How Catalytic Order Drives the Complexification of Molecular Replication Networks

Catalytic replication networks have frequently served to study emergent phenomena in complex mixtures. In a series of recent research papers, we have analyzed the effects of the autocatalytic reaction order on various behaviors of these networks, and in particular, on their possibility to evolve and mimic functions often observed in cell biochemistry. In this review, we first discuss and derive properties of minimal self-replication, with an emphasis on catalytic order, reaction order, and properties directly affected by the order. We then expand our discussion to include catalytic networks, and review some of the implications of symmetry and order in these networks. Consequently, we look at open catalytic networks and their oscillations in replication product formation, again emphasizing the critical role played by the catalytic order. Finally, we describe an extension of the catalytic networks research using the quasispecies model, where we note the implications of the order on the phase transitions observed in these systems. Further implications of these results for emergence and evolution are discussed.