The regulatory role for magnesium in glycolytic flux of the human erythrocyte.

31P NMR was used to measure the intracellular free magnesium concentration ([Mg2+]i) in human erythrocytes while [Mg2+]i was changed between 0.01 and 1.2 mM using the divalent cationophore A23187. 13C NMR and [2-13C]glucose were used to determine the kinetic effects of [Mg2+]i by measuring the flux through several parts of the glucose pathway. Glucose utilization was strongly dependent on [Mg2+]i, with half-maximal flux occurring at 0.03 mM. The rate-limiting step was most likely at phosphofructokinase, which has a Km(Mg2+) of 0.025 mM in the purified enzyme. Phosphorylated glycolytic intermediate concentration was also strongly dependent on [Mg2+]i and [MgATP], and glucose transport plus hexokinase may have been partially rate-determining at [Mg2+]i below ∼0.1 mM. The pentose phosphate shunt activity was too low to determine the dependence on [Mg2+]i. Phosphoglycerate kinase and 2,3-diphosphoglycerate mutase fluxes were also measured, but were not rate-limiting for glycolysis and showed no Mg2+ dependence. Human erythrocyte [Mg2+]i varies between 0.2 mM (oxygenated) and 0.6 mM (deoxygenated), well above the measured [Mg2+]i(1/2). It is unlikely, then, that [Mg2+]i plays a regulatory role in normal erythrocyte glycolysis.

P NMR was used to measure the intracellular free magnesium concentration ([Mg 2؉ ] i ) in human erythrocytes while [Mg 2؉ ] i was changed between 0.01 and 1.2 mM using the divalent cationophore A23187. 13  Many of the enzymes in the metabolic pathways that utilize glucose have a requirement for magnesium as demonstrated in kinetic studies of isolated enzymes (1)(2)(3). The K m values for Mg 2ϩ in the glycolytic enzymes of the human erythrocyte are between 1 and 2.3 mM for hexokinase (maximum activity at 37°C ϭ 11 mol/h/ml of erythrocytes), 0.025 mM for phosphofructokinase (PFK) 1 (200 mol/h/ml), 0.3 mM for phosphoglycerate kinase (PGK) (3000 mol/h/ml), and 1 mM for pyruvate kinase (230 mol/h/ml) (1,3). [Mg 2ϩ ] i in oxygenated erythrocytes is 0.2 mM, which rises to 0.6 mM in the absence of oxygen due to the oxygen-dependent behavior of ATP binding to hemoglobin (4). Glucose utilization is concurrently increased by ϳ23-33% in the deoxygenated cell (5,6). Since [Mg 2ϩ ] i is near the measured K m for three of the potentially rate-limiting kinases and because both [Mg 2ϩ ] i and the glycolytic rate are modulated as oxygen tension changes, it stands to reason that [Mg 2ϩ ] i is important in erythrocyte glycolysis.
The divalent cationophore A23187 was used to change the concentration of intracellular Mg 2ϩ in human erythrocytes, which are otherwise impermeable to magnesium. The distribution of Mg 2ϩ across the cell membrane is then a function of membrane potential, V m (Equation 1) (7). ͓Mg 2ϩ ͔ i ϭ exp͑Ϫ2FV m /RT͓͒Mg 2ϩ ͔ e (Eq. 1) Intracellular Mg 2ϩ was measured from the chemical shift of the 31 P NMR signals of the ␣and ␤-phosphate groups of ATP (4). 13 C NMR was used to measure [2-13 C]glucose utilization and to estimate the flux through several of the enzyme systems in the glycolytic pathway at [Mg 2ϩ ] e between 0.01 and 1.00 mM: total glucose utilization, PFK flux, 2,3-DPG turnover, PGK flux, and pentose phosphate pathway flux (6).

