The GTPase signaling module

In the previous section, we obtained the steady state population of the phosphorylated protein in a phosphorylation-dephosphorylation network that consists of a kinase and a phosphatase. Based on the homologous reaction networks, the mathematics for the phosphorylation network translates immediately to the GTPase system. 

If we consider a single GTPase protein, the chemical physics of macromolecules dictates that it fluctuates between the GDP-bound and GTP-bound states. In this case / then can be interpreted as the probability of a single substrate protein in the GTP state. In addition to this steady state probability, we would also like to know how frequently the signaling protein switches between the on and off states. The rate of cycling per unit time is directly related to the mean dwell time in the activated state. 

Denoting T as the time in the GTPase-GTP state, then the number of switching cycles per unit time is simply f /T. More precisely, each time the protein is 

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In analyzing the temporal behavior of a biochemical switching molecule, we can study either of the equivalent models of the phosphorylation-dephosphorylation cycle or the GTPase signaling module. In particular, we are interested in the duration of each activation event at the single-molecule level. 

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