calcium buffer solutions and how to make them: a do it yourself guide
TRANSCRIPT
Calcium buffer solutions and how to make them: A do it yourself guide'
JOHN A. S. ~ ~ G U I G A N , ' DANIEL LOTHI, AND AWLETTE B U W I ~ hstibube of Physiology, Biihlphba 5, 3012 Benae, Switzerland
Received December 3 1 , 1990
MCGUIGAN, J. A, S . , Lii~nr, D., and Buar , A. 1991. Calcium buffer solutions and how to make them: A do it yourself guide. Can. J . Physiol. Bharmacol. 69: 1'333 - 1749.
In measurements of the intracellular free calcium concentration ([Ca2+]) using either microelectrodes or fluorescent probes, calibration is normally carr id out in EGTA calcium buffer solutions. In the first part of the article the general proper- ties of calcium buffer solutions are discussed, the equations used to calculate the apparent calcium binding constant (!Cap,) are derived, and the difficulties in the calculation are discussed. The effects of the purity of EGTA as well as the influence of calcium contamination om the buffer solutions are explained. Because of the difficulties in calculating Ka,,, and the impor- tance of EGTA purity and calcium contamination? it is suggested that it is. easier to measure all three under the appropriate experimental conditions using the method of Bers (1982). In the second part a do-it-yourself guide to the preparation of EGTA calcium buffer solutions is given. An experimental example is provided using the Bers method ts measure purity, csntarnina- tion, and Kap,. It is concluded that unless all three factors are known it is not possible to prepare accurate EGTA calcium buffer solutions.
Key w ~ P P C ~ S : Ca buffers, EGTA, CaEGTA, Ca contamination, purity of EGTA.
McGurca~ , J. A. S., LUTHI, D., et BURI, A. 1991. Calcium buffer solutions and how to make them: A do it yourself guide. Can. J . Physiol, Pharmacol. 69 : 1733 - 1749.
Eorsqu'on mesure la concentration de calcium libre intracellulaire ([Ca2+]) avec des microClectrodes ou des sondes flusrescentes, la calibration est genkralement effectude dans des solutions tampons calcium-EGTA. Dans la premikre partis de cet article, on discute de propribtbs gbnCrales des solution tampons calciques, des tquations utilis6.e~ pour calculer la con- smite de fixation apparente du calcium (Ka,,) ainsi que des difficultts du cflcul. On explique les effets de la puretk de 1'EGTA et i'influence de Ba contamination calcique sur les solution tampons. A cause des difficultds que prCsente le calcul de Ka,, et de l'irnportance de la purett de 1'EGTA et de la contamination calcique, on sugg5re qu'il est plus facile de les mesurer tous les trois dans les conditions experimentales appropribes en utilisant la mCthode de Bers (1982). Dans la seconde partie, on prCsente un guide pour la prearation de solutions tampons calcium-EGTA. On donne un exemple de l'utilisation de la mkthode de Bers p u r mesurer la puretC, la contamination et la &,,. On csnclut qu98 msins de connajitre les trois fac- teurs, il est impossible de prkparer des solutions tampons calcium-EGTA qui soient justes.
Mobs clks : tampons Ca, EGTA, EGTA Ca, contamination Ca, puritC d'EGTA. [Traduit par la rbdaction]
Hntrodwtion and
Calcium buffer solutions The free or ionized intracellular calcium concentration in It follows that
cells is around 208 nmol/l, and to accurately measure this level of calcium it is necessary for the microelectrodes or the [la51 1% [CaEGTAl 1% [Ca2'3 + log [EmAI + log# calcium probes to be calibrated in calcium buffer solutions. In general, metal ion buffers are solutions containing the metal - Bog [Ca2 +] = log K + log ( [EGTA] / [CaEGTA] )
ion (M) and a chelating agent or ligand (&) (Perrin and Demp- or sey 1979). The equilibrium for such a reaction is
C1.61 pCa = log K + log ([EGTA]/[CaEGTA]) [1.13 ~~l+neLl*eh/fL,zl
In these equations calcium and EGTA are expressed in terms where n is the number of reacting molecules. The absolute of concentrations, which means that pCa is defined as --log of binding or stability constant is defined as follows the calcium concentration.
Calcium buffers solutions are normally made up with a cal- cium chelating agent such as ethylene glycol-bis(P-arninoethyl ether)-N,N,Nt,N'-tetraacetic acid (EGTA) and in this specific case
[1 .3] [EGTA] + [Ca"] * [CaEGTA]
- -- - - - - -
'Papers appearing in the Graham W. Mainwood Memorial Issue have undergone the Journal's usual peer review.
2Author for correspondence. 3Present address: Kantonsspital, 1'900 Fribourg , Switzerland.
Prlnted in Canada ! lmprirnC au Canada
From this equation it is clear that the Ca2+ concentration depends on both log In: and the ratis [EGTA]/[CaEGTA]. While this is true, the manufacture of accurate calcium buffer solu- tions with EGTA is not an easy task, for not only is it difficult to calculate the appropriate value for K, it is also necessary to take into account the purity of the EGTA and the calcium csn- tamination of the solutions.
While there are numerous articles on EGTA and its proper- ties, there is no simple guide to calcium buffers and how to make them. In Part I of this article we discuss the general properties of calcium buffers using EGTA as an example and derive the equations that are commonly used to calculate K. In Part 2 we will present a step by step guide of how EGTA buffer solutions are made in our laboratory.
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1734 CAN. 9. PHYSIOL. PHARMACOL. VOL. 69, 1991
Part 1: General properties of calcium buffer solutions Reactions qf EGEA
While it is common to express the reaction of EGTA and Ca2+ in the above form, it is a simplification because, as shown below, EGTA binds not only Ca2+ but also H+ ions (see Smith 1983; Smith and Miller 1985).
11% 5
Ca-H-lEGTA1- 7 Ca2+ + H-EGTA3- + H
1 1 1 1 ~ ~ These forms bind calcium
where K19 K2, K3, and K4 are the proton binding constants and Kc-, and Kc,, are the calcium binding constants. They are defined as follows: K1 = [H-EGTA~]/[H+J[EGTA~-] K2 = [HZ-EGTA2-]/[H+l[M-EGTA3-1, K3 = [H3-EGTAi -]/ [Hf ][H2-EGTA2-3, K4 = [H4-EGTA]/[H+] [H3-EGTAi -1, Kc, - [CaEGTA2-]/[Ca2 + ] [EGTAGs] , and Kca2 -- [Ca-W-EGTA1 -1 /[Ca2+] [H-EGTA3 -1. At a pH from around 6 to just over 7, 99% of EGTA is in the form of HI2-EGTA2-, so the overall reaction can be written as
Cajcium and profon binding of E W A As seen above, EGTA binds $Q+ ions, and only two of these forms bind Ca2+. Under certain conditions the metal ion (M)
can also bind OH- ions (i.e., can be hydrolysed) and forms MOH, IVB(OHB2, M(OH)3, etc. This does not occur to any great extent with either Ca2+ or Mg2+ and such binding can be neglected. Because of the protonation of EGTA, it is useful to intro- duce the term '"apparent" or "cc~nditiomal" binding constant. This is similar to the absolute constant defined above, except that the free form of EGTA or H-EGTA is replaced by all forms of EGTA or H-EGTA not actually bound to Ca2& (see Bortzehl et al. 1964; Perrin and Dempsey 1979).
