A robust transition to homochirality in complex chemical reaction networks

TL;DR

This paper investigates how large, out-of-equilibrium chemical networks can undergo a phase transition to homochirality, providing a robust mechanism potentially relevant to the origin of life.

Contribution

It clarifies measurement conventions, introduces chiral symmetry concepts, and generalizes Frank's model using random matrix theory for large and sparse networks.

Findings

Homochirality emerges as a robust phase transition in large chemical networks.

The transition is influenced by the number of chiral species and energy input.

The generalized model applies to both dense and sparse networks.

Abstract

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 G. Laurent et al., PNAS (2021) based on the properties of large out of equilibrium chemical networks. We showed that in such networks, a phase transition towards an 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 analyze 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 can be extended to sparse networks, which shows that the emergence of homochirality is a robust transition.