Ionized concentrations in Ca2+ and Mg2+ buffers must be measured, not calculated.

NEW FINDINGS: What is the topic of this review? The [Ca2+ ]/[Mg2+ ] in buffers are usually calculated using one of eight programs. These all give different values, thus [Ca2+ ]/[Mg2+ ] must be measured. What advances does it highlight? The ligand optimization method (LOM) using electrodes is an accurate method to do this. The limitations of the method are described. The LOM has been generalized to include calibration of fluorochromes and aequorin. It is the method of choice to measure intracellular equilibrium constants. Owing to the uncertainties for the values of resting [Ca2+ ], ∆[Ca2+ ] and the pK' values for intracellular Ca2+ /Mg2+ binding used in modelling, these values must now be re-examined critically. ABSTRACT: Modelling intracellular regulation of Ca2+ /Mg2+ is now an established part of physiology. However, the conclusions drawn from such studies depend on accurate knowledge of intracellular [Ca2+ ], ∆[Ca2+ ] and the pK' values for the intracellular binding of Ca2+ /Mg2+ . Calculation of [Ca2+ ]/[Mg2+ ] in buffers is normal. The eight freely available programs all give different values for the [Ca2+ ]/[Mg2+ ] in the buffer solutions, varying by up to a factor of 4.3. As a result, concentrations must be measured. There are two methods to do this, both based on the ligand optimization method (LOM): (1) calibration solutions from 0.5 to 4 mmol l-1 ; and (2) calibration solutions from 0.1 µmol l-1 to 2 mmol l-1 . Both methods can be used to calibrate Ca2+ /Mg2+ electrodes. Only Method 2 can be used directly to calibrate fluorochromes and aequorin. Software in the statistical program R to calculate the [Ca2+ ]/[Mg2+ ] in buffers is provided for both methods. The LOM has now been generalized for use with electrodes, fluorochromes and aequorin, making it the ideal method to determine the pK' values for intracellular binding of Ca2+ /Mg2+ . The [Ca2+ ]/[Mg2+ ] in buffers must be measured routinely, which is best done by calibrating electrodes with the LOM and software written in R. If [Ca2+ ]/[Mg2+ ] in buffers are calculated, the parameters used in modelling show the same degree of variability as the software programs. Uncritical acceptance of such parameters means that conclusions reached from such studies are relative, not absolute, and must now be re-examined.

Ionised concentrations in calcium and magnesium buffers: Standards and precise measurement are mandatory.

In Ca2+ and Mg2+ buffer solutions the ionised concentrations ([X2+]) are either calculated or measured. Calculated values vary by up to a factor of seven due to the following four problems: The calculated [X2+] in buffers are so inconsistent that calculation is not an option. Until standards are available, the [X2+] in the buffers must be measured. The Ligand Optimisation Method is an accurate and independently verified method of doing this (McGuigan & Stumpff, Anal. Biochem. 436, 29, 2013). Lack of standards means it is not possible to compare the published [Ca2+] in the nmolar range, and the apparent constant (K/) values for Ca2+ and Mg2+ binding to intracellular ligands amongst different laboratories. Standardisation of Ca2+/Mg2+ buffers is now essential. The parameters to achieve this are proposed.

Ionised concentrations in calcium and magnesium buffers: Standards and precise measurement are mandatory.

