Journal of Applied Physiology
Vol. 83, No. 1, pp. 297-311, July 1997
SYSTEMIC CIRCULATION AND FLUID BALANCE

A simplified strong ion model for acid-base equilibria: application to horse plasma

Peter D. Constable

College of Veterinary Medicine, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

ABSTRACT

INTRODUCTION

HENDERSON-HASSELBALCH EQUATION

STRONG ION MODEL

MATERIALS AND METHODS

RESULTS

DISCUSSION

APPENDIX

FOOTNOTES

REFERENCES

ABSTRACT

Constable, Peter D. A simplified strong ion model for acid-base equilibria: application to horse plasma. J. Appl. Physiol. 83(1): 297-311, 1997.The Henderson-Hasselbalch equation and Stewart's strong ion model are currently used to describe mammalian acid-base equilibria. Anomalies exist when the Henderson-Hasselbalch equation is applied to plasma, whereas the strong ion model does not provide a practical method for determining the total plasma concentration of nonvolatile weak acids ([A_tot]) and the effective dissociation constant for plasma weak acids (K_a). A simplified strong ion model, which was developed from the assumption that plasma ions act as strong ions, volatile buffer ions (HCO₃), or nonvolatile buffer ions, indicates that plasma pH is determined by five independent variables: PCO₂, strong ion difference, concentration of individual nonvolatile plasma buffers (albumin, globulin, and phosphate), ionic strength, and temperature. The simplified strong ion model conveys on a fundamental level the mechanism for change in acid-base status, explains many of the anomalies when the Henderson-Hasselbalch equation is applied to plasma, is conceptually and algebraically simpler than Stewart's strong ion model, and provides a practical in vitro method for determining [A_tot] and K_a of plasma. Application of the simplified strong ion model to CO₂-tonometered horse plasma produced values for [A_tot] (15.0 ± 3.1 meq/l) and K_a (2.22 ± 0.32 × 10⁷ eq/l) that were significantly different from the values commonly assumed for human plasma ([A_tot] = 20.0 meq/l, K_a = 3.0 × 10⁷ eq/l). Moreover, application of the experimentally determined values for [A_tot] and K_a to published data for the horse (known PCO₂, strong ion difference, and plasma protein concentration) predicted plasma pH more accurately than the values for [A_tot] and K_a commonly assumed for human plasma. Species-specific values for [A_tot] and K_a should be experimentally determined when the simplified strong ion model (or strong ion model) is used to describe acid-base equilibria.

acid-base balance; acidosis; alkalosis; alphastat; strong ion difference

INTRODUCTION

TWO METHODS ARE CURRENTLY used clinically to describe the physicochemical determinants of plasma pH in mammals: the Henderson-Hasselbalch equation (20) and Stewart's strong ion model (44-46). The purpose of this study is to briefly discuss the strengths and weaknesses of the Henderson-Hasselbalch equation and Stewart's strong ion model and to develop a simplified strong ion model that is conceptually and algebraically simpler than Stewart's strong ion model. The simplified strong ion model also explains many of the anomalies observed when the Henderson-Hasselbalch equation is applied to plasma.

HENDERSON-HASSELBALCH EQUATION

The traditional approach used to clinically describe mammalian acid-base equilibria focuses on how PCO₂, HCO₃ concentration ([HCO₃]), the negative logarithm of the equilibrium constant (pK₁), and the solubility of CO₂ in plasma (S_CO2) interact to determine the plasma pH (35). This relationship is most commonly expressed as the Henderson-Hasselbalch equation (20, 23, 31)

(1)

where pK₁ is a collective equilibrium constant for the reaction

(2)

The Henderson-Hasselbalch equation has proven to be invaluable in aiding our understanding of mammalian acid-base physiology and is routinely and widely used in the clinical management of acid-base abnormalities in humans and animals (2, 7, 25, 40). However, it was evident as early as 1922 that factors other than PCO₂, [HCO₃], pK₁, and S_CO2 influence plasma pH (52). S_CO2 varies with ionic strength, temperature, and protein concentration, and accurate values are available for mammalian plasma (3). Determination of accurate pK₁ values for plasma has been more problematic, inasmuch as the experimental value for pK₁ in plasma (called the apparent dissociation constant) differs marginally from the value obtained in aqueous, nonplasma solutions (1, 8, 19, 21, 27, 29, 31, 34, 38, 39). Moreover, like all equilibrium constants based on molalities, the value for pK₁ is dependent on the ionic strength (21) and temperature (8). A number of studies have demonstrated that the apparent value for pK₁ in plasma is also influenced by pH (1, 27, 29, 34, 38), protein concentration (27, 29), and Na⁺ concentration (22), leading to routine adjustment of the pK₁ for plasma by nomograms (40, 41), tables (3, 27, 34), and polynomial equations (19, 22). The mechanistic basis for these adjustments is unknown.

