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. 2002 Aug;83(2):619–632. doi: 10.1016/S0006-3495(02)75196-5

Modeling shape and topology of low-resolution density maps of biological macromolecules.

Pedro A De-Alarcón 1, Alberto Pascual-Montano 1, Amarnath Gupta 1, Jose M Carazo 1
PMCID: PMC1302174  PMID: 12124252

Abstract

In the present work we develop an efficient way of representing the geometry and topology of volumetric datasets of biological structures from medium to low resolution, aiming at storing and querying them in a database framework. We make use of a new vector quantization algorithm to select the points within the macromolecule that best approximate the probability density function of the original volume data. Connectivity among points is obtained with the use of the alpha shapes theory. This novel data representation has a number of interesting characteristics, such as 1) it allows us to automatically segment and quantify a number of important structural features from low-resolution maps, such as cavities and channels, opening the possibility of querying large collections of maps on the basis of these quantitative structural features; 2) it provides a compact representation in terms of size; 3) it contains a subset of three-dimensional points that optimally quantify the densities of medium resolution data; and 4) a general model of the geometry and topology of the macromolecule (as opposite to a spatially unrelated bunch of voxels) is easily obtained by the use of the alpha shapes theory.

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Selected References

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  1. Ankerst M., Kastenmüller G., Kriegel H. P., Seidl T. Nearest neighbor classification in 3D protein databases. Proc Int Conf Intell Syst Mol Biol. 1999:34–43. [PubMed] [Google Scholar]
  2. Artymiuk P. J., Bath P. A., Grindley H. M., Pepperrell C. A., Poirrette A. R., Rice D. W., Thorner D. A., Wild D. J., Willett P., Allen F. H. Similarity searching in databases of three-dimensional molecules and macromolecules. J Chem Inf Comput Sci. 1992 Nov-Dec;32(6):617–630. doi: 10.1021/ci00010a007. [DOI] [PubMed] [Google Scholar]
  3. Baumeister W., Steven A. C. Macromolecular electron microscopy in the era of structural genomics. Trends Biochem Sci. 2000 Dec;25(12):624–631. doi: 10.1016/s0968-0004(00)01720-5. [DOI] [PubMed] [Google Scholar]
  4. Berman H. M., Westbrook J., Feng Z., Gilliland G., Bhat T. N., Weissig H., Shindyalov I. N., Bourne P. E. The Protein Data Bank. Nucleic Acids Res. 2000 Jan 1;28(1):235–242. doi: 10.1093/nar/28.1.235. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Bohm J., Frangakis A. S., Hegerl R., Nickell S., Typke D., Baumeister W. Toward detecting and identifying macromolecules in a cellular context: template matching applied to electron tomograms. Proc Natl Acad Sci U S A. 2000 Dec 19;97(26):14245–14250. doi: 10.1073/pnas.230282097. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Bárcena M., Ruiz T., Donate L. E., Brown S. E., Dixon N. E., Radermacher M., Carazo J. M. The DnaB.DnaC complex: a structure based on dimers assembled around an occluded channel. EMBO J. 2001 Mar 15;20(6):1462–1468. doi: 10.1093/emboj/20.6.1462. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Connolly M. L. Solvent-accessible surfaces of proteins and nucleic acids. Science. 1983 Aug 19;221(4612):709–713. doi: 10.1126/science.6879170. [DOI] [PubMed] [Google Scholar]
  8. Grimes J. M., Fuller S. D., Stuart D. I. Complementing crystallography: the role of cryo-electron microscopy in structural biology. Acta Crystallogr D Biol Crystallogr. 1999 Oct;55(Pt 10):1742–1749. doi: 10.1107/s0907444999009956. [DOI] [PubMed] [Google Scholar]
  9. Holm L., Sander C. Protein structure comparison by alignment of distance matrices. J Mol Biol. 1993 Sep 5;233(1):123–138. doi: 10.1006/jmbi.1993.1489. [DOI] [PubMed] [Google Scholar]
