Detecting Motifs in a Large Data Set: Applying Probabilistic Insights to Motif Finding

We give a probabilistic algorithm for Consensus Sequence, a NP-complete subproblem of motif recognition, that can be described as follows: given set of l-length sequences, determine if there exists a sequence that has Hamming distance at most d from every sequence. We demonstrate that distance between a randomly selected majority sequence and a consensus sequence decreases as the size of the data set increases. Applying our probabilistic paradigms and insights to motif recognition we develop pMCL-WMR, a program capable of detecting motifs in large synthetic and real-genomic data sets. Our results show that detecting motifs in data sets increases in ease and efficiency when the size of set of sequence increases, a surprising and counter-intuitive fact that has significant impact on this deeply-investigated area.