Numerous experiments have demonstrated that the in vitro log PCO₂-pH equilibration curve for plasma is well approximated by a straight line over the normal physiological range (2, 40, 52) (Fig. 1). The Henderson-Hasselbalch equation partially explains this finding, inasmuch as rearrangement of Eq. 1 provides

(3)

indicating that the log PCO₂-pH relationship is linear with an intercept value of log([HCO₃]/K₁S_CO2). Experimental studies have also found that the linear relationship between log PCO₂ and pH is displaced by changes in the protein concentration (2) or the addition of Na⁺ or Cl (2, 39) (Fig. 1), suggesting that the intercept value has changed. Other studies have found that the in vitro relationship between log PCO₂ and pH becomes nonlinear in markedly acidic plasma (40), suggesting that the intercept value is pH dependent and is nonlinear during in vivo CO₂ equilibration studies (6, 10) (Fig. 1). The Henderson-Hasselbalch equation provides no explanation for these phenomena.

Because the Henderson-Hasselbalch equation does not satisfactorily explain why the apparent value of pK₁ in plasma depends on pH, protein concentration, and Na⁺ concentration and why a nonlinear relationship exists between log PCO₂ and pH in vitro over a wide range of pH and in vivo during CO₂ equilibration studies, the approach can only be accurately applied to mammalian plasma at approximately normal pH, protein concentration, and Na⁺ concentration. Moreover, the empiric nature of the adjustments to the value of K₁ in plasma indicates that the Henderson-Hasselbalch equation is more descriptive than mechanistic.

STRONG ION MODEL

Dissatisfaction with the Henderson-Hasselbalch approach prompted Singer and Hastings (41) to propose in 1948 that plasma pH was determined by two independent factors, PCO₂ and net strong ion charge, equivalent to the strong ion difference ([SID⁺]) (41). Stewart (44-46) later proposed that a third variable, the total plasma concentration of nonvolatile weak acids ([A_tot]), also exerted an independent effect on plasma pH. By combining equations for conservation of charge, conservation of mass, and dissociation equilibrium reactions, Stewart developed a polynomial equation relating the plasma H⁺ concentration [H⁺] to three independent variables (PCO₂, [SID⁺], and [A_tot]) and five "constants" (K_a, K_w, K₁, K₃, and S_CO2) (45, 46)

(4)

where K_a is the effective equilibrium dissociation constant for plasma weak acids, K_w is the ion product of water, K₁ is the apparent equilibrium constant for the Henderson-Hasselbalch equation, S_CO2 is the solubility of CO₂ in plasma, and K₃ is the apparent equilibrium dissociation constant for HCO₃.

Although the strong ion model offers a unique insight into the pathophysiology of acid-base derangements in mammals and is mechanistic (11, 25), Stewart's approach has not been widely accepted, because it does not provide a practical method for determining [A_tot] and K_a (7). The most commonly used value for [A_tot] is 20 meq/l {calculated from the net protein charge, where [A_tot] (in meq/l) = 2.4 × [total protein] = 8.3 g/dl, where [total protein] is total protein concentration} (25, 50); however, a recent study suggested that the correct value for [A_tot] in human plasma is ~14 meq/l {calculated as [A_tot] (meq/l) = 1.7 × [total protein] = 7 g/dl + 1.8 × phosphate concentration = 1 mmol/l} (13). A number of different values for K_a (2 × 10⁷, 3 × 10⁷, 4 × 10⁷, and 4 × 10⁸ eq/l) have been suggested (44-46), with 3 × 10⁷ eq/l being the most commonly used value (11, 15, 25, 26, 30, 53). It is unclear which values for [A_tot] and K_a should be used when the strong ion model is applied to nonhuman plasma, inasmuch as it is likely that species differences in values for [A_tot] and K_a exist (15). From an experimental viewpoint, the strong ion model is considered by some authors to offer no significant improvement over the conventional Henderson-Hasselbalch equation (7, 22). However, from a clinical viewpoint, the strong ion model is invaluable, in that it offers a novel insight into the pathophysiology of mixed acid-base disorders (11, 15, 25). In particular, the effects of hypoproteinemia and hyperproteinemia on acid-base status (35) can be satisfactorily explained only by the strong ion model.