  10. Joshua-Tor L., Xu H. E., Johnston S. A., Rees D. C. Crystal structure of a conserved protease that binds DNA: the bleomycin hydrolase, Gal6. Science. 1995 Aug 18;269(5226):945–950. doi: 10.1126/science.7638617. [DOI] [PubMed] [Google Scholar]
  11. Kalko S. G., Chagoyen M., Jiménez-Lozano N., Verdaguer N., Fita I., Carazo J. M. The need for a shared database infrastructure: combining X-ray crystallography and electron microscopy. Eur Biophys J. 2000;29(6):457–462. doi: 10.1007/s002490000089. [DOI] [PubMed] [Google Scholar]
  12. Keller P. A., Henrick K., McNeil P., Moodie S., Barton G. J. Deposition of macromolecular structures. Acta Crystallogr D Biol Crystallogr. 1998 Nov 1;54(Pt 6 1):1105–1108. doi: 10.1107/s0907444998008464. [DOI] [PubMed] [Google Scholar]
  13. Liang J., Edelsbrunner H., Woodward C. Anatomy of protein pockets and cavities: measurement of binding site geometry and implications for ligand design. Protein Sci. 1998 Sep;7(9):1884–1897. doi: 10.1002/pro.5560070905. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Liang J., Edelsbrunner H., Woodward C. Anatomy of protein pockets and cavities: measurement of binding site geometry and implications for ligand design. Protein Sci. 1998 Sep;7(9):1884–1897. doi: 10.1002/pro.5560070905. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Murata K., Mitsuoka K., Hirai T., Walz T., Agre P., Heymann J. B., Engel A., Fujiyoshi Y. Structural determinants of water permeation through aquaporin-1. Nature. 2000 Oct 5;407(6804):599–605. doi: 10.1038/35036519. [DOI] [PubMed] [Google Scholar]
  16. Norel R., Petrey D., Wolfson H. J., Nussinov R. Examination of shape complementarity in docking of unbound proteins. Proteins. 1999 Aug 15;36(3):307–317. [PubMed] [Google Scholar]
  17. Pascual-Montano A., Donate L. E., Valle M., Bárcena M., Pascual-Marqui R. D., Carazo J. M. A novel neural network technique for analysis and classification of EM single-particle images. J Struct Biol. 2001 Feb-Mar;133(2-3):233–245. doi: 10.1006/jsbi.2001.4369. [DOI] [PubMed] [Google Scholar]
  18. Peters K. P., Fauck J., Frömmel C. The automatic search for ligand binding sites in proteins of known three-dimensional structure using only geometric criteria. J Mol Biol. 1996 Feb 16;256(1):201–213. doi: 10.1006/jmbi.1996.0077. [DOI] [PubMed] [Google Scholar]
  19. Shindyalov I. N., Bourne P. E. Protein structure alignment by incremental combinatorial extension (CE) of the optimal path. Protein Eng. 1998 Sep;11(9):739–747. doi: 10.1093/protein/11.9.739. [DOI] [PubMed] [Google Scholar]
  20. Sussman J. L., Lin D., Jiang J., Manning N. O., Prilusky J., Ritter O., Abola E. E. Protein Data Bank (PDB): database of three-dimensional structural information of biological macromolecules. Acta Crystallogr D Biol Crystallogr. 1998 Nov 1;54(Pt 6 1):1078–1084. doi: 10.1107/s0907444998009378. [DOI] [PubMed] [Google Scholar]
  21. Volkmann N., Hanein D. Quantitative fitting of atomic models into observed densities derived by electron microscopy. J Struct Biol. 1999 Apr-May;125(2-3):176–184. doi: 10.1006/jsbi.1998.4074. [DOI] [PubMed] [Google Scholar]
  22. Westhead D. R., Slidel T. W., Flores T. P., Thornton J. M. Protein structural topology: Automated analysis and diagrammatic representation. Protein Sci. 1999 Apr;8(4):897–904. doi: 10.1110/ps.8.4.897. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Wriggers W., Birmanns S. Using situs for flexible and rigid-body fitting of multiresolution single-molecule data. J Struct Biol. 2001 Feb-Mar;133(2-3):193–202. doi: 10.1006/jsbi.2000.4350. [DOI] [PubMed] [Google Scholar]
  24. Wriggers W., Milligan R. A., McCammon J. A. Situs: A package for docking crystal structures into low-resolution maps from electron microscopy. J Struct Biol. 1999 Apr-May;125(2-3):185–195. doi: 10.1006/jsbi.1998.4080. [DOI] [PubMed] [Google Scholar]
  25. Wriggers W., Milligan R. A., Schulten K., McCammon J. A. Self-organizing neural networks bridge the biomolecular resolution gap. J Mol Biol. 1998 Dec 18;284(5):1247–1254. doi: 10.1006/jmbi.1998.2232. [DOI] [PubMed] [Google Scholar]

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