Origin and length distribution of unidirectional prokaryotic overlapping genes

Prokaryotic unidirectional overlapping genes can be originated by disrupting and replacing of the start or stop codon of one protein-coding gene with another start or stop codon within the adjacent gene. However, the probability of disruption and replacement of a start or stop codon may differ significantly depending on the number and redundancy of the start and stop codons sets. Here, we performed a simulation study of the formation of unidirectional overlapping genes using a simple model of nucleotide change and contrasted it with empirical data. Our results suggest that overlaps originated by an elongation of the 3'-end of the upstream gene are significantly more frequent than those originated by an elongation of the 5'-end of the downstream gene. According to this, we propose a model for the creation of unidirectional overlaps that is based on the disruption probabilities of start codon and stop codon sets and on the different probabilities of phase 1 and phase 2 overlaps. Additionally, our results suggest that phase 2 overlaps are formed at higher rates than phase 1 overlaps, given the same evolutionary time. Finally, we propose that there is no need to invoke selection to explain the prevalence of long phase 1 unidirectional overlaps. Rather, the overrepresentation of long phase 1 relative to long phase 2 overlaps might occur because it is highly probable that phase 2 overlaps are retained as short overlaps by chance. Such a pattern is stronger if selection against very long overlaps is included in the model. Our model as a whole is able to explain to a large extent the empirical length distribution of unidirectional overlaps in prokaryotic genomes.