Mathematical expression for the rate of initiation and certain prediction on the non-competitive binding operon: the Escherichia coli lactose operon

Abstract

The relationship between the structure of regulatory region of operons and the function on control mechanisms is studied theoretically by the use of kinetic model for the lactose operon of Escherichia coli. The initial interaction of RNA polymerase with a promoter is assumed to be non-competitive with the binding of repressor to an operator (non-competitive binding model). It is shown that the transcription initiation rate is given as a linear combination of two times; one required for RNA polymerase to initiate transcription without affecting repression mechanism and the other required for the bound repressor to dissociate from the operator. In the non-competitive binding model the coefficient of the latter time is the probability that transcription initiation is blocked by the binding of repressor. The evaluated initiation rates suggest that the operon expression is little affected by RNA polymerase concentration and that the repressor controls gene expression independent of cyclic AMP receptor protein or other components. This property results mainly from the fact that the coefficient of the binding time of repressor is the probability and always takes the value nearly unity. Theoretical procedures developed here can be also applied to the studies of other systems with repressor-operator interaction, such as tryptophan, L-arabinose, and galactose operons of E. coli.