Justin Eilertsen, Santiago Schnell, Sebastian Walcher
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引用次数: 0
摘要
我们证明,当初始底物浓度较低时,迈克尔斯-门顿(Michaelis-Menten)反应机制可以用线性系统来精确近似。这导致了伪一阶动力学,简化了数学计算和实验分析。我们的证明利用了系统的单调性属性和卡姆克比较定理。这种线性近似产生了闭式解,即使没有时标分离,也能对反应速率常数进行精确建模和估算。在先前工作的基础上,我们确定了这一近似的充分条件是 s 0 ≪ K,其中 K = k 2 / k 1 是 Van Slyke-Cullen 常数。这一条件与初始酶浓度无关。此外,我们还研究了线性系统中的时标分离,确定了必要条件和充分条件,并推导出相应的简化一元方程。
The Michaelis-Menten Reaction at Low Substrate Concentrations: Pseudo-First-Order Kinetics and Conditions for Timescale Separation.
We demonstrate that the Michaelis-Menten reaction mechanism can be accurately approximated by a linear system when the initial substrate concentration is low. This leads to pseudo-first-order kinetics, simplifying mathematical calculations and experimental analysis. Our proof utilizes a monotonicity property of the system and Kamke's comparison theorem. This linear approximation yields a closed-form solution, enabling accurate modeling and estimation of reaction rate constants even without timescale separation. Building on prior work, we establish that the sufficient condition for the validity of this approximation is , where is the Van Slyke-Cullen constant. This condition is independent of the initial enzyme concentration. Further, we investigate timescale separation within the linear system, identifying necessary and sufficient conditions and deriving the corresponding reduced one-dimensional equations.
期刊介绍:
The Bulletin of Mathematical Biology, the official journal of the Society for Mathematical Biology, disseminates original research findings and other information relevant to the interface of biology and the mathematical sciences. Contributions should have relevance to both fields. In order to accommodate the broad scope of new developments, the journal accepts a variety of contributions, including:
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