## Abstract

The mechanism for an acid-base disturbance can be determined by using the strong ion approach, which requires species-specific values for the total concentration of plasma nonvolatile buffers (A_{tot}) and the effective dissociation constant for plasma weak acids (*K*_{a}). The aim of this study was to experimentally determine A_{tot} and *K*_{a} values for human plasma by using in vitro CO_{2} tonometry. Plasma Pco_{2} was systematically varied from 25 to 145 Torr at 37°C, thereby altering plasma pH over the physiological range of 6.90–7.55, and plasma pH, Pco_{2}, and concentrations of quantitatively important strong ions (Na^{+}, K^{+}, Ca^{2+}, Mg^{2+}, Cl^{-}, lactate) and buffer ions (total protein, albumin, phosphate) were measured. Strong ion difference was estimated, and nonlinear regression was used to calculate A_{tot} and *K*_{a} from the measured pH and Pco_{2} and estimated strong ion difference; the A_{tot} and *K*_{a} values were then validated by using a published data set (Figge J, Rossing TH, and Fencl V, *J Lab Clin Med* 117: 453–467, 1991). The values (mean ± SD) were as follows: A_{tot} = 17.2 ± 3.5 mmol/l (equivalent to 0.224 mmol/g of protein or 0.378 mmol/g of albumin); *K*_{a} = 0.80 ± 0.60 × 10^{-7}; negative log of *K*_{a} = 7.10. Mean estimates were obtained for strong ion difference (37 meq/l) and net protein charge (13+.0 meq/l). The experimentally determined values for A_{tot}, *K*_{a}, and net protein charge should facilitate the diagnosis and treatment of acid-base disturbances in critically ill humans.

- plasma pH
- strong ion difference
- anion gap
- metabolic acidosis

the strong ion approach to acid-base balance emphasizes that the pH and bicarbonate concentration ([HCO_{3}]) of an aqueous biological solution are determined by three independent variables (for review, see Refs. 4, 5, 36): *1*) Pco_{2}; *2*) strong ion difference (SID), which is the difference between the charge of strong cations (sodium, potassium, calcium, magnesium) and strong anions (chloride, lactate, sulfate, ketoacids, nonesterified fatty acids, and many others) that are completely dissociated in biological solutions; and *3*) the total weak acid concentration (A_{tot}), which includes all nonvolatile weak acids in the system, such as proteins and inorganic phosphates that are modeled as having a single effective dissociation constant (*K*_{a}). The physicochemical interactions between the independent and dependent variables in an acid-base system recognize the constraints imposed by the law of electrical neutrality, the dissociation equilibrium of weak acids, and the conservation of mass (4, 36). The strong ion approach can be used to determine the contribution of the three independent variables (Pco_{2}, SID, A_{tot}) to plasma pH and [HCO_{3}], thereby improving our understanding of physiological and pathophysiological interactions in biological aqueous solutions.

Plasma proteins provide the major contribution to A_{tot}, and, therefore, plasma protein concentration independently affects acid-base balance. The role of plasma protein concentration in acid-base balance is well recognized in human and veterinary medicine, with hypoproteinemia and hyperproteinemia causing alkalemia and acidemia, respectively (5, 11, 20, 29). The most widely used method to assign a value for A_{tot} in human plasma has been calculation from the plasma protein concentration by using the estimate of net protein charge obtained by Van Slyke and colleagues (39) in 1928. To obtain this estimate, human plasma proteins were assumed to have the same alkali titration curve as horse serum proteins (40); this assumption provided an estimate for the net protein charge of human plasma ([total protein] = 70 g/l, where brackets denote concentration) of 16.9 meq/l. In a 1964 study, Van Leewen (38) estimated that the net protein charge in human plasma was 12.6 meq/l, a value that was similar to the estimate of 12.0 meq/l obtained by Figge and colleagues (10) in 1992. Many investigators assumed that these estimated values for net protein charge (16.9, 12.6, or 12.0 meq/l) were equivalent to the value for A_{tot}; however, this is an erroneous assumption, because the value for A_{tot} must always be greater than that of net protein charge, and because A_{tot} is expressed in different units (mmol/l) than net protein charge (meq/l) (6).

