Spontaneous emergence of homochirality via coherently coupled antagonistic and reversible reaction cycles.

Asymmetric synthesis aims at obtaining enantio-enriched products in stereoselective reactions under a chiral influence. We demonstrate both mathematically and numerically that, even under nominally achiral conditions, fully homochiral steady states can be obtained in open reactive systems by spontaneous mirror-symmetry breaking in the homogenous solution phase when the autocatalytic reaction network is closed in the form of coherently coupled antagonistic reversible reaction cycles which, paradoxically, allow for complete recycling of the reactant. We show that the fully reversible Frank mechanism for spontaneous mirror-symmetry breaking is closely related to the Lotka-Volterra system, which models predator-prey relations in ecosystems. Amplification of total enantiomeric excess and the principle of microscopic reversibility are not in conflict for all conceivable reactions. A viable and widely applicable reaction protocol is introduced and discussed, and it permits the theoretical implications to be applied to practical laboratory examples. Implications for the possible origin of biological homochirality on early earth are discussed.