Depression kinetics of ornithine transcarbamylase in Escherichia coli

A mathematical model for the derepression of ornithine transcarbamylase (OTC) in Escherichia coli strain W was derived from a set of 14 assumptions concerning the arginine regulon. The model assumes that active repressor for the arginine regulon is unstable and is only formed when the level of arginyl-tRNA is in excess of the level necessary to maintain protein synthesis for a given cell doubling time. The presence of active repressor was assumed to inhibit the synthesis of messenger RNA coding for the synthesis of the enzymes of the arginine biosynthetic pathway. Numerical estimates of the model's parameters were made and, by simulation on a digital computer, the model was shown to fit kinetic data for derepression of OTC in E. coli W cells in minimal medium growing in flask culture with a doubling time of 60 min and growing in a chemostat with a generation time of 460 min for an assumed OTC-specific mRNA half-life (t(1/2)) of 9 min. The model was also shown to predict the increase in the size of bursts of OTC synthesis elicited by addition of arginine to cultures of derepressing E. coli cells with the increase in the delay time before arginine addition. Approximate analytical solutions to the model were obtained for the early phase of derepression and for repression of OTC. These were used to derive graphical methods for determining t(1/2) from repression and derepression transient changes in the OTC level.