Anal. Chem. 1985, 57, 1511-1517
Naturally, during the preequilibrium phase, the “zero-current membrane condition” is not a precondition. LITERATURE CITED (1) (2) (3) (4) (5)
(6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18)
Mod, W. E. Anal. Chem. 1983, 55, 1165-1168. Lindner, E.; Tbth, K.; Pungor, E. Anal. Chem. 1982, 54, 202-207. Hulanicki, A.; Lewenstam, A. Anal. Chem. 1981, 53, 1401-1405. Rechnitz, G. A.; Kugler, G. C. Anal. Chem. 1967, 39, 1682. Rechnitz, G. A. “Ion-Selective Electrodes”; Durst, R. A., Ed.; US. Natlonal Bureau of Standards: Washington, DC, 1969; NBS Spec. Pubi. 314, Chapter 9. Tomita, T. “Glass Microelectrodes”; Lavalle, M., Schane, 0. F., Herbert, N. C., Eds.; Wiley: New York, 1969; Chapter 8. Grundfest, H. ”Glass Mlcroelectrodes”; Lavalle, M., Schane, 0. F., Herbert, N. C., Eds.; Wlley: New York, 1969; Chapter 10. Karlberg. B. J. Electroanal. Chem. 1973, 42, 115. Bagg, J.; Vinen, R. Anal. Chem. 1972, 44, 1773. Mathis, D. E.; Stover, F. S.; Buck, R. P. J. Membr. Sci. 1979, 4 , 395. Reinsfelder, R. E.; Schuitz, F. A. Anal. Chim. Acta 1973, 65, 425. Cammann. K. “Das Arbeiten mk ionenselektlven Elektroden”; Springer Verlag: Berlln, Heidelberg, New York, 1977. Morf, W. E. Anal. Lett. 1977, 70, 87. Beiljustln, A. A.; Valova, I. V.; Ivanovskaja, I. S. “Ion-Selectlve Electrodes”; Pungor, E., Ed.; Akademiai Kiadb: Budapest, 1978; p 235. Llndner, E.; Tbth, K.; Pungor, E. Anal. Chem. 1982, 54, 72-76. Jaenlcke, W.; Haase, M. 2. Electrochem. 1959, 63, 521-532. Schwab, G.-M. KolloidZ. 1942, 707, 204. Rhodes, R. K.; Buck, R. P. Anal. Chim. Acta 1980, 713, 67-78.
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(19) Nicolsky, B. P. Zh. Flz. Khim. 1937, 70, 495. (20) Pungor, E.; Tbth, K.; HrabBczy-PPII, A. Pure Appl. Chem. 1979, 57, 1913- 1980. (2 1) Umezawa, K.; Umezawa, Y. “Selecthrlty Coefficients for Ion-Selective Electrodes”; University of Tokyo Press: Tokyo, 1983. (22) Hulanlckl, A.; Lewenstam, A. Talanta 1977, 24, 171-175. (23) Crank, J. “The Mathematics of Diffusion”; Oxford University Press: Oxford, 1956. (24) Carslaw, H. S.; Jaeger, J. C. “Conduction of Heat in Soilds”; Oxford Universlty Press: Oxford, 1947. (25) Robinson, R. A.; Stokes, R. H. “Electrolyte Solutions”; Butterworth: London, 1955. (26) Markovic, P. L.; Osburn, J. 0. AICHE J. 1973, 79, 564. (27) Buck, R. P. “Ion-Selective Electrodes in Analytical Chemlstry”; Freiser, H. Ed.; Plenum: New York, 1978; Chapter 1. (28) Morf, W. E.; Lindner, E.; Simon, W. Anal. Chem. 1975, 47, 1596. (29) Hulanlckl, A.; Lewenstam, A.; Maj-Zurawska, M. Anal. Chim’. Acta 1979, 107, 121. (30) Hargnyi, E. G.; Tbth, K.; Pblos, L.; Pungor, E. Anal. Chem. 1982, 54, 1094. (31) Lindner, E.; Farkas, A.; HarsPnyi, E. G.; TBth, K.; Pungor, E., In preparation. (32) Hardnyl, E. 0.; Tbth, K.; Pungor, E. Paper presented on the “Fourth Scientific Sectlon on Ion-Selective Electrodes”, 8-12 October 1984, MPtrafured, Hungary.
