Free magnesium-ion concentration in erythrocytes by

NMR IN BIOMEDICINE, VOL. 10, 129–137 (1997)

Free Magnesium-Ion Concentration in Erythrocytes by 31P NMR: the Effect of Metabolite–Haemoglobin Interactions Peter J. Mulquiney and Philip W. Kuchelw Department of Biochemistry, University of Sydney, NSW 2006, Australia

The effects that haemoglobin–metabolite interactions have on estimates of free magnesium-ion concentration in human erythrocytes, determined by 31P NMR [Gupta, R. K. et al., J. Biol. Chem. 253, 6172–6176 (1978)], were investigated. If the metabolite–haemoglobin association constants of Berger et al. [Eur. J. Biochem. 38, 553–562 (1973)] are used in the analysis then the estimates of intracellular free magnesium-ion concentration made by Gupta et al. (0.25 and 0.67 mM) become 0.43 and 0.60 mM, for oxygenated and deoxygenated cells, respectively. In oxygenated cells, this difference is primarily due to the lower value of KHbMgATP, given by Berger et al. These newly calculated concentrations are in closer agreement with those of Flatman (0.40 mM for oxygenated cells; 0.62 mM for deoxygenated cells) [Flatman, P. W., J. Physiol. 300, 19–30 (1980)] obtained with the ‘zero-point titration’ method. In addition, the assumptions that the chemical shift separations between the a- and bphosphorus resonances of ATP and MgATP are unchanged on association with Hb were shown to be false. Under normal intracellular conditions this may lead to errors of 5–10%. Much larger errors would be possible in cases where significant amounts of ATP or MgATP are bound to Hb. These outcomes place doubt on measurements of intracellular free Mg2 + concentration made using 31P NMR if there is no consideration given to the total concentration of 2,3-bisphosphoglycerate (BPG), ATP and Hb in the sample; the same principle would apply to other cell-types. © 1997 John Wiley & Sons, Ltd. NMR Biomed. 10, 129–137 (1997)

No. of Figures: 2

No. of Tables: 4

No. of References: 41

31

Keywords: magnesium ion concentration; erythrocyte; P NMR; haemoglobin metabolite interaction Received 28 October 1996; revised 24 February 1997; accepted 24 February 1997

INTRODUCTION Gupta et al.1 introduced a 31P NMR method to measure intra-cellular free Mg2 + concentrations in erythrocytes; this technique has gained widespread use.2–18 Although some potential sources of error in the measurement have been noted, namely the value of the MgATP association constant used in the data analysis,13, 19–23 and the chemical-shift limits of the free and Mg2 + -bound forms of ATP,24 no investigation has been carried out on the effect of metabolite–haemoglobin (Hb) binding on these measurements. That no study of this nature appears to have been performed is surprising given that the zero-point titration (ZPT) method,25, 26 another commonly used one for determining intracellular free Mg2 + concentration, has consistently given values ~ 100% higher than those determined by the NMR method.1, 14, 18, 25, 27 In addition, the ZPT method indicates that intracellular free Mg2 + concentrations increase by only ~ 55% with deoxygenation, while measurements by 31P NMR indicate increases of ~ 160–170%. The most complete studies of metabolite binding to Hb have been performed by the groups of Rose1, 28, 29 and Rapoport.30 The data from these groups show two major differences. First, the binding constant characterising the w

Correspondence to: P. W. Kuchel at the Department of Biochemistry, University of Sydney, NSW 2006, Australia. Contract grant sponsor: Australian National Health and Medical Research Council. Contract grant sponsor: Australian Commonwealth Government.

© 1997 John Wiley & Sons, Ltd.

association of MgATP with oxygenated-Hb (oxyHb), obtained by Rose et al. is approximately five times larger than that obtained by the Rapoport et al. Second, values of the deoxygenated-Hb (deoxyHb)-MgATP binding constants obtained by Rose et al. are larger than those obtained by Rapoport et al. To our knowledge, all uses of the 31P NMR method to measure free Mg2 + in erythrocytes have employed the metabolite-Hb binding constants of Gupta et al.1, 28 In addition, many studies on intracellular free Mg2 + in oxygenated-erythrocytes have used a simplified 31P NMR method that neglects the effects of metabolite binding to Hb.2–13 This method implicitly assumes that ATP and MgATP bind to oxyHb with equal affinity. The use of 31P NMR to measure free Mg2 + in erythrocytes also relies on the assumptions that the chemical shift separations between the a- and b-phosphorus resonances of ATP and MgATP are unchanged on association with Hb. Although experimental evidence has been presented in support of this,1, 28 these experiments were performed at low field strength (40.5 MHz) and under conditions in which relatively low proportions of the ATP and MgATP would have been bound to Hb. Therefore, we have measured the effect of Hb on the 31P chemical shifts of ATP and MgATP at higher field strength and under conditions of higher Hb : metabolite association. In addition, we present a re-evaluation of the data of Gupta et al.1 using the metabolite–Hb association constants of Berger et al.,30 and show that the results then compare favourably with measurements of intracellular free Mg2 + made by the ZPT method. The general implications that CCC 0952–3480/97/030129–09 $17.50

130

P. J. MULQUINEY AND P. W. KUCHEL

these results have for measurements of intracellular free Mg2 + concentration in cells, using NMR spectroscopy, are discussed.

EXPERIMENTAL

Materials D2O (99.75%) was purchased from the Australian Institute for Nuclear Science and Engineering (Lucas Heights, NSW, Australia). Triethylphosphate and MgCl2 . 6H2O were obtained from BDH Chemicals Ltd. (Poole, UK). N2 and O2 were from BOC gasses (Chatswood, NSW, Australia), while CO was obtained from Commonwealth Industrial Gasses (Alexandria, NSW, Australia). Adenosine 5'-triphosphate (grade I; disodium salt), penicillin-G (sodium salt) and streptomycin sulfate were obtained from Sigma Chemical Co. (St Louis, MO, USA). Amphotericin B.P. was obtained from E.R. Squibb and Sons Pty. Ltd. (Melbourne, Victoria, Australia). All other reagents were A.R. grade.