Species-specific values for A_{tot} and *K*_{a} should be experimentally determined when using the strong ion approach to describe acid-base equilibria (4, 35, 36). Values for A_{tot} (14.9 or 15.0 mmol/l) and *K*_{a} (2.1 or 2.2 × 10^{-7}) have been experimentally determined for equine plasma (4, 35), but different values have been experimentally determined for cattle plasma (A_{tot} = 25.0 mmol/l; *K*_{a} = 0.9 × 10^{-7}; Ref. 7) and cat plasma (A_{tot} = 27.4 mmol/l; *K*_{a} = 1.0 × 10^{-7}; Ref. 21). For human plasma, only theoretical estimates for A_{tot} (24.1 mmol/l) and *K*_{a} (1.1 × 10^{-7}) are available (6). Interestingly, these theoretical A_{tot} and *K*_{a} estimates predicted that net protein charge in human plasma was 15.3 meq/l, which was similar to the estimate of Van Slyke et al. (16.9 meq/l) (39), but greater than that of Van Leeuwen (12.6 meq/l) (38) and Figge et al. (12.0 meq/l) (11). The purpose of this study was, therefore, to experimentally determine A_{tot} and *K*_{a} values for human plasma and, from this information, calculate net protein charge. We accomplished our objectives by performing in vitro CO_{2} tonometry of plasma from eight healthy humans. We also validated the experimentally determined values for A_{tot} and *K*_{a} using published data (11) and compared the predictive accuracy of these values with theoretical estimates (6) or derived estimates (10, 32).

## MATERIALS AND METHODS

*Blood and plasma collection.* Twenty milliliters of venous blood were collected into lithium-heparin tubes from the antecubital veins of eight healthy humans (26–46 yr old; 4 men, 4 women). Lithium-heparin tubes were used instead of sodium-heparin tubes for blood collection, because the measured sodium component of plasma collected into sodium-heparin can be increased by up to 2 meq/l, increasing the measured SID (44). In addition, lithium-heparin dissociates in plasma into a strong cation (lithium) and strong anion (sulfite), with no change in actual SID or measured SID, because plasma lithium and heparin concentrations are not routinely measured.

One milliliter of venous blood was immediately analyzed to characterize the normal values, and plasma was harvested from the remaining 19 ml by centrifugation that was completed within 30 min of collection. Plasma was frozen at -70°C and stored for up to 2 mo before being thawed at room temperature immediately before CO_{2} tonometry was performed. The University of Guelph ethics committee approved this study.

*CO*_{2} *tonometry of plasma.* Plasma samples were tonometered (IL 235, Instrumentation Laboratory, Lexington, MA) for 20 min at 37°C over a Pco_{2} range of 25–145 Torr by using a gas mixture containing 20% CO_{2} and 80% normal air. This produced a pH range of 6.90–7.55.

*Blood and plasma analyses.* The fresh blood sample and all tonometered plasma samples were analyzed in duplicate on a Statprofile 9+ (NOVA Biomedical, Canada, Mississauga, Ontario) for blood-plasma gas analysis (pH, Pco_{2}) and determination of [Na^{+}], [K^{+}], [Ca^{2+}], [Cl^{-}], and [lactate^{-}]. Table 1 provides a summary of the variability and measurement methodology for each variable. An untonometered plasma sample was analyzed in duplicate (Dacos multianalyzer, Coulter Electronics, Hialeah, FL) to determine strong cation (Mg^{2+}) and nonvolatile buffer ion (total protein, albumin, and inorganic phosphate) concentrations.

*Calculation of SID.* Strong cation (Na^{+} + K^{+} + Ca^{2+} + Mg^{2+}) and strong anion (Cl^{-} + lactate) concentrations were assumed to be constant during CO_{2} tonometry and an ionic equivalency assigned to those variables (Mg^{2+}, lactate) not measured by using ion-selective potentiometry. Accurate measurements of SID are difficult to obtain in plasma (6, 31, 42) because of cumulative measurement error, presence of unknown strong anions (12, 15), and differences in equipment and methodology (18, 28); SID was, therefore, initially estimated by using three methods: SID_{3} = {([Na^{+}] + [K^{+}]) - [Cl^{-}]}; SID_{4} = {([Na^{+}] + [K^{+}]) - ([Cl^{-}] + [lactate])}; and SID_{6} = {([Na^{+}] + [K^{+}] + [Ca^{2+}] + [Mg^{2+}]) - ([Cl^{-}] + [lactate])}. A constant value for SID_{3}, SID_{4}, and SID_{6} was assigned by using the mean value for all CO_{2} tonometered samples from each subject. This minimized the effect of measurement variability in strong ion concentrations. A constant value for SID is one of the assumptions of the strong ion approach; SID is invariant over the physiological range of pH, because strong ions are fully dissociated at physiological pH (4, 6, 33). Because SID_{3}, SID_{4}, and SID_{6} represented constant values, the terms were expressed as [SID_{3}]_{constant}, [SID_{4}]_{constant}, and [SID_{6}]_{constant}, respectively.

