Measurement of Calcium Activity in Oral Fluids by Ion Selective Electrode: Method Evaluation and Simplified Calculation of Ion Activity Products

The activity of calcium in plaque fluid is needed to calculate the saturation level of that fluid relative to the tooth mineral. One method to determine the calcium activity in very small plaque fluid samples is by micro ion-selective electrode (ISE). Two commercially available calcium ionophores, a neutral-carrier and a charged-carrier, were evaluated in micro ISEs and compared to a commercially available macro ISE using saliva as a model for plaque fluid. The neutral-carrier containing ISEs gave results consistent with those of the macro ISE. Calcium activity measurements made with micro ISEs that contained the neutral ion-carrier of whole plaque samples and plaque fluid samples obtained by centrifugation of whole plaque showed that the activities did not change due to centrifugation. Estimates of the saturation with respect to hydroxyapatite were made from these measurements. A simplified calculation method is presented to estimate the ion activity product (IAP) of the calcium-phosphate minerals. The method is based on the relative abundance of some of the possible calcium-binding species and a fixed ionic strength for plaque fluid. Calculations show that within a normal pH range for plaque fluid (5.0 to 7.5) the differences in the IAP calculations for hydroxyapatite using the simplified method are less than those estimated from propagation of uncertainty calculations.

The activity of calcium in plaque fluid is needed to calculate the saturation level of that fluid relative to the tooth mineral. One method to determine the calcium activity in very small plaque fluid samples is by micro ion-selective electrode (ISE). Two commercially available calcium ionophores, a neutral-carrier and a charged-carrier, were evaluated in micro ISEs and compared to a commercially available macro ISE using saliva as a model for plaque fluid. The neutral-carrier containing ISEs gave results consistent with those of the macro ISE. Calcium activity measurements made with micro ISEs that contained the neutral ion-carrier of whole plaque samples and plaque fluid samples obtained by centrifugation of whole plaque showed that the activities did not change due to centrifugation. Estimates of the saturation with respect to hydroxyapatite were made from these measurements. A simplified calculation method is presented to estimate the ion activity product (IAP ) of the calcium-phosphate minerals. The method is based on the relative abundance of some of the possible calcium-binding species and a fixed ionic strength for plaque fluid. Calculations show that within a normal pH range for plaque fluid (5.0 to 7.5) the differences in the IAP calculations for hydroxyapatite using the simplified method are less than those estimated from propagation of uncertainty calculations.

Introduction
The concentration of calcium in the fluid phase surrounding teeth is one of the primary factors that determines whether a tooth remineralizes or demineralizes [1]. Specifically, it is the concentration of ionic calcium (the calcium not bound by anionic species, [Ca 2+ ]) that is the relevant form of calcium in determining saturation within plaque fluid (PF) with respect to enamel minerals [2]. The introduction of the calcium ion-selective electrode (Ca-ISE) and the development of ultramicro ion-selective electrode methods for the measurement of calcium in nanoliter volumes of plaque fluid [2,3] makes it possible to directly determine the ionic calcium concentration in PF.
The measurement of [Ca 2+ ] in PF by Ca-ISE has proven to be difficult due to several factors, which includes small sample size, protein poisoning, and interfering ions found in PF [4,5]. Although many of the difficulties inherent to Ca-ISE measurements have apparently been surmounted [2,6,7], a methodical evaluation of Ca-ISEs suitable for use in the analysis of PF has not been presented. In this report, two different commercially available calcium ionophores were used to fabricate micro Ca-ISEs, the responses of which were compared to that of a commercially available macro Ca-ISE designed for the analysis of blood and serum calcium. Whole pooled saliva was used as a model for plaque fluid. One potential advantage of ISE methods is the possibility of direct measurements of PF [Ca 2+ ] without the need for sample centrifugation. Using micro Ca-ISEs that are shown to agree with the macro Ca-ISE in saliva determinations, comparisons of the pH and [Ca 2+ ] between whole plaque and PF centrifuged from the same whole plaque samples are presented.
One important advantage that the Ca-ISE affords is that the activity of calcium ({Ca 2+ }) is directly determined. Note that in this report quantities in square brackets [ ] represent free ion concentrations and quantities in curly brackets { } represent ion activities, and thus

