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. 1998 Jun;74(6):2760–2775. doi: 10.1016/S0006-3495(98)77984-6

Low-resolution structures of proteins in solution retrieved from X-ray scattering with a genetic algorithm.

P Chacón 1, F Morán 1, J F Díaz 1, E Pantos 1, J M Andreu 1
PMCID: PMC1299618  PMID: 9635731

Abstract

Small-angle x-ray solution scattering (SAXS) is analyzed with a new method to retrieve convergent model structures that fit the scattering profiles. An arbitrary hexagonal packing of several hundred beads containing the problem object is defined. Instead of attempting to compute the Debye formula for all of the possible mass distributions, a genetic algorithm is employed that efficiently searches the configurational space and evolves best-fit bead models. Models from different runs of the algorithm have similar or identical structures. The modeling resolution is increased by reducing the bead radius together with the search space in successive cycles of refinement. The method has been tested with protein SAXS (0.001 < S < 0.06 A(-1)) calculated from x-ray crystal structures, adding noise to the profiles. The models obtained closely approach the volumes and radii of gyration of the known structures, and faithfully reproduce the dimensions and shape of each of them. This includes finding the active site cavity of lysozyme, the bilobed structure of gamma-crystallin, two domains connected by a stalk in betab2-crystallin, and the horseshoe shape of pancreatic ribonuclease inhibitor. The low-resolution solution structure of lysozyme has been directly modeled from its experimental SAXS profile (0.003 < S < 0.03 A(-1)). The model describes lysozyme size and shape to the resolution of the measurement. The method may be applied to other proteins, to the analysis of domain movements, to the comparison of solution and crystal structures, as well as to large macromolecular assemblies.

