A variant of the Frank chiral amplification model

Abstract

The Frank model for chiral amplification consists of two elementary chemical reactions: the autocatalytic formation of the enantiomers L and D, and an interaction between L and D by which they eliminate one another. Originally, both steps were assumed to be irreversible. We consider a modification of Frank's model in which the open-flow-reactor character of the process is pointed out and its first step is allowed to be reversible. The basis features of this modified Frank model (MFM) are established, in spite of the fact that the solution of the respective system of differential equations is not known. Three distinct time-evolutions of the MFM can occur, one in which both L and D completely disappear from the system, another leading to complete monochirality, and a third resulting in a racemic final state. The conditions for each of the three possible directions of evolution are established: they depend on the relative magnitudes of rate constants and are independent of the initial composition.