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.     

The ELLIPS suite of macromolecular conformation algorithms

This paper describes a series of four programmes for the PC based on ellipsoidal representations of macromolecular shape in solution using Universal shape functions. ELLIPS1 is based on simple ellipsoid of revolution models (where two of the three axes of the ellipsoid are fixed equal to each other). If the user types in a value for a shape function from sedimentation or other types of hydrodynamic measurement, it will return a value for the axial ratio of the ellipsoid. ELLIPS2 is based on the more general triaxial ellipsoid with the removal of the restriction of two equal axes. The user enters the three semi-axial dimensions of the molecule or the equivalent two axial ratios and ELLIPS2 returns the value of all the hydrodynamic shape functions. It also works of course for ellipsoids of revolution. ELLIPS3 and ELLIPS4 do the reverse of ELLIPS2, that is they both provide a method for the unique evaluation of the triaxial dimensions or axial ratios of a macromolecule (and without having to guess a value for the so-called „hydration”) after entering at least three pieces of hydrodynamic information: ELLIPS3 requires EITHER the intrinsic viscosity with the second virial coefficient (from sedimentation equilibrium, light scattering or osmometry) and the radius of gyration (from light or x-ray scattering) OR the intrinsic viscosity with the concentration dependence term for the sedimentation coefficient and the (harmonic mean) rotational relaxation time from fluorescence depolarisation measurements. ELLIPS4 evaluates the tri-axial shape of a macromolecule from electro-optic decay based Universal shape functions using another Universal shape function as a constraint in the extraction of the decay constants. Accepted: 1 November 1996     

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.     

The distribution of pressure behind a soft contact lens

We determine the pressure distribution behind a soft contact lens that is necessary to keep the lens in conformity with an axisymmetric substrate. The substrate consists of two regions: a central portion, the cornea, supposed to be an ellipsoid; and a peripheral region, the sclera, taken to be a sphere. The pressure is obtained as part of a numerical solution of the axisymmetric equilibrium equations for an initially curved, linearly elastic membrane. The relaxed shape of the lens is assumed to be an axisymmetric ellipsoid with a central curvature and a shape factor different from those of the cornea. The variation in the thickness of the lens from its center to edge is approximated by a polynomial. Pressure distributions are obtained for several typical soft contact lens fittings.     

Elf Dosage in Ellipsoidal Models of Man Due to High Voltage Transmission Lines

The fields, flux, and power density produced inside an ellipsoidal model of man by overhead high-voltage transmission lines have been calculated. The values depend strongly on the conductivity and the shape of the ellipsoid and, in general, vary from point to point within it. The maximum energy flux is the more reliable indicator of exposure to the electromagnetic field.     

A Method for Calculating the Volume and Surface Area in Rice Mesophyll Cells

A method was developed for determining the surface area and volume of rice mesophyll cells of elaborate configuration. The method was employed to calculate these indices in several types of rice mesophyll cells found in seventy samples (53 species) of diverse origin coming from Japan, China, Korea, India, Nepal, Australia, France, Italy, Uzbekistan, Afghanistan, and Krasnodar and Primorskii regions. The cultivars of diverse geographic origin varied in cell shape and size due to the number, size, and arrangement of chloroplasts. When the volumes and surface areas of leaf mesophyll cells were compared using the method reported herein and a simple empirical model of the cell as a single ellipsoid, the two methods produced relatively similar data for cell volume; however, the surface area calculated by the former method was about two times larger than in the latter case. The method described in this paper allows for accurate calculations of the volume and surface area of rice mesophyll cells when data are available on the cell shape and linear dimensions and the number of chloroplasts per cell.     

木兰属3种植物花粉形态研究

用光学显微镜和扫描电镜观察木兰属（Magnolia)3种植物的花粉粒,其形态特征是：花粉粒长球形,具单沟：外壁光滑或粗糙,结果表明：该属3种植物花粉形态在种的水平上具有分类学意义,而且具有明显的深化趋势。     

Determination of the topological shape of integral membrane protein light-harvesting complex LH2 from photosynthetic bacteria in the detergent solution by small-angle X-ray scattering

The topological shape of the integral membrane protein light-harvesting complex LH2 from photosynthetic bacteria Rhodobacter spheroides 2.4.1 in detergent solution has been determined from synchrotron small-angle X-ray scattering data using direct curve-fitting by the ellipsoid, ab initio shape determination methods of simulated annealing algorithm and multipole expansion, respectively. The results indicate that the LH2 protein in aqueous solution is encapsulated by a monolayered detergent shell. The detergent-stabilized structure has the shape of an oblate plate, with a thickness of 40 A, a long axis of 110 A, and a short axis of 85 A. After correction for the detergent shell, the shape of the LH2 core is also an oblate plate with a height of 40 A, a long axis of 80 A, and a short axis of 55 A. In contrast to the cylindrical crystal structure with a height of 40 A and a diameter of 68 A, the molecular shape of the LH2 complex in detergent solution clearly deviates from the ringlike crystal structure, with an eccentricity found to be 0.59-consistent with the result of single molecular spectroscopy study of the isolated single LH2 molecules.     

