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.

Comparing different ODE modelling approaches for gene regulatory networks

“…Michaelis-Menten enzymatic kinetics). Experimental evidence suggests a monotonic sigmoidal-shaped function [50,51] which increases when p i is an activator and decreases when p i is an inhibitor. A useful function satisfying this property is the Hill function.…”

The induction of a C4‐dicarboxylic acid anion translocator inAzotobacter vinelandii

“…Recently a paper by Yagil and Yagil [2] appeared, in which a relationship was derived which allows one to determine graphically the number of inducer molecules that have to be bound to the represser in order to inactivate it. In table 3 the rate of translocator synthesis (as measured by the succinate oxidation) as a function of the external mesotartrate concentration is given.…”

“…case of the lactose repressor [2] it turned out to be two. Presently we attempt to determine this number also with the metabolizable Krebs-cycle intermediates using an experimental set-up in which the externally added inducer concentration is kept constant during the adaptation.…”

Two-component feedback loops and deformed mechanics

“…Allolactose binds to inhibit LacI, and so R depends on the half-saturation concentration of allolactose binding (X 0 ) and a Hill coefficient n that has been experimentally determined to be n ≈ 2 [16]. It is clear that (41) is of the form (23) and therefore a q-deformed Hamiltonian system with q = −τ Y /τ X .…”