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Comparison between measured and calculated ionised concentrations in Mg 2+/ATP, Mg 2+/EDTA an |
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Magnesium Research. Volume 20, Numéro 1, 72-81, March 2007, Original article |
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DOI : 10.1684/mrh.2007.0092 |
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Auteur(s) : John AS McGuigan, James W Kay, Hugh Y Elder, Daniel LÜthi , Institute of Biomedical and Life Sciences, West Medical Building, University of Glasgow, G12 8QQ, UK, Department of Statistics, Mathematics Building, University of Glasgow, G12 8QW, UK, Institute of Physiology, B±hlplatz 5, 3012 Bern, Switzerland. |
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ARTICLE
Auteur(s) : John AS McGuigan1, James W Kay2, Hugh Y Elder1, Daniel Lüthi3 1Institute of Biomedical and Life Sciences, West
Medical Building, University of Glasgow, G12 8QQ, UK Materials and methodsMacroelectrodesThe macroelectrodes were manufactures from polyurethane tubing (internal diameter, 1.5 mm). A ceramic plug was milled to fit into the end of the tubing and the plug was then coated with the selective layer. The macroelectrodes were backfilled with 150 mmol/L KCl containing 1 mmol/L MgCl2 (Mg2+-macroelectrodes) or 1 mmol/L CaCl2 (Ca2+-macroelectrode). To establish electrical contact an Ag/AgCl wire was carefully pushed into the tubing. A detailed description of the manufacture of such macroelectrodes is given in the book by Fry and Langley [7], and the paper by Zhang et al. [8] specifically deals with the manufacture of Mg2+-selective macroelectrodes.RecordingThe indifferent electrode was either an uncoated macroelectrode filled with 3 mol/L KCl or an Orion reference electrode. Recording was via a WPI high input impedance interface and the potential was read from a pH meter in mV mode. In the majority of experiments an AD converter (Mac-Lab) was used.SolutionsThe manufacture of calibrating and buffer solutions, experimental procedures and methods are described in detail in [2, 5, 6, 9, 10] so only a brief description is given here.Background solutionThis was based on intracellular measured values and contained 142.5 mmol/L KCl, 15 mmol/L NaCl, buffered with 5 mmol/L pipes, hepes or Tris to the appropriate pH. This solution was the basis for both the calibration solutions and the buffer solutions.Calibration solutionsThe background solution was manufactured containing concentrations of MgCl2 or CaCl2 of 0.5 mmol/L, 0.8 mmol/L, 1.5 mmol/L 2.5 mmol/L, 4 mmol/L, 6 mmol/L and 10 mmol/L.Buffer solutionsThese were manufactured using the two solution method. In this method two background solutions are manufactured, one containing the ligand (EDTA, ATP, EGTA) and the other containing equal concentrations of ligand and MgCl2 (EDTA, ATP) and CaCl2 (EGTA). These two solutions could then be mixed in the appropriate volumes to give [Mg2+] ranging for Mg2+/EDTA from 2 μmol/L to 50 μmol/L, Mg2+/ATP from 0.01 mmol/l to 0.4 mmol/L and for Ca2+/EGTA from 140 nmol/L to 2.5 μmol/L.TemperatureExperiments were carried out at both 25°C and 37°C. Temperature variation was 1 ± 0.1°C.pHThe pH meter was calibrated daily and pH was measured to ± 0.01 units. Since pH is a function of temperature the pH electrode was calibrated either at 25°C or 37°C.Measurement of Kapp and [Ligand]TThe electrode potential measurements in the calibration solutions provided the characteristics of the macroelectrode, namely the slope s and the constant of the recording system E0. Using the ligand optimisation method [2], both Kapp and [Ligand]T can be calculated from the electrode potential measurements in the buffer solutions and the constants s and E0 of the macroelectrode. The calculations of Kapp and [Ligand]T were carried out using the Excel program described in [3].Calculation of ionised concentrationsFor the calculation of the [X2+] in the buffer solutions either 1) the tabulated stoichiometric constants in [11-14] or 2) programs that are freely available either on the internet or on request were used. The programs were, Chelator [15], Maxchelator [16] or at www.stanford.edu/~cpatton/maxc.html and the program developed by Robert Godt [17]. The results illustrated were calculated by Professor R. Godt, using his program.Correction for pHc (H+-concentration) to pHa (H+-activity) was carried out using either the Davies equation [18] or the equation in [19] to calculate the mean activity coefficient (γ±) for H+-ions. The