Analytical Biochemistry 436 (2013) 29–35
Contents lists available at SciVerse ScienceDirect
Analytical Biochemistry
journal homepage: www.elsevier.com/locate/yabio
Calculated and measured [Ca2+] in buffers used to calibrate Ca2+ macroelectrodes
John A.S. McGuigan ⇑, Friederike Stumpff ⇑
Institute for Veterinary Physiology, Department of Veterinary Medicine, Freie Universität Berlin, 14163 Berlin, Germany
a r t i c l e
i n f o
Article history:
Received 20 September 2012
Received in revised form 12 December 2012
Accepted 29 December 2012
Available online 16 January 2013
Keywords:
Ca2+ macroelectrodes
Ca2+ buffer solutions
Measured Ca2+
Calculated Ca2+
Ionized calcium
Physiological buffer solutions
a b s t r a c t
The ionized concentration of calcium in physiological buffers ([Ca2+]) is normally calculated using either
tabulated constants or software programs. To investigate the accuracy of such calculations, the [Ca2+] in
EGTA [ethylene glycol-bis(b-aminoethylether)-N,N,N|,N|-tetraacetic acid], BAPTA [1,2-bis(o-aminophenoxy)ethane-N,N,N|,N|-tetraacetic acid], HEDTA [N-(2-hydroxyethyl)-ethylenediamine-N,N|,N|-triacetic
acid], and NTA [N,N-bis(carboxymethyl)glycine] buffers was estimated using the ligand optimization
method, and these measured values were compared with calculated values. All measurements overlapped in the pCa range of 3.51 (NTA) to 8.12 (EGTA). In all four buffer solutions, there was no correlation
between measured and calculated values; the calculated values differed among themselves by factors
varying from 1.3 (NTA) to 6.9 (EGTA). Independent measurements of EGTA purity and the apparent dissociation constants for HEDTA and NTA were not significantly different from the values estimated by the
ligand optimization method, further substantiating the method. Using two calibration solutions of pCa
2.0 and 3.01 and seven buffers in the pCa range of 4.0–7.5, calibration of a Ca2+ electrode over the pCa
range of 2.0–7.5 became a routine procedure. It is proposed that such Ca2+ calibration/buffer solutions
be internationally defined and made commercially available to allow the precise measurement of
[Ca2+] in biology.
Ó 2013 Elsevier Inc. All rights reserved.
The pH of physiological solutions is measured with a pH electrode calibrated with commercially available, internationally defined standards. In contrast, the free concentrations of calcium
([Ca2+])1 and magnesium ([Mg2+]) in physiological buffer solutions
are normally calculated using either tabulated constants or various
software routines. It has been shown that such calculations can be
seriously misleading [1], and this has major repercussions for fields
in which precise buffering of [Ca2+] is essential such as in patch
clamping, measurement of intracellular [Ca2+], and molecular biology. Given the crucial role that [Ca2+] and [Mg2+] play in determining
the behavior of numerous physiologically important proteins [2], the
lack of precision in Ca2+ and Mg2+ buffering may well rank high on
the list of factors contributing to the variability of experimental outcomes in physiology and biology.
In a review of the various methods to measure the ionized concentrations in buffer solutions [3], the ligand optimization method
⇑ Corresponding authors. Fax: +49 30 838 62510.
E-mail
addresses:
[email protected]
(J.A.S.
McGuigan),
[email protected] (F. Stumpff).
1
Abbreviations used: [Ca2+], ionized concentration of calcium; [Mg2+], ionized
concentration of magnesium; EGTA, ethylene glycol-bis(b-aminoethylether)N,N,N|,N|-tetraacetic acid; ATP, adenosine-5 0 -triphosphate; EDTA, 2,20 ,2 00 ,2 000 (ethane-1,2-diyldinitrilo)tetraacetic acid; BAPTA, 1,2-bis(o-aminophenoxy)
ethane-N,N,N|,N|-tetraacetic acid; HEDTA, N-(2-hydroxyethyl)-ethylenediamineN,N|,N|-triacetic acid; NTA, N,N-bis(carboxymethyl)glycine; [Ca]T, total calcium
concentration; SD, standard deviation; CV, coefficient of variation; [Ligand]T, total
concentration of chelating ligand.
0003-2697/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved.
http://dx.doi.org/10.1016/j.ab.2012.12.020
[4] based on Ca2+/Mg2+ macroelectrodes was shown to be the most
accurate. Using this method, it was possible to determine both ligand purity and the [Ca2+] and [Mg2+] in Ca2+–EGTA [ethylene glycol-bis(b-aminoethylether)-N,N,N|,N|-tetraacetic acid], Mg2+–ATP
(adenosine-50 -triphosphate), and Mg2+–EDTA [2,20 ,200 ,2000 -(ethane1,2-diyldinitrilo)tetraacetic acid] buffers. Ionized concentrations
calculated using software programs or tabulated constants differed
among themselves and from the measured values up to a factor of
3 [1].
