Dynamical Stability of Autocatalytic Sets

Theoretical investigations of autocatalytic sets rendered the occurrence of self-sustaining sets of molecules to be a generic property of random reaction networks. This stands in some contrast to the experimental difficulty to actually find such systems. In this work, we argue that the usual approach, which is based on the study of static properties of reaction graphs has to be complemented with a dynamic perspective in order to avoid overestimation of the probability of getting autocatalytic sets. Especially under the, from the experimental point of view, important flow reactor conditions, it is not sufficient just to have a pathway generating a given type of molecules. The respective process has also to happen with a sufficient rate in order to compensate the outflow. Reaction rates are therefore of crucial importance. Furthermore, processes such as cleavage are on one hand advantageous for the system, because they enhance the molecular variability and therefore the potential for catalysis. On the other hand, cleavage may also act in an inhibiting manner by the destruction of vital components: therefore, an optimal balance between ligation and cleavage has to be found. If energy is included as a limiting resource, the concentration profiles of the components of autocatalytic sets are altered in a manner that renders a certain range for the energy supply rate as optimal for the realization of robust autocatalytic sets. The results presented are based on a theoretical model and obtained by numerical integration of systems of ODE. This limits the number of involved molecular species which implies that the quantitative findings of this work may have no direct relevance for experimental situations, whereas the qualitative insights in the dynamics of the systems under consideration may generalize to systems of truly combinatorial size.