For KCal, this is defined as follows:
Since
It follows that
and
[ I . 141 Let a = (1 + [H-EGTA3-]/[EGTA4-] + [H2-EGTA2-]/[EGTA4-1 + [H3-EGTAI-]/[EGTA4-]
It follows from the definition of K , that
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MCGUIGAM ET AL.
[ I . 161 [H2-EGTA2-]/[EGTA4-1 = ([H-EGTA3-] [H']/[EGTA4 -] ) X ([PI2-EGTA"]/[H f ] [H-EGTA~-])
so that
[I. 1'71 [H~-EGTA'-]/[EGTA~-] = K,K~[H+]~
Similarly?
[1.18] [H~-EGTA'-]/[EGTA'~-~ - K1K2K3[HC13 [l.l9] [H4-EGTA]/[EGTA4-]-K1K2K3K4[H+]4
and
[1.20] a = (1 + K,[H+] + K,K2[H'I2 + KaK2K3[H+I3 + K1K2K3K4[H+J4) and
[I-211 Kappl=K~al/a
A similar set of equations can be written for Kca2, as folBows,
[I. 221 KaW2 = [Ca-H-EGTA '-1 / [Ca2+] ([EGTA4-] + [H-EGTA3-] + [Hz-EGTA2-] + [H3-EGTA1 -1 + [H4-EGTAJ )
Since
[I -231 Kc,, = [Ca-H-EGTAi -]/[Ca2+] [H-EGTA3-]
It follows that
[I .24] Kapp2[Ca2+] ([EGTA4-] + [H-EGTAF] + [Hz-EGTA2-] + [H3-EGTA1-I + [H4-EGTA]) = KC,2[C$+~[H-EGT~3-]
and
[1.25] Kam2 = Kca2[H-EGTA3-]/([Ern4-] + [H-EGTA3-] + [H2-EGTA2-] + [H3-EGTA1 -1 + [HI-EGTA] )
[1.27] Let 6 = ([EGTA4-]/[H-EGTA3-] + 1 + [Hz-EGTA2-]/[H-EGTA3-] + [W3-EGTAB -]/[El-EGTA3 -1
+ [H4-EGTA]/[H-EGTA3-] )
It follows from the definition of Ki and K2 that
[ I .29] [H2-EGT~2-] /[H-EGTA3-] = K2[H+]
since
[1 .30] [H3-EGTA1-]/[H-EGTA"] = ([H + ][Hz-EGTA2-]/[H-EGTA3-1) >< ([H3-EGTA1-]/[H+][H2-EGTA2-])
It foBlows that
[I. 3 13 [H3-EGTAG]/&H-EGTA"] = K2K3[H+j2
and similarly,
[ I , 321 [H4-EGTA]/[H-EGTA3-1 = K2K3K4[H+I3
SO that
[I -331 6 - (l/(K1[Hf ]) + 1 + K2[H+] + K2K3[H+I2 + K2K3K4[H+I3) and
h1.341 Kapp2 = K~a2/8
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In a calcium buffer solution both sites can bind calcium and in keeping with the above definitions it is possible to define an overall apparent binding constant such that
-351 Kvp = tCa-EGTA,,i 1 /[Ca2 + I [EmAtota~I
where [Ca-EGTAtotalj and [lEGTAtObI] are the total concentrations s f all the bound and free forms of EGTA, respectively. Since
Calculae9tioab of the apparerzt binding cos~stant These equations as defined above can be used to calculate the apparent binding constant. However, it is more usual to use
the log form of the equations, which simplifies the calculation (Perrin and Dempsey 19'79).
[I -381 Let log Kl = pKl and similarly for K2, and K4
and
E1.391 pH,- -log[H9]
Then it follows that
[lQ4%] 0 = (I(~-(P#I -P&> + 1 + ~ @ P K ~ - P % I + ~(~(FK~+P&-~PH,) + lQ(plY2 +PK~+P%-~PI%,))
since
11.421 I @ - p H c ) = = [ H + j
and
Magnesium binding to EGEA It is usual in calcium buffer solutions to add around 1 mmol/L Mg2+ to mimic the intracellkalar hag2+ concentration. How-
ever, Mg2+ also binds to EGTA and although the effect is small it does have the effect of slightly increasing the free @aD ccon- centration. The apparent binding constant for Mg2+ can be calculated exactly as for Ca2+. The equations to be solved are then,
where Kc,.,, and Kbfg,,, are the apparent binding constants for Ca2+ and Mg2+, respectively. Since only Ca2+ and Mg2+ are involved, a closed solutton to these solutions is possible. (The following solution is due to Milton Pressler, Krannert Institute of Cardiology, Indianapolis. 1 Let
where [EGTAIa9 [CaD+lT, and [Mg2+IT are the total concentrations of EGTA, calcium, and magnesium, respectively. Simple algebra and elimination give the following equation:
[1,49] x 3 + A x 2 + B x + @ = 0
where
1 -501 x = %EaAtotar4
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MCGUIGAN ET AL.
This cubic equation can be solved by standard techniques. Normally C is approximately zero and the equation then becomes a quadratic
which simplifies the solution. With calcium and magnesium in the buffer solution it is possible to solve the equations. However, if other ligsands are added,
such as ATP, then an iterative method must be used. In theory it would appear that the calculation of the apparent binding constant is relatively straightforward. However, the tabu-
lated constants are hnctions of temperature, ionic strength, and pH of the solution and appropriate corrections have to be applied to obtain the constants under the conditions of the experiment. Before considering these correction factors, the pertinent phys- icochemical properties of solutions will be first considered.
Basic phy~i~o~hernicd properties Concentration There are two fundamentally different ways of expressing concentration, namely molarity (M, moll%, solution) and molality
(m, mollkg H20). The second method is temperature independent, but at any given temperature in the concentrations used in physiology (Tyrode solution or artificial sea water) the difference is minimal and both methods of expressing concentration can be taken as equal.
