Mapping sequences by parts.

BACKGROUND

We present the N-map method, a pairwise and asymmetrical approach which allows us to compare sequences by taking into account evolutionary events that produce shuffled, reversed or repeated elements. Basically, the optimal N-map of a sequence s over a sequence t is the best way of partitioning the first sequence into N parts and placing them, possibly complementary reversed, over the second sequence in order to maximize the sum of their gapless alignment scores.

RESULTS

We introduce an algorithm computing an optimal N-map with time complexity O (|s| x |t| x N) using O (|s| x |t| x N) memory space. Among all the numbers of parts taken in a reasonable range, we select the value N for which the optimal N-map has the most significant score. To evaluate this significance, we study the empirical distributions of the scores of optimal N-maps and show that they can be approximated by normal distributions with a reasonable accuracy. We test the functionality of the approach over random sequences on which we apply artificial evolutionary events.

PRACTICAL APPLICATION

The method is illustrated with four case studies of pairs of sequences involving non-standard evolutionary events.