In 1953, Charles Frank proposed a model to demonstrate that homochirality is a consequence of autocatalysis. In his model the  and  enantiomers of a chiral molecule are autocatalytically produced from an achiral molecule A
while suppressing each other through a reaction that he called mutual antagonism
In this model the racemic state is unstable in the sense that the slightest enantiomeric excess will be amplified to a completely homochiral state. This can be shown by computing the reaction rates from the law of mass action:
where  is the rate constant for the autocatalytic reactions,  is the rate constant for mutual antagonism reaction, and the concentration of A is kept constant for simplicity.
The analytical solutions for are found to be 
Linear stability analysis of this equation shows that the racemic state  is unstable. Starting from almost everywhere in the concentration space, the system evolves to a homochiral state.
It is generally understood that autocatalysis alone does not yield to homochirality, and the presence of the mutually antagonistic relationship between the two enantiomers is necessary for the instability of the racemic mixture. However, recent studies show that homochirality could be achieved from autocatalysis in the absence of the mutually antagonistic relationship, but the underlying mechanism for symmetry-breaking is different.