In summary, deficiencies exist in present methods to describe mammalian acid-base equilibria. Accordingly, Stewart's strong ion model was conceptually and algebraically reduced in the hope that a simpler model would 1) explain the apparent dependence of plasma pK₁ on pH, protein concentration, and Na⁺ concentration; 2) explain why the log PCO₂-pH relationship for plasma is displaced by changes in plasma protein, Na⁺, and Cl concentration and is nonlinear in vivo and in markedly acidic plasma; 3) provide a practical method for experimentally determining values for [A_tot] (in meq/l) and K_a (in eq/l) in plasma; and 4) provide an acid-base model that unites the Henderson-Hasselbalch equation and strong ion model.

MATERIALS AND METHODS

2

Table  1.   Categorization of simple ions in equine plasma and approximate values for their normal concentration Nonbuffer Ions (Strong Ions) Buffer Ions Cation Concn, meq/l Anion Concn, meq/l Volatile anion Concn, meq/l Nonvolatile anion Concn, meq/l Na 140 Cl 105 HCO3 27.2 Protein 12.0 K 4 Lactate 1.0 Phosphate 2.7 Ca 5 Sulfate 1.0 Citrate 0.3 Mg 2 Nonesterified   fatty acid 0.6 NH4 0.1 Urate 0.5 Succinate 0.5 Ketone bodies 0.2 Pyruvate 0.1 Values were derived from unpublished data and Refs. 17, 18, and 49. Ionic contribution of amino acids is ignored in this scheme, because at normal pH the sum of the positive and negative free amino acid charge approximates zero.

(5)

(6)

Table  2.   Approximate pKa values for acids that produce nonbuffer ions (strong ions) or buffer ions in plasma at physiological pH Ion Acid pKa Nonbuffer ions (strong ions) Sulfate HSO4 1.3-2.0 H2PO4 Phosphoric acid 1.9-2.2 Pyruvate Pyruvic acid 2.3-2.5 Acetoacetate Acetoacetic acid 3.6 Lactate Lactic acid 3.7-3.9 Carboxyl protein group R-COOH 3.7-4.0  -OH butyrate  -OH butyric acid 4.3 Succinate Succinic acid 5.2-5.6 Urate Uric acid 5.6 NH+4 NH+4 9.2-9.3 CO23 HCO3 9.8-10.3  -Amino protein group R-NH+3 9.8-10.6 Guanidine protein group R-NH+2 11.9-13.3 Buffer ions Volatile   Bicarbonate Carbonic acid 6.0-6.4 Nonvolatile   Citrate Citric acid 5.7-6.4   Imidazole protein group ImH+ 6.4-7.0   -Amino protein group RNH+3COO 7.4-7.9   HPO24 H2PO4 6.7 Values were obtained from Refs. 9 and 42. Range of values reflects value for pKa at ionic strengths of 0-0.5 (ionic strength of plasma = 0.16).

(7)

(8)

2

2

2

2

(9)

-amino

Table  3.   Approximate intrinsic pKa values and number of dissociable groups on plasma albumin Group pKa Human Serum Albumin Bovine Serum Albumin Number Attributed charge, eq Number Attributed charge, eq Strong     (dissociated)     ions   Carboxyl 3.7-4.0 106  106 100  100   -Amino 9.8-10.6 56 +56 57 +57   Guanidine 11.9-13.3 24 +24 22 +22 Dissociable ions   Imidazole 6.4-7.0 16 +2.7 16 +2.7   -Amino 7.4-7.9 4  1.3 1  0.3 Values were derived from Refs. 47 and 48.

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

2

Table  4.   Comparison of plasma pH predicted by Stewart's strong ion model (Eq. 4) and that predicted by the simplified strong ion model (Eq. 15) for equine plasma from known PCO2, [SID+], and [Atot] PCO2, Torr [SID+], meq/l [Atot], meq/l pH Predicted by Stewart's strong ion model (Eq. 4) Simplified strong ion model (Eq. 15) Normal values 44 40 15 7.432 7.432 50% change in PCO2 22 40 15 7.716 7.718 66 40 15 7.268 7.268 50% change in [SID+] 44 20 15 6.987 6.988 44 60 15 7.663 7.664 50% change in [Atot] 44 40 7.5 7.521 7.522 44 40 22.5 7.329 7.329 Values for the other variables in each model at 37°C were as follows: Ka = 2.22 × 107 eq/l, Kc = K 1SCO2 = 2.281 × 1011 eq · l1 · Torr1, K w = 4.4 × 1014 eq2/l2, K3 = 6.0 × 1011 eq/l. [SID+], strong ion difference; [Atot], total plasma concentration of volatile weak acids.

