INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

TWO PHYSICOCHEMICAL MECHANISTIC acid-base models based on the strong ion approach have been developed to assess acid-base status: the strong ion model (35) and the simplified strong ion model (4). The strong ion approach requires species-specific values for the total concentration of plasma nonvolatile buffers (A_tot) and the effective dissociation constant for plasma nonvolatile buffers (K_a) (4, 32). Values for A_tot (14.9 or 15.0 mol/l) and K_a (2.1 or 2.2 × 10⁷ eq/l) have been experimentally determined for equine plasma (4, 32), but accurate values are unavailable for human plasma; thus it is difficult to apply the strong ion approach to acid-base disturbances in humans (14, 16). Wilkes (41) suggested that the values used for A_tot (17 meq/l) and K_a (3.0 × 10⁷) of human plasma are incorrect, and Lindinger and colleagues (20) preferred to use a higher value for A_tot (19 meq/l). Stewart (35) originally assigned an empirical value of 19 meq/l to A_tot.

The most widely used method to assign a value for A_tot of human plasma is calculation from the total protein concentration ([total protein]) (15, 20, 36), whereby

(1)

At a normal plasma protein and albumin concentration of 7.0 and 4.3 g/dl, respectively, A_tot = 17 meq/l.

There appear to be three errors with this approach. First, the correct units for A_tot are millimoles per liter (instead of meq/l), where millimoles per liter refers to dissociable groups capable of donating or accepting a proton, because an assumption in the strong ion approach is that plasma nonvolatile buffer mass (and not charge) is conserved (see Eq. A6). Second, Eq. 1 purportedly calculates the net charge of nonvolatile plasma buffers (albumin, globulin, and phosphate), which equals A concentration ([A], 15.0 meq/l when pH = 7.40 and K_a = 3.0 × 10⁷), instead of A_tot (which has units of mmol/l) (4, 15). Because A_tot = [HA] + [A] (where [HA] is weak acid concentration and is uncharged), Eq. 1 must underestimate the true value of A_tot when A_tot is expressed in the correct units of millimoles per liter, inasmuch as rearrangement of Eq. A3 provided

(2)

A_tot has the same numeric value as [A] when plasma weak acids are fully dissociated, and [A] has the same numeric value when it is expressed in milliequivalents per liter or millimoles per liter, because A is defined as a univalent base in the strong ion approach (4, 35). Third, the calculated value of 15 meq/l for [A] (15) is lower than that originally proposed by van Slyke and colleagues in 1928 (38), who extrapolated values for the net negative charge of equine albumin and globulin to human plasma, resulting in an estimated value for net protein charge of 16.9 meq/l. Because the three major components of A_tot are plasma albumin, globulin, and phosphate and the charge attributed to phosphate in normal human plasma is ~2.2 meq/l, application of the value of van Slyke and colleagues for net protein charge suggested that [A] = 16.9 + 2.2 = 19.1 meq/l, rather than 15 meq/l. Lower values for the net protein charge of human plasma were first reported by van Leeuwen in 1964 (12.6 meq/l) (36) and, more recently, by Figge and colleagues in 1992 (12.0 meq/l) (9), suggesting that [A] = 14.8 and 14.2 meq/l, respectively, which is closer to, but lower than, the value calculated using Eq. 1. In summary, the currently used method for assigning a value to A_tot produces a result that appears numerically and dimensionally incorrect.

The most commonly used value for K_a of human plasma is 3.0 × 10⁷. This empirical value was first used by Stewart in 1983 (35), although Stewart used different K_a values (0.4 × 10⁷, 2.0 × 10⁷, and 4.0 × 10⁷) at other times (33-35). A K_a value of 3.0 × 10⁷ appears incorrect, inasmuch as in vitro CO₂ tonometry of human plasma indicates maximal buffering at pH ~7.1 (30). Because buffering is maximal when pH = pK_a (24, 37), the effective K_a value for human plasma should approximate 0.8 × 10⁷ (pK_a = 7.1), rather than 3.0 × 10⁷ (pK_a = 6.5).