Activify In an ideal solution the freezing point is depressed by 1.86"C per mole ion, i. e., a 1 moll% CaClz would, in theory, depress
the freezing point by 5.58"C. However, no solution is ideal and in reality the colligative properties do not adhere to the phys- icochernical laws developed assuming no interaction among ions. As solutions become more concentrated, and in physiological concentrations, the depression of the freezing point and elevation of the boiling point are always less than expected for that con- centration. In other words, owing to the interaction of the ions, solutions have an "effective concentration" that is less than the actual concentration of the solution. This "effective concentration'' is designated activity and the ratio, activity/concentration of the solution is the mean activity coefficient of the solution.
Mean activity coeflkcient The mean activity coefficient of a solution at varying concentrations can be measured and extensive tables for the pure solutions
are now available (Hamer and Wu 1972; Staples and Nuttall 1997; Goldberg and Nuttall 1978). These tables are for 25"C, but the activity coefficient can be corrected to other temperatures by using the Debye-Hiiickel equation (Baumgartear 1981). This paper also gives the equations to calculate the activity coefficients of the common physiological ions based on the equations deve- loped by Pitzer and Mayorga. These activity coefficients are referred to as mean activity coefficients because they refer to both ions in the solution, for instance, to both the Ca2+ and the C1- ions in CaCI2. What is tabulated is the molal activity coefficient, y,, not the molar activity coefficient, y, . The two are related as follows, y* = y_+ domlM9 where do is the density of pure water (Robinson and Stokes 1970). The difference in physiological solutions is minimal and can be neglected.
Single ion activity coeflicie~zt The mean activity coefficient refers to both ions in solution, but what is redly sf interest is the activity of the calcium or the
chloride ion in the solution, or the single ion activity. There is no way of measuring the single ion activity coefficient by+ or Y-) and these coefficients can only be calculated using some nonthermodynamic assumption. One common method of doing this is based on the Debye-Hiiickel theory (Ammann 8986) and sets
10~11'~ ,~fE~Zgfh At any given temperature the mean activity coefficients and hence the single ion activity coefficients depend on the concentra-
tion of the solution. This reflects the distance between the various ions and also the charge of the ions. These factors are combined in the concept of ionic strength defined as follows:
where I is the ionic strength (mollkg) and mi and zi are the molality and valency of the ith ion. For physiological solutions molar- ity would be used. This definition means that for a univalent electrolyte, ionic strength and concentration are equal. For CaCB, this is not so, ionic strength being three times the concentration, reflecting the fact that calcium carries two charges. This is impor- tant to bear in mind when the calcium in a solution is increased by adding CaC12.
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1738 CAN. J . PHYSIOL. PHAWMACOL. VOL. 69, 1991
In some publications (e.g., Smith and Miller 1984) the cdculation of the apparent binding constant is based not on the classical ionic strength but rather on the ionic equivalent, which is defined as follows:
11.581 Ieq = (112) mi lzi]
While the concepts of both ionic strength and ionic equivalent are similar, what is important in any calculation is to note which definition the authors used.
PH While it is often thought that pH is defined as -log [Hf], this is not the case, the modern definition of pH being -lognH,
where a~ is the single ion activity of the hydrogen ions (Bates 1973, 11981). This means that
where yp~ is the single ion activity coefficient of the hydrogen ions, estimated under well-defined conditions. It is also possible to define pH, as being equal to -log [M+] (see eq. [ 1.391).
A problem arises because the modern definition of pH is only valid up to an ionic strength of 0.1 mollkg. Physiological soHu- tisns have ionic strengths of around 0.15 msllkg and the definition is not vdid at this ionic strength. It can be extended by using the calibration solutions proposed by Bates and colleagues (Bates et al. 1948). If these solutions are used, pH becomes 0.045 units more alkaline than when using the National Bureau of Standards (NBS) solutions (see Blatter and McGuigan 11991). This point is of more than theoretical interest, for, as we will show below, to calculate the apparent binding constant, an accurate measurement of pH is necessary (see Pig. 9).
Activity or concentratiogl This can be a very vexing question, but at the onset it should be stated that normally it does not matter, provided the ionic
strength remains constant. If activity is used, it must be stated whether it is the mean or single ion activity. If single ion activity is used, then whatever convention or assumptions were used in the calculation must also be quoted. Finally, it is essential to give the composition of the calibration solution, so that other workers can also do the necessary conversions.
However, if the ionic strength is increased by, say the addition of Ca&112, then the use of concentration becomes inappropriate and activity must be used. This also occurs if NaCl in the solution is substituted for sucrose. Activity should also be used when comparing concentrations in Tyrode solution and sea water because of the differences in ionic strength.
Buflei- sohtions A calcium buffer sslbation can be defined as a solution that resists changes in the free calcium concentration on the addition
of small amounts of calcium. The changes in pCa when titrating a solution of EGTA with calcium can be deduced as follows:
If the total calcium concentration in the solution is and the initial concentration sf EGTA is [EGTAIT, it follows that
thus
re-arranging gives
so that
Since pCa = -log [Ca2+], [Ca2+] = 10'-pea). Let logK,,, = pK,,.
since
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MCGUIGAN ET AL.
FIG. 1 . ECZA buffer action. (A) Titration curve of EGTA with calcium. The EGTA concentration was set at 4 mmol/L and the curves from left to right are for log Kapp of 6.89 (pH 7.71, 6.54 (pH 7.21, and 5.25 (pH 6.7). (B) The difference in the log ratio when titrating ECXA with calcium. The EGTA concentration was 4 rnmol/L and increments sf 0.09 mmol/L calcium were taken.
It is usual to express the total calcium and EGTA concentrations in millimoles per litre instead of moles per litre. In this case the equation becomes
Titration curves of total calcium against pCa for the three different log Kapp values, namely 6.89, 6.54, and 5.25 measured at pH values of 7.7, 7.2, and 6.7, respectively (see Fig. 9) are shown in Fig, 1A. As the pH decreases so does the log KaPp and the curves are moved parallel to the right. At both high and low pCa values small additions of calcium cause large changes in the free calcium concentration and only in the middle region where the curve is steepest is there efficient buffering.
At a calcium concentration of 4 mmol/L all the EGTA is bound to calcium, the solution has no buffering power, and a further addition of calcium causes an increase in the calcium concentration corresponding to the amount of calcium added. This is the cause of the increase in the slope of the curve at the lower pCa values.
This can be derived as follows:
At low @a values the expression lllO(-pCa+pKapp) tends to zero so that
which means, for instance, that at a total calcium of 5 mmol/L and an [EGTA]*I- of 4 mmol/L the pCa value is 3, as is shown in Fig. 1A.
