An algorithm for finding signals of unknown length in DNA sequences

Pattern discovery in unaligned DNA sequences is a challenging problem in both computer science and molecular biology. Several different methods and techniques have been proposed so far, but in most of the cases signals in DNA sequences are very complicated and avoid detection. Exact exhaustive methods can solve the problem only for short signals with a limited number of mutations. In this work, we extend exhaustive enumeration also to longer patterns. More in detail, the basic version of algorithm presented in this paper, given as input a set of sequences and an error ratio ε < 1, finds all patterns that occur in at least q sequences of the set with at most εm mutations, where m is the length of the pattern. The only restriction is imposed on the location of mutations along the signal. That is, a valid occurrence of a pattern can present at most [εi] mismatches in the first i nucleotides, and so on. However, we show how the algorithm can be used also when no assumption can be made on the position of mutations. In this case, it is also possible to have an estimate of the probability of finding a signal according to the signal length, the error ratio, and the input parameters. Finally, we discuss some significance measures that can be used to sort the patterns output by the algorithm