7

7

1

11

14

7

7

1

1

RESULTS

7

7

Table  5.   [Atot] and Ka determined from nonlinear regression of equine plasma equilibrated with different PCO2 Animal No. n pH Range R2 Simplified Strong Ion Model Stewart's Strong Ion Model [Atot], meq/l Ka, 107 eq/l [Atot], meq/l Ka, 107 eq/l Females   1 7 7.34-8.29 0.99 16.5 2.64 NA NA   2 10 7.28-7.95 0.96 13.3 2.11 NA NA   3 8 7.28-7.84 0.98 15.0 1.99 16.0 1.46 Males   1 8 7.30-7.93 0.98 15.3 1.95 15.1 2.23   2 7 7.40-7.81 0.98 19.7 1.99 20.7 1.44   3 11 7.32-7.86 0.94 10.4 2.61  9.0 0.06 n, No. of samples; NA, not available (values could not be estimated).

9

7

Table  6.   Calculation of [Atot] and Ka for equine albumin, globulin, and serum protein using published values for PCO2, [SID+], pH, ionic strength, temperature, pK 1, and SCO2 Protein n pH Range R2 [Atot], meq/l Ka, 107 eq/l Ref. Albumin 5 6.67-7.37 0.999 (2.2 ± 1.0) × [Alb] 2.3 ± 1.5  48, Table I Albumin 6 6.81-7.52 0.998 (2.3 ± 1.1) × [Alb] 2.3 ± 2.3  48, Table II Globulin 5 6.66-7.38 0.999 (1.4 ± 0.6) × [Glob] 3.4 ± 1.9  48, Table IV Serum protein 4 7.07-7.74 1.000 (2.0 ± 0.9) × [TP] 2.0 ± 0.6  47, Table V Serum protein 4 7.16-7.73 1.000 (2.1 ± 1.3) × [TP] 2.0 ± 0.8  47, Table VI Values for [Atot] and Ka were determined using nonlinear regression and are expressed as mean estimate ± SE of estimate; n, no. of samples. [Alb], albumin concentration (in g/dl); [Glob], globulin concentration (in g/dl); [TP], total protein concentration (in g/dl); SCO2, solubility of CO2 in plasma.

7

Table  7.   Summary of linear regression analysis of the relationship between calculated and measured plasma pH Model 1 [Atot] (meq/l) = 2.24 [TP] (g/dl) Ka = 2.22 × 107 eq/l Model 2 [Atot] (meq/l) = 20 Ka = 3.0 × 107 eq/l Model 3 [Atot] (meq/l) = 2.4 [TP] (g/dl) Ka = 3.0 × 107 eq/l Ref. pHc = 1.08 pHm  0.60 [0.93] pHc = 1.01 pHm  0.15 [0.96] pHc = 1.18 pHm  1.37 [0.93] 36, Figs. 1, 2, 3 pHc = 1.18 pHm  1.34 [0.78] pHc = 1.96 pHm  7.26 [0.75] pHc = 1.22 pHm  1.66 [0.74] 17, Table 2 pHc = 1.02 pHm  0.15 [0.94] pHc = 1.58 pHm  4.42 [0.96] pHc = 1.09 pHm  0.71 [0.95] 17, Table 3 pHc = 0.93 pHm + 0.54 [0.96] pHc = 1.44 pHm  3.40 [0.97] pHc = 1.00 pHm  0.02 [0.96] 17, Table 4 pHc = 1.28 pHm  2.05 [0.86] pHc = 1.68 pHm  5.15 [0.87] pHc = 1.35 pHm  2.59 [0.86] 17, Table 5 pHc = 1.02 pHm  0.18 [0.95] pHc = 1.03 pHm  0.37 [0.94] pHc = 1.10 pHm  0.79 [0.95] 18, Table 1 pHc = 1.20 pHm  1.52 [0.92] pHc = 1.52 pHm  4.02 [0.95] pHc = 1.27 pHm  2.05 [0.92] 18, Table 2 pHc = 1.20 pHm  1.43 [0.96] pHc = 1.23 pHm  1.82 [0.95] pHc = 1.23 pHm  1.69 [0.95] 18, Table 3 Mean ± SD pHc = (1.11 ± 0.12)pHm  (0.84 ± 0.88) pHc = (1.43 ± 0.33)pHm  (3.32 ± 2.44) pHc = (1.18 ± 0.10)pHm  (1.36 ± 0.73) Plasma pH was calculated using [Atot] and Ka values determined by simplified strong ion model (model 1), Stewart's commonly used values (model 2), and values commonly used for human plasma (model 3). Plasma pH was calculated from published values (Refs. 17, 18, and 36) for PCO2, [SID+], and [TP]. Values in brackets are R2. pHc, calculated pH; pHm, measured pH.

