Total weak acid concentration and effective dissociation constant of nonvolatile buffers in human plasma

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1 J Appl Physiol 91: , Total weak acid concentration and effective dissociation constant of nonvolatile buffers in human plasma PETER D. CONSTABLE Department of Veterinary Clinical Medicine, College of Veterinary Medicine, University of Illinois, Urbana, Illinois Received 9 January 2001; accepted in final form 12 April 2001 Constable, Peter D. Total weak acid concentration and effective dissociation constant of nonvolatile buffers in human plasma. J Appl Physiol 91: , The strong ion approach provides a quantitative physicochemical method for describing the mechanism for an acid-base disturbance. The 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 ), but these values have not been determined for human plasma. Accordingly, the purpose of this study was to calculate accurate A tot and K a values using data obtained from in vitro strong ion titration and CO 2 tonometry. The calculated values for A tot (24.1 mmol/l) and K a ( ) were significantly (P 0.05) different from the experimentally determined values for horse plasma and differed from the empirically assumed values for human plasma (A tot 19.0 meq/l and K a ). The derivatives of ph with respect to the three independent variables [strong ion difference (SID), PCO 2, and A tot ] of the strong ion approach were calculated as follows: dph/dsid [1 10 (pka ph) ] 2 /(2.303 {SPCO 2 10 (ph pk 1) [1 10 (pka ph ] 2 A tot 10 (pka ph) }); dph/dpco 2 S10 pk 1 /{2.303[A tot 10 ph (10 ph 10 pka ) 2 SID 10 ph ]}, dph/ da tot 1/{2.303[SPCO 2 10 (ph pk 1) SID 10 (pka ph) ]}, where S is solubility of CO 2 in plasma. The derivatives provide a useful method for calculating the effect of independent changes in SID,PCO 2, and A tot on plasma ph. The calculated values for A tot and K a should facilitate application of the strong ion approach to acid-base disturbances in humans. buffer value; plasma ph; strong ion difference; strong ion gap; anion gap 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 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 ( ) 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 A tot meq/l 2.43 total protein g/dl (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 ), 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 A tot mmol/l A 1 10 pk a ph (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 Address for reprint requests and other correspondence: P. D. Constable, Dept. of Veterinary Clinical Medicine, College of Veterinary Medicine, University of Illinois, 1008 W. Hazelwood Dr., Urbana, IL ( p-constable@uiuc.edu). The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact /01 $5.00 Copyright 2001 the American Physiological Society

2 HUMAN PLASMA ATOT AND KA VALUES 1365 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 ] 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 This empirical value was first used by Stewart in 1983 (35), although Stewart used different K a values ( , , and ) at other times (33 35). A K a value of appears incorrect, inasmuch as in vitro CO 2 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 (pk a 7.1), rather than (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 ( ) of human plasma are incorrect. MATERIALS AND METHODS Graphical representation of the A tot-pk a relationship for human plasma. For normal human plasma at 37 C, ph 7.40, PCO 2 40 Torr, and strong ion difference (SID ) 41.7 meq/l (28, 31). The normal plasma HCO 3 concentration ([HCO 3 ], in mmol/l) at 37 C and ionic strength (0.16) can be calculated using the Henderson-Hasselbalch equation, whereby: [HCO 3 ] SPCO 210 (ph pk 1) 22.9 mmol/l, when S (solubility of CO 2 in plasma) mmol l 1 Torr 1 (1) and pk 1 (negative logarithm of the equilibrium constant) (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 7 H A ) A tot SID HCO pka ph (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 3 ] (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 10 ph K 1 SPCO 2 K a A tot K a SID K 1 SPCO 2 (4) K a SID K a A tot 2 4K 2 a SID A tot /2SID to the reported values for ph, PCO 2, and SID, the latter variable being calculated from the reported base excess value for plasma as follows: SID (meq/l) base excess (meq/l) 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 PCO 2 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. The algebraic form of the simplified strong ion equation used in Eq. 4 was selected, because it provided the narrowest confidence intervals for the estimates of A tot and K a when ph was changed by strong ion titration. Data analysis was restricted to SID values from 30 to 56 meq/l, inasmuch as residual plots developed during nonlinear regression indicated deviation of fitted from actual values outside this range, presumably because the hypertonic solutions used for strong ion titration increased ionic strength, thereby altering the effective values for K a and the apparent equilibrium constant (K 1) (28). As titration was accomplished at 38 C, temperature-adjusted values for S ( mmol l 1 Torr 1 ) (1) and pk 1 (6.120) were used (12, 22). The calculated value for A tot was indexed to the reported mean total protein concentration (7 g/dl). The calculated value for K a (obtained at 38 C) was corrected to 37 C using van t Hoff s equation pk 1 pk 2 H /2.303R 1/T 1 1/T 2 (5) where H 6,940 cal/mol, R (the gas constant) cal K 1 mol 1, and T is the temperature (in Kelvin) (23). This provided the following equation: pk a (at 37 C) pk a (at 38 C) The second data set was obtained from an in vitro study involving hydrochloric acid and sodium hydroxide titration of human plasma at 38 C (28). Data analysis was completed as described previously. The calculated value for A tot was indexed to the reported mean plasma protein concentration (6.98 g/dl). The calculated value for K a (obtained at 38 C) was corrected to 37 C using van t Hoff s equation, as described previously. The third and fourth data sets were obtained from an in vitro study involving CO 2 tonometry of two human serum