In preliminary data analysis, strong ion (Na^{+}, K^{+}, Ca^{2+}, and Cl^{-}) concentrations measured by ion-selective electrodes were regressed against pH. Neither [K^{+}] or [Cl^{-}] varied with pH; however, [Na^{+}] varied inversely with pH for six of the eight plasma samples (mean linear regression equation: [Na^{+}] = -3.98 pH + 173.5), and [Ca^{2+}] varied inversely with pH for all eight plasma samples (mean linear regression equation: [Ca^{2+}] = -1.29 pH + 11.9), where [Na^{+}] and [Ca^{2+}] were in meq/l. Over the pH range in this study (6.90–7.55), this corresponds to a mean change in [Na^{+}] and [Ca^{2+}] of 2.6 and 0.8 meq/l, respectively. A possible reason for the observed pH dependence of measured [Na^{+}] and [Ca^{2+}] was poor selectivity of the sodium and calcium electrodes to H^{+}. The potentiometric selectivity coefficient defines the ability of an ion-selective electrode to distinguish the primary ion from other ions in the same solution; the smaller the value for the selectivity coefficient, the less susceptible is the electrode to changes in the concentration of the interfering ion (3). Although reported selectivity coefficients of the Ca^{2+}, Na^{+}, and K^{+} electrodes for H^{+} are 0.16–16, 0.2–3.2, and <0.0001, respectively (1), these selectivity coefficient values were not high enough to explain the pH dependency of [Na^{+}] and [Ca^{2+}] during CO_{2} tonometry over a pH range of 6.90–7.55.

The most likely reason for the pH dependency of measured [Na^{+}] and [Ca^{2+}] was salt-type binding of sodium and calcium to plasma protein; as pH decreases, the net protein charge decreases (becomes less negative), thereby “releasing” electrostatically bound sodium and calcium and increasing plasma [Na^{+}] and [Ca^{2+}] when measured by ion-selective potentiometry (3, 19, 23). As we observed, the magnitude of this effect was more pronounced for Na^{+} than Ca^{2+}, because 36 mmol of sodium and 0.8 mmol of calcium are electrostatically bound to plasma proteins for each liter of human plasma (3). To account for the effect of pH on electrostatically bound sodium and calcium, we calculated the SID for each tonometered plasma sample from the measured values for [Na^{+}], [K^{+}], [Ca^{2+}], [Mg^{2+}], [Cl^{-}], and [lactate] and termed this value [SID_{6}]_{variable}, because the value varied with pH during CO_{2} tonometry.

*Calculation of A*_{tot} *and K*_{a}. Measured values for pH and Pco_{2}, calculated values for [SID_{3}]_{constant}, [SID_{4}]_{constant}, [SID_{6}]_{constant}, and [SID_{6}]_{variable}, the six-factor simplified strong ion electroneutrality equation (4) 1 and the Marquardt nonlinear regression procedure (13, 30) were used to solve simultaneously for A_{tot} and *K*_{a}, where [A^{-}] in *Eq. 1* is the net charge of plasma nonvolatile buffers. To facilitate accurate calculation of values for A_{tot} and *K*_{a}, *Eq. 1* was expressed in the following form 2 by applying known values for the solubility of CO_{2} in plasma (S; 0.0307 mmol · l^{-1} · mmHg^{-1}) (2) and the negative logarithm of the apparent equilibrium dissociation constant (p*K*′_{1}; 6.120 at [NaCl] = 0.16 mmol/l; interpolated from Table II, Ref. 14). With the use of the value of 6.120 for p*K*′_{1} calculated actual plasma [HCO_{3}] (mmol/l) at 37°C (25); similarly, the four methods used to calculate SID provided a value in terms of concentration. This means that *Eq.* 2 estimated a value for A_{tot} in terms of concentration (mmol/l). The form of the simplified strong ion electroneutrality equation used in *Eq.* 2 was selected because it provided the narrowest confidence intervals for the estimated values of A_{tot} and *K*_{a}. Initial estimates for A_{tot} of 5–30 mmol/l in increments of 5 mmol/l and initial estimates for *K*_{a} of 0.1–3.0 × 10^{-7} in increments of 0.1 × 10^{-7} were used for the nonlinear regression procedure.

