Some Notes on the Complexity of Protein Similarity Search under mRNA Structure Constraints

Abstract

In [2], Backofen et al. propose the MRSO problem, that is to compute an mRNA sequence of maximal similarity to a given mRNA and a given protein, that additionally satisfies some secondary structure constraints. The study of this problem is motivated by an application in the area of protein engineering. Modeled in a mathematical framework, we would like to compute a string ${s\in\{a,b,\overline{a},\overline{b}\}}^{3n}$ which maximizes the sum of the values of n functions, which are blockwise applied to triples of s, and additionally satisfies some complementary constraints on the characters of s given in terms of position pairs. While the decision version of this problem is known to be NP-complete (see [2]), we prove here the APX-hardness of the general as well as of a restricted version of the problem. Moreover, we attack the problem by proposing a 4-approximation algorithm.