Noise-induced symmetry breaking of self-regulators: Nonequilibrium transition toward homochirality

We present a theoretical model to study the origin of chiral symmetry breaking of a racemic mixture of optically active biomolecules. We consider a collection of Brownian particles, which can stay in any of the three possible isomeric states: one achiral and two enantiomers. Isomers are undergoing self-regulatory reaction along with chiral inhibition and achiral decay processes. The reaction rates of the isomeric states are guided by their neighbors as well as the thermal fluctuations of the system. We find that an alteration in the relative dominance of self-regulation, chiral inhibition, and achiral decay processes breaks the chiral symmetry of the system, which is either partial or complete. This results in four different asymmetric population states, viz., three-isomer coexistence, enantiomeric coexistence, chiral-achiral coexistence, and homochiral state. A change in the reaction condition induces nonequilibrium transition among these states. We also report that a fast stochastic self-regulation and a slow chiral inhibition and achiral decay process along with a threshold population of interacting neighbors suffice for the requisite for transition toward a completely symmetry broken state, i.e., homochirality.