Because the true value for SID was unknown, a fifth nonlinear regression procedure was performed to simultaneously estimate values for A_{tot}, *K*_{a}, and SID (called [SID]_{estimated}), with initial estimates for [SID]_{estimated} of 30–45 meq/l in increments of 5 meq/l.

A sixth nonlinear regression procedure was performed to calculate A_{tot} and *K*_{a}. This was done to compare A_{tot} and *K*_{a} values obtained by using the six-factor simplified strong ion model (described previously) with Stewart's eight-factor strong ion model (36). Although we have shown algebraically (4) and graphically (6) that Stewart's eight-factor strong ion model contains two redundant factors [apparent equilibrium dissociation constant for the ion product of water () and apparent equilibrium dissociation constant for ], it was of interest to determine whether the eight-factor model provided more accurate estimates for A_{tot} and *K*_{a}. Measured values for pH and Pco_{2}, calculated values for [H^{+}](= 10^{-pH}), either [SID]_{variable} or [SID]_{estimated}, the carbonate ion concentration ([]), and the hydroxyl ion concentration ([OH^{-}]), Stewart's eight-factor strong ion electroneutrality equation (36) 3 and the Marquardt nonlinear regression procedure (30) were used to solve simultaneously for A_{tot} and *K*_{a}. To facilitate the nonlinear regression procedure, *Eq. 3* was expressed in the following form 4 Where p*K*′_{3} is the negative logarithm (10.22) of the apparent equilibrium dissociation constant for HCO_{3} (*K*′_{3} = 6 × 10^{-11}) and p*K*′_{w} is the negative logarithm (13.36) of the ion product of water (*K*′_{w} = 4.4 × 10^{-14}). The form of the strong ion electroneutrality equation used in *Eq. 4* was selected because it provided the narrowest confidence intervals for the estimated values of A_{tot} and *K*_{a} when pH was changed by CO_{2} tonometry.

*R*^{2} values were calculated for the seven fitted nonlinear regression models by using the values obtained during CO_{2} tonometry of each human plasma sample: the six-factor simplified strong ion model and five different methods ([SID_{3}]_{constant}, [SID_{4}]_{constant}, [SID_{6}]_{constant}, [SID_{6}]_{variable}, [SID]_{estimated}) for estimating SID, and the eight-factor strong ion model and two different methods ([SID_{6}]_{variable}, [SID]_{estimated}) to estimate SID. The calculated A_{tot} values were indexed to the total protein (A_{tot tp}) and albumin (A_{tot-alb}) concentration, and mean ± SD values for A_{tot}, A_{tot tp}, A_{tot alb}, and *K*_{a} were determined. A *P* value <0.05 was considered significant.

*Comparison and validation of calculated A*_{tot} *and K*_{a} *values.* Serum electrolyte concentrations, Pco_{2}, protein concentrations, and pH values were extracted from a published data set of human serum filtrands with experimentally induced changes in Pco_{2}, SID (expressed as concentration), and [total protein] (Ref. 11, Table 2). These data were used to compare and validate the mean A_{tot tp}, A_{tot alb}, and *K*_{a} values obtained by using the six-factor simplified strong ion model and five different methods for assigning a value to SID, [SID_{3}]_{constant}, [SID_{4}]_{constant}, [SID_{6}]_{constant}, [SID_{6}]_{variable}, and [SID]_{estimated}, or the eight-factor strong ion model using [SID_{6}]_{variable} and [SID]_{estimated}. In addition, the calculated A_{tot tp} and *K*_{a} values were compared with previous estimates [A_{tot tp} = 0.344 mmol/g of total protein, *K*_{a} = 1.05 × 10^{-7} (6); A_{tot tp} = 0.340 mmol/g of total protein, *K*_{a} = 0.56 × 10^{-7} (32); A_{tot tp} = 0.334 mmol/g of total protein, *K*_{a} = 0.42 × 10^{-7} (10, 11)]. Calculated A_{tot alb} values were also compared with previous A_{tot} estimates derived from the albumin concentration [A_{tot alb} = 0.572 mmol/g of albumin (6); A_{tot alb} = 0.553 mmol/g of albumin (32); A_{tot alb} = 0.545 mmol/g of albumin (10, 11)].

