Design Principles for Regulator Gene Expression in a Repressible Gene Circuit

We consider the design of a type of repressible gene circuit that is common in bacteria. In this type of circuit, a regulator protein acts to coordinately repress the expression of effector genes when a signal molecule with which it interacts is present. The regulator protein can also independently influence the expression of its own gene, such that regulator gene expression is repressible (like effector genes), constitutive, or inducible. Thus, a signal-directed change in the activity of the regulator protein can result in one of three patterns of coupled regulator and effector gene expression: direct coupling, in which regulator and effector gene expression change in the same direction; uncoupling, in which regulator gene expression remains constant while effector gene expression changes; or inverse coupling, in which regulator and effector gene expression change in opposite directions. We have investigated the functional consequences of each form of coupling using a mathematical model to compare alternative circuits on the basis of engineering-inspired criteria for functional effectiveness. The results depend on whether the regulator protein acts as a repressor or activator of transcription at the promoters of effector genes. In the case of repressor control of effector gene expression, direct coupling is optimal among the three forms of coupling, whereas in the case of activator control, inverse coupling is optimal. Results also depend on the sensitivity of effector gene expression to changes in the level of a signal molecule; the optimal form of coupling can be physically realized only for circuits with sufficiently small sensitivity. These theoretical results provide a rationale for autoregulation of regulator genes in repressible gene circuits and lead to testable predictions, which we have compared with data available in the literature and electronic databases.