Spontaneous Emergence of Transient Chirality in Closed, Reversible Frank-like Deterministic Models

To explore abiotic theories related to the origin of biomolecular homochirality, we analyze two entirely reversible kinetic models composed of an enantioselective autocatalysis with limited stereoselectivity that is coupled to an enantiomeric mutual inhibition (Frank-like models). The two models differ in their autocatalytic steps in respect to the formation of monomer species in one model and of dimer species in the other. While fully reversible and running in a closed system, spontaneous mirror symmetry breaking (SMSB) gives rise to transient chiral excursions, even when starting from a strictly achiral situation. Before the SMSB, the two models differ in the main dissipative processes. At the SMSB, the entropy production rate reaches its maximum in both models. Here it is the enantioselective autocatalysis with retention of the winner enantiomer that dominates. During the terminal phase, the enantioselective autocatalysis with inversion prevails, while the entropy production rate vanishes, thus fulfilling the conditions of microscopic reversibility. SMSB does not occur if the autocatalytic rate constant is too strong or too weak. However, when the autocatalysis is relatively weak, the temporary chiral excursions last for long periods of time and could be the starting point of a cascade of asymmetric reactions. The realism of such Frank-like models is discussed from the viewpoint of their relevance to prebiotic chemistry.