Serum pH was calculated by using the six-factor simplified strong ion equation (3) in the following form 5 the measured variables Pco_{2}, SID = ([Na^{+}] + [K^{+}] + [Ca^{2+}] + [Mg^{2+}] - [Cl^{-}] - 1.5), and [total protein]; known values for S (0.0307 mmol · l^{-1} · mmHg^{-1}) (2) and p*K*′_{1} (6.120) (14, 25); and the calculated values for A_{tot tp}, A_{tot alb}, and *K*_{a}. The subtraction of 1.5 from the SID value represented the estimated charge on the unmeasured strong anion sulfate in the serum filtrand (11). The calculated pH was then compared with the measured pH by using linear regression analysis, and the *R*^{2}, coefficient, and intercept values were used for comparison with the line of identity (slope = 1; intercept = 0).

*Calculation of net protein charge.* The [A^{-}] (in meq/l) at physiological pH (7.40) was calculated from the experimentally determined values for A_{tot} and negative log of acidic dissociation constant (p*K*_{a}) (8) as 6 The value for [A^{-}] calculated in *Eq. 6* represents the net negative charge of nonvolatile plasma buffers (albumin, globulin, phosphate); the value for [A^{-}] is, therefore, pH dependent. Protein and phosphate also have a pH-independent negative charge that acts as a strong anion charge (41). In albumin and globulin, this is due to carboxyl, phenolic, and guanidium groups (37), and on phosphate it is due to the moiety.

The pH-dependent component of net phosphate charge ([phosphate^{-}]; in meq/l) at physiological pH (7.40) was calculated as 7 The net protein charge (in meq/l) at physiological pH (7.40) was calculated as [A^{-}] - [phosphate^{-}]. This calculates the pH-dependent component of protein charge and not the total protein charge.

## RESULTS

*Blood and plasma analyses.* The values for venous blood from eight humans are presented in Table 2. A total of 157 CO_{2} tonometered plasma samples were analyzed, representing 16–23 tonometered samples from each human. Representative Pco_{2} and pH values obtained during CO_{2} tonometry of plasma from two humans are shown in Fig. 1.

*Calculation of SID.* For normal plasma, mean values for [SID_{3}] (40.9 meq/l), [SID_{4}] (40.0 meq/l), and [SID_{6}] (43.0 meq/l) were obtained (Table 2). Different mean values for [SID_{3}]_{constant} (43.8 meq/l) (Tables 3, 4, 5), [SID_{4}]_{constant} (41.9 meq/l), [SID_{6}]_{constant} (46.0 meq/l) (Tables 3, 4, 5), and [SID]_{estimated} (37.1 meq/l) were obtained during tonometry (Tables 6 and 7). The mean range for [SID_{6}]_{variable} during tonometry was 7.5 meq/l (Tables 8 and 9).

*Calculation of A*_{tot} *and K*_{a}. The *R*^{2} value for all nonlinear regression models was >0.98, indicating excellent fit to the data. The calculated values for A_{tot} and *K*_{a} depended markedly on the value assigned to SID (Tables 3, 4, 5, 6, 7, 8, 9; Fig. 2).

When pH = 7.40 and Pco_{2} = 40 Torr, the actual [HCO_{3}] = 23.4 mmol/l (calculated from the Henderson-Hasselbalch equation when S = 0.0307 mmol · l^{-1} · mmHg^{-1} and p*K*′_{1} = 6.120). Accordingly, the true SID of human plasma at pH = 7.40 can be calculated by using the simplified strong ion electroneutrality equation (*Eq. 2*) so that SID = 23.4 + 11.5 = 34.9 meq/l. The calculated value for true SID was within the 95% confidence interval (29–45 meq/l) estimated by using nonlinear regression (Table 6). Applying the measured values for the mean venous blood values in this study Table 2; pH = 7.37, Pco_{2} = 51 Torr, A_{tot} = 17.2 mmol/l (calculated from a [total protein] of 76.9 g/l), *K*_{a} = 0.80 × 10^{-7}, S = 0.0307 mmol · l^{-1} · mmHg^{-1}, p*K*′_{1} = 6.120} to *Eq. 5* predicted that SID = 39 meq/l, which was also within the 95% confidence interval (29–45 meq/l) for the calculated SID value.

