Local sequence alignments with monotonic gap penalties

Motivation: Sequence alignments obtained using affine gap penalties are not always biologically correct, because the insertion of long gaps is over-pe nalised. There is a need for an efficient algorithm which can find local al ignments using non-linear gap penalties. Results: A dynamic programming algorithm is described which computes optima l focal sequence alignments for arbitrary, monotonically increasing gap pen alties, i.e. where the cost g(k) of inserting a gap of k symbols is such th at g(k) greater than or equal to g(k - 1). The running time of the algorith m is dependent on the scoring scheme; if the expected score of art alignmen t between random, unrelated sequences of lengths m, n is proportional to lo gmn, then with one exception, the algorithm has expected running time O(mn) . Elsewhere, the running time is no greater than O(mn(m + n)). Optimisation s are described which appear to reduce the worst-case run-time to O(mn) in many cases. We show how using a non-affine gap penalty cart dramatically in crease the probability of detecting a similarity containing a long gap. Availability: The source code is available to academic collaborators under licence.