mean activity coefficient was equated with the single ion activity coefficient for H+-ions (γH+). For Mg2+ binding to EDTA the method described in [16] to correct for ionic strength and to calculate γ+ for H+ ions was also used. Calculation of the Kapp for the appropriate temperature and ionic strength was similar to that described in [20]. A detailed description is found in the Appendix to [1] which is available at www.stats.gla.ac.uk/~jim/ligopt.html. StatisticsSample results are summarised as mean ± standard deviation (SD) or as mean ± coefficient of variation (CV = (SD/mean)*100). To test differences between means, the Student paired t-test was employed and the Kolmogorov-Smirnoff test was used as a formal test of normal distribution. The program KaleidaGraph™ (Synergy Software, Reading, PA, USA) was used for curve fitting. This employs a least squares curve fitting routine and the regression coefficient r, was taken to express the goodness of fit.ResultsMg2+ binding to ATP: apparent dissociation constantThe original data as well as unpublished data have been recalculated for both the titration experiments and the experiments in which the two solution method was used. Applying the paired t test to the results at 25°C and 37°C showed no significant difference in the means except for pHa of 7.2 at 25°C (p = 0.033) which was just significantly different. The results have been fitted with an equation of the form [4]:In equation (1) pKMg-1 and pKMg-2 are the negative logarithm of the dissociation constants for the binding of Mg2+ to ATP and H-ATP respectively; pKH-1 is the negative logarithm of the first mixed dissociation constants for H+ binding to ATP. The new fit to the points at 25°C and 37°C is illustrated in figure 1A. These values do not depend on using Mg2+/EDTA buffers to calibrate and determine the Mg2+-macroelectrode which introduces an additional source of error [2] and, because of this, they are regarded as more accurate than those in [4]. Additional experiments were carried out in which the [K+] was either decreased to 72 mmol/L or increased to 285 mmol/L to change the ionic strength from 0.16 mol/L to 0.087 mol/L or 0.3 mol/L respectively. The results of these experiments at pHa of 7.2 are illustrated in figure 1B; as the ionic strength increases, Kapp increases in an apparently linear fashion (see also Discussion). Mg2+ binding to EDTA: apparent dissociation constantThe Kapp of Mg2+ binding to EDTA was measured over a pHa range from 5.5 to 7.7 at 25°C and at an ionic strength of 0.16 mol/L. The data were fitted by the following simplified equation for Kapp as it ignores the third and fourth H+ binding sites to EDTA and is illustrated in figure 2A. (The data at 37°C shown in table 1 are not included because of the limited range of the measurements, namely from pHa 6.7 to 7.7).Table 1 CV for the calculated [Mg2+] in EDTA and ATP buffer solutions.
Ca2+ binding to EGTA: apparent dissociation constantThe most extensive series of measurements was at 25°C and an ionic strength of 0.16 mol/L at pHa 7.2; the mean±standard deviation (SD) for Kapp was 290.4±79.5 nmol/L (n = 63). This SD corresponds to a coefficient of variation of 27.4%. However, in a Ca2+/EGTA buffer solution the measured Kapp depends critically on the pHa, the temperature of the solution as well as an adequate correction for drift of the electrode; failure to adequately control these parameters increases the coefficient of variation (CV) of the estimated Kapp (see Discussion). Despite the variation of the measurements, based on the Kolmogorov-Smirnoff test of normality it is reasonable to assume that these data were generated from a normal probability distribution (p > 0.15). This supports the conclusion that the mean value of 290.4 nmol/L represents the true mean under these conditions.Comparison between measured and calculated [X2+]The re-estimation in this paper of the Kapp for the binding of Mg2+ to ATP and EDTA and Ca2+ binding to EGTA allowed a comparison between measured and calculated [X2+] in buffer solutions, using either tabulated constants or freely available computer programs (see Material and Methods). To make the comparison, the buffer solutions 1 to 10, with the buffer ratios 7:1 to 1:9 as proposed in McGuigan et al. (fifth table in [1]) were used.Mg2+/ATPFigure 3A illustrates the Mg2+ binding to ATP, calculated for 25°C a pHa of 7.2 and an [ATP]T of 4 mmol/L. The calculations have been carried out with and without including K+ binding to ATP. In figure 3A the filled