93-12-075
Abstract:
The Influence of Mutation on Autocatalytic Reaction Networks
Peter F. Stadler and Juan Carlos Nu\~no
A particular class of ordinary differential equations (ODE) describing
catalyzed, template-induced, and erroneous replication is investigated. The
ODEs can be split into a replicator part accounting for the correct replication
and a mutation term accounting for all miscopying processes. The set of all
species is divided into the catalytically active ``viable'' species and an
error-tail subsuming all othe species. Neglecting both the inter-mutation
among the viable species and the re-flux from the error-tail allows for an
extensive analysis of the autocatalytic network. If mutation rates are small
enough a perturbation approach is feasible showing that mutation in general
simplifies the qualitative behavior of the dynamical system. Special cases,
such as Sch\"ogl's model, the uniform model, and the hypercycle show that the
viable species become unstable beyond a critical mutation rate: there is an
analogue to the error-threshold of the quasispecies model also in non-linear
autocatalytic reaction networks with mutation.
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