NMR spectroscopy 31

P NMR spectra were acquired at 161.9 MHz on a Bruker AMX400 spectrometer (Bruker, Karlsruhe, Germany) with a wide-bore 9.4 T superconducting magnet (Oxford Instruments, Oxford, UK). Composite-pulse 1H WALTZ-16 decoupling31 was applied continuously to remove proton– phosphorus coupling. Sample heating caused by the decoupling was estimated to be ~ 2 °C by the method of Bubb et al.,32 and hence the temperature control on the spectrometer was set to 35 °C. All spectra were derived from 2 k transients, 10 k data points and a spectral width of 5 kHz. A pulse angle of p /6 and a repetition time of 1 s were used. D2O was used as a field/frequency lock. All chemical shifts were measured relative to triethyl phosphate (d 0.44 ppm relative to 85% H3PO4 at 0.000 ppm33 ). The centre of the a-ATP doublet and the central component of the b-ATP triplet were used for these chemical shifts. Hb solutions Haemoglobin was purified essentially according to the method described by Lennon et al.:34 Human erythrocyte suspensions obtained from the Red Cross Blood Transfusion Service (Sydney, NSW, Australia) were washed three times in four volumes of 150 mM KCl (which had been gassed with CO for 20 min) and then packed by centrifugation (3000g, 5 min, 4 °C). The supernatant was removed by aspiration, and the packed cells transferred to a separating funnel to which an equal volume of diethyl ether was added. The mixture was shaken vigorously to ensure complete lysis of the cells and maximum extraction of the membrane components into the ether phase, and then left to stand for 2 h at 4 °C. The lower aqueous phase was then centrifuged (8000g, 20 min), and the uppermost portion (containing residual ether) was discarded. The remaining solution was filtered through Whatman no. 1 paper (Whatman, Ltd., Maidstone, UK) in a Buchner funnel. Residual ether was removed by rotary evaporation under reduced pressure © 1997 John Wiley & Sons, Ltd.

(room temperature, 45 min). The resulting (dilute) Hb solution was gently swirled in the presence of humidified CO to ensure CO saturation of the Hb. The solution was then washed with ~ 20 volumes of 150 mM KCl containing low concentrations of antibiotics (2.5 mg L 2 1 amphotericin B.P., 27 mg L 2 1 penicillin G, and 50 mg L 2 1 streptomyocin sulfate) by diafiltration (over 72 h) and then concentrated in an Amicon (Danvers, MA) ultrafiltration cell (Diaflo YM 10 membrane) at 4 °C, under 300 kPa pressure provided by a nitrogen cylinder. The concentrated Hb solution was then resaturated with humidified CO and stored at 2 4 °C until required. Carbonmonoxygenated-Hb (carbonmonoxyHb) was converted to oxyHb according to the method of Lennon et al.34 In experiments with carbonmonoxyHb, concentrated Hb aliquots were thawed and resaturated with humidified CO for 5 min. NMR samples were prepared by adding concentrated carbonmonoxyHb or oxyHb to a solution containing ATP (final concentration ~ 4 mM), 100 mM triethanolamine 150 mM KCl (pH 6.9) and a calibrated volume of 0.15 M KOH. 150 mM KCl in D2O (final concentration 10% v/v) and triethyl phosphate (final concentration 5 mM) were added to each sample, while 1 M MgCl2 was added to some samples (final concentration ~ 10 mM). The pH was then determined using a glass-body combination pH probe with a calomel reference designed for use with protein solutions (model no. AEP342, Activon Scientific Products, Thornleigh, NSW, Australia). 3 mL of the sample was then loaded into a 10 mm o.d. NMR tube (Wilmad, Buena, NJ, USA), and humidified CO or O2 was blown above the sample before the tube was capped, and sealed with Parafilm (American Can Company, Greenwich, CT). Some samples containing oxyHb were converted to samples containing deoxyHb by gassing with humidified N2 for 20 min in a rotating tonometer. These samples were loaded into NMR tubes with humidified N2 layered above. The percentage of metHb was measured for all samples using the spectroscopic method of Van Kampen and Zijlstra35 and found to be below 8%. Final Hb concentration in the NMR samples were determined at the completion of the experiment using one of the functions of a Sysmex CC130 particle counter (Toa Medical Electronics, Kobe, Japan). The measurements were shown to be within 1% of the Hb concentration determined using the cyanomethaemoglobin method (« = 44 mM 2 1 cm 2 1 for tetrameric Hb36). The concentration of Mg2 + in concentrated Hb solutions was found to be less than 30 mM in all samples by atomic absorption spectroscopy (SpectrAA-20-Plus, Varian Pty. Ltd., Mulgrave, Victoria, Australia).

THEORY The basic assumptions about the 31P NMR chemical shifts of the ATP resonances for the free and Mg-bound states, used in the following analysis, are the same as those originally used by Gupta et al.;1 the new development here is eq. (6), which accounts for the effect of other metabolite– Hb interactions on the estimates. Assuming that the only other species in the human erythrocyte which bind significant amounts of Mg2 + and Hb, are ATP and BPG,30 the following relationships can be derived from the conservation of mass equations for each of the species: NMR IN BIOMEDICINE, VOL. 10, 129–137 (1997)

FREE MAGNESIUM-ION CONCENTRATION

[BPG]f =

[BPG]T 1 + [Mg]fKMgBPG + [Hb]fKHbBPG

(1)

[ATP]T 1 + [Mg]fKMgATP + [Hb]fKHbATP + [Mg]f[Hb]fKMgATPKHbMgATP

[ATP]f =

(2)

[Hb]T 2 [Hb]f(1 + [BPG]fKHbBPG + [ATP]fKHbATP + [Mg]f[ATP]fKMgATPKHbMgATP) = 0 (3) where the subscripts f and T denote free and total concentrations, respectively, and Kx is the association constant for species X. Defining F=

[ATP]f + [HbATP] [ATP]T

(4)

it is readily shown , using the basic procedure employed by Gupta et al.,1 that F=

d 2d 2d

obs MgATP/HbMgATP ab ab ATP/HbATP MgATP/HbMgATP ab ab

d

1 KMgATP

S DS 12F F

D

1 + [Hb]fKHbATP . 1 + [Hb]fKHbMgATP

(6)

