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Facilitated Diffusion of Oxygen and Carbon Dioxide

Ferdinand Kreuzer, Louis Hoofd

10.1002/cphy.cp030406

Source: Supplement 13: Handbook of Physiology, The Respiratory System, Gas Exchange

Originally published: 1987

Published online: January 2011

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Facilitated Diffusion of O2
1.1 Experimental Basis
1.2 Molecular Mechanism
1.3 Quantitative Interpretation
1.4 Diffusion Coefficients of O2 and Hemoglobin
1.5 Facilitated Diffusion of CO
1.6 Facilitated O2 Diffusion in Non‐Steady‐State Oxygenation
1.7 Physiological Significance of Facilitated O2 Diffusion
2 Facilitated Diffusion of CO2
2.1 Theory
2.2 Experimental Studies
2.3 Physiological Significance
Figure 1. Figure 1.

Basic characteristics of facilitated diffusion of O2. Upper panel, steady‐state O2 fluxes (μl/min) through layer of Hb solution vs. partial pressure of O2 () at chemical equilibrium in absence of back pressure at low‐pressure side. Millipore membrane 150 μm, Hb concentration 19 g/100 ml, temperature 25°C. ↔, Plain diffusion component (Hb inactivated as metHb, ‐ ‐ ‐ ‐ ‐) of total O2 flux (‐ ‐ ‐), ↔, Hb‐augmented component. In ascending part of facilitated flux, 2 curves reflect 2 HbO2 dissociation curves, pH 7.3 and 6.0. Lower panel, dimensionless relative facilitation (Fac): (total flux — plain flux)/plain flux = facilitated flux/plain flux vs. . Maximum facilitation ∼8 at pH 7.3 and ∼3 at pH 6.0. Maximum at pH 7.3 occurs at lower than at pH 6.0, due to respective position of HbO2 dissociation curve. Two curves do not pass through origin where quotient mentioned above is 0/0 or undefined.

Upper panel adapted from Hemmingsen 68 and Wittenberg 198
Figure 2. Figure 2.

Regions where approximate analytic solutions can be obtained (for one reaction and one permeant S), depending on concentration difference ΔS, equilibrium (association) constant K, and Damköhler number γ. Two extreme asymptotic regimes are hatched (left, near‐diffusion regime; right, near‐equilibrium regime).

From Schultz et al. 157
Figure 3. Figure 3.

Profiles of O2 pressure (, bottom), O2 saturation (Sat, top), and nonequilibrium facilitation (Fac,.….) plotted against distance (x) in 5‐μm‐thick layer of 15 g/100 ml Mb solution at steady state, exposed to of 10 (left) and 0 (right) Torr. Curves are scaled for same flux contribution. Saturation scale only covers range from 75% to 100%. _____, Calculated profiles for nonequilibrium 76,102; at boundaries, slopes are equal (steady state) and slopes of MbO2 saturation are 0 (no flux). ‐ ‐ ‐ ‐ ‐, Equilibrium core extensions. ‐ ‐ ‐ ‐ ‐, Profiles for equilibrium presumed throughout layer. Top, ‐ ‐ ‐ ‐ ‐: saturation starts at equilibrium value of <100% because a of 10 Torr is not sufficient for complete saturation and would continue to 0 on right side. , Penetration depth λ for nonequilibrium 39; although this penetration depth is smaller at low‐pressure boundary, its effect of raising the MbO2 saturation is enormous (from 0% at equilibrium to 77% at nonequilibrium) due to steep course of MbO2 dissociation curve in this range.
Figure 4. Figure 4.

Comparison of various approximate analytic approaches to describe facilitated diffusion in plot of facilitation (Fac) against layer thickness L and Damköhler number γ. Calculations for Hb solution of 15 g/100 ml and difference of 200 vs. 2 Torr to compare with numerical results (•) of Kutchai et al. 109.‐ ‐ ‐ ‐ ‐, Asymptotes; near‐diffusion asymptote (left) coincides with thin‐layer first‐order solution 161 and near‐equilibrium asymptote (top) corresponds with thick‐layer zero‐order solutions (maximum facilitation). Lines and ‐ ‐ ‐ ‐ ‐ (approximate formulas) indicate the solutions: 1, weak boundary layer, first order 46,130; 2, weak boundary layer, second order 46,152; 3, strong boundary layer 101; 4, strong boundary layer 102; 5, thick layer, first order 161; 6, thick layer, second order 161; 7, thin layer, second order 161; 8, slow reaction 189; 9, single‐point linearization 39,46; 10, wide range, improved for flat layers 76; 11, interpolation formula, modified for nonzero back pressure 203; see ref. 160 for similar solution; 12, approximation for sufficiently thick layers 161.
Figure 5. Figure 5.

