Chiral autocatalysis: reaction noise, micro-reversibility and chiral inhibition in mirror symmetry breaking

Applying the constraints dictated by the principle of detailed balance, we analyze a recent proposal for spontaneous mirror symmetry breaking (SMSB) based on enantioselective autocatalysis coupled to a linear decay of the enantiomers and in the presence of reaction noise. We find the racemic state is the final stable outcome for both deterministic as well as for stochastic dynamics, and for both well-mixed and small spatially-coupled systems. The racemic outcome results even when the autocatalytic cycles are driven irreversibly by external reagents, in manifestly non-equilibrium conditions. Our findings suggest that first-order autocatalysis coupled to reactions involving \textit{non-linear} heterochiral dynamics is a necessary pre-condition for any mechanism purporting to lead to molecular homochirality.