Accurate A_tot and K_a values are required to apply the strong ion approach to acid-base disturbances in humans. Because the currently used values for A_tot and K_a appear to be incorrect, the purpose of this study was to calculate accurate A_tot and K_a values for human plasma. This was accomplished using four approaches: 1) graphical representation of the nonlinear relationship between plasma A_tot and pK_a, 2) calculation of plasma A_tot and K_a values using published data, 3) calculation of albumin A_tot and K_a values using published data, and 4) calculation of the albumin K_a value using the estimated pK_a values for the 14 dissociable amino acids that act as nonvolatile buffers at physiological pH. The calculated A_tot and K_a values for human plasma were then validated using two approaches: 1) data obtained from in vivo studies in humans and 2) published values for the buffer value () of human plasma. The results indicate that the currently used values for A_tot {2.43 × [total protein] (g/dl) = 17 meq/l (18, 25, 40) or 19 meq/l (35)} and K_a (3.0 × 10⁷) of human plasma are incorrect.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Graphical representation of the A_tot-pK_a relationship for human plasma. For normal human plasma at 37°C, pH = 7.40, PCO₂ = 40 Torr, and strong ion difference (SID⁺)  41.7 meq/l (28, 31). The normal plasma HCO concentration ([HCO], in mmol/l) at 37°C and ionic strength (0.16) can be calculated using the Henderson-Hasselbalch equation, whereby: [HCO] = SPCO₂ = 22.9 mmol/l, when S (solubility of CO₂ in plasma) = 0.0307 mmol · l¹ · Torr¹ (1) and pK'₁ (negative logarithm of the equilibrium constant) = 6.129 (12, 22). These normal values for human plasma were applied to the simplified strong ion model electroneutrality equation (see Eq. A1) after substitution for A into the conventional dissociation reaction for a weak acid (HA  H⁺ + A)

(3)

The A_tot-pK_a relationship was then graphically depicted by plotting A_tot against pK_a using Eq. 3 and normal physiological values for SID⁺ (41.7 meq/l), [HCO] (22.9 mmol/l), and pH (7.40).

Calculation of A_tot and K_a values for human plasma using published data. Data were obtained from four in vitro studies: one set from Siggaard-Andersen and Engel (29), one set from Siggaard-Andersen (28), and two sets from Figge et al. (10). The first data set was obtained from an in vitro study involving hydrochloric acid, acetic acid, lactic acid, and sodium carbonate titration of human plasma at 38°C (29). The simplified strong ion equation (4) was applied as

(4)

to the reported values for pH, PCO₂, and SID⁺, the latter variable being calculated from the reported base excess value for plasma as follows: SID⁺ (meq/l) = base excess (meq/l) + 41.7. The base excess value in plasma titration studies reflects the millimolar concentration of strong acid or base added to plasma (and, therefore, millimolar change in SID⁺ from the normal value) and differs from the standard base excess value, which assumes a hemoglobin concentration of 5 g/dl. The addition of 41.7 to the reported base excess value was required to calculate SID⁺, because base excess is defined as zero when pH = 7.40 and PCO₂ = 40 Torr (28, 31), although it is recognized that the value of 41.7 is only approximate. The equation for calculating SID⁺ is only valid when the albumin-to-globulin ratio and plasma protein and phosphate concentrations are normal.

1

1

(5)

1

1

(6)

1

1

7

7

7

Calculation of A_tot and K_a values for human albumin using published data. Data were obtained from an in vitro study involving CO₂ tonometry of one human albumin solution at 37°C (Table A in Ref. 10) and analyzed as stated previously for the two human serum protein solutions.

Calculation of human albumin K_a value using the pK_a values for dissociable amino acid groups. Figge et al. (9) reanalyzed data from an earlier study (10) and identified 212 dissociable groups on human albumin that could be categorized into 6 different groups, with 5 groups having an "effective K_a" as follows: 1 carboxy-terminus group, pK_a = 3.10; 98 Asp and Glu groups, pK_a = 4.00; 1 amino-terminus group, pK_a = 8.00; 1 Cys group, pK_a = 8.50; 18 Tyr groups, pK_a = 9.60; and 77 Arg and Lys groups, pK_a = 9.40. On the basis of data obtained from magnetic resonance imaging of human albumin (2) and an iterative computing routine, the remaining 16 His groups were assigned the following pK_a values: 4.85, 5.20, 5.76, 5.82, 6.17, 6.36, 6.73, 6.75, 7.01, 7.10, 7.12, 7.22, 7.30, 7.30, 7.31, and 7.49 (9). An apparent pK_a for human albumin was calculated from these data as the weighted mean average of the 12 dissociable His groups and 2 other dissociable groups (Cys and amino-terminus) that acted as nonvolatile buffer ions at physiological pH (pK_a = 7.4 ± 1.5) (4).

