Antonenko Y N, Denisov G A, Pohl P
A.N. Belozersky Institute of Physico-Chemical Biology, Moscow State University, Russia.
Biophys J. 1993 Jun;64(6):1701-10. doi: 10.1016/S0006-3495(93)81542-X.
This paper presents a simple model to describe experimental data on weak acid transport across planar bilayer lipid membrane separating two buffered solutions. The model takes into account multiple proton-transfer reactions occurring in the unstirred layers (ULs) adjacent to the membrane. Differential equations of the model are shown to be reduced to a set of nonlinear algebraic equations. Since the latter equations depend monotonically on unknown variables, they can be easily solved numerically, using bisection method. For the particular system studied experimentally (with acetate as the weak acid and TRIS+MES as the buffer mixture) pH profiles in the ULs are calculated from the model. These results are compared with experimental data obtained using pH microelectrode. The agreement between theoretical and experimental pH profiles is found to be satisfactory. The most pronounced deviations are observed at the UL/bulk solution boundary. To obtain a better correlation between the theoretical and experimental results, two other, less idealized models are considered. They take into account, respectively, (a) the electric field arising in the ULs from ion diffusion and (b) finiteness of the rates of proton-transfer reactions. However, both acetate membrane fluxes and pH profiles in the ULs computed from these models are found to be close to those of the simple model. One can thus conclude that the difference between experimental and theoretical pH profiles is due to the inconsistency of the generally accepted model of the "unstirred layer", assuming the existence of a strict boundary between the regions of "pure diffusion" and "ideal stirring".
本文提出了一个简单模型，用于描述弱酸在分隔两种缓冲溶液的平面双层脂质膜上转运的实验数据。该模型考虑了在膜相邻的未搅拌层（ULs）中发生的多个质子转移反应。模型的微分方程被证明可简化为一组非线性代数方程。由于后一组方程单调依赖于未知变量，因此可以使用二分法轻松地进行数值求解。对于实验研究的特定系统（以乙酸盐作为弱酸，TRIS + MES作为缓冲混合物），从未搅拌层中的pH分布由该模型计算得出。这些结果与使用pH微电极获得的实验数据进行了比较。理论和实验pH分布之间的一致性被认为是令人满意的。最明显的偏差出现在未搅拌层/本体溶液边界处。为了在理论和实验结果之间获得更好的相关性，考虑了另外两个不太理想化的模型。它们分别考虑了（a）由离子扩散在未搅拌层中产生的电场，以及（b）质子转移反应速率的有限性。然而，从这些模型计算出的乙酸盐膜通量和未搅拌层中的pH分布都与简单模型的结果相近。因此可以得出结论，实验和理论pH分布之间的差异是由于普遍接受的“未搅拌层”模型不一致所致，该模型假定在“纯扩散”区域和“理想搅拌”区域之间存在严格边界。