7

7

DISCUSSION

The simplified strong ion model provides a quantitative mechanistic acid-base model that explains many of the anomalies of the Henderson-Hasselbalch equation. The model explains why the apparent value for pK₁ in plasma is dependent on pH, protein concentration, and Na⁺ concentration and provides a mechanistic explanation for the temperature dependence of plasma pH. The simplified strong ion model provides a practical method for experimentally determining [A_tot] and K_a that produces values for horse plasma that are significantly different from those most commonly used for human plasma. Finally, the model simplifies to the Henderson-Hasselbalch equation when applied to aqueous nonprotein solutions, thereby providing an acid-base model that unites the Henderson-Hasselbalch equation and strong ion model.

(19)

pH

pH

pH

7

pH

pH

pH

pH

7

7

7

7

2

2

2

7

7

7

(20)

FOOTNOTES

Address for reprint requests: P. D. Constable, Dept. of Veterinary Clinical Medicine, College of Veterinary Medicine, University of Illinois at Urbana-Champaign, 1008 West Hazelwood Dr., Urbana, IL 61801.

Received 19 December 1994; accepted in final form 14 February 1997.

APPENDIX A

An estimate for the value of [A_tot] in milliequivalents per liter can be obtained by determining the molar concentration and attributing a valence to [HA] and [A] for the four nonvolatile plasma buffers and then summing the resultant values for [HA] and [A] when expressed in milliequivalents per liter. Accurate data are available for human and bovine albumin (47, 48), and the following estimate for [A_tot] is calculated for a solution resembling human plasma that has no globulin.

For imidazole at pH 7.40, the ratio of [HA] to [A] equals 0.2, inasmuch as K_a = 2 × 10⁷ eq/l. For human albumin the value for [HA] in milliequivalents per liter can be calculated as

(A1)

Human albumin contains 16 dissociable imidazole groups and 4 dissociable -amino groups (47), with the fully dissociated groups producing a net valence of 26 eq (Table 3). Because the valence for HA_imidazole = +1, the following equations can be derived for a solution containing 4.1 g/dl albumin (mol wt of human albumin = 69,000)

(A2)

(A3)

For -amino groups at pH 7.40, the ratio of [HA] to [A] equals 2.0, inasmuch as K_a = 2 × 10⁸ eq/l. Because the valence for [HA]_-amino = 0, the following equations can be derived for a solution containing 4.1 g/dl albumin

(A4)

(A5)

For phosphate at pH 7.40, the ratio of [H₂PO₄] to [HPO²₄] (where [H₂PO₄] and [HPO²₄] are concentrations of H₂PO₄ and HPO²₄) equals 0.2, inasmuch as K_a = 2 × 10⁷ eq/l. For human plasma with a phosphate concentration of 4 mg/dl (1.29 mmol/l), the following equations can be calculated

(A6)

(A7)

For citric acid at pH 7.40, the ratio of [R · COOH] to [R · COO] equals 1.2, inasmuch as K_a = 7.9 × 10⁷ eq/l. For human plasma with a citrate concentration of 0.6 mmol/l, the following equations can be calculated

(A8)

(A9)

The value for [A_tot] in milliequivalents per liter for an electrolyte solution containing human albumin can now be estimated

(A10)

where [HA]_i and [A]_i are the ith value for [HA] and [A].

The value derived for [A_tot] in milliequivalents per liter is approximate, inasmuch as the number of dissociated groups in albumin is approximate (47, 48). A similar approach for a solution resembling bovine plasma (Table 3) (48), which has no globulin (assuming [albumin] = 3.2 g/dl; mol wt of albumin = 65,000; [phosphate] = 1.29 mmol/l) produces an estimate for [A_tot] of 12.8 meq/l, which differs from that obtained for human albumin solution. This suggests that the value for [A_tot] will vary among species.