On addition of a small increment of calcium (A), the buffer ratio will change from [EGTA]/[CaEGTA] to ([EGTA] - A)/ Q [CaEGTA] + A) (Bates 1973). The change in the log (ratio) will then be
[I .74] log (ratio difference) = log ( [EGTA]/[CaEGTA] ) -log ( ([EGTA] - A)/([CaEGTA] + A) )
At an initial EGTA concentration of [EGTAJT
[I .75] [EGTA] + [CaEGTA] = [EGTAIT
and
[I .7$] log (ratio difference) - log ( [EGTA]/([EGTAIT - [EGTA] ) ) -log ( ( [EGTAI - A)/( [EGTAIT - [EGTA) + A) )
A plot of this curve is shown in Fig. IB for A equal to 0.09 rnmol/L and an [EGTAIT s f 4 rnmol/L. The log ratio difference changes most at the low and high concentrations of the free EGTA and passes through a minimum at an [EGTA] of 2 mmol/L, or when the [EGTA] equals the [CaEGTA]. This corresponds to the steepest part of the curves in Fig. 1A and is the point where the buffering capacity is largest.
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1740 CAN. J . PHYSIOL. PHARMACOL. VOL. 69, 1991
Bufer capacity For pH the buffer capacity (P) is defined as the amount of strong base (moB/L) that must be added to a solution to produce
one unit change in pH (P - dB/dpH) (see Ross and Boron 1981). A similar definition for calcium buffers makes
since
Differentiating gives
since
[I . $01 d{ (constant) lo(-pCa)) /dpCa = (constant)in(IO) 10(-m
and
If concentrations are in millimoles per litre the equation becomes
[I. 821 ~(mrnol l l . p@a) = {ln(lO)[EGTA](mmollL)10(-@a + PKapp) ) / { (1 + 10(-pC"fKap~))2) + 1000 ln(lO) ~g)(-~ca)
A plot of the buffer capacity for the three binding constants is shown in Fig. 2A. Each curve has a maximum value for the buffer capacity and this maximum occurs when BPIdpCa = 0.
The apparent increase in buffer capacity at pCa values less than 4 is due to the fact that at calcium concentrations greater than 0.1 rnmoH/L small additions of calcium do not greatly change the calcium concentration, but this can hardly be described as buffer action.
For the differentiation sf @, the term 1000 Bn(10)lO(-~~~) is negligible in the effective buffer range and can be neglected. In this case
When dD/dpCa = 8, either (1 - 10(-pCa+pKa*p)) or BO(-pCa+pKapp) must = 0. Since 10~-@a+~Kapp) = 0 has no solution, so
and it follows that
f1.851 -pCa + pKa, = log 1, or pKa,, = pCa
The maximum buffer capacity then occurs when lsg([EGTA]I[CaEGTA]) is zero or when the two concentrations are equal, in agreement with the data in Fig. 1 .
Eflective bufler range It is clear from Fig. 2A that on either side of the maximum buffer value (pCa = log K:,,,), the buffer capacity decreases and
satisfactory buffering ody occurs within the range of + 1 pCa unit. This effective range of buffering is shown in Fig. 2B for two concentrations of EGTA, namely 4 rnmolll and 8 mmol/l, with a log&,, of 6.54. As is seen from the graph, adequate buffering occurs in the range from pCa 5.54 to pCa 7.54. Increasing the [EGTA] from 4 to 8 rnmol/L doubles the buffer capacity at any given p@a value. However, it brings with it the disadvantage of an increase in ionic strength (see General con- clusions).
Bindi'ing constants Up to now in this article the binding constants for Ca2+ and H+ to EGTA have been expressed in terms of concentration.
However, there are three different ways of expressing these constants, thermodynamic. stoichiometric, and in the case of H + a mixed constant as well (see Smith 1983). These will now be briefly described.
~ermsdynnamk bindiaeg constam Activities instead of concentrations are used so that
where ~H-EGT '~ , Y ~ I , and Y E ~ A are the respective single ion activity coefficients for H-EGTA3-, H + , and EGTA4--.
Stoichiornetric constant In this constant, concentrations are used.
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MGGUIGAN E'T AL.
FIG. 2. Buffer capacity. (A) Plot of the buffer capacities for the three log K8,, shown in Fig. IA, namely from left to right 6.88, 6.54, and 5.25. The EGTA concentration was 4 mrnd/k. (B) Buffer capacity at 4 rnrnol/L (lower curve) and 8 rnrnoi/E (upper curve) of EGTA and a logKa,, of 6.54. The horizontal lines show the effective buffer range for both curves. For simplicity the second term in the equation for 0 has not been included in the calculation.
Mixed consfam This constant is a combination of both activity and concentration and occurs because of the definition of pH (see above). It
is defined as follows:
since
In making up calcium buffer solutions the thermodynamic constants are rarely if ever used. Both the stoichiometric and the mixed constants are used, but if the stoichiometric constant is used and pH is measured, then a~ has to be converted to [Ha] by using the appropriate activity coefficient.
Specijic problems with EGTA ca1cicetn befler solutions In determining the free calcium concentration of a calcium buffer solution, not only is it essential that the appropriate apparent
binding constant be used, but also that the effects of the purity of the EGTA sample and the calcium contamination be considered. These two problems when using EGTA cannot be neglected (Miller and Smith 1984; see also Williams and Fay 1998).
Copp2gIications in the calculation of the apparent esnstaat The tabulated constants for Ca and H are the absolute stoichiometrlc constants for a given temperature and at a given ionic
strength. These constants have to be corrected to the appropriate ionic strength and temperature of the experimental conditions. The methods for correction are well described in Harrison and Bers (1989).
The correction for calcium is straightforward in that the stoichiormetric constant is used, and this is the constant that is tabulated. However, the corrections that have to be made for the hydrogen ion binding constants are not so simple. AS mentioned earlier, pH is defined in terms of activity and what is tabulated is the stoichiometric constant. This correction is complicated by the Fdct that the normal NBS buffer soHutions are only valid up to an ionic strength of 0.1 mol/kg. Blatter and McGuigan (1991) found that if the solutions of Bates and colleagues were used, which extend the definition to an ionic strength of 0.14 rno%/kg, the differ- ence was 0.045 pH units in the alkaline direction. One simple way around this is to add the factor 0.045 to the measured pH based on the NBS buffer so8utisns. The activity of the hydrogen ions can them be converted to concentration by using the activity coefficient for hydrogen ions. This can be calculated using the empirical equation given in Harrison and Bers (1989). However, this method can hardly be described as satisfactory and will introduce an error into the calculation. An exact method is to calibrate in buffer solutions of the appropriate ionic strength, but this is time consuming (Smith 1983; Harrison and Bers 1987; Blatter and McGuigan 1991). It might be thought that there would be agreement in the literature regarding the value of the absolute constants, but this is not so. There are six main groups and the constants from all six groups differ slightly, and depending on the choice of absolute constant, the calculated apparent constant will differ slightly (see Harrison and Bers 1989; Durham 8983). The difficulties involved in these calculations can be demonstrated from the fact that in 12 measurements of the binding constant, the mean Bog value was 6.54 + 0.09 SD (ionic strength, 0.16 mol/L; pH, 7.2; temperature, 25°C) compared with the value of 6.81 calculated from the tabulated values in Martell and Smith (1974).
