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A representation of DNA primary sequences by random walk. (English) Zbl 1120.92018
Summary: We describe the DNA primary sequences by random walks. With this 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 and some numerical characterizations of random sequences, we introduce some new invariants for DNA primary sequences. Then using these invariants, we make comparisons among primary sequences for exon 1 of β-globin genes belonging to nine species for the analysis of similarity and dissimilarity.
MSC:
92C40Biochemistry, molecular biology
60G50Sums of independent random variables; random walks
92D10Genetics