Thus [Mg]f is a function of two variables: the experimentally determined F and [Hb]f. By measuring F, [Hb]T, [ATP]T and [BPG]T, it is possible to use these values to solve eqs (6) and (3), simultaneously, to determine the values of [Mg]f and [Hb]f; this was readily accomplished by substituting eq. (6) into eq. (3) and using Newton’s method to solve these non-linear algebraic equations for [Hb]f. The concentrations of all other species were then readily calculated by substitution, using eqns (6), (1) and (2). The present analysis is different from that of Gupta et al.;1 they introduced the extra variable

u=

[ATP]T [ATP]f

(7)

and evaluations of [Mg]f involved solving simulateous equations for u (or [ATP]f) and [Mg]f, as opposed to our use of [Hb]f and [Mg]f. The advantage of using the present method is that the functions are numerically ‘better behaved’ than the previous ones of Gupta et al.,1 thus enabling less problematic application of Newton’s method (see below). For all values of F used, an initial estimate of [Hb]f, that was between 0 and [Hb]T, routinely yielded the appropriate root (estimate of concentration). The numerical analyses were performed with Mathematica; a copy of the program is given in the Appendix. In all calculations, dissociation constants of 0.038 mM and 1.5 mM for MgATP and MgBPG,1 respectively, were used. © 1997 John Wiley & Sons, Ltd.

RESULTS

Effect of the values of Hb–metabolite binding constants on the determination of intracellular Mg2 + by 31P NMR Table 1 shows the previously reported association constants for ATP, MgATP and BPG with Hb. Table 2 is a comparison of the results of Gupta et al.1 with those recalculated using the association constants of Berger et al.30 (Table 1). For oxygenated cells the differences in the estimates of the concentrations of the species arise largely from the difference in KHbMgATP . When [Mg]f is calculated using the values of Gupta et al.1 for all constants except KHbMgATP , a value of 0.39 mM is obtained. For deoxygenated cells, the lower value of [Mg]f calculated using the constants of Berger et al.30 is a result of the lower association constants relative to those of Gupta et al.1 Table 3 shows the recalculated values of [Mg]f using data from another source17, 18 and compares them to results obtained using other methods.

(5)

31 where dobs ab is the P NMR chemical shift separation (in Hz) between the a- and b-phosphorus resonances of ATP observed in erythrocytes, dATP/HbATP is the shift separation ab of free ATP and HbATP, and dMgATP/HbMgATP is the ab shift separation of MgATP and HbMgATP. In other words HbATP the derivation of eq. (5) requires that dATP and ab = d ab MgATP HbMgATP . Thus, from eq. (4) it can be shown thatdab = dab that

[Mg]f =

131

Effect of Hb and Mg2 + on the chemical shift difference between the a- and b-phosphate resonances of ATP The chemical shift separation between the a- and bphosphorus resonances of ATP (dobs ab ) was shown to vary with different Hb concentrations and oxygenation states in the presence and absence of Mg2 + (Table 4). Assuming that ATP is present in only four different species in the samples (ATP, MgATP, HbATP and HbMgATP) and assuming that these are in rapid equilibrium (on the NMR timescale), then dobs is equal to the concentrationab weighted average of the chemical shifts for each of these four individual species. From this assumption it was possible to calculate dobs ab for each sample to within 6 Hz HbATP with dATP = 1794 Hz, d = 1704 Hz, dMgATP = 1333 Hz and ab ab ab HbMgATP dab = 1407 Hz. Thus the binding of Hb to ATP causes a 5% decrease in dab, while the binding of Hb to MgATP causes a 6% increase in dab. When dobs ab was optimized for each different oxygenation state alone dHbATP varied from ab varied from 1370 to 1703 to 1706 Hz, while dHbMgATP ab 1423 Hz. DISCUSSION

Effect of the values of Hb–metabolite binding constants on the determination of intracellular Mg2 + by 31P NMR From Table 3 it is seen that measurements of [Mg]f calculated with the constants of Berger et al.30 are in good agreement with values obtained by the ZPT method. Table 1. Association constants for Mg2 + and haemoglobin complexes of ATP and BPG at pH 7.2, 37°C and m ~ 0.15 from two different literature sources Association constant (M 2 1)

OxyHb Gupta et al.1 Berger et al.30

DeoxyHb Gupta et al.1 Berger et al.30

KHbATP KHbMgATP KHbBPG

2.92 3 10 1.9 3 102 2.11 3 102

7.87 3 103 8.70 3 102 9.71 3 103

2

3.6 3 10 3.9 3 10 2.5 3 102 2

2.6 3 103 1.4 3 102 5.0 3 103


132


Table 2. The distribution of Hb, ATP, BPG and Mg2 + in the human erythrocytea calculated from the data of Gupta et al.1 using their association constants (A) and those of Berger et al.30 (B) Molecular/ionic species

Intracellular concentration Oxygenated Non-oxygenated A B A B b b mM (%) mM (%) mM (%)b mM (%)b

Mg2 + MgTc

0.25 (10) 2.45 (100)

0.43 (15) 2.84 (100)

0.67 (27) 2.49 (100)

0.60 (25) 2.44 (100)

ATP MgATP HbATP HbMgATP

0.16 (7) 1.00 (49) 0.18 (9) 0.74 (35)

0.13 (6) 1.51 (72) 0.20 (10) 0.25 (12)

0.05 (2) 0.83 (40) 0.41 (20) 0.80 (38)

0.08 (4) 1.31 (63) 0.38 (18) 0.32 (15)

BPG MgBPG HbBPG

2.69 (50) 0.44 (8) 2.21 (41)

2.29 (43) 0.66 (12) 2.39 (45)

0.44 (8) 0.20 (4) 4.71 (88)

0.53 (10) 0.21 (4) 4.6 (86)

Hb HbATP HbMgATP HbBPG

3.9 (56) 0.18 (3) 0.74 (11) 2.21 (31)

4.18 (60) 0.20 (3) 0.25 (4) 2.39 (34)

1.10 (16) 0.41 (6) 0.80 (11) 4.71 (67)

1.73 (25) 0.38 (5) 0.32 (5) 4.6 (66)

[ATP]T, 2.09 mM; [BPG]T, 5.34 mM; [Hb]T, 7.02 mM; F, 0.16 and 0.22 in aerobic and anaerobic cells, respectively. b Percentage values refer to percentage of [Mg]T, [ATP]T, [BPG]T and [Hb]T, respectively. c MgT refers to the sum of the concentrations of all the magnesium-containing complexes and free magnesium. a

Table 3. Comparison between erythrocyte intracellular free Mg2 + concentrations determined with a variety of experimental methods Oxygenated cells (mM)

Method

[Mg]f Deoxygenated cells (mM)

Relative change (%)

Reference

31

P NMR–Hb association constants from Gupta et al.1

0.25 0.194 0.200

0.67 0.50

168 158

1 17, 18 14a

31

P NMR–Hb association constants from Berger et al.30

0.43 0.300

0.60 0.450

40 50

1 17, 18

Zero-point titration

0.40 0.311 0.55

0.62

55

25 37 14

Ion-exchange method with haemolysate

0.45

0.57

27

38

a

The study of Geven et al.14 is the only one which directly compares the NMR and ZPT methods. However, because values for [Hb]T, [ATP]T and [BPG]T were not given in this paper, a recalculation [Mg]f could not be performed.

