Novel size-independent modeling of the dilute solution conformation of the immunoglobulin IgG Fab' domain using SOLPRO and ELLIPS

The proliferation of hydrodynamic modeling strategies to represent the shape of quasirigid macromolecules in solution has been hampered by ambiguities caused by size. Universal shape parameters, independent of size, developed originally for ellipsoid modeling, are now available for modeling using the bead-shell approximation via the algorithm SOLPRO. This paper validates such a "size-independent" bead-shell approach by comparison with the exact hydrodynamics of 1) an ellipsoid of revolution and 2) a general triaxial ellipsoid (semiaxial ratios a/b, b/c) based on a fit using the routine ELLIPSE (. J. Mol. Graph. 1:30-38) to the chimeric (human/mouse) IgG Fab' B72.3; a similar fit is obtained for other Fabs. Size-independent application of the bead-shell approximation yields errors of only approximately 1% in frictional ratio based shape functions and approximately 3% in the radius of gyration. With the viscosity increment, errors have been reduced to approximately 3%, representing a significant improvement on earlier procedures. Combination of the Perrin frictional ratio function with the experimentally measured sedimentation coefficient for the same Fab' from B72.3 yields an estimate for the molecular hydration of the Fab' fragment of approximately (0.43 +/- 0.07) g/g. This value is compared to values obtained in a similar way for deoxyhemoglobin (0.44) and ribonuclease (0.27). The application of SOLPRO to the shape analysis of more complex macromolecules is indicated, and we encourage such size-independent strategies. The utility of modern sedimentation data analysis software such as SVEDBERG, DCDT, LAMM, and MSTAR is also clearly demonstrated.     

Modeling biological macromolecules in solution: 3. The Λ-R intersection method for triaxial ellipsoids

The general triaxial ellipsoid model for the gross conformation of macromolecules in solution represents a signficiant advance over the previously, almost ubiquitously used ellipsoid of revolution model. A new method is presented which involves the graphical intersection of two triaxial hydrodynamic functions (Λ and R) involving viscosity, sedimentation and fluorescence depolarization. The method is restricted to macromolecules asymmetric enough for the functions to be sufficiently sensitive but not so asymmetric for there to be problems of internal rotations between parts of the macromolecules. The method is illustrated by application to data for neurophysin II monomers and dimers.     

A macromolecular shape function based on sedimentation velocity parameters

A volume-independent shape function, experimentally determinable from sedimentation velocity experiments, was formulated explicitly in terms of the axial ratio of a macromolecule considered as an ellipsoid of revolution. Use of this function offers a simple first approach to the elucidation of macromolecular geometry as illustrated by calculations for ovalbumin, bovine serum albumin, and myosin.     

The shape of myosin subfragment-1. A equivalent oblate ellipsoid model based on hydrodynamic properties

The molecular weights of the two heads of myosin subfragment-1, S-1(A1) and S-1(A2), based on sedimentation equilibrium are 120 000 and 110 000. Hydrodynamically, the two heads are indistinguishable, with intrinsic viscosity, [eta], of 0.064-0.065 dL/g and sedimentation coefficient, s(0)20,w, of 5.8 S.Together with the rotational correlation time taken from the literature (235 ns), all three hydrodynamic properties can be better fitted with an equivalent oblate ellipsoid of revolution than a prolate model. The width of the equatorial axis of the ellipsoid is about 135 A (the axial ratio is about 6). Probably, the S-1(A1) and S-1(A2) molecules have a half-doughnutlike or a flattened pearlike shape rather than an elongated one.     

An estimation of the dimensions of the phycocyanin molecule

Knowledge of the total particle volume and the specific volumes of the constituent polar and nonpolar amino acid residues of a globular protein may be used in suitable instances to estimate the size and shape, of the macromolecule. Use has been made of the data, which is available in the literature for phycocyanin from Plectonema calothricoidcs, to predict possible models for the monomer and hexamer forms of this protein. The monomer is well represented by a prolate ellipsoid with semiaxes of 45 and 17Å and an approximate molecular weight of (46000). The hexamer is envisaged as the aggregate of six such monomers, in juxtaposition, with their major axes parallel so as to form a closed ring structure of about 268000 molecular weight. These proposed models are consistent with the previously published electron micrographs and hydrodynamic properties of this protein.     

