Subunit Structure of Regulator Proteins Influences the Design of Gene Circuitry: Analysis of Perfectly Coupled and Completely Uncoupled Circuits

Cells regulate expression their genome by means of a diverse repertoire of molecular mechanisms. However, little is known about their design principles or how these are influenced by underlying physical constraints. An early theory of gene regulation for inducible systems predicted that expression of the regulator and regulated proteins would be perfectly coupled (coordinate expression of regulator) when the regulator is a repressor and completely uncoupled (invariant expression of regulator) when the regulator is an activator. The experimental data then available tended to support these predictions, but there were notable exceptions. Here, we describe an extended theory, which takes into account the subunit structure of regulator proteins. The number of subunits determines the allowable range of values for the regulatory parameters, and, as a consequence, new rules for the prediction of gene circuitry emerge. The theory predicts perfectly coupled circuits with repressors, but only when the capacity for induction is "small"; it predicts completely uncoupled circuits with repressors when the capacity is "large". This theory also predicts completely uncoupled circuits with activators when the capacity for induction is small; it predicts perfectly coupled circuits with activators when the capacity is large. These new predictions are more fully in accord with available experimental evidence.