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Developing a mathematical understanding of autocatalysis in reaction networks has both theoretical and practical implications. We review definitions of autocatalytic networks and prove some properties for minimal autocatalytic subnetworks (MASs). We show that it is possible to classify MASs in equivalence classes, and develop mathematical results about their behavior. We also provide linear-programming algorithms to exhaustively enumerate them and a scheme to visualize their polyhedral geometry and combinatorics. We then define cluster chemical reaction networks, a framework for coarse-graining real chemical reactions with positive integer conservation laws. We find that the size of the list of minimal autocatalytic subnetworks in a maximally connected cluster chemical reaction network with one conservation law grows exponentially in the number of species. We end our discussion with open questions concerning an ecosystem of autocatalytic subnetworks and multidisciplinary opportunities for future investigation. 

Abstract Here, we report an approach to the synthesis of highly charged enantiopure cyclophanes by the insertion of axially chiral enantiomeric binaphthyl fluorophores into the constitutions of pyridinium‐based macrocycles. Remarkably, these fluorescent tetracationic cyclophanes exhibit a significant AIE compared to their neutral optically active binaphthyl precursors. A combination of theoretical calculations and time‐resolved spectroscopy reveal that the AIE originates from limited torsional vibrations associated with the axes of chirality present in the chiral enantiomeric binaphthyl units and the fine‐tuning of their electronic landscape when incorporated within the cyclophane structure. Furthermore, these highly charged enantiopure cyclophanes display CPL responses both in solution and in the aggregated state. This unique duality of AIE and CPL in these tetracationic cyclophanes is destined to be of major importance in future development of photonic devices and bio‐applications.