Figure 5:

Validity of the timescale $t_{s_2}^{\ast }$ and the reduced ordinary differential equation given by (63) for the substrate depletion of the indicator reaction when the indicator reaction is much slower than the non-observable reaction (δ_S ≫ 1). The solid black curve is the numerical solution to the mass action equations (7) and the solid red curve corresponds to the numerical solution to (63) extended to t ≥ 0. In this numerical simulation k₃ = 0.1, k₄ = 1, k₋₃ = 10, $s_2^0=10000$, and k₁ = 25, k₂ = 100, k₋₁ = 1, $e_1^0=1$ and $s_1^0=100$. The respective values of λ^max and δ_S are ≈ 0.009 and ≈ 0.01. Time has been mapped to the t_∞ scale: t_∞ (t) = 1 – 1/ ln(t + e).