A General Method for Modeling Macromolecular Shape in Solution: A Graphical (II-G) Intersection Procedure for Triaxial Ellipsoids

A general method for modeling macromolecular shape in solution is described involving measurements of viscosity, radius of gyration, and the second thermodynamic virial coefficient. The method, which should be relatively straightforward to apply, does not suffer from uniqueness problems, involves shape functions that are independent of hydration, and models the gross conformation of the macromolecule in solution as a general triaxial ellipsoid. The method is illustrated by application to myosin, and the relevance and applicability of ellipsoid modeling to biological structures is discussed.     

Evidence for a folded conformation of the cell wall protein fromAcetabularia (Polyphysa) cliftonii

Summary The cell wall protein fromAcetabularia has a non-random structure in aqueous solution at pH 5.3, as determined on the basis of intrinsic viscosity, sedimentation velocity and small angle X-ray scattering experiments. This non-random structure is stable in a pH range of 4.5–6.8, as observed on the basis of circular dichroism and viscosity measurements, supporting that the cell wall protein has a specific folded structure. All hydrodynamic measurements, including small angle X-ray scattering in solution, in this pH range are consistent with a prolate ellipsoid model for the shape of this protein, with overall dimensions ofc=86.0 Å,b=7.0 Å, anda=7.5 Å, and with a radius of gyration ofR=39.5 Å. The possibility of a coiled shape was investigated using a worm-like chain model, but it was inconsistent with the experimental data. Instead, a filled particle with uniform density which is equivalent in the scattering behavior is proposed. By a comparison of the observed radius of gyration, R_g=39.5 Å, and the radius of gyration of the cross section,R _c =7.5 Å, we were able to describe the cell wall protein in terms of a prolate ellipsoid of revolution. Comparisons of the experimental scattering curve, plotted as logl (h) versus logh, with the corresponding plots of normalized intensities, calculated for particles of particular shape and various axial ratios indicate a very asymmetric shape for the cell wall protein fromAcetabularia.This research was supported by a grant of the Deutsche Forschungsgemeinschaft.     

Physicochemical characterization of γ-crystallins from bovine lens—Hydrodynamic and biochemical properties

A detailed hydrodynamic study has been made on the γ-crystallin of the bovine lens. Sedimentation study indicates that γ-crystallin shows a nearly gaussian peak throughout the course of sedimentation at high speed, using a synthetic boundary cell. The diffusion and sedimentation coefficients are 10.3×10^?7 cm²/sec and 2.51 S, respectively. The weight-average molecular weight of the unfractionated γ-crystallin calculated from sedimentation equilibrium is 21,800. The four major subfractions of γ-crystallin show similar hydrodynamic properties with an intrinsic viscosity of 2.50 ml/g and a Stokes radius of 21 Å. The distinct electrophoretic mobilities exhibited by the four subfractions show gel-concentration dependence and similar slopes in the Ferguson plot, indicative of being charge isomers of the same molecular species. Amino acid analysis of these four subfractions corroborated the conclusions that these γ-crystallin polypeptides are closely related and comprise a multigene family of crystallins. Based on the sedimentation and intrinsic viscosity data, γ-crystallin can be modeled as a prolate ellipsoid with an axial ratio of approximately 3.0 and a hydration factor of 0.27 g water per gram protein. The circular dichroism data for γ-crystallins showed a minimum at about 217 nm, characteristic of a β-sheet conformation. These structural characteristics are in good accord with those derived from X-ray diffraction data for γ-crystallin II.     

Preferential solvent binding and change in conformation of bovine serum albumin in 2-chloroethanol-water mixed solvents.

Solvent binding to bovine serum albumin in 2-chloroethanol-water mixed solvents of different composition, measured previously by Inoue and Timasheff (Biopolymers (1972) 11 , 737–43) is applied to a hydrodynamic study of the solvated protein. From sedimentation and diffusion data, the apparent molecular weight of the solvated protein particle can be calculated, provided an average partial specific volume, computed from the composition of the particle, is introduced in Svedberg's equation. The unsolvated molecular weight of the protein can than be calculated by subtraction of the bound solvent. Further data on the hydrodynamic particle (f/f_min and axial ratio of the equivalent ellipsoid) are readily calculated from these experiments, and reinforce the supposition that 2-chloroethanol is a strong helix-inducing solvent.     