3 1366 HUMAN PLASMA ATOT AND KA VALUES protein solutions (subjects A and B) performed at 37 C (10). The simplified strong ion equation (4) was applied in the following form HCO 3 SID A tot K a / K a 10 ph (6) to each subset of three CO 2-tonometered values for ph, PCO 2, and SID at constant total protein concentration. Inasmuch as titration in this study was accomplished at 37 C, temperature-adjusted values for S ( mmol l 1 Torr 1 ) (1) and pk 1 (6.129) (12, 22) were used. SID was calculated as follows: SID (Na K Ca 2 Mg 2 ) (Cl 1.5) (10). The addition of 1.5 to the strong anion calculation represented the estimated charge on SO 4 2 in human plasma (10). The form of the simplified strong ion equation used in Eq. 6 was preferred over the form expressed in Eq. 4, because Eq. 6 provided narrower confidence intervals for the estimated values of A tot and K a when ph was changed by CO 2 tonometry. The A tot and K a estimates for each subset of three CO 2-tonometered serum samples were averaged to produce a mean SD value for A tot and K a in the third and fourth data sets (subjects A and B, respectively), provided that the standard errors of the estimate for the A tot and K a values were 25% of the estimated values. For each of the four data sets, nonlinear regression was used to solve simultaneously for A tot and K a using reported or derived values for ph, PCO 2, and SID, known values for S and pk 1, the stated form of the simplified strong ion model, and Marquardt s expansion algorithm (PROC NLIN) (11, 27). Nonlinear regression simultaneously adjusts the estimated values for A tot and K a to provide the best fit of the model to the data. The six-factor simplified strong ion model (4) was used for nonlinear regression, instead of the eight-factor strong ion model (35), because reducing the number of parameters in the model leads to more precise parameter estimates (11). Initial values for A tot of 5 30 mmol/l in 5 mmol/l increments and for K a of in increments were used in the nonlinear regression procedure. The application of a coarse grid search spanning the likely values for A tot and K a facilitated accurate estimation of the values for A tot and K a. The final estimate for A tot was indexed to total protein (all 4 data sets) and albumin (3rd and 4th data sets) concentrations. Because plasma albumin concentration was not stated in the first two data sets (28, 29), albumin concentration ([albumin]) was calculated as follows: [albumin] (g/dl) 0.6 [total protein] (g/dl). From the four data sets, overall estimates for A tot and K a were calculated as means SD. Calculation of A tot and K a values for human albumin using published data. Data were obtained from an in vitro study involving CO 2 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 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 ) (4). RESULTS 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 (pk a 6.52), then A tot ( )[1 10 ( ) ] 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. 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 ), and K a (95% confidence interval ). K a at 37 C was calculated using van t Hoff s equation as A tot in terms of plasma albumin concentration was calculated as follows: A tot (mmol/l) 6.47 [albumin] (g/dl). Fig. 1. Relationship between total concentration of plasma nonvolatile buffers (A tot) and negative logarithm of effective equilibrium dissociation constant for plasma weak acids (pk a) for human plasma, with assumption of normal values for plasma ph (7.40), strong ion difference (SID, 41.7 meq/l), and PCO 2 (40 Torr). E, Commonly used values for A tot {(2.43 [total protein], g/dl) 17.0 meq/l} and pk a (6.52; K a ); {, Stewart s (35) empirically assigned A tot of 19 meq/l; vertical dashed line, pk a for maximal buffering of human plasma (value obtained from Ref. 30);, A tot and pk a calculated for human plasma in this study (bars represent 95% confidence intervals for A tot and pk a).

