Finding longest common segments in protein structures in nearly linear time

Yen Kaow Ng, Hirotaka Ono, Ling Ge, Shuai Cheng Li

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 ∈ ℝ 3, 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 ∈ . We give an algorithm of time complexity when the first requirement applies, where 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(nlog 2 n/ε 5) when consecutive points in A are separated by the same distance (which is the case with protein structures).

Original languageEnglish
Title of host publicationCombinatorial Pattern Matching - 23rd Annual Symposium, CPM 2012, Proceedings
Pages334-348
Number of pages15
DOIs
Publication statusPublished - Jul 4 2012
Event23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012 - Helsinki, Finland
Duration: Jul 3 2012Jul 5 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7354 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012
CountryFinland
CityHelsinki
Period7/3/127/5/12

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Ng, Y. K., Ono, H., Ge, L., & Li, S. C. (2012). Finding longest common segments in protein structures in nearly linear time. In Combinatorial Pattern Matching - 23rd Annual Symposium, CPM 2012, Proceedings (pp. 334-348). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7354 LNCS). https://doi.org/10.1007/978-3-642-31265-6_27