For background information about the quantitative approach to human acid-base physiology,
visit the related site:
http://www.acidbase.org/.
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 Labro and
colleagues (1986) and 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. Furthermore, the Figge-Mydosh-Fencl model does not account for the
neutral-to-base (N–B) structural transition that occurs in human serum albumin between pH 6 and pH 9. This
structural transition features a downward shift in the pKA values of five histidine residues as the
albumin molecule transitions from the N state to the B state. The Figge-Mydosh-Fencl model is limited as it
employs pKA values exclusively from NMR data representing the N state. Hence, the model fails to
account for the B state.
Because of the above limitations, the Figge-Mydosh-Fencl 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.acid-base.org/. The Figge-Fencl model
version 3.0 was designed to replicate the key results of the Figge-Mydosh-Fencl (1992) model within the pH range of
biologic interest (6.9 to 7.9), while at the same time incorporating the contribution of all 59 lysine
residues.
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.
Key Features of the model include:
● The expression employed for the carbon dioxide - bicarbonate equilibrium is mathematically equivalent to the
Henderson-Hasselbalch equation.
● 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.
● The 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 model incorporates 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.
● The model successfully accounts for the contribution of all 59 lysine residues in human serum albumin and
incorporates information about lysine residues with unusually low apparent 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).
● The model accounts for the neutral-to-base (N-B) structural transition of human serum albumin over the pH range
of 6 to 9.
● The model accounts for the anomalously low average pK(a) value of glutamic and aspartic acid residues in
albumin. This feature allows the model to provide useful functionality down to a pH of approximately 4.0.