In this study, the reliability of the ligand optimization method
was further scrutinized by (i) measuring the pCa of buffer solutions
using not only EGTA as previously [1] but also BAPTA [1,2-bis(oaminophenoxy)ethane-N,N,N|,N|-tetraacetic acid], HEDTA [N-(2hydroxyethyl)-ethylenediamine-N,N|,N|-triacetic acid], and NTA
[N,N-bis(carboxymethyl)glycine] and (ii) independently estimating
EGTA purity by measuring changes in pH when titrating an EGTA
solution with CaCl2 [3]. The excellent correlation among the results
obtained by the four buffers and the agreement of the EGTA purity
estimated by the ligand optimization method and the pH method
underpins the accuracy of this method for the determination of
the [Ca2+] and/or [Mg2+] in the buffers. Calculated [Ca2+] for the
four buffer solutions from published constants or programs yielded
results that again deviated from one another and from the measured values.
This study emphasizes once again the need for exactly defined
standards for [Ca2+] and [Mg2+] buffers. We also demonstrate that
Calculated and measured [Ca2+] in buffers / J.A.S. McGuigan, F. Stumpff / Anal. Biochem. 436 (2013) 29–35
30
if such standards were available, calibration of Ca2+ and Mg2+ electrodes for the determination of [Ca2+] and [Mg2+] in physiological
solutions would become simple, routine, and accurate.
meter in mV mode; input impedance of both channels was
1012 O. pH was independently monitored and corrected when necessary to 7.4. When changing solutions, excess fluid was blotted
from the electrodes using laboratory grade tissue paper.
Materials and methods
Measurement of [Ligand]T and Kapp via ligand optimization method
Solutions
Potentials were measured with the Ca2+ electrode in both the
calibration and buffer solutions. Measurement was commenced
in the calibration solutions of 10 mM CaCl2 and then stepped down
to 0.5 mM, yielding a calibration curve in the Nernstian range.
After the calibration solutions in the Nernstian range, the electrode
potential in the 10 buffer solutions (with unknown pCa values) was
measured from solution 1 (largest [Ca]T) to solution 10 (lowest
[Ca]T). To check for drift, the potential was again measured in the
10-mM calibration solution. Here, 3 min in the calibration solutions and 4 min in the buffer solutions gave a steady potential.
The total time for a complete calibration was approximately
70 min. Subsequently, the data were fitted with the Excel program
ALE [6], which optimizes the values for [Ligand]T (total concentration of chelating ligand), the Kapp in the buffer solutions, and a
parameter describing the nonlinearity of the electrode to obtain
the best fit of the data to the Nikolsky–Eisenman equation (see
Ref. [7], p. 68). From the value of Kapp, the [Ligand]T, and the
[Ca]T, the [Ca2+] (or pCa) can be calculated for each of the buffer
solutions (for details, see Ref. [3] and http://www.stats.gla.ac.uk/
jim/ligopt.html).
Background
The experiments were carried out in a sodium background solution whose concentration was 5 mM KCl, 126 mM NaCl, 4 mM
NaOH, and 10 mM Hepes. The pH was set to 7.4 by back-titration
with 1 M HCl.
Calibration solutions
These were used to calibrate the Ca2+ electrode in the Nernstian
range (pCa 2.00–3.30) and were based on a commercially available,
1-M standard CaCl2 solution (Sigma–Aldrich). The calibration solutions contained nominal calcium concentrations in the background
solution of 10, 6, 4, 2.5, 1.5, 0.8, and 0.5 mM. For the actual concentrations, dilution was taken into account.
Buffer solutions
The ratio method for the preparation of the buffer solutions was
used. In this method, two background solutions are prepared: one
containing only ligand and the other containing Ca–ligand. The two
solutions are then mixed in the appropriate ratios to give the 10
buffer solutions (see Ref. [3]) in which the total calcium ([Ca]T) is
known but the ionized [Ca2+] needs to be determined. Sufficient
NaOH was substituted for NaCl to compensate for the acidity of
the ligands so that the pH of both the ligand solution and the
Ca–ligand solution was just slightly more alkaline than pH 7.4.
Both solutions were titrated to pH 7.4 with 1 M HCl. The calcium
concentration in EGTA, HEDTA, and NTA was 4.0 mM with similar
nominal ligand concentrations; for BAPTA, the calcium concentration was 1 mM with a similar nominal BAPTA concentration. The
10 ratios of Ca–ligand/ligand were 7:1, 6:1, 5:1, 4:1, 3:1, 2:1, 1:1,
1:2, 1:4, and 1:9 (see Table 5 in Ref. [3]).
Calculation of apparent dissociation constants
The tabulated stoichiometric constants were obtained from
either Ref. [8] or Ref. [9]. pHa (activity) was converted to pHc (concentration) using the empirical equation for the single ion activity
coefficient for H+ in Ref. [10]. The details of the method of calculation are given at http://www.stats.gla.ac.uk/jim/ligopt.html. The
[Ca2+] in the buffer solutions was also calculated with the program
Chelator [11].