EXPERIMENTAL PROCEDURES
Erythrocyte Preparation-7 ml of venous blood was taken from healthy volunteers who had given informed consent, under the guidelines of the George Washington University Medical Center IRB. After centrifugation, the resultant erythrocytes were washed twice in phosphate-buffered saline (pH 7.4) and once in experimental buffer (110 mM NaCl, 5 mM KCl, 40 mM HEPES, 15 mM Na 2 HPO 4 , 1 mM EGTA, and 5 mM adenine (pH 7.5)). Cells were diluted to 3% hematocrit in buffer containing 10 mM glucose, 6 M A23187, and the appropriate Mg 2ϩ concentration and incubated at 37°C for 60 min in order to ensure equilibrium of Mg 2ϩ across the cell membrane (7). Cells were then washed twice with the same buffer without glucose, resuspended at 50% hematocrit, and oxygenated by swirling in a 10-ml glass bulb on ice under hydrated oxygen. They were placed in a 10-mm NMR tube, and hydrated oxygen was passed over the cells during the NMR experiment.
NMR Experiment-All spectra were taken at 34°C in a Bruker AC300 spectrometer equipped with a 10-mm proton low frequency probe that is tunable to either carbon or phosphorus. Two protondecoupled 31 P NMR spectra were taken (10 min each, 60°pulse, 2-s relaxation delay, CPD decoupling). 10 mM [2-13 C]glucose was added, and 15 proton-decoupled 13 C NMR spectra were taken (10 min each, 60°p ulse, 2-s relaxation delay, CPD decoupling, nuclear Overhauser effect development), followed by two final 31 P NMR spectra. Glucose, lactate, Mg 2ϩ e , pH, pO 2 , and hematocrit were measured immediately before and after the experiment. The sample was stored at Ϫ50°C until extracted with 6% perchloric acid.
Neutralized extracts were lyophilized and dissolved in 0.4 ml of 2 H 2 O, and fully relaxed proton-decoupled 13 C NMR spectra were acquired (60°pulses, 10-s delays, CPD bilevel decoupling) for determination of the C-3/C-2 [ 13 C]lactate ratio used to calculate the pentose phosphate shunt activity. Extracellular Magnesium Determination-A commercial electrode was used for determination of buffer free Mg 2ϩ concentrations (NOVA Biomedical, Waltham, MA). The Mg 2ϩ -sensitive divalent cation electrode in this instrument is also very sensitive to calcium concentration and ionic strength and is factory-calibrated for whole blood and plasma. We therefore constructed calibration curves for calcium-free solutions using 150 mM KCl in filtered, double-distilled water and stock solutions of MgCl 2 and MgSO 4  spectra using the equations and dissociation constants found in Gupta et al. (4). A computer program written in Mathematica (Wolfram Research, Champaign, IL) was used to solve the four independent equations for each experiment. The limiting constants ⌬ATP ␣␤ and ⌬MgATP ␣␤ were corrected for pH i (8), and pH i was calculated from pH e (9,10).
Metabolite Concentrations-2,3-DPG was measured in trichloroacetic acid using a spectrophotometric method (Sigma) and corrected for the hematocrit, determined by a NOVA Stat 9 clinical analyzer. Total ATP was derived from the corrected 2,3-DPG/ATP ratio measured in 31 P NMR spectra. Hemoglobin concentration was assumed to be 7.02 mM (4).
NMR Data-The correction factors for saturation for both 31 P and 13 C NMR data were determined from spectra of solutions of commercially prepared metabolites in experimental buffer that contained no magnesium (Sigma). Spectra were acquired at 34°C under the same conditions used for the NMR experiment (2-s delays), which were then repeated with a 15-s delay period. The solution for 31 P-labeled metabolites contained NaATP, 2,3-DPG (cyclohexylammonium salt), and Na 2 HPO 4 , and the ratios of the saturated to fully relaxed resonance intensities (normalized to 2,3-DPG) were used to correct the cell spectra. Saturation under our conditions required that the 2,3-DPG/ATP ratio be corrected by a factor of 1.6. The solution of 13 C-labeled metabolites contained [2-13 C]glucose, unlabeled lactate, and 2,3-DPG. Resonance areas were normalized to the ␤-[2-13 C]glucose peak, and correction ratios were 1.0 for [2-13 C]lactate and [2-13 C]DPG and 0.94 for Kinetic Data-Fluxes through several points of the glucose pathways were determined essentially as described by Schrader et al. (6). All fluxes are reported as mol of glucose/min/g of hemoglobin to facilitate comparison between different parts of the pathway.
