Finding Longest Common Segments in Protein Structures in Nearly Linear Time

  • Yen Kaow Ng
  • Hirotaka Ono
  • Ling Ge
  • Shuai Cheng Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7354)

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 = (a1, …, an) and B = (b1, …, bn) where ak, bk ∈ ℝ3, we are to find, among all the segments f = (ai,…,aj) and g = (bi,…,bj) 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, ||ak − bk|| ≤ 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, ||ak − bk|| ≤ (1 + ε) t, thus fulfilling the second requirement approximately. The algorithm has a time complexity of O(nlog2n/ε5) when consecutive points in A are separated by the same distance (which is the case with protein structures).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yen Kaow Ng
    • 1
  • Hirotaka Ono
    • 2
  • Ling Ge
    • 3
  • Shuai Cheng Li
    • 4
  1. 1.Department of Computer Science, Faculty of Information and Communication TechnologyUniversiti Tunku Abdul RahmanMalaysia
  2. 2.Department of Economic Engineering, Faculty of EconomicsKyushu UniversityJapan
  3. 3.College of BusinessUniversity of Massachusetts DartmouthNorth DartmouthUSA
  4. 4.Department of Computer ScienceCity University of Hong KongHong Kong

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