Dynamical stability of autocatalytic sets

occurrence of self-sustaining sets of molecules to be a genericproperty of random reaction networks. This stands in somecontrast to the experimental difficulty to actually find suchsystems. In this work, we argue that the usual approach,which is based on the study of static properties of reactiongraphs has to be complemented with a dynamic perspectivein order to avoid overestimation of the probability of gettingautocatalytic sets. Especially under the, from the experimentalpoint of view, important flow reactor conditions, it is notsufficient just to have a pathway generating a given type ofmolecules. The respective process has also to happen with asufficient rate in order to compensate the outflow. Reactionrates are therefore of crucial importance. Furthermore, processessuch as cleavage are on one hand advantageous for thesystem, because they enhance the molecular variability andtherefore the potential for catalysis. On the other hand, cleavagemay also act in an inhibiting manner by the destructionof vital components: therefore, an optimal balance betweenligation and cleavage has to be found. If energy is included asa limiting resource, the concentration profiles of the componentsof autocatalytic sets are altered in a manner that rendersa certain range for the energy supply rate as optimal for therealization of robust autocatalytic sets.The results presented are based on a theoretical model and obtainedby numerical integration of systems of ODE. This limitsthe number of involved molecular species which impliesthat the quantitative findings of this work may have no directrelevance for experimental situations, whereas the qualitativeinsights in the dynamics of the systems under considerationmay generalize to systems of truly combinatorial size.