Statistics
pH, temperature, glassware, and pipetting
Results, where appropriate, are expressed as means ± standard
deviations (SDs). The coefficient of variation (CV, mean
100), exSD
pressed as a percentage, is used to describe the level of imprecision
of the results (see Ref. [1]).
pH was calibrated once or twice daily to an accuracy of ±0.01 pH
units. The experiments were carried out at room temperature. During the experiments, the room temperature was routinely measured and the temperature was 23.0 ± 1.0 °C (n = 21). All
glassware was washed three times in high-resistivity distilled
water to reduce Ca2+ contamination. To increase the accuracy of
the pipetting [3], automatic Eppendorf pipettes were used.
Results
Calibration of Ca2+ macroelectrode
The results of the calculations for the four Ca2+ buffers are illustrated in Table 1 and Fig. 1. There were five measurements for both
EGTA and BAPTA, six measurements for HEDTA, and one measurement for NTA. For clarity, the mean values for EGTA, BAPTA, and
HEDTA are shown; however, the fit to the Nikolsky–Eisenman
equation was to all of the data. As illustrated in Fig. 1, the buffer
ranges for NTA, HEDTA, BAPTA, and EGTA overlap, especially the
latter three. The electrode shows a Nernstian response down to a
Electrodes and recording system
Electrodes were obtained from Metrohm (Switzerland): calcium
polymer membrane (6.0504.100) and 3 M KCl reference
(6.0726.107). The measuring system is described in detail in Ref.
[5]. In brief, 100-ml beakers were used, and these were stirred continuously. Recording was between the Ca2+ electrode and the 3 M
KCl reference electrode. The potential was measured using a pH
Table 1
Ligand purity and apparent dissociation constants.
Ligand
Kapp
±SD
CV%
n
pKapp
pKapp range
Purity (%)
±SD (%)
EGTA
BAPTA
HEDTA
NTA
60.75 nM
131.59 nM
1.88 lM
78.57 lM
4.24 nM
8.22 nM
0.04 lM
–
6.97
6.24
2.12
5
5
6
1
7.22
6.88
5.72
4.10
6.22–8.22
5.88–7.88
4.72–6.72
3.10–5.10
91.05
91.56
100.0
100.0
0.87
0.54
–
–
Calculated and measured [Ca2+] in buffers / J.A.S. McGuigan, F. Stumpff / Anal. Biochem. 436 (2013) 29–35
pCa of approximately 5.0; between pCa 5.0 and 8.0, the electrode
deviates from a Nernstian response. From the Nikolsky–Eisenman
equation, the limit of detection (defined in Ref. [7], p. 69) of the
macroelectrode was a pCa of 7.22. The measurements show that
for both EGTA and BAPTA, the CV of the Kapp lies between 6 and
7%; in HEDTA buffers, where the electrode is within the Nernstian
range, the CV is only 2%. The buffer range is taken as ±1 pCa unit
from the pKapp [3], and as shown in Table 1, the range of these buffers is from pCa 8.22 (EGTA) to 3.10 (NTA). The purity of both EGTA
and BAPTA is some 91% due to bound water [3], but that of both
HEDTA and NTA is 100%.
31
Table 2
[Ca2+] in the buffer solutions.
Reproducibility of [Ca2+] in buffer solutions
Buffer
number
EGTA (n = 5)
lM
±SD
CV%
pCa
lM
±SD
CV%
pCa
1
2
3
4
5
6
7
8
9
10
1.343
0.910
0.627
0.427
0.279
0.164
0.073
0.035
0.017
0.007
0.098
0.064
0.043
0.029
0.193
0.011
0.005
0.002
0.001
0.0005
7.3
7.0
6.9
6.9
6.9
6.9
6.9
6.9
6.9
6.9
5.87a
6.04
6.20
6.37
6.55
6.78
7.13
7.45
7.77
8.12
1.995
1.501
1.112
0.799
0.543
0.331
0.153
0.073
0.036
0.015
0.212
0.138
0.091
0.060
0.038
0.022
0.009
0.004
0.002
0.001
10.6
9.2
8.2
7.5
7.0
6.7
6.4
6.4
6.3
6.3
5.70a
5.82
5.95
6.10
6.26
6.48
6.81
7.13
7.44
7.80
BAPTA (n = 5)
HEDTA (n = 6)
Table 2 summarizes the [Ca2+], pCa values, SDs, and CVs in the 10
buffer solutions for EGTA, BAPTA, HEDTA, and NTA. As shown in this
table, the EGTA buffer solution 1, with a pCa of 5.87, lies outside of
the buffer range shown in Table 1. The BAPTA solution 1 also lies
outside of the range, although it is on the borderline; with HEDTA
and NTA, all buffer solutions lie within the accepted range. The CV
for EGTA, with the exception of solution 1, is 7%; the CV for BAPTA
is slightly larger, being between 6.3 and 9.2% (solution 1 is outside
of the selected range). HEDTA, which lies mostly in the Nernstian
range of the electrode, has a CV of only 2% (see Discussion).