Hydrodynamic studies on chitosans in aqueous solution

Three commercial chitosans with a degree of acetylation of 25–30% were studied by light scattering (static and dynamic), analytical ultracentrifugation (sedimentation velocity and sedimentation equilibrium), and capillary viscometry in 0.02 M acetate buffer/0.1 M NaCl, pH 4.5. The molecular masses obtained by sedimentation equilibrium measurements or sedimentation and diffusion coefficients according to the Svedberg equation agreed well or fairly well with those from static light scattering whereas the molecular masses calculated via the Scheraga–Mandelkern equation were found too low by almost 50%. The various Mark–Houwink type relationships suggested a nearly free-draining flexible worm-like chain. A prolate ellipsoid of revolution with an axial ratio a/b25 was shown to be a hydrodynamically equivalent body of the flexible worm-like chain that had been derived from static light scattering. The findings illustrate the fact that a hydrodynamically strongly asymmetric shape need not mean a strongly elongated shape of the molecules in reality.     

A study of rhodopsin-detergent micelles by transient electric birefringence.

The hydrodynamic method of transient electric birefringence has been used to study bovine rhodopsin solubilized in two detergents, 0.02% Ammonyx LO and 0.045% digitonin. All measurements are interpreted as the sum of two exponentials by which the relaxation times yield the rotary diffusion coefficients for ellipsoids of revolution. The semi-major and minor axes for prolate ellipsoid models have been calculated and their axial ratio, 6.8, in both detergents, is in line with recent reports on the structure of rhodopsin. Studies on bleached rhodopsin showed a large increase in axial ratio in 0.02% Ammonyx LO.     

On the subunit structure of crotoxin: hydrodynamic and shape properties of crotoxin, phospholipase A and crotapotin.

This paper reports physical-chemical properties of the subunit structure of crotoxin, phospholipase A and crotapotin. The native crotoxin has a sedimentation coefficient of 3S and a radius of gyration of R_g = 16.5 Å and a molecular weight of 30,900. Dissociation of the 3S particle results in two proteins of unequal size with sedimentation coefficients of 1.5 S (crotapotin) and 1S (phospholipase A). These dissociated species and the reconstituted complex were investigated by means of hydrodynamic methods including small angle X-ray scattering. The actual frictional ratios were obtained indicating that crotoxin is a sphere with a Stokes' radius of R_o = 22.5 Å and an axial ratio of 1:3, whereas phospholipase A, depending on the degree of association, has a radius of gyration of R_g = 32.4 Å and a high axial ratio of 1:14 for the monomer. Crotapotin has a radius of gyration of R_g = 12.4 Å, indicating an oblate ellipsoid of revolution of an axial ratio of 1:4. Evidently, the crotoxin complex consists of one highly asymmetric molecule (phospholipase A) and an oblate ellipsoid (crotapotin), which reconstitutes to a spherical 3S-particle (crotoxin).     

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.     

Multiple forms of molybdate-stabilized glucocorticoid-receptor complexes from HeLa cell cytosol

Summary The investigation on hydrodynamic parameters of molybdate-stabilized glucocorticoid-receptor complexes from HeLa cell cytosol permitted resolution of four distinct forms. The first one could be detected in concentrated cytosols at low salt concentrations, and had the following properties: sedimentation coefficient = 9 S; R _s = 9.3 nm; M _r = 357,800; f/f _o = 1.83; axial ratio (prolate ellipsoid) = 16. When these cytosol extracts were diluted, a second form could be detected with sedimentation coefficient = 8.3 S; R _s = 9.05 nm; M _r = 320,700;f/f _o = 1.84; axial ratio = 16. Under high salt conditions, glucocorticoid-receptor complexes in concentrated cytosol had the following properties: sedimentation coefficient = 6.4 S; R _s, = 6.7 nm; M _r = 183,100;f/f _o = 1.64; axial ratio = 12. When either these cytosol extracts were diluted, or glucocorticoid-receptor complexes were subjected to repeated analysis, a fourth form was detected with sedimentation coefficient = 3.76 S; R _s = 5.67; M _r = 91,000; f/f _o = 1.75; axial ratio = 14. Besides salt concentration and dilution, the time elapsed between sample dilution and analysis appeared to affect the hydrodynamic properties of glucocorticoid-receptor complexes. On the basis of our findings, it has been concluded that the most likely structure of molybdate-stabilized glucocorticoid-receptor complexes of HeLa cell cytosol can be represented by association of monomers in homodimers, and homotetramers. A homotrimer form could not be deduced from our findings, and the 320,700 glucocorticoid-receptor complex we observed has been suggested to represent an unresolved mixture of trimers and tetramers.     