APPENDIX B

Equation 12 can be rearranged to provide

(B1)

Which can be expanded to

(B2)

Substituting for [HCO₃] from the overall equilibrium reaction for the Henderson-Hasselbalch equation (Eq. 1), such that [HCO₃] = K₁S_CO2PCO₂/a_H⁺ provides

(B3)

Multiplying both sides of Eq. B3 by [H⁺] (i.e., a_H⁺) provides

(B4)

The general solution of the quadratic equation ax² + bx + c = 0 is x = (b ± )/2a. The solution for Eq. B4 is therefore

(B5)

Expansion and rearrangement provides

(B6)

which is equivalent to

(B7)

which can be further simplified to

(B8)

Taking the logarithm of the reciprocal of both sides of Eq. B8 produces only one real solution

(B9)

APPENDIX C

Stewart developed the following equation relating [H⁺] to 3 independent variables (PCO₂, [SID⁺], [A_tot]) and 4 "constants" (K_a, K_w, K₃, and K_c), where K_c = K₁ × S_CO2

(C1)

Simplification of Eq. C1 for mammalian plasma at 37°C requires recognition that the equation can be rewritten as

(C2)

and that using appropriate units, the approximate values of [SID⁺] and [A_tot] are 4 × 10² and 2 × 10² eq/l, respectively, PCO₂ is ~4 × 10¹ Torr, [H⁺] is 40 × 10⁹ eq/l, K_a is on the order of 2 × 10⁷ eq/l, K_c and K₃ are ~2.5 × 10¹¹ eq · l¹ · Torr¹ and 6.0 × 10¹¹ eq/l, respectively, and K_w is 4.4 × 10¹⁴ eq²/l². On this basis Substituting the above into Eq. C2 provides

(C3)

Substituting for PCO₂ from Eq. 1 provides

(C4)

which simplifies to

(C5)

Simplification of Eq. C5 for physiological plasma requires recognition that Eq. C5 can be rewritten as

(C6)

The approximate values of each term in Eq. C6 can now be calculated, given that [HCO₃] = 2.5 × 10² eq/l, [CO²₃] = 3.8 × 10⁵ eq/l, and [OH] = 1.1 × 10⁶ eq/l (calculated from above) The [H⁺]³ term can therefore be ignored, and Eq. C6 can be simplified to

(C7)

The general solution of the quadratic equation ax² + bx + c = 0 is x = (b ± )/2a. The solution for Eq. C7 is therefore

(C8)

which is equivalent to

(C9)

This can be simplified to

(C10)

on the basis that and that Equation C10 can be expressed as

(C11)

The only real solution of Eq. C11 is

(C12)

which simplifies to

(C13)

Taking the logarithm of the reciprocal of both sides of Eq. C13 produces

(C14)

which is similar to Eq. 14 developed from the simplified strong ion model, assuming that Stewart's parameter [H⁺] approximates the H⁺ activity.

