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

Abstract

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.

Pulsed-field gel electrophoresis studies of Rhizobiaceae

“…Second-and especially third-order Markov chains were better predictors of enzymes that produced the fewest fragments, but they generally underestimated the average fragment size at least ten-fold (Tables 3 and 4). Our results are in general agreement with similar analyses of other bacterial sequences (Phillips et al, 1987a(Phillips et al, , 1987bMcClelland et al, 1987), and reiterate the usefulness of Markov chain analysis in showing higher order sequence asymmetry (Elton, 1975;Algamor, 1983;Blaisdell, 1985, Rogerson, 1989) and in predicting site frequencies (McClelland et al, 1987;Phillips et al, 1987aPhillips et al, , 1987b in genomic DNAs.…”

“…Based on G+C content of Rhizobiaceae (Jordan, 1984;Herdman, 1985) and on sequence information, the rarity of five AT-rich restriction sites was calculated by using different statistical techniques (Almagor, 1983;Upholt, 1977;Phillips et al, 1987aPhillips et al, , 1987bMcClelland, 1985;McClelland et al, 1987). These predictions were used as guidelines to select 82 the most rare-cutting enzymes.…”

“…Predictions were based on G+C molar ratios (Upholt, 1977), mono-, di-, tri-, and tetranucleotide frequencies (Almagor, 1983;Blaisdell, 1985;Phillips et al, 1987aPhillips et al, , 1987bMcClelland, 1985;McClelland et al, 1987). Note the differences in predictions made by using different frequencies as generators.…”

“…Calculations using G+C molar ratios ar Upholt et al (1977). Other calculations are based on Markov chain analysi coli by Phillips et al (1987aPhillips et al ( , 1987b. NC = not calculated.…”

“…These DNA sequences were grouped by species and used to make predictions about rarecutting restriction enzymes in Rhizobiaceae. Using statistical methods (Almagor, 1983;Phillips et al, 1987aPhillips et al, , 1987bMcClelland, 1985;McClelland et al, 1987) (Martin and Long, 1984) or by reaction with strain-specific FAs (Schmidt et al, 1986 respectively. B. iaponicum was grown in AG medium (Sadowsky et al, 1987) and R. meliloti.…”