Repeated sequences in bacterial genomes
Bias in the frequency of short nucleotide sequences (1999-2001)


Elhai J (2001). Determination of bias in the relative abundance of oligonucleotides in DNA sequences. J Comp Biol 8:151-175.

Vogel S, Hoke K, Elhai J (2001) Appendix: Simplified expressions of a measure of compositional bias. J Comp Biol 8:170-175.

Short DNA sequences are not equally likely and randomly disposed in our genomes -- if they were, we wouldn't be having this conversation. However, the degree of bias of short sequences (underrepresentation or overrepresentation with respect to chance) is not great in bacterial genomes. In E. coli (Figure 1), the bias of most 6-nucleotide sequences is confined to a narrow range centered around 1 (same frequency as chance). The story is different for a small fraction of these sequences, those that are palindromes. Palindromes are double-stranded sequences that read the same left-to-right (5' to 3') as right-to-left (5' to 3') and are often the target of proteins that bind DNA. Palindromic hexamers are decidedly biased towards underrepresentation.


Figure 1. Bias in hexanucleotide sequences of Escherichia coli strain K12. Bias is computed as total compositional bias (explained in the text). The 64 possible palindromic hexanucleotide sequences are treated separately from the 4032 non-palindromic sequences. Bias values were binned every 0.05 units.
The palindromic hexameric sequences may be divided into two sub-populations. The majority of such sequences are only slightly underrepresented (on average), but there is a separate, more extreme sub-population of hexamers. The most underrepresented hexamers are almost all targets for restriction enzymes identified in some species of Escherichia. This phenomenon may be explained (Figure 2) by postulating that restriction enzymes come and go rapidly in evolutionary time, traded amongst related strains. When present, there is strong selection against their target sites, and the bias persists even when the restriction enzyme is no longer present in a strain.

Figure 2. Model to explain underreprentation of targets for restriction enzymes in related strains.

Bias is computed as the ratio of actual frequency to expected frequency. The expected frequency of a sequence is generally calculated by one of two methods. The simpler method uses a Markov model and is based on three extreme sub-sequences. The more complext method, total compositional bias, takes into account all possible sub-sequences. Even though the calculations by these two methods are quite dissimilar, we showed that mathematically the Markov calculation is, surprisingly, equivalent to total compositional bias when gapped sequences contribute nothing to the bias (Figure 3).



Figure 3. Relationship between methods of calculating bias. EB is the value calculated via total compositional bias. EM is the value calculated from a maximal Markov model. The rest of the equation is the product of all biases from gapped sequences.