6 Recommendations, 7 Nomenclature,
8 References, 9 Appendix

Contents of Section

6 Recommendations on Thermodynamic Tables
7 Nomenclature
8 References
9 Appendix: Survey of Current Biochemical Tables

The papers by Alberty (ref. 5) and Alberty and Goldberg (ref. 7) show four types of tables of thermodynamic properties of biochemical reactants: (1) G ^o and H ^o for species at 298.15 K, 1 bar (0.1 MPa), I = 0. (2) G ^o and H ^o for species at 298.15 K, 1 bar, I = 0.25 M. (3) G '^o and H '^o for species at 298.15 K, 1 bar, pH = 7, pMg = 3, and I = 0.25 M. (4) G '^o and H '^o for reactants (sum of species) at 298.15 K, 1 bar, pH = 7, pMg = 3, and I = 0.25 M. Table 1 contains the most basic information for calculating G ^o and H ^o for reference reactions at I = 0 and corresponds with the NBS and CODATA Tables. Table 4 is the most convenient for calculating G '^o and H '^o under normal experimental conditions of 298.15 K, 1 bar, pH = 7, pMg = 3, and I = 0.25 M. Currently, thermodynamic information in biochemistry is stored as K ' and H '^o when pH and pMg are specified and as K and H ^o for reactions in terms of species. In order to calculate K ' and H '^o or K and H ^o for a reaction that has not been studied, it is currently necessary to add and subtract known reactions. It would be more convenient to be able to look up reactants in a table and add and subtract their formation properties to calculate K ' and H '^o or K and H ^o, as is usually done for chemical reactions. One reactant can be involved in hundreds of reactions, and so it is more economical to focus on the reactants. The usefulness of such a table increases rapidly with its length. As mentioned in Section 4.3, columns for _H(i ) and _Mg(i ) can be included so that thechange in binding of H and Mg at specified T, P, pH, pMg, and I can be readily calculated by use of equations 30 and 31.

The choice of 298.15 K, 1 bar, pH = 7, pMg = 3, and I = 0.25 M is arbitrary, but these conditions are often used. Tables can be constructed for other conditions (T, pH, pMg, and I) if sufficient information is available. H₂O has to be included in this table because its G '^o(H₂O) and H '^o(H₂O) have to be included in the summations in equations 40 and 41 when it is a reactant, even though H₂O is omitted in the expression for the apparent equilibrium constant.

The most basic principle is that thermodynamic tables on biochemical reactants at pH = 7 and pMg = 3 should be consistent with the usual thermodynamic tables to as great an extent as possible. A great deal is already known about the thermodynamics of reactions in aqueous solution, and this is all of potential value in biochemistry. The standard transformed formation properties of inorganic phosphate and glucose 6-phosphate at pH = 7 and pMg = 3 can be calculated since the standard formation properties of inorganic phosphate and glucose are well known and the properties of glucose 6-phosphate can be calculated from G '^o and H '^o for the glucose 6-phosphatase reaction. This is true for many other biochemical reactants. Sometimes it is necessary to use the convention that G ^o = H ^o = 0 for a reference species, as described in the discussion of the ATP series. It is difficult and expensive to obtain these missing data because biochemical reactants are often rather large molecules and contain a large number of elements. The methods described here make it possible to calculate G '^o and H '^o for P_i , glucose 6-phosphate, adenosine, AMP, ADP, and ATP at temperatures in the approximate range 273-320 K, pH in the approximate range 3-10, pMg in the range above about 2, and ionic strengths in the approximate range 0-0.35 M. Since the choice of reference species is arbitrary to a certain extent, it is desirable to have international agreement on these choices. This agreement is required so that thermodynamic properties in different tables of this type can be used together.

For many biochemical reactants, the acid and magnesium complex dissociation constants have not been measured, but this does not mean that these reactants cannot be included in a table of G '^o and H '^o at 298.15 K, pH = 7, pMg = 3, and I = 0.25 M. What is required is that the apparent equilibrium constant K ' for a reaction involving this reactant (or pair of reactants) with reactants with known properties has been determined at pH = 7, pMg = 3, and I = 0.25 M at more than one temperature. If the pKs of a reactant are unknown, there is a problem in calculating the equilibrium pMg, but this uncertainty may not be large if the concentration of Mg²⁺ is controlled by a buffer with known binding properties and the equilibrium concentration of the reactants is low.

The fact that biochemical reactions are often organized in series will facilitate the construction of thermodynamic tables. When a series starts or ends with a reactant with known formation properties, knowlege of the apparent equilibrium constants in the series makes it possible to calculate G '^o for reactants in the series at pH = 7. For example, consider glycolysis for which the apparent equilibrium constants for the 10 reactions have been known for some time. Since the standard transformed thermodynamic properties of glucose in aqueous solution are known, the G '^o values for the 17 reactants at pH = 7, including pyruvate, can be calculated with just one problem. Since G ^o is not known for NAD or NADH, one of the species has to be assigned G ^o = H ^o = 0. Since the thermodynamic properties of pyruvate are known, this provides a check on the calculation of G_i '^o of the reactants in glycolysis.

