Local multiple alignment via subgraph enumeration

Abstract

We discuss three problems, which we call blocking, chaining and flattening, that arise when computing a multiple-sequence alignment from given pairwise alignments. Blocking is the construction of gap-free multiple alignments, each called a “block”, from the pairwise alignments; it is formalized here as the enumeration of maximal cliques in a certain graph. Chaining is the identification of a collection of blocks that can appear together in a multiple alignment, which we formalize as determining a maximal connected subgraph (of a different graph) that satisfies certain consistency conditions. Flattening is the introduction of gaps within a chain of blocks to create a multiple alignment, which involves solving a problem of dynamic bipartite matching. For each problem, practical algorithms are presented and shown to be effective for analyzing sequences containing internal repeats.