Glucose Utilization-␣-and ␤-[2-13 C]glucose resonance areas were combined, and the results were normalized by setting peaks in the first 13 C NMR spectra (t ϭ 0 -10 min) equal to the total solution [glucose] measured at t ϭ 0. The resultant concentrations were plotted against time and fit to a second-order polynomial. The early and late rates of glucose utilization were measured as the slope of this function at 30 and 120 min.
Pentose Phosphate Shunt and PFK Flux-The method of Schrader et al. (6) rests on the fact that the [2-13 C]glucose that passes through PFK yields 50% [2-13 C]lactate and 50% unlabeled lactate, whereas glucose loses its C-1 as CO 2 in the 6-phosphogluconate dehydrogenase reaction of the pentose phosphate pathway, yielding a family of [1-13 C]pentose 5-phosphates. These compounds then go on to form [1-13 C]Fru-6-P, [1,3-13 C]Fru-6-P, and unlabeled glyceraldehyde 3-phosphate. The Fru-6-P thus formed can return to the pentose phosphate shunt as Glc-6-P or continue through glycolysis. Therefore, the production of [3-13 C]lactate and [1-13 C]lactate is a measure of the pentose phosphate pathway. In Equations 2-4, PC is defined as the fraction of glucose uptake that is converted to glyceraldehyde 3-phosphate (GAP).
3 Glc 3 3 CO 2 ϩ 2Fru-6-P ϩ 1 GAP pentose pathway A is a correction factor of 0.03 to account for natural abundance 13

2,3-DPG Bypass and Phosphoglycerate
Kinase-In the erythrocyte, 2,3-DPG is produced from 1,3-DPG by 2,3-DPG mutase. This enzyme, along with 2,3-DPG phosphatase, constitutes a shunt past PGK, an ATP-producing reaction. Glycolysis produces 2 molecules of ATP/molecule of glucose, so the 2,3-DPG bypass allows glycolytic flux to proceed without net ATP production. The 13 C NMR experiment can be used to measure the ratio of the fluxes through 2,3-DPG mutase and PGK. The 2,3-[2-13 C]DPG time course is fit to a modification of Equation 6, where A 0 is the concentration of the substrate (1,3-DPG), and k 1 and k 2 are the rate constants for 2,3-DPG mutase and phosphatase, respectively (6). This equation did not produce a good fit to the NMR data. A better fit was made to Equation 7, where the rate of label flowing into the 2,3-DPG pool was assumed to be linearly changing, rather than a constant. Presumably, this is due to the changing pH that occurs throughout the experiment and affects the PFK flux. The parameters are k 1 A 0 , k 2 A 0 , and k 3 .
The initial rate is given by k 2 A 0 .  8) and to two simple straight lines, which would be similar to estimating a fit "by eye." The Michaelis-Menten formalism is generally applicable only to initial rates measured for a single isolated enzyme with one substrate, but the general form is similar to that for a more complicated enzyme series that contains a single rate-limiting step, with a single limiting substrate. It cannot be expected to fit data gleaned from a whole cell.

RESULTS
Free Magnesium- Fig. 1 shows 10-min 31 P NMR spectra of a 50% suspension of washed human erythrocytes taken before  ] e appears to be buffered by the erythrocyte and changes in such a way as to approach 0.32 mM. For both intra-and extracellular magnesium ions, this delta is a direct function of the original concentration. Table I shows the average pH and ATP, 2,3-DPG, hemoglobin, glucose, and lactate concentrations at 0 and 150 min for all 15 experiments. Although there was variation between samples, there were few changes in high energy phosphates during the experiment. The glycolytic rate is substantially depressed by acidic pH (as much as 250% rate change/pH unit (9,11)), yet the change in pH in our experiments due to lactate production correlated positively with the rate of glycolysis (r 2 ϭ 0.81). Therefore, there was a tendency toward lower pH and probably slightly lower glycolytic fluxes measured toward the end of the experiments with the highest magnesium levels.
