An analytic approach to the modeling of stop-flow amperometric measurements of cellular metabolism with thin glucose oxidase and lactate oxidase electrodes would provide a mechanistic understanding of the various factors that affect the measured signals. We divide the problem into two parts: (1) analytic formulas that provide the boundary conditions for the substrate and the hydrogen peroxide at the outer surface of the enzyme electrode layers and the electrode current expressed through these boundary conditions, and (2) a simple diffusion problem in the liquid compartment with the provided boundary conditions, which can be solved analytically or numerically, depending on the geometry of the compartment. The current in an amperometric stop-flow measurement of cellular glucose or lactate consumption/excretion is obtained analytically for two geometries, corresponding to devices developed at the Vanderbilt Institute for Integrative Biosystems Research and Education: a multianalyte nanophysiometer with effective one-dimensional diffusion and a multianalyte microphysiometer, for which plentiful data for metabolic changes in cells are available. The data are calibrated and fitted with the obtained time dependences to extract several cellular fluxes. We conclude that the analytical approach is applicable to a wide variety of measurement geometries and flow protocols.

中文翻译：

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使用薄酶电极模拟微生物反应器装置中细胞通量的测量

使用薄葡萄糖氧化酶和乳酸氧化酶电极对细胞代谢的停流电流测量建模进行建模的分析方法将提供对影响测量信号的各种因素的机械理解。我们将问题分为两部分：（1）提供底物和酶电极层外表面过氧化氢的边界条件以及通过这些边界条件表示的电极电流的解析公式，以及（2）一个简单的具有提供的边界条件的液体隔室中的扩散问题，可以根据隔室的几何形状进行解析或数值求解。细胞葡萄糖或乳酸消耗/排泄的电流停流测量中的电流是针对两种几何形状分析获得的，对应于范德比尔特综合生物系统研究和教育研究所开发的设备：具有有效一维扩散和多分析物微生理计，可提供大量有关细胞代谢变化的数据。数据经过校准并与获得的时间相关性进行拟合，以提取多个细胞通量。我们得出结论，该分析方法适用于各种测量几何形状和流量协议。具有有效一维扩散的多分析物纳米生理计和多分析物微生理计，可提供有关细胞代谢变化的大量数据。数据经过校准并与获得的时间相关性进行拟合，以提取多个细胞通量。我们得出结论，该分析方法适用于各种测量几何形状和流量协议。具有有效一维扩散的多分析物纳米生理计和多分析物微生理计，可提供有关细胞代谢变化的大量数据。数据经过校准并与获得的时间相关性进行拟合，以提取多个细胞通量。我们得出结论，该分析方法适用于各种测量几何形状和流量协议。