Biochemical Systems Theory: A Review

Figure 1

Similar shapes do not imply similar functions. Although the shapes of the two graphs are very similar, the models generating them are structurally distinctly different. The blue line is the plot of a three-parameter Hill function, namely, 𝐻(𝑥)=𝑉_max𝑥^𝑛/[𝐾^𝑛_𝑀+𝑥^𝑛] with 𝑉_max=4, 𝐾_𝑀=2, and 𝑛=4, while the red line is the plot of a generalized logistic function 𝐿(𝑥)=𝑎/[(1+exp(𝑏−𝑐⋅𝑥))]^𝑑 with the four parameters 𝑎=3.9, 𝑏=3.4, 𝑐=1.9, and 𝑑=1.5. Other sigmoidal models are compared in [4].