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Graphical representation of the A_tot-pK_a relationship for human plasma. Equation 3 indicates that if K_a is empirically assigned the value of 3.0 × 10⁷ (pK_a = 6.52), then A_tot = (41.7  22.9)[1 + 10^{(6.52  7.40)}] = 21.9 mmol/l, which differs in magnitude and units from the empirical value for A_tot (17.0 meq/l) calculated using Eq. 1 with the assumption of a normal plasma protein concentration of 7.0 g/dl (Fig. 1) and differs in units from the value of 19 meq/l assigned by Stewart (35). Figure 1 also demonstrates that the empirical pK_a value (6.52) differs from the pH value for maximal buffering of human plasma (30), where pK_a = pH (24, 37). One or both of the empirically assigned values for A_tot and K_a must therefore be in error.

View larger version (15K): [in this window] [in a new window]   Fig. 1.   Relationship between total concentration of plasma nonvolatile buffers (Atot) and negative logarithm of effective equilibrium dissociation constant for plasma weak acids (pKa) for human plasma, with assumption of normal values for plasma pH (7.40), strong ion difference (SID+, 41.7 meq/l), and PCO2 (40 Torr). , Commonly used values for Atot {(2.43 × [total protein], g/dl) = 17.0 meq/l} and pKa (6.52; Ka = 3.0 × 107); , Stewart's (35) empirically assigned Atot of 19 meq/l; vertical dashed line, pKa for maximal buffering of human plasma (value obtained from Ref. 30); , Atot and pKa calculated for human plasma in this study (bars represent 95% confidence intervals for Atot and pKa).

Calculation of A_tot and K_a values for human plasma using published data. Analysis of the first data set containing 26 data points from strong ion titration at 38°C of plasma samples from 12 humans (29) provided the following equations: A_tot (mmol/l) = 3.88 × [total protein] (g/dl) (95% confidence interval for coefficient value = 3.87-3.89), and K_a = 0.938 × 10⁷ (95% confidence interval = 0.934-0.942 × 10⁷). K_a at 37°C was calculated using van't Hoff's equation as 0.904 × 10⁷. A_tot in terms of plasma albumin concentration was calculated as follows: A_tot (mmol/l) = 6.47 × [albumin] (g/dl).

7

7

7

7

7

7

7

Calculation of A_tot and K_a values for human albumin using published data. Analysis of data from CO₂ tonometry of a solution containing albumin and no globulin at 37°C (10) provided the following equations: A_tot (mmol/l) = 4.60 × [albumin] (g/dl) (95% confidence interval for coefficient = 3.20-10.00), K_a = 1.40 × 10⁷ (95% confidence interval = 0.50-3.14 × 10⁷), and pK_a = 6.85 (95% confidence interval = 6.50-7.30). The calculated value was similar to that predicted by Reeves (K_a = 1.77 × 10⁷) for canine albumin at 37.5°C (23).

Calculation of K_a for human albumin using the pK_a values for dissociable amino acid groups. Reanalysis of data in an earlier study involving titration of human albumin produced an apparent pK_a for albumin of 7.17 (9): pK_a = [1 × (6.17 + 6.36 + 6.73 + 6.75 + 7.01 + 7.10 + 7.12 + 7.22 + 7.30 + 7.30 + 7.31 + 7.49) + (1 × 8.00) + (1 × 8.50)]/14. The estimated pK_a value was within the 95% confidence interval (6.50-7.30) for the K_a value of human albumin calculated previously using nonlinear regression.

Validation of calculated A_tot and K_a values using in vivo data. The calculated values for A_tot and K_a of human plasma were applied to data obtained from an in vivo study involving six humans with acute respiratory acidosis and alkalosis (8). Plasma pH was calculated using the simplified strong ion equation (4)

(7)

from the reported values for SID⁺ and PCO₂ and calculated values for A_tot (3.44 × [total protein], g/dl) and K_a (1.05 × 10⁷). A normal value for A_tot of 24.1 mmol/l ([total protein] = 7.0 g/dl) was assumed, and SID⁺ was assumed to be 41.7 meq/l for the first baseline value. Subsequent values for SID⁺ were calculated as SID⁺ = Na⁺ + K⁺  Cl + 41.7. The calculated pH value (pH_calc) was regressed against the measured pH value (pH_meas) using 54 data points.

