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
2Department of Statistics, Mathematics Building,
University of Glasgow, G12 8QW, UK
3Institute of Physiology, Bühlplatz 5, 3012 Bern,
Switzerland
Absolute values for ionised magnesium and calcium concentrations
([Mg2+] and [Ca2+]) in the μmolar and nmolar
range respectively are essential to characterise amongst others,
ion channels in patch clamping, the measurement of the apparent
dissociation constant (Kapp) for the binding of
Mg2+ and Ca2+ to physiologically important
anions (e.g. ATP, malate, citrate) and to
Mg2+/Ca2+ fluorochromes as well as for
calcium regulation in muscle. Such experiments entail the
manufacture of accurate Mg2+/Ca2+ buffer
solutions in the μmolar and nmolar range but, since internationally
defined buffer standards are lacking, individual laboratories are
compelled to prepare their own standards. In these buffer standards
the ionised concentrations are either 1) calculated using tabulated
constants or freely available computer programs or 2) measured.
Because different laboratories use different methods for the
measurements, and since levels of accuracy for the manufacture of
such buffer solutions remain undefined, an exact comparison between
measured values from individual laboratories is difficult.In a
previous paper [1] it was shown that the most general way to
estimate both the total ligand concentration ([Ligand]T)
and the Kapp in buffer solutions was the ligand
optimisation method of Lüthi et al. [2], a method based on
macroelectrode measurements. The method is iterative and a major
drawback to using this iterative method was the time involved in
the calculations, a drawback which has now been overcome by using
an Excel program which carries out the calculations within less
than five minutes instead of at least an hour [3]. The use of this
program gave us an unique opportunity to 1) systematically
recalculate the Kapp and [Ligand]T from our
extensive macroelectrode measurements for Mg2+ binding
to ATP and EDTA [2, 4, 5] and JAS McGuigan (unpublished) and for
Ca2+ binding to EGTA [6] and JAS McGuigan (unpublished)
and 2) compare the values of [Mg2+] and
[Ca2+] estimated from the measured Kapp and
[Ligand]T with the calculated values for
[Mg2+] and [Ca2+] in the μmolar and nmolar
range respectively.The results of these recalculations showed only
limited agreement between measured and calculated values for
[Mg2+] and [Ca2+]. Moreover, the calculated
values differed amongst themselves depending on the constants
chosen or the program used. The calculated [Mg2+] in
Mg2+/ATP or Mg2+/EDTA solutions varied by
factors of 2.5 and 3 respectively. In the Ca2+/EGTA
buffer solutions the difference was up to a factor of 2; if ligand
purity was not considered, the factor increased to around three.
Inaccuracy or imprecision in the manufacture of
Mg2+/Ca2 buffer solutions has not yet been
systematically considered. In this paper we show that a range of
±10% of the [X2+] in the buffer solutions is attainable,
which entails maintaining the temperature within ± 0.5°C, pH within
± 0.01 units and pipetting errors of less than 0.25%.These findings
emphasise the need to measure rather than calculate the
[X2+] in buffer solutions, until internationally defined
Mg2+ and Ca2+ buffer solutions are
commercially available.
Materials and methods
Macroelectrodes
The 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.
Recording
The 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.
Solutions
The 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 solution
This 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 solutions
The 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 solutions
These 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.
Temperature
Experiments were carried out at both 25°C and 37°C. Temperature
variation was 1 ± 0.1°C.
pH
The 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]T
The 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 concentrations
For 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.
Statistics
Sample 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.
Results
Mg2+ binding to ATP: apparent dissociation
constant
The 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
constant
The 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.
|
EDTA
|
ATP
|
|
Temp (°C)
|
pHa
|
Number
|
CV (%)
|
pHa
|
Number
|
CV (%)
|
|
25
|
6.7
|
5
|
4.78
|
5.5
|
6 (2 × 3)
|
6.84
|
|
25
|
7.2
|
6
|
3.74
|
6.0
|
6 (2 × 3)
|
1.16
|
|
25
|
7.2
|
4
|
2.94
|
6.7
|
4
|
5.05
|
|
25
|
7.2
|
6
|
3.63
|
7.2
|
4
|
1.46
|
|
25
|
7.2
|
6
|
3.44
|
7.2
|
6
|
6.22
|
|
25
|
7.2 all
|
22
|
9.82
|
7.2 all
|
13
|
12.05
|
|
37
|
6.7
|
4
|
6.95
|
5.9
|
4
|
2.73
|
|
37
|
7.2
|
5
|
3.15
|
7.2
|
4
|
4.63
|
|
37
|
7.7
|
5
|
7.90
|
7.7
|
4
|
3.50
|
Ca2+ binding to EGTA: apparent dissociation
constant
The 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+/ATP
Figure 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+/EDTA
The 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+/EGTA
The 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
imprecision
Allowable range for [X2+] in buffer solutions
In 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 pKapp
To 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]T
These 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 imprecision
Imprecision 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+.
Recording
Drift
To 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 solutions
Apparent dissociation constant
The 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 concentrations
To 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.
Discussion
Consequences
The 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 imprecision
Macroelectrode 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%.
Conclusion
1) 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.
Acknowledgements
We 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.
References
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