Restricting SBH Ambiguity via Restriction Enzymes

Abstract. The expected number of n-base long sequences consistent with a given SBH spectrum grows exponentially with n, which severely limits the potential range of applicability of SBH even in an error-free setting. Restriction enzymes (RE) recognize specific patterns and cut the DNA molecule at all locations of that pattern. The output of a restriction assay is the set of lengths of the resulting fragments. By augmenting the SBH spectrum with the target string’s RE spectrum, we can eliminate much of the ambiguity of SBH. In this paper, we build on [20] to enhance the resolving power of restriction enzymes. We give a hardness result for the SBH+RE problem, and supply improved heuristics for the existing backtracking algorithm. We prove a lower bound on the number restric-tion enzymes required for unique reconstruction, and show experimental results that are not far from this bound.

On the Complexity of Positional Sequencing by Hybridization

In sequencing by hybridization (SBH), one has to reconstruct a sequence from its l-long substrings. SBH was proposed as an alternative to gel-based DNA sequencing approaches, but in its original form the method is not competitive. Positional SBH (PSBH) is a recently proposed enhancement of SBH in which one has additional information about the possible positions of each substring along the target sequence. We give a linear time algorithm for solving PSBH when each substring has at most two possible positions. On the other hand, we prove that the problem is NP-complete if each substring has at most three possible positions. We also show that PSBH is NP-complete if the set of allowed positions for each substring is an interval of length k, and provide a fast algorithm for the latter problem when k is bounded. Key Words: Positional Sequencing by Hybridization, Complexity, Eulerian Graphs, NP-Hardness, Parameterized Algorithms. 1 Introduction Sequencing by hybridization (SBH) was proposed ..