7

(8)

7

(9)

7

(10)

View larger version (20K): [in this window] [in a new window]   Fig. 2.   Scatter plots of the relationship between calculated pH and measured pH for plasma from humans undergoing acute respiratory acidosis and alkalosis. Solid line, regression line; dashed lines, 95% confidence interval for the regression line. Left: pH calculated with the commonly used values for Atot and Ka. Middle: pH calculated using Stewart's empirical values (35) for Atot and Ka. Right: pH calculated using values for Atot and Ka determined in this study. Only in the right panel does the 95% confidence interval for the regression line include the line of identity. Data were obtained from Ref. 8.

7

7

7

Validation of calculated A_tot and K_a values using  of human plasma. Equation A8 produced the following relationship between nonvolatile buffer concentration (A_tot, in mmol/l),  (the Van Slyke buffer value, in meq/l), pH, and pK_a

(11)

The calculated values for A_tot (24.1 mmol/l = 0.344 mmol/g protein when plasma protein concentration = 7 g/dl) and pK_a (6.98) of human plasma were applied to Eq. 11, and the solution at pH 7.40 was  = 0.115 meq/g protein (95% confidence interval = 0.079-0.138 meq/g). This estimate was similar to experimentally determined values for  of human plasma [0.109 meq/g (13) and 0.110 meq/g (30)] and human serum [0.103 meq/g (26) and 0.107 meq/g (36)]. With the use of Eq. 11 and the pK_a (6.85) and A_tot (0.46 mmol/g) calculated previously for human albumin,  was calculated as 0.142 meq/g, which was similar to that determined by Figge et al. in 1991 (0.148 meq/g) (10).

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

The findings of this study indicate that the currently used A_tot and K_a values for human plasma are incorrect and that species-specific values for A_tot and K_a are required when the strong ion approach is applied to acid-base disturbances.

It is customary to perform a sensitivity analysis after use of nonlinear regression to estimate values for one or more factors in a model. The sensitivity of the dependent variable to changes in input variables can be conveyed by a spider plot (39), which graphically depicts the relationship between the dependent variable and percent change in one input factor while the remaining input factors are held constant at their normal values. The spider plot (Fig. 3), based on the eight factors in Stewart's strong ion model (35), graphically indicated that plasma pH was most sensitive to changes in SID⁺ and was more sensitive to changes in A_tot than to changes in K_a. The latter finding was recently reported by Watson (40).

View larger version (27K): [in this window] [in a new window]   Fig. 3.   Spider plot of the dependence of plasma pH on changes in the 3 independent variables (SID+, PCO2, and Atot) and 5 constants [solubility of CO2 in plasma (S), apparent equilibrium constant (K'1), effective equilibrium dissociation constant (Ka), apparent equilibrium dissociation constant for HCO (K'3), and ion product of water (K'w)] of Stewart's strong ion model (35). The spider plot is obtained by systematically varying one input variable, while holding the remaining input variables at their normal values for human plasma. The influence of S and K'1 on plasma pH cannot be separated from that of PCO2, inasmuch as the 3 factors always appear as 1 expression. Large changes in 2 factors (K'3 and K'w) do not change plasma pH, indicating that Stewart's strong ion model is overparameterized.

The tangent to each line in the spider plot reflects the sensitivity of human plasma pH to that factor. With the use of the simplified strong ion model equation (Eq. 7), the derivatives of pH with respect to the three independent factors (SID⁺, PCO₂, and A_tot) of the strong ion approach were calculated to provide an index of the sensitivity of pH to changes in each of the independent factors

(12)

(13)

(14)

Equations 12-14 were solved using normal physiological values for human plasma (SID⁺ = 41.7 meq/l, PCO₂ = 40 Torr, A_tot = 24.1 mmol/l, S = 0.0307 mmol · l¹ · Torr¹, pK'₁ = 6.129, and pK_a = 6.98), whereby dpH/dSID⁺ = +0.0157 (meq/l)¹, dpH/dPCO₂ = 0.0086 Torr¹, and dpH/dA_tot = 0.0112 (mmol/l)¹ = 0.039 (g total protein/dl)¹. This indicated that, at normal pH (7.40), a 1 meq/l increase in SID⁺ will increase pH by 0.016, a 1-Torr increase in PCO₂ will decrease pH by 0.009, and a 1 g/dl increase in total protein will decrease pH by 0.039. These values provide useful rules of thumb for the clinical assessment of acid-base disturbances in humans.