4 HUMAN PLASMA ATOT AND KA VALUES 1367 Analysis of the second data set containing 26 data points from strong ion titration at 38 C of plasma samples from 4 humans (28) provided the following equations: A tot (mmol/l) 3.59 [total protein] (g/dl) (95% confidence interval for coefficient value ), and K a (95% confidence interval ). K a at 37 C was calculated using van t Hoff s equation as A tot in terms of plasma albumin concentration was calculated as follows: A tot (mmol/l) 5.98 [albumin] (g/dl). Analysis of the third data set containing 12 data points from 4 sets of CO 2 -tonometered human serum samples for subject A at 37 C (10) provided the following equations: A tot (mmol/l) ( ) [total protein] (g/dl) or ( ) [albumin] (g/dl), and K a ( ) Analysis of the fourth data set containing 30 data points from 10 sets of CO 2 -tonometered human serum samples for subject B at 37 C (10) provided the following equations: A tot (mmol/l) ( ) [total protein] (g/dl) or ( ) [albumin] (g/dl), and K a ( ) The values (means SD) of the four data sets indicated that, at 37 C, A tot (mmol/l) ( ) [total protein] (g/dl) or ( ) [albumin] (g/dl), K a ( ) 10 7, and pk a 6.98 (95% confidence interval ). For a normal plasma protein concentration of 7.0 g/dl, A tot mmol/l. The 95% confidence interval for the calculated A tot (in mmol/l) and pk a values included the line depicting the nonlinear relationship between A tot and pk a and the ph value (7.1) for maximal buffering of human plasma (when pk a ph) (30) but did not include the values empirically assumed for human plasma (Fig. 1). The calculated A tot and K a values were significantly different from the experimentally determined values (4) for horse plasma: A tot mmol/l (t 4.56, P ), and K a ( ) 10 7 (t 6.47, P ). Calculation of A tot and K a values for human albumin using published data. Analysis of data from CO 2 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 ), K a (95% confidence interval ), and pk a 6.85 (95% confidence interval ). The calculated value was similar to that predicted by Reeves (K a ) 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 ( ) (1 8.00) (1 8.50)]/14. The estimated pk a value was within the 95% confidence interval ( ) 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) ph 2SID / log 10 K 1 SPCO 2 K a A tot K a SID (7) K 1 SPCO 2 K a SID K a A tot 2 4K a 2 SID A tot from the reported values for SID and PCO 2 and calculated values for A tot (3.44 [total protein], g/dl) and K a ( ). 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 The calculated ph value (ph calc ) was regressed against the measured ph value (ph meas ) using 54 data points. For the in vivo validation data set, ph ranged from 7.26 to 7.66, PCO 2 from 15 to 62 Torr, and SID from 38.5 to 49.2 meq/l. When the calculated values for A tot (24.1 mmol/l) and K a ( ) were used, an excellent correlation between ph calc and ph meas was observed (r 0.94; Fig. 2), and the regression equation relating ph calc to ph meas was not significantly different from the line of identity ph calc ph meas (8) The parentheses include the estimate and the standard error of the estimate. The mean difference between ph calc and ph meas was In contrast, when the empirical values for A tot ( [total protein], g/dl) and K a ( ) were used to calculate ph from the same data set, the regression equa- 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 A tot and K a. Middle: ph calculated using Stewart s empirical values (35) for A tot and K a. Right: ph calculated using values for A tot and K a 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.