1
2
3
4
5
6
7
8
9
10
a
NTA (n = 1)
lM
±SD
CV%
pCa
lM
pCa
12.833
11.071
9.280
7.461
5.619
3.758
1.880
0.942
0.471
0.209
0.260
0.226
0.190
0.154
0.116
0.078
0.039
0.019
0.009
0.004
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
4.89
4.96
5.03
5.13
5.25
5.43
5.73
6.03
6.33
6.68
309.6
287.3
260.4
227.3
186.3
135.4
73.0
37.6
19.0
8.5
3.51
3.54
3.58
3.64
3.73
3.87
4.14
4.42
4.72
5.07
Buffer outside of the accepted buffer range.
Accuracy of ligand optimization method
The values in Table 1 have been calculated from the ligand optimization method using the program ALE. The fact that all of the
buffers in Fig. 1 overlap indirectly supports the validity of the
method (see also Ref. [3]). In this series of experiments, the opportunity was also taken to check the validity of the ligand optimization method against other methods of measuring purity and the
apparent dissociation constants.
compared with the purity determined on the same batch of EGTA
by the ligand optimization method using the Excel program ALE
[6]. There was no significant difference between the value of
3.797 ± 0.099 mM (n = 6) obtained using the pH method and the
value of 3.803 ± 0.057 mM (n = 7) measured using the ligand optimization method [6]. (Note that determination was carried out on
a different batch of EGTA than in the experiments shown in Fig. 1.)
Purity
To check estimation of purity, the purity of EGTA determined by
the pH method (see Ref. [12]; see also Fig. 6D in Ref. [3]) was
Apparent dissociation constant
In a first step, a complete calibration of the electrode was carried out in both EGTA and BAPTA using the ligand optimization
method. Based on this calibration, the [Ca2+] in both the HEDTA
and NTA could then be estimated from the measured potentials.
A plot of [Ca2+] against the bound Ca2+ ([Ca–ligand]B) could be fitted by the hyperbolic (see Fig. 1A in Ref. [13]):
0
Calibration (pCa 2.00-3.30)
Potential difference, E (mV)
-20
-40
½Ca—LigandB ¼
-60
NTA (pCa 3.51-5.07)
-80
-100
HEDTA (pCa 4.90-6.67)
-120
BAPTA (pCa 5.67-7.80)
-140
EGTA (pCa 5.87-8.12)
-160
9
8
7
6
5
4
3
2
pCa
Fig.1. Calibration of the Ca2+ macroelectrode. To calibrate the electrode in the
Nernstian range, solutions with a free calcium concentration from approximately
pCa 2.004 to 3.301 were prepared by dilution from a 1-M stock solution. For lower
concentrations of free calcium, buffer solutions of known [Ca]T but unknown [Ca2+]
were prepared using NTA (closed triangles), HEDTA (open circles), BAPTA (open
squares), and EGTA (closed circles). Values for the pCa of these buffer solutions were
then obtained using the ligand optimization method [3,6] to fit the data to the
Nikolsky–Eisenman equation, yielding E = 57.190 + 28.533 log (10pCa + 6.0554 108); r = 0.999743.
½LigandT ½Ca2þ ðK app þ ½Ca2þ Þ
:
ð1Þ
Using this procedure, Kapp for HEDTA was determined as
1.87 ± 0.025 lM (n = 7), which is in excellent agreement with the
previous value of 1.88 ± 0.039 lM estimated by ALE; there is no
significant difference. A further experiment was carried out with
NTA. Kapp estimated from ALE was 78.6 lM (Table 1) and that from
measuring [Ca2+] was 81.0 lM. Both of these results independently
support the validity of the ligand optimization method (see also
Discussion).
Comparison between measured and calculated values of [Ca2+] in Ca2+
buffers
EGTA
Fig. 2A shows the comparison with EGTA buffers. [Ca2+] was calculated using the constants from Ref. [8] for both 100% purity and
the measured purity. Calculations were also carried out using the
tabulated constants in Ref. [9] and the program Chelator [11] but
using the measured purity for EGTA. There was no agreement between the values calculated using the constants of Refs. [8] and
[9] or the program Chelator; these differences versus the measured
Calculated and measured [Ca2+] in buffers / J.A.S. McGuigan, F. Stumpff / Anal. Biochem. 436 (2013) 29–35
32
values were on the order of 2. If purity was ignored, the values decreased by a maximum factor of one-third. The maximum difference between the extreme values was by a factor of 6.9.
either greater or less than the measured concentrations by a factor
of 1.4 (i.e., no agreement between measured and calculated
values).
BAPTA
The measured and calculated values for BAPTA buffer solutions
are illustrated in Fig. 2B. The constants for BAPTA were taken from
Ref. [14], and the [Ca2+] was calculated assuming either 100% purity or the measured purity for BAPTA. Both the program Chelator
[11] and calculations using the constants from Ref. [14] gave similar results, which is not surprising given that the constants used in
both cases were the same. There is no agreement between calculated and measured values. Calculation using the measured purity
increased the [Ca2+] by a factor of 1.8, assuming that 100% purity
decreased the [Ca2+] by a factor of 1.5. The difference between
the minimum and maximum calculated values was 2.8.