Complications of parity In making up these solutions, the assumption is often made that it is possible to accurately weigh out a given amount of E G A .
This is not the case because EGTA is not 100% pure. The solutions described in Bart 2 do not contain 4 rnmol/L EGTA but rather about 3.8 mmol/L, for the EGTta is around 95 % pure. This means that the CaEGTA solution contains 3.8 mmol/& CaEGTA
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1742 CAN. J . PHYSIBL. PHARMACOL. VOL. 69. 1991
and 0.2 mmsB/L free calcium. When the two solutions are mixed together this free calcium binds with the EGTA and reduces the free EGTA even further. These effects are not minimal (Miller and Smith 1984).
Let the fractional purity be P and taking a specific example, i.e., we mix x mE EGTA and y mL of CaEGTA together. Define the nominal [EGTA] or [CaEGTA] as [EGTAJN or [CaEGTAIN. The true concentration sf EGTA and CaEGTA is defined as [EGTAIT or [CaEGTAIT. Thus
The Ca2+ concentration in the mixture is
[I .92] { ([CaEGTAIN - [CaEGTA],P)y)/(x + y) (in mmoZ/L)
The EGTA concentration in the mixture is
[1.93] ([EGTA),Px - ([CaEGTAjN - [CaEGTA],P)y) / (x + y)
The CaECXA concentration in the mixture is
eH.941 ([CaEGTA],Py)/Qx+y)
The ratio [EGTA)/[CaEGTA] is
91.951 ([EGTA],P-x - ( [CaEGTAJN - [CaEGTA],P)y )/ { [CaEGTAJNPy)
which simplifies to
hl.961 ([EGTA]N(P~ - j7 + Py)) /([CaEGTA],Py)
but since
[I .97] [EGTAIN = [CaEGTAjN
for that is the way the solutions were made, it follows that the true ratio is not xly but is
(1.983 ((xly) - 1/P + 1) To show the importance of the effect of purity, in Fig. 3 the difference between the pCa values calculated from the nominal ratio (xly) and the true ratio ((xly) - I IP + 1) is plotted against the nominal ratio. The nominal ratio of EGTAICaEGTA was varied from 0.1 to 2. At the lower ratios the effect of purity can be quite large. At a ratio of 0.1 the difference is from pCa 5.496 (purity 100%) to a pCa sf 5.093 (purity 94.3%) or from 3.19 to 8.06 ,%rnol/L.
Ca kciurn cs~ztarnintation In the above calculation the cont;amination of calcium in the solutions was ignored. This is possible because the glassware that
is used is carefaally cleaned and rinsed in double-distilled water. The measured free calcium concentration in the background solu- tion with no EGTA is about 10 pmolIL, and as shown below, at this concentration the contaminating calcium does not affect the calculated pCa.
Ca!cuhtisn of the eflects of contamination Let the contamination Bevel be C (rnmol/L). The calcium concentration in the mixture is
The EGTA concentration in the mixture is
[ I . 1001 {[EGTAlraP~ - ([CaEGTA]IN - [CaEGTAINP)y - C(x + y))/(x 4- y)
The CaEGTA concentration in the mixture is
[1.101) Q[CZ~EGTA]~P~+ C(X + y ) ) / ( ~ + y )
The ratio [EGTA]/[CaEGTA] is
[1.102] ([EGTA],Px - ([CaEGTAIN - [CaEGTA],P)y - C(x + y))/([CaEGTAJNPy + C(x + y ) )
which simplifies to
[I . 1031 ([EGT'A],(P(xly) - B + P ) - C(x/y + 1)) / ([CaEGTAlNP + C(x/y + 1))
The difference this makes to the pCa values is presented in Fig. 4 in a similar way to Fig. 3. There is only a minimal difference between zero calcium contamination and a contamination of 50 pmol1E at a nominal EGTA concentration of 4 mrnol1L (lower curve). However, if the EGTA concentration is B mmolIL, a contamination of 50 pmol1L introduces a considerable error into the estimated pCa values. Thus calcium contamination should be reduced to a minimum.
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Nominal Ratio [EGf A]/[CaEGf A]
FIG. 3. The effect of purity of EGTA on the pCa values. The abscissa is the nominal ratio of [EGTAJIECaEGTA] and the ordinate is the difference in pGa between this ratio and after it has been cor- rected for purity, which in this case was 94.3%.
Ratio [EGPA]/[CaEGPA]
FIG. 4. The influence of contamination on pCa values. The abscissa is the nominal ratio of [EGTA]/[GaEGTA]. The ordinate is the differ- ence between the pCa values assuming no calcium contamination and a solution with a given level of contamination. In the lower curve the contamination level was assumed to be 50 grnol/k, and the nominal [EGTA], 4 rnmol/L. The upper curve is drawn for the same Bevel of contamination but with a nominal [EGTA] of 1 mrnsl/l. Purity in both cases was 94.3 % .
In csnclusiorm, in the preparation of a calcium buffer, the purity of the EGTA must be known, care must be taken to maintain the calcium contamination at as low a level as possible, and in the caiculation of the apparent constant numerous assumptions have to be made. Because of all these difficulties it is actually easier to measure the purity, the apparent constant, and the contami- nation level using the method devised by Bers (1982). Botentiometric methods have also been used (see Smith and Miller 1985; Williams and Fay 1990), but we used the Bers' method because it allowed us to determine the free calcium in the calibrating solutions.
Method of Bers (1982) The method is based on the use of a commercial calcium electrode. This is first calibrated in the background solution with
no added EGTA but containing known concentrations of calcium in the millimolar region, e.g., 0.2, 0.4, 1.0, and 4.0 mrnol/L. This calibration curve allows a linear extrapolation to calcium concentrations of around 180 nmol/L. The initial assumption is made that the electrode is linear down to this value.
