Induction kinetics of RNA and proteins in exponentially growing organisms

A mathematical model of the induction kinetics of RNAs and proteins in exponentially growing organisms is derived, and the cellular concentrations of the induced macromolecules at a given time after induction are related to three parameters: the fraction of the synthesis of these macromolecules in total synthesis, the half life of the inducible macromolecules, and the generation time of the organisms. The model predicts that the concentrations of the inducible macromolecules reach one half of the maximum induction level within one generation time after the onset of the induction. The model also predicts that induction curves of proteins are parabolic when their mRNAs are short-lived, but sigmoid when they are stable. Observed induction curves of beta-galactosidase in Escherichia coli cells fit in the theoretical induction curves.