Red blood cell thickness is evolutionarily constrained by slow, hemoglobin-restricted diffusion in cytoplasm

Abstract

During capillary transit, red blood cells (RBCs) must exchange large quantities of CO₂ and O₂ in typically less than one second, but the degree to which this is rate-limited by diffusion through cytoplasm is not known. Gas diffusivity is intuitively assumed to be fast and this would imply that the intracellular path-length, defined by RBC shape, is not a factor that could meaningfully compromise physiology. Here, we evaluated CO₂ diffusivity (D_CO2) in RBCs and related our results to cell shape. D_CO2 inside RBCs was determined by fluorescence imaging of [H⁺] dynamics in cells under superfusion. This method is based on the principle that H⁺ diffusion is facilitated by CO₂/HCO₃^- buffer and thus provides a read-out of D_CO2. By imaging the spread of H⁺ ions from a photochemically-activated source (6-nitroveratraldehyde), D_CO2 in human RBCs was calculated to be only 5% of the rate in water. Measurements on RBCs containing different hemoglobin concentrations demonstrated a halving of D_CO2 with every 75 g/L increase in mean corpuscular hemoglobin concentration (MCHC). Thus, to compensate for highly-restricted cytoplasmic diffusion, RBC thickness must be reduced as appropriate for its MCHC. This can explain the inverse relationship between MCHC and RBC thickness determined from >250 animal species.

Figure 1. H⁺ mobility in the cytoplasm of human RBCs is a read-out of CO₂/HCO₃⁻ diffusivity.

(A) Buffer (e.g. hemoglobin) facilitated H⁺ diffusion from a local H⁺-uncaging site (photolysis of 6-nitroveratraldehyde). (B) H⁺ diffusion facilitated additionally by CO₂/HCO₃⁻. Membrane HCO₃⁻ permeability is set by AE1 (anion exchanger 1) activity. (C) Human RBC superfused in CO₂/HCO₃⁻-free buffer (at pH 7.8). H⁺ ions diffuse slowly from uncaging site, as shown by maps of intracellular pH (pH_i) before and after 2 s of uncaging and pH_i time courses in regions of interest (ROIs) at increasing distance from the uncaging site. The width of each ROI was 1/10^th of RBC’s major diameter; data for ROIs 1 (uncaging site), 2, 3, 4, 5, 6 and 8 shown. Grey curves are best fit using a diffusion equation. (D) Experiment on RBCs superfused with 5% CO₂/HCO₃⁻ (at pH 7.8). The diffusion equation is solved using the finite element method which takes fully into account differences in cell outline, as observed between the cells shown in panels C and D. (E) Apparent H⁺ diffusion coefficients (D_H^app; mean ± SEM of 10–35 cells), showing the small effect of the CO₂/HCO₃⁻ buffer-shuttle. Where indicated, DIDS was added to block AE1. Symbols α and β denote significance (P < 0.05; P < 0.02) compared to measurements in the absence of CO₂/HCO₃⁻.

Figure 2. Hemoglobin concentration restricts cytoplasmic diffusivity.

(A) Probing the diffusive tortuosity of RBC cytoplasm using calcein. (i) Localized bleaching (purple band) of calcein in intact human red blood cells (mean ± SEM of 16 cells) with a high-intensity 488 nm laser evoked a diffusive flux of calcein from non-bleached regions. Fluorescence maps normalized to the cell-averaged signal before bleaching (left) and after 20 s of localized bleaching (right). (ii) Calcein diffusivity was derived by best-fitting fluorescence time courses averaged in 10 regions of interest (ROIs; defined in the same way as for H⁺ uncaging experiments). (iii) Calcein diffusion coefficient (mean ± SEM of 16 cells). (B) Osmotic swelling of human RBCs (flow cytometry repeated thrice; >50,000 cells each) dilutes hemoglobin concentration. (C) Apparent H⁺ diffusivity (D_H^app) increases as hemoglobin concentration is reduced, but the relationship is steeper in the presence of CO₂/HCO₃⁻ (plus 12.5 μM DIDS), indicative of increasing diffusive freedom for CO₂/HCO₃⁻ to facilitate H⁺ mobility (mean ± SEM of 9–28 cells).

Figure 3. Measuring cytoplasmic H⁺ mobility in RBCs from different animal species.

