The Goodwin Model: Behind the Hill Function
Figure 8
Comparison of the response curve of the phosphorylation/dephosphorylation module (Eqs. (S44), equivalent to Eqs. (7) with ) and the Hill function. The parameter values are: , , , , , and . The blue curve corresponds to the steady state value of as a function of the total concentration of the kinase, (cf Text S1, Section D). The red curve is the Hill function plotted for and . Note that a Hill curve with better fits the middle part but not the upper and lower parts of the response curve of the phosphorylation/dephosphorylation module (not shown).