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

International audienceIn 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