Polynucleotide evolution and branching processes
The theory of multitype branching processes has been applied to the description of the kinetics of polynucleotide replication. The stochastic model is consistent in mean with the usual kinetic differential equations of deterministic chemical kinetics. Qualitatively new consequences of the stochastic model are: after a transient period the supercritical multitype branching process either leads to extinction (corresponding to zero fluctuations) or the total population size becomes very large (corresponding to negligible relative fluctuations). The stochastic as well as the deterministic treatments of replication with errors yield error threshold relations which attest that the maximum length of faithfully replicated sequences are proportional to the inverse single digit error rate. The stochastic threshold provides a stronger condition than the deterministic relation.
scientific article; zbMATH DE number 3922436