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Selected References

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  1. Andreu J. M., Bordas J., Diaz J. F., García de Ancos J., Gil R., Medrano F. J., Nogales E., Pantos E., Towns-Andrews E. Low resolution structure of microtubules in solution. Synchrotron X-ray scattering and electron microscopy of taxol-induced microtubules assembled from purified tubulin in comparison with glycerol and MAP-induced microtubules. J Mol Biol. 1992 Jul 5;226(1):169–184. doi: 10.1016/0022-2836(92)90132-4. [DOI] [PubMed] [Google Scholar]
  2. Bax B., Lapatto R., Nalini V., Driessen H., Lindley P. F., Mahadevan D., Blundell T. L., Slingsby C. X-ray analysis of beta B2-crystallin and evolution of oligomeric lens proteins. Nature. 1990 Oct 25;347(6295):776–780. doi: 10.1038/347776a0. [DOI] [PubMed] [Google Scholar]
  3. Beavil A. J., Young R. J., Sutton B. J., Perkins S. J. Bent domain structure of recombinant human IgE-Fc in solution by X-ray and neutron scattering in conjunction with an automated curve fitting procedure. Biochemistry. 1995 Nov 7;34(44):14449–14461. doi: 10.1021/bi00044a023. [DOI] [PubMed] [Google Scholar]
  4. Boehm M. K., Mayans M. O., Thornton J. D., Begent R. H., Keep P. A., Perkins S. J. Extended glycoprotein structure of the seven domains in human carcinoembryonic antigen by X-ray and neutron solution scattering and an automated curve fitting procedure: implications for cellular adhesion. J Mol Biol. 1996 Jun 21;259(4):718–736. doi: 10.1006/jmbi.1996.0353. [DOI] [PubMed] [Google Scholar]
  5. Curmi P. M., Stone D. B., Schneider D. K., Spudich J. A., Mendelson R. A. Comparison of the structure of myosin subfragment 1 bound to actin and free in solution. A neutron scattering study using actin made "invisible" by deuteration. J Mol Biol. 1988 Oct 5;203(3):781–798. doi: 10.1016/0022-2836(88)90209-4. [DOI] [PubMed] [Google Scholar]
  6. Dandekar T., Argos P. Folding the main chain of small proteins with the genetic algorithm. J Mol Biol. 1994 Feb 25;236(3):844–861. doi: 10.1006/jmbi.1994.1193. [DOI] [PubMed] [Google Scholar]
  7. Dandekar T., Argos P. Identifying the tertiary fold of small proteins with different topologies from sequence and secondary structure using the genetic algorithm and extended criteria specific for strand regions. J Mol Biol. 1996 Mar 1;256(3):645–660. doi: 10.1006/jmbi.1996.0115. [DOI] [PubMed] [Google Scholar]
  8. Dandekar T., Argos P. Potential of genetic algorithms in protein folding and protein engineering simulations. Protein Eng. 1992 Oct;5(7):637–645. doi: 10.1093/protein/5.7.637. [DOI] [PubMed] [Google Scholar]
  9. Diamond R. Real-space refinement of the structure of hen egg-white lysozyme. J Mol Biol. 1974 Jan 25;82(3):371–391. doi: 10.1016/0022-2836(74)90598-1. [DOI] [PubMed] [Google Scholar]
  10. Díaz J. F., Pantos E., Bordas J., Andreu J. M. Solution structure of GDP-tubulin double rings to 3 nm resolution and comparison with microtubules. J Mol Biol. 1994 Apr 29;238(2):214–225. doi: 10.1006/jmbi.1994.1282. [DOI] [PubMed] [Google Scholar]
  11. Evans R. W., Crawley J. B., Garratt R. C., Grossmann J. G., Neu M., Aitken A., Patel K. J., Meilak A., Wong C., Singh J. Characterization and structural analysis of a functional human serum transferrin variant and implications for receptor recognition. Biochemistry. 1994 Oct 18;33(41):12512–12520. doi: 10.1021/bi00207a019. [DOI] [PubMed] [Google Scholar]
  12. Forrest S. Genetic algorithms: principles of natural selection applied to computation. Science. 1993 Aug 13;261(5123):872–878. doi: 10.1126/science.8346439. [DOI] [PubMed] [Google Scholar]
