Variation in concentrations of RNAs and proteins involved in gene expression of Escherichia coli.

A growing cell is not a steady-state situation. At some point in the cell cycle each gene doubles its concentration, which may result in a doubling of the production rate of its mRNA. The variations in concentration of mRNAs and proteins in an individual exponentially growing cell are studied for a gene which is constitutive, autorepressed, or autoactivated. Analysis of the mathematical model for a constitutive gene shows a fixed variation in concentration of a stable RNA between its minimum and maximum concentration of approximately 6%, independent of cell cycle time or gene location. The variation in the concentrations of the mRNA and protein for a constitutive gene are studied as gene position, molecular stability, and cell cycle time are varied. One result shows that doubling the growth rate can more than double the percentage of product from a gene near the origin of replication compared to one near the terminus. Results from these theoretical studies compare favorably to experimental results for rRNAs and the fully induced lac gene. Additional studies were performed to determine the effects of autorepression and autoactivation on the variation of concentration of mRNAs and proteins. The studies show that RNA and protein products of an autorepressed gene have almost the same variation in concentration as products of a constitutively expressed gene though the absolute concentrations are decreased. It is shown that the stability of an mRNA or protein affects variation in its concentration throughout the cell cycle, much more than the type of genetic control. The strength of repression has no effect on the variation in concentration of RNA and protein gene products through a cell cycle. Studies of an autoactivated gene show that it is significantly more responsive to a shift up or down, such as those caused by nutritional changes. An example is provided where the autoactivated gene is not expressed at one growth rate, but turns on at a higher growth rate. Furthermore, it is shown that gene position may determine whether or not the autoactivated gene is expressed.