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. 2009 Mar 15;587(Pt 6):1153-67.
doi: 10.1113/jphysiol.2008.165027. Epub 2009 Jan 12.

Extra- and intracellular unstirred layer effects in measurements of CO2 diffusion across membranes--a novel approach applied to the mass spectrometric 18O technique for red blood cells

Volker Endeward  1 , Gerolf Gros
Affiliations

Extra- and intracellular unstirred layer effects in measurements of CO2 diffusion across membranes--a novel approach applied to the mass spectrometric 18O technique for red blood cells

Volker Endeward et al. J Physiol. .

Abstract

We have developed an experimental approach that allows us to quantify unstirred layers around cells suspended in stirred solutions. This technique is applicable to all types of transport measurements and was applied here to the (18)O technique used to measure CO(2) permeability of red cells (PCO2). We measure PCO2 in well-stirred red cell (RBC) suspensions of various viscosities adjusted by adding different amounts of 60 kDa dextran. Plotting 1/PCO2 vs. viscosity nu gives a linear relation, which can be extrapolated to nu=0. Theoretical hydrodynamics predicts that extracellular unstirred layers vanish at zero viscosity when stirring is maintained, and thus this extrapolation gives us an estimate of the PCO2 free from extracellular unstirred layer artifacts. The extrapolated value is found to be 0.16 cm s(-1) instead of the experimental value in saline of 0.12 cm s(-1) (+30%). This effect corresponds to an unstirred layer thickness of 0.5 microm. In addition, we present a theoretical approach modelling the actual geometrical and physico-chemical conditions of (18)O exchange in our experiments. It confirms the role of an extracellular unstirred layer in the determination of PCO2. Also, it allows us to quantify the contribution of the so-called intracellular unstirred layer, which results from the fact that in these transport measurements--as in all such measurements in general--the intracellular space is not stirred. The apparent thickness of this intracellular unstirred layer is about 1/4-1/3 of the maximal intracellular diffusion distance, and correction for it results in a true PCO2 of the RBC membrane of 0.20 cm s(-1). Thus, the order of magnitude of this is PCO2 unaltered compared to our previous reports. Discussion of the available evidence in the light of these results confirms that CO(2) channels exist in red cell and other membranes, and that PCO2 of red cell membranes in the absence of these channels is quite low.

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Figures

Figure 2
Figure 2. Time course of decay of C18O16O in RBC suspension
A, original mass spectrometric recording of an experiment with red cells (black dashed line), which were added at about 100 s, giving a characteristic biphasic acceleration of C18O16O decay. Temperature 37°C. Superimposing the experimental curve is the theoretical curve obtained from the fitting procedure of the evaluation program (grey dashed line). B, the black dashed curve represents the result of a mathematical simulation of 18O exchange under the geometrical conditions indicated in Fig. 3. This curve was then subjected to the same evaluation program with fitting procedure as the curve in A. The grey dashed curve obtained from this superimposes the simulated curve, indicating excellent agreement of the two curves. The fitting procedure of the evaluation program not only yields the grey curves shown, but also the values of formula image and formula image that fit the black curves best.
Figure 3
Figure 3. Model simulation of 18O exchange between a well-stirred bulk solution and human red blood cells suspended in it
The bulk solution is separated from the red cell membrane by an extracellular unstirred layer, USLe, of a thickness that was varied between 0 and 1 μm. The length of the red cell compartment, i.e. the diffusion path within the red cell, was taken to be the half-thickness of the red cell, 0.8 μm, as introduced for purposes of diffusion calculations by Forster (1964). The volume ratio of red cells to extracellular solution was ∼0.0003 : 1. The arrows indicate diffusion of the labelled species C18O16O, HC18O16O2− and H218O between the volume elements into which each compartment was divided (usually 20–50) and across the red cell membrane. ‘Reaction’ indicates the reaction processes described by eqns (3)–(5). While the same reactions occur in the bulk solution, diffusion is not considered there as this compartment is well stirred. Deviations from the situation depicted in the figure are (i) the RBC interior is alternatively considered well-stirred, no diffusion occurs then within the RBC, and USLi= 0, (ii) the extracellular unstirred layer is omitted, setting USLe= 0. The results for these 3 situations are given in Table 1. Constants used in the model calculation are: half-thickness of the red cell 0.8 μm, RBC volume to bulk solution volume ratio 0.0003, formula image in saline 2.4 × 10−5 cm2 s−1, formula image inside RBC 1.2 × 10−5 cm2 s−1 (Gros & Moll, 1971), formula image in saline 1.2 × 10−5 cm2 s−1 (Gros et al. 1976), formula image inside RBC 0.6 × 10−5 cm2 s−1 (same reduction by intracellular Hb assumed as in the case of formula image), pK1' 6.10, pHe 7.40, pHi 7.20, ku 0.15 s−1, ACA inside RBC 20 000.
Figure 1
Figure 1. Reaction chamber connected to the mass spectrometer
There is continuous diffusion of very small amounts of C18O16O and C16O2 from the (extracellular) solution in the reaction chamber across the 25 μm thick Teflon membrane into the high vacuum of the mass spectrometer, the rate of which is proportional to the concentration of both species in the fluid. Thus, the concentration of both gases in the solution is monitored continuously. Before red cells are added to the solution, pH is adjusted to 7.40. Chamber volume is 1.70 ml.
Figure 4
Figure 4. Permeabilities of the human red cell membrane at 37°C, at various concentrations of dextran established in the solution in which the red cells were suspended
A shows that formula image does not vary with dextran concentration, but B shows that formula image decreases markedly with increasing dextran concentration.
Figure 5
Figure 5. Kinematic viscosities, ν, of NaCl solutions of various dextran concentrations
Measured at 37°C in an Ubbelohde viscometer.
Figure 6
Figure 6. Red cell membrane permeabilities at 37°C and at various viscosities of the suspending medium
Data points from Figs 4 and 5. A, bicarbonate permeability; B, CO2 permeability. At a viscosity of 4 × 10−6 m2 s−1formula image fell to almost 1/3 of its value in dextran-free saline.
Figure 7
Figure 7. Reciprocal of RBC CO2 permeability as a function of solution viscosity ν
A, 37°C. Regression equation: formula image (s.d.± 0.43) + 3.48 (s.d.± 0.21) ·ν. r= 0.994. The y-axis intercept corresponds to a formula image of 0.16 cm s−1. Data from Fig. 6B. B, 23°C. Regression equation: formula image (s.d.± 0.58) + 3.84 (s.d.± 0.20) ·ν. r= 0.996. The y-intercept gives a formula image of 0.14 cm s−1.
Figure 8
Figure 8. Unstirred layer thickness δ as a function of solution viscosity
δ was calculated from the formula image measured at each viscosity and the formula image at zero viscosity obtained from the y-axis intercepts in Fig. 7 using eqn (7). A, 37°C. Regression equation: δ= 0.0001 (s.d.± 0.051) + 0.835 (s.d.± 0.051) ·ν. r= 0.994. B, 23°C. Regression equation: δ= 0.152 (s.d.± 0.098) + 0.652 (s.d.± 0.034) ·ν. r= 0.996. At both temperatures, the y-axis intercept is not significantly different from zero, indicating that a direct proportionality exists between δ and ν.
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