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.

[1]  Joachim Frank,et al.  A 9 Å Resolution X-Ray Crystallographic Map of the Large Ribosomal Subunit , 1998, Cell.

[2]  V. Luzzati,et al.  Information content and retrieval in solution scattering studies. I. Degrees of freedom and data reduction , 1982 .

[3]  A W Ashton,et al.  Pentameric and decameric structures in solution of serum amyloid P component by X-ray and neutron scattering and molecular modelling analyses. , 1997, Journal of molecular biology.

[4]  A. Wonacott,et al.  Structure of UDP-N-acetylglucosamine enolpyruvyl transferase, an enzyme essential for the synthesis of bacterial peptidoglycan, complexed with substrate UDP-N-acetylglucosamine and the drug fosfomycin. , 1996, Structure.

[5]  G J Williams,et al.  The Protein Data Bank: a computer-based archival file for macromolecular structures. , 1978, Archives of biochemistry and biophysics.

[6]  E Pantos,et al.  Low-resolution structures of proteins in solution retrieved from X-ray scattering with a genetic algorithm. , 1998, Biophysical journal.

[7]  M. Koch,et al.  [52] Neutron-scattering studies of ribosomes , 1979 .

[8]  H. Stuhrmann,et al.  Elimination der intrapartikulären Untergrundstreuung bei der Röntgenkleinwinkelstreuung an kompakten Teilchen (Proteinen) , 1967 .

[9]  F. Dauvergne,et al.  The localisation method used at EMBL , 1982 .

[10]  V. Ramakrishnan,et al.  Structural evidence for specific S8-RNA and S8-protein interactions within the 30S ribosomal subunit: ribosomal protein S8 from Bacillus stearothermophilus at 1.9 A resolution. , 1996, Structure.

[11]  Dmitri I. Svergun,et al.  New developments in direct shape determination from small angle scattering , 1991 .

[12]  D I Svergun,et al.  Protein hydration in solution: experimental observation by x-ray and neutron scattering. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[13]  C. Boulin,et al.  Data acquisition systems for linear and area X-ray detectors using delay line readout , 1988 .

[14]  T. Steitz,et al.  Structural basis of asymmetry in the human immunodeficiency virus type 1 reverse transcriptase heterodimer. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Crystal structure of Escherichia coli thioredoxin reductase refined at 2 A resolution. Implications for a large conformational change during catalysis. , 1994 .

[16]  Dmitri I. Svergun,et al.  New developments in direct shape determination from small-angle scattering. 2. Uniqueness , 1996 .

[17]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[18]  D. Svergun,et al.  Solution scattering structural analysis of the 70 S Escherichia coli ribosome by contrast variation. I. Invariants and validation of electron microscopy models. , 1997, Journal of molecular biology.

[19]  Claus Müller,et al.  The General Theory , 1998 .

[20]  D. I. Svergun,et al.  Shape Determination from Solution Scattering of Biopolymers , 1997 .

[21]  R P May,et al.  Inter‐protein distances within the large subunit from Escherichia coli ribosomes. , 1992, The EMBO journal.

[22]  D. Svergun,et al.  CRYSOL : a program to evaluate X-ray solution scattering of biological macromolecules from atomic coordinates , 1995 .

[23]  D. Svergun,et al.  Studies on the conformational changes in the bacterial cell wall biosynthetic enzyme UDP-N-acetylglucosamine enolpyruvyltransferase (MurA). , 1998, European journal of biochemistry.

[24]  H. Stuhrmann,et al.  Ein neues Verfahren zur Bestimmung der Oberflächenform und der inneren Struktur von gelösten globulären Proteinen aus Röntgenkleinwinkelmessungen , 1970 .

[25]  D I Svergun,et al.  A model of the quaternary structure of the Escherichia coli F1 ATPase from X-ray solution scattering and evidence for structural changes in the delta subunit during ATP hydrolysis. , 1998, Biophysical journal.

[26]  J. Frank,et al.  A model of protein synthesis based on cryo-electron microscopy of the E. coli ribosome , 1995, Nature.

[27]  D. I. Svergun,et al.  ASSA, a Program for Three‐Dimensional Rendering in Solution Scattering from Biopolymers , 1997 .

[28]  O. Glatter,et al.  19 – Small-Angle X-ray Scattering , 1973 .

[29]  J. Nyborg,et al.  The crystal structure of elongation factor EF-Tu from Thermus aquaticus in the GTP conformation. , 1993, Structure.

[30]  C. Boulin,et al.  Data appraisal, evaluation and display for synchrotron radiation experiments: Hardware and software , 1986 .

[31]  J A Langer,et al.  A complete mapping of the proteins in the small ribosomal subunit of Escherichia coli. , 1987, Science.

[32]  D. Svergun,et al.  A direct indirect method of small-angle scattering data treatment , 1993 .

[33]  J Kuriyan,et al.  Crystal Structure of Escherichia coli Thioredoxin Reductase Refined at 2 Å Resolution , 1994 .

[34]  J. Stull,et al.  Structures of calmodulin and a functional myosin light chain kinase in the activated complex: a neutron scattering study. , 1997, Biochemistry.

[35]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[36]  B. Roy Frieden,et al.  VIII Evaluation, Design and Extrapolation Methods for Optical Signals, Based on Use of the Prolate Functions , 1971 .

[37]  D. I. Svergun,et al.  Structure Analysis by Small-Angle X-Ray and Neutron Scattering , 1987 .

[38]  Lester Ingber,et al.  Simulated annealing: Practice versus theory , 1993 .

[39]  D. I. Svergun,et al.  Solution scattering from biopolymers: advanced contrast‐variation data analysis , 1994 .

[40]  P. B. Moore,et al.  Small-angle scattering. Information content and error analysis , 1980 .

[41]  D I Svergun,et al.  Solution structure of the ternary complex between aminoacyl-tRNA, elongation factor Tu, and guanosine triphosphate. , 1998, Biochemistry.

[42]  V. Ramakrishnan,et al.  The structure of ribosomal protein S5 reveals sites of interaction with 16S rRNA , 1992, Nature.

[43]  H. Stuhrmann,et al.  Interpretation of small-angle scattering functions of dilute solutions and gases. A representation of the structures related to a one-particle scattering function , 1970 .

[44]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[45]  Helena Berglund,et al.  Solution structure of the ribosomal RNA binding protein S15 from Thermus thermophilus , 1997, Nature Structural Biology.

[46]  William H. Press,et al.  Numerical recipes , 1990 .