Glycolysis- Fig. 3 shows 13 C NMR spectra taken at 10, 30, 60, and 120 min after the addition of  Fig. 5A shows the [2-13 C]glucose utilization rates measured at 30 and 120 min of each experiment plotted against the appropriate [Mg 2ϩ ] i . These data were fit both to a Michaelis-Menten equation and to two straight lines. The second, linear fit is statistically better in most cases and is likely to be no less appropriate than the Michaelis-Menton equation, given the complex intact cell system being studied. Table II shows  Because many enzymes in the glycolytic pathway are dependent on both MgATP and Mg 2ϩ , [MgATP] was calculated for each experiment from measured Mg 2ϩ , pH, and total ATP and 2,3-DPG using the equations from Gupta et al. (4) and LaNoue and co-workers (8). As can be seen in Fig. 6, when [MgATP], calculated assuming a constant total ATP concentration of 2.08 mM (4), is plotted against [Mg 2ϩ ], it has a shape that is similar to the dependence of glucose utilization on [Mg 2ϩ ] i . The glucose utilization rates are replotted against [MgATP] in Fig. 5B and show a correlation as expected.   Fig. 7 (A and B).
PGK, 2,3-DPG Shunt, and ATP Production-The initial rates for 2,3-[2-13 C]DPG and [2-13 C]lactate appearance in 13 C NMR spectra (Figs. 3 and 4) yield the fluxes through 2,3-DPG mutase and PGK. Fig. 9 shows these rates plotted as a function of PFK flux. Flux through both enzymes appears to be a constant fraction of PFK flux, and therefore, the ratio of the two exhibits no clear unique dependence on [Mg 2ϩ ] i or [MgATP]. On average, 75.3% of all carbons pass through the 2,3-DPG shunt, and 24.3% flow through PGK.
Phosphomonoesters: PFK Versus Hexokinase-The phosphomonoester metabolites were very difficult to quantitate in the 31 P NMR spectrum (4 -6 ppm) due to the many small broad peaks. It was not possible to measure changes in individual phosphorylated glycolytic intermediates, but it was possible to report the area under the entire phosphomonoester region.   Table II. cycle, [Mg 2ϩ ] i varies between 0.2 mM (oxygenated) and 0.6 mM (deoxygenated) (4), but at constant oxygen tension, appears to be well buffered. Erythrocytes contain ϳ3.5 mmol of total magnesium/kg of water and three to four distinct pools of buffering molecules: 100 M buffer with K m Ϸ 0.03 M, 2 mM buffer with K m Ϸ 25-50 M, and ϳ20 -30 mM buffer with K m Ϸ 1-4 mM (7). Under certain pathological conditions, human erythrocyte [Mg 2ϩ ] i can decrease, but falls to only 0.13 Ϯ 0.02 mM in renal magnesium loss (12) or to 0.16 mM after 3 weeks of magnesium deficiency (13).
