Iterated function systems for DNA replication

The kinetic equations of DNA replication are shown to be exactly solved in terms of iterated function systems, running along the template sequence and giving the statistical properties of the copy sequences, as well as the kinetic and thermodynamic properties of the replication process. With this method, different effects due to sequence heterogeneity can be studied, in particular, a transition between linear and sublinear growths in time of the copies, and a transition between continuous and fractal distributions of the local velocities of the DNA polymerase along the template. The method is applied to the human mitochondrial DNA polymerase γ without and with exonuclease proofreading.