Abstract
Multisite phosphorylation is a common form of posttranslational protein regulation which has been used to increase the switchlike behavior of the protein response to increasing kinase concentrations. In this letter, we show that the switchlike response of multisite phosphoproteins is strongly enhanced by nonessential phosphorylation sites, a mechanism that is robust to parameter changes and easily implemented in nature. We obtained analytic estimates for the Hill exponent (or coefficient) of the switchlike response, and we observed that a tradeoff exists between the switch and the kinase threshold for activation. This also suggests a possible evolutionary mechanism for the relatively large numbers of phosphorylation sites found in various proteins.