On protein structure alignment under distance constraint

Authors:
Shuai Cheng Li;Yen Kaow Ng
Affiliations:
David R. Cheriton School of Computer Science, University of Waterloo, Waterloo ON N2L 3G1, Canada;Faculty of Information and Communication Technology, Universiti Tunku Abdul Rahman, Jalan Universiti, Bandar Barat, 31900 Kampar, Perak, Malaysia
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

In this paper we study the protein structure comparison problem where each protein is modeled as a sequence of 3D points, and a contact edge is placed between every two of these points that are sufficiently close. Given two proteins represented this way, our problem is to find a subset of points from each protein, and a bijective matching of points between these two subsets, with the objective of maximizing either (A) the size of the subsets (the LCP problem), or (B) the number of edges that exist simultaneously in both subsets (the CMO problem), under the requirement that only points within a specified proximity can be matched. It is known that the general CMO problem (without the proximity requirement) is hard to approximate. However, with the proximity requirement, it is known that if a minimum inter-residue distance is imposed on the input, approximate solutions can be efficiently obtained. In this paper we mainly show that the CMO problem under these conditions: (1) is NP-hard, but (2) allows a PTAS. The rest of this paper shows algorithms for the LCP problem which improve on known results.