5 1368 HUMAN PLASMA ATOT AND KA VALUES tion relating ph calc to ph meas was significantly different from the line of identity (Fig. 2) ph calc ph meas (9) The mean difference between ph calc and ph meas was When Stewart s empirical values (35) for A tot (19 meq/l) and K a ( ) were used to calculate ph from the same data set, the regression equation relating ph calc to ph meas was also significantly different from the line of identity (Fig. 2) ph calc ph meas (10) The mean difference between ph calc and ph meas was The calculated A tot and K a values were also applied to the mean values of 219 arterial blood samples obtained from 91 human patients in a critical care population, providing SID 38.2 meq/l, PCO Torr, [total protein] 5.32 g/dl, and ph (40). Solving Eq. 7 using the stated values for SID,PCO 2, and total protein concentration and the calculated values for A tot (3.44 [total protein], g/dl) and K a ( ) provided a predicted ph value of (a difference of 0.002). In contrast, the solution of Eq. 7 using the empirical values for A tot (2.43 [total protein], g/dl) and K a ( ) provided a predicted ph value of (a difference of 0.030), and solution of Eq. 7 using Stewart s empirical values for A tot (19 meq/l) and K a ( ) provided a predicted ph value of (a difference of 0.059). 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 2.303A tot / 1 10 ph pka 1 10 pk a ph 2 (11) The calculated values for A tot (24.1 mmol/l 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 meq/g protein (95% confidence interval meq/g). This estimate was similar to experimentally determined values for of human plasma [0.109 meq/g (13) and meq/g (30)] and human serum [0.103 meq/g (26) and 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 meq/g, which was similar to that determined by Figge et al. in 1991 (0.148 meq/g) (10). DISCUSSION 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). 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,PCO 2, and A tot )ofthe strong ion approach were calculated to provide an index of the sensitivity of ph to changes in each of the independent factors dph/dsid 1 10 pk a ph SPCO 2 10 ph pk pk a ph 2 (12) A tot 10 pk a ph dph/dpco 2 S10 pk A tot 10 ph 10 ph 10 pk a (13) 2 SID 10 ph dph/da tot (14) 1/ SPCO 2 10 ph pk 1 SID 10 (pk a ph } Equations were solved using normal physiological values for human plasma (SID 41.7 meq/l, PCO 2 40 Torr, A tot 24.1 mmol/l, S mmol l 1 Torr 1, pk , and pk a 6.98), whereby dph/dsid (meq/l) 1, dph/ dpco Torr 1, and dph/da tot (mmol/l) (g total protein/dl) 1. This indicated that, at normal ph (7.40), a1meq/l increase in SID will increase ph by 0.016, a 1-Torr increase in PCO 2 will decrease ph by 0.009, and a 1 g/dl increase in total protein will decrease ph by 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 SIG SID meas HCO 3 protein charge phosphate charge (15)

6 HUMAN PLASMA ATOT AND KA VALUES 1369 Fig. 3. Spider plot of the dependence of plasma ph on changes in the 3 independent variables (SID, PCO 2, and A tot) and 5 constants [solubility of CO 2 in plasma (S), apparent equilibrium constant (K 1), effective equilibrium dissociation constant (K a), apparent equilibrium dissociation constant for HCO 3 (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 PCO 2, 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. 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) SIG SID meas HCO 3 albumin g/dl)(1.23ph (16) 6.31 phosphate mmol/l 0.31pH 0.47 An alternative and more general method for calculating the SIG was developed in 1998 (7).This method required measurement of six factors {ph, PCO 2,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 3 ]), and [HCO 3 ] SPCO 2 10 (ph pk 1) SIG meq/l A tot mmol/l / 1 10 pk a ph anion gap (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 SIG meq/l 3.44 total protein g/dl ph anion gap (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 3 A 0. Application of the accepted values for normal human plasma SID (41.7 meq/l) and PCO 2 (40 Torr, HCO 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, PCO 2 40 Torr, A tot 24.1 mmol/l, S mmol l 1 Torr 1,pK , K a ) were then applied to the simplified strong ion equation, producing a predicted ph of 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,PCO 2,A tot, K 1,S,K a, the apparent equilibrium dissociation constant for HCO 3 (K 3 ), 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,PCO 2,A tot, K 1,S,andK a ). The spider plot includes the two additional factors (K 3 and K w ) in Stewart s strong ion model (Fig. 3). Although K 3 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 K 3 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. APPENDIX The electroneutrality equation from the simplified strong ion model (Eq. 7 in Ref. 4) provided SID HCO 3 A 0 (A1)

7 1370 HUMAN PLASMA ATOT AND KA VALUES Koppel and Spiro in 1914 (24) and Van Slyke in 1922 (37) defined as the derivative of plasma nonbicarbonate buffer ions (A ) with respect to ph da /dph (A2) Although the value for varies with species, ph, and temperature, the value is generally taken to be constant in the physiological ph range, independent of PCO 2, and dependent only on the protein concentration (30). Rearrangement of Eq. 10 from the simplified strong ion model (4) provided A A tot K a / K a 10 ph (A3) Taking the derivative of Eq. A3 with respect to ph provided da /dph A tot K a 10 ph / K a 10 ph 2 (A4) where A tot represents the concentration of plasma nonvolatile buffers in millimoles per liter (3). Combination of Eqs. A2 and A4 and algebraic rearrangement provided 2.303A tot / 10 ph pka 2 10 pka ph (A5) Equation A5 calculates a value for in millimoles per liter, because the units for A tot are millimoles per liter. 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