Two combinatorial optimization problems for SNP discovery using base-specific cleavage and mass spectrometry

BACKGROUND: The discovery of single-nucleotide polymorphisms (SNPs) has important implications in a variety of genetic studies on human diseases and biological functions. One valuable approach proposed for SNP discovery is based on base-specific cleavage and mass spectrometry. However, it is still very challenging to achieve the full potential of this SNP discovery approach. RESULTS: In this study, we formulate two new combinatorial optimization problems. While both problems are aimed at reconstructing the sample sequence that would attain the minimum number of SNPs, they search over different candidate sequence spaces. The first problem, denoted as [Formula: see text] , limits its search to sequences whose in silico predicted mass spectra have all their signals contained in the measured mass spectra. In contrast, the second problem, denoted as [Formula: see text] , limits its search to sequences whose in silico predicted mass spectra instead contain all the signals of the measured mass spectra. We present an exact dynamic programming algorithm for solving the [Formula: see text] problem and also show that the [Formula: see text] problem is NP-hard by a reduction from a restricted variation of the 3-partition problem. CONCLUSIONS: We believe that an efficient solution to either problem above could offer a seamless integration of information in four complementary base-specific cleavage reactions, thereby improving the capability of the underlying biotechnology for sensitive and accurate SNP discovery.