COMPLEX DYNAMICS OF A CATALYTIC NETWORK HAVING FAULTY REPLICATION INTO ERROR-SPECIES

We examine the dynamics of catalytic networks when error is introduced through faulty self-replication into a mutant molecular species. The model consists of n species that individually self-replicate through noncatalytic and catalytic action, and catalyze the replication of other species. Faulty replication produces error mutants which are assumed to be kinetically indistinguishable from one another. This aggregate error-species (error-tail) undergoes noncatalyzed self-replication, but has no effect on the catalytic species. A constant-population criterion produces competition among all reactants. The time evolution of the catalytic species can be expressed by a set of ordinary differential equations. We provide a detailed parametric analysis of the dynamics in a computationally tractable reduced model. Kinetic constants K(ji) controlling the enzymatic reactions can be used as bifurcation parameters to generate a rich repertoire of periodic and complex chaotic dynamics. Except for changes in the parametric position of bifurcation points, system dynamics is stable in response to changes in the quality of replication Q, where 1 - Q is the mutation rate, and in the amplification constant A for the catalytic species. At low values of Q, the system falls out of chaotic regimes and into a ''random-replication'' state at which there are no catalytic species present. There is a similar insensitivity to changes in the amplification factor for the error species, A(e), except for A(e) = 0, at which the chaotic regimes remain stable throughout the full range of Q. We discuss the behavior of our model against one in which error is handled by means of mutual intermutation between the catalytic species. Complex behavior in this intermutation model is extremely sensitive to the mutation rate. Because the error-tail is expressed only in terms of the catalytic species themselves rather than in variables representing the error-species, the error-tail model may provide a useful method with which to examine models of error-utilization in neuronal and other biological systems involving competitive interactions among their constituent parts.