REFERENCES

1.	Alexander, S. C., R. Gelfand, and C. J. Lambertson. The pK of carbonic acid in cerebrospinal fluid. J. Biol. Chem. 236: 592-596, 1961[Free Full Text].
2.	Astrup, P. A simple electrometric technique for the determination of carbon dioxide tension in blood and plasma, total content of carbon dioxide in plasma, and bicarbonate content in separated plasma at a fixed carbon dioxide tension (40 mmHg). Scand. J. Clin. Lab. Invest. 8: 33-43, 1956[Medline].
3.	Austin, W. H., E. Lacombe, P. W. Rand, and M. Chatterjee. Solubility of carbon dioxide in serum from 15 to 38°C. J. Appl. Physiol. 18: 301-304, 1963[Abstract/Free Full Text].
4.	Bjerrum, N. Die Dissoziation der starken Elektrolyten. Z. Electrochem. 24: 321-328, 1918.
5.	Bos, O. J. M., J. F. A. Labro, M. J. E. Fischer, J. Wilting, and L. H. M. Janssen. The molecular mechanism of the neutral-to-base transition of human serum albumin. J. Biol. Chem. 264: 953-959, 1989[Abstract/Free Full Text].
6.	Brackett, N. C., J. J. Cohen, and W. B. Schwartz. Carbon dioxide titration curve of normal man. N. Engl. J. Med. 272: 6-12, 1965.
7.	Cameron, J. N. Acid-base homeostasis: past and present perspectives. Physiol. Zool. 62: 845-865, 1989.
8.	Cullen, G. E., H. R. Keeler, and H. W. Robinson. The pK of the Henderson-Hasselbalch equation for hydrion concentration of blood and serum. J. Biol. Chem. 66: 301-322, 1925[Free Full Text].
9.	Edsall, J. T., and J. Wyman. Biophysical Chemistry. New York: Academic, 1958, vol. 1, p. 406-662.
10.	Elkinton, J. R., R. B. Singer, E. S. Barker, and J. F. Clark. Effects in man of acute experimental respiratory alkalosis and acidosis on ionic transfers in the total body fluids. J. Clin. Invest. 34: 1671-1690, 1955.
11.	Fencl, V., and D. E. Leith. Stewart's quantitative acid-base chemistry: applications in biology and medicine. Respir. Physiol. 91: 1-16, 1993[Medline].
12.	Figge, J., T. Mydosh, and V. Fencl. Serum proteins and acid-base equilibria: a follow-up. J. Lab. Clin. Med. 120: 713-719, 1992[Medline].
13.	Figge, J., T. H. Rossing, and V. Fencl. The role of serum proteins in acid-base equilibria. J. Lab. Clin. Med. 117: 453-467, 1991[Medline].
14.	Forster, H. V., C. L. Murphy, A. G. Brice, L. G. Pan, and T. F. Lowry. Plasma [H+] regulation and whole blood [CO2] in exercising ponies. J. Appl. Physiol. 68: 309-315, 1990[Abstract/Free Full Text].
15.	Frischmeyer, K. J., and P. F. Moon. Evaluation of quantitative acid-base balance and determination of unidentified anions in swine. Am. J. Vet. Res. 55: 1153-1157, 1994[Medline].
16.	Glantz, S. A., and B. K. Slinker. Primer of Applied Regression and Analysis of Variance. New York: McGraw-Hill, 1990, p. 1-777.
17.	Gossett, K. A., D. D. French, B. Cleghorn, and G. E. Church. Effect of acute acidemia on blood biochemical variables in healthy ponies. Am. J. Vet. Res. 51: 1375-1379, 1990[Medline].
18.	Gossett, K. A., D. D. French, B. Cleghorn, and G. E. Church. Blood biochemical response to sodium bicarbonate infusion during sublethal endotoxemia in ponies. Am. J. Vet. Res. 51: 1370-1374, 1990[Medline].
19.	Harned, H. S., and F. T. Bonner. The first ionization of carbonic acid in aqueous solutions of sodium chloride. J. Am. Chem. Soc. 67: 1026-1031, 1945.
20.	Hasselbalch, K. A. Die Berechnung der Wasserstoffzahl des blutes auf der freien und gebundenen Kohlensaure desselben, und die Sauerstoffbindung des Blutes als Funktion der Wasserstoffzahl. Biochem. Z. 78: 112-144, 1916.
21.	Hastings, A. B., and J. Sendroy. The effect of variation in ionic strength on the apparent first and second dissociation constants of carbonic acid. J. Biol. Chem. 66: 445-455, 1925.
22.	Heisler, N. Acid-Base Regulation in Animals. New York: Elsevier, 1986.
23.	Henderson, L. J. The theory of neutrality regulation in the animal organism. Am. J. Physiol. 21: 427-428, 1908.
24.	Johnson, R. E., H. T. Edwards, D. B. Dill, and J. W. Wilson. Blood as a biochemical system. XIII. The distribution of lactate. J. Biol. Chem. 157: 461-473, 1945[Free Full Text].
25.	Jones, N. L. Blood Gases and Acid-Base Physiology. New York: Thieme, 1987, p. 83-185.
26.	Kowalchuk, J. M., G. J. F. Heigenhauser, M. I. Lindinger, J. R. Sutton, and N. L. Jones. Factors influencing hydrogen ion concentration in muscle after intense exercise. J. Appl. Physiol. 65: 2080-2089, 1988[Abstract/Free Full Text].
