The inertia-equivalent ellipsoid: a link between atomic structure and low-resolution models of small globular proteins determined by small-angle x-ray scattering

Low-resolution three-parameter models of the shape of a biopolymer in solution can be determined by a new indirect method from small-angle X-ray scattering without contrast-variation experiments. The basic low-resolution model employed is a triaxial ellipsoid - the inertia-equivalent ellipsoid (IEE). The IEE is related to the tensor of inertia of a body and the eigenvalues and eigenvectors of this tensor can be calculated directly from the atomic coordinates and from the homogeneous solvent-excluded body of a molecule. The IEE defines a mean molecular surface (like the sea level on earth) which models the molecular shape adequately if the IEE volume is not more than 30% larger than the dry volume of the molecule. Approximately 10 to 15% of the solvent excluded volume is outside the ellipsoid; the radii of gyration of the IEE and of the homogeneous molecular body are identical. The largest diameter of the IEE is about 5 to 15% (approximately 0.2-0.8 nm) smaller than the maximum dimension of globular molecules with molecular masses smaller than 65 000 daltons. From the scattering curve of a molecule in solution the IEE can be determined by a calibration procedure. 29 proteins of known crystal structure have been used as a random sample. Systematic differences between the axes of the IEE, calculated directly from the structure, and the axes of the scattering-equivalent ellipsoids of revolution, estimated from the scattering curve of the molecule in solution, are used to derive correction factors for the axial dimensions. Distortions of model dimensions of 20 to 40% (up to 1 nm), caused by misinterpretation of scattering contributions from electron density fluctuations within the molecule, are reduced to a quarter by applying these correction factors to the axes of the scattering-equivalent ellipsoids of revolution. In a computer experiment the axes of the inertia-equivalent ellipsoids have been determined for a further nine proteins with the same accuracy. The automated estimation of the IEE from the scattering curve of a molecule in solution is realized by the Fortran77 program AUTOIEE

A study of high-resolution x-ray scattering data evaluation by the maximum-entropy method

The ability of the maximum-entropy method (in the program MAXENT) to estimate the distance-distribution function from high-resolution X-ray scattering data is studied. It is demonstrated that a key element for the successful application of MAXENT is the use of a good prior estimate for the distance-distribution function. For simulated as well as experimental data, the effects of different priors, noise levels, smearing and measuring intervals are investigated. For practical applications of MAXENT, various methods for the calculation of priors are treated and a principle for the subsequent choice between the priors is suggested. It is demonstrated that, when the construction of the prior is given sufficient consideration, MAXENT provides a very useful method for estimating the distance distribution from the scattering data

AKIMA interpolation: A tool used in direct slit-length desmearing procedures of non-frequency- limited X-ray scattering curves

X-ray small- and medium-angle scattering of partially ordered or semicrystalline materials is composed of background scattering from the form scattering of the components and from the amorphous phase and of peaks from the scattering of the crystallites. By the slit geometry of X-ray diffractometers constructed for registration of small- and medium-angle X-ray scattering, the diffuse scattering and the peaks are distorted and the peak positions and half-widths are changed. A program module based on the Akima interpolation [Akima (1970). J. Assoc. Comput. Mach. 17, 589-602] is proposed for calculation of the first derivative of the complete smeared scattering curve, which is then explicitly used in direct collimation-correction procedures. The desmearing of scattering curves from semicrystalline starch samples proves the convenience of the method for low-noise conditions and exhibits a significant gain of measuring time in comparison with data of comparable accuracy but measured with Soller-slit collimation systems or desmeared with direct methods using frequency filtering

Glass-capillary collimator for distance compensation and partial monochromatization at rotating-anode X-ray generators

Access to the beam ports of rotating-anode X-ray generators is often obstructed by direct-coupled or belt-driven target drives. The construction of an easily adjustable stable glass-capillary collimator is described, which renders possible the unrestricted use of beam ports of these generators. Transmitted intensity and monochromaticity of the primary beam are sufficient for precession photographs of proteins after additional 20 mu m Ni filtering as demonstrated by a precession photograph of hen egg lysozyme. The straight capillary collimator is now a routinely usable low-cost device for each X-ray laboratory

Crystal structure of KorA bound to operator DNA: insight into repressor cooperation in RP4 gene regulation

KorA is a global repressor in RP4 which regulates cooperatively the expression of plasmid genes whose products are involved in replication, conjugative transfer and stable inheritance. The structure of KorA bound to an 18-bp DNA duplex that contains the symmetric operator sequence and incorporates 5-bromo-deoxyuridine nucleosides has been determined by multiple-wavelength anomalous diffraction phasing at 1.96-A resolution. KorA is present as a symmetric dimer and contacts DNA via a helix-turn-helix motif. Each half-site of the symmetric operator DNA binds one copy of the protein in the major groove. As confirmed by mutagenesis, recognition specificity is based on two KorA side chains forming hydrogen bonds to four bases within each operator half-site. KorA has a unique dimerization module shared by the RP4 proteins TrbA and KlcB. We propose that these proteins cooperate with the global RP4 repressor KorB in a similar manner via this dimerization module and thus regulate RP4 inheritance

The database BIOSCAT: a tool for structure research by scattering and hydrodynamic methods

The crystal structures of a large number of proteins and nucleic acids are known and the corresponding sets of coordinates are stored in the Brookhaven Protein Data Bank. For structure investigations of biological macromolecules in solution, scattering and hydrodynamical methods are powerful biophysical tools when starting the data interpretation on the basis of the crystal structure of the molecules. The database BIOSCAT covers the main structural parameters estimable by X-ray scattering, translation and rotation diffusion methods and the X-ray scattering intensities and low- and high-resolution real-space electron distance distribution functions of 70 biological macromolecules and of oligonucleotides in standard conformation. The parameters and the scattered intensities are calculated from the atomic coordinates using the improved cube method and the real-space functions are estimated via a termination-error-reduced Fourier sine transformation. The database access is organized by the program PASSDB, which can generally be used for 'readable' databases. A simple query language allows enquiries into the database without knowledge of a programming language. The program CONVSQL converts the database into normalized relations that can be handled by structured query languages (SQLs)

Multimodal particle size distribution or fractal surface of acrylic acid copolymer nanoparticles: A small-angle X-ray scattering study using direct Fourier and indirect maximum entropy methods

Acrylic acid copolymers are potential carriers for drug delivery. The surface, surface rugosity and the absolute dimension of the particles are parameters that determine the binding of drugs or detergents, diffusion phenomena at the surface and the distribution of the carrier within the human body. The particle-size distribution and surface rugosity of the particles have been investigated by small-angle X-ray scattering and dynamic light scattering. Direct Fourier transform as well as a new strategy for the indirect maximum-entropy method MAXENT are used for data evaluation. Scattering equivalence of a pure multimodal distribution of hard spheres (five populations) and a mixed multimodal-surface-fractal model (four populations) was found. Model calculations and dynamic light-scattering experiments gave evidence of the multimodal particle-size distribution combined with the fractal surface of the carrier The main moiety consists of particles 90 nm in diameter which are surface fractals in the 10 nm region