Table 4. Effect of Hb and Mg2 + on the chemical shift difference between the a- and bphosphate resonances of ATPa Hb oxygenation state

Hb concentration (mM)

ATP boundb (%)

MgATP boundb (%)

MgATP freeb (%)

dab measured (Hz)

dab predictedc (Hz)

No Hb — 0.0 ± 0.0 — — 1794 ± 7 1794 ± 0 CarbonmonoxyHb 1.81 33.1 — — 1761 1764 CarbonmonoxyHb 3.50 ± 0.03 55.2 ± 0.6 — — 1747 ± 2 1744 ± 1 OxyHb 3.65 ± 0.10 57.1 ± 1.7 — — 1742 ± 1 1743 ± 2 DeoxyHb 3.79 ± 0.16 79.5 ± 1.8 — — 1722 ± 1 1722 ± 2 No Hb — — — 99.3 ± 0.0 1336 ± 6 1336 ± 0 CarbonmonoxyHb 3.30 ± 0.01 1.3 ± 0.0 19.6 ± 0.2 78.6 ± 0.2 1348 ± 2 1354 ± 0 OxyHb 3.38 ± 0.02 1.3 ± 0.0 20.1 ± 0.2 78.1 ± 0.2 1351 ± 1 1354 ± 0 DeoxyHb 3.74 ± 0.14 4.9 ± 0.1 37.2 ± 0.2 57.5 ± 0.2 1387 ± 1 1381 ± 2 a Mean pH of samples, 6.89 ± 0.02; mean [ATP], 3.92 ± 0.11; mean [Mg2 + ], 9.85 ± 0.27. All values, mean ± maximum deviation; samples without Hb, n = 4; samples with Hb, n = 2. b Values calculated using the model of Mulquiney and Kuchel.39 c HbATP Predicted values calculated assuming that dATP = 1704 Hz, dMgATP = 1333 Hz ab = 1794 Hz, dab ab and dHbMgATP = 1407 Hz. These parameters were determined from the data using a leastab squares fitting method.




Assuming ZPT to yield an accurate estimate of free Mg2 + concentration, this implies that the binding constants of Berger et al.30 are a better description of in vivo binding. This conclusion is also supported by the work of Lennon et al.:33 in a study of Hb affinity for BPG in intact erythrocytes using pulsed-field gradient NMR, they found that the association constants reported by Berger et al.30 described the relative affinities of deoxyHb and oxyHb for BPG in a manner that was more consistent with their data, than those of Hamasaki and Rose.29 In addition, the values of Berger et al.30 are in better agreement with the data of Garby et al.;40 at pH 7.2 with [Hb]T = 3.1 mM, [ATP]T = 1.0 mM and [Mg2 + ]T = 3.0 mM, these workers measured that ~ 0.05 moles of ATP were bound per mole of Hb. Using the association constants of Gupta et al.1 a value of 0.11 was calculated for the same experimental conditions. The Hb– ligand association constants of Berger et al.30 gave a value of 0.04. However, it should be noted that the measurements of Garby et al.40 were made at 0 °C, and since metabolite– Hb binding decreases with an increase in temperature29 it is expected that the value of 0.05 would be an overestimate at 37 °C. The same trend was found with the data obtained by Garby et al.40 with deoxygenated haemoglobin; they measured an ATP : Hb mole ratio of 0.15, while the values calculated with the binding constants of Gupta et al.,1 and Berger et al.30 were 0.231 and 0.11, respectively. There appears to be another problem with the way that Gupta et al.28 determined KHbMgATP. The constant was calculated from small (0–2 Hz) changes in dobs ab that occurred in various mixtures of Mg and ATP on addition of oxyHb. Their method of estimating the binding constants required a knowledge of [Hb]T, [ATP]T and [Mg]T as well as KHbATP, KHbMgATP, and dobs ab . A test of their newly calculated value for KHbMgATP, was that they were able to calculate dobs ab to within ± 1 Hz for 11 different solutions with various concentrations of ATP, Mg and oxyHb. The inadequacy of this method is shown by the fact that on repeating these calculations using the values of Berger et al.30 for KHbATP and KHbMgATP, and with a slightly larger value of KMgATP (although still within the experimental error for KMgATP), it was possible to calculate dobs ab to within ± 1 Hz for nine out of 11 of the solutions and to within 2 Hz for the remaining two solutions. Also, assuming that each 31P NMR chemical shift can be measured to a precision of ± 1 Hz, the best precision that can be achieved for a measurement of dobs ab is ± 2 Hz. Thus it seems valid to assume that no change was observed in dobs ab on addition of oxyHb, thus making a value of KHbATP = KHbMgATP satisfy these data as well. The ZPT method involves treating cells with the ionophore A23187. The ionophore does not alter the quantity or nature of the intracellular magnesium buffers, and thus the ionophore-treated cell is thought to have the same intracellular environment as the untreated cell.25, 26 It is suggested, however, that the washing process used for the ZPT method may cause a decrease in ATP concentration (6–15%), thus causing an increase in [Mg]f.14 The advantage of ZPT over the NMR method is that it requires no assumptions or knowledge about Mg2 + or Hb binding to ATP.

