Regular Expression Constrained Sequence Alignment

Abstract

Given strings S1, S2, and a regular expression R, we introduce regular expression constrained sequence alignment as the problem of finding the maximum alignment score between S1 and S2 over all alignments such that in these alignments there exists a segment where some substring s1 of S1 is aligned with some substring s2 of S2, and both s1 and s2 match R, i.e. s1, s2 ∈ L(R) where L(R) is the regular language described by R. A motivation for the problem is that protein sequences can be aligned in a way that known motifs guide the alignments. We present an O(nmr) time algorithm for the regular expression constrained sequence alignment problem where n, and m are the lengths of S1, and S2, respectively, and r is in the order of the size of the transition function of a finite automaton M that we create from a nondeterministic finite automaton N accepting L(R). M contains O(t 2 ) states if N has t states.

Constrained sequence alignment: A general model and the hardness results

“…Myers and coauthors [18] had adopted a different definition of constraints, and applications admitted are different from those in [20,6,21,2,7]. In [18], a constraint is an order relation of two characters on two different sequences in the input set of sequences.…”

“…The input sequences are in effect annotated with the substrings representing the candidate occurrences of each pattern. This generalizes the previous formulations since, given patterns defined in [20,6,21,16,2,7], the occurrences can be easily annotated in the sequences by well-established pattern matchers (e.g., the UNIX utility grep for regular expression patterns), thereby transforming the original patterns into an instance of our formulation. The formulation here also enables one to adopt mixed pattern definitions simultaneously in the analysis, for example some patterns can be specified by regular expressions and the others by strings with mismatch tolerance.…”

“…. x i,k ] responsible for this witness are then said to satisfy pattern k. This formulation follows the logic in the previous works [20,6,21,16,2,7] that, for each pattern, a legal occurrence on each sequence is chosen to support the feasibility of a constrained alignment, while those occurrences not chosen are treated as normal characters. Unlike the previous studies, we do not specify how the characters in the substrings S i [x i,k .…”

“…To facilitate further discussion we say that in all these works a constraint is a sequence of patterns; a pattern is a simple character in [20,6], a substring allowing mismatches in [21,16] and a regular expression in [2,7]. Each pattern is described by its sequence content in these works.…”

“…Lu and Huang [16] then reduced the memory requirement of the algorithm in [21], which significantly improves the applicability of the tool. Arslan introduced the regular expression constrained sequence alignment (RECSA) problem [2], in which a constraint is a regular expression, and a feasible solution is an alignment containing a run of contiguous columns corresponding to two substrings, one for each input sequence, such that both substrings match the regular expression constraint. Chung and coauthors [7] followed the formulation of Arslan and gave more time and space efficient algorithms for RECSA.…”