Nanosecond fluorometric investigation of hydrodynamic properties of adenosine triphosphatase from thermophilic bacterium PS3

The soluble portion (TF1) of proton-translocating ATPase from thermophilic bacterium PS3 was labeled with a fluorescent dye N-(1-pyrene)maleimide. The decay of fluorescence anisotropy of the adduct showed that TF1 in aqueous solution was characterized by a volume of equivalent sphere of 1,120 nm3. This value is 2.4 times the volume calculated from the molecular weight and partial specific volume, indicating a non-spherical shape and/or extensive hydration. A prolate ellipsoid with an axial ratio of 2 to 3 is suggested as a first approximation of the shape of hydrated TF1. The presence or absence of ATP, ADP, or Mg2+ did not alter the volume of the equivalent sphere appreciably; the probable conformational change of TF1 induced by these ligands does not lead to a gross alteration of its hydrodynamic properties.     

Solution properties of synthetic polypeptides. II. Sedimentation and viscosity of poly-γ-benzyl-L-glutamate in dimethylformamide

Nine samples of poly-γ-benzyl-L -glutamate (PBLG), ranging in M?_w from 19,000 to 410,000, were examined viscomctrically and by ultracentrifugation with dimethylforma-mide (DMF) at 25°C. as helicogenic solvent. The data for [η] and s₀ (limiting sedimentation coefficient) as functions of M?_w were fitted well by the theories for a rigid prolate ellipsoid of revolution whose major axis increases linearly with M?_w, but whose minor axis is independent of M?_w. This implies that the overall shape of the PBLG molecule in DMF is represented by a straight cylinder whose cross section is independent of its length. The length per monomeric residue h evaluated from [η] is about 1.3 A., whereas that from s₀ is about 1.6 A. No adequate explanation for this difference in h can be found at present. More serious is the fact that these hydrodynamically evaluated values of h are appreciably larger than, the value obtained from our light-scattering measurements reported previously. All these values of h from our studies are not consistent with the value characteristic of the α-helix, for which h is 1.5 A. The concentration dependence of s₀ was found to agree well with the recent theoretical prediction of Peterson for cylindrical macromolecules.     

The combination of the viscosity increment with the harmonic mean rotational relaxation time for determining the conformation of biological macromolecules in solution.

A new hydrodynamic shape function, lambda, is derived for determining the conformation of biological macromolecules in solution, adding to the increasing number of shape parameters whose experimental determination does not require a knowledge of the particle swelling due to solvation in solution. lambda can be found from a knowledge of the molecular weight, intrinsic viscosity and the harmonic mean rotational relaxation time. A table of values and a plot of lambda as a function of axial ratio for both oblate and prolate ellipsoids of revolution are given.     

A comparative study on the hydrodynamic shape, conformation, and stability of E. coli ribosomal subunits in reconstitution buffer.

We have compared the hydrodynamic shape, conformation, and stabilities of active, unwashed ribosomal subunits, as well as their susceptibilities to changes in temperature and ionic strength. Both intrinsic viscosity and sedimentation velocity measurements indicate that the 30 S subunit has a more asymmetric hydrodynamic shape. The intrinsic viscosity of this subunit in reconstitution buffer has been found to be significantly larger than the value reported previously. While the RNA conformation in both subunits may be very similar as suggested by the near uv CD spectra, the average conformation of the protein in the two subunits is drastically different. The 30 S subunit has a lower T_m. The 50 S subunit is rather stable toward changes of ionic strength, whereas the 30 S subunit is quite susceptible to changes in ionic strength.     

Size, shape, and hydration of a self-associating human IgG myeloma protein: axial asymmetry as a contributing factor in serum hyperviscosity

Studies of sedimentation, diffusion, viscosity, and buoyant density have been carried out on a human IgG1-lambda myeloma protein (IgG-MIT) isolated from the serum of a patient with multiple myeloma and the hyperviscosity syndrome. In comparison with pooled normal IgG, IgG-MIT exhibits smaller sedimentation and diffusion coefficients, a larger intrinsic viscosity, and a larger frictional ratio. The preferential hydration of IgG-MIT in cesium chloride was found to be within the range of values typically observed for globular proteins. The data are consistent with prolate ellipsoid geometry, and suggest that the axial ratio of the IgG-MIT monomer is approximately 50% greater than that typically observed for IgG. The concentration dependencies of the hydrodynamic data for IgG-MIT confirm the previous finding of reversible, concentration-dependent self-association for this protein. IgG-MIT thus represents the first reported instance of an IgG paraprotein for which in vivo hyperviscosity effects appear attributable to a twofold mechanism involving geometric asymmetry and concentration-dependent polymerization. The results are discussed in terms of the significant heterogeneity in molecular dimensions which may exist among normal IgG proteins.