97-07-065
Abstract:
Selection Dynamics in Autocatalytic Systems:
Templates Replicating Through Binary Ligation
Peter R. Wills, Stuart A. Kauffman, Bärbel M.R. Stadler
and Peter F. Stadler
The theory of autocatalytic binary ligation is
reviewed within the context of a rigorously applies 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 case 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.
keywords:
template instructed replication - autocatalytic networks -
kinetic equations - evolution
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