133

F=

[ATP]f [ATP]T

(8)

and hence that

[Mg]f =

S D

12F 1 . KMgATP F

(9)

In other words the free Mg2 + concentration is estimated without knowledge of [Hb]T, [ATP]T and [BPG]T. Despite being shown to give inaccurate values for deoxygenated cells41 it is still (erroneously, in our opinion) widely used for studies on oxygenated cells. From eq. (6) it can be seen that eq. (9) is only valid if: KHbATP = KHbMgATP; or if [Hb]f = 0. In erythrocytes eq. (9) can only apply if KHbATP = KHbMgATP. Hence this is why the 31P NMR method does not give the correct estimate of free Mg2 + for deoxygenated cells (since KHbATP @ KHbMgATP). In conclusion, it appears likely that eq. (9) will not be applicable to oxygenated cells as well. The ‘true’ value of free Mg2 + relative to what would be calculated from 31P NMR measurements using eq. (9) ([Mg]o) is given by [Mg]f 1 + [Hb]fKHbATP = . [Mg]o 1 + [Hb]fKHbMgATP

(10)

Thus the error arising from eq. (9) will depend only on [Hb]f, KHbATP and KHbMgATP. In oxygenated erythrocytes [Hb]f is typically around 4 mM.39 At this value of [Hb]f, and using the values of KHbATP and KHbMgATP given by Gupta et al.,1 the ‘true’ value of [Mg2 + ]f is 23% larger than the value determined by eq. (9). When the KHbATP and KHbMgATP values from Berger et al.30 are used the ‘true’ value of [Mg2 + ]f is 111% higher. Thus application of eq. (9) may produce large errors in the estimate of the absolute value of free [Mg2 + ], determined by NMR spectroscopy. The actual size of the discrepancy clearly depends on the ‘true’ values of KHbATP and KHbMgATP. If KHbATP > KHbMgATP the error resulting from eq. (9) will increase with an increase in [Hb]f (eq. (10), Fig. 1). Since [Hb]f depends on the total concentrations of Mg2 + , Hb, ATP and BPG in the erythrocyte, different concentrations of these metabolites will yield different values of [Hb]f and hence different relative errors in [Mg2 + ]f measured using eq. (9). Thus relative changes in [Mg2 + ]f measured using eq. (9) may be in error as well. According to eq. (9) all samples

Effect of neglecting metabolite–Hb interactions In many studies on free Mg2 + in erythrocytes ATP : Hb interactions have been ignored.2–13 These studies have assumed that © 1997 John Wiley & Sons, Ltd.

Figure 1. The concentration of free Mg2 + ([Mg]f) as a function of [Hb]f relative to the value at [Hb]f = 0 mM ([Mg]0) calculated from eq. (10); (——), association constants of Berger et al.;30 (– – –), association constant of Gupta et al.1 NMR IN BIOMEDICINE, VOL. 10, 129–137 (1997)

134


with the same F have the same concentration of free Mg2 + . However, if [Hb]f = 5 mM in one sample and 4 mM in another, and both give the same value of F, then from eq. (6) [Mg]f in the sample with [Hb]f = 5 mM will be 12% greater than that in the other sample, assuming that the binding constants of Berger et al.30 apply. This situation would occur with [Hb]T = 7 mM, [ATP]T = 2 mM, [BPG]T = 6 mM and [Mg2 + ]T = 2.6 mM in one sample and [Hb]T = 7 mM, [ATP]T = 2 mM, [BPG]T = 3 mM and [Mg2 + ]T = 2.3 mM in the other. Conversely, a change in [Mg]f may be predicted from 31P NMR data by using eq. (9), but in fact the data may simply reflect changes in [Hb]T, [ATP]T or [BPG]T. For example, a change in F which, from eq. (9), would imply a 10% decrease in [Mg]f can be fully explained by an increase in [Hb]f from 4 to 5 mM rather than a decrease in [Mg]f, assuming that the binding constants of Berger et al.30 apply. To illustrate how changing total concentrations of a metabolite ([Hb]T, [ATP]T, and [BPG]T) can affect the accuracy of [Mg]f determinations made using 31P NMR, the theoretical values of [Mg]f and F were calculated for a system containing 7 mM Hb, 2.1 mM ATP, 3 mM Mg2 + , and from 0 to 8 mM BPG using the association constants of Berger et al.30 Then, the theoretical values of F were used to determine [Mg]f by using eqs (1)–(6) in the analysis employed with 31P NMR data, but now using the association constants of Gupta et al.1 Figure 2 shows the results of these calculations; it was found that at normal intracellular concentrations of BPG ( ~ 6 mM) the 31P NMR method with the association constants of Gupta et al.1 underestimated the ‘true’ value of [Mg]f by ~ 40%, while the method using eq. (9) underestimated it by ~ 50%. At [BPG]T = 0 these errors increased to ~ 50 and ~ 60%, respectively. The method of determining free Mg2 + by using eq. (9) was first applied to erythrocytes by Resnick et al.11 In their paper the neglect of metabolite binding to Hb was justified by reporting that dobs ab did not change when oxyHb was added to solutions containing Hb and MgATP. As mentioned above, in earlier work Gupta et al.28 found a small (0–2 Hz) change in dobs ab ; however, this can be considered to be within experimental error. From the new analysis presented here it is seen that the fact that oxyHb does not alter the value of F

(within experimental error) is not sufficient in itself to enable one to ignore the effect of metabolite binding to Hb; to justifiably ignore these interactions it would be necessary that KHbATP = KHbMgATP, and this is not the case.

Validity of the assumption that Hb has no effect on the chemical shift difference between the a- and bphosphate resonances of ATP and MgATP The derivation of eq. (6) relies on the assumptions that HbATP dATP and that dMgATP = dHbMgATP . These assumptions a b = d ab ab ab were supported previously by work on solutions containing 4 mM ATP and 2 mM Hb at pH 7.2. However, under these conditions significant amounts of ATP and MgATP would have remained unbound to Hb. We calculated using the model of Mulquiney and Kuchel39 that the shifts obtainable 28 in dobs ab from the samples of Gupta et al. ranged from 2 to 9 Hz; not much larger than the reported error in a single measurement of ± 2 Hz. By reducing the pH to 6.9 and increasing the concentration of Hb, it was possible to increase the percentage of ATP and MgATP bound. In addition, the previous experiments were carried out at low field strength (40.5 MHz). At 40.5 MHz dATP ab was measured to be only 438 Hz, while at 161.9 MHz it was measured to be 1794 Hz. MgATP on binding to Hb The detected changes in dATP ab and dab HbATP HbMgATP are quite large; but dab 2 dab is only 64% of MgATP dATP . This finding therefore places doubt on the ab 2 d ab assumptions used to derive eq. (5) and hence on the equality of the RHS of eq. (4) with the RHS of eq. (5). According to binding analysis,39 human erythrocytes, fully oxygenated at pH 7.2, have ATP partitioned in the following ratios: free ATP, 0.07; HbATP, 0.10; MgATP, 0.72; HbMgATP, 0.11. From these data it can be calculated that the standard 31P NMR method will overestimate the true concentration of free Mg2 + by 4.4%. In deoxygenated cells at pH 7.2, and overestimate of 9.4% would be made. The errors are relatively small because the concentration of HbATP and HbMgATP are low in both cases; namely, 21% in oxygenated cells and 26% in deoxygenated cells. However, these errors would become much larger under conditions where significant amounts of MgATP or ATP were bound to Hb, such as would occur with elevated Hb concentrations.

