Attaining the 2nd Chargaff Rule by Tandem Duplications

Erwin Chargaff in 1950 made an experimental observation that the count of A is equal to the count of \mathrm{T} and the count of \mathrm{C} is equal to the count of \mathrm{G} in DNA. This observation played a crucial role in the discovery of the double stranded helix structure by Watson and Crick. However, this symmetry was also observed in single stranded DNA. This phenomenon was termed as the 2nd Chargaff Rule. This symmetry has been verified experimentally in genomes of several different species not only for mononucleotides but also for reverse complement pairs of larger lengths upto a small error. While the symmetry in double stranded DNA is related to base pairing and replication mechanisms, the symmetry in a single stranded DNA is still a mystery in its function and source. In this work, we define a sequence generation model based on reverse complement tandem duplications. We show that this model generates sequences that satisfy the 2nd Chargaff Rule even when the duplication lengths are very small when compared to the length of sequences. We also provide estimates on the number of generations that are needed by this model to generate sequences that satisfy the 2nd Chargaff Rule. We provide theoretical bounds on the disruption in symmetry for different values of duplication lengths under this model. Moreover, we experimentally compare the disruption in the symmetry incurred by our model with what is observed in human genome data.