For background information about the quantitative approach to human acid-base physiology,
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The original text of Peter Stewart's classic book, How to Understand Acid-Base: A Quantitative Acid-Base Primer for Biology and Medicine, is available without charge. In addition, the second edition of the book, entitled Stewart's Textbook of Acid-Base (John A. Kellum and Paul W.G. Elbers, editors, 2009), is now available for purchase at http://www.acidbase.org/. The second edition features Stewart's original text plus over 20 new chapters that highlight advances in the field.
Stewart (1983) introduced a quantitative physicochemical model of acid-base balance
in blood plasma. The Stewart model incorporates three fundamental
physicochemical principles as they apply to a single body fluid compartment (such as
arterial blood plasma) under steady-state conditions: the law of conservation of mass is
always obeyed; electrical neutrality is always maintained; and all statements of chemical
equilibria are simultaneously satisfied. Dissociation equilibria for the carbon
dioxide - bicarbonate - carbonate system are explicitly included. The expression employed
for the carbon dioxide - bicarbonate equilibrium is mathematically equivalent to the
Henderson-Hasselbalch equation. All nonvolatile weak acids
(such as H2PO4-, and plasma proteins) are
characterized by a single equilibrium dissociation constant in Stewart's model.
Figge, Rossing and Fencl (1991) produced electrolyte solutions resembling human serum that contained albumin as the sole protein moiety. Data collected from these solutions were used in a least-squares algorithm to develop a more robust quantitative physicochemical model. This model treats albumin as a polyprotic macromolecule with multiple apparent equilibrium dissociation constants corresponding to different classes of amino acid side chains (i.e., Arg, Lys, Asp, Glu, Cys, His, Tyr, amino terminus, carboxyl terminus). The number of side chains in each class is taken from the known human serum albumin amino acid sequence. The Figge-Rossing-Fencl model accounts mathematically for two distinct categories of side chains with respect to their contribution to charge balance. The first category consists of those side chains with a positively charged acidic form and a neutral conjugate base (i.e., Arg, Lys, His, and the amino terminus). For example:
-NH3+ ⇄ -NH2 + H+
The second category consists of those side chains with a neutral acidic form and a negatively charged conjugate base (i.e., Asp, Glu, Cys, Tyr, and carboxyl terminus). For example:
-COOH ⇄ -COO- + H+
As demonstrated in the x-ray crystal structure of human serum albumin, of the 35 cysteine residues in the protein, 34 form 17 disulfide bridges; hence only one Cys residue is free to ionize.
Apparent equilibrium dissociation constants from the work of Sendroy and Hastings (1927) for the phosphoric acid - phosphate system ( [ H3PO4 ], [ H2PO4- ], [ HPO42- ], and [ PO43- ] ), as applicable to plasma at 38 degrees Celsius, are explicitly included: pK'1 = 1.915; pK'2 = 6.66; and pK'3 = 11.78. The Figge-Rossing-Fencl model simultaneously solves the equilibrium equations governing the following dissociation reactions, and accounts for the net negative charge contributed by all three ionized species:
H3PO4 ⇄ H2PO4- + H+
H2PO4- ⇄ HPO42- + H+
HPO42- ⇄ PO43- + H+
Within the physiologic pH range, the vast majority of charge attributable to phosphate species derives from H2PO4- and HPO42-.
The Figge-Rossing-Fencl model is successful in calculating the pH of albumin-containing electrolyte solutions as well as the pH of filtrands of serum.
Figge, Mydosh and Fencl (1992) further refined the quantitative physicochemical model by incorporating pKA values for albumin histidine residues as determined by NMR spectroscopy in the study of Bos and colleagues (1989). The pKA values are temperature-corrected to 37 degrees Celsius in the model. This model accounts for the effects of the microenvironments within the macromolecule of albumin on the pKA values of individual histidine residues. Although the Figge-Mydosh-Fencl model is successful in many aspects, it does not account for the presence of all 59 lysine residues in human serum albumin. Because of this limitation, the model provides useful results restricted to the pH range of biologic interest (6.9 to 7.9); outside of this range the model is unreliable.