circles represent the [Mg2+] calculated using the Kapp value calculated using equation (1). If the constants from [13] or the program Chelator are used and no binding of K+ to ATP is assumed then there is excellent agreement between measured and calculated values (open circles and triangles). However, as pointed out by Kushmerick [21], because the [K+] in intracellular solutions is around 150 mmol/L this binding has to be included. If this is done, the ionised concentrations are increased. Again there is limited agreement amongst the calculated values; the variation being between 1.8 to 2.5. Deviation between measured and calculated varies between 27% to 78%.A similar situation occurs when calculating the [Mg2+] at a pHa of 7.2 as the ionic strength is varied from 0.06 mol/L to 0.3 mol/L (figure 3B). The calculations were carried out with 4 mmol/L [ATP]T and 3.5 mmol/L [Mg]T. If no binding of K+ to ATP is assumed there is reasonable agreement between [Mg2+] calculated from measured Kapp values and [Mg2+] calculated from the constants in [13] and using the program Chelator. Other than that, the calculated [Mg2+] are either underestimations or overestimations; the deviation between the measured and calculated values at an ionic strength of 0.3 mol/L was an increase of 59.5% or a decrease of 31.6%. Mg2+/EDTAThe calculations for [Mg2+] have been carried out for a pHa of 7.2, an [EDTA]T of 4.0 mmol/L. The results of the calculations are shown in figure 4A. The closed circles are calculated using the value of Kapp calculated from equation (2). There is little agreement amongst the calculated values and the calculated values vary by around a factor of three. The difference between measured and calculated values vary between 17.5% to some 62%. Moreover, the constants from [12] give two different answers depending on the method of calculation used to determine the [Mg2+].Ca2+/EGTAThe measured value at pHa of 7.2 for the Kapp for Ca2+/EGTA buffer solutions shows a CV of 27.4% but since there was no systematic error in these experiments the mean value has been taken as representative. The results of the calculations are illustrated in figure 4B where the closed circles are the results calculated from the mean value for Kapp at pHa of 7.2, for a purity of 95% and a nominal total EGTA concentration of 4.0 mmol/L. To show the importance of purity measurements, calculations using the program in [17] were carried out using both the [EGTA]N (4.0 mmol/L) and the [EGTA]T (3.8 mmol/L). The mean values overlap with the values calculated using the constants from [11]. The results illustrate variability amongst the calculated values for [Ca2+]. Assuming the actual EGTA concentration, the [Ca2+] vary by a factor of around 2. If a [EGTA]N concentration of 4 mmol/L is assumed the variation increases to a factor of 3. The variation between the measured and calculated results varies between 6% and a maximum of 65%.Mg2+/Ca2+ buffer solutions; inaccuracy or imprecisionAllowable range for [X2+] in buffer solutionsIn a buffer solution the parameter of interest is the [X2+] and the variation of this concentration from the mean value. Table 1 illustrates the CV for the calculated [Mg2+] in the EDTA and ATP buffer solutions. This table includes measurements for the binding of Mg2+ to EDTA at 37°C, but excludes measurements at a given pHa where the total number of experiments was 3 or less. It also excludes the CV of the Ca2+/EGTA because of the lack of precision of these early experiments. For EDTA, the within batch variation is under 5% for all pHa values at 25°C and for pHa 7.2 at 37°C. The other two values at this temperature having values of 6.95% and 7.90% respectively. The picture is similar with ATP. From the six within batch measurements, four are under 5% and the other two are just slightly larger. The overall CV varies from 1.16% for the two groups (each of 3 measurements) at pHa of 6.0 to 12.05% for the 13 measurements at pHa of 7.2. The results in table 1, indicate that a within batch CV of 5% or less is attainable for the [X2+] in buffer solutions. A CV of 5% corresponds to a range of ±10% from the mean value for [X2+], where range is defined to be the interval mean ± 2 SD. The ramifications this proposed range for [X2+] has on the permissible range for the individual parameters, pKapp, total magnesium/calcium concentrations ([X]T) and [Ligand]T, are considered below.Allowable range for pKappTo investigate the extent of a variation of pKapp on the calculated [X2+], the [X2+] was calculated