"We're working on some innovative new feedback mechanisms."
Principal Investigator
Peter Stadler
The project supposes to investigate the connection between realistic reaction-mechanisms of autocatalytic reactions and simplified versions thereof. Good examples are models of RNA-replication. The dynamics of such reaction-networks is readily described by a set of ordinary differntial equations (ODEs), which are based on mass action kinetics. There is a relationship of these dynamical systems to much simpler models of prebiotic evolution, the so-called Replicator equations. These resemble models describing interactions of B-cell and T-cell networks, such as are used in theoretical immunology.
The main interest of this project is to elucidate changes in the dynamics of such a reaction-network, if additional intermediates and/or side-reactions are introduced explicitly. It is particularly interesting, under which circumstances the new variables can be taken as a "structural perturbation" of a simpler mechanism.
To obtain answers to this complex of questions, the extension of a perturbation theory that has been developed by Peter F. Stadler and Peter Schuster is intended. Furthermore, methods such as singular perturbation theory will be applied in order to find out the circumstances, under which Replicator equations are suitable for describing the dynamics of more complicated reaction mechanisms. It is intended to apply both analytical and numerical means to gain information about qualitative differences between the dynamics of complicated and somewhat simplified reaction mechanisms.