A stochastic model of the emergence of autocatalytic cycles

We here introduce a novel stochastic model of catalytic reaction networks, in order to investigate the emergence of autocatalytic cycles, sensibly considering the importance of noise, of small-number effects and the possible growth of the number of different elements in the system.Furthermore, the introduction of a temporal threshold that defines how long a specific reaction is kept in the reaction graph allows to univocally define cycles also within an asynchronous framework.The foremost analyses have been focused on the study of the variation of the composition of the incoming flux. It was possible to show that the activity of the system is enhanced, with particular regard to the emergence of autocatalytic sets, if a larger number of different elements is present in the incoming flux, while the specific length of the species seems to entail minor effects on the overall dynamics.The investigation of the generic properties of catalytic reaction networks, with specific regard to the emergence of the so-called autocatalytic cycles or sets (referred to as ACS hereafter), is one of the key issues in systems chemistry and, particularly, in the research concerning the origin of life.The debate on the transition from non-living to living is still open and compelling [1-4] and several different theoretical frameworks have been proposed, such as the metabolic-first hypothesis [5-10], the protein - first scenario [11-13], the compartmentalization [14], the compositional approach [15,16] and the well-known gene - first hypothesis embodied in the RNA world theory [4,17-22].Despite the differences, the underlining principle beyond these theories is the necessity for the existence of robust reaction pathways for the production of the molecular species involved in the transition. Some authors hypothesised the existence of linear chemical processes capable of produce substantial amount of the species under plausible prebiotic conditions [23] or at energy-rich site such as hydrother