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The alignment of protein structures in three dimensions

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Abstract

This article extends the use of dynamic programming algorithms in molecular sequence comparison to the alignment of the α-carbon (Cα-) coordinates of two protein structures in three dimensions. The algorithm is described in detail and is applied to the comparison of α-lactalbumin with both hen egg white lysozyme and T4 lysozyme. In the first case, the structures are similar, while the second comparison is between two distantly related molecules. References are made to the usual sequence alignments. A variety of complementary methods are introduced to display the results.

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Literature

  • Altschul, S. F. and B. W. Erickson. 1986. “Optimal Sequence Alignment using Affine Gap Costs.”Bull. Math. Biol. 48, 603–616.

    Article  MATH  MathSciNet  Google Scholar 

  • Blumenthal, L. M. 1953.Theory and Application of Distance Geometry. Oxford: Clarendon Press.

    Google Scholar 

  • Claverie, J. M. and I. Sauvaget. 1985. “A New Protein Sequence Databank.”Nature 318, 19.

    Article  Google Scholar 

  • Cohen, F. E. and M. J. E. Sternberg. 1980. “On the Prediction of Protein Structure: The Significance of the Root-Mean-Square Deviation.”J. Molec. Biol. 138, 321–333.

    Article  Google Scholar 

  • Cornish-Bowden, A. 1980. “Critical Values for Testing the Significance of Amino Acid Composition Indexes.”Anal. Biochem. 105, 233–238.

    Article  Google Scholar 

  • Coulson, A. F. W., J. F. Collins and A. Lyall. 1987. “Protein and Nucleic Acid Sequence Database Searching: A Suitable Case for Parallel Processing.”Comput. J. 30, 420–424.

    Google Scholar 

  • Dayhoff, M. O., R. M. Schwartz and B. C. Orcutt. 1978. “A Model of Evolutionary Change in Proteins.” InAtlas of Protein Sequence and Structure, Vol. 5, Suppl. 3. 345–352. Washington: National Biomedical Research Foundation.

    Google Scholar 

  • Diamond, R. 1987. “A Note on the Rotational Superposition Problem.”Acta Cryst. A44, 211–216.

    Google Scholar 

  • Evans, D. J. 1977. “On the Representation of Orientation Space.”Molec. Phys. 34, 317–325.

    Article  Google Scholar 

  • Fitch, W. M. and T. F. Smith. 1983. “Optimal Sequence Alignments.”Proc. Natn. Acad. Sci. U.S.A. 80, 1382–1386.

    Article  Google Scholar 

  • Goldstein, H. 1965.Classical Mechanics, Reading, MA: Addison-Wesley.

    Google Scholar 

  • Levitt, M. 1976. “A Simplified Representation of Protein Conformations for Rapid Simulation of Protein Folding.”J. Molec. Biol. 104, 59–107.

    Article  Google Scholar 

  • Lipman, D. J. and W. R. Pearson. 1985. “Rapid and Sensitive Protein Similarity Searches.”Science 227, 1435–1441.

    Google Scholar 

  • Louie, A. H. and R. L. Somorjai. “Differential Geometry of Proteins: A Morphological Metric for Structural Comparisons.” (To be submitted.)

  • Maizel, J. V. and R. P. Lenk. 1981. “Enhanced Graphic Matrix Analysis of Nucleic Acid and Protein Sequences.”Proc. Natn. Acad. Sci. U.S.A. 78, 7665–7669.

    Article  MathSciNet  Google Scholar 

  • McLachlan, A. D. 1979. “Gene Duplications in the Structural Evolution of Chymotrypsin.”J. Molec. Biol. 128, 49–79.

    Article  Google Scholar 

  • — 1984. “How Alike are the Shapes of Two Random Chains?”Biopolymers 23, 1325–1331.

    Article  Google Scholar 

  • Needleman, S. B. and C. D. Wunsch. 1970. “A General Method Applicable to the Search for Similarities in the Amino Acid Sequence of Two Proteins.”J. Molec. Biol. 48, 443–453.

    Article  Google Scholar 

  • Remington, S. J. and B. W. Matthews. 1978. “A General Method to Assess Similarity of Protein Structures, with Applications to T4 Bacteriophage Lysozyme.”Proc. Natn. Acad. Sci. U.S.A. 75, 2180–2184.

    Article  Google Scholar 

  • Rossmann, M. G. and P. Argos. 1976. “Exploring Structural Homology of Proteins.”J. Molec. Biol. 105, 75–95.

    Article  Google Scholar 

  • Schulz, G. E. 1977. “Recognition of Phylogenetic Relationships from Polypeptide Chain Fold Similarities.”J. Molec. Evol. 9, 339–342.

    Article  Google Scholar 

  • Sellers, P. H. 1974. “An Algorithm for the Distance Between Two Finite Sequences.”J. Combinatorial Theory 16A, 253–258.

    Article  MathSciNet  Google Scholar 

  • Sippl, M. J. 1982. “On the Problem of Comparing Protein Structures. Development and Applications of a New Method for the Assessment of Structural Similarities of Polypeptide Conformations.”J. Molec. Biol. 156, 359–388.

    Article  Google Scholar 

  • Smith, T. F., M. S. Waterman and W. M. Fitch. 1981. “Comparative Biosequence Metrics.”J. Molec. Evol. 18, 38–46.

    Article  Google Scholar 

  • Stuart, D. I., K. R. Acharya, N. P. C. Walker, S. G. Smith, M. Lewis and D. C. Phillips. 1986. “α-Lactalbumin Possesses a Novel, Calcium Binding Loop.”Nature 324, 84–87.

    Article  Google Scholar 

  • Waterman, M. S. 1984. “General Methods of Sequence Comparison.”Bull Math. Biol. 46, 473–500.

    Article  MATH  MathSciNet  Google Scholar 

  • Weaver, L. H., M. G. Gruetter, 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. Molec. Evol. 21, 97–111.

    Article  Google Scholar 

  • Wilkinson, J. H. 1960. “Householder's Method for the Solution of the Algebraic Eigenproblem.”Comput. J. 3, 23–27.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Division of Biological Sciences, National Research Council of Canada, K1A 0R6, Ottawa, Canada

    M. Zuker & R. L. Somorjai

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  1. M. Zuker
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  2. R. L. Somorjai
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National Research Council of Canada Publication No. 29461.

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Zuker, M., Somorjai, R.L. The alignment of protein structures in three dimensions. Bltn Mathcal Biology 51, 55–78 (1989). https://doi.org/10.1007/BF02458836

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