RECEIVED for review November 16,1984. Accepted February 25, 1985.
Calibration of Ionized Calcium and Magnesium with Ligand Mixtures for Intracellular Ion-Selective Electrode Measurements Matthias Otto
Department of Chemistry, Bergakademie Freiberg, 9200 Freiberg, German Democratic Republic Peter M. May, Kevin Murray,’ and J. D. R. Thomas*
Department of Applied Chemistry, University of Wales Institute of Science and Technology, P.O.Box 13, Cardiff CFl 3XF, Wales, United Kingdom
Standard free calcium Ion concentrations from IO-’ M to M may be obtained by means of a single calibrating tltratlon with a calcium solution of a mixture of calclum-buffering iigands, namely, ethylene glycol bls(&amlnoethyl ester)-N,N,N’,N’-tetraacetic acid (EGTA), N-( 2-hydroxyethy1)ethylenediaminetrlacetic acid (HEDTA), and nltrllotriacetic acid (NTA). The accuracy of the procedure is evaluated by computer simulations. PVC matrlx membrane ion-selective electrodes (ISEs) based on organophosphate and neutral carrier materials have been used to Investigate the effectiveness of the callbration procedure with submicromolar levels of caiclum ions In the presence of millimolar levels of magnesium ions. The neutral carrier calcium ISE may be used down to lo-’ M [Ca2+] In the presence of millimolar levels of magnesium. A PVC matrix membrane organophosphate based electrode can be used to determine the ionized magnesium.
Ionized calcium and magnesium are present in single cells a t submicromolar and millimolar concentration levels, re-
’
Present address: N a t i o n a l Chemical Research Laboratory, CSIR, Pretoria, S o u t h Africa.
spectively (1). Such concentrations can be determined with ion-selective electrodes (ISEs) (1-4); the Ca2+ion determination is made possible by the sensitivity and selectivity of available calcium ISEs at micromolar levels while the Mg2+ ion determination is made with the less specific divalent ion electrodes since the calcium ion levels are sufficiently low to avoid interferences. The accuracy and precision of the determination of calcium ions in the submicromolar range are dependent on the selectivity of calcium ISEs in the presence of relatively high magnesium levels and on factors controlling the level of the calcium ions themselves. To obtain standards of ionized calcium concentrations down to M, methods have been proposed that are based either on the serial dilution of solutions containing the metal ion with a single complexing ligand, such as, NTA, EDTA (5-8), or EGTA (2-4,8, 9) or on the variation of pH in a solution of fixed metal to ligand concentrations (6, 10-12). Calibrations by these methods are laborious and the conditionsare not applicable to those found in vivo, since both the pH and the concentration of calcium buffering ligands vary only slightly in the cell. In vivo conditions are more closely approached by a recent method where free calcium ion concentrations are adjusted by adding increments of total calcium to a 1 X lo3 M EGTA solution a t
0003-2700/85/0357-1511$01.50/00 1985 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 57, NO. 8, JULY 1985
pH 7.4 (13). This method is essentially a titration of EGTA by Ca2+ions and, therefore, lacks precision in the unbuffered region near to the equivalence point. With regard to these shortcomings, the first objective of this work concerns the adjustment of free Ca2+ion concentrations down to M in solutions of fixed pH and constant concentrations of Ca-buffering ligands. This is achieved by using a mixture of ligands rather than just a single ligand. The second objective concerns the selectivity of calcium ISEs in the presence of magnesium, since it has not been shown hitherto how