The model was updated in 2007-2009 and published by Figge (2009) in Stewart's Textbook of Acid-Base (Chapter 11)
under the title of the Figge-Fencl Quantitative Physicochemical Model of Human Acid-Base Physiology. This model
successfully accounts for all 59 lysine residues in human serum albumin and incorporates information about lysine
residues with unusually low pKA values, in accord with the prior work of Halle and Lindman (1978), and as
suggested by data from tryptophan and tyrosine fluorescence emission spectroscopy studies by Dockal and colleagues
(2000). As in the Figge-Mydosh-Fencl (1992) model, pK(a) values for 13 of 16 albumin histidine residues in the
Figge-Fencl model are based on NMR spectroscopy data (temperature-corrected from 25 to 37 degrees Celsius).
The model also accounts for the neutral-to-base (N-B) structural transition of human serum albumin over the pH range
of 6 to 9. The titration curve of human serum albumin at 37 degrees Celsius as predicted by the Figge-Fencl model
closely tracks with the experimental data points of Niels Fogh-Andersen and colleagues (1993) over the pH range of
5 to 9.
The Figge-Fencl model was updated in 2012, and the most recent version is 3.0, which is
now featured on http://www.Figge-Fencl.org/ and http://www.acid-base.org/.
The model is also described in the appendix of Figge, Bellomo and Egi (2018).
Version 3.0 incorporates key enhancements from earlier models, and features an improved least squares fit to the original data of Figge, Rossing and Fencl (1991) compared with the Figge-Mydosh-Fencl (1992) model and the Figge-Fencl model of 2009. Version 3.0 also improves the performance of the model down to pH 4, extending the useful range from pH 4 to 9. The titration curve of human serum albumin at 37 degrees Celsius as predicted by the Figge-Fencl model version 3.0 closely tracks with the experimental data points of Niels Fogh-Andersen and colleagues (1993) over the pH range of 4 to 9. The Figge-Fencl model version 3.0 gives results equivalent to those of the Figge-Mydosh-Fencl model within the pH range of biologic interest (6.9 to 7.9). Technical details about model version 3.0 can be accessed through the links below.
The Figge-Fencl Quantitative Physicochemical Model of Human Acid-Base Physiology (Version 3.0) can be used to develop
scanning tools for the detection of increased concentrations of anions in various pathologic states. This is of
particular importance for the detection of unmeasured anions in acutely ill patients presenting with metabolic
acidosis. The simplest tool for this purpose is the traditional anion gap (AG, and AGK when including
potassium) as described by Emmett and Narins (1977).
The traditional anion gap can be calculated with or without the inclusion of [ K+ ]:
AGK = [ Na+ ] + [ K+ ] - [ Cl- ] - [ HCO3- ]
AG = [ Na+ ] - [ Cl- ] - [ HCO3- ]
where all quantities are expressed in mEq/L.
Figge, Jabor, Kazda and Fencl (1998) described the albumin-corrected anion gap (cAG, and cAGK). This tool features a very simple, approximate adjustment that corrects the anion gap for fluctuations in the albumin concentration. The adjustment takes into account the intrinsic net negative charge contributed by the ionized amino acid side chains of albumin, as well as the positive charge contributed by albumin-bound calcium ions.
The Figge-Jabor-Kazda-Fencl equation for calculating the albumin-corrected anion gap can also be used with or without the inclusion of [ K+ ]:
cAGK = AGK + z x ([Normal Albumin] - [Observed Albumin])
cAG = AG + z x ([Normal Albumin] - [Observed Albumin])
where [Normal Albumin] and [Observed Albumin] are in g/dL, and cAGK, AGK, cAG and AG are expressed in mEq/L.
The usual default value for [Normal Albumin] is 4.4 g/dL. The parameter, z, is the net negative charge contributed by each 1.0 g/dL of albumin (including the charge contributed by albumin-bound calcium). The usual value for z ranges from 2.3 to 2.5 mEq/L as determined by Feldman and colleagues (2005), and Figge and colleagues. Figge (2015) subsequently demonstrated that z can be directly calculated using the physicochemical model taking into account calcium binding to albumin per the equations of Marshall and Hodgkinson (1983) [ See Table 1 via this link to http://www.nejm.org/doi/full/10.1056/NEJMc1414731 ].
Chawla and colleagues (2008) provided evidence demonstrating that the albumin-corrected anion gap (cAG), in comparison with its traditional counterpart (AG), is more sensitive in predicting the presence of severe hyperlactatemia (defined as [lactate] > 4.0 mEq/L).
Likewise, Figge, Bellomo and Egi (2018) confirmed that cAGK is more sensitive than AGK in predicting [Lactate] > 4.0 mEq/L.
Both clinical studies are open access online through the links below.