Abstract
The theorem presented in this paper is a general solution for the optimal superimposition between two protein structures, which is actually the problem of the weighted optimal rigid superimposition between two vector sets with the same size. The theorem gives not only the rotational and translational parameters, but also the minimal value of the mean squared deviation of the optimal superimposition.
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References
Holm, L., Sander, C.: Searching Protein Structure Databases has come of Age. Proteins 19(3), 165–173 (1994)
Gibrat, J.F., Madej, T., Bryant, S.H.: Surprising Similarities in Structure Comparison. Curr. Opin. Struct. Biol. 6(3), 377–385 (1996)
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. 28(1), 235–242 (2000)
Kolodny, R., Koehl, P., Levitt, M.: Comprehensive Evaluation of Protein Structure Alignment Methods: Scoring by Geometric Measures. J. Mol. Biol. 346(4), 1173–1188 (2005)
Mcachlan, A.D.: A Mathematical Procedure for Superimposing Atomic Coordinates of Proteins. Acta Crystallogr. Sect. A 28(6), 656–657 (1972)
Mcachlan, A.D.: Gene Duplications in the Structural Evolution of Chymotrypsin. J. Mol. Biol. 128(1), 49–79 (1979)
Mcachlan, A.D.: Rapid Comparison of Protein Structures. Acta Crystallogr. Sect. A 38(6), 871–873 (1982)
Kabsch, W.: A Solution for the best Rotation to Relate two Sets of Vectors. Acta Crystallogr. Sect. A 32(5), 922–923 (1976)
Kabsch, W.: A Discussion of the Solution for the Best Rotation to Relate two Sets of Vectors. Acta Crystallogr. Sect. A 34(5), 827–828 (1978)
Diamond, R.: On the Comparison of Conformations Using Linear and Quadratic Transformations. Acta Crystallogr. Sect. A 32(1), 1–10 (1976)
Diamond, R.: A Note on the Rotational Superposition Problem. Acta Crystallogr. Sect. A 44(2), 211–216 (1988)
Ferro, D.R., Hermans, J.: A Different Best Rigid-body Molecular Fit Routine. Acta Crystallogr. Sect. A 33(2), 345–347 (1977)
Lesk, A.M.: A Toolkit for Computational Molecular Biology. II. On the Optimal Superpose- tion of two Sets of Coordinates. Acta Crystallogr. Sect. A 42(2), 110–113 (1986)
Kaindl, K., Steipe, B.: Metric Properties of the Root-Mean-Square Deviation of Vector Sets. Acta Crystallogr. Sect. A 53(6), 809 (1997)
Steipe, B.: A Revised Proof of the Metric Properties of Optimally Superimposed Vector Sets. Acta Crystallogr. Sect. A 58(5), 506 (2002)
Umeyama, S.: Least-squares Estimation of Transformation Parameters Between two Point Patterns. IEEE Trans. on Pattern Anal. Mach. Intell. 13(4), 376–386 (1991)
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Li, Q., Shu, J., Shi, Z., Zhang, D. (2006). A General Solution for the Optimal Superimposition of Protein Structures. In: Huang, DS., Li, K., Irwin, G.W. (eds) Computational Intelligence and Bioinformatics. ICIC 2006. Lecture Notes in Computer Science(), vol 4115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11816102_39
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DOI: https://doi.org/10.1007/11816102_39
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