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Beyond homogeneity: Assessing the validity of the Michaelis–Menten rate law in spatially heterogeneous environments

Fig 3

The sQSSA_p, but not the tQSSA_p, poses a risk when the enzyme is localized within cells, unlike in an in vitro experiment.

(A) Enzymes localized within cellular organelles. (B) The heterogeneous ICs where the sQSSA_o are invalid near x = 15μm (red region) but valid in the other region (blue region). Here S₀ ≡ 39 μM, E₀(x) = 5 ⋅ f(x)μM, where f(x) is the normalized probability density function of the normal distribution with the mean of 15 μm and the standard deviation of 0.2 μm. (C-D) Unlike the sQSSA_p model, the tQSSA_p model accurately captures the production of P throughout the domain (C) and its spatial average (D). (E) The ICs in (B) were homogenized so that the validity condition of the sQSSA_o is satisfied throughout the domain while maintaining the spatial average concentration. Specifically, S₀ ≡ 39 μM and E₀ ≡ 5μM were used. (F-G) Both the sQSSA_p and tQSSA_p models are accurate. (H) Enzyme distributions with varying heterogeneity were constructed using E₀(x) = 5 ⋅ f(x|σ) μM, where f(x|σ) is the normalized probability density function of the normal distribution with the mean of 15μm and the standard deviation of σ. As σ decreases, the heterogeneity increases (see Method for details). (I) For the enzyme distribution with varying heterogeneity, the tQSSA_p model, but not the sQSSA_p model, accurately captures the initial velocity (I). For all simulations, we used k_f = 6.7 ⋅ 10⁵M⁻¹s⁻¹, k_b = 0.53s⁻¹, k_cat = 0.13s⁻¹, K_M = 1μM, and the diffusion coefficients: D_E = D_C = 0μm²/s, and D_P = D_S = 0.2μm²/s. Some parts of Fig 3 were retrieved from Biorender.

doi: https://doi.org/10.1371/journal.pcbi.1012205.g003