calcium ISEs respond to submicromolar Ca2+ ion concentrations in, say, intracellular solutions of varying free Mg2+ion concentrations (1-6 mM) at a fixed pH in the presence of complexing ligands. In previous investigations either the influence of Mg2+ ions on the calcium ISE was studied in the absence of Ca2+ions (14) or measurements in calcium/magnesium mixtures were carried out in unbuffered solutons at a Mg2+ion concentration (0.333 M) much higher than those in the cell (15). However, it has been shown that magnesium (unlike manganese) does not displace calcium from the calcium EGTA complex (9). The studies are based on two representative long range calcium ISEs (11),namely, a laboratory assembled alkylphenyl phosphate based PVC matrix membrane ISE with dioctyl phenylphosphonate solvent mediator and a commercial PVC matrix membrane neutral carrier-based calcium ISE. In the tests involving calcium and magnesium ion mixtures, the magnesium ions are determined with a PVC matrix membrane divalent electrode (16) in which the organophosphate sensor is present with a mixed solvent mediator of dioctyl phenylphosphonate and decan-1-01 (1:lO). EXPERIMENTAL SECTION Apparatus and Computations. Potentiometric data were measured with a Radiometer Model PHM64 pH millivolt meter. The digitized emf readings were used for computation on a VAX 11/780 computer interconnected with a Model 4014-1 Tektronix plotter. Concentrations of free Ca2+and Mg2+ions in the presence of complexhgligands were calculatedby the computer program ESTA (17),which solves the mass balance equations in systems of up to ten components. The ruggedness of the method was evaluated using ESTA to simulate titrations with a 0.02 M calcium containing solution, 0.2-mL increments being added over the range 0.4-0.5 mL (three-ligand mixture) and 0.2-2.6 mL (EGTA alone). These titration volumes were chosen to cover the same -log [Ca"] range (8.4-3.3) for each of the ligand systems. The influence of errors in the titration volumes and in the equilibrium constants on the calibration procedure was estimated by a Monte Carlo approach, superimposing random Gaussian noise of a given standard deviation. The reported data are averaged over five titrations. Multiple linear regression was used for fitting the ISE responses empiricallyto concentrationsof free calcium and magnesium ions. This was based on the Householder transformation and iterative refinement of the solution vector in order to obtain an accurate least-squares solution (18). Isometric projections of three-dimensionalsurfaces were drawn according to the algorithm of Hall (19). The surface heights at the nodes of a regular mesh were generated either from polynomials obtained by multiple regression or from splines in its Bspline representation (20). The spline coefficients were calculated by fitting the emf values to [Ca2+]and [Mg2+]with a weighted least-squares bicubic spline routine (21). Electrodes. Organophosphate liquid-membrane electrodes for sensing ea2+ions were based on calcium bis(di[4-(1,1,3,3tetramethylbutyl)phenyl] phosphate) sensor (DTMBPP) and di-n-octyl phenylphosphonate solvent mediator (DOPP) immobilized in PVC fabricated as previously described (22). The neutral carrier calcium ISE was the Philips commercial plastic IS561 calcium membrane part no. 9436 094 75861. The magnesium ISE was prepared from the organophosphate (DTMBPP) sensor used for the calcium ISE but with a solvent
\
0
1
2
\
3
4
5
Volume 0.02M CaC12 /mL
Figure 1. Simulated titration of EGTA alone and of EGTA, HEDTA, NTA mixtures with 0.02 M [Ca*] ion solutions. Tibands: 5 X lo4 M EDTA, 5 X lo4 M HEDTA, 5 X lo4 M NTA, pH 7.4 (0.05 M Tris), 0.1 M ionic strength, 25 OC.