  13. Fujiwara S., Kull F. J., Sablin E. P., Stone D. B., Mendelson R. A. The shapes of the motor domains of two oppositely directed microtubule motors, ncd and kinesin: a neutron scattering study. Biophys J. 1995 Oct;69(4):1563–1568. doi: 10.1016/S0006-3495(95)80028-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Garrigos M., Mallam S., Vachette P., Bordas J. Structure of the myosin head in solution and the effect of light chain 2 removal. Biophys J. 1992 Dec;63(6):1462–1470. doi: 10.1016/S0006-3495(92)81743-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Grossman J. G., Hasnain S. S., Yousafzai F. K., Smith B. E., Eady R. R. The first glimpse of a complex of nitrogenase component proteins by solution X-ray scattering: conformation of the electron transfer transition state complex of Klebsiella pneumoniae nitrogenase. J Mol Biol. 1997 Mar 7;266(4):642–648. doi: 10.1006/jmbi.1996.0846. [DOI] [PubMed] [Google Scholar]
  16. Grossmann J. G., Abraham Z. H., Adman E. T., Neu M., Eady R. R., Smith B. E., Hasnain S. S. X-ray scattering using synchrotron radiation shows nitrite reductase from Achromobacter xylosoxidans to be a trimer in solution. Biochemistry. 1993 Jul 27;32(29):7360–7366. doi: 10.1021/bi00080a005. [DOI] [PubMed] [Google Scholar]
  17. Grossmann J. G., Neu M., Pantos E., Schwab F. J., Evans R. W., Townes-Andrews E., Lindley P. F., Appel H., Thies W. G., Hasnain S. S. X-ray solution scattering reveals conformational changes upon iron uptake in lactoferrin, serum and ovo-transferrins. J Mol Biol. 1992 Jun 5;225(3):811–819. doi: 10.1016/0022-2836(92)90402-6. [DOI] [PubMed] [Google Scholar]
  18. Gultyaev A. P., van Batenburg F. H., Pleij C. W. The computer simulation of RNA folding pathways using a genetic algorithm. J Mol Biol. 1995 Jun 30;250(1):37–51. doi: 10.1006/jmbi.1995.0356. [DOI] [PubMed] [Google Scholar]
  19. Henderson S. J. Monte Carlo modeling of small-angle scattering data from non-interacting homogeneous and heterogeneous particles in solution. Biophys J. 1996 Apr;70(4):1618–1627. doi: 10.1016/S0006-3495(96)79725-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Hill C. P., Johnston N. L., Cohen R. E. Crystal structure of a ubiquitin-dependent degradation substrate: a three-disulfide form of lysozyme. Proc Natl Acad Sci U S A. 1993 May 1;90(9):4136–4140. doi: 10.1073/pnas.90.9.4136. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Jones G., Willett P., Glen R. C., Leach A. R., Taylor R. Development and validation of a genetic algorithm for flexible docking. J Mol Biol. 1997 Apr 4;267(3):727–748. doi: 10.1006/jmbi.1996.0897. [DOI] [PubMed] [Google Scholar]
  22. Jones G., Willett P., Glen R. C. Molecular recognition of receptor sites using a genetic algorithm with a description of desolvation. J Mol Biol. 1995 Jan 6;245(1):43–53. doi: 10.1016/s0022-2836(95)80037-9. [DOI] [PubMed] [Google Scholar]
  23. Kobe B., Deisenhofer J. Crystal structure of porcine ribonuclease inhibitor, a protein with leucine-rich repeats. Nature. 1993 Dec 23;366(6457):751–756. doi: 10.1038/366751a0. [DOI] [PubMed] [Google Scholar]
  24. Kuntz I. D. Hydration of macromolecules. IV. Polypeptide conformation in frozen solutions. J Am Chem Soc. 1971 Jan 27;93(2):516–518. doi: 10.1021/ja00731a037. [DOI] [PubMed] [Google Scholar]
  25. Li L., Darden T. A., Freedman S. J., Furie B. C., Furie B., Baleja J. D., Smith H., Hiskey R. G., Pedersen L. G. Refinement of the NMR solution structure of the gamma-carboxyglutamic acid domain of coagulation factor IX using molecular dynamics simulation with initial Ca2+ positions determined by a genetic algorithm. Biochemistry. 1997 Feb 25;36(8):2132–2138. doi: 10.1021/bi962250r. [DOI] [PubMed] [Google Scholar]
  26. Mayans M. O., Coadwell W. J., Beale D., Symons D. B., Perkins S. J. Demonstration by pulsed neutron scattering that the arrangement of the Fab and Fc fragments in the overall structures of bovine IgG1 and IgG2 in solution is similar. Biochem J. 1995 Oct 1;311(Pt 1):283–291. doi: 10.1042/bj3110283. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Ogata H., Akiyama Y., Kanehisa M. A genetic algorithm based molecular modeling technique for RNA stem-loop structures. Nucleic Acids Res. 1995 Feb 11;23(3):419–426. doi: 10.1093/nar/23.3.419. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Pedersen J. T., Moult J. Ab initio structure prediction for small polypeptides and protein fragments using genetic algorithms. Proteins. 1995 Nov;23(3):454–460. doi: 10.1002/prot.340230319. [DOI] [PubMed] [Google Scholar]