In Ca(2+) and Mg(2+) buffer solutions the ionised concentrations ([X(2+)]) are either calculated or measured. Calculated values vary by up to a factor of seven due to the following four problems: 1) There is no agreement amongst the tabulated constants in the literature. These constants have usually to be corrected for ionic strength and temperature. 2) The ionic strength correction entails the calculation of the single ion activity coefficient, which involves non-thermodynamic assumptions; the data for temperature correction is not always available. 3) Measured pH is in terms of activity i.e. pHa. pHa measurements are complicated by the change in the liquid junction potentials at the reference electrode making an accurate conversion from H(+) activity to H(+) concentration uncertain. 4) Ligands such as EGTA bind water and are not 100% pure. Ligand purity has to be measured, even when the [X(2+)] are calculated. The calculated [X(2+)] in buffers are so inconsistent that calculation is not an option. Until standards are available, the [X(2+)] in the buffers must be measured. The Ligand Optimisation Method is an accurate and independently verified method of doing this (McGuigan & Stumpff, Anal. Biochem. 436, 29, 2013). Lack of standards means it is not possible to compare the published [Ca(2+)] in the nmolar range, and the apparent constant (K(/)) values for Ca(2+) and Mg(2+) binding to intracellular ligands amongst different laboratories. Standardisation of Ca(2+)/Mg(2+) buffers is now essential. The parameters to achieve this are proposed.

An improvement to the ligand optimisation method (LOM) for measuring the apparent dissociation constant and ligand purity in Ca2+ and Mg2+ buffer solutions.

In Ca(2+)/Mg(2+) buffers the calculated ionised concentrations ([X(2+)]) can vary by up to a factor of seven. Since there are no defined standards it is impossible to check calculated [X(2+)], making measurement essential. The ligand optimisation method (LOM) is an accurate method to measure [X(2+)] in Ca(2+)/Mg(2+) buffers; independent estimation of ligand purity extends the method to pK(/) < 4. To simplify calculation, Excel programs ALE and AEC were compiled for LOM and its extension. This paper demonstrates that the slope of the electrode in the pX range 2.000-3.301 deviates from Nernstian behaviour as it depends on the value of the lumped interference, Σ. ALE was modified to include this effect; this modified program SALE, and the programs ALE and AEC were used on simulated data for Ca(2+)-EGTA and Mg(2+)-ATP buffers, to calculate electrode and buffer characteristics as a function of Σ. Ca(2+)-electrodes have a Σ < 10(-6) mol/l and there was no difference amongst the three methods. The Σ for Mg(2+)-electrodes lies between 10(-5) and 1.5 (∗) 10(-5) mol/l and calculated [Mg(2+)] with ALE were around 3% less than the true value. SALE and AEC correctly predicted [Mg(2+)]. SALE was used to recalculate K(/) and pK(/) on measured data for Ca(2+)-EGTA and Mg(2+)-EDTA buffers. These results demonstrated that it is pK(/) that is normally distributed. Until defined standards are available, [X(2+)] in Ca(2+)/Mg(2+) buffers have to be measured. The most appropriate method is to use Ca(2+)/Mg(2) electrodes combined with the Excel programs SALE or AEC.

Automatic determination of ligand purity and apparent dissociation constant (K(app)) in Ca(2+)/Mg(2+) buffer solutions and the K(app) for Ca(2+)/Mg(2+) anion binding in physiological solutions from Ca(2+)/Mg(2+)-macroelectrode measurements.

Calibration of Ca(2+)/Mg(2+) macroelectrodes and flurochromes in the nmolar and mumolar range, respectively, require the use of buffer solutions. In these buffers the apparent dissociation constant (K(app)) has to be measured since calculation based on tabulated constants gives variable results. The ligand concentration [Ligand](T) has also to be estimated. The most accurate and general method for measuring both is the ligand optimisation method based on macroelectrode potential measurements, but this iterative method is time consuming, thus limiting its application. This paper describes an automatic program based on the method, which on entering the measured macroelectrode data calculates K(app), [Ligand](T) and the ionised concentration [X(2+)] within minutes. This optimisation method cannot be used at K(app) values greater than 0.1mM, but can be extended into this region if the anion concentration is known. The program has been modified to cover this eventuality. Ca(2+)/Mg(2+) macroelectrodes in conjunction with these programs offer an accurate, routine method for determining K(app) and [Ligand](T) in buffer solutions at the appropriate ionic strength, temperature and pH and the K(app) for divalent cations binding to physiological anions under experimental conditions.