Sample Manipulation
Immediately after collection, the samples of saliva, whole plaque, and plaque fluid were placed in a mineral oil-filled dish equilibrated with a gas mixture containing a volume fraction of 5 % CO 2 in nitrogen and saturated with water (5 % CO 2 Ϫ95 % N 2 ϪH 2 O Sat ) to avoid evaporative loss of water or change in pH due to CO 2 loss from the sample. Samples were stored less than 30 min before analysis. The physiological range for the partial pressure of CO 2 (p CO 2 ) in the parotid saliva has been reported to be between venous and arterial levels, with an average of approximately 5 % for a moderate salivary flow rate (0.25 mL/min) [8]. For this reason 5 % CO 2 Ϫ95 % N 2 ϪH 2 O Sat gas mixture was used to equilibrate plaque fluid and saliva samples during measurements.

Collection of Saliva Samples
Fresh-pooled, unstimulated saliva samples were collected by expectoration from 15 individuals. The first 2 mL of saliva were discarded and the following 5 mL were analyzed. Saliva samples were analyzed for pH and {Ca 2+ } by ISE under 5 % CO 2 Ϫ95 % N 2 ϪH 2 O Sat equilibrated mineral oil immediately after collection and without further sample preparation.

Collection of Whole Dental Plaque and Plaque Fluid Separation
Supragingival dental plaque was collected as described in [9] from the buccal surfaces of individual upper and lower molars. Plaque fluid was separated from the whole plaque by centrifugation at 117 680 m/s 2 (12 000 g ), 15 min, 4 ЊC and the fluid removed via micropipette [2]. All samples were placed under 5 % CO 2 Ϫ95 % N 2 ϪH 2 O Sat mineral oil for analysis.

Electrode Construction
Reference, pH, and calcium selective microelectrode construction has been described previously [3]. Two types of calcium ion exchanger material were tested in the calcium microelectrodes: a neutral carrier, N,N'di (11-ethoxycarbonyl) [11]. The macro calcium selective electrode (ICA1, Radiometer, Copenhagen), that was used as the "standard electrode" had the same charged carrier material as above in its membrane. The sensing membrane was further protected from macromolecular interference with a dialysis membrane [12,13].

Ion-Selective Electrode Determination 2.5.1 Calcium Activity Standards
Standards were made from a standardized CaCl 2 solution (Fischer Scientific, Lanham, MD) with a 150 mmol/L KCl ionic strength background (similar to the ionic strength of plaque fluid [14]). The total calcium concentrations of the standards were (0.1, 0.5, 1.0, and 5.0) mmol/L for an activity of (0.033, 0.166, 0.331, and 1.625) mmol/L respectively. The activity of calcium in the standards was calculated from the ionic strength and using the Davies' modification of the Extended Debye-Hückel Equation [15].

Saliva
Ca-ISE analysis of saliva samples was carried out under 5 % CO 2 Ϫ95 % N 2 ϪH 2 O Sat mineral oil. Samples were deposited on the surface of the inverted macro Ca-ISE. The micro Ca-ISEs and a micro reference electrode were positioned in the sample. In this manner the responses of two or more microelectrodes and the macro electrode could be measured simultaneously for paired analyses of the results. This method also eliminated the effect of reference electrode error because the measurements were simultaneous and had the same reference electrode.

Whole Plaque and Plaque Fluid
Samples were placed in dishes filled with 5 % CO 2 Ϫ95 % N 2 ϪH 2 O Sat mineral oil for microelectrode analysis. Calcium and pH microelectrodes and a micro reference electrode were positioned in the sample for simultaneous analysis [2,3].

