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

Gad Yagil*, Ezra Yagil

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 - αb) = ± n log [E] + log αb ± log K1. 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, K1, the dissociation constant of this interaction and K2/Rt, 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. K1 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 K1 = 50 ±20 × 10-12 M2. In some strains, separate binding constants for the first and second IPTG molecules can be evaluated.

Original languageEnglish
Pages (from-to)11-27
Number of pages17
JournalBiophysical Journal
Issue number1
StatePublished - 1971


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