  29. Pedersen J. T., Moult J. Protein folding simulations with genetic algorithms and a detailed molecular description. J Mol Biol. 1997 Jun 6;269(2):240–259. doi: 10.1006/jmbi.1997.1010. [DOI] [PubMed] [Google Scholar]
  30. Perkins S. J., Nealis A. S., Sutton B. J., Feinstein A. Solution structure of human and mouse immunoglobulin M by synchrotron X-ray scattering and molecular graphics modelling. A possible mechanism for complement activation. J Mol Biol. 1991 Oct 20;221(4):1345–1366. doi: 10.1016/0022-2836(91)90937-2. [DOI] [PubMed] [Google Scholar]
  31. Perkins S. J., Smith K. F., Kilpatrick J. M., Volanakis J. E., Sim R. B. Modelling of the serine-proteinase fold by X-ray and neutron scattering and sedimentation analyses: occurrence of the fold in factor D of the complement system. Biochem J. 1993 Oct 1;295(Pt 1):87–99. doi: 10.1042/bj2950087. [DOI] [PMC free article] [PubMed] [Google Scholar]
  32. Pessen H., Kumosinski T. F., Timasheff S. N. Small-angle x-ray scattering. Methods Enzymol. 1973;27:151–209. doi: 10.1016/s0076-6879(73)27011-8. [DOI] [PubMed] [Google Scholar]
  33. Pilz I., Glatter O., Kratky O. Small-angle X-ray scattering. Methods Enzymol. 1979;61:148–249. doi: 10.1016/0076-6879(79)61013-3. [DOI] [PubMed] [Google Scholar]
  34. Pilz I., Schwarz E., Kilburn D. G., Miller R. C., Jr, Warren R. A., Gilkes N. R. The tertiary structure of a bacterial cellulase determined by small-angle X-ray-scattering analysis. Biochem J. 1990 Oct 1;271(1):277–280. doi: 10.1042/bj2710277. [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Sun S. A genetic algorithm that seeks native states of peptides and proteins. Biophys J. 1995 Aug;69(2):340–355. doi: 10.1016/S0006-3495(95)79906-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Svergun D. I., Koch M. H., Serdyuk I. N. Structural model of the 50 S subunit of Escherichia coli ribosomes from solution scattering. I. X-ray synchrotron radiation study. J Mol Biol. 1994 Jul 1;240(1):66–77. doi: 10.1006/jmbi.1994.1418. [DOI] [PubMed] [Google Scholar]
  37. Svergun D. I., Pedersen J. S., Serdyuk I. N., Koch M. H. Solution scattering from 50S ribosomal subunit resolves inconsistency between electron microscopic models. Proc Natl Acad Sci U S A. 1994 Dec 6;91(25):11826–11830. doi: 10.1073/pnas.91.25.11826. [DOI] [PMC free article] [PubMed] [Google Scholar]
  38. Wakabayashi K., Tokunaga M., Kohno I., Sugimoto Y., Hamanaka T., Takezawa Y., Wakabayashi T., Amemiya Y. Small-angle synchrotron x-ray scattering reveals distinct shape changes of the myosin head during hydrolysis of ATP. Science. 1992 Oct 16;258(5081):443–447. doi: 10.1126/science.1411537. [DOI] [PubMed] [Google Scholar]
  39. Willett P. Genetic algorithms in molecular recognition and design. Trends Biotechnol. 1995 Dec;13(12):516–521. doi: 10.1016/S0167-7799(00)89015-0. [DOI] [PubMed] [Google Scholar]
  40. Wistow G., Turnell B., Summers L., Slingsby C., Moss D., Miller L., Lindley P., Blundell T. X-ray analysis of the eye lens protein gamma-II crystallin at 1.9 A resolution. J Mol Biol. 1983 Oct 15;170(1):175–202. doi: 10.1016/s0022-2836(83)80232-0. [DOI] [PubMed] [Google Scholar]
  41. Zheng Y., Doerschuk P. C., Johnson J. E. Determination of three-dimensional low-resolution viral structure from solution x-ray scattering data. Biophys J. 1995 Aug;69(2):619–639. doi: 10.1016/S0006-3495(95)79939-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  42. van Batenburg F. H., Gultyaev A. P., Pleij C. W. An APL-programmed genetic algorithm for the prediction of RNA secondary structure. J Theor Biol. 1995 Jun 7;174(3):269–280. doi: 10.1006/jtbi.1995.0098. [DOI] [PubMed] [Google Scholar]

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