Figure 18: The component-wise error when the indicator reaction is fast in the auxiliary reaction mechanism (47)–(48).

The thick black curve is the numerically-integrated solution to the mass action equations (49a)–(49d), the dashed/dotted red curve is the c₂-nullcline and the dashed/dotted blue curve is a snapshot of s₂-nullcline when t ≈ 1.1 · t_s1. The black dot is the corresponding snapshot of the numerical solution to (49a)–(49d). In this simulation, $t_{s_2}^{\chi }∕t_{s_1}\approx 0.0001<{\mu }_2\approx 0.005$; consequently, the trajectory sits “just behind” and slightly above x* (green dot) since the trajectory will be closer to the s₂-nullcline than the c₂-nullcline (see Movie 2 in Supplementary Materials). The constants (without units) used in the numerical simulation are: $e_1^0=1$, $s_1^0=100$, $e_2^0=100$, k₁ = 1, k₂ = 1, k₃ = 1, k₋₃ = 1, k₄ = 2 and k₋₀ = 1.