Fixed-Parameter Algorithms for Protein Similarity Search Under mRNA Structure Constraints

Guillaume Blin 1 Guillaume Fertin 1 Danny Hermelin 2 Stéphane Vialette 3
1 LINA - Laboratoire d'Informatique de Nantes Atlantique
2 Department of Computer Science [Haifa]
3 LRI - Laboratoire de Recherche en Informatique
Abstract : In the context of protein engineering, we consider the problem of computing an mRNA sequence of maximal codon-wise similarity to a given mRNA (and consequently, to a given protein) that additionally satisfies some secondary structure constraints, the so-called MRSO problem introduced in [3]. Since the MRSO problem is known to be APX-hard [8], Bongartz proposed in [8] to attack the problem using the concept of parameterized complexity. We prove in this paper that the MRSO problem is fixed-parameter tractable parameterized by the number of degree 3 vertices or by the number of crossing edges in the implied structure graph. This latter result answers an open problem posed in [8]. Aiming at precisely defining the complexity landscape of the problem, we refine the NP-hardness result of [3] and complement this result by showing that the MRSO problem is fixed-parameter tractable parameterized by an additional parameter. Finally, we present a fixed parameter algorithm parameterized by the similarity score in a restrictive model.
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Guillaume Blin, Guillaume Fertin, Danny Hermelin, Stéphane Vialette. Fixed-Parameter Algorithms for Protein Similarity Search Under mRNA Structure Constraints. 31st International Workshop on Graph-Theoretic Concepts in Computer Science (WG'05), Jun 2005, Metz, France, France. pp.271-282. ⟨hal-00620363⟩

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