On the complexity of deriving position specific score matrices from positive and negative sequences

Authors:
Tatsuya Akutsu;Hideo Bannai;Satoru Miyano;Sascha Ott
Affiliations:
Bioinformatics Center, Institute for Chemical Research, Kyoto University, Gokasho, Uji-city, Kyoto 611-0011, Japan;Human Genome Center, Institute of Medical Science, University of Tokyo, 4-6-1 Shirokanedai, Minato-ku, Tokyo 108-8639, Japan;Human Genome Center, Institute of Medical Science, University of Tokyo, 4-6-1 Shirokanedai, Minato-ku, Tokyo 108-8639, Japan;Wolfson Institute for Biomedical Research, University College London, Cruciform Building, Wing 3.2 Gower Street, London WC1E 6A, UK
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

Position-specific score matrices (PSSMs) have been applied to various problems in computational molecular biology. In this paper, we study the following problem: given positive examples (sequences) and negative examples (sequences), find a PSSM which correctly discriminates between positive and negative examples. We prove that this problem is solved in polynomial time if the size of a PSSM is bounded by a constant. On the other hand, we prove that this problem is NP-hard if the size is not bounded. We also prove hardness results for deriving multiple PSSMs and related problems.