Integration of the phosphomonoester region indicates that the phosphorylated intermediates including such compounds as Glc-6-P (4.7 ppm) and DHAP (4.37 ppm) increase during the incubation with glucose at high [Mg 2ϩ ] i and decrease at low [Mg 2ϩ ] i . The crossover point is ϳ0.1 mM Mg 2ϩ or ϳ0.5 mM MgATP. Even though glucose utilization is very slow at low [Mg 2ϩ ] i , the concentration of phosphorylated glycolytic intermediates falls, indicating that transport and/or phosphorylation of glucose (these steps cannot be distinguished in the present experiment) is lagging behind other potentially ratelimiting steps. At higher [Mg 2ϩ ] i , the rate-limiting step must be later in the glycolytic pathway since phosphorylated intermediate pools build up. This implies that the combination of transport and phosphorylation of glucose is at least partially rate-limiting for glycolysis at low [Mg 2ϩ ] i . The K a(Mg 2ϩ ) for purified hexokinase from human erythrocytes is between 1.0 and 2.3 mM, with a Mg 2ϩ dependence observed up to 4 mM, and the K m(MgATP) is between 1 and 2 mM (1,2). Since at even the highest [Mg 2ϩ ] i studied the change in phosphomonoesters had not reached a maximum, our results in the intact cell are consistent with this rather high K a(Mg 2ϩ ) for hexokinase (Fig.  10). This activation of the early steps in glycolysis may be important for increasing glycolytic intermediates in deoxygenated cells, which have much higher [Mg 2ϩ ] i and higher glycolytic rates.
The 13 C NMR experiment does not clearly indicate which step in the glycolytic pathway is rate-limiting. It may in fact change throughout the experiment; lactate accumulation changes the intracellular NADH/NAD ϩ ratio and inhibits glyceraldehyde-3-phosphate dehydrogenase (10). On the other hand, decreases in pH have the greatest effect on PFK (11). The present experiments do demonstrate a distinct Mg 2ϩ depend-ence of glycolysis, and PFK has a clear dependence on Mg 2ϩ and MgATP, while glyceraldehyde-3-phosphate dehydrogenase does not. The K m(Mg 2ϩ ) for purified human erythrocyte PFK has been reported to be 0.025 mM (1). In an analysis of the kinetics of PFK from rat erythrocytes, it appeared that Mg 2ϩ in itself did not directly activate the enzyme (3). It instead served three distinct roles: as part of the substrate MgATP (K m(MgATP) ϭ 0.07 mM), to release inhibition by uncomplexed ATP (K i(ATP) ϭ 0.01 mM), and to inhibit PFK (K i(Mg 2ϩ ) ϭ 0.44 mM). In the present study, there was no apparent decline in PFK flux at [Mg 2ϩ ] i near or above the reported K i , and the MgATP and ATP concentrations at half-maximal velocity were on the order of 0.4 and 0.6 mM, respectively, well above the reported activation and inhibition coefficients. Our results do not support this second model of PFK regulation. However, because of the similarity of our measured [Mg 2ϩ ] i( 1 ⁄2) to the reported K m for the isolated human enzyme, PFK does appear to be the primary rate-determining enzyme under our experimental conditions (1).
The pentose phosphate pathway and PGK flux were too low to solidly define their Mg 2ϩ dependence in the present experiments. It is interesting that unlike other cells that do not have the 2,3-DPG shunt, low activity of PGK does not limit glycolytic flux in the erythrocyte. Purified PGK has a strong dependence on Mg 2ϩ , with a reported K m(Mg 2ϩ ) of 0.3 mM and K m(MgATP) ϭ 0.44 mM (1). Our data show no rate dependence around these points, indicating that PGK flux is being limited by something else. Since PGK is the point at which net ATP production is regulated, perhaps its flux is limited by low ATP utilization in these experiments. PGK flux is more or less linear with PFK flux (Fig. 9), which implies that the concentration of the substrate 1,3-diphosphoglycerate is important.
In many studies, including one done with 13 C NMR, the time-averaged pentose phosphate shunt activity was significant, ϳ17% of total glucose utilization in oxygenated human erythrocytes (5,6,14), whereas in the present study, it was at most 4%. This may be due to differences in the experimental design. The previous experiments were carried out for very long periods of time, and it appears from the time courses of [2-13 C]lactate and [3-13 C]lactate that the pentose phosphate shunt activity was increased at the later times, when 2,3-DPG was falling and P i was probably rising. It was important to keep 2,3-DPG, total ATP, and P i constant in these experiments because all three regulate glycolysis. 2,3-DPG inhibits PFK, hexokinase, PGK, and pyruvate kinase. PGK and pyruvate kinase may be inhibited by ϳ80% at the normal 2,3-DPG concentrations (1). P i inhibits PFK and strongly stimulates hexokinase (11). It is possible that as high energy phosphates fall and P i increases, pentose phosphate shunt activity is increased.
