In the preceding chapters we assumed the genome sequence under study to be known. Now it is time to look at strategies for how to assemble fragments of DNA into longer contiguous blocks, and eventually into chromosomes. This chapter is partitioned into sections roughly following a plausible workflow of a de novo assembly project, namely, error correction, contig assembly, scaffolding, and gap filling. To understand the reason for splitting the problem into these realistic subproblems, we first consider the hypothetical scenario of having error-free data from a DNA fragment.

Sequencing by hybridization

Assume we have separated a single DNA strand spelling a sequence T, and managed to measure its k-mer spectrum; that is, for each k-mer W of T we have the frequency freq (W) telling us how many times it appears in T. Microarrays are a technology that provides such information. They contain a slot for each k-mer W such that fragments containing W hybridize to the several copies of the complement fragment contained in that slot. The amount of hybridization can be converted to an estimate on the frequency count freq(W) for each k-mer W. The sequencing by hybridization problem asks us to reconstruct T from this estimated k-mer spectrum.

Another way to estimate the k-mer spectrum is to use high-throughput sequencing on T; the k-mer spectrum of the reads normalized by average coverage gives such an estimate.

Now, assume that we have a perfect k-mer spectrum containing no errors. It turns out that one can find in linear time a sequence T′ having exactly that k-mer spectrum. If this problem has a unique solution, then of course T′ = T.

The algorithm works by solving the Eulerian path problem (see Section 4.2.1) on a de Bruijn graph (see Section 9.7) representing the k-mers.

Here we need the following expanded de Bruijn graph G = (V, E).