Latent Periodicities in Genome Sequences

A novel approach is presented for the detection of periodicities in DNA sequences. A DNA sequence can be modelled as a nonstationary stochastic process that exhibits various statistical periodicities over different regions. The coding part of the DNA, for instance, exhibits statistical periodicity with period three. Such regions in DNA are modelled as generated from a collection of information sources (with an underlying probability distribution) in a cyclic manner, thus exhibiting cyclostationarity. The maximum likelihood estimates are developed for the distributions of the information sources and for the statistical period of the DNA sequence. Such probabilistic sources are further investigated for decomposition into constituent cyclostationary sources. Since the symbolic sources do not admit an algebraic structure, a composition of cyclostationary probabilistic sources is studied that models DNA replication process. This composition is shown to give a rich mathematical structure on the collection of cyclostationary sources and allows a uniqueness theorem for the decomposition.