(A,B) H⁺ diffusion measurements in chicken and alpaca RBCs were performed according to the protocol for human RBCs (superfusate pH 7.8 and 37 °C). (C) For cold-blooded Xenopus RBCs, superfusates were at pH 7.5 and 25 °C. N.B.: For measuring fluorescence in ROIs, the signal from the nuclei was excluded. Measured pH_i time courses (black; in ROIs 1, 2, 3, 4, 5, 6, 8) are superimposed with best-fit time courses (grey), determined by the least-squares method. (D) D_H^app in chicken, alpaca and Xenopus RBCs measured in isotonic CO₂/HCO₃⁻-free buffer (0NT; mean ± SEM of 14, 21, 19 cells), isotonic CO₂/HCO₃⁻-containing buffer (BNT; mean ± SEM of 18, 25, 13 cells) or hypotonic BNT (mean ± SEM of 7, 19 cells). Superfusates were at pH 7.8 and 37 °C for mammals, and pH 7.5 and 25 °C for Xenopus. Osmotic swelling increases D_H^app (not tested in Xenopus RBCs due to osmotic fragility). Symbols α, β and γ denote significance (P < 0.0005) compared to measurements in isotonic 0NT. (E) D_H^app decreases with increasing mean corpuscular hemoglobin concentration (MCHC). Hu-human, Ch-chicken, Al-alpaca, X.-Xenopus; hypo: osmotically-swollen cells. The facilitatory effect of CO₂/HCO₃⁻ on D_H^app diminishes at higher MCHC.

Figure 4. CO₂ diffuses slowly in RBC cytoplasm.

(A) Cytoplasmic CO₂ and HCO₃⁻ diffusion coefficients calculated from D_H^app (37 °C for human, chicken and alpaca, 25 °C for Xenopus) compared to data for pure water. (B) Cytoplasmic CO₂ diffusivity fitted to an exponentially-declining function of mean corpuscular hemoglobin concentration (MCHC). Filled circles: data from human, chicken and alpaca RBCs; open circle: data for water (all 37 °C). Cytoplasmic CO₂ diffusivity halves for every 75 g/L increase in MCHC. Inset: plot on linear y-axis, with data from ref. (dashed line) and ref. (dotted line) for gas diffusion coefficients normalized to CO₂ diffusivity in water (2500 μm²/s).

Figure 5. Results of mathematical simulations.

(A) Time-to-complete 90% equilibration (τ₉₀) of pCO₂ inside RBC in response to an increase in ambient [CO₂] (a respiratory acidosis of 7.2). (i) Extracellular pCO₂. (ii) Simulations with fast D_CO2 diffusivity: 40% of rate in water, as determined in cell-free solutions. Intracellular pCO₂ in a flattened human RBC (continuous line) and a hypothetical spherical version of the same diameter (dashed line). Circles indicate τ₉₀. (iii) Simulations repeated with more restricted D_CO2 diffusivity: at 5% of rate in water. The benefit of a flattened shape is more apparent with slow D_CO2. (B) Time-to-complete 90% (τ₉₀) of acid uptake by an RBC in response to a decrease in ambient [HCO₃⁻] (a metabolic acidosis of 7.2). (i) Extracellular [HCO₃⁻]. (iii) Simulations with fast D_CO2 for flattened (continuous line) and spherical (dashed line) cells. Circles indicate τ₉₀. (iii) Simulations repeated with more restricted D_CO2. (C) Heat map showing binned data on MCHC and RBC half-thickness data from >250 species of cold- and warm-blooded animals (see inset for look-up table). Superimposed contours (units: ms) show model predictions for time-to-complete 90% equilibration τ₉₀ of pCO₂ in RBCs, based on human RBC data modified accordingly for thickness, MCHC and hence diffusivity of CO₂, HCO₃⁻ and hemoglobin. Most species fall in the range 0.03 s < τ₉₀ < 0.3 s. (D) Heat map superimposed with model predictions for time-to-complete 90% (τ₉₀) acid uptake into RBCs, based on human RBC data modified according for thickness, MCHC and hence diffusivity of CO₂, HCO₃⁻ and hemoglobin. Most species fall in the range 0.3 s < τ₉₀ < 1 s.