Curve of diffusion coefficient of O2 (, top) from Gold‐stick and Fatt 48 and Kreuzer 100 and values of DHb obtained by various authors as a function of Hb concentration at 25°C. Symbols, tracer DHb, (Dt, except •): □, Keller and Friedlander 92, pH 7.4; ▪, Moll 132; ○, Adams and Fatt 1; •, Keller et al. 90, mutual Dm, pH 7.3; , Keller et al. 90, tracer Dt, pH 7.3; Δ, Riveros‐Moreno and Wittenberg 149, pH 7.3; ▴, Gros 51, pH 7.2, ionic strength I = 150 mM; ×, Spaan et al. 164. Numbered lines, mutual DHb, (Dm): 1, Wilson et al. 193, pH 7.0; 2, Alpert and Banks 2, pH 7.0, I = 100 mM; 3, Veldkamp and Votano 185, pH 7.2, I = 125 mM; 4, Jones et al. 81, pH 6.9 = isoelectric point IP, I = 100 mM; 5, Hall et al. 63, pH 6.7 = IP of deoxy Hb, I = 200 mM; 6, LaGattuta et al. 115, pH 6.9, I = 150 mM; ‐ ‐ ‐ ‐ ‐, Dt, calculated from Dm according to Hall et al. 63 up to 16 g/100 ml;.…., Dt calculated from Dm 63 extrapolated up to 35 g/100 ml;.…., Dt calculated from Stokes‐Einstein equation according to Equation 1 in Young et al. 202 with values of viscosity coefficient obtained by Kreuzer 99.
Figure 6. Figure 6.

Schematic profiles of species important in facilitated CO2 diffusion across a layer. Conditions assumed: , difference from 45 Torr (x = 0) to 15 Torr (x = L); mean concentrations: Na+ = 150 mM, Cl− = 130 mM (not bound to Hb), Hb = 5 mM. Temperature, 21°C. Values at upper (x = 0) vs. lower (x = L) boundary.‐ ‐ ‐, With potential;‐ ‐ ‐ ‐, without potential.

With Potential

Without Potential

Parameter

45 Torr

15 Torr

45 Torr

15 Torr

Na+, mM

146.6

154.4

150

150

Cl−, mM

133.0

126.3

130

130

, mM

17.7

16.1

21.1

12.2

, mM1

0.03

0.07

0.04

0.04

pH

7.09

7.53

7.17

7.41

Hb, mM

5.02

4.82

5

5

Facilitation (Fac)

0.322

4.32

CO2, mM

2.00

0.67

2.00

0.67

Charge of Hb (zHb)

+0.8

‐2.5

+0.2

‐1.6

Potential (U), mV

0

‐1.3

0

Not shown on figure.

Mean values over the whole layer.

.

according to De Koning et al. 24


Figure 1.

Basic characteristics of facilitated diffusion of O2. Upper panel, steady‐state O2 fluxes (μl/min) through layer of Hb solution vs. partial pressure of O2 () at chemical equilibrium in absence of back pressure at low‐pressure side. Millipore membrane 150 μm, Hb concentration 19 g/100 ml, temperature 25°C. ↔, Plain diffusion component (Hb inactivated as metHb, ‐ ‐ ‐ ‐ ‐) of total O2 flux (‐ ‐ ‐), ↔, Hb‐augmented component. In ascending part of facilitated flux, 2 curves reflect 2 HbO2 dissociation curves, pH 7.3 and 6.0. Lower panel, dimensionless relative facilitation (Fac): (total flux — plain flux)/plain flux = facilitated flux/plain flux vs. . Maximum facilitation ∼8 at pH 7.3 and ∼3 at pH 6.0. Maximum at pH 7.3 occurs at lower than at pH 6.0, due to respective position of HbO2 dissociation curve. Two curves do not pass through origin where quotient mentioned above is 0/0 or undefined.

Upper panel adapted from Hemmingsen 68 and Wittenberg 198


Figure 2.

Regions where approximate analytic solutions can be obtained (for one reaction and one permeant S), depending on concentration difference ΔS, equilibrium (association) constant K, and Damköhler number γ. Two extreme asymptotic regimes are hatched (left, near‐diffusion regime; right, near‐equilibrium regime).

From Schultz et al. 157


Figure 3.

Profiles of O2 pressure (, bottom), O2 saturation (Sat, top), and nonequilibrium facilitation (Fac,.….) plotted against distance (x) in 5‐μm‐thick layer of 15 g/100 ml Mb solution at steady state, exposed to of 10 (left) and 0 (right) Torr. Curves are scaled for same flux contribution. Saturation scale only covers range from 75% to 100%. _____, Calculated profiles for nonequilibrium 76,102; at boundaries, slopes are equal (steady state) and slopes of MbO2 saturation are 0 (no flux). ‐ ‐ ‐ ‐ ‐, Equilibrium core extensions. ‐ ‐ ‐ ‐ ‐, Profiles for equilibrium presumed throughout layer. Top, ‐ ‐ ‐ ‐ ‐: saturation starts at equilibrium value of <100% because a of 10 Torr is not sufficient for complete saturation and would continue to 0 on right side. , Penetration depth λ for nonequilibrium 39; although this penetration depth is smaller at low‐pressure boundary, its effect of raising the MbO2 saturation is enormous (from 0% at equilibrium to 77% at nonequilibrium) due to steep course of MbO2 dissociation curve in this range.



