1. (Competitive inhibition) Derive the expression of the production rate of X∗ in a phosphorylation cycle in the presence of a competitive inhibitor I for Z.
2. (Non-absolute activator) Derive the expression of the production rate of X∗ in a phosphorylation cycle in the presence of a non-absolute activator A for Z.
3. Consider the model of phosphotransfer systems of equation (2.32) and determine how the steady state transfer curve changes when the values of k3 and k4 are changed.
