On the Validity of the Stochastic Quasi-Steady-State Approximation in Open Enzyme Catalyzed Reactions: Timescale Separation or Singular Perturbation?
On the Validity of the Stochastic Quasi-Steady-State Approximation in Open Enzyme Catalyzed Reactions: Timescale Separation or Singular Perturbation?
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DOI：
10.1007/s11538-021-00966-5
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发表时间：
2021-11-26
影响因子：
3.5
通讯作者：
Schnell S
中科院分区：
文献类型：
--
作者：
Eilertsen J;Schnell S
准稳态近似被广泛用于建立酶催化反应的简化确定性或随机性模型。在确定性模型中，准稳态近似可以从奇异摄动理论中得到数学证明。对于几个闭合的酶反应，对随机区域的准稳态近似的相应推广被称为随机准稳态近似，在允许确定性对应的准稳态还原的相似条件下被证明是准确的。然而，最近的研究表明，将随机准稳态近似推广到开放的Michaelis-Menten反应机制，只有在比保证其相应的确定性准稳态近似的有效性的限定词更严格的条件下才是有效的。在本文中，我们从几何奇异微扰理论的角度提出了一种可能的解释。在这样做的过程中，我们说明了准稳态近似应用中的一个误解：时间尺度分离并不意味着奇异微扰。
The quasi-steady-state approximation is widely used to develop simplified deterministic or stochastic models of enzyme catalyzed reactions. In deterministic models, the quasi-steady-state approximation can be mathematically justified from singular perturbation theory. For several closed enzymatic reactions, the homologous extension of the quasi-steady-state approximation to the stochastic regime, known as the stochastic quasi-steady-state approximation, has been shown to be accurate under the analogous conditions that permit the quasi-steady-state reduction of the deterministic counterpart. However, it was recently demonstrated that the extension of the stochastic quasi-steady-state approximation to an open Michaelis–Menten reaction mechanism is only valid under a condition that is far more restrictive than the qualifier that ensures the validity of its corresponding deterministic quasi-steady-state approximation. In this paper, we suggest a possible explanation for this discrepancy from the lens of geometric singular perturbation theory. In so doing, we illustrate a misconception in the application of the quasi-steady-state approximation: timescale separation does not imply singular perturbation.
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