http://www.acid-base.org/
An Educational Web Site about Modern Human Acid-Base Physiology:  The Quantitative Physicochemical Model of Human Acid-Base Physiology in Blood Plasma

Presented by James Figge, MD
Bethlehem, New York

Dedicated to the memory of Vladimir Fencl, MD, CSc (PhD)


The Model Defined

"Figge's model:  a mathematical formula, used to estimate non-respiratory acid-base disorders, using serum electrolyte concentrations and Pco2."

- Saunders Comprehensive Veterinary Dictionary.  Editors:  Virginia P. Studdert, Clive C. Gay, Douglas C. Blood, and John Grandage.  Edinburgh, London, New York, Oxford, Philadelphia, St. Louis, Sydney, Toronto:  Elsevier.  4TH Edition.  2012.


Background Information

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.


Resources

I.  Dedication to Dr. Vladimir Fencl

Dedication




II.  Original Publications Regarding the Model

Stewart 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 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 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 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 further refined the quantitative physicochemical model by incorporating pKA values for albumin histidine residues as determined by NMR spectroscopy.  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.


Peter A. Stewart.  Modern quantitative acid-base chemistry.  Canadian Journal of Physiology and Pharmacology.  1983; 61:1444-1461.  [ Abstract on PubMed ].


James Figge, Thomas H. Rossing, and Vladimir Fencl.  The role of serum proteins in acid-base equilibria.  The Journal of Laboratory and Clinical Medicine.  1991; 117:453-467.  [ Abstract on PubMed ].


James Figge, Thomas Mydosh, and Vladimir Fencl.  Serum proteins and acid-base equilibria:  a follow-up.  The Journal of Laboratory and Clinical Medicine.  1992; 120:713-719.  [ Abstract on PubMed ].


Julius Sendroy, Jr. and A. Baird Hastings.  Studies of the solubility of calcium salts.  II.  The solubility of tertiary calcium phosphate in salt solutions and biological fluids.  The Journal of Biological Chemistry.  1927; 71:783-796.  [ Full Text ].


Octaaf J.M. Bos, Jan F.A. Labro, Marcel J.E. Fischer, Jaap Wilting, and Lambert H.M. Janssen.  The molecular mechanism of the neutral-to-base transition of human serum albumin.  Acid/base titration and proton nuclear magnetic resonance studies on a large peptic and a large tryptic fragment of albumin.  The Journal of Biological Chemistry.  1989; 264:953-959.  [ Full Text ].




III.  Clinical Application of the Model:  Diagnosis of Metabolic Acid-Base Disturbances

Vladimir Fencl, Antonín Jabor, Antonín Kazda, and James Figge.  Diagnosis of metabolic acid-base disturbances in critically ill patients.  American Journal of Respiratory and Critical Care Medicine.  2000; 162:2246-2251.  [ Full Text ]; [ Online Supplement ].




IV.  Review Article

E. Wrenn Wooten.  Science review:  Quantitative acid–base physiology using the Stewart model.  Critical Care.  2004; 8:448-452.  [ Full Text ].




V.  The Figge-Fencl Quantitative Physicochemical Model of Human Acid-Base Physiology in Blood Plasma

The model was updated in 2007-2009 and published 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 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, and as suggested by data from tryptophan and tyrosine fluorescence emission spectroscopy studies.  As in the Figge-Mydosh-Fencl 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-Anderson and colleagues over the pH range of 5 to 9.  Technical details about the model can be accessed through the links below.


James Figge.  Role of Non-Volatile Weak Acids (Albumin, Phosphate and Citrate).  In Stewart's Textbook of Acid-Base.  Kellum JA and Elbers PWG, editors.  Amsterdam:  AcidBase.org.  2009.  Chapter 11, pages 217 - 232.


Bertil Halle and Björn Lindman.  Chloride ion binding to human plasma albumin from chlorine-35 quadrupole relaxation.  Biochemistry.  1978; 17:3774-3781.  [ Abstract on PubMed ].


Michael Dockal, Daniel C. Carter, and Florian Rüker.  Conformational transitions of the three recombinant domains of human serum albumin depending on pH.  J Biol Chem.  2000; 275:3042-3050.  [ Full Text ].


Niels Fogh-Andersen, Poul Jannik Bjerrum, and Ole Siggaard-Andersen.  Ionic binding, net charge, and Donnan effect of human serum albumin as a function of pH.  Clinical Chemistry.  1993; 39:48-52.  [ Full Text ].



Model

Statistical Validation of Model

Validation against Independent Data

Albumin Titration Curve

Online Model Application




VI.  Human Serum Albumin X-Ray Crystal Structure

X-Ray Crystal Structure




VII.  Open Access:  Chapter 11 from Stewart's Textbook of Acid-Base

This chapter manuscript is provided without charge on http://www.acid-base.org/ with permission of the copyright owner (AcidBase.org / Paul WG Elbers, Amsterdam, The Netherlands).  Please note that the chapter is protected by copyright and is provided on this web site for educational / academic use only.  Please cite the original source when referencing this publication:

James Figge.  Role of Non-Volatile Weak Acids (Albumin, Phosphate and Citrate).  In Stewart's Textbook of Acid-Base.  Kellum JA and Elbers PWG, editors.  Amsterdam:  AcidBase.org.  2009.  Chapter 11, pages 217 - 232.



