Ultrasensitivity and the zeroth-order phosphorylation-dephosphorylation cycle

2 Ultrasensitivity and the zeroth-order phosphorylation-dephosphorylation cycle 

To analyze this system, we assume that the enzymes obey the flux expression of Equation (4.10). Using this Michaelis-Menten expression, we replace Equation (5.5) with the following 

Again examining the steady state, the fraction of phosphorylated / = [S ]-Si/S0 satisfies 

Equation (5.18) is the general equation for a phosphorylation-dephosphorylation switch with Michaelis-Menten kinetics [163], Two limiting cases are particularly worth mentioning. First, if the kinase and the phosphatase are not saturated with respect to the substrate, i.e., S0 K. K.%, then we have 

Second, if the free energy is infinite, i.e., y — oo, and the basal level of phosphorylation is zero, i.e., n = 0, then we have 

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