NTA
The comparison between the calculated and measured [Ca2+]
values for NTA is illustrated in Fig. 2D. Both calculated values for
[Ca2+] are greater; Chelator increases the values by approximately
a factor of 1.1, and calculation using the constants from Ref. [8] increases the values by approximately 1.5 times. Again, there is no
agreement between calculated values or between calculated and
measured values for [Ca2+].
HEDTA
Fig. 2C shows the comparison between calculated and measured [Ca2+] in HEDTA buffer solution. The calculated values are
3.2
Electrode calibration with buffers of known concentration
Calibration of the electrode in the self-prepared calibration and
buffer solutions is both tedious and time-consuming, with the
measurements taking approximately 70 min. However, having
measured the [Ca2+] in the buffer solutions, it was possible to
calibrate the electrode directly in such solutions. The calibration
4.0
A: EGTA
2.8
a
3.5
b
2.4
2.0
c
1.6
1.2
0.8
Calculated concentration (µM)
Calculated concentration (µM)
B: BAPTA
a
d
0.4
3.0
2.5
2.0
1.5
b
1.0
0.5
0.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.0
0.5
Measured concentration (µM)
20
450
1.5
2.0
2.5
D: NTA
C: HEDTA
a
a
400
Calculated concentration (µM)
18
Calculated concentration (µM)
1.0
Measured concentration (µM)
16
14
12
10
b
8
6
4
350
b
300
250
200
150
100
50
2
0
0
0
2
4
6
8
10
Measured concentration (µM)
12
14
0
40
80
120
160
200
240
280
320
360
Measured concentration (µM)
Fig.2. (A) Comparison between measured values (Table 2) and calculated values of [Ca2+] in EGTA buffers: (a) program Chelator [11] calculated using measured purity; (b)
calculated from the constant in Ref. [9] and measured purity; (c) calculated from the constant in Ref. [8] and measured purity; (d) calculated from the constant in Ref. [8] but
assuming 100% purity. For orientation, the dashed line has been added to this panel and the subsequent panels to represent points of equality between measured and
calculated values. (B) Comparison between measured values (Table 2) and calculated values of [Ca2+] in BAPTA buffers: (a) calculated from the constant in Ref. [14] and
measured purity; (b) calculated from the constants in Ref. [14] but assuming 100% purity. (C) Comparison between measured values (Table 2) and calculated values of [Ca2+]
in HEDTA buffer solutions: (a) calculated from the constant in Ref. [8]; (b) program Chelator. (D) Comparison between measured values (Table 2) and calculated values of
[Ca2+] for NTA: (a) calculated from the constant in Ref. [8]; (b) program Chelator [11].
Calculated and measured [Ca2+] in buffers / J.A.S. McGuigan, F. Stumpff / Anal. Biochem. 436 (2013) 29–35
33
Table 3
Electrode calibration with standard solutions.
Solution
pCa
Concentration
Eight-point calibration
Seven-point calibration
Six-point calibration
Calibration
10 mmol/L
0.8 mmol/L
2.004
3.097
9.900 mM
0.799 mM
Buffer
NTA-7
HEDTA-3
BAPTA-1
BAPTA-3
BAPTA-6
BAPTA-8
BAPTA-9
4.11
5.03
5.70
5.95
6.48
7.13
7.44
77.2 lM
9.28 lM
1.99 lM
1.11 lM
0.33 lM
73.4 nM
36.0 nM
0
Calibration
It is well known that the function of proteins is dramatically affected by changes in [Ca2+] and [Mg2+] [2]. Despite this, a standard
procedure for the buffering of physiological solutions in the nanomolar and micromolar range for [Ca2+] and [Mg2+], respectively, is
currently lacking.
pCa 3.097
-40
NTA-7
-60
Discussion
pCa 2.004
-20
Potential difference, E (mV)
Ligand optimization method
-80
HEDTA-3
The ligand optimization method has now been used to determine the [Ca2+] not only in EGTA buffer solutions as previously
[1] but also in solutions buffered with BAPTA, HEDTA, and NTA.
In addition, we present two approaches that directly substantiate
the method:
-100
BAPTA-3
-120
BAPTA-6
-140
BAPTA-8
BAPTA-9
-160
8
7
6
5
4
3
2
pCa
Fig.3. Comparison between calibration using the ligand optimization method and
calibration with eight buffer solutions of known [Ca2+]. The mean calibration curve
is shown as the dashed line, and the two continuous lines are ±SD of the measured
mV potentials. Open squares and closed circles represent two measurements using
the eight solutions in Table 3. These potential measurements lie within ±SD of the
calibration curve; the eight measurements have been highlighted with arrows.
