Stochastic kinetic models of chiral autocatalysis: A general tool for the quantitative interpretation of total asymmetric synthesis

A continuous time discrete state stochastic kinetic approach is used to study various chiral autocatalytic models in which the possibility of total asymmetric synthesis arises. It is shown that this approach is superior to the deterministic approaches used earlier and is able to interpret many aspects of chiral autocatalysis. First-order autocatalysis, independently of further kinetic details of the system, leads to a unique final statistical distribution of enantiomers. Higher order autocatalysis, on the other hand, leads to a final state where one of the enantiomers is in overwhelming excess over the other. Criteria are postulated to differentiate between inherently stochastic phenomena in chiral autocatalytic reactions and irreproducibility because of insufficient control of external factors.