Dynamics of autocatalytic replicator networks based on higher-order ligation reactions.
A class of autocatalytic reaction networks based on template-dependent ligation and higher-order catalysis is analysed. Apart from an irreversible ligation reaction we consider only reversible aggregation steps that provide a realistic description of molecular recognition. The overall dynamics can be understood by means of replicator equations with highly non-linear interaction functions. The dynamics depends crucially on the total concentration c0 of replicating material. For small c0, in the hyperbolic growth regime, we recover the familiar dynamics of second-order replicator equations with its wealth of complex dynamics ranging from multi-stability to periodic and strange attractors as well as to heteroclinic orbits. For large c0, in the parabolic growth regime, product inhibition becomes dominating and we observe a single globally stable equilibrium tantamount to permanent coexistence. In an intermediate parameter range we sometimes observe a behavior that is reminiscent of 'survival of the fittest'. Independently replicating species (Schlögl's model) and the hypercycle are discussed in detail.
Stadler
B M
BM
Institut für Theoretische Chemie und Molekulare Strukturbiologie, Universität Wien, Vienna, Austria. baer,studla,pks@tbi.univie.ac.at
Stadler
P F
PF
Schuster
P
P
D002384:Catalysis; D003198:Computer Simulation; D007700:Kinetics; D008954:Models, Biological; D008956:Models, Chemical; D012313:RNA / Q000737:chemistry; D013698:Templates, Genetic
D012313:RNA