Chapter 11 Text from Stewart's Textbook of Acid-Base

Figure 11.1 from Stewart's Textbook of Acid-Base

Figure 11.2 from Stewart's Textbook of Acid-Base

Figure 11.3 from Stewart's Textbook of Acid-Base

Figure 11.4 from Stewart's Textbook of Acid-Base




VIII.  The Figge-Fencl Quantitative Physicochemical Model of Human Acid-Base Physiology in Blood Plasma (Version 3.0)

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/.

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 compared with the Figge-Mydosh-Fencl 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-Anderson and colleagues 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.


Model Version 3.0

Statistical Validation of Model Version 3.0

Albumin Titration Curve as Predicted by Model Vesion 3.0

Online Model Application Featuring Model Version 3.0



IX.  The Anion Gap and the Albumin-Corrected Anion Gap

The Figge-Fencl Quantitative Physicochemical Model of Human Acid-Base Physiology (Version 3.0) can be used to develop 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 classic anion gap (AG, and AGK when including potassium) as described by Emmett and Narins.

The classic 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 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 albumin-bound calcium).  The usual value for z ranges from 2.3 to 2.5 mEq / L as determined by Feldman and colleagues, and Figge and colleagues.  Figge 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 [ See Table 1 via this link to http://www.nejm.org/doi/full/10.1056/NEJMc1414731 ].


Michael Emmett and Robert G. Narins.  Clinical use of the anion gap.  Medicine (Baltimore).  1977; 56:38-54.  [ Abstract on PubMed ].


R.W. Marshall, and A. Hodgkinson.  Calculation of plasma ionised calcium from total calcium, proteins and pH:  comparison with measured values.  Clinica Chimica Acta.  1983; 127:305-310.


Sara D. Winter, J. Richard Pearson, Patricia A. Gabow, Arnold L. Schultz, and Ronald B. Lepoff.  The fall of the serum anion gap.  Archives Internal Medicine.  1990; 150:311-313.  [ Abstract on PubMed ].


James Figge, Antonín Jabor, Antonín Kazda, and Vladimir Fencl.  Anion gap and hypoalbuminemia.  Critical Care Medicine.  1998; 26:1807-1810.  [ Abstract on PubMed ].


M. Feldman, N. Soni, and B. Dickson. Influence of hypoalbuminemia or hyperalbuminemia on the serum anion gap. J Lab Clin Med. 2005; 146(6): 317-320. [ Abstract on PubMed ].

J.A Kraut JA, and N.E. Madias. Serum anion gap: its uses and limitations in clinical medicine. Clin J Am Soc Nephrol. 2007; 2: 162–174. [ Full Text is available online at http://cjasn.asnjournals.org/content/2/1/162.long ].

L.S Chawla, S. Shih, D. Davison, C. Junker, and M.G. Seneff. Anion gap, anion gap corrected for albumin, base deficit and unmeasured anions in critically ill patients: implications on the assessment of metabolic acidosis and the diagnosis of hyperlactatemia. BMC Emergency Medicine. 2008; 8: 18. [ Full Text is available online at http://www.biomedcentral.com/1471-227X/8/18 ].

T.J. Morgan. Unmeasured ions and the strong ion gap. In Stewart's Textbook of Acid-Base. Kellum JA and Elbers PWG, editors. Amsterdam: AcidBase.org. 2009. Chapter 18, pages 323-337.

M. Berkman, J. Ufberg, L.A. Nathanson, and N.I. Shapiro. Anion gap as a screening tool for elevated lactate in patients with an increased risk of developing sepsis in the emergency department. J Emerg Med. 2009; 36: 391-394. [ Abstract on PubMed ].

J.A. Kraut, and N.E. Madias. Metabolic acidosis: pathophysiology, diagnosis and management. Nat. Rev. Nephrol. 2010: 6: 274–285. [ Abstract on PubMed ].

J. Mallat, D. Michel, P. Salaun, D. Thevenin, and L. Tronchon. Defining metabolic acidosis in patients with septic shock using Stewart approach. Am J Emerg Med. 2012; 30: 391-398. [ Abstract on PubMed ].

M.S. Lipnick, A.B. Braun, J.T.-W. Cheung, F.K. Gibbons, and K.B. Christopher. The difference between critical care initiation anion gap and prehospital admission anion gap is predictive of mortality in critical illness. Crit Care Med. 2013; 41: 49–59. [ Abstract on PubMed ].

K. Berend K, A.P.J de Vries, and R.O.B. Gans. Physiological approach to assessment of acid-base disturbances. N Engl J Med. 2014; 371: 1434-1445. [ Abstract on PubMed ].

James Figge.  Integration of Acid-Base Disorders and Electrolyte Disorders [correspondence].  The New England Journal of Medicine.  2015; 372:390.  [ Full Text ].





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