A second explanation for the low pentose phosphate shunt activity is the low rate of Ca 2ϩ pumping that takes place in the presence of 1 mM EGTA. When A23187 and even the minute calcium concentrations found in deionized water are present simultaneously, erythrocyte heat and lactate production are both increased, and ATP falls precipitously due to a very active ATP-dependent Ca 2ϩ -H ϩ exchanger in the membrane (15)(16)(17). Normal erythrocyte intracellular Ca 2ϩ is maintained at vanishingly low levels by this Ca 2ϩ pump and an impermeable cell membrane in the face of ϳ1.2 mM ion in the plasma. The basal level of the Ca 2ϩ -ATPases most likely causes some turnover of nucleotides and associated pentose phosphate pathway activity, which would be absent in the present experiments (14).
The slope of the intracellular versus extracellular free magnesium concentration is a measure of the square of the Donnan potential (r), which is a function of membrane potential, and is highly dependent on pH, ion concentrations, and cell volume (7). The Donnan potential has apparently changed during the experiment from 0.90 to 0.76. If true, this would largely explain the tight correlation between the change in [Mg 2ϩ ] i and its initial concentration (r 2 ϭ 0.983). However, [Mg 2ϩ ] e also changes, but in such a way as to approach the concentration 0.32 mM. This implies a large extracellular buffer for magnesium with a K D in the range of its normal plasma concentration (0.5 mM). The existence of such a buffer has been noted in the literature (18) and may consist of membrane-bound phospholipids. We hoped to fill all magnesium sites in the cells by a long preincubation at the experimental magnesium ion and ionophore concentrations. The changes in [Mg 2ϩ ] e may therefore indicate a shift in the binding site concentration or dissociation constant. Clearly, it cannot be assumed that either [Mg 2ϩ ] e or [Mg 2ϩ ] i is constant when experiments with A23187 are con-ducted for long periods of time at high hematocrits.
The ionophore seems to increase glycolysis; in our studies, it went up ϳ100% from 2.1 ϫ 10 Ϫ4 in controls (data not shown) to 4 ϫ 10 Ϫ4 mmol/min/g of hemoglobin. This is similar to the results of Engstrom et al. (15,16), who found an increase in glycolysis from 6.7 ϫ 10 Ϫ5 to 1.3 ϫ 10 Ϫ4 mmol/min/g of hemoglobin in the presence of A23187 and 3 mM Mg 2ϩ . It was also noted that the rates of glucose and [2-13 C]glucose utilization are always greater than production of total lactate or labeled trioses (see Fig. 3 and Table I). This is not a new finding (6,10). Since there is no apparent large increase in [2-13 C]pyruvate or other labeled intermediates, it probably indicates slow lactate transport across the membrane or binding of lactate to cellular components accompanied by a decrease in NMR visibility of the bound fraction.
In summary, [Mg 2ϩ ] i( 1 ⁄2) has been determined for glycolysis in the human erythrocyte and found to be 0.03 mM. The ratelimiting site is most likely to be PFK. Pentose phosphate shunt activity was too low to explore the magnesium dependence under these experimental conditions. 2,3-DPG mutase and PGK flux were not rate-limiting and therefore showed no Mg 2ϩ dependence. Glucose transport and phosphorylation, as determined by concentration of and changes in total phosphomonoester compounds, have a strong dependence on [Mg 2ϩ ] i and [MgATP]. These results indicate that there is a strong regulatory role for [Mg 2ϩ ] i in the glycolytic pathways of the erythrocyte, but that [Mg 2ϩ ] i( 1 ⁄2) is far lower than the normal range of [Mg 2ϩ ] i in the cell.