*Comparison and validation of calculated A*_{tot} *and K*_{a} *values.* With the use of a data set containing 72 serum filtrands from two humans and calculating A_{tot} from the [total protein], the highest *R*^{2} value (0.967) was obtained from the A_{tot} and *K*_{a} estimates obtained with [SID]_{estimated} in the six-factor strong ion model and A_{tot} indexed to [total protein] (Table 10). The most accurate values were, therefore, A_{tot} = 17.2 ± 3.5 mmol/l (equivalent to 0.224 mmol/g of protein), *K*_{a} = 0.80 ± 0.60 × 10^{-7}, and p*K*_{a} = 7.10. These estimated values for A_{tot} and *K*_{a} were only one of four pairs of values where the fitted regression line was the same as the line of identity (slope = 1; intercept = 0); the values for A_{tot} and *K*_{a} obtained by Siggaard-Andersen et al. in 1977 (32) and Constable in 2001 (6) also fitted the line of identity, but had lower *R*^{2} values. In addition, Stewart's eight-factor strong ion model with [SID]_{estimated} (Table 10) was very close to the six-factor strong ion model (*R*^{2} = 0.965). The A_{tot} and *K*_{a} values derived by Figge et al. in 1992 (10) from their data set (11) did not fit the line of identity.

With the use of the same data set and calculating A_{tot} from the albumin concentration, the highest *R*^{2} value (0.960) was obtained from the A_{tot} and *K*_{a} value obtained with [SID]_{estimated}, followed very closely by Stewart's eight-factor model with [SID]_{estimated} (*R*^{2} = 0.959) (Table 11). The A_{tot} value was equivalent to 0.378 mmol/g of albumin. As before, the estimated values for A_{tot} and *K*_{a} obtained with [SID]_{estimated} was one of four, where the fitted regression line was the same as the line of identity; the values for A_{tot} and *K*_{a} obtained by Siggaard-Andersen in 1977 (32) and Constable in 2001 (6) also fitted the line of identity, but had lower *R*^{2} values. The A_{tot} and *K*_{a} values derived by Figge et al. in 1992 (10) from their data set (11) did not fit the line of identity.

*Calculation of net protein charge.* The [A^{-}] at physiological pH (7.40) for each tonometered human plasma sample was calculated from the experimentally determined values for A_{tot} and p*K*_{a} obtained by using [SID]_{estimated}: [A^{-}] = A_{tot}/[1 + 10^{(} ^{pKa-pH)}] = 10.8 ± 4.0 meq/l (Table 6). This estimate for [A^{-}] reflected the charge assigned to the pH-dependent components of albumin, globulin, and phosphate; because the pH-dependent component of phosphate charge at physiological pH (7.4) was 1.0 meq/l (calculated by using *Eq. 7* and data in Table 2), the mean net protein charge in the eight human plasma samples attributed to nonvolatile buffer ions was 9.8 ± 4.0 meq/l = 0.215 meq/g albumin ([albumin] = 45.5 g/l) or 0.127 meq/g total protein ([total protein] = 76.9 g/l).

## DISCUSSION

In this study, we experimentally determined and validated values for A_{tot} (17.2 mmol/l) and *K*_{a} (0.8 × 10^{-7}) of human plasma. We also found that the values for A_{tot} and *K*_{a} depended markedly on the estimated value for SID. Determining the true value for SID remains the major difficulty in applying the strong ion approach to acid-base disturbances.

This appears to be the first study to use nonlinear regression to simultaneously estimate values for A_{tot}, *K*_{a}, and SID; the values obtained for A_{tot} and *K*_{a} at the same time as SID provided the most accurate prediction of pH from known values for Pco_{2}, [Na^{+}], [K^{+}], [Ca^{2+}], [Mg^{2+}], [Cl^{-}], [lactate], and [total protein] in filtrands of human plasma. This suggests that the true mean SID of the eight plasma samples was 37 meq/l. This value was lower than that estimated as [SID_{3}] ([Na^{+}] + [K^{+}] - [Cl^{-}] = 41 meq/l), [SID_{4}] ([Na^{+}] + [K^{+}] - [Cl^{-}] - [lactate] = 40 meq/l), and [SID_{6}] ([Na^{+}] + [K^{+}] + [Ca^{2+}] + [Mg^{2+}] - [Cl^{-}] - [lactate] = 43 meq/l); less than the estimated value of 40–42 meq/l (15, 16, 17, 33); but similar to the value calculated by Watson in 1999 (41) (38 meq/l). Clearly, unidentified strong anions are present in human plasma. These unidentified strong anions include sulfate, d-lactate, nonesterified fatty acids, and ketoacids; however, concentrations of these anions are too low to explain all of the unmeasured anion charge.

