The selection of a single molecular handedness, or homochirality across all living matter, is a mystery in the origin of life. Frank’s seminal model showed in the ’50s how chiral symmetry breaking can occur in nonequilibrium chemical networks. However, an important shortcoming in this classic model is that it considers a small number of species, while there is no reason for the prebiotic system, in which homochirality first appeared, to have had such a simple composition. Furthermore, this model does not provide information on what could have been the size of the molecules involved in this homochiral prebiotic system. Here, we show that large molecular systems are likely to undergo a phase transition toward a homochiral state, as a consequence of the fact that they contain a large number of chiral species. Using chemoinformatics tools, we quantify how abundant chiral species are in the chemical universe of all possible molecules of a given length. Then, we propose that Frank’s model should be extended to include a large number of species, in order to possess the transition toward homochirality, as confirmed by numerical simulations. Finally, using random matrix theory, we prove that large nonequilibrium reaction networks possess a generic and robust phase transition toward a homochiral state.

The problem of the emergence and survival of self-replicating molecules in origin-of-life scenarios is plagued by the error catastrophe, which is usually escaped by considering effects of compartmentalization, as in the stochastic corrector model. By addressing the problem in a simple system composed of a self-replicating molecule (a replicase) and a parasite molecule that needs the replicase for copying itself, we show that transient (rather than permanent) compartmentalization is sufficient to the task. We also exhibit a regime in which the concentrations of the two kinds of molecules undergo sustained oscillations. Our model should be relevant not only for origin-of-life scenarios but also for describing directed evolution experiments, which increasingly rely on transient compartmentalization with pooling and natural selection.

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.