Enzyme Sharing in Phosphorylation-Dephosphorylation Cascades: The Case where One Protein Kinase (or Phosphatase) Acts on Two Different Substrates

Abstract

In several metabolic cascades, distinct phosphorylation-dephosphorylation cycles share the same protein kinase or phosphatase. To deal with such a situation, the analysis of covalent modification cycles is extended to the case where one converter enzyme acting on two different substrates is shared by two cycles of protein covalent modification. The steady-state behavior of such a bicyclic cascade is determined as a function of the activity of the common converter enzyme; while the latter may be a kinase or a phosphatase, the model also applies to other modes of covalent modification. The analysis indicates that thresholds in phosphorylation owing to zero-under ultrasensitivity may still occur in this bicyclic system, as in the case of a single cycle of covalent modification or of multiple cycles possessing distinct converter enzymes. As the activity of the common kinase is progressively increased, the phosphorylation of the two substrates occurs at the same threshold or at distinct thresholds, depending on the values of the parameters. Approximate expressions for these thresholds are obtained. When the phosphorylation of the substrate in one cycle is caused by the inhibition of the associated phosphatase by some effector, rebound phosphorylation of the substrate of the second cycle is observed, even if the converter enzymes of the latter cycle are not controlled by the effector.