Rules for coupled expression of regulator and effector genes in inducible circuits

The induction of effector genes that encode enzymes is often controlled by the protein product of a regulator gene that is directly involved in the control of its own expression. This coupling of elementary gene circuits can lead to three patterns of regulator and effector gene expression. As effector gene expression increases, regulator gene expression can increase, remain the same, or decrease, and these are referred to as directly coupled, uncoupled, or inversely coupled patterns. To determine the relative merits of each pattern, we have constructed appropriate mathematical models for the alternative gene circuits and made well-controlled comparisons using a priori criteria to evaluate their functional effectiveness. We have considered both negatively and positively controlled systems that are induced by an intermediate of the regulated pathway. Different results are obtained in the two cases. Our results indicate that direct coupling is better than inverse coupling or uncoupling for negatively controlled systems, while inverse coupling is better than the other two patterns for positively controlled systems. These optimal forms of coupling promote a fast response to inducer. Our results also indicate that realization of the optimal forms of coupling is influenced by the subunit structure of regulator proteins and requires a low capacity for induction, i.e. the ratio of maximal to minimal level of effector gene expression is small. These results lead to testable predictions, which we have compared with experimental data from over 30 systems.