We believe that unaccounted protein and phosphate charge are responsible for most of the unmeasured strong anion charge in human plasma. Protein and phosphate charge have two components: a fixed charge that functions as a strong anion [the net difference in charge between carboxyl, epsilon-amino, phenolic, and guanidium groups in proteins (41) and in phosphate], and a variable charge that functions as a nonvolatile buffer ion (due mainly to imidazole groups in protein and and in phosphate) (Fig. 3). To quantify the pH-independent and -dependent components of protein and phosphate charge, the concentrations of protein and phosphate would need to be varied. When the effect of variations in protein concentration on pH was investigated in human plasma, the net anionic charge assigned to albumin at pH = 7.40 has been 0.25 meq/g (9), 0.268 meq/g (24), 0.27 meq/g (41), 0.33 meq/g (20), or 0.408 meq/g (29). All five estimates for net anionic charge for albumin were higher than that obtained in this study (0.215 meq/g albumin at pH = 7.40); however, our estimate reflects only the pH-dependent (nonvolatile buffer ion) charge of albumin and not the strong ion charge. Accordingly, the negative charge on albumin should be compartmentalized into a pH-independent strong ion charge (∼0.305 - 0.215 = 0.090 meq/g albumin, where 0.305 is the mean of the 5 estimates for the net anion charge of albumin and 0.215 is our estimate for the nonvolatile buffer ion charge of protein, assuming only albumin contributes to protein charge), a pH-dependent nonvolatile buffer ion charge, which can be calculated from the known values for pH, phosphate concentration, and the negative logarithm to the base 10 of the dissociation constant (1.58 × 10^{-7}) of , and experimentally determined values for A_{tot} and *K*_{a}. The formula for calculating net protein charge (in meq/l) from the albumin concentration (in g/l) and the phosphate concentration (in mmol/l) is, therefore 8 where protein charge is indexed to the albumin concentration, and the pH-dependent component of phosphate charge is subtracted from the assigned nonvolatile buffer ion charge. At normal values for pH (7.40), [albumin] (41 g/l), and [phosphate] (1.2 mmol/l), *Eq. 8* calculates pH-independent protein charge = 3.7 meq/l, pH-dependent nonvolatile buffer ion charge = 10.3 meq/l, and pH-dependent phosphate charge = 1.0 meq/l; the net protein charge of human plasma = 3.7 + 10.3 - 1.0 = 13.0 meq/l. This value for net protein charge was similar to that obtained by Van Leewen in 1964 (38) (12.6 meq/l) and Figge et al. in 1992 (10) (12.0 meq/l).

A similar approach can be applied to calculating net protein charge from the [total protein]. The net anionic charge assigned to total protein in human plasma has been 0.179 meq/g (38), 0.243 meq/g (29), or 0.26 meq/g (20). These three estimates for net total protein charge were higher than that obtained in this study (0.127 meq/g total protein at pH = 7.40); however, as discussed previously, our estimate reflects only the pH-dependent component and not the pH-independent (strong anion) component. Of these three estimates, the value obtained by Van Leewen (0.179 meq/g) (38) appears to be the most accurate, as it was developed from a net protein charge of 12.6 meq/l. Accordingly, protein charge can be compartmentalized into a pH-independent strong ion charge (∼0.179 - 0.127 = 0.052 meq/g total protein, where 0.179 is Van Leewen's estimate and 0.127 is our estimate for the nonvolatile buffer ion charge of plasma proteins) and a pH-dependent buffer ion charge, which can be calculated as described previously for albumin (*Eq. 8*). The formula for calculating net protein charge (in meq/l) from the [total protein] (in g/l) and the [phosphate] (in mmol/l) is, therefore 9 where protein charge is indexed to the [total protein] and the pH-dependent component of phosphate charge is subtracted from the assigned nonvolatile buffer ion charge. At normal values for pH (7.40), [total protein] (70 g/l), and [phosphate] (1.2 mmol/l), *Eq. 9* calculates the net protein charge of human plasma = 3.6 + 10.4 - 1.0 = 13.0 meq/l. This value for net protein charge was identical to that obtained from the albumin concentration alone.

Which method should we use clinically to calculate net protein charge? The *R*^{2} values from linear regression of calculated pH against measured pH (Tables 10 and 11) indicated that expressing A_{tot} in terms of [total protein] provided the most accurate fit to the data.

