A robust transition to homochirality in complex chemical reaction networks

Homochirality, i.e. the dominance across all living matter of one enantiomer over the other among chiral molecules, is thought to be a key step in the emergence of life. Building on ideas put forward by Frank and many others, we proposed recently one such mechanism in Laurent et al. (Laurent, 2021 Proc. Natl Acad. Sci. USA 118, e2012741118. (doi:10.1073/pnas.2012741118)) based on the properties of large out of equilibrium chemical networks. We showed that in such networks, a phase transition towards a homochiral state is likely to occur as the number of chiral species in the system becomes large or as the amount of free energy injected into the system increases. This paper aims at clarifying some important points in that scenario, not covered by our previous work. We first analyse the various conventions used to measure chirality, introduce the notion of chiral symmetry of a network and study its implications regarding the relative chiral signs adopted by different groups of molecules. We then propose a generalization of Frank's model for large chemical networks, which we characterize completely using methods of random matrices. This analysis is extended to sparse networks, which shows that the emergence of homochirality is a robust transition.