The accuracy of the sQSSA_p and the tQSSA_p in heterogeneous environments.

(A) Homogeneous ICs that satisfy the validity condition of the sQSSA_o throughout the domain (blue region). E₀ ≡ 2μM, S₀ ≡ 2μM and K_M = 18.5μM. (B-C) Both the sQSSA_p and the tQSSA_p accurately capture the production of P throughout the domain (B) and the spatial average (C). (D) The ICs in (A) were heterogenized so that the validity condition of the sQSSA_o model does not hold near x = 30μm (red region), unlike the other region (blue region). Here, E₀(x) = S₀(x) = 18.5(tanh(20x/3 − 190) + 1) + 10⁻⁴μM, which maintain the spatial average concentration with the ICs in (A), was used. (E-F) The tQSSA_p model, but not the sQSSA_p model, is accurate. (G) The homogeneous ICs that do not satisfy the validity condition of the sQSSA_o through the domain. Here, E₀ ≡ 400μM, S₀ ≡ 300μM, and K_M = 18.5μM. (H-I) The tQSSA_p model, but not the sQSSA_p model, is accurate. (J) The ICs in (G) were heterogenized so that the validity condition of the sQSSA_o is satisfied in x < 15μm (blue region), but not in x ≥ 15μm (red region). Here, E₀(x) = 300(tanh(2x/3 − 10) + 1) + 100μM and S₀(x) = 290(tanh(10 − 2x/3) + 1) + 10μM, which keep the spatial average concentration with the ICs in (G), were used. (K-L) Both the sQSSA_p and tQSSA_p models are accurate. For all simulations, C₀ ≡ 0μM, P₀ ≡ 0μM and k_f = 3.4 ⋅ 10⁶M⁻¹s⁻¹, k_b = 60s⁻¹, k_cat = 3.2s⁻¹, D_E = D_S = D_C = D_P = D_* = 0.2μm²/s.