As we will show later (see Fig. 8), this assumption is not true; deviation from linearity occurs at a pCa bust over 6. However, the Scatchard plot shows up such deviations from linearity and these measurements are not included in the final analysis. This problem of linearity is hrther considered in Part 1: The accuracy of the Bers Method and in Part 2: Bers Method under Stage 4 of Procedure.
If a series of calcium buffer solutions are now prepared, the free calcium concentration can be measured in each solution. Each buffer solution is a mixture of EGTA and CaEGTA and since the calcium was accurately pipetted from a B mol/L CaC12 solution, the total calcium in each solution is also known. Using a Scatchard plot analysis it is possible to calculate both purity and the apparent constant. Having obtained these values, it is then possible to measure the free Ca2+ in the nominally calcium- free solution and so measure the contamination level.
Scatchard plot
[I. 1041 [CaEGTA]/[Ca2 [EGTA] = K,,
where [EGTAJ is taken to mean all forms of EGTA not bound to Ca2+. If total EGTA concentration is in moles per litre [EGTAIT, then it follows that
[ I . 1051 [CaEGTA] + [EGTA] = [EGTAJT
11.1061 [CaEGTA] = K,,, [Ca2+] [EGTA]
but
[1 .I071 [EGTA] = [EGTA], - [CaEGTA]
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1744 CAN. 9. PHYSHOL. PWARMACOL. VOL. 69, 1991
whence
[ I . 1081 [CaECiTA] = ( [EGTAJT&,,[Ca2 '1 )/(I + K,,,[Ca2+1 )
and
which is in the form
A plot of boundlfree on the y axis and bound on the x axis will give a straight line with a slope sf Kpp and an intercept on the x axis equal to the concentration of the EGTA.
For convenience it is usual to plot the bound concentration on the x axis as millirnoles per litre; this transforms the equation into the following form:
or the slope is reduced by 1000. The intercept on the x axis remains the same. If Km,, is the measured slope, then this must be multiplied by 1000 to get Ka,, when the quantities are in moles per litre since
Accuracy of the Bee-s method This method does depend on the calcium electrode being linear down to at least a pCa of 6 and this linearity is the crux of
the method. Another way of looking at these data is to see the effect of purity alone on the shape of the curve. In Fig. 5 , the results of an actual experiment are shown. The logK,,, was calculated using the constants tabulated in Martell and Smith (1934). If 100% purity is assumed, then it is seen that the line connecting the calculated points is curved and in no way could the extrapolated calibration curve fit the points. If the purity is reduced to 90%, then the curve slopes over the other way and again there is no way there could be a fit to the extrapolated curve. In both cases a fit would also not be possible even if the calcium electrode was nonlinear. At a purity of 95.1 % the calculated points lie on a straight line and this line can then be shifted over to meet the calibration line. If this is done then the logKa,, for the solution can be estimated (cf. Allen et d. 1977). When this method was compared with the Bers method, both gave the same result for purity and log&,,, namely 95.1 % and 6.56, respectively. This is an indirect substantiation of the validity of the Bers method.
Par& 2: How ealeium buffers are actually made and calibrated
General iaformation Ghsswaw This has to be scrupulously clean. All glassware is soaked
for 24 h in detergent (2 % Decon 75, Decon Laboratories Ltd., Conway Street, Hove, England). It is then rinsed 7 times in tap water and 5 times in double-distilled water. If possible, a final rinse in Milli-Q water should be carried out.
Chemicals Suprapure NaCl and KC1 from Merck, Darmstadt, Germany
are recommended. EGTA must be kept in a desiccator, as it absorbs water. HCI, KOH, and NaOH are obtained as 1 mol1L sslufisns from BDH Pharmaceuticalis, London, U.K. For the magnesium it is recommended that either a standard solution be bought or a 1 mol/E solution is made up and checked by measuring the C1 concentration. The NaCl is added from a 1 m l / L NaCl solution. The 1 moll$, BDH calcium volumetric solution is used (accuracy f 0.01%). The accuracy of this solution can be checked by measuring out 100 rnL at 25 "C and weighing it. The density can then be calculated and checked against tables (Blatter and Blinks 1991). In the method that fol- lows the gold standard is the CaC12 solution.
Calcium contamination This can be checked in the background solution by the cali-
brated ealcium electrode. If care is taken, the contamination levels can be as low as 10 prnollL.
Preparation of Egtf( buflem In making these buffers it is usual to make them up in a
background solution mimicking the intracellular cation con- centration of the cell. In ferret heart muscle we used a back- ground solution containing the measured concentrations of Na, K, and Mg, buffered with Hepes to the measured intracellular pH of '7.2 (see Blatter and McGuigan 199 1).
Two solutions are made up: one of pure EGTA and a second solution to which CaC12 has been added to form CaEGTA. The calcium buffer solutions are then made up by mixing the appropriate quantities of both these solutions.
Ira making up the EGTA solutions it must be borne in mind that EGTA is a very acidic substance and will not dissolve unless the solution is more alkaline than about pH 4. Hepes is also acidic, thus sufficient alkali has to be added to the solution to ensure that the pH is within the desired range. This is nor- mally done by initially titrating a Hepes and EGTA solution with an alkali to empirically determine the necessary qwantity that has to be added. Moreover, the addition of calcium to an EGTA solution causes the release of protons and in order to maintain a constant pH, this release has to be allowed for. Again this is easiest done empirically by adding Ca and then titrating with alkali to measure the necessary quantity that has to be added to bring the pH back to the desired level. As the overall reaction for EGTA and Ca2+ shows there are apgroxi- mately two Hi ions released for every CaD bound to EGTA, which allows a rough calculation of the expected change in pH.
The solutions contain the following concentrations.
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casibration curve
-60
-70
-80
- 9 0
160
a 5 4
FIG. 5. Effect of purity on the shape of the pCa potential curve of the E m solutions. (0) Purity assumed to 100% ; (0) purity 95.1 96, and (v) purity 90%. This experiment was at 25"C, pH 7.2 in the standard background solution.
TABLE I . Composition of the EGTA buffer solutions
- - - -
Substance mrnol/L
KCI KBH NaCl MgC12 Hepes EGTA
Because sf the mixture sf KC1 and KOH, the K csncentra- tion is 142.5 mrnol/L and the pH of the solution is around 7.4. In making up the solution it can be back titrated to pH 7.2 with B mol/L HCl. The concentrations of the cations thus remain constant.
The CaEGTA solution has the added complication that the addition of Ca causes the release of protons-and the solution goes acid. This is compensted for by adding a mixture s f NaCl and NaOH, so chosen that the mixture again gives an end pH of around 7 -4.
