Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Trojdena 4, 02-109, Warsaw, Poland.
Sci Rep. 2021 Nov 12;11(1):22150. doi: 10.1038/s41598-021-00899-y.
Separation of two ionic solutions with a permselective membrane that is impermeable to some of the ions leads to an uneven distribution of permeating ions on the two sides of the membrane described by the Gibbs-Donnan (G-D) equilibrium with the G-D factors relating ion concentrations in the two solutions. Here, we present a method of calculating the G-D factors for ideal electroneutral multi-ion solutions with different total charge of non-permeating species on each side of a permselective membrane separating two compartments. We discuss some special cases of G-D equilibrium for which an analytical solution may be found, and we prove the transitivity of G-D factors for multi-ion solutions in several compartments interconnected by permselective membranes. We show a few examples of calculation of the G-D factors for both simple and complex solutions, including the case of human blood plasma and interstitial fluid separated by capillary walls. The article is accompanied by an online tool that enables the calculation of the G-D factors and the equilibrium concentrations for multi-ion solutions with various composition in terms of permeating ions and non-permeating charge, according to the presented method.
使用对某些离子不可渗透的选择透过性膜将两种离子溶液分离，会导致渗透离子在膜两侧不均匀分布，这种分布可以用 Gibbs-Donnan（G-D）平衡来描述，其中 G-D 因子与两种溶液中的离子浓度有关。在这里，我们提出了一种计算理想电中性多离子溶液的 G-D 因子的方法，该方法适用于在分离两个隔室的选择透过性膜的每一侧具有不同非渗透物种总电荷的情况。我们讨论了一些 G-D 平衡的特殊情况，对于这些情况可以找到解析解，并且我们证明了通过选择透过性膜相互连接的多个隔室中的多离子溶液的 G-D 因子的传递性。我们展示了一些简单和复杂溶液的 G-D 因子计算的示例，包括毛细血管壁分隔的人体血浆和间质液的情况。本文还提供了一个在线工具，根据所提出的方法，该工具可以计算各种组成的多离子溶液的 G-D 因子和平衡浓度，这些溶液的组成涉及渗透离子和非渗透电荷。