Because the two measurements for the seven- and six-point calibrations overlapped
with the eight-point calibration, for clarity they are not illustrated.
solutions and the buffer solutions used are tabulated in Table 3,
which also shows the [Ca2+] as well as the pCa values of the solutions used in the calibration procedures. BAPTA was chosen over
EGTA because BAPTA is much less pH sensitive than EGTA (see
Fig. 12A in Ref. [3]). Fig. 3 illustrates a comparison between the
standard calibration as illustrated in Fig. 1 and that using standard
buffer solutions. The calibration with eight solutions is based on an
interval of 1 pCa unit down to pCa 5 (Nernstian response of the
electrode). The last five BAPTA buffer solutions (i.e., pCa 5.70,
5.95, 6.48, 7.13 and 7.44) cover the non-Nernstian response of
the electrode. The time in each solution was 4 min, making the total time of such a calibration 32 min because in order to correct for
drift the potential was remeasured in pCa 2.00.
Standardized calibration was also carried out with seven and six
solutions (see Table 3). These are not illustrated in Fig. 3 because
they overlapped with the eight-point calibration, giving identical
results. By reducing the number of solutions, the time for calibration is greatly reduced. With no standard solutions, a full calibration took some 70 min; eight standard solutions reduced the
time to 32 min, seven standard solutions reduced it to 29 min,
and six standard solutions reduced it to 25 min. In principle, a
calibration should be possible with a smaller number of solutions,
albeit at the expense of accuracy.
1. [EGTA]T: As shown in this article, measurement of the purity of
EGTA by the pH method [12] gave identical results to the purity
estimations using the optimization method.
2. pKapp values: Calibrating the Ca2+ electrode in the EGTA and
BAPTA buffers and then calculating the Kapp of HEDTA from
the measured [Ca2+] gave a value for the Kapp that was not significantly different from that estimated by the ligand optimization method. Only one measurement was made of the Kapp for
NTA, but again the two methods of estimating the Kapp gave
very similar results.
Indirect support for the method comes from the results in Fig. 1
for the estimated [Ca2+] for all four buffers because all lie on the
same calibration curve. In view of these findings and previous ones
[4,13], it can be concluded that the ligand optimization method
accurately estimates the [Ca2+] and [Mg2+] in buffer solutions.
Coefficient of variation
Previously, it has been argued that the CV of the [X2+] in the buffer solutions should be less than 5% [1], which corresponds to a
range of ±10% for the mean value of [Ca2+]. As shown in this article,
(i) an increase in accuracy of solution preparation, (ii) an increase
in accuracy of pipetting, and (iii) improved control of pH in the
buffer solution reduced the CV for EGTA from 27.4% [1] to the 7%
in this study (Table 2). For HEDTA, an even lower CV (2%) was
observed. For BAPTA, CV varies from 10.6 to 6.3%. Solution 1 is
outside of the permissible range for this buffer.
Calibration in standardized solutions
Calibrating electrodes using the ligand optimization method
even with the program ALE takes longer than 1 h, and the procedure can only be regarded as a research tool. However, if standardized solutions for both calibration and buffer solutions are used,
Calculated and measured [Ca2+] in buffers / J.A.S. McGuigan, F. Stumpff / Anal. Biochem. 436 (2013) 29–35
34
the procedure can be greatly simplified and becomes routine. The
eight-point calibration illustrated in Fig. 3 using standardized solutions of pCa values (in rounded numbers) of 2 and 3 (calibration
solutions) and 4.0 (NTA-7), 5.0 (HEDTA) 6.0 (BAPTA-3), 6.5 (BAPTA-6), 7.0 (BAPTA-8), and 7.4 (BAPTA-9) overlaps the calibration
curve of Fig. 1 and can be completed in approximately 30 min.
We further show that the calibration of the Ca electrode can be tailored to meet the requirements of the experiment. Calibration over
the pCa range from 2.0 to 4.0 takes only some 12 min; calibration
over the pCa range from 2.0 to 8.0 is necessary only when [Ca2+] is
in the nanomolar to micromolar range.
Ramifications of using calculated values of [Ca2+] for calibration
Fig. 4A represents the problems that arise when attempting to
calibrate a calcium macroelectrode using calculated values of
[Ca2+]. The dashed line through the calibration solutions (pCa
2.004–3.301) illustrates the slope of the electrode. If the calculated
minimal values for both EGTA and BAPTA are used (filled squares
and circles, respectively), it is not possible to fit the Nikolsky–
Eisenman equation to the calibration solutions and the buffer solutions. If the maximum [Ca2+] values for both EGTA and BAPTA are
used (open squares and circles, respectively), the fit becomes
E ¼ 60:920 þ 30:3947 log ð½Ca2þ þ 1:3243 107 Þ;
r ¼ 0:99965:
ð2Þ
The fit is shown as the solid line and exhibits hyper-Nernst
characteristics (cf. Fig. 1 in Ref. [15]). If this fit is used to estimate
the Kapp of HEDTA, the mean ± SD (n = 6) of the estimated Kapp is
3.05 ± 0.04 lM (i.e., greater than the true value of 1.88 lM). A similar estimation of Kapp for NTA gives a value of 111.8 lM compared
with the true value of 78.6 lM.
