Significance of two transmembrane ion gradients for human erythrocyte volume stabilization

Abstract

Functional effectiveness of erythrocytes depends on their high deformability that allows them to pass through narrow tissue capillaries. The erythrocytes can deform easily due to discoid shape provided by the stabilization of an optimal cell volume at a given cell surface area. We used mathematical simulation to study the role of transport Na/K-ATPase and transmembrane Na+ and K+ gradients in human erythrocyte volume stabilization at non-selective increase in cell membrane permeability to cations. The model included Na/K-ATPase activated by intracellular Na+, Na+ and K+ transmembrane gradients, and took into account contribution of glycolytic metabolites and adenine nucleotides to cytoplasm osmotic pressure. We found that this model provides the best stabilization of the erythrocyte volume at non-selective increase in the permeability of the cell membrane, which can be caused by an oxidation of the membrane components or mechanical stress during circulation. The volume of the erythrocyte deviates from the optimal value by no more than 10% with a change in the non-selective permeability of the cell membrane to cations from 50 to 200% of the normal value. If only one transmembrane ion gradient is present (Na+), the cell loses the ability to stabilize volume and even small changes in membrane permeability cause dramatic changes in the cell volume. Our results reveal that the presence of two oppositely directed transmembrane ion gradients is fundamentally important for robust stabilization of cellular volume in human erythrocytes.

Fig 1. Interaction of transport Na/K-ATPase and glycolysis in human erythrocytes.

Solid and dotted purple arrows show active and passive ion fluxes through the cell membrane, respectively. Ion symbols size inside and outside the cell is proportional to the ion concentration. The red arrows show activation (+) and inhibition (-) of different metabolic processes by ions and adenylates. Green arrows show the interconversions between ATP, ADP and AMP. The additional ATPase represents the ATP consuming processes in the cell other than the active transmembrane Na⁺ and K⁺ transport.

Fig 2. The effect of non-selective permeability of the cell membrane for cations (g) on the erythrocyte volume and on intracellular Na⁺ and K⁺ concentrations in three different models.

The dependence of the relative stationary volume of the erythrocyte (A) and stationary intracellular Na⁺ (blue lines) and K⁺ (red lines) concentrations (B) on the relative non-selective permeability of the cell membrane for cations ($g=\frac{G_{Na}}{G_{Na0}}\approx \frac{G_K}{G_{K0}}$). Kinetics of changes in erythrocyte volume (C) and intracellular Na⁺ concentration (D) after an instant 4-fold increase in the non-selective permeability of the cell membrane for cations. The kinetics of the K⁺ concentration is the same as for Na⁺, but changes occur in the direction of decreasing concentration. The black circle in the panel A indicates physiologically normal state of erythrocyte. The numbers on the curves correspond to the model versions: 1 –the version of the model with actively maintained transmembrane Na⁺ and K⁺ gradients and transport Na/K-ATPase activated by intracellular Na⁺; 2 –version with actively maintained transmembrane gradient only for Na⁺ and transport Na-ATPase activated by intracellular Na⁺; 3 –version with actively maintained transmembrane gradient only for Na⁺ and transport Na-ATPase independent of intracellular Na⁺. The red stripe in the panel A marks the area of maximal erythrocyte volume (V/V₀ = 1.7–1.8) at which the cell takes a spherical shape.

Fig 3. The effect of non-selective permeability of the cell membrane for cations (g) on erythrocyte energy metabolism in different models.

(A)—The steady-state rate of ATP consumption by ion pumps; (B)—ATP concentration; (C)–Energy charge (([ATP] + 0.5[ADP])/([ATP] + [ADP] + [AMP])); (D)–Adenylate pool ([ATP] + [ADP] + [AMP]). The numbers on the curves indicate model versions as in Fig 2.

Fig 4. The dependence of the relative steady-state erythrocyte volume (V/V₀) on the passive permeability of the cell membrane for K⁺ (G_K/G_K0) and Na⁺ (G_Na/G_Na0).

The model includes actively maintained transmembrane Na⁺ and K⁺ gradients and transport Na/K-ATPase activated by intracellular Na⁺ (Version 1). The black circle indicates the normal physiological state of the erythrocyte.

Fig 5

The dependence of erythrocyte transmembrane potential (A) and intracellular ion concentrations (B) on the non-selective cell membrane permeability for cations (g) in different models. (A)-The numbers on the curves indicate model versions as in Fig 2; (B)-the red, blue, green, and black lines show concentrations of K⁺, Na⁺, Cl^-, and total concentration of intracellular macromolecules and metabolites (W/V) respectively. Solid and dashed lines show data obtained for the model with Na/K-ATPase (model version 1), and with Na-ATPase (model version 2) respectively.

Fig 6. The effect of variation of transport Na/K- or Na- ATPase and hexokinase (HK) activity on erythrocyte volume stabilization.

Panels (A) and (B) show the dependence of the relative erythrocyte cell volume on the non-selective cell membrane permeability for cations (g) at different values of transport Na/K-ATPase activity (A) or HK activity (B) in the base version of the model (model version 1). The numbers on the curves indicate relative activity of the corresponding enzyme. Panel (C) shows the dependence of the physiological erythrocyte volume on the activity of the transport Na/K-ATPase (model version 1, curve 1) or transport Na-ATPase (model versions 2 and 3). Panel (D) shows the dependence of the physiological erythrocyte volume on HK activity in the models with Na/K-ATPase (curve 1) or with Na-ATPase (curves 2 and 3). The red stripes mark the area of maximal erythrocyte volume (V/V₀ = 1.7–1.8) at which the cell takes a spherical shape. For curve 2 (panel A) and for curve 0.5 (panel B) at high g values as well as for curve 3 (panel D) at low HK activity values the steady state in glycolysis disappears.

Fig 7. The dependence of the erythrocyte steady-state volume on the content of impermeable molecules in cytoplasm (A) and on the osmolarity of the external medium (B) in the model with two ion gradients.

In panel (A) parameter W (Table 1) was varied above and below its physiological value. In panel (B) parameters [Na⁺]_ext, [K⁺]_ext, and [Cl^-]_ext (Table 1) were varied above and below the physiological values simultaneously at the same proportion. The black circles indicate physiologically normal state of erythrocyte. The red stripes mark the area of maximal erythrocyte volume (V/V₀ = 1.7–1.8) at which the cell takes a spherical shape.