27.	Maas, A. H. J., A. N. P. van Heijst, and B. F. Visser. The determination of the true equilibrium constant (pK1g) and the practical equilibrium coefficient (pK1g) for the first ionization of carbonic acid in solutions of sodium bicarbonate, cerebrospinal fluid, plasma, and serum at 25 and 38°. Clin. Chim. Acta 33: 325-343, 1971[Medline].
28.	Mecher, C., E. C. Rackow, M. E. Astiz, and M. H. Weil. Unaccounted for anion in metabolic acidosis during severe sepsis in humans. Crit. Care Med. 19: 705-711, 1991[Medline].
29.	Mitchell, R. A., D. A. Herbert, and C. T. Carman. Acid-base constants and temperature coefficients for cerebrospinal fluid. Am. J. Physiol. 20: 27-30, 1965.
30.	Pieschl, R. L., P. W. Toll, D. E. Leith, L. J. Peterson, and M. R. Fedde. Acid-base changes in the running greyhound: contributing variables. J. Appl. Physiol. 73: 2297-2304, 1992[Abstract/Free Full Text].
31.	Putnam, R. W., and A. Roos. Which value for the first dissociation constant of carbonic acid should be used in biological work? Am. J. Physiol. 260 (Cell Physiol. 29): C1113-C1116, 1991[Abstract/Free Full Text].
32.	Reeves, R. B. An imadazole alphastat hypothesis for vertebrate acid-base regulation: tissue carbon dioxide content and body temperature in bullfrogs. Respir. Physiol. 14: 219-236, 1972[Medline].
33.	Reeves, R. B. Error proved and corrected: net anionic charge on serum albumin. J. Lab. Clin. Med. 117: 437, 1991[Medline].
34.	Rispens, P., C. W. Dellebarre, D. Eleveld, W. Helder, and W. G Zijlstra. The apparent first dissociation constant of carbonic acid in plasma between 16 and 42.5°. Clin. Chim. Acta 22: 627-637, 1971.
35.	Rossing, T. H., N. Maffeo, and V. Fencl. Acid-base effects of altering plasma protein concentration in human blood in vitro. J. Appl. Physiol. 61: 2260-2265, 1986[Abstract/Free Full Text].
36.	Rumbaugh, G. E., G. P. Carlson, and D. Harrold. Clinicopathologic effects of rapid infusion of 5% sodium bicarbonate in 5% dextrose in the horse. J. Am. Vet. Med. Assoc. 178: 267-271, 1981[Medline].
37.	SAS Institute. SAS/STAT User's Guide, release 6.03. Cary, NC: SAS, 1988, p. 675-712.
38.	Severinghaus, J. W., M. Stupfel, and A. F. Bradley. Variations of serum carbonic acid pK with pH and temperature. J. Appl. Physiol. 9: 197-200, 1956[Abstract/Free Full Text].
39.	Siggaard-Andersen, O. The first dissociation exponent of carbonic acid as a function of pH. Scand. J. Clin. Lab. Invest. 14: 587-597, 1962[Medline].
40.	Siggaard-Andersen, O. The Acid-Base Status of the Blood. Copenhagen: Munksgaard, 1963.
41.	Singer, R. B., and A. B. Hastings. An improved clinical method for the estimation of disturbances of the acid-base balance of human blood. Medicine 27: 223-242, 1948[Medline].
42.	Smith, R. B., and A. E. Martell. Critical Stability Constants. New York: Plenum, 1989, vol. 6, suppl. 2.
43.	Stainsby, W. N., and P. D. Eitzman. Role of CO2, O2, and acid in arteriovenous [H+] difference during muscle contractions. J. Appl. Physiol. 65: 1803-1810, 1988[Abstract/Free Full Text].
44.	Stewart, P. A. Independent and dependent variables of acid-base control. Respir. Physiol. 33: 9-26, 1978[Medline].
45.	Stewart, P. A. How to Understand Acid-Base. New York: Elsevier, 1981.
46.	Stewart, P. A. Modern quantitative acid-base chemistry. Can. J. Physiol. Pharmacol. 61: 1444-1461, 1983[Medline].
47.	Tanford, C. Preparation and properties of serum and plasma proteins. XXIII. Hydrogen ion equilibria in native and modified human serum albumins. J. Am. Chem. Soc. 72: 441-451, 1950.
48.	Tanford, C., S. A. Swanson, and W. S. Shore. Hydrogen ion equilibria in bovine serum albumin. J. Am. Chem. Soc. 77: 6414-6421, 1955.
49.	Van Leeuwen, A. M. Net cation equivalency (base binding power) of the plasma proteins. Acta Med. Scand. Suppl. 422: 1-212, 1964.
50.	Van Slyke, D. D., A. G. Hastings, A. Hiller, and J. Sendroy. Studies of gas and electrolyte equilibria in blood. XIV. The amounts of alkali bound by serum albumin and globulin. J. Biol. Chem. 79: 769-780, 1928[Free Full Text].
51.	Van Slyke, D. D., H. Wu, and F. C. McLean. Studies of gas and electrolyte equilibria in the blood. Factors controlling the electrolyte and water distribution in the blood. J. Biol. Chem. 55: 765-849, 1923.
52.	Warburg, E. J. Studies on carbonic acid compounds and hydrogen ion activities in blood and salt solutions. Biochem. J. 16: 153-340, 1922.
53.	Weinstein, Y., A. Magazanik, A. Grodjinovsky, O. Inbar, R. A. Dlin, and P. A. Stewart. Reexamination of Stewart's quantitative analysis of acid-base status. Med. Sci. Sports Exer. 23: 1270-1275, 1991[Medline].