Abstract
The Local/Global Alignment (Zemla, 2003), or LGA, is a popular method for the comparison of protein structures. One of the two components of LGA requires us to compute the longest common contiguous segments between two protein structures. That is, given two structures A = (a 1, …, a n ) and B = (b 1, …, b n ) where a k , b k ∈ ℝ3, we are to find, among all the segments f = (a i ,…,a j ) and g = (b i ,…,b j ) that fulfill a certain criterion regarding their similarity, those of the maximum length. We consider the following criteria: (1) the root mean square deviation (RMSD) between f and g is to be within a given t ∈ ℝ; (2) f and g can be superposed such that for each k, i ≤ k ≤ j, ||a k − b k || ≤ t for a given t ∈ ℝ. We give an algorithm of \(O(n\log n+n\mbox{\it \textbf{l}})\) time complexity when the first requirement applies, where \(\mbox{\it \textbf{l}}\) is the maximum length of the segments fulfilling the criterion. We show an FPTAS which, for any ε ∈ ℝ, finds a segment of length at least l, but of RMSD up to (1 + ε)t, in O(nlogn + n/ε) time. We propose an FPTAS which for any given ε ∈ ℝ, finds all the segments f and g of the maximum length which can be superposed such that for each k, i ≤ k ≤ j, ||a k − b k || ≤ (1 + ε) t, thus fulfilling the second requirement approximately. The algorithm has a time complexity of O(nlog2 n/ε 5) when consecutive points in A are separated by the same distance (which is the case with protein structures).
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References
Arun, K.S., Huang, T.S., Blostein, S.D.: Least-squares fitting of two 3-d point sets. IEEE Trans. Pattern Anal. Mach. Intell. 9(5), 698–700 (1987)
Bowie, J.U., Luthy, R., Eisenberg, D.: A method to identify protein sequences that fold into a known 3-dimensional structure. Science 253(5016), 164–170 (1991)
Bryant, S.H., Altschul, S.F.: Statistics of sequence-structure threading. Current Opinion in Structural Biology 5(2), 236–244 (1995)
Choi, V., Goyal, N.: A Combinatorial Shape Matching Algorithm for Rigid Protein Docking. In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, pp. 285–296. Springer, Heidelberg (2004)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. The MIT Press (2009)
Cristobal, S., Zemla, A., Fischer, D., Rychlewski, L., Elofsson, A.: A study of quality measures for protein threading models. BMC Bioinformatics 2(5) (2001)
Jones, D.T., Taylor, W.R., Thornton, J.M.: A new approach to protein fold recognition. Nature 358, 86–89 (1992)
Kabsch, W.: A solution for the best rotation to relate two sets of vectors. Acta Crystallographica Section A 32(5), 922–923 (1976)
Kabsch, W.: A discussion of the solution for the best rotation to relate two sets of vectors. Acta Crystallographica Section A 34(5), 827–828 (1978)
Leszek, R., Daniel, F., Arne, E.: Livebench-6: large-scale automated evaluation of protein structure prediction servers. Proteins 53(suppl. 6), 542–547 (2003)
Li, S.C., Bu, D., Xu, J., Li, M.: Finding nearly optimal GDT scores. J. Comput. Biol. 18(5), 693–704 (2011)
Siew, N., Elofsson, A., Rychlewski, L., Fischer, D.: Maxsub: an automated measure for the assessment of protein structure prediction quality. Bioinformatics 16(9), 776–785 (2000)
Simons, K.T., Kooperberg, C., Huang, E., Baker, D.: Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and bayesian scoring functions. J. Mol. Biol. 268(1), 209–225 (1997)
Umeyama, S.: Least-squares estimation of transformation parameters between two point patterns. IEEE Trans. Pattern Anal. Mach. Intell. 13(4), 376–380 (1991)
Wu, S., Skolnick, J., Zhang, Y.: Ab initio modeling of small proteins by iterative tasser simulations. BMC Biology 5(17) (2007)
Zemla, A.: LGA: a method for finding 3D similarities in protein structures. Nucleic Acids Research 31(13), 3370–3374 (2003)
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Ng, Y.K., Ono, H., Ge, L., Li, S.C. (2012). Finding Longest Common Segments in Protein Structures in Nearly Linear Time. In: Kärkkäinen, J., Stoye, J. (eds) Combinatorial Pattern Matching. CPM 2012. Lecture Notes in Computer Science, vol 7354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31265-6_27
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DOI: https://doi.org/10.1007/978-3-642-31265-6_27
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