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J Theor Biol. 2012 Sep 21;309:185-203. doi: 10.1016/j.jtbi.2012.06.016. Epub 2012 Jun 20.

A reaction-diffusion model of CO2 influx into an oocyte.

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1
Department of Mathematics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA.

Abstract

We have developed and implemented a novel mathematical model for simulating transients in surface pH (pH(S)) and intracellular pH (pH(i)) caused by the influx of carbon dioxide (CO(2)) into a Xenopus oocyte. These transients are important tools for studying gas channels. We assume that the oocyte is a sphere surrounded by a thin layer of unstirred fluid, the extracellular unconvected fluid (EUF), which is in turn surrounded by the well-stirred bulk extracellular fluid (BECF) that represents an infinite reservoir for all solutes. Here, we assume that the oocyte plasma membrane is permeable only to CO(2). In both the EUF and intracellular space, solute concentrations can change because of diffusion and reactions. The reactions are the slow equilibration of the CO(2) hydration-dehydration reactions and competing equilibria among carbonic acid (H(2)CO(3))/bicarbonate (HCO(3)(-)) and a multitude of non-CO(2)/HCO(3)(-) buffers. Mathematically, the model is described by a coupled system of reaction-diffusion equations that-assuming spherical radial symmetry-we solved using the method of lines with appropriate stiff solvers. In agreement with experimental data [Musa-Aziz et al. 2009, PNAS 106 5406-5411], the model predicts that exposing the cell to extracellular 1.5% CO(2)/10 mM HCO(3)(-) (pH 7.50) causes pH(i) to fall and pH(S) to rise rapidly to a peak and then decay. Moreover, the model provides insights into the competition between diffusion and reaction processes when we change the width of the EUF, membrane permeability to CO(2), native extra- and intracellular carbonic anhydrase-like activities, the non-CO(2)/HCO(3)(-) (intrinsic) intracellular buffering power, or mobility of intrinsic intracellular buffers.

PMID:
22728674
PMCID:
PMC3471386
DOI:
10.1016/j.jtbi.2012.06.016
[Indexed for MEDLINE]
Free PMC Article
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