Autocatalytic networks with translation |
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Authors: | Robert Happel Robert Hecht Peter F Stadler |
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Institution: | 1. Theoretische Biochemie, Institut für Theoretische Chemie, Universit?t Wien, Vienna, Austria 2. Santa Fe Institute, 87501, Santa Fe, NM, U.S.A.
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Abstract: | We consider the kinetics of an autocatalytic reaction network in which replication and catalytic actions are separated by
a translation step. We find that the behaviour of such a system is closely related to second-order replicator equations, which
describe the kinetics 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 toward 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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