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Homochirality, i.e. the dominance across all living matter of one enantiomerover the other among chiral molecules, is thought to be a key step in theemergence of life. Building on ideas put forward by Frank and many others, weproposed recently one such mechanism in G. Laurent et al., PNAS (2021) based onthe properties of large out of equilibrium chemical networks. We showed that insuch networks, a phase transition towards an homochiral state is likely tooccur as the number of chiral species in the system becomes large or as theamount of free energy injected into the system increases. This paper aims atclarifying some important points in that scenario, not covered by our previouswork. We first analyze the various conventions used to measure chirality,introduce the notion of chiral symmetry of a network, and study itsimplications regarding the relative chiral signs adopted by different groups ofmolecules. We then propose a generalization of Frank's model for large chemicalnetworks, which we characterize completely using methods of random matrices.This analysis can be extended to sparse networks, which shows that theemergence of homochirality is a robust transition.

A robust transition to homochirality in complex chemical reaction networks