Alignment-free Sequence Analysis Using Extensible Markov Models

Profile models based on Hidden Markov Models (HMM) for sequence studies have gained visibility among researchers. While the mathematical foundation, the proven algorithms such as Viterbi, Forward and Backward algorithms have certainly provided a rigorous probabilistic platform, the requirement of classic alignment has ensured an extremely high time complexity. We propose the use of another kind of Markov model called Extensible Markov Models (EMM) to create profile architectures that are more efficient in space and time complexity than their HMM counter parts. EMM efficiency comes from an alignment-free paradigm through use of an improved statistical signature form of sequences. The EMM aproach is based on the use sliding p-mers that count every possible p-mer pattern along equal sized segments of a sequence which are then clustered into Markov states. The resulting count vectors shift the position based letter-by-letter sequence analysis problem for phylogenetic trees, classification and search to a more efficient numerical vector space. Using adapted Karlin-Altschul statistics from the Basic Local Alignment Search Tool (BLAST) literature, the EMM based sequence classification also computes a p-value for statistical significance. We present a comparison between profiles generated using profile HMM and EMM.