Protein structure probed by polarization spectroscopy. II. A time-resolved fluorescence study of human fibrinogen

Human fibrinogen in solution was studied by monitoring the time-resolved depolarization of the fluorescence emitted by two spectroscopic labels of which the fluorescence lifetimes differ by an order of magnitude. Contrary to a long-held view, no evidence of molecular flexibility was found in the 10-1000 ns range. In addition, from the rate of the overall rotation, it is proposed that a prolate and symmetric ellipsoid of 47 X 10.5 nm may represent the time-averaged hydrodynamic size and shape of the protein in solution. This rigid and highly hydrated structure (4 g water/g protein) accommodates the latest nodular models obtained from electron microscopy, explains the singular hydrodynamics of fibrinogen and, apparently, it would perform the two main functions of the protein in haemostasis, blood coagulation and platelet aggregation, more efficiently than the flexible molecule.     

A general solution for the time delay introduced by a low-pass Butterworth digital filter: An application to musculoskeletal modeling

Low-pass Butterworth digital filters are commonly used in biomechanics-related research. In general, the input signal is filtered in the forward and reverse directions so that a temporal shift in the output signal does not occur. There are times, however, when introducing a specific time delay is an important consideration when modeling a physiological event. Filtering the data in the forward direction only can be used as an efficient method to account for a specific time delay. Specific delays are possible by carefully selecting the filter order and cut-off frequency. The purpose of this paper is to present the analytical formulation of a general solution for the time delay introduced by a low-pass Butterworth digital filter.     

Reinvestigation of the shape and state of hydration of the skeletal myosin subfragment 1 monomer in solution

Hydrodynamic calculations lead to the conclusion that chymotryptic (or ethylenediaminetetraacetic acid) myosin S1 in solution (hydrated), at 1-5 degrees C, can be modeled as a prolate ellipsoid, with an axial ratio lying between p = 1.0 and 2.5 (major axis between 100.5 A, for p = 1.0, and 162.5 A, for p = 2.5). The degree of hydration is considerable (1.24 g/g for p = 2.5 and 2.02 g/g for p = 1.0). The dehydrated myosin head is pear-shaped under the electron microscope, and its narrowest part is located near the junction with the tail [Elliott, A., & Offer, G. (1978) J. Mol. Biol. 123, 505-519]. Mendelson & Kretzschmar [Mendelson, R. A., & Kretzschmar, K.M. (1980) Biochemistry 19, 4103-4108] have shown that the pear-shaped molecule does not predict the experimental X-ray scattering curve. Nor is this model able to predict the hydrodynamic values. The three-dimensional model for S1 used by Mendelson and Kretzschmar gives a rather good fit to the experimental X-ray scattering curve, but it does not predict the hydrodynamic values. In order to try to reconcile the three models and to fit the X-ray scattering curve and the hydrodynamic data, we suggest that, in solution, the S1 monomer has the shape of a prolate ellipsoid and that an inclusion of bound water exists at one extremity of the protein. The rest of bound water surrounds the protein. As first approximation, the dry protein and the hole are assumed to have the same shape as the hydrated molecule (prolate ellipsoid; p).(ABSTRACT TRUNCATED AT 250 WORDS)     

木兰属几种药用植物花粉粒形态扫描电镜观察

用扫描电镜方法观察木兰属（Ｍａｇｎｏｌｉａ）几种药用植物的花粉粒及花药,其共同形态特征是：花粉粒近球形或长球形,具单沟或不具沟;外壁光滑或较粗糙。花药表皮细胞纺锤形或柱形,排列紧密,具条状纹饰。     

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.     

Shape of Ocr, the gene 0.3 protein of bacteriophage T7: modeling based on light scattering experiments

Ocr, the first protein expressed by bacteriophage T7, inhibits type Iota DNA restriction enzymes by preventing them from binding to DNA. This inhibition allows the phage to successfully infect the host. The shape of ocr is modeled on the basis of static and dynamic light scattering measurements. The static light scattering data confirm previous observations that ocr exists in solution as a dimer. The diffusion constant determined by dynamic light scattering indicates a nonspherical shape of the ocr dimer. Hydrodynamic models of ellipsoids are presented, and it is argued that ocr is best described by a prolate ellipsoid with dimensions of 10.4 nm by 2.6 nm. The size and shape predicted by this model are consistent with ocr acting as a mimic of the DNA structure bound by type Iota restriction enzymes.     

Shape of protein L11 from the 50S ribosomal subunit of Escherichia coli.

