A representation of DNA primary sequences by random walk.

We describe the DNA primary sequences by random walk. With the description, two random sequences {Y(m)} and {X(n)} corresponding to a DNA sequence, as well as graphical representations of DNA sequences are given. We further prove that two random sequences {Y(m)} and {X(n)} are both Markov chains. Based on transition probability distributions of Markov chains, some numerical characterizations of random sequences, we introduce some new invariants for the DNA primary sequences. Then using these invariants, we make comparisons among primary sequences for exon 1 of beta-globin genes belonging to nine species for analysis of the similarity and dissimilarity.