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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