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Mathematical modeling of the microenvironment beneath a surface pH electrode tip
Author(s) -
Occhipinti Rossana,
Calvetti Daniela,
Boron Walter F,
Somersalo Erkki
Publication year - 2016
Publication title -
the faseb journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.709
H-Index - 277
eISSN - 1530-6860
pISSN - 0892-6638
DOI - 10.1096/fasebj.30.1_supplement.1300.1
Subject(s) - electrode , chemistry , microelectrode , membrane , biophysics , extracellular , diffusion , analytical chemistry (journal) , permeability (electromagnetism) , chromatography , biochemistry , thermodynamics , physics , biology
The time course of extracellular surface pH (pH S ), recorded by a blunt pH microelectrode, is the key physiological data to assess membrane permeability to CO 2 ( P M,CO2 ) when exposing an oocyte to a solution containing CO 2 /HCO 3 − . In an effort to extract P M,CO2 values from pH S measurements, we previously developed a reaction‐diffusion mathematical model of CO 2 influx into a spherical cell. The model accounts for the slow interconversion of CO 2 and HCO 3 − as well as the reactions of a multitude of non‐CO 2 /HCO 3 − buffers. When compared to physiological experiments, the model can predict the essential features of the measured pH S transients. However, it is clear that further improvements in the quantitative agreement of the model with the physiological data, will require additional refinements of the model, including a detailed modeling of the micro‐environment under the pH S electrode tip, when pushed against the cell membrane. In the present study, we propose two computational models for studying the effect of the pH S electrode on pH S measurements. In the first approach, we develop a two‐dimensional model of the pH S electrode and the extracellular microenvironment underneath the electrode by assuming that the electrode‐membrane interface is an infinitely thin homogenous disc within which diffusion occurs only in the tangential direction along the disc surface as well as at the interface between the disc and the bulk extracellular fluid. In addition, transmembrane gas exchange occurs between the disc and the cytoplasm, in a direction perpendicular to the disc. Mathematically, this model is described by two‐dimensional reaction‐diffusion equations that are solved numerically by a combination of finite difference (FD) schemes and stiff solvers. Because this model does not reveal the dependence of the pH S transient on the distance of the pH S electrode from the cell membrane, in the second approach, we develop a three‐dimensional reaction‐diffusion model of the pH S electrode tip and of its surrounding environment, where the reaction‐diffusion equations are now solved by a combination of the finite element method (FEM) with stiff solvers. Our preliminary results corroborate the hypothesis that diffusion is slower in the micro‐environment under the electrode tip, resulting in substantially larger pH S transients than those on a free membrane surface. The work points towards the possibility of defining a reliable electrode gain function that corrects the effect of the electrode. Support or Funding Information Supported by grants from NIH (U01‐GM111251, K01‐DK107787)