A clinically important problem is identifying and quantifying the presence of strong anions in plasma that are not routinely measured, such as lactate, -hydroxybutyrate, acetoacetate, and uremic anions. Shortly after Stewart developed the strong ion approach, it was evident that calculating the difference between measured and predicted strong ion difference would provide a method for quantifying the unmeasured strong ion concentration in plasma (15). This led to definition of the strong ion gap (SIG) by Kellum and colleagues in 1995 (17, 18), where the SIG is the difference between the charge assigned to unmeasured strong cations and anions. Calculation of the SIG for human plasma was based on an electroneutrality equation developed by Figge et al. in 1992 (9), whereby

(15)

Because Figge and colleagues concluded that the protein charge in human plasma was entirely due to albumin (9, 10) and that the negative charge exhibited by albumin and phosphate varied in an approximately linear manner with pH, they expressed Eq. 15 as (9)

(16)

An alternative and more general method for calculating the SIG was developed in 1998 (7).This method required measurement of six factors {pH, PCO₂, Na⁺ concentration ([Na⁺]), K⁺ concentration ([K⁺]), Cl concentration ([Cl]), and total protein concentration}, accurate values for A_tot and K_a, and calculation of the anion gap as follows: anion gap = ([Na⁺] + [K⁺])  ([Cl] + [HCO]), and [HCO] = SPCO₂

(17)

With the use of the values for A_tot and K_a of human plasma developed in this study, Eq. 17 was expressed as

(18)

Equations 16 and 18 offer promise as methods to quantify the unmeasured strong anion concentration in human plasma. It remains to be determined whether Eq. 18 offers any advantages over Eq. 16.

Solving Eq. 2 using the calculated A_tot and pK_a values indicated that [A] = 17.5 meq/l and that the net negative charge of human plasma protein was therefore 15.3 meq/l, because normal phosphate charge is 2.2 meq/l. This estimate for net protein charge was greater than that obtained by van Leeuwen in 1964 (12.6 meq/l, [A] = 14.8 meq/l) (36) and Figge et al. in 1992 (12.0 meq/l, [A] = 14.2 meq/l) (9); however, the higher net protein charge estimate provided a better fit to the simplified strong ion electroneutrality equation (4): SID⁺  HCO  A ~ 0. Application of the accepted values for normal human plasma SID⁺ (41.7 meq/l) and PCO₂ (40 Torr, HCO = 22.9 mmol/l at pH 7.40) to the electroneutrality equation predicted that [A] ~ 18.8 meq/l. Because the spider plot (Fig. 3) indicated that predicted normal human plasma pH was 7.42, instead of 7.40, the assumed value for SID⁺ (41.7 meq/l) may be too high by 1.3 meq/l (obtained by subtracting 17.5 meq/l from 18.8 meq/l), which would result in a predicted pH that was 0.02 units too high (from Eq. 12). Revised normal human plasma values (SID⁺ = 40.4 meq/l, PCO₂ = 40 Torr, A_tot = 24.1 mmol/l, S = 0.0307 mmol · l¹ · Torr¹, pK'₁ = 6.129, K_a = 1.05 × 10⁷) were then applied to the simplified strong ion equation, producing a predicted pH of 7.400. Additional studies are required to verify that 40.4 meq/l provides a better estimate for normal human plasma SID⁺ than 41.7 meq/l assigned by Singer and Hastings in 1948 (31).

Stewart's strong ion model states that plasma pH is a function of eight factors [SID⁺, PCO₂, A_tot, K'₁, S, K_a, the apparent equilibrium dissociation constant for HCO (K₃), and the ion product of water (K'_w)] (35), whereas the simplified strong ion model states that plasma pH is a function of six factors (SID⁺, PCO₂, A_tot, K'₁, S, and K_a). The spider plot includes the two additional factors (K₃ and K'_w) in Stewart's strong ion model (Fig. 3). Although K₃ and K'_w have been shown algebraically to be redundant when the strong ion approach is used (4), Fig. 3 provides strong graphical evidence that the value for K₃ or K'_w does not alter pH under physiological conditions, indicating that neither factor influences plasma pH and therefore both factors should be neglected. When models are compared, the preferred model should have greater explanatory power, mathematical simplicity, or theoretical elegance (21). Because the simplified strong ion model is mathematically simpler than Stewart's strong ion model and has similar explanatory power (see Refs. 5 and 6 for review), Fig. 3 suggests that the simplified strong ion model should be preferred when the strong ion approach is used.