Demand theory of gene regulation. II. Quantitative application to the lactose and maltose operons of Escherichia coli.

Induction of gene expression can be accomplished either by removing a restraining element (negative mode of control) or by providing a stimulatory element (positive mode of control). According to the demand theory of gene regulation, which was first presented in qualitative form in the 1970s, the negative mode will be selected for the control of a gene whose function is in low demand in the organism's natural environment, whereas the positive mode will be selected for the control of a gene whose function is in high demand. This theory has now been further developed in a quantitative form that reveals the importance of two key parameters: cycle time C, which is the average time for a gene to complete an ON/OFF cycle, and demand D, which is the fraction of the cycle time that the gene is ON. Here we estimate nominal values for the relevant mutation rates and growth rates and apply the quantitative demand theory to the lactose and maltose operons of Escherichia coli. The results define regions of the C vs. D plot within which selection for the wild-type regulatory mechanisms is realizable, and these in turn provide the first estimates for the minimum and maximum values of demand that are required for selection of the positive and negative modes of gene control found in these systems. The ratio of mutation rate to selection coefficient is the most relevant determinant of the realizable region for selection, and the most influential parameter is the selection coefficient that reflects the reduction in growth rate when there is superfluous expression of a gene. The quantitative theory predicts the rate and extent of selection for each mode of control. It also predicts three critical values for the cycle time. The predicted maximum value for the cycle time C is consistent with the lifetime of the host. The predicted minimum value for C is consistent with the time for transit through the intestinal tract without colonization. Finally, the theory predicts an optimum value of C that is in agreement with the observed frequency for E. coli colonizing the human intestinal tract.