Kinetic analysis of multisite phosphorylation using analytic solutions to Michaelis-Menten equations

Phosphorylation-induced expression or modulation of a functional protein is a common signal in living cells. Many functional proteins are phosphorylated at multiple sites and it is frequently observed that phosphorylation at one site enhances or suppresses phosphorylation at another site. Therefore, characterizing such cooperative phosphorylation is important. In this study, we determine a temporal progress curve of multisite phosphorylation by analytically integrating the Michaelis-Menten equations in time. Using this theoretical progress curve, we derive the useful criterion that an intersection of two progress curves implies the presence of cooperativity. Experiments generally yield noisy progress curves. We fit the theoretical progress curves to noisy progress curves containing 4% Gaussian noise in order to determine the kinetics of the phosphorylation. This fitting correctly identifies the sites involved in cooperative phosphorylation.