CONCLUSION

Figure 2. The concentration of free Mg2 + as a function of total concentration of BPG in a model of Mg2 + binding in human erythrocytes. The concentration of free Mg2 + and F were calculated using the association constants of Berger et al.30 as a function of [BPG]T for a system containing 7 mM Hb, 2.1 mM ATP, and 3 mM Mg2 + : (——) shows the calculated values of [Mg]f; (– – –) shows the values of [Mg]f that would be calculated using the theoretical values of F and the 31P NMR method with the association constants of Gupta et al.1 used in eqs (1)–(6), and (- · - · -) shows the values of [Mg]f determined using the theoretical values of F and eq. (9). © 1997 John Wiley & Sons, Ltd.

The values estimated for intracellular [Mg2 + ]f by using 31P NMR data are in closer agreement with those determined by the ZPT method if the Hb association constants of Berger et al.30 are used in the analysis, rather than those of Gupta et al.1 If ZPT values of [Mg2 + ]f are valid then this implies that the association constants of Berger et al.30 describe the association of metabolites with Hb in vivo more accurately than those of Gupta et al. In oxygenated cells, the different estimates are primarily due to the lower value of KHbMgATP measured by Berger et al.30 In addition, the assumptions that the chemical shift differences between the a- and bphosphorus peaks of ATP and MgATP are unchanged on association with Hb were shown to be false. Under normal intracellular conditions this may lead to errors of 5–10% in the determined value of free Mg2 + . Much larger errors NMR IN BIOMEDICINE, VOL. 10, 129–137 (1997)


would occur in cases where significant amounts of ATP or MgATP were bound to Hb. These outcomes place doubt on measurements of intracellular free Mg2 + concentration made using 31P NMR if there is no consideration given to the total concentration of BPG, ATP and Hb in the sample.

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Acknowledgements Dr Julia Raftos is thanked for valuable discussions. This work was supported by a grant to P.W.K. from the Australian National Health and Medical Research Council. P.J.M. received an Australian Postgraduate Research Award from the Australian Commonwealth Government.

REFERENCES

1. Gupta, R. K., Benovic, J. L. and Rose, Z. B. The determination of the free magnesium level in the human red blood cell by 31P NMR. J. Biol. Chem. 253, 6172–6176 (1978). 2. Barbagallo, M., Gupta, R. K. and Resnick, L. M. Cellular ionic effects of insulin in normal human erythrocytes: a nuclear magnetic resonance study. Diabetologia 36, 146–149 (1993). 3. Bock, J. L., Wenz, B. and Gupta, R. K. Studies on the mechanism of decreased NMR-measured free magnesium in stored erythrocytes. Biochim. Biophys. Acta 928, 8–12 (1987). 4. Bock, J. L., Wenz, B. and Gupta, R. K. Changes in intracellular Mg adenosine triphosphate and ionised Mg2 + during blood storage: detection by 31P nuclear magnetic resonance spectroscopy. Blood 65, 1526–1530 (1985). 5. Jelicks, L. A., Weaver, J., Pollack, S. and Gupta, R. K. NMR studies of intracellular free calcium free magnesium and sodium in the guinea pig reticulocyte and mature red cell. Biochim. Biophys. Acta 1012, 261–266 (1989). 6. Resnick, L. M., Altura, B. T., Gupta, R. K., Laragh, J. H., Alderman, M. H. and Altura, B. M. Intracellular and extracellular magnesium depletion in type 2 (non-insulin dependent) diabetes mellitus. Diabetologia 36, 767–770 (1993). 7. Resnick, L. M., Barbagallo, M., Gupta, R. K. and Laragh, J. H. Ionic basis of hypertension in diabetes mellitus. Role of hyperglycemia. Am. J. Hyperten. 6, 413–417 (1993). 8. Resnick, L. M., Gupta, R. K., Bhargava, K. K., Gruenspan, H., Alderman, M. H. and Laragh, J. H. Cellular ions in hypertension, diabetes, and obesity. A nuclear magnetic resonance spectroscopy study. Hypertension 17, 951–957 (1991). 9. Resnick, L. M., Gupta, R. K. and Laragh, J. H. Possible effects of diet and other factors on 31P nuclear magnetic resonance measurement of intracellular magnesium in hypertension. Clin. Sci. 76, 565–566 (1989). 10. Resnick, L. M., Gupta, R. K., Sosa, R. E., Corbett, M. L. and Laragh, J. H. Intracellular pH in human and experimental hypertension. Proc. Natl Acad. Sci. U.S.A. 84, 7663–7667 (1987). 11. Resnick, L. M., Gupta, R. K. and Laragh, J. H. Intracellular free magnesium in erythrocytes of essential hypertension: relation to blood pressure and serum divalent cations. Proc. Natl Acad. Sci. U.S.A. 81, 6511–6515 (1984). 12. van Waarde, A., Lombarts, A., van den Thillart, G., Erkelens, C. and Lugtenberg, J. 31P NMR studies on rejuvenation of outdated red blood cells: complete regeneration of ATP is accompanied by partial Mg–ATP recomplexation. Haematologia 22(2), 79–87 (1989). 13. Woods, K. L., Walmsley, D., Heagerty, A. M., Turner, D. L. and Lian, L. Y. 31P nuclear magnetic resonance measurement of free erythrocyte magnesium concentration in man and its relation to blood pressure. Clin. Sci. 74, 513–517 (1988). 14. Geven, W. B., Vogels-Mentink, G. M., Willems, J. L., Os, C. H. v., Hilbers, C. W., Joordens, J. J. M., Rijksen, G. and Monnens, L. A. H. 31P nuclear magnetic resonance and zero-point titration compared for measuring free magnesium concentration in erythrocytes. Clin. Chem. 37, 2076–2080 (1991). 15. Matsuura, T., Kanayama, Y., Inoue, T., Takeda, T. and Morishima, I. cAMP-induced changes of intracellular free Mg2 + levels in human erythrocytes. Biochim. Biophys. Acta 1220, 31–36 (1993). 16. Matsuura, T., Kohno, M., Kanayama, Y., Yasunari, K., Maurakawa, K., Takeda, T., Ishimori, K., Morishima, I. and Yonezawa, T. Decreases in intracellular free magnesium in erythrocytes of spontaneously hypertensive rats. Biochem. Biophys. Res. Commun. 143, 1012–1017 (1987). © 1997 John Wiley & Sons, Ltd.

