Generalizations of Markov model to characterize biological sequences

Background: The currently used k(th) order Markov models estimate the probability of generating a single nucleotide conditional upon the immediately preceding ( gap = 0) k units. However, this neither takes into account the joint dependency of multiple neighboring nucleotides, nor does it consider the long range dependency with gap>0. Result: We describe a configurable tool to explore generalizations of the standard Markov model. We evaluated whether the sequence classification accuracy can be improved by using an alternative set of model parameters. The evaluation was done on four classes of biological sequences - CpG-poor promoters, all promoters, exons and nucleosome positioning sequences. Using di- and trinucleotide as the model unit significantly improved the sequence classification accuracy relative to the standard single nucleotide model. In the case of nucleosome positioning sequences, optimal accuracy was achieved at a gap length of 4. Furthermore in the plot of classification accuracy versus the gap, a periodicity of 10 - 11 bps was observed which might indicate structural preferences in the nucleosome positioning sequence. The tool is implemented in Java and is available for download at ftp://ftp.pcbi.upenn.edu/GMM/. Conclusion: Markov modeling is an important component of many sequence analysis tools. We have extended the standard Markov model to incorporate joint and long range dependencies between the sequence elements. The proposed generalizations of the Markov model are likely to improve the overall accuracy of sequence analysis tools.