Stability of racemic and chiral steady states in open and closed chemical systems

The stability properties of models of spontaneous mirror symmetry breaking in chemistry are characterized algebraically. The models considered here all derive either from the Frank model or from autocatalysis with limited enantioselectivity. Emphasis is given to identifying the critical parameter controlling the chiral symmetry breaking transition from racemic to chiral steady-state solutions. This parameter is identified in each case, and the constraints on the chemical rate constants determined from dynamic stability are derived.

💡 Research Summary

The paper presents a comprehensive theoretical investigation of spontaneous mirror‑symmetry breaking (SMSB) in chemical reaction networks, focusing on the stability of racemic (achiral) and chiral steady states in both open‑flow and closed‑batch systems. The authors start from a general kinetic scheme that includes non‑catalytic production of the two enantiomers (L and D), enantioselective autocatalysis, limited enantioselectivity (cross‑catalysis that converts one enantiomer into the other), and reversible homo‑ and heterodimerization steps. All reactions are assumed reversible to satisfy detailed balance, although in many practical cases forward rates dominate.

For open systems the concentration of the achiral substrate A is held constant, allowing the authors to nondimensionalize time and concentrations. This reduces the original ten kinetic parameters to seven dimensionless groups: u (non‑catalytic monomer influx), g (the ratio of the reverse autocatalytic rate to the heterodimerization rate), w (limited enantioselectivity strength), p and r (rates of homo‑ and heterodimer removal), and q, s (combinations governing dimer dynamics). The parameter g emerges as the critical control variable.

The authors rewrite the kinetic equations in terms of total chiral matter χ =