Spectrophotometric Determination of Total Calcium and Total Phosphate 2.6.1 Plaque Fluid
Nanoliter volumes (10 nL to 50 nL) of plaque fluid samples were analyzed as has been described [16] by use of precalibrated nanoliter pipettes for samples and standards. Total calcium ([Ca] Tot ) determinations utilized the Arsenazo III reagent and a microspectrophotometer with a 2.3 L cell volume [2,16,17]. The relative standard deviation (RSD) observed from this calcium method, determined by the repeated analysis of known samples, has been found to be less than 2 % [16]. The total phosphate ([PO 4 ] Tot ) concentration was colorimetrically determined by use of a phosphomolybdate method [17] and a microspectrophotometer [2]. The RSD of this phosphate analysis technique, determined by the repeated analysis of known samples, has been found to be less than 1 % [16]. Phosphate analyses for some PF samples were also made by capillary electrophoresis methods [18]. Paired analyses of the results from the colorimetric and capillary electrophoresis methods, to determine phosphate concentration in PF, indicated no significant difference between the values obtained by these techniques (significance level a > 0.1, n = 13 pairs, paired t -test).

Rigorous Calculation of the Ion Activity Product for the Calcium-Phosphate Salts
The ion activity products (IAP s) were calculated for the calcium-phosphate minerals with the measured quantities {H + }, {Ca 2+  , were known, as can be seen from Eqs. (1)- (5): Here, DCPD is dicalcium phosphate dihydrate, ␤ TCP is beta-tricalcium phosphate, OCP is octacalcium phosphate, HAp is hydroxyapatite, and ACP is amorphous calcium phosphate.
In this report the {Ca 2+ } and {H + } were measured directly by ion-selective electrodes, leaving only esti- 3Ϫ }, {HPO 4 2Ϫ } and ionic strengths needed to calculate the IAP s. These activities were calculated, as described below, from the binding constants of the various inorganic phosphate binding moieties found in plaque fluid (Table 1) and the appropriate activity coefficients ␥ . The activity coefficients were calculated at an assumed ionic strength of 150 mmol/L for plaque fluid [14] using the Davies' modification of the Extended Debye-Hückel Equation [15] and the Debye factor A ( where and Here the terms K P 1 , K P 2 , and K P 3 in Eqs. (7)- (9) are the dissociation constants for phosphoric acid and the terms K CaH 2 PO 4 + , K CaHPO 4 0 , and K CaPO 4 Ϫ in Eq. (9) are the association constants for the indicated ion pairs and are presented in Table 1 ..] to include other phosphate-binding substances such as sodium and magnesium, which were not measured for the current paper. The concentration and/or the binding constants of these other phosphate-binding substances appear to be small in comparison to the concentration of total phosphate in PF [19] and do not affect the computation significantly. The quantity {HPO 4 2Ϫ } is obtained by dividing both sides of Eq. (7) by the expression in the square brackets and from this result the activity of PO 4 3Ϫ is calculated: The IAP for the Ca-PO 4 minerals can then be calculated by use of Eqs. (1)-(5).

Simplified Calculation of the PF-IAP s for the Calcium-Phosphate Salts Suitable for Spreadsheets
Two observations about the phosphate ion activities in PF can lead to an acceptable estimate of the {PO  } is reduced by less than 10 % when the calcium is present at a concentration of 3 mmol/L and the pH of the PF is 7.5, therefore G (H, ␥ , K ) = 0 (i.e., the value of Eq. (9) is 0.

