Figure 1: The validity of t_c1 for the Michaelis-Menten reaction mechanism (12).

The solid black curve is the numerically-computed solution to (13a)–(13b). The dashed vertical curve is corresponds to $t_{c_1}=[k_1(K_{M_1}+s_1^0){]}^{-1}$. The dotted horizontal line corresponds to $\ell c_1∕c_1^{\max }=\ell$. The initial concentrations and rate constants used in the numerical simulation are: k₁ = 0.1, k₂ = 10, k₋₁ = 1, $e_1^0=1$ and $s_1^0=100$ (units have been omitted). Time has been mapped to the t_∞ scale: t_∞(t) = 1 – 1/ln[t + exp(1)].