Competition effects shape the response sensitivity and kinetics of phosphorylation cycles in cell signaling

Phosphorylation cycles are a core component of cell signaling networks. The response sensitivity and kinetics of these cycles are controlled by thermodynamic, kinetic, and structural factors, including binding affinities, catalytic activities, and the phosphorylation order of multiple sites. Based on mathematical models, we interpret the role of these factors in terms of competition effects. For the regulation of a single phosphorylation site, two kinds of competition effects turn out to shape behavior: the competition between kinase and phosphatase to bind the substrate, and the competition between the distinct phosphorylation forms of the substrate for binding to either enzyme. Depending on the concentrations and mutual affinities of the enzymes and the target, the response function can be graded, ultrasensitive, or biphasic. In multiply phosphorylatable proteins, additional factors generating competition effects are present and more complex responses can be obtained. For example, the combination of a cooperative kinetics with the conditions for zero-order ultrasensitivity may yield a bistable response. We show that a repeated competition between kinase and phosphatase for binding the substrate and/or between the phosphorylation and dephosphorylation reactions at each phosphorylation site generally result in a threshold response. The phosphorylation time is also strongly affected by the kinetic design of the cycle. In particular, threshold responses are generally associated with very long phosphorylation times. We also argue here that a description in terms of elementary binding and reaction steps is required for an appropriate analysis of these cycles in cell signaling.