Bulletin of Mathematical Biology

, Volume 56, Issue 5, pp 923–943 | Cite as

A differential geometric treatment of protein structure comparison

  • Ding Da-Fu
  • Qian Jiang
  • Feng Zu-Kang


The technique of model-building a protein of known sequence but unknown tertiary structure from the structures of homologous proteins is probably so far the most reliable means of mapping from primary to tertiary structure. A key step towards the realization of the aim is to develop ways of aligning three-dimensional structures of homologus proteins, thereby deriving the rules useful for protein modelling. We have developed a generalized differential-geometric representation of protein local conformation for use in a protein comparison program which aligns protein sequences on the basis of their sequence and conformational knowledge. Because the differetial-geometric distance measure between local conformations is independent of the coordinate frame and remains chirality information, the comparison program is easily implemented, relatively rational and reasonably fast. The utility of this program for aligning closely and distantly related homologous proteins is demonstrated by multiple alignment of globins, serine proteinases and aspartic proteinase domains. Particularly, the method has reached the rational alignment between the mammalian and microbial serine proteinases as compared with many published alignment programs.


Aspartic Proteinase Dissimilarity Matrix Global Similarity Simulated Annealing Procedure Protein Structure Comparison 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Barton, G. J. and M. J. E. Sternberg. 1987a. Evaluation and improvements in the automatic alignment of protein sequences.Protein Engin.1, 89–94.Google Scholar
  2. Barton, G. J. and M. J. E. Sternberg. 1987b. A strategy for the rapid multiple alignment of protein sequences: confidence levels from tertiary structure comparisons.J. Mol. Biol.198, 327–337.CrossRefGoogle Scholar
  3. Bashford, D., C. Chothia and A. M. Lesk. 1987. Determinants of a protein fold, unique features of the globin amino acid sequences.J. Mol. Biol. 196, 199–216.CrossRefGoogle Scholar
  4. Bernstein, F. C. T. F. Koetzle, G. J. B. Williams, E. F. J. R. Meyer, M. D. Brice, J. R. Rodgers, O. Kennard, T. Shimanouchi and M. Tasumi 1977. The protein data bank: a computer-based archival file for macromolecular structures.J. Mol. Biol. 112, 535–542.Google Scholar
  5. Blundell, T. L. J. A. Jenkins, B. T. Sewell, L. H. Pearl, J. B. Cooper, I. J. Tickle, V. Veerapandian and S. P. Wood. 1990. X-ray analysis of aspartic proteinases.J. Mol. Biol. 211, 919–941.CrossRefGoogle Scholar
  6. Dayhoff, M. D., W. C. Barker and L. T. Hunt, 1983. Establishing homologies in protein sequences.Methods Enzymol.91, 524–545.Google Scholar
  7. Eisenmenger, F. P. Argos and R. Abagyan. 1993. A method to configure protein side-chains from the main-chain trace in homology modelling.J. Mol. Biol. 231, 849–860.CrossRefGoogle Scholar
  8. Gotoh, O. 1982. An improved algorithm, for matching biological sequences.J. Mol. Biol. 162, 705–708.CrossRefGoogle Scholar
  9. Kabsch, W. and C. Sander. 1983. A dictionary of protein secondary structure.Biopolymers 22, 2577–2673.CrossRefGoogle Scholar
  10. Lesk, A. M. and C. Chothia. 1980. How different amino acid sequences determine similar protein structures.J. Mol. Biol. 136, 225–270.CrossRefGoogle Scholar
  11. Matthews, B. W. and M. G. Rossmann. 1985. Comparison of protein structures.Methods Enzymol.115, 397–420.CrossRefGoogle Scholar
  12. Rossmann, M. G. and P. Argos. 1976. Exploring structure homology of proteins.J. Mol. Biol.105, 75–95.CrossRefGoogle Scholar
  13. Russell, R. B. and G. J. Barton. 1992. Multiple protein sequence alignment from tertiary structure comparison: assignment of global and residue confidence levels.Proteins 14, 309–323.CrossRefGoogle Scholar
  14. Rackovsky, S. and H. A. Scherage. 1980. Differential geometry and polymer conformation. 2. Development of a conformational distance function.Macromolecules 13, 1440–1453.CrossRefGoogle Scholar
  15. Sali, A. and T. L. Blundell. 1990. Definition of general topological equivalence in protein structures.J. Mol. Biol. 212, 403–428.CrossRefGoogle Scholar
  16. Smith, T. F. F. Fischel-Ghodsian and G. Mathiowitz. 1990. Alignment of protein sequences using secondary: a modified dynamic programming method.Protein Engin.3, 577–581.Google Scholar
  17. Sutcliffe, M. J. L. Haneef, D. Carney and T. L. Blundell 1987. Knowledge based modeling of homologous proteins. Part 1.Protein Engin.1, 377–384.Google Scholar
  18. Taylor, W. R. and C. A. Orengo. 1989. Protein structure alignment.J. Mol. Biol.208, 1–22.CrossRefGoogle Scholar
  19. Waterman, M. S., 1984. General methods of sequence comparison.Bull. Math. Biol. 46, 473–500.MATHMathSciNetCrossRefGoogle Scholar
  20. Weaver, L. H., M. G. Grütter, S. J. Remington, T. M. Gray, N. W. Isaacs and B. W. Matthews. 1985. Comparison of goose-type, chicken-type and phage-type lysozymes illustrates the changes that occur in both amino acid sequence and three-dimensional structure during evolution.J. Mol. Evol. 21, 97–111.CrossRefGoogle Scholar
  21. Zhang Bao-Hong and Ding Da-Fu. 1993. A new method for pairwise comparison of protein structures (in Chinese).Acta Biophysica Sinica 3, 353–361.Google Scholar
  22. Zhang-Yang Zhu, A. Sali and T. L. Blundell. 1992. A variable gap penality function and feature weights for protein 3-D structure comparison.Protein Engin 5, 43–51.Google Scholar
  23. Zuker, M. and R. L. Somorjai. 1989. The alignment of protein structures in three dimensions.Bull. Math. Biol.51, 55–78.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1994

Authors and Affiliations

  • Ding Da-Fu
    • 1
  • Qian Jiang
    • 1
  • Feng Zu-Kang
    • 1
  1. 1.Laboratory of Computational Molecular BiologyShanghai Institute of Biochemistry, Academia SinicaShanghaiChina

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