Nonlinear physics approach to RNA cross-replication: Marginal stability, generalized logistic growth, and impacts of degradation

It is nowadays believed that the evolution of life involved as an intermediate step an RNA world. In such an RNA world RNA molecules replicate themselves in catalytic reactions. Recent experiments on cross-replicating RNA support the RNA world hypothesis. We derive a nonlinear mass-action kinetics model to explain logistic growth patterns and non-symmetric saturation levels observed in those experiments. We also demonstrate that fixed points of the RNA growth process are only marginally stable rather than asymptotically stable.

► RNA cross-replication is a marginally stable but not asymptotically stable process.
► RNA enzymes exhibits a generalized logistic growth pattern with exponent equal to 2.
► Degradation results in non-symmetric saturation levels of cross-replicating RNAs.