Abstract Michaelis–Menten kinetics describe a broad range of physical, chemical, and biological processes. Since they are non-linear, spatial averaging of reaction kinetics is non-trivial, and it is not known how concentration gradients affect the global effective kinetics. Here, we use numerical simulations and theoretical developments to investigate the effective kinetics of diffusing solute pulses locally subject to Michaelis–Menten reaction kinetics. We find that coupled diffusion and reaction lead to non-monotonic effective kinetics that differ significantly from the local kinetics. The resulting effective reaction rates can be significantly enhanced compared to those of homogeneous batch reactors. We uncover the different regimes of effective kinetics as a function of the Damkohler number and Michaelis–Menten parameters and derive a theory that explains and quantifies these upscaled kinetics using a weakly-coupled description of reaction and diffusion. We illustrate the consequences of these findings on the accelerated consumption of nutrient pulses by bacteria. These results are relevant to a large spectrum of reactive systems characterized by heterogeneous concentration landscapes.

中文翻译：

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Michaelis-Menten 反应下溶质脉冲的增强和非单调有效动力学

摘要 Michaelis-Menten 动力学描述了广泛的物理、化学和生物过程。由于它们是非线性的，反应动力学的空间平均是重要的，并且不知道浓度梯度如何影响全局有效动力学。在这里，我们使用数值模拟和理论发展来研究受 Michaelis-Menten 反应动力学影响的局部扩散溶质脉冲的有效动力学。我们发现耦合扩散和反应导致与局部动力学显着不同的非单调有效动力学。与均相间歇式反应器相比，产生的有效反应速率可以显着提高。我们揭示了作为 Damkohler 数和 Michaelis-Menten 参数的函数的不同有效动力学机制，并推导出了一个理论，该理论使用反应和扩散的弱耦合描述来解释和量化这些放大的动力学。我们说明了这些发现对细菌加速消耗营养脉冲的影响。这些结果与以异质浓度景观为特征的大范围反应系统有关。