TABLE 2. Composition of C&mA buffer sotuaion
Substance mmol/L
KC1 KOH NaCl NaQH MgCh Hepes E m CaC1,
KC[ 19.311e8 g
KOH 26 mb
HEPES 2.3830 g
EGTA 3.0428 g
MgCi2 2 mL
make rep lo 4 L
NaCl 15 mL
make up to 900 mL
titrrte to pH 7.2
mske up to 1 L
NeOH 8 mL
CaCB, 4 m k
mske up to 900 mL
titrate to pH 7.2
make up to 1 L
butter I
EGTA solution
mixtures I
CaEGTA eo!otion
FIG. 6 . Plow chart for the preparation of Ca buffer solutions. The initial 1-L solution contains the quantities for 2 L of solution. This is then split into 580-mL portions to ensure that the concentrations in both solutions are similar. Volumes refer to moles per litre stock solutions and pH is set by titrating with 1 mol/L HC1.
Preparation sf EGZA and &EWA solutions The aim is to make up 1 L of EGTA and 1 L CaEGTA solu-
tion ensuring that the EGTA concentration is the same in both solutions. To ensure this the solutions are made up in two stages. In stage 1, all the chemicals except NaCL, NaOH, and CaC12 are weighed or pipetted. A 1-L solution containing the quantities of KC!, KOH, Mepes, EGTA, and MgC12 for 2 L is made up. This is then split into two 500-mL portions. This is to ensure that the final EGTA concentrations in both the EGTA and CaEGTA solutions are as similar as possible.
In the second phase NaCl is added to one 500-mL portion and this is then made up to 1 L. This is the EGTA solution. To the second portion CaCL, NaC1, and NaOH are added. This gives the CaEGTA solution.
Weighing, gipetting, and solution making must be as accurate as possible. The various stages are described in detail below and Fig. 6 shows a flow chart of the procedure.
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CAN. B . PHYSIOL. PHAWMACOL. VOL. 69, 1991
TABLE 3. Stage 1
Substance I$a, or molarity g or mL for 2 L
KC1 74.56 19.3110 g KOH 1 moBIk 26 mL Hepes 238.3 2.383 g EGTA 380.35 3.0428 g w $ 1 2 1 rnolIL 2 mL
This should have a pH of around 7.4. Make up to 1 L and split into two 500-mL portions.
stage 2 EGEA solutiope: Add 15 mL of 1 rnol/E NaC1, make up to
around 900 mL, titrate to pH 7.2 with 1 moll%, HC1, then make up to 1 L.
CaECZE-A solution: Add 7 mL sf 1 mol/L NaCl, 8 mL 1 mollb, NaOH, and 4 mL CaC12. Make up to 900 mL and titrate to pH 7.2 with HCl, then make up to 1 L. This method then gives the two solutions. The solutions contain, in addition to the above concentrations, the following (in mmoB/L).
TABLE 4.
Solution NaCl NaOH CaC1,
The following mixtures are used, chosen so that they can be accurately pipetted .
TABLE 5.
Volumes (mL) Solution EGTAI
no. CaEGTA EGTA CaEGTA Total
Solution no. Ca content (rnmoH1L)
Calibrating solutions The four calibrating solutions contain 0.2, 8.4, B -0, and
4.0 mmol/L CaC12, and 250 mL of each solution are made up. To allow for the acid effect of the Hepes, K is a mixture of KC1 and KOH, so chosen that the pH is around 7.4. The solutions are then back titrated to pH 9.2. This method ensures that the concentrations of K and Na remain constant. The com- position of the calibrating solutions is shown below.
TABLE 7.
Solution M, or rnolarity rnanolll g or mL for 250 mL
KC1 74.56 140.0 KOH 250 mmol/L 2.5 NaCl 58.442 15.0 Mgelz 1 ~ I Q ~ / L 1.0 Hepes 238.3 5.0 CaCI, 108 mmol/L 4.0
1 .o 0.4 0.2
KOH and CaC12 are made up from the standard solutions. The calcium contamination is measured in a sample of the
calibrating solution to which no calcium has been added.
125 Bers method 80
150 In this method, using a calcium electrode the potential of the
100 calibrating solutions, as well as the buffer mixtures, is first
158 measured. On the assumption of linearity of the calcium elec- trode, the pCa values of the buffer solutions can be derived by
Solution number 1 has the lowest pCa (highest calcium con- centration) and number 10 has the highest pCa value (lowest calcium concentration).
Calcium content of these soku~ions The total calcium in the CaEGTA solution is 4 mmol/L.
Each sslutisn is a mixture of EGTA and CaEGTA. If the mix- ture is made up of x mL EGTA and y mL CaEGTA then
[%.I] Ca content of each solution = ((4y x
linear extrapolation from the measured potential of the cali- brating solutions. From these pCa values, the free and bound calcium concentrations can be calculated, as well as the bound/ free ratio. A Scatchard plot analysis can then be carried out on these results to obtain both the purity and apparent binding constant of the EGTA. As is shown below, deviations from linearity of the calcium electrode can be picked up from this plot.
A commercial calcium electrode and reference electrode, a pH electrode, and a water bath are needed. The measurements are carried out at the temperature of the experiments. We use 188-mL beakers and small magnetic fleas to ensure that the solution is continually stirred. The water bath is placed over the magnetic stirrer. It might be necessary to isolate the mag- netic stirrer from the water bath by polystyrene to prevent overheating by the magnetic stirrer.
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FIG. 7. Method for calculating the purity and apparent binding constant for EmA. (A) Calibration curve for the four calibrating solutions. The regression line through the points was y = 69.531 + 2 9 . 0 2 2 ~ ~ r = 1.000. (B) Scatchard plot analysis. The three points at the lower calcium concentrations have not been included in the analysis. The regression line drawn through the remaining points was y = 12786.0 - 3444.&, r = 0.977. From this regression Iine, purity is obtained by setting y = 0, making x = 3.71 1. With a nominal EGTA purity of 4 mmol/L, the purity becomes 92.7%. The apparent binding constant is log(3444.8 x 1800) or 6.537.
Procedure The calcium potential is first measured in the four calibrat-
ing solutions. The pH is brought to the necessary value by either KOH or HC1. After this, the calcium potential of the buffer solutions is then measured after they have been brought to the correct pH within f 0.01 pH units. This can be tedious. At the very end of this procedure the potential of the back- ground solution with no added calcium or EGTA is measured. This checks for calcium contamination.
To demonstrate the method, a sample measurement is shown below. The experiment was carried out 25°C.
TABLE 8.
Solution rnV Relative rnV pH
4.0 mmol/L 1.0 mmoI/L 0.4 mmsl/L 0.2 mmol/L Solution no.
