Rate Equation Approaches to Amplification of Enantiomeric Excess and Chiral Symmetry Breaking

Abstract

Theoretical models and rate equations relevant to the Soai reaction are reviewed. It is found thatin production of chiral molecules from an achiral substrate autocatalytic processes can induce either enantiomericexcess (ee) amplification or chiral symmetry breaking. The former means that the final ee value islarger than the initial value but is dependent upon it, whereas the latter means the selection of a uniquevalue of the final ee, independent of the initial value. The ee amplification takes place in an irreversiblereaction such that all the substrate molecules are converted to chiral products and the reaction comes toa halt. Chiral symmetry breaking is possible when recycling processes are incorporated. Reactionsbecome reversible and the system relaxes slowly to a unique final state. The difference between thetwo behaviors is apparent in the flow diagram in the phase space of chiral molecule concentrations. Theee amplification takes place when the flow terminates on a line of fixed points (or a fixed line),whereas symmetry breaking corresponds to the dissolution of the fixed line accompanied by the appearanceof fixed points. The relevance of the Soai reaction to the homochirality in life is also discussed.