17. Ouwerkerk, R., van Echteld, C. J. A., Staal, G. E. J. and Rijksen, G. Intracellular free magnesium and phosphorylated metabolites in hexokinase- and pyruvate kinase-deficient red cells measured using 31P-NMR spectroscopy. Biochim. Biophys. Acta 1010, 294–303 (1989). 18. Ouwerkerk, R., van Echteld, C. J. A., Staal, G. E. J. and Rijksen, G. Distribution of phosphorylated metabolites and magnesium in the red cells of a patient with hyperactive pyruvate kinase. Blood 72, 1224–1229 (1988). 19. Gupta, R. K. and Gupta, P. NMR studies of intracellular metal ions in intact cells and tissues. Ann. Rev. Biophys. Bioeng. 13, 221–246 (1984). 20. Gupta, R. K., Gupta, P., Yushok, W. D. and Rose, Z. B. Measurement of the dissociation constant of MgATP at physiological nucleotide levels by a combination of 31P NMR and optical absorbance spectroscopy. Biochem. Biophys. Res. Commun. 117, 210–216 (1983). 21. Gupta, R. K., Gupta, P., Yushok, W. D. and Rose, Z. B. On the non-invasive measurement of intracellular free magnesium by 31P NMR spectroscopy. Physiol. Chem. Phys. Med. NMR 15, 265–80 (1983). 22. Garfinkel, L. and Garfinkel, D. Calculation of free-Mg2 + concentation in adenosine 59-triphosphate containing solutions in vitro and in vivo. Biochemistry 23, 3547–3552 (1984). 23. Wu, S. T., Pieper, G. M., Salhany, J. M. and Eliot, R. S. Measurement of free magnesium in perfused and ischemic arrested heart muscle. A quantitative phosphorus-31 nuclear magnetic resonance and multiequilibria analysis. Biochemistry 20, 7399–7403 (1981). 24. Mosher, T. J., Williams, G. D., Doumen, C., LaNoue, K. F. and Smith, M. B. Error in the calibration of the MgATP chemical-shift limit: effects on the determination of free magnesium by 31P NMR spectroscopy. Magn. Reson. Med. 24, 163–169 (1992). 25. Flatman, P. W. The effect of buffer composition and deoxygenation on the concentration of ionized magnesium inside human red blood cells. J. Physiol. 300, 19–30 (1980). 26. Flatman, P. and Lew, V. L. Use of ionophore A23187 to measure and to control free and bound cytoplasmic Mg in intact red cells. Nature 267, 360–362 (1977). 27. Millart, H., Durlach, V. and Durlach, J. Red blood cell magnesium concentrations: analytical problems and significance. Magnes. Res. 8, 65–76 (1995). 28. Gupta, R. K., Benovic, J. L. and Rose, Z. B. Magnetic resonance studies of the binding of ATP and cations to human hemoglobin. J. Biol. Chem. 253, 6165–6171 (1978). 29. Hamasaki, N. and Rose, Z. B. The binding of phosphorylated red cell metabolites to human hemoglobin A. J. Biol. Chem. 249, 7896–7901 (1974). 30. Berger, H., Jänig, G.-R., Gerber, G., Ruckpaul, K. and Rapoport, S. M. Interaction of haemoglobin with ions: interactions among magnesium, adenosine 59-triphosphate, 2,3-bisphosphoglycerate, and oxygenated and deoxygenated human haemoglobin under simulated intracellular conditions. Eur. J. Biochem. 38, 553–562 (1973). 31. Shaka, A. J., Keeler, J., Frenkeil, T. and Freeman, R. An improved sequence for broadband decoupling: WALTZ-16. J. Magn. Reson. 52, 335–338 (1983). 32. Bubb, W. A., Kirk, K. and Kuchel, P. W. Ethylene glycol as an X nucleus thermometer for biological samples. J. Magn. Reson. 77, 363–368 (1988). 33. Kirk, K., Raftos, J. E. and Kuchel, P. W. Triethyl phosphate as an internal 31P NMR reference in biological samples. J. Magn. Reson. 70, 484–487 (1986). 34. Lennon, A. J., Scott, N. R., Chapman, B. E. and Kuchel, P. W. Hemoglobin affinity for 2,3-bisphosphoglycerate in soluNMR IN BIOMEDICINE, VOL. 10, 129–137 (1997)

136

35. 36. 37. 38.

P. J. MULQUINEY AND P. W. KUCHEL tions and intact erythrocytes: studies using pulsed-field gradient nuclear magnetic resonance and Monte Carlo simulations. Biophys. J. 67, 2096–2109 (1994). van Kampen, E. J. and Zijlstra, W. G. Determination of hemoglobin and its derivatives. Adv. Clin. Chem. 8, 141–187 (1965). van Kampen, E. J. and Zijlstra, W. G. Standardization of hemoglobinometry. II. The hemiglobincyanide method. Clin. Chim. Acta 6, 538–544 (1961). Bock, J. L. and Yusif, Y. Further studies on alterations in magnesium binding during cold storage of erythrocytes. Biochim. Biophys. Acta 941, 225–231 (1988). Achilles, W., Kluger, R., Scheidt, B. and Frunder, H. Determination of the concentration of free magnesium ions in haemolysates of oxygenated and deoxygenated packed

human erythrocytes (in German). Acta Biol. Med. Germ. 37, 1161–1166 (1978). 39. Mulquiney, P. J. and Kuchel, P. W. Model of the pHdependence of the concentrations of complexes involving metabolites, haemoglobin and magnesium ions in the human erythrocyte. Eur. J. Biochem. 245, 71–83 (1997). 40. Garby, L., Gerber, G. and de Verdier, C.-H. Binding of 2,3-diphosphoglycerate and adenosine triphosphate to human haemoglobin A. Eur. J. Biochem. 10, 110–115 (1969). 41. Peterson, A., Kristensen, S. R., Jacobsen, J. P. and Hørder, M. 31P-NMR measurements of ATP, ADP, 2,3-diphosphoglycerate and Mg2 + in human erythrocytes. Biochim. Biophys. Acta 1035, 169–174 (1990).