However, albumin is the most important buffer in plasma (73% of total buffering), with globulins contributing 22% of total buffering and phosphate 5% of total buffering (32). It is widely believed that the net protein charge is more accurately calculated from albumin (9, 20, 24, 29, 41) than total protein (20, 29, 38), principally because of individual variations in the albumin-to-globulin ratio. However, the widespread use of ion-selective electrodes has lowered the reference range of the anion gap {[Na^{+}] - ([Cl^{-}] + [])} for human plasma from 8–16 meq/l (9, 24) to 3–11 meq/l (43), indicating that the Σunmeasured anions exceed the Σunmeasured cations by 3–11 meq/l. By attributing charges to quantitatively important anions, protein (13.0 meq/l when calculated from albumin or total protein in humans with normal albumin-to-globulin ratios), phosphate (2.2 meq/l), lactate (0.9 meq/l), and quantitatively important cations, potassium (4.2 meq/l), calcium (2.3 meq/l), and magnesium (1.6 meq/l), the net charge that can be attributed to the quantitatively important components of the anion gap is 8.0 meq/l. Because this estimate lies within the range of the normal anion gap (3–11 meq/l) for human plasma, net protein charge can be calculated from either albumin concentration or protein concentration.

Because of difficulties in obtaining the true value for SID, the major clinical utility in using the strong ion approach in critically ill patients is to calculate the strong ion gap to detect and quantify the unmeasured strong cation or anion concentration (7, 8). Based on the previous discussion and the results of this study, the two most accurate equations for calculating strong ion gap (in meq/l) in human plasma are 10 and 11 where anion gap (in meq/l) = [Na^{+}] - ([Cl^{-}] + []), and [albumin] and [total protein] are in g/l. *Equations 10* and *11* assume that the unmeasured strong cation concentration (K^{+}, Ca^{2+}, Mg^{2+}) equals the unmeasured strong anion concentration (lactate, sulfate, nonesterified fatty acids, ketoacids, pH-independent phosphate charge, and other strong anions); the strong ion charge of albumin or protein is included in *Eq. 10* or *11*. At normal values of pH (7.40), [albumin] = 41 g/l, and anion gap = 7 meq/l, *Eq. 10* calculates the strong ion gap ≈ -0.4 meq/l. At normal values of pH (7.40), [total protein] = 70 g/l, and anion gap = 7 meq/l, *Eq. 11* calculates the strong ion gap ≈ -0.2 meq/l. For the venous blood samples from the eight humans in this study, pH (7.37), [albumin] = 45.5 g/l, anion gap = 6.5 meq/l, *Eq. 10* calculates the strong ion gap ≈ 0.6 meq/l, and with the use of [total protein] = 76.9 g/l, *Eq. 11* calculates the strong ion gap ≈ 0.7 meq/l. These calculations suggest that the strong ion gap equations (*Eqs. 10* and *11*) provide a useful method for detecting the presence and quantifying the magnitude of unmeasured anions in the plasma of critically ill human patients; presently the unmeasured anions are suspected to be predominantly associated with uremia (22, 26).

Finally, which value for SID should be used in the strong ion approach? Because the mean actual SID (37 meq/l) for the eight plasma samples was estimated to be 4 meq/l less than [SID_{3}] = ([Na^{+}] + [K^{+}]) - [Cl^{-}] = 41 meq/l (Table 2), 3 meq/l less than [SID_{4}] = ([Na^{+}] + [K^{+}]) - ([Cl^{-}] + [lactate]) = 40 meq/l, and 6 meq/l less than [SID_{6}] = ([Na^{+}] + [K^{+}] + [Ca^{2+}] + [Mg^{2+}]) - ([Cl^{-}] + [lactate]) = 43 meq/l, and because mean plasma [K^{+}] = 4 meq/l, we suggest the following equations for calculating actual SID from measured SID 12 13 14 15 Obviously, *Eqs. 12–15* assume that the Σunmeasured anions equal the Σunmeasured cations and that plasma albumin and total protein concentrations are normal.

## DISCLOSURES

This study was supported by EP Taylor Equine trust fund, by Natural Sciences and Engineering Research Council of Canada, and by Ontario Ministry of Agriculture, Food and Rural Affairs-Equine Program.

## Acknowledgments

The technical expertise of Dr. Susanne Misiaszek, Bonnie Lambert, and Dr. Nevil Sukra is greatly appreciated.

## Footnotes

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- Copyright © 2003 the American Physiological Society