Mono-through hexanucleotide composition of the Escherichia coli genome: a Markov chain analysis

Several statistical methods were tested for accuracy in predicting observed frequencies of di- through hexanucleotides in 74,444 bp of E. coli DNA. A Markov chain was most accurate overall, whereas other methods, including a random model based on mononucleotide frequencies, were very inaccurate. When ranked highest to lowest abundance, the observed frequencies of oligonucleotides up to six bases in length in E. coli DNA were highly asymmetric. All ordered abundance plots had a wide linear range containing the majority of the oligomers which deviated sharply at the high and low ends of the curves. In general, values predicted by a Markov chain closely followed the overall shape of the ordered abundance curves. A simple equation was derived by which the frequency of any nucleotide longer than four bases in the E. coli genome (or any genome) can be relatively accurately estimated from the nested set of component tri- and tetranucleotides by serial application of a 3rd order Markov chain. The equation yielded a mean ratio of 1.03 +/- 0.94 for the observed-to-expected frequencies of the 4,096 hexanucleotides. Hence, the method is a relatively accurate but not perfect predictor of the length in nucleotides between hexanucleotide sites. Higher accuracy can be achieved using a 4th order Markov chain and larger data sets. The high asymmetry in oligonucleotide abundance means that in the E. coli genome of 4.2 X 10(6) bp many relatively short sequences of 7-9 bp are very rare or absent.