Stoichiometric relationship between Na(+) ions transported and glucose consumed in human erythrocytes: Bayesian analysis of (23)Na and (13)C NMR time course data

Abstract

We examined the response of Na(+),K(+)-ATPase (NKA) to monensin, a Na(+) ionophore, with and without ouabain, an NKA inhibitor, in suspensions of human erythrocytes (red blood cells). A combination of (13)C and (23)Na NMR methods allowed the recording of intra- and extracellular Na(+), and (13)C-labeled glucose time courses. The net influx of Na(+) and the consumption of glucose were measured with and without NKA inhibited by ouabain. A Bayesian analysis was used to determine probability distributions of the parameter values of a minimalist mathematical model of the kinetics involved, and then used to infer the rates of Na(+) transported and glucose consumed. It was estimated that the numerical relationship between the number of Na(+) ions transported by NKA per molecule of glucose consumed by a red blood cell was close to the ratio 6.0:1.0, agreeing with theoretical prediction.

Figure 1

Schematic diagram of the key pathways examined in the RBCs. The cell phosphorylates ADP to ATP using free energy from glucose via glycolysis. Under normal conditions and like those used in this work, some (∼10%) of the carbon flux is via the pentose phosphate pathway (PPP). Because in this pathway one carbon atom is lost as CO₂ per glucose molecule, less ADP is phosphorylated per carbon atom than if the glucose flowed directly into the glycolytic pathway. The Na⁺,K⁺-ATPase (NKA) hydrolyzes an ATP molecule to transport three Na⁺ ions outside and two K⁺ ions inside against their concentration gradients, resulting in low Na⁺ and high K⁺ intracellular concentrations relative to the extracellular concentrations. NKA is continually active and it offsets leakage of ions, which occur across the membrane, driven by the concentration gradients. In our experiment monensin, a Na⁺ ionophore was added to suspensions of RBCs. This caused extracellular Na⁺ to be carried inside at a greater rate than normal, thus perturbing the steady-state concentrations of Na⁺ and K⁺. We recorded the amounts of Na⁺ in each compartment, and the total amount of glucose, using NMR spectroscopy after the addition of monensin, with and without ouabain, as the specific inhibitor of NKA. TmDOTP⁵⁻, a chemical shift reagent, was added to the RBC suspensions to resolve intra- and extracellular ²³Na⁺ in the ²³Na NMR spectra (Fig. 2A). To monitor the glucose concentration using ¹³C NMR, the cells were suspended in a medium that contained [1-¹³C] d-glucose.

Figure 2

²³Na (105.84 MHz) and ¹³C (100.61 MHz) NMR spectra of a suspension of RBCs (Ht = 0.70) containing 5 mM TmDOTP⁵⁻, 20 mM HEPES, 5 mM K⁺, 70% D₂O v/v, ∼160 mM Na⁺, and ∼8 mM [1-¹³C] d-glucose, incubated at 37°C. (A) ²³Na NMR spectrum showing separate intra- and extracellular Na⁺ resonances in the presence of TmDOTP⁵⁻. (Inset) Progressive ²³Na NMR spectra after the addition of monensin at t = 0, with the central time of acquisition of each spectrum indicated on the figure. (B) ¹³C NMR spectrum showing four resonances of [1-¹³C] d-glucose (two for each anomer, α and β, of glucose; the splitting is due to J-coupling to the attached H atom). (Inset) Spectrum zoomed in on the glucose resonances. (Red solid line) Cumulative integral over its frequency range. (Dashed red line) Designated baseline. There were no observable resonances for [1-¹³C] l-lactate of ¹³CO₂ in any of the ¹³C time-course spectra.

Figure 3

Triplicate time courses of the mole amounts of Na⁺ outside and inside human RBCs in suspensions, based on the ²³Na NMR spectra acquired after the addition of monensin (final concentration 60 nM, t = 0 min) either without (A) or with (B) the addition of ouabain (final concentration 1 mM, t = −15 min), incubated at 37°C. Mole amounts (μmol) were estimated on the basis of the peak areas of the relevant NMR resonances for Na⁺ (as shown in Fig. 2A), and calibrated against a standard (see Materials and Methods). (Solid lines) Model output (Eq. 1) using the maximum-probability parameter values given in Table 1.

Figure 4

Triplicate time courses of the mole amounts of glucose in suspensions of human RBCs based on the ¹³C NMR spectra acquired after the addition of monensin (final concentration 60 nM, t = 0 min) either without (A) or with (B) the addition of ouabain (final concentration 1 mM, t = −15 min), incubated at 37°C. Molecular amounts (μmol) were estimated on the basis of the peak areas of the relevant NMR resonances for glucose (as shown in Fig. 2B), and calibrated against a standard (see Materials and Methods). (Solid lines) Model output (Eq. 1) using the maximum-probability parameter values given in Table 2. (Insets) Progressive ¹³C NMR spectra after the addition of monensin with and without ouabain as contained in their respective figures, with the central time of acquisition of each spectrum indicated on the figure.

Figure 5

Probability distributions of the estimated (A) net Na⁺ influx (with and without ouabain, as indicated by the key) and (B) NKA rate (taken from the difference in panel A) using a Bayesian analysis of the experimental time-course data (Figs. 3 and 4). (In each figure, the solid line indicates the position of maximum probability of the distribution of parameter values, whereas the shaded region denotes two SDs about this value and contains ∼95% of the probability density.) Assuming an RBC volume of 86 fL gives the relationship 1 mmol (L RBC)⁻¹ h⁻¹ = 14.4 × 10³ ions cell⁻¹ s⁻¹.

Figure 6

Probability distributions of the effective stoichiometry ratio between Na⁺ transported by NKA and the (indirect) glucose consumption as described by Eq. 14. The values of a₀(t), b₀, σ₀(t), and σ_b were estimated from the probability distributions of NKA activity (Fig. 5B) and ouabain-sensitive glycolytic rate (Table 2). (A) The change in the distribution of values of the stoichiometry ratio with time for discrete time points, as indicated by the key, is shown. (B) Distribution of the values of the stoichiometry ratio over the full duration of experiment is shown (solid red line indicates position of maximum probability); contours indicate 50, 70, 95, and 99% confidence intervals (integrals from the contours position to r = 6 contains this much probability density) as indicated on the figure. (The darker the shade between the contours, the greater is the probability.)