1 2 3 4 5 6 7 8 9 10
Contamination
The calculation is carried out in four stages. Stage 1 : The calibration curve is first plotted and a regres-
sion line is drawn through the points. The calibration is shown in Fig. 7A.
Stage 2: From the calibration curve the pCa values are cal- culated for,
e2.31 pCa = (mV - 69.53 1)/29.022
This allows the calculation of the free calcium concentration and the ratio of the bsund/free. This is shown below.
TABLE 9.
Solution Free Ca Bound no. pCa (rnmol/L) ((mmol1L) Boundlfree
The contamination was found to be 12.5 pmol/L. Stage 3: This is the plot of bound/free against bound. A
regression line is then drawn through the linear part of this curve, as is shown in Fig. 7B. This is to account for nonlinear- ity in the calcium electrode.
Stage 4: In this last stage the pCa of the buffer solutions is calculated from the binding constant and the purity. In this case the equation is
e2.41 pCa = 6.537 + log ((x/y) - 0.8787)
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1748 CAN. J. PMYSIOL. PHARMACOL. VOL. 69, 8991
'%~BLE 10.
Solution no. RatioN RatioT pCaN pCa, Relative mV
The results are given in Table 10 where ratioN and pCaN are the nominal ratio and pCa. RatPti* and pCaT are the true or correct ratio and pCa, respectively. Also tabulated are the relative mV values for these solutions from Table 8.
Table 18 demonstrates that the effects sf purity cannot be neglected; compare for instance the ratio and pCa vdues of buffer solution 1 . The pCaT values, together with the four calibrating solutions can now be plotted against the relative mV values. Such a plot is shown in Fig. 8 where it can be seen that deviation from linearity is just beginning with solution number 8 (pCa of 6.16). This solution, as well as solution numbers 9 and 10 were not included in the Scatchard plot and- ysis because of this.
General conclusions It is normal to make up the calcium buffer solutions in a
background mimicking the intracellular ionic concentration of the cells under investigation, i.e., for a given temperature, ionic strength, and pH. While it is possible to calculate the apparent binding constants for calcium and magnesium, because of the various correction factors involved it is difficult to judge the accuracy of the calculation. Moreover, the calculation of the apparent binding constant is only one factor, for in order to estimate the free calcium both the purity of the ECXA and the calcium contamination of the solutions must dso be known.
pH is a much misunderstood measurement and unless care is taken the measured pH value can vary among electrodes (Illingworth 1981). Such differences are due to technical rea- sons but emphasize the difficulties involved in the measure- ment of pH. With EGTA an accurate measurement of pH is absolutely necessary, for as shown in Fig. 9 the apparent bind- ing constant is markedly pH dependent. As the figure shows a small change in pH around pH 7.2 would cause rather large changes in the apparent binding constant. Not only does pH cause difficulties, but if Mg or indeed some other ligand is also present in the solution, the binding of calcium to these ligmds has to be allowed for. Because of all these uncertainties it is much easier to actually measure the apparent binding constant under the appropriate experimental conditions. With the Bers method not only is the apparent binding constant determined, but also the purity and the contamination level. The method has the advantage that even if the pH electrode is not perform- ing ideally, it does not matter because all parameters have been measured at the same nominal pH and all measurements then become internally consistent. This pH dependence for EGTA is important and we find it necessary to check the pH of all our calibration solutions on the day of the experiment. The ade- quate buffer range is log Ka,, f I pCa unit, which for the cal-
FIG. 8. pCaipotential plot sf the four calibrating solutions and the calcium buffer solutions using the measured apparent binding sons- tant and each solution being corrected for the purity of the EGTA. The regression line drawn through the points was y = 68.806 + 28.788~.
cium buffer solutions described in this paper would be from pCa 5.54 to pCa 7.54. Although the ratios chosen for the buffer mixtures in this paper theoretically lie within this range, because of the complications of purity of the EGTA buffer, solutions 1, 2, and 3 lie just outside this range (cf. pCaw and pCaT in Table 10). For calibration, a range of buffers is taken and any marked change in the pCa of a solution would of course be spotted. However, this does demonstrate the impor- tance of measuring the purity of the EGTA. If buffers are desired to buffer outside of this range, either the pH of the solutions cam be changed (see Fig. 9) or the EGTA concentra- tion can be increased (see Fig. 2B). However, it must be remembered that increasing the EGTA concentration will increase the ionic strength and since CaEGTA carries two charges this effect cannot be overlooked.
The effects of both purity and calcium contamination are most marked at low EGTAICaEGTA ratios (see Figs. 3 and 4). The problems of contamination can be more or less eliminated by careful preparation of the buffer solutions and by using a nornind EGTA concentration of 4 mmol1L. This is not the case with the effects of purity. The purity musf be measured, and as discussed above it will exert a maximum effect at the lower p@a values.
This article has been confined to the use of EGTA as a calcium buffer substance. However. it will equally well apply to 1 ,2-bis(o-aminophenoxy)etBaane-NPN9N',N'-tetraacetic acid (BAPTA) or dibromo-BAWA (Harrison and Bers 1987). BAPTA
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6.5 7.0 7 . 5 8 . 0
p H
FIG. 9. pH dependence of the apparent binding constant. The results are the mean 9 SD from 12 measurements at pH 6.7, 7.2, and 7.7 using the Bers method. The experiments were carried out at 25°C in the standard background solution.
has the advantage that it is not nearly so pH dependent as EGTA (see Fig. 8 in Harrison and Bers, 1987), but has the dis- advantage that it is difficult to weigh out accurately and it is, in comparison to EGTA, relatively expensive.
Hn this article we have pointed out the numerous pitfalls involved in the manufacture of accurate calcium buffer solu- tions and have tried to explain why simply mixing EGTA and CaEGTA (or Ca@12) will not suffice, and in our opinion should no longer be done! However, if minimum care is taken, it is possible to make accurate Ca buffer solutions.
Acknowledgements This work was supported by the Swiss National Science
Foundation grant no. 3.210-0.85. It was initially written at the University of Oxford where J.McG. was an Overseas Visiting Fellow of the British Heart Foundation. A. B. was supported by both the Stanley Thomas Johnson Foundation and the Brit- ish Heart Foundation. A.B. and J .McG. would like to thank Professor D. Noble, Oxford, for his hospitality. We would also like to thank the students at Oxford University who insisted that we should write this work up. In the course of this work, discussions have taken place with numerous colleagues, and we would like to especially thank the following: C. H. Fry, D. J. Miller, G . L. Smith, and M. Pressler. We also wish to thank Miss H. Kennedy, Bristol University, for her comments on the manuscript.
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