The problems with calculated values for both HEDTA and NTA
are illustrated in Fig. 4B. In this figure, the dashed line again represents the slope of the electrode. Calculated values for HEDTA and
NTA (open symbols) simply do not superimpose on the measured
0
slope of the Ca2+ electrode (filled diamonds). Also shown are the
[Ca2+] values estimated using the Kapp values for NTA and HEDTA
from the calibration curve in Fig. 4A (filled circles).
Measured and calculated [Ca2+]
Attempts to calculate [Ca2+] from binding constants are not
new. Scharff [16] found nearly identical results between measured
and calculated concentrations in EGTA and NTA. His results, however, are based on calibrating his electrode in buffer solutions
where the [Ca2+] was calculated, not measured. Furthermore, in
Scharff’s calculations, he used the measured pHa, did not convert
to pHc, and did not allow for purity of the EGTA. In his NTA buffers
at a measured pHa of 9.0, he did not allow for 1:2 binding of Ca2+ to
NTA, which is important at this alkaline pHa. With hindsight, his
results hardly support a similarity between measured and calculated values for [Ca2+] in EGTA and NTA buffer solutions.
The discrepancy between measured and calculated values of
[Ca2+] and [Mg2+] has been repeatedly shown. Thus, Kim and Padilla [17] calibrated the Ca2+ electrode by dilution, taking care to reduce Ca2+ contamination to an absolute minimum and found that
the measured free concentrations of NTA, EDTA, and EGTA were
six to seven times greater than the calculated values. This was confirmed by the current study of [Ca2+] in EGTA, BAPTA, HEDTA, and
NTA buffers in an extracellular solution (high sodium and low
potassium) and by a previous study [1] of Ca2+ binding to EGTA
in intracellular solution (high potassium and low sodium). Similar
discrepancies between measured and calculated values arise for
Mg2+ binding to ATP and EDTA [1].
To emphasize just how large the differences between measured
and calculated values can be, the percentage change of the lowest
and largest calculated [Mg2+] and [Ca2+] for the buffers ATP, EDTA,
and EGTA (intracellular background) and EGTA, BAPTA, HEDTA,
and NTA (extracellular background) are illustrated in Fig. 5. Given
the central role that [Mg2+] and [Ca2+] play in the conformation of
various proteins in biological systems, efforts should be made to
develop commercially available systems for measuring the ionized
0
A
Calibration
-20
-40
Potential difference, E (mV)
Potential difference, E (mV)
-20
-60
-80
-100
EGTA/BAPTA
-120
-40
-60
NTA
-80
HEDTA
-100
-120
-140
-160
B
Calibration
9
8
7
6
5
pCa
4
3
2
-140
7
6
5
4
3
2
pCa
Fig.4. (A) Result of attempting to calibrate a Ca2+ electrode using calculated [Ca2+] in EGTA and BAPTA buffer solutions. The open diamonds at the top of the figure represent
the measurements in the calibration solutions, and the dashed line represents the slope of the electrode. Filled squares and circles represent minimum calculated values for
[Ca2+] for EGTA and BAPTA, respectively, whereas open squares and circles represent maximum calculated values for [Ca2+] in EGTA and BAPTA buffer solutions, respectively.
The Nikolsky–Eisenman fit to the values obtained for the calibration solutions and these EGTA/BAPTA buffer solutions is depicted by the solid line. (B) Ca2+ electrode
calibration using calculated [Ca2+] in HEDTA and NTA buffer solutions. Black filled diamonds depict the values measured in the calibration solutions, and the dashed line
represents the slope of the electrode. Open triangles represent [Ca2+] calculated in NTA buffers using the constants from Ref. [8]. Open circles and squares represent [Ca2+] in
HEDTA buffer solutions as calculated using the program Chelator and the constants in Ref. [8], respectively. The filled circles and filled triangles were calculated using the Kapp
values of 111.8 and 3.05 lM for NTA and HEDTA, respectively, values obtained using the calibration curve shown in panel A.
Calculated and measured [Ca2+] in buffers / J.A.S. McGuigan, F. Stumpff / Anal. Biochem. 436 (2013) 29–35
250
6.90
Intracellular
Extracellular
35
than EGTA. Finally, it is recommended that steps be undertaken
to make internationally defined Ca2+ calibration and buffer solutions of known pCa values commercially available.
200
References
1.84
2.06
1.32
Ca-NTA
Ca-HEDTA
Ca-BAPTA
1.85
Ca-EGTA
100
Mg-EDTA
3.10
Ca-EGTA
150
Mg-ATP
% Change
2.82
50
0
Fig.5. Variation between the measured and calculated values for both [Mg2+] and
[Ca2+]. The open circles represent the measured values for an intracellular-like
background (high potassium and low sodium, first three from Figs. 3 and 4 in Ref.