Protein L11 from the 50S ribosomal subunit of Escherichia coli A19 was purified by a method using nondenaturing conditions. Its shape in solution was studied by hydrodynamic and low-angle x-ray scattering experiments. The results from both methods are in good agreement. In buffers similar to the ribosomal reconstitution buffer, the protein is monomeric at concentrations up to 3 mg/mL and has a molecular weight of 16 000-17 000. The protein molecule resembles a prolate ellipsoid with an axial ratio of 5-6:1 a radius of gyration of 34 A, and a maximal length of 150 A. From the low-angle x-ray diffraction data, a more refined model of the protein molecule has been constructed consisting of two ellipsoids joined by their long axes.     

Interactions of the Neurotoxin Vipoxin in Solution Studied by Dynamic Light Scattering

The neurotoxin vipoxin is the lethal component of the venom of Vipera ammodytes meridionalis. It is a heterodimer of a basic toxic His-48 phospholipase A₂ (PLA₂) and an acidic nontoxic Gln-48 PLA₂. The shape of the neurotoxin and its separated components in solution as well as their interactions with calcium, the brain phospholipid phosphatidylcholine, and two inhibitors, elaidoylamide and vitamin E, were investigated by dynamic light scattering. Calcium binding is connected with a conformational change in vipoxin observed as a change of the hydrodynamic shape from oblate ellipsoid to a shape closer to a sphere. The Ca²⁺-bound form of vipoxin, which is catalytically active, is more compact and symmetric than the calcium-free heterodimer. Similar changes were observed as a result of the Ca²⁺-binding to the two separated subunits. In the presence of aggregated phosphatidylcholine, the neurotoxic complex dissociates to subunits. It is supposed that only the toxic component binds to the substrate, and the other subunit, which plays a chaperone function, remains in solution. The inhibition of vipoxin with the synthetic inhibitor elaidoylamide and the natural compound vitamin E changes the shape of the toxin from oblate to prolate ellipsoid. The inhibited toxin is more asymmetric in comparison to the native one. Similar, but not so pronounced, effects were observed after the inhibition of the monomeric and homodimeric forms of the toxic His-48 PLA₂. Circular dichroism measurements in the presence of urea, methylurea, and ethylurea indicate a strong hydrophobic stabilization of the neurotoxin. Hydrophobic interactions stabilize not only the folded regions but also the regions of intersubunit contacts.     

Substrate interactions with the alpha-subunit of the Escherichia coli tryptophan synthase. A kinetic study of the wild-type alpha-subunit.

Small-angle X-ray scattering has been used to determine the size and shape of human antithrombin III and its complex with heparin. The scattering data obtained show that antithrombin III behaves like an ellipsoid with semi-axes of 1.9, 3.7, and 5.2 nm. The antithrombin III-heparin complex produces a scattering curve very similar to that of pure antithrombin III, indicating that there is no major change in size and shape upon binding of heparin. The nature of the heparin binding site is discussed.     

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.     

A small angle X-ray study of the elongation factor complex Tu . GDP from Escherichia coli.

The protein elongation factor complex Tu. GDP from Escherichia coli was investigated in the presence of 0.01 mM GDP using the small-angle X-ray method. The overall shape and the molecular parameters of the Tu . GDP complex were determined using a least-squares method where the experimental data were used directly without desmearing. The best fit to the experimental data was obtained assuming the molecule to be an ellipsoid of revolution with the semiaxes A = B = 4.08 nm, and C = 1.18nm. Determination of the molecular weight gave the result Mr = 46 000, which corresponds to a water content equal to 26% (by weight).     

Segmentation by classification: A novel and reliable approach for semi-automatic selection of HIV/SIV envelope spikes

We describe a semiautomated approach to segment Env spikes from the membrane envelope of Simian Immunodeficiency Virus visualized by cryoelectron tomography of frozen-hydrated specimens. Multivariate data analysis is applied to a large set of overlapping subvolumes extracted semiautomatically from the viral envelope and does not utilize a template of the target structure. The major manual step used in the method involves determination of six points that define an ellipsoid approximating the virion shape. The approach is robust to departures of the actual virion from this starting ellipsoid. A point cage of sufficient density is generated to ensure that any spike-like protein is identified multiple times. Subsequently translational alignment of class averages to a cylindrical reference on a curved surface separates subvolumes with spikes from those without. Spike containing subvolumes identified multiple times are removed by proximity analysis. Slightly different procedures segment spikes in the equatorial and the polar regions. Once all spikes are segmented, further alignment of class averages using separately the polar and spin angles produces recognizable spike images. Our approach localized 96% of the equatorial spikes and 85% of all spikes identified manually; it identifies a significant number of additional spikes missed by manual selection. Two types of spike shapes were segmented, one with near 3-fold symmetry resembling the conventional spike, the other had a T-shape resembling the spike structure obtained when antibodies such as PG9 bind to HIV Env. The approach should be applicable to segmentation of any protein spikes extending from a cellular or virion envelope.