The following conventions are recommended:

1. When a reactant exists only in an electrically neutral form at pH = 7 and pMg = 3 and G ^o and H ^o for that form in dilute aqueous solution are known, the values of G '^o and H '^o are calculated by adjusting for the content of H. An example is glucose.

2. When a reactant exists in a single ionized form in the neighborhood of pH = 7 and pMg = 3, the values of G ^o and H ^o for that form in the usual tables (which apply at I = 0) have to be adjusted to I = 0.25 M with the extended Debye-Hückel theory and adjusted for H to obtain the entry to the table of G '^o and H '^o values. Obviously, thermodynamic properties of H⁺ and Mg²⁺ will not be found in the table of G '^o values. Also, ions like Ca²⁺ which bind significantly with multiply charged negative species of biochemical reactants cannot be put in the table because they require treatment like Mg²⁺. Values of G ^o and H ^o for Krebs cycle intermediates that exist at pH = 7 and pMg = 3 in a single ionic form calculated by Miller and Smith-Magowan (Appendix, ref. 8) can be adjusted for H and Mg and used in the proposed table after the values have been corrected to I = 0.25 M. An example is succinate.

3. When a reactant exists in several ionized or complexed forms that are at equilibrium at pH = 7 and pMg = 3 and the standard thermodynamic properties of all of the ionized and complexed forms are known, the values of G '^o and H '^o of reactants at pH = 7, pMg = 3 , I = 0.25 M can be calculated using isomer group thermodynamics. Examples are inorganic phosphate (P_i), pyrophosphate, carbonate, citrate, and glucose 6-phosphate.

4. When a reactant exists in several ionized or complexed forms with known dissociation constants and G ^o and H ^o are not known for any species of the reactant, G '^o and H '^o for the species can only be calculated by assigning one of them G ^o = H ^o = 0 in dilute aqueous solution. The G ^o and H ^o values of the various species have to be adjusted to an ionic strength of 0.25 M, and adjusted for H and Mg, so that G '^o and H '^o can be calculated for the reactant (sum of species) by use of isomer group thermodynamics, as illustrated here for the ATP series. NAD and NADH also provide an example, which is a little different because the acid and magnesium complex dissociation constants are believed to be identical.

5. If acid dissociation and magnesium dissociation constants are not known for a reactant, it can still be put into a table at pH = 7 and pMg = 3 if apparent equilibrium constants have been measured under these conditions for a reaction involving this reactant with other reactants whose transformed thermodynamic properties are known. Examples are the many reactants in glycolysis other than glucose, ATP, ADP, Pi, NAD, NADH, and H₂O.

6. It is not necessary to have columns in tables for S '^o and S ^o because these can be treated as dependent properties and can be calculated from equations 25 and 42.

7. NOMENCLATURE

Symbol	Name	Unit
A	extensive Helmholtz energy of a system	kJ
B	parameter in the extended Debye-Hückel theory	L-1/2 mol-1/2
ci	concentration of species i	mol L-1
co	standard state concentration (1 M)	mol L-1
CPo	standard heat capacity at constant pressure of reaction at T, P, and I	J K-1 mol-1
CP'o	standard transformed heat capacity of reaction at constant T, P, pH, pMg, and I	J K-1 mol-1
E	electromotive force	V
Eo	standard electromotive force of a cell or half cell	V
E '	apparent electromotive force at specified pH	V
E 'o	standard apparent electromotive force of a cell or half cell at specified pH	V
F	Faraday constant (96 485.31 C mol-1)	C mol-1

G	extensive Gibbs energy of a system	kJ
G '	extensive transformed Gibbs energy of a system	kJ
G	reaction Gibbs energy for specified concentrations of species at specified T, P, and I	kJ mol-1
Go	standard reaction Gibbs energy of a specified reaction in terms of species at specified T, P, and I	kJ mol-1
G '	transformed reaction Gibbs energy in terms of reactants (sums of species) for specified concentrations of reactants and products at specified T, P, pH, pMg, and I	kJ mol-1
G 'o	standard transformed reaction Gibbs energy of a specified reaction in terms of reactants (sums of species) at specified T, P, pH, pMg and I	kJ mol-1
G(i)	Gibbs energy of formation of species i at a specified concentration of i and specified T, P, and I	kJ mol-1
Go(i)	standard Gibbs energy of formation of species i at specified T, P, and I	kJ mol-1
G '(i)	transformed Gibbs energy of formation of species i or reactant i (sum of species) at specified concentration and specified T, P, pH, pMg, and I	kJ mol-1
G 'o(i)	standard transformed Gibbs energy of formation of species i or reactant i (sum of species) at specified T, P, pH, pMg, and I	kJ mol-1

