface of the compact shape can be covered by carbohydrate residues.

Hydrodynamic properties of complex, rigid, biological macromolecules: theory and applications

Among the Various methods for characterizing macromolecules in solution, hydrodynamic techniques play a major role. Since the advent of the ultracentrifuge and the development of viscometric apparatus, sedimentation coefficients and intrinsic viscosities have been extensively used to learn about the size and shape of synthetic and biological polymers. More recently, refined techniques such as quasielastic light scattering, transient electric birefringence and fluorescence anisotropy decay have made it possible to obtain in a simple and rapid way quantitative information of high precision on the translational and rotational brownian dynamics of dissolved macromolecules.