title: On the relation between effector concentration and the rate of induced enzyme synthesis.
abstract: The Jacob and Monod scheme for the regulation of enzyme formation leads to the following relation between the relative rate of enzyme synthesis alpha and cellular effector concentration E (the lower sign is for repressible systems): log (alpha/1 - alpha - alpha(b)) = +/- n log [E] + log alpha(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 x 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 x 10(-12) M(2). In some strains, separate binding constants for the first and second IPTG molecules can be evaluated.
mesh_terms: D000469:Alkaline Phosphatase / Q000096:biosynthesis*; D001665:Binding Sites; D004790:Enzyme Induction; D004794:Enzyme Repression; D004926:Escherichia coli / Q000201:enzymology; D005796:Genes; D007700:Kinetics; D007785:Lactose / Q000096:biosynthesis; D008433:Mathematics; D009876:Operon
chemical_list: D000469:Alkaline Phosphatase; D007785:Lactose