Sequence selection by dynamical symmetry breaking in an autocatalytic binary polymer model

Template-directed replication of nucleic acids is at the essence of all living beings and a major milestone for any origin of life scenario. We present an idealized model of prebiotic sequence replication, where binary polymers act as templates for their autocatalytic replication, thereby serving as each others reactants and products in an intertwined molecular ecology. Our model demonstrates how autocatalysis alters the qualitative and quantitative system dynamics in counterintuitive ways. Most notably, numerical simulations reveal a very strong intrinsic selection mechanism that favors the appearance of a few population structures with highly ordered and repetitive sequence patterns when starting from a pool of monomers. We demonstrate both analytically and through simulation how this "selection of the dullest" is caused by continued symmetry breaking through random fluctuations in the transient dynamics that are amplified by autocatalysis and eventually propagate to the population level. The impact of these observations on related prebiotic mathematical models is discussed.