Figure 4.

Comparison of various approximate analytic approaches to describe facilitated diffusion in plot of facilitation (Fac) against layer thickness L and Damköhler number γ. Calculations for Hb solution of 15 g/100 ml and difference of 200 vs. 2 Torr to compare with numerical results (•) of Kutchai et al. 109.‐ ‐ ‐ ‐ ‐, Asymptotes; near‐diffusion asymptote (left) coincides with thin‐layer first‐order solution 161 and near‐equilibrium asymptote (top) corresponds with thick‐layer zero‐order solutions (maximum facilitation). Lines and ‐ ‐ ‐ ‐ ‐ (approximate formulas) indicate the solutions: 1, weak boundary layer, first order 46,130; 2, weak boundary layer, second order 46,152; 3, strong boundary layer 101; 4, strong boundary layer 102; 5, thick layer, first order 161; 6, thick layer, second order 161; 7, thin layer, second order 161; 8, slow reaction 189; 9, single‐point linearization 39,46; 10, wide range, improved for flat layers 76; 11, interpolation formula, modified for nonzero back pressure 203; see ref. 160 for similar solution; 12, approximation for sufficiently thick layers 161.



Figure 5.

Curve of diffusion coefficient of O2 (, top) from Gold‐stick and Fatt 48 and Kreuzer 100 and values of DHb obtained by various authors as a function of Hb concentration at 25°C. Symbols, tracer DHb, (Dt, except •): □, Keller and Friedlander 92, pH 7.4; ▪, Moll 132; ○, Adams and Fatt 1; •, Keller et al. 90, mutual Dm, pH 7.3; , Keller et al. 90, tracer Dt, pH 7.3; Δ, Riveros‐Moreno and Wittenberg 149, pH 7.3; ▴, Gros 51, pH 7.2, ionic strength I = 150 mM; ×, Spaan et al. 164. Numbered lines, mutual DHb, (Dm): 1, Wilson et al. 193, pH 7.0; 2, Alpert and Banks 2, pH 7.0, I = 100 mM; 3, Veldkamp and Votano 185, pH 7.2, I = 125 mM; 4, Jones et al. 81, pH 6.9 = isoelectric point IP, I = 100 mM; 5, Hall et al. 63, pH 6.7 = IP of deoxy Hb, I = 200 mM; 6, LaGattuta et al. 115, pH 6.9, I = 150 mM; ‐ ‐ ‐ ‐ ‐, Dt, calculated from Dm according to Hall et al. 63 up to 16 g/100 ml;.…., Dt calculated from Dm 63 extrapolated up to 35 g/100 ml;.…., Dt calculated from Stokes‐Einstein equation according to Equation 1 in Young et al. 202 with values of viscosity coefficient obtained by Kreuzer 99.



Figure 6.

Schematic profiles of species important in facilitated CO2 diffusion across a layer. Conditions assumed: , difference from 45 Torr (x = 0) to 15 Torr (x = L); mean concentrations: Na+ = 150 mM, Cl− = 130 mM (not bound to Hb), Hb = 5 mM. Temperature, 21°C. Values at upper (x = 0) vs. lower (x = L) boundary.‐ ‐ ‐, With potential;‐ ‐ ‐ ‐, without potential.

With Potential

Without Potential

Parameter

45 Torr

15 Torr

45 Torr

15 Torr

Na+, mM

146.6

154.4

150

150

Cl−, mM

133.0

126.3

130

130

, mM

17.7

16.1

21.1

12.2

, mM1

0.03

0.07

0.04

0.04

pH

7.09

7.53

7.17

7.41

Hb, mM

5.02

4.82

5

5

Facilitation (Fac)

0.322

4.32

CO2, mM

2.00

0.67

2.00

0.67

Charge of Hb (zHb)

+0.8

‐2.5

+0.2

‐1.6

Potential (U), mV

0

‐1.3

0

Not shown on figure.

Mean values over the whole layer.

.

according to De Koning et al. 24
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Article Title: Facilitated Diffusion of Oxygen and Carbon Dioxide
 

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Ferdinand Kreuzer, Louis Hoofd. Facilitated Diffusion of Oxygen and Carbon Dioxide. Compr Physiol 2011, Supplement 13: Handbook of Physiology, The Respiratory System, Gas Exchange: 89-111. First published in print 1987. doi: 10.1002/cphy.cp030406