Fixed-parameter algorithms for protein similarity search under mRNA structure constraints

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 mRNA Structure Optimization (MRSO) problem. Since MRSO is known to be APX-hard, Bongartz [D. Bongartz, Some notes on the complexity of protein similarity search under mRNA structure constraints, in: Proc. of the 30th Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM), 2004, pp. 174–183] suggested to attack the problem using the approach of parameterized complexity. In this paper we propose three fixed-parameter algorithms that apply for several interesting parameters of MRSO. We believe these algorithms to be relevant for practical applications today, as well as for possible future applications. Furthermore, our results extend the known tractability borderline of MRSO, and provide new research horizons for further improvements of this sort.