H	extensive enthalpy of a system	kJ
H '	extensive transformed enthalpy of a system	kJ
H(cal)	calorimetrically determined enthalpy of reaction that includes the enthalpies of reaction of H+ and Mg2+ (consumed or produced) with any buffer in solution	kJ mol-1
H	enthalpy of reaction of a specified reaction in terms of species at specified T, P, and I	kJ mol-1
Ho	standard enthalpy of reaction of a specified reaction in terms of species at specified T, P, and I	kJ mol-1
H '	transformed enthalpy of reaction of a specified reaction in terms of reactants (sums of species) for specified concentrations of reactants and products at specified T, P, pH, pMg, and I	kJ mol-1
H 'o	standard transformed enthalpy of a specified reaction in terms of reactants (sums of species) at specified T, P, pH, pMg and I	kJ mol-1
H(i)	enthalpy of formation of species i at specified T, P, and I	kJ mol-1
Ho(i)	standard enthalpy of formation of species i at specified T, P, and I	kJ mol-1
H '(i)	transformed enthalpy of formation of species i or reactant i (sum of species) at specified T, P, pH, pMg, and I	kJ mol-1
H 'o(i)	standard transformed enthalpy of formation of species i or reactant i (sum of species) at specified T, P, pH, pMg, and I	kJ mol-1

I	ionic strength	mol L-1
K	equilibrium constant for a specified reaction written in terms of concentrations of species at specified T, P, and I (omitting H2O when it is a reactant)	dimensionless
K '	apparent equilibrium constant for a specified reaction written in terms of concentrations of reactants (sums of species) at specified T, P, pH, pMg, and I (omitting H2O when it is a reactant)	dimensionless
mi	molality of i	mol kg-1
ni or n(i)	amount of species i	mol
n'(i)	amount of species (bound and unbound) or amount of reactant i (that is, sum of species)	mol

NH(i)	number of H atoms in species i	dimensionless
NMg(i)	number of Mg atoms in species i	dimensionless
H(i)	average number of H atoms in reactant i at specified T, P, pH, pMg, and I	dimensionless
N(H+)	change in binding of H+ in a biochemical reaction at specified T, P, pH, pMg, and I	dimensionless
N(Mg2+)	change in binding of Mg+2 in a biochemical reaction at specified T, P, pH, pMg, and I	dimensionless
NI	number of isomers in an isomer group	dimensionless
pH	-log10([H+]/c o)	dimensionless
pMg	-log10([Mg2+]/c o)	dimensionless
pX	-log10([X]/c o)	dimensionless
P	pressure	bar
Q	reaction quotient of specified concentrations of species in the same form as the equilibrium constant expression	dimensionless
Q '	apparent reaction quotient of specified concentrations of reactants and products (sum of species) in the same form as the apparent equilibrium constant expression	dimensionless
R	gas constant (8.31451 J K-1 mol-1)	J K-1 mol-1
ri or r(i)	equilibrium mole fraction of i within a specified class of molecules	dimensionless

S	extensive entropy of a system	J K-1
S '	extensive transformed entropy of a system	J K-1
	standard molar entropy of species i at specified T, P, and I	J K-1 mol-1
	standard molar transformed entropy of species i or reactant i at specified T, P, pH, pMg, and I	J K-1 mol-1
S	entropy of reaction of a specified reaction in terms of species at specified T, P, and I	J K-1 mol-1
So	standard entropy of reaction of a specified reaction in terms of ionic species at specified T, P, and I	J K-1 mol-1
S '	transformed entropy of reaction of a specified reaction in terms of reactants (sums of species) for specified concentrations of reactants and products at specified T, P, pH, pMg, and I	J K-1 mol-1
S 'o	standard transformed entropy of a specified reaction in terms of sums of species at specified T, P, pH, pMg and I	J K-1 mol-1
So(i)	standard entropy of formation of species i at specified T, P, and I	J K-1 mol-1
S 'o(i)	standard transformed entropy of formation of species i or reactant i (sum of species) at specified T, P, pH, pMg, and I	J K-1 mol-1

T	temperature	K
U	extensive internal energy of a system	kJ
V	volume	L
zi	charge of ion i with sign	dimensionless
	density	kg m-3
(i )	chemical potential of species i at specified T, P, and I	kJ mol-1
'(i )	transformed chemical potential of species i or reactant (sum of species) at specified T, P, pH, pMg, and I [can be replaced by G '(i )]i	kJ mol-1
o(i )	standard chemical potential of species i at specified T, P, and I [can be replaced by Go(i )]	kJ mol-1
e	number of electrons in a cell reaction	dimensionless
i or (i )	stoichiometric number of species i in a specified chemical reaction	dimensionless
'(i )	apparent stoichiometric number of reactant i in a specified biochemical reaction	dimensionless

8. REFERENCES

1. Wadsö, I., Gutfreund, H., Privlov, P., Edsall, J. T., Jencks, W. P., Strong, G. T., and Biltonen, R. L. (1976) Recommendations for Measurement and Presentation of Biochemical Equilibrium Data, J. Biol. Chem. 251, 6879-6885; (1976) Q. Rev. Biophys. 9, 439-456.

2. Wadsö, I., and Biltonen, R. L.(1985) Recommendations for the Presentation of Thermodynamic Data and Related Data in Biology, Eur. J. Biochem. 153, 429-434.

3. Mills, I., Cvitas, T., Homann, K., Kallay, N., and Kuchitsu, K. (1