Mutation in Autocatalytic Reaction Networks:

An Analysis based on Perturbation Theory

Peter F. Stadler and Peter Schuster

A class of kinetic equations describing catalyzed and template induced replication, and mutation is introduced. This ODE in its most general form is split into two vector fields, a replication and a mutation field. The mutation field is considered as a perturbation of the replicator equation. The perturbation expansion is a Taylor series in a mutation parameter $\lambda$. First second and higher order contributions are computed by means of the conventional Raleigh-Schr"odiger approach. Qualitative shifts in the positions of rest points and limit cycles on the boundary of the physically meaningful part of concentration space are predicted from flow topologies. The results of the topological analysis are summarized in two theorems which turned out to be useful in applications: the restpoint migration theorem (RPM) and the limit cycle migration theorem (LCM). Quantitative expressions for the shifts of rest points are computed directly from the perturbation expansion. The concept is applied to a collection of selected examples from biophysical chemistry and biology.
Return to 1990 working papers list.