Dmitri I. Svergun

Determination of the regularization parameter in indirect-transform methods using perceptual criteria

A method is proposed for the determination of the optimum value of the regularization parameter (Lagrange multiplier) when applying indirect transform techniques in small-angle scattering data analysis. The method is based on perceptual criteria of what is the best solution. A set of simple criteria is used to construct a total estimate describing the quality of the solution. Maximization of the total estimate is straightforward. Model computations show the effectiveness of the technique. The method is implemented in the program GNOM [Svergun, Semenyuk & Feigin (1988). Acta Cryst. A44, 244–250].

CRYSOL : a program to evaluate X-ray solution scattering of biological macromolecules from atomic coordinates

A program for evaluating the solution scattering from macromolecules with known atomic structure is presented. The program uses multipole expansion for fast calculation of the spherically averaged scattering pattern and takes into account the hydration shell. Given the atomic coordinates (e.g. from the Brookhaven Protein Data Bank) it can either predict the solution scattering curve or fit the experimental scattering curve using only two free parameters, the average displaced solvent volume per atomic group and the contrast of the hydration layer. The program runs on IBM PCs and on the major UNIX platforms.

PRIMUS: a Windows PC-based system for small-angle scattering data analysis

A program suite for one-dimensional small-angle scattering data processing running on IBM-compatible PCs under Windows 9x/NT/2000/XP is presented. The main program, PRIMUS, has a menu-driven graphical user interface calling computational modules to perform data manipulation and analysis. Experimental data in binary OTOKO format can be reduced by calling the program SAPOKO, which includes statistical analysis of time frames, averaging and scaling. Tools to generate the angular axis and detector response files from diffraction patterns of calibration samples, as well as binary to ASCII transformation programs, are available. Several types of ASCII files can be directly imported into PRIMUS, in particular, sasCIF or ILL-type files are read without modification. PRIMUS provides basic data manipulation functions (averaging, background subtraction, merging of data measured in different angular ranges, extrapolation to zero sample concentration, etc.) and computes invariants from Guinier and Porod plots. Several external modules coupled with PRIMUS via pop-up menus enable the user to evaluate the characteristic functions by indirect Fourier transformation, to perform peak analysis for partially ordered systems and to find shape approximations in terms of three-parametric geometrical bodies. For the analysis of mixtures, PRIMUS enables model-independent singular value decomposition or linear fitting if the scattering from the components is known. An interface is also provided to the general non-linear fitting program MIXTURE, which is designed for quantitative analysis of multicomponent systems represented by simple geometrical bodies, taking shape and size polydispersity as well as interparticle interference effects into account.

Restoring Low Resolution Structure of Biological Macromolecules from Solution Scattering Using Simulated Annealing

A method is proposed to restore ab initio low resolution shape and internal structure of chaotically oriented particles (e.g., biological macromolecules in solution) from isotropic scattering. A multiphase model of a particle built from densely packed dummy atoms is characterized by a configuration vector assigning the atom to a specific phase or to the solvent. Simulated annealing is employed to find a configuration that fits the data while minimizing the interfacial area. Application of the method is illustrated by the restoration of a ribosome-like model structure and more realistically by the determination of the shape of several proteins from experimental x-ray scattering data.

Uniqueness of ab initio shape determination in small-angle scattering

Scattering patterns from geometrical bodies with different shapes and anisometry (solid and hollow spheres, cylinders, prisms) are computed and the shapes are reconstructed ab initio using envelope function and bead modelling methods. A procedure is described to analyze multiple solutions provided by bead modeling methods and to estimate stability and reliability of the shape reconstruction. It is demonstrated that flat shapes are more difficult to restore than elongated ones and types of shapes are indicated, which require additional information for reliable shape reconsrtuction from the scattering data.

Determination of Domain Structure of Proteins from X-Ray Solution Scattering

An ab initio method for building structural models of proteins from x-ray solution scattering data is presented. Simulated annealing is employed to find a chain-compatible spatial distribution of dummy residues which fits the experimental scattering pattern up to a resolution of 0.5 nm. The efficiency of the method is illustrated by the ab initio reconstruction of models of several proteins, with known and unknown crystal structure, from experimental scattering data. The new method substantially improves the resolution and reliability of models derived from scattering data and makes solution scattering a useful technique in large-scale structural characterization of proteins.

New developments in the ATSAS program package for small-angle scattering data analysis.

The paper presents new developments and amendments to the ATSAS package (version 2.4) for processing and analysis of isotropic small-angle scattering data.

Automated matching of high- and low-resolution structural models

A method is presented for automated best-matching alignment of three-dimensional models represented by ensembles of points. A normalized spatial discrepancy (NSD) is introduced as a proximity measure between three-dimensional objects. Starting from an inertia-axes alignment, the algorithm minimizes the NSD; the final value of the NSD provides a quantitative estimate of similarity between the objects. The method is implemented in a computer program. Simulations have been performed to test its performance on model structures with specified numbers of points ranging from a few to a few thousand. The method can be used for comparative analysis of structural models obtained by different methods, e.g. of high-resolution crystallographic atomic structures and low-resolution models from solution scattering or electron microscopy.

DAMMIF, a program for rapid ab-initio shape determination in small-angle scattering

DAMMIF, an enhanced and significantly faster implementation of the ab-initio shape-determination program DAMMIN for small-angle scattering data, is presented.

Small-angle scattering studies of biological macromolecules in solution

Small-angle scattering (SAS) of x-rays and neutrons is a fundamental tool in the study of biological macromolecules. The major advantage of the method lies in its ability to provide structural information about partially or completely disordered systems. SAS allows one to study the structure of native particles in near physiological environments and to analyse structural changes in response to variations in external conditions. In this review we concentrate on SAS studies of isotropic systems, in particular, solutions of biological macromolecules, an area where major progress has been achieved during the last decade. Solution scattering studies are especially important, given the challenge of the ‘post-genomic’ era with vast numbers of protein sequences becoming available. Numerous structural initiatives aim at large-scale expression and purification of proteins for subsequent structure determination using x-ray crystallography and NMR spectroscopy. Because of the requirement of good crystals for crystallography and the low molecular mass requirement of NMR, a significant fraction of proteins cannot be analysed using these two high-resolution methods. Progress in SAS instrumentation and novel analysis methods, which substantially improve the resolution and reliability of the structural models, makes the method an important complementary tool for these initiatives. The review covers the basics of x-ray and neutron SAS, instrumentation, mathematical methods used in data analysis and major modelling techniques. Examples of applications of SAS to different types of biomolecules (proteins, nucleic acids, macromolecular complexes, polyelectrolytes) are presented. A brief account of the new opportunities offered by third and fourth generation synchrotron radiation sources (time-resolved studies, coherent scattering and single molecule scattering) is also given.