mediator mixture of DOPP/decan-1-01in the ratio of 1:lO (v/v). Reagents. If not specified, all chemicals were of analytical reagent grade. The complexing ligands ethylene glycol bis(paminoethyl ester)-N,N,N',N'-tetraaceticacid (EGTA, 97-98%, Sigma Chemical Co.), nitrilotriacetic acid (NTA, 99%, disodium salt, Sigma Chemical Co.), N-(2-hydroxyethyl)ethylenediaminetriacetic acid (HEDTA,99%, Aldrich ChemicalCo.), and the pH buffer tris(hydroxymethy1)aminomethane (Tris, 99.9%, Sigma Chemical Co.) were used as received. The chemicals for preparing the organophosphatebased electrodeswere prepared as described elsewhere (22-24). Procedures. Calibration of free calcium ion concentrations was carried out by titration of a mixture of the ligands EGTA, HEDTA, and NTA with Ca2+ion solutions. In a typical experM EGTA, 5 X iment, 50.0 mL of a solution containing 5 X lo4 M HEDTA, 5 X lo4 M NTA, and 10" M Tris (pH 7.4, adjusted with hydrochloric acid), in the presence of potassium chloride or sodium chloride to an ionic strength of 0.1 M, was titrated using a Metrohm buret with 0.02 M calcium chloride up to the addition of 5 mL. The emf values of up to three ISEs were measured at 25 OC relative to a saturated calomel electrode. The reported emfs are averages from three titrations. A temperature of 25 "C was chosen because of the availability of calcium-ligand stability data. This temperature is either the same or near to that used by other workers, e.g., see ref 4, 5, 8, 9,and 13. RESULTS AND DISCUSSION Calibration of Free Calcium Ions. Adjustment of calcium ion concentrations down to M a t constant pH and fixed ligand concentration was attempted following the procedure proposed by Bers (13)and monitoring by means of the organophosphate sensor (DTMBPP) calcium ISE, For this, different amounts of total Ca2+ion concentrations were added to a 1X M EGTA solution at pH 7.4 and an ionic strength of 0.1 M (KC1). The experimental emf readings for replicated M were only reprofree Ca2+ion concentrations below ducible to within 5 mV. Furthermore, response of the calcium ISE at these low concentrations was much slower (2 to 3 min) than for measurements of concentrations >W4M. These features can be attributed to the calibration procedure itself rather than to the quality of the calcium ion sensor. M EDTA solution Addition of calcium ions to a 1 X at fixed pH is, basically, a titration of the ligand by the metal ion. This is demonstrated in Figure 1by a simulated plot of log [Ca2+]values vs. the volume of added calcium-containing solution. As expected, the log [Ca2+]changes are very steep near the equivalence point because of poor buffering for -log [Ca2+]values of 4 to 7 , resulting in poor reproducibility of calibration measurements.
ANALYTICAL CHEMISTRY, VOL. 57, NO. 8,JULY 1985
Table I. Equilibrium Model for Computation of Ionized Calcium and Magnesium in Ligand Mixtures of EGTA, HEDTA, NTA, and Tris Buffer species H-EGTA H 2- EGTA H8EGTA HI-EGTA Ca-EGTA Ca-H-EGTA ME-EGTA
M~-H-EGTA H-HEDTA Hw HEDTA
H;-HEDTA
log stability constanta 9.40 18.18 20.84 22.84 10.86 14.76 5.21 7.62 9.81 15.20 17.80
species Ca-HEDTA Ca-H-HEDTA Mg-HEDTA H-NTA HyNTA HS-NTA Ca-NTA Ca-NTA2 Mg-NTA H-Tris
log stability constanta 8.20 11.00 7.0 9.65 12.13 14.03 6.39 8.76
1513
-180,
.\
I
h
-1ooL
5.47
8.09
"At 25 "C and 0.1 M ionic strength.