for a buffer system in which the [Ligand]T was 3.8 mmol/L, [X]T 3.6 mmol/L and pKapp was varied from 1.5 to 10. The pKapp values were then changed by ±0.04, ±0.02 and ±0.01 units and [X2+] recalculated. The results are expressed as the ratio of estimated ionised concentration to the actual or true concentration, RE/T. The results of the calculations are illustrated in figure 2B. The ratio, RE/T reaches a limiting value because at pKapp values greater than 6, [X2+] << [X]T. At the limit, if the [X2+] has to be less than ±10%, then the range of RE/T is from 0.9 to 1.1 and the range of pKapp must be less than ± 0.04 units (see Appendix). Since the range represents 2*SD, the SD of the measurements must be less then ± 0.02 units for pKapp at pKapp values greater than 6.Allowable range for [X]T and [Ligand]TThese are considered together since they are interrelated; an increase in [X]T can be mimicked by a decrease in [Ligand]T or vice versa. Similar calculations to those illustrated in figure 2B for changes in [X]T at a constant [Ligand]T showed that the value of RE/T depended not only on the deviation of [X]T from the mean value but also on the initial value of [X]T. With a [X]T of 3.6 mmol/L and a [Ligand]T of 3.8 mmol/L the permissible range of RE/T of 0.9 to 1.1 allows only a deviation of 0.45% for [X]T. If the [X]T is 1.0 mmol/L, then deviation can increase up to 5% and still be within the permissible range. At the limiting value of RE/T, to ensure that all buffer solutions conform to the range of ±10%, the range of [X]T at a constant [Ligand]T has to be less than ±0.5% of the mean [X]T value. A similar calculation for RE/T for changes in the [Ligand]T at a constant [X]T for a ±10% of [X2+] in the buffer solutions shows that the variation in the [Ligand]T should also be less than ±0.5%.Sources of imprecisionImprecision or inaccuracy can arise from two sources, namely potential recording by the macroelectrodes or from the buffer solutions (i.e. in the estimation of pKapp, [Ligand]T and [X]T), the latter depending on the accuracy of the pipetting of X2+.RecordingDriftTo investigate the maximum effect of drift, calculations were carried out using the simulated Ca2+/EGTA data set in [1] in conjunction with the Excel program [3]. Uncorrected positive drift will lead to an over-estimate of the [Ligand]T and Kapp and vice-versa. Since the changes in Kapp and [Ligand]T are in the same direction they do, to some extent cancel out. As a rule of thumb, the percentage deviation in the [Ca2+] in the EGTA buffer solutions is roughly equal to the drift in mV/h. With care, drift can be less than ± 1 mV/h [2] which corresponds to a deviation of ±1% if uncorrected.Buffer solutionsApparent dissociation constantThe Kapp of buffer ligands depends on 1) ionic strength 2) temperature and 3) the pHa of the solution.1) Ionic strength Increasing ionic strength to 0.2 mol/L from 0.16 mol/L increases the Kapp by around 1.05 times, while decreasing the ionic strength to 0.12 mol/L decreases Kapp by 0.95 times. Since a change of ionic strength of ± 0.04 M is equivalent to a change in concentration of ± 20 mmol/L, it seems unlikely that a change in ionic strength will contribute to significant imprecision in the estimation of Kapp. 2) Temperature This is normally controlled within the range ± 1°C which corresponds to a deviation of 2%. If the temperature is controlled to within ±0.5°C, then this can be reduced to 1% and ideally, the temperature should be maintained between these limits. 3) pHa To illustrate the maximum effect of pH, the effect of pH on a Ca2+/EGTA buffer was investigated. At a pHa value between 7.0 and 7.5, changes in pHa of ± 0.12 unit decreases the estimated [Ca2+] approximately by a factor of 0.6 and increases it by a factor of 1.7 times. To remain within the set overall limits of 1.1 to 0.9 the permissible range is ± 0.02 pHa units. To reduce the deviation even further a deviation of pHa of less than 0.01 units should be striven for. Within this pHa range, changes of 0.12 units for BAPTA had only minimal effect on the [Ca2+] in contrast to that of EGTA. Total concentrationsTo investigate the maximum effect of systematic pipetting inaccuracies, the effect was mimicked by increasing/decreasing the [Ca]T in the buffer solutions in the range ±6%. In each buffer solution the [Ca2+] was calculated from the actual [Ca]T, allowing the potentials in the buffer solution to be calculated using [3]. An increase or decrease in [Ca]T caused by inaccurate pipetting was compensated for