We consider different reaction mechanisms to study the substrate phosphorylation process catalyzed by the activated ERK2 enzyme. Such reaction schemes are constituted by three Michaelis-Menten (MM) reactions namely the ERK2 activation (phosphorylation), deactivation of phosphorylated ERK2 (dephosphorylation) and substrate phosphorylation catalyzed by the activated ERK2. We theoretically examine and analyze the phosphorylation/dephosphorylation networks to probe dynamic disorder which is a manifestation of multiple competing reaction timescales. We apply the waiting time distribution formalism based on the chemical master equation approach to obtain exact analytical expressions for the turnover time distribution for the substrate phosphorylation event from which we can obtain the mean reaction time and randomness parameter for the quantification of the temporal fluctuations on the different reaction pathways.
Single molecule study, phosphorylation-dephosphorylation kinetics, dynamic disorder