In order to improve ISE calibration at low calcium ion levels, calibration sets consisting of two or three ligands including the complexing agents EDTA, trans- and cis-CDTA (transor cis-1,2-diaminocyclohexane-N,N,N',N'-tetraaceticacid), citric acid, HEDTA, NTA, DTPA (diethylenetriaminepentaacetic acid), and EEDTA (1,2-diaza-4-oxaheptane1,1,7,7-tetraacetic acid) were tested by computer simulations using ESTA. The best results were obtained by combining EGTA and HEDTA for -log [Ca2+]values between 8 and 5 and by use of a three ligand mixture (EGTA, HEDTA, NTA) for the full -log [Ca2+]range between 8 and 3. (These agents have previously been used by Tsien and Rink (14) in single ligand solutions.) The protolysis and Ca2+ligand stability constants used for calculation of free metal ion concentrations were taken from the literature (25) and are summarized in Table I. Tris was used as the pH buffer since various Ca2+ ion activity standards and several studies (e.g., ref 4 and 5) are based on this system. However, other pH buffers could have been used, in particular HEPES which is now being assessed by the International Federation of Clinical Chemistry (26). The simulated titration curves for the ligand mixtures (Figure 1)suggest that in the presence of three ligands, the log [Ca2+]and, hence, the emf change gradually because the equivalence points are obscured by competing equilibria among the different metal-ligand complexes. Experimental calibration of a calcium ISE vs. free Ca2+ion concentrations under the conditions outlined in Figure 1 in the presence of all three ligands gave poor agreement between the calculated and experimental titration curves. At free Ca2+ ion concentrations between and 10+ M, the emf readings were about 5 mV lower than computed values. The deviations became more pronounced (up to 10 mV) when the concentration of 0.05 M Tris was increased to 0.2 M. On the other hand, the deviations were minimized by decreasing the buffer concentration to 0.01 M, resulting in the reasonable agreement between theoretical and experimental titrations in 0.1 M potassium chloride for emf values in the range -30 to -130 mV (Figure 2). The calibration plot of measured emf values vs. free Ca2+ion concentrations in Figure 3 shows that the emf readings cover -log [Ca2+]values between about 7 and 3. The deviations at -log [Ca2+]values of E 120.
-6
o o o o o o o o
0
x .
O
\
130-
* -loor -120;
/ /
x
x
"
~
x*
*
140
8
7
6
5
4
3
-Log [C&]
Figure 5. Calibration of a neutral carrier electrode by condltioning of the ISE in a solution of 0.1 M calcium chloride (X) or M calcium condRions as in Figure 2; slope, 27.25 mV; intercept 125.2 chloride (0);
mV. bo
electrode with respect to alkali metal ions. (In the presence of 0.1 M ammonium ions, the linear range is limited to 2 X IO-' M [Ca2+]and there is worse agreement between the experimental and calculated values.) The neutral carrier calcium ISE behaves similarly as long as the electrode is conditioned in 0.1 M [Ca2+]solution, but there is a greater tendency for this electrode to drift compared with negligible drift for the DTMBPP ISE. In contrast to the DTMBPP sensor the detection limit of the neutral carrier electrode can be improved by 1order of magnitude if the ISE is conditioned in a solution of about 10" M [Ca2+]for at least 1 h, as demonstrated in Figure 5. Conditioning of the electrodes a t low [Ca2+]was found to improve the reproducibility of both types of electrodes. In addition, after conditioning at M [Ca2+]and following the three-ligand calibration procedure, the speed of response of both electrodes did not differ significantly, either between measurements in unbuffered solutions at concentrations>lo4 M [Ca2+]or for buffered solutions at concentrations of SlO-' M [Ca2+]. Calibration of Calcium and Magnesium Mixtures. Titrations based on the model in Table I were simulated for free magnesium ion concentrations between 1 and 6 mM in order to prepare calibration mixtures with defined concentrations of free Ca2+and Mg2+ions. As a result of the competing equilibria between the two metal ions and the three ligands, the ligand concentrations of the calibration mixture had to be modified in order to retain its highly buffered properties. The concentrations of EGTA and NTA were increased to low3M. HEDTA concentration was 3 X M for 1 mM free [Mg2+]and M for 6 mM free [Mg2+]. The responses of calcium ISEs in mixed calcium/magnesium solutons after conditioning of the electrodes in 0.1 M calcium chloride solution are shown in Figure 6A for the DTMBPP-ISE and in Figure 6B for the neutral carrier electrode. The concentrations differ slightly from those used in the simulations. As seen from Figure 3A, the organophosphate calcium ISE is strongly affected by free Mg2+ions even at 1.35 mM [Mg2+]while the neutral carrier electrode shows deviations from the straight l i e only at 6 mM [Mg2+]. Further analysis of data for the neutral carrier electrode (Figure 6B) indicated that deviations a t