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.

The apparent dissociation constants (Kapp) and total ligand concentrations ([Ligand]T) from extensive published and unpublished macroelectrode measurements for Mg2+/ATP, Mg2+/EDTA and Ca2+/EGTA buffers have been recalculated. These calculations were made feasible by the introduction of an Excel program which reduced the time of calculation for Kapp and [Ligand]T from over an hour to under five minutes. These estimations of Kapp and [Ligand]T allowed, not only a comparison between measured and calculated ionised magnesium and calcium concentrations ([Mg2+] and [Ca2+]) for Mg2+/ATP, Mg2+/EDTA and Ca2+/EGTA buffers but also a comparison amongst calculated values. Calculated [X2]1 values always differed from measured, and calculated values differed amongst themselves by factors of at least 2. These variations cast doubts on the published absolute values for intracellular [Mg2+] estimated by 31P-NMR and the resting values for [Ca2+] in cells. The allowable range for [X2+] in the buffers and consequently for Kapp and [Ligand]T has not been defined, which introduces uncertainties into published absolute values for [X2+]. This paper shows that an upper limit of +/- 10% deviation from the mean value for [X2+] is attainable. This requires the temperature to be maintained within +/- 0.5 degrees C, pH within +/- 0.01 units and pipetting errors of less than 0.25%. Until internationally defined buffer standards are available, the lack of correlation between measured and calculated [X2+] means that measurement of Kapp and [Ligand]T and hence [X2+] is more reliable than calculation.

Critical review of the methods used to measure the apparent dissociation constant and ligand purity in Ca2+ and Mg2+ buffer solutions.

Using simulated Ca2+ and Mg2+ buffers, methods proposed to measure both ligand purity and the apparent dissociation constant (Kapp) were investigated regarding (1) predicted accuracy of both parameters and (2) generality of the solution. The Bers' Ca2+ macroelectrode method [Bers, D. M., 1982 A simple method for the determination of free [Ca] in Ca-EGTA solutions Am. J. Physiol. 242, C404-C408] cannot be used with Mg2+ -macroelectrodes and is partly arbitrary since the linear part of the Scatchard plot is judged subjectively. Iterative methods have therefore been introduced. Iteration based on Bers' method or the lumped interference in the Nicolsky-Eisenman equation also failed with Mg2+ macroelectrodes. The Oiki et al., method [Oiki, S., Yomamoto, T., Okada, Y., 1994. Apparent stability constants and purity of Ca-chelating agents evaluated using Ca-sensitive electrodes by the double-log optimization method Cell Calcium 15, 209-46.] cannot be applied to Mg2+ macroelectrodes. The pH titration method of Moisescu and Pusch (Pflügers, Arch., 355, R122, 1975) predicted EGTA purity and Ca2+ contamination, but Kapp values for EGTA were approximate. It cannot be applied to Mg2+ binding. The partition method [Godt, R.E., 1974. Calcium-activated tension of skinned muscle fibres of the frog. Dependence on magnesium adenosine triphosphate concentration J. Gen. Physiol. 63, 722-739.] only approximately estimated the K(app). Calibration, maintaining contaminating [Ca2+]/[Mg2+] at < 1micromol l(-1), and setting standards by dilution, is the ultimate check of calculated ionised concentrations, although technically difficult. The macroelectrode method of Lüthi et al. [1997. Calibration of Mg2+ -selective macromolecules down to 1 micromol l(-1) in intracellular and Ca+ - containing extracellular solutions. Exp. Physiol. 82, 453-467] accurately predicted purity and Kapp at pKapp values > 4 and was independent of electrode characteristics. It is considered the method of choice. Macroelectrode primary calibration should be carried out in solutions varying from 0.5 to 10 mmol l(-1) combined with either Ca-EGTA or Mg-EDTA buffers; the [Ca2+] and [Mg2+] in other buffer ligands can be measured in a secondary calibration.