Autocatalytic Networks with Translation
Robert Happel, Robert Hecht, and Peter F. Stadler
We consider the kinetics of an autocatalytic reaction network in which
replication and catalytic action is separated by a translation step.
We find that the behavior of such a system is closely related to
second order replicator equations, which describe the kinetic of
autocatalytic reaction networks in which the replicators act also
as catalysts. In fact, the qualitative dynamics seems to be
described almost entirely be the second order reaction rates of
the replication step. For two species we recover the qualitative
dynamics of the replicator equations. Larger networks show some
deviations, however. A hypercyclic system consisting of three
interacting species can converge towards a stable limit cycle in
contrast to the replicator equation case. A singular perturbation
analysis shows that the replication translation system reduces
to a second order replicator equation if translation is fast. The
influence of mutations on replication translation networks is
also very similar to the behavior of selection-mutation equations.
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