Compartments can improve the efficiency of cascade reactions through retainment of ephemeral intermediates by minimizing competing elimination pathways. Numerous examples of compartments exist in biocatalysis, one such example being oxygen sensitive nitrogenases in microbes, where the enzyme is spatially located in an anaerobic domain to prevent deactivation. Recently, extensive efforts have been devoted to developing models and guiding design principles for compartmentalization of biocatalytic cascades. However, little to no effort has been devoted to analyzing compartmentalization of organometallic catalytic cycles from a theoretical perspective, which reasonably may benefit from compartmentalization given their numerous, common deactivation pathways. Herein, we develop a mathematical model for compartmentalization of a general three step organometallic catalytic cycle operating within a nanowire array electrode as an example nanostructure. Under the same kinetic parameters, the model predicts that compartmentalization enhances key reaction metrics, being intermediate elimination/outflux, reaction conversion, and turnover frequency in comparison to a non-compartmentalized cycle. We show that tuning mass transport through variation of nanostructure geometry is a viable approach to optimizing the turnover of a solution cascade reaction. Furthermore, we demonstrate that elimination reactions occurring outside of the compartment establish a concentration gradient that with feasible diffusive conductance, augments intermediate outflux. We posit that a well designed nanostructure will circumvent this issue even with fast eliminations. The model serves as a starting point and may be adapted to suit any organometallic catalytic cycle and nanostructure geometry.

中文翻译：

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开发有机金属催化区室化的通用模型

隔室可通过最小化竞争性消除途径，通过保留短暂中间体来提高级联反应的效率。在生物催化中存在许多隔室的例子，其中一个例子是微生物中对氧敏感的固氮酶，其中该酶在空间上位于厌氧域中以防止失活。近来，已经进行了广泛的努力来开发用于生物催化级联的分隔的模型和指导设计原理。然而，从理论的角度分析有机金属催化循环的间隔化几乎没有花任何精力，考虑到它们的许多常见的失活途径，合理地可能受益于间隔化。在这里 我们开发了一个数学模型，用于对作为示例纳米结构的纳米线阵列电极内的一般三步有机金属催化循环进行分区。在相同的动力学参数下，该模型预测，与非间隔化循环相比，间隔化可增强关键反应指标，即中间消除/流出，反应转化率和周转频率。我们表明，通过改变纳米结构的几何形状来调节质量传输是优化溶液级联反应的周转率的可行方法。此外，我们证明了发生在隔室外部的消除反应建立了一个浓度梯度，该浓度梯度具有可行的扩散电导，增加了中间流出量。我们认为，即使快速淘汰，设计良好的纳米结构也将规避这一问题。该模型作为起点，可以进行调整以适合任何有机金属催化循环和纳米结构的几何形状。