Selection dynamics in autocatalytic systems: templates replicating through binary ligation

The theory of autocatalytic binary ligation is reviewed within the context of a consistently applied Michaelis-Menten quasi-steady-state approximation to obtain explicit analytical results describing time-course data from experiments. A detailed protocol for the step-wise elucidation of a minimal set of experimental parameters is outlined. The kinetic equations are then generalized to cases of self- and cross-catalysis among an arbitrary number of different templates and applied to experiments involving just two templates. Depending on the values of various kinetic parameters such systems can display exclusionary Darwinian selection corresponding to an exponential growth law, selective coexistence or coexistence of all species characteristic of a parabolic growth law; the intermediate behaviour arises as a property of the full mechanism analysed here. Our results are applicable to the classical case of self-replicating nucleic acids and their analogues as well as to newly discovered self-replicating peptides.