APPENDIX The Mathematica program, used for determining [Mg]f. **** Input: Total Concentrations of Metabolites (M) **** ^ ATPt = 2.09*10 -3; (*total ATP concentration*) ^ BPGt = 5.34*10 -3; (*total BPG concentration*) ^ Hbt = 7.02*10 -3; (*total Hb concentration*) **** Input: Association Constants of Complexes (M 2 1) **** Kmgatp = 1/0.000038; (*Association constant for the MgATP complex*) Kmgbpg = 1/0.0015; (*Association constant for the MgBPG complex*) Khbmgatp = 39; (*Association constant for the HbMgATP complex*) Khbatp = 360; (*Association constant for the HbATP complex*) Khbbpg = 250; (*Association constant for the HbBPG complex*) **** Value of f **** q1 = 0.16; **** Eqn 1 **** BPG1Hb ,q ] = BPGt/(1 + Mg[Hb,q]*Kmgbpg + Hb*Khbbpg); **** Eqn 2 **** ATP[Hb ,q ] = ATPt/(1 + Mg[Hb,q]*Kmgatp + Hb*Khbatp + Mg[Hb,q]*Hb*Kmgatp*Khbmgatp); **** Eqn 6 **** Mg[Hb ,q ] = (1 2 q)/(q*Kmgatp)*((1 + Hb*Khbatp)/(1 + Hb*Khbmgatp)); **** Eqn 3 **** h[Hb ,q ] = Hbt-Hb*(1 + BPG[Hb,q]*Khbbpg + ATP[Hb,q]*Khbatp + Mg[Hb,q]*ATP[Hb,q]*Kmgatp*Khbmgatp); **** Plot Eqn 3 with f fixed at q1 and Hb varying from 0 to 7.2 mM **** ^ Plot[h[Hb,q1],{Hb,0,7.2*10 -3}]; **** Determination of root of Eqn 3 in interval 0 < Hb < Hbt with Newton’s method—starting value 3 mM Hb **** ^ Hb1 = Hb/.FindRoot[h[Hb,q1] = = 0,{Hb,3.0*10 -3}]; **** Generates the output matrix shown below **** MatrixForm[N[{{metabolite, value, percent}, {mg,Mg[Hb1,q1],x}, {x,x,x}, {atp,ATP[Hb1,q1],ATP[Hb1,q1]/ATPt*100}, {mgatp,ATP[Hb1,q1]*Mg[Hb1,q1]*Kmgatp,ATP[Hb1,q1]*Mg[Hb1,q1]*Kmgatp/ATPt *100}, {hbatp,ATP[Hb1,q1]*Hb1*Khbatp,ATP[Hb1,q1]*Hb1*Khbatp/ATPt*100}, {hbmgatp,ATP[Hb1,q1]*Mg[Hb1,q1]*Hb1*Kmgatp*Kmgatp*Khbmgatp,ATP[Hb1,q1] *Mg[Hb1,q1]*Hb1*Kmgatp*Khbmgatp/ATPt*100}, {x,x,x}, {bpg,BPG[Hb1,q1],BPG[Hb1,q1]/BPGt*100}, {mgbpg,BPG[Hb1,q1]*Mg[Hb1,q1]*Kmgbpg,BPG[Hb1,q1]*Mg[Hb1,q1]*Kmgbpg /BPGt*100}, {hbbpg,BPG[Hb1,q1]*Hb1*Khbbpg,BPG[Hb1,q1]*Hb1*Khbbpg/BPGt*100}, {x,x,x}, {hb,Hb1,Hb1/Hbt*100}, {hbatp,ATP[Hb1,q1]*Hb1*Khbatp,ATP[Hb1,q1]*Hb1*Khbatp/Hbt*100}, {hbmgatp,ATP[Hb1,q1]*Mg[Hb1,q1]*Hb1*Kmgatp*Khbmgatp,ATP[Hb1,q1] © 1997 John Wiley & Sons, Ltd.



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*Mg[Hb1,q1]*Hb1*Kmgatp*Khbmgatp/Hbt*100}, {hbbpg,BPG[Hb1,q1]*Hb1*Khbbpg,BPG[Hb1,q1]*Hb1*Khbbpg/Hbt*100}, {x,x,x}, {magnesiumtotal,ATP[Hb1,q1]*Mg[Hb1,q1]*Kmgatp + ATP[Hb1,q1]*Mg[Hb1,q1] *Hb1*Kmgatp*Khbmgatp + Mg[Hb1,q1] + BPG[Hb1,q1]*Mg[Hb1,q1]*Kmgbpg, (ATP[Hb1,q1]*Mg[Hb1,q1]*Kmgatp + ATP[Hb1,q1]*Mg[Hb1,q1]*Hb1*Kmgatp ^ *Khbmgatp + Mg[Hb1,q1] + BPG[Hb1,q1]*Mg[Hb1,q1]*Kmgbpg)/(3.5*10 -3)*100} },3]] **** Output Matrix **** metabolite value percent mg 0.00043 x x x x atp 0.000134 6.39 mgatp 0.00151 72.2 hbatp 0.000201 9.61 hbmgatp 0.00246 11.8 x x x bpg 0.00229 42.9 mgbpg 0.000656 12.3 hbbpg 0.00239 44.8 x x x hb 0.00418 59.5 hbatp 0.000201 2.86 hbmgatp 0.000246 3.51 hbbpg 0.00239 34.1 x x x magnesium total 0.00284 81.2

