Selection Dynamics in Autocatalytic Systems: Templates Replicating Through Binary Ligation

Peter R. Wills, Stuart A. Kauffman, Bärbel M. R. Stadler, and Peter F. Stadler

97-07-065

The theory of autocatalytic binary ligation is reviewed within the context of a rigorously 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. It is observed that in systems incorporating multiple templates, coexistence of all species is the norm because their synthesis follows a parabolic growth law. Only under certain stringent conditions is exponential growth, and hence, Darwinian competition, observed. Our results are applicable to classical case of self-replicating nucleic acids and their analogues as well as to newly discovered self-replicating peptides.