Sensitivity and robustness in covalent modification cycles with a bifunctional converter enzyme

Regulation by covalent modification is a common mechanism to transmit signals in biological systems. The modifying reactions are catalyzed either by two distinct converter enzymes or by a single bifunctional enzyme (which may employ either one or two catalytic sites for its opposing activities). The reason for this diversification is unclear, but contemporary theoretical models predict that systems with distinct converter enzymes can exhibit enhanced sensitivity to input signals whereas bifunctional enzymes with two catalytic sites are believed to generate robustness against variations in system's components. However, experiments indicate that bifunctional enzymes can also exhibit enhanced sensitivity due to the zero-order effect, raising the question whether both phenomena could be understood within a common mechanistic model. Here, I argue that this is, indeed, the case. Specifically, I show that bifunctional enzymes with two catalytic sites can exhibit both ultrasensitivity and concentration robustness, depending on the kinetic operating regime of the enzyme's opposing activities. The model predictions are discussed in the context of experimental observations of ultrasensitivity and concentration robustness in the uridylylation cycle of the PII protein, and in the phosphorylation cycle of the isocitrate dehydrogenase, respectively.