Calcium Ionophore Evaluation
The [Ca 2+ ] in whole pooled saliva determined by inverted macro Ca-ISE, protected with a dialysis membrane, was (0.88 Ϯ 0.12) mmol/L (mean Ϯ 1 standard deviation of the mean, n = 20). The [Ca 2+ ] in saliva determined with micro Ca-ISEs that utilized neutral and charged carriers was (0.84 Ϯ 0.17) mmol/L (n = 41) and (0.66 Ϯ 0.20) mmol/L (n = 99), respectively. The paired difference in the [Ca 2+ ] determined by the two types of micro Ca-ISEs of (0.24 Ϯ 0.18) mmol/L (n = 41 pairs) was significant (a < 0.001). No significant difference was found in the [Ca 2+ ] determined by the charged carrier type inverted macro calcium electrode and the microelectrodes with the neutral carrier (a > 0.1, n = 20 pairs). Because of the observed discrepancy in the values derived from the charged carrier micro ISEs versus those from the macro and neutral carrier ISEs, the only [Ca 2+ ] results reported in this study are from analysis made with micro Ca-ISEs that contained the neutral carrier micro-or inverted macro Ca-ISEs.  Table 2. Table 3 presents a comparison between the microelectrode determined values for pH and [Ca 2+ ] for whole plaque and the PF recovered by centrifugation from the same whole plaque sample. No significant differences in the pH or [Ca 2+ ] were caused by the centrifugation and separation of PF from the plaque mass (a > 0.1, Student t -test).  } for a range of pH values from 5.0 to 7.5 when calculated by the rigorous and simplified methods as described in Eqs.

Discussion
The evaluation of Ca-ISE ion exchangers found significant differences in the responses between the neutral carrier and charged carrier types of microelectrodes when determining the activity of calcium in whole pooled saliva. These differences in response were not always consistent, resulting in a wider range of responses between electrodes containing the charged carrier. One interesting observation was that microelectrodes of the charged carrier type that were constructed with very fine tips (tip opening Յ 1 m) responded similarly to the micro ISEs made with the neutral-carrier. These very fine-tipped ISEs tended to have a shorter useable lifetime and required more time to stabilize between readings. Macro electrodes that contained the charged carrier that were protected with dialysis membranes always gave the same response as the neutral carrier type microelectrodes. It is not clear what caused the difference in the responses between the neutral carrier and charged carrier type of ISE that was not protected. However, because the effect could be removed by protection of the ion exchange fluid with a dialysis membrane, it is probable that the charged-carrier suffered some interference from macromolecules. It is suggested that to assure reliable results, any calcium electrode be thoroughly checked in saliva samples of known calcium activity, or against a macro Ca-ISE that has been protected against macromolecules, before measurement in plaque or plaque fluid samples.
No significant differences were found between the pH and [Ca 2+ ] measured with microelectrodes in the extracellular fluid of whole plaque (before centrifugation) and the fluid obtained by centrifugation of those same samples (Table 3). This result agrees with earlier results where the potassium activity was determined before and after centrifugation [20]. This indicates that the composition of plaque fluid derived from fresh whole plaque by centrifugation is not significantly altered during the process of centrifugation. The composition results for pH, {Ca 2+ }, [Ca] Tot , and [PO 4 ] Tot for starved (no food for more than 12 h) PF compare favorably with earlier reports [6,7] (see Table 2).
The calculation of the ion activity product with respect to Ca-PO 4 4 ] Tot with good accuracy even when the effect of binding by cations to phosphate was ignored ( Table 4). The benefit of such simplification is that the activity of the phosphate species, and thus the IAP with respect to the calcium-phosphate salts, can be calculated with good accuracy directly on a spreadsheet by use of simple equations such as Eqs. (13) and (14). The difference introduced from such assumptions is about 20 % in the activity of a phosphate species at pH 7.5 but much less at lower pH values. Even at the high pH where this systematic difference is largest, the difference in the calculation of the Ϫlog(IAP HAp ) (0.244) is smaller than the uncertainty calculated from the uncertainties inherent in the analytical techniques for pH, [PO 4 ] Tot , and {Ca 2+ }. Propagation of uncertainty (sometimes called propagation of error) calculations based on the uncertainties in the determination of pH, [PO 4 ] Tot , and {Ca 2+ } yields an estimate of Ϯ 0.3 [16] for the smallest uncertainty that can be determined for Ϫlog(IAP HAp ) with the analytical methods used for this study. The reason that the systematic difference is small is that the abundance of phosphate in PF is much higher than that of calcium (Table 2), and therefore the calcium binding cannot reduce the phosphate activity by a large amount. The use of an ion selective electrode that measures the activity of HPO 4 2Ϫ [21] in solution will further simplify and improve the uncertainty of IAP estimates with respect to the Ca-PO 4 salts.