A Double Combinatorial Approach to Discovering Patterns in Biological Sequences

We present in this paper an algorithm for nding degenerated common features by multiple comparison of a set of biological sequences (nucleic acids or proteins). The features that are of interest to us are words in the sequences. The algorithm uses the concept of a model we introduced earlier for locating these features. A model can be seen as a generalization of a consensus pattern as deened by Waterman 42]. It is an object against which the words in the sequences are compared and which serves as an identiier for the groups of similar ones. The algorithm given here innovates in relation to our previous work in that the models are deened over what we call a weighted combinatorial cover. This is a collection of sets among all possible subsets of the alphabet of nucleotides or amino acids, including the wild card fg, with a weight attached to each of these sets indicating the number of times it may appear in a model. In this way, we explore both the space of models and that of alphabets. The words that are related to a model deened over such a combinatorial cover, and thus considered to be similar, are then the ones that either belong to the model or present at most a certain number of errors with a nearest element of it. We use two algorithmic ideas that allow us to deal with such double combinatorics, one concerns a left-to-right minimality of the sets composing a model, the other involves making a sketch of the solution space before exploring it in detail.