On the Relation between Effector Concentration and the Rate of Induced Enzyme Synthesis

The Jacob and Monod scheme for the regulation of enzyme formation leads to the following relation between the relative rate of enzyme synthesis α and cellular effector concentration E (the lower sign is for repressible systems): log (α/1 - α - α b ) =± n log [ E ] + log α b ±log K 1 . This equation permits linear plotting of experimental data and the evaluation of three quantities: n, the number of effector molecules combining with a repressor molecule, K 1 , the dissociation constant of this interaction and K 2 / R t , the ratio of repressor-operator dissociation constant to total repressor concentration. Measurements on the repression of alkaline phosphatase in Escherichia coli as a function of phosphate concentration are reported and fit the proposed equation with n = 1, indicating that the binding of a single phosphate to the repressor species may be sufficient to cause repression. K 1 of this interaction was found to be 0.58±0.11×10 -3 M. The available data regarding the enzymes of the lac operon in a variety of E. coli strains, and several other enzymes are analyzed. It is confirmed that the lac repressor interacts with 2 isopropyl thiogalactoside (IPTG) molecules to relieve repression with a K 1 = 50±20×10 -12 M 2 . In some strains, separate binding constants for the first and second IPTG molecules can be evaluated.