Multiscale Modeling &Simulation, Volume 18, Issue 2, Page 1053-1075, January 2020.
The mechanism of gas transport across cell membranes remains a topic of considerable interest, particularly regarding the extent to which lipids versus specific membrane proteins provide conduction pathways. Studies of transmembrane carbon dioxide ($CO_2$) transport often rely on data collected under controlled conditions, using pH-sensitive microelectrodes at the extracellular surface to record changes due to extracellular $CO_2$ diffusion and reactions. Although recent detailed computational models can predict a qualitatively correct behavior, a mismatch between the dynamical ranges of the predicted and observed pH curves raises the question of whether the discrepancy may be due to a bias introduced by the pH electrode itself. More specifically, it is reasonable to ask whether bringing the electrode tip near or in contact with the membrane creates a local microenvironment between the electrode tip and the membrane, so that the measured data refer to the microenvironment rather than to the free surface. Here, we introduce a detailed computational model, designed to address this question. We find that, as long as a zone of free diffusion exists between the tip and the membrane, the microenvironment behaves effectively as the free membrane. However, according to our model, when the tip contacts the membrane, partial quenching of extracellular diffusion by the electrode rim leads to a significant increase in the pH dynamics under the electrode, matching values measured in physiological experiments. The computational schemes for the model predictions are based on semidiscretization by a finite element method and on an implicit-explicit time integration scheme to capture the different time scales of the system.

中文翻译：

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电极诱导的微环境对细胞膜附近 pH 测量的影响的计算模型

多尺度建模与仿真，第 18 卷，第 2 期，第 1053-1075 页，2020 年 1 月。
跨细胞膜的气体运输机制仍然是一个相当有趣的话题，特别是关于脂质与特定膜蛋白提供传导途径的程度。跨膜二氧化碳 ($CO_2$) 转运的研究通常依赖于在受控条件下收集的数据，使用细胞外表面的 pH 敏感微电极记录由于细胞外 $CO_2$ 扩散和反应引起的变化。尽管最近的详细计算模型可以预测定性正确的行为，但预测的和观察到的 pH 曲线的动态范围之间的不匹配引发了这样一个问题，即这种差异是否可能是由于 pH 电极本身引入的偏差。进一步来说，询问使电极尖端靠近或接触膜是否会在电极尖端和膜之间产生局部微环境是合理的，因此测量数据指的是微环境而不是自由表面。在这里，我们介绍了一个详细的计算模型，旨在解决这个问题。我们发现，只要尖端和膜之间存在自由扩散区，微环境就会有效地表现为自由膜。然而，根据我们的模型，当尖端接触膜时，电极边缘对细胞外扩散的部分猝灭导致电极下的 pH 动态显着增加，与生理实验中测量的值相匹配。