[1]) and for an extracellular-like background solution (high sodium and low
potassium, last four circles) from measurements in this study (Fig. 2), expressed as
100%. The error bars demonstrate the lowest and highest calculated values for these
buffers expressed as a percentage change from 100%. The numbers at the top of the
error bars represent the ratios of the highest calculated values to the lowest
calculated values.
concentration of both ions in physiological buffer solutions in analogy to the ubiquitous pH electrode.
Conclusions
Several conclusions can be drawn from this study. First, the ligand optimization method [4] is a robust and accurate method to
determine both Kapp and ligand purity. Second, there is no agreement between calculated and measured [Ca2+] in EGTA, BAPTA,
HEDTA, and NTA buffers. This also is the case for [Mg2+] in ATP
and EDTA buffers [1]. Calculation is simply not an option. Third,
accurate calibration of Ca2+ electrodes in the pCa range from 7.5
to 2.0 is possible in calibration and buffer solutions of known
[Ca2+]. Nine such solutions would be sufficient to cover this range;
pCa 2.0 and 3.0 can be set by dilution, pCa 4.0 can be set by NTA,
pCa 5.0 can be set by HEDTA, and pCa 6.0, 6.5, 7.0, 7.5, and 8.0
can be set by BAPTA because BAPTA is much less pH dependent
[1] J.A.S. McGuigan, J.W. Kay, H.Y. Elder, D. Lüthi, Comparison between measured
and calculated ionised concentrations in Mg2+/ATP, Mg2+/EDTA, and Ca2+/EGTA
buffers: influence of changes in temperature, pH, and pipetting errors on the
ionised concentrations, Magnes. Res. 20 (2007) 72–81.
[2] B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, P. Walter, Molecular Biology
of the Cell, fifth ed., Garland Science, Milton Park, UK, 2008.
[3] J.A.S. McGuigan, J.W. Kay, H.Y. Elder, 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. 92 (2006) 333–370.
[4] D. Lüthi, U. Spichiger, I. Forster, J.A.S. McGuigan, Calibration of Mg2+-selective
macroelectrodes down to 1 lmol l1 in intracellular and Ca2+-containing
extracellular solutions, Exp. Physiol. 82 (1997) 453–467.
[5] W. Zhang, A.C. Truttmann, D. Lüthi, J.A.S. McGuigan, The manufacture and
characteristics of magnesium selective macroelectrodes, Magnes. Bull. 17
(1995) 125–130.
[6] J.W. Kay, R. Stevens, J.A.S. McGuigan, H.Y. Elder, Automatic determination of
ligand purity and apparent dissociation constant (Kapp) in Ca2+/Mg2+ buffer
solutions and the Kapp for Ca2+/Mg2+ anion binding in physiological solutions
from Ca2+/Mg2+-macroelectrode measurements, Comput. Biol. Med. 38 (2008)
101–110.
[7] D. Ammann, Ion-Selective Micro-Electrodes: Principles, Design, and
Application, Springer-Verlag, Berlin, 1986.
[8] A.E. Martell, R.M. Smith, Critical Stability Constants, vol. 1: Amino Acids,
Plenum, New York, 1974.
[9] A. Fabiato, F. Fabiato, Calculator programs for computing the composition of
solutions containing multiple metals and ligands used for experiments on
skinned muscle cells, J. Physiol. (Paris) 75 (1979) 463–505.
[10] D.M. Bers, C.W. Patton, R. Nuccitelli, A practical guide to the preparation of
Ca2+ buffers, Methods Cell Biol. 40 (1994) 3–29.
[11] T.J.M. Schoenmakers, G.J. Visser, G. Flik, A.R.P. Theuvenet, Chelator: an
improved method for computing metal ion concentrations in physiological
solutions, Biocomputing 12 (1992) 870–879.
[12] D.G. Moisescu, H. Pusch, A pH-metric method for the determination of
the relative concentrations of calcium to EGTA, Pflügers Arch. 355 (1975)
R122.
[13] W. Zhang, A.C. Truttmann, D. Lüthi, J.A.S. McGuigan, Apparent Mg2+–adenosine
5-triphosphate dissociation constant measured with Mg2+ macroelectrodes
under conditions pertinent to 31P NMR ionized magnesium determinations,
Anal. Biochem. 251 (1997) 246–250.
[14] R.Y. Tsien, New calcium indicators and buffers with a high selectivity against
magnesium and protons: design, synthesis, and properties of prototype
structures, Biochemistry 19 (1980) 2396–2404.
[15] A. Coray, J.A.S. McGuigan, Measurement of intracellular ionic calcium
concentration in guinea pig papillary muscle, in: E. Syková, P. Hník, L.
Vyklicky (Eds.), Ion-Selective Microelectrodes and Their Use in Excitable
Tissues, Plenum, New York, 1981, pp. 299–301.
[16] O. Scharff, Comparison between measured and calculated concentrations of
calcium ions in buffers, Anal. Chem. Acta 109 (1979) 291–305.
[17] Y.S. Kim, G.M. Padilla, Determination of free Ca ion concentrations with an ionselective electrode in the presence of chelating agents in comparison with
calculated values, Anal. Biochem. 89 (1978) 521–528.