by an increase/decrease in ligand purity, rather than a change in Kapp, which remained remarkably constant. However, the change in estimated ligand purity has consequences on the estimated [Ca2+] in the buffer solutions. Calculation of [Ca2+] shows that for a +10% deviation in the estimated [Ca2+] in the buffer solutions, the error in pipetting has to be less than 1.23%; the corresponding value for –10% deviation in the buffer solution the pipetting error has to be less than 0.25%. Commercial pipettes (Brand, Germany) can achieve errors of less than 0.2%, so such accuracy is possible.DiscussionConsequencesThe difference between measured and calculated values for [Mg2+] and [Ca2+] as well as the variation amongst calculated values has implications for the published absolute values for intracellular [Mg2+] estimated by 31P-NMR and the resting estimated intracellular [Ca2+] values. 31P-NMR measurements of intracellular [Mg2+] depend on the Kapp for Mg2+/ATP binding and such estimates were initially based on the Kapp measurements of Gupta and colleagues at a pHa of 7.2 (25°C [22], 37°C [23]). In heart muscle, the resting intracellular [Mg2+] measured by microelectrodes at 25°C is 0.81 mmol/L (first table in [24]). If this value had been calculated from 31P-NMR measurements using the Kapp from figure 1, then using the different constants the value would become 0.35 mmol/L [22], 0.58 mmol/L [11], 0.64 mmol/L [16], 0.80 mmol/L [13] and 0.86 [15]. These variations, with an extracellular [Mg2+] of 0.5 mmol/L [24] correspond to an alteration in the reversal potential for Mg2+ from – 7.0 mV to +4.5 mV; a not insignificant change. The consequences for resting values for [Ca2+] in cells are equally disturbing. Taking the value of 200 nmol/L [24] and assuming this value had been determined using the measured Kapp for the buffer solutions from figure 4B, the range of values using the calculated Kapp values would be 104 nmol/L ([17], assuming 100% EGTA purity), 108 nmol/L ([12], H+ activity calculated from [19]), 118 nmol/L ([12], H+ activity calculated from [18]), 118 nmol/L [16], 114 nmol/L [17], 144 nmol/L [14], 199 nmol/L [11] and 212 nmol/L [15]. In this case the calculated reversal potential, with an extracellular [Ca2+] of 2.7 mmol/L [24] would vary from + 130.6 mV to + 121.4 mV, a difference of 9.2 mV.These variations in the estimations of [Mg2+] for 31P-NMR estimations and the resting measurements for [Ca2+] emphasise the difficulties in the interpretation of published absolute values in the literature for the intracellular [Mg2+] and [Ca2+]. Imprecision - Sources of imprecisionMacroelectrode drift can be measured and corrected for. Changes in ionic strength of around 1%, have negligible effects on the estimated Kapp. The main sources of error for the estimation of Kapp are changes in temperature and pHa. To maintain the range of the [X2+] in EGTA buffer solutions within ± 10% the limits should be ±0.5°C and < ±0.01 pH. Because drift can be allowed for, the [Ligand]T is influenced mainly by the accuracy of pipetting. There is an approximately linear relationship between % inaccuracy of pipetting and the % deviation in the estimation of the [Ligand]T. A minus 0.25% pipetting error is sufficient to decrease the estimated [X2+] in the buffer solutions by 10%.Conclusion1) There is limited agreement between measured and calculated values of [X2+], and any agreement can only be described as fortuitous, depending on which set of constants is chosen and the method of calculation employed.2) The calculated concentrations vary amongst themselves due to differences in the estimation of Kapp from the tabulated stoichiometric constants for Mg2+, Ca2+ and H+ binding to the ligand. These tabulated constants have to be corrected for temperature, ionic strength and pH and pHc has to be converted into pHa all of which introduce ambiguities into the calculation of the Kapp. 3) Mg2+ buffer solutions are required to measure [Mg2+] in patch clamp solutions, Kapp values for Mg2+ binding to organic anions and Mg2+ flux measurements. Because of the uncertainties in the calculated concentrations for [Mg2+] in the μmolar range (variation of up to three times), quoted values in this range can hardly be regarded as absolute. 4) Calculated [Ca2+] differ by almost a factor of two or even three if the [EGTA]T is not accurately determined (figure 4B) and again, there seems little sense in calibrating intracellular [Ca2+] measurements in absolute units. 5) Because of the uncertainties involved in such calculation, measurement is at present preferable to calculation. Standardisation for Mg2+/Ca2+ buffer solutions to allow not only the measurement of absolute concentrations but also comparison amongst different laboratories can no longer be regarded as a luxury ; it has become essential. AcknowledgementsWe wish to thank Professor Robert Godt for carrying out the calculations for us. PD Dr Dorothee Günzel and Dr Friederike Stumpff made very helpful suggestions regarding the paper.References1 McGuigan JAS, Kay JW, Elder HY. Critical review of the methods used to measure the apparent dissociation constant and ligand purity in Ca2+ and Mg2+ buffer solutions. Prog Biophys Mol Biol 2006; 92: 333-70.2 Lüthi D, Spichiger U, Forster I, McGuigan JAS. Calibration of Mg2+-selective macroelectrodes down to 1 μmol l-1 in intracellular and Ca2+-containing extracellular solutions. Exp Physiol 1997; 82: 453-67. 3 Kay JW, Stevens R, McGuigan JAS, Elder HY. Automatic determination of ligand purity and apparent equilibrium constant in divalent cation buffer solutions and apparent equilibrium constant in physiological solutions. J Physiol Proc 2004; 557P: D1. 4 Lüthi D, Günzel D, McGuigan JAS. Mg-ATP binding: Its modification by spermine, the relevance to cytosolic Mg2+ buffering, changes in the intracellular ionised Mg2+ concentration and the estimation of Mg2+ by 31P-NMR. Exp Physiol 1999; 84: 231-52. 5 Zhang W, Truttmann AC, Lüth D, McGuigan JAS. Apparent Mg2+-adenosine 5-triphosphate dissociation constant measured with Mg2+ macroelectrodes under conditions pertinent to 31P-NMR ionised magnesium determinations. Anal Biochem 1997; 251: 246-50. 6 McGuigan JAS, Lüthi D, Buri A. Calcium buffer solutions and how to make them; a do it yourself guide. Canad J Physiol Pharmacol 1991; 69: 1733-49. 7 Fry CH, Langley EM. Ion-selective Electrodes for Biological Systems. Sydney: Harwood Academic Publishers, 2001. 8 Zhang W, Truttmann AC, Lüthi D, McGuigan JAS. The manufacture and characteristics of magnesium selective macroelectrodes. Mag Bull 1995; 17: 125-30. 9 Günzel D, McGuigan JAS, Schlue W-R. Use of Mg2+ and Ca2+ macroelectrodes to measure binding in extracellular-like physiological solutions. Front Biosci 2005; 10: 905-18. 10 McGuigan JAS, Günther T, Lüthi D, Elder H, Johnson A. Advantages and pitfalls when using Mg2+-macroelectrodes to measure the free Mg2+ concentration in cell or membrane vesicle suspensions, or in Mg2+-ligand studies. Mag Bull 1997; 19: 110-8. 11 Fabiato A, Fabiato F. Calculator programmes for computing the composition of solutions containing multiple metals and ligands used for experiments on skinned muscle cells. J Physiol 1979; 75: 463-505; (Paris). 12 Martell AE, Smith RM. Critical stability constants 1; Amino acids, 1. New York: Plenum Press, 1974. 13 Martell AE, Smith RM. Critical Stability Constants 2: Amines, 2. New York: Plenum Press, 1975. 14 Smith GL, Miller DJ. Potentiometric measurements of stoichiometric and apparent affinity constants of EGTA for protons and divalent ions including calcium. Biochim Biophys Acta 1985; 893: 287-99. 15 Schoenmakers TJM, Visser GJ, Flik G, Theuvenet ARP. Chelator: an improved method for computing metal ion concentrations in physiological solutions. Biocomputing 1992; 12: 870-9. 16 Bers DM, Patton CW, Nuccitelli R. A practical guide to the preparation of Ca2+ buffers. Methods Cell Biol 1994; 40: 3-29. 17 Godt RE, Lindley BD. Influence of temperature upon contractile activation and isometric force production in mechanically skinned fibres of the frog. J Gen Physiol 1982; 80: 279-97. 18 Davies CW. Ion Association. London: Butterworth, 1962. 19 Hamer WJ, Wu Y-C. Osmotic coefficients and mean activity coefficients of uni-univalent electrolytes in water at 25°C. J Phys Chem Ref Data 1972; 4: 1047-99. 20 Harrison SM, Bers DM. Correction of proton and Ca association constants of EGTA for temperature and ionic strength. Am J Physiol 1989; 256: C1250-C1256. 21 Kushmerick MJ. Multiple equilibria of cations with metabolites in muscle bioenergetics. Am J Physiol 1997; 272: C1739-C1747. 22 Gupta RK, Gupta P, Yushok WD, Rose ZB. 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 1983; 117: 210-6. 23 Gupta RK, Benovic JL, Rose ZB. The determination of the free magnesium level in the human red cell by 31P NMR. J Biol Chem 1978; 253: 6172-6. 24 McGuigan JAS, Elder HY, Günzel D, Schlue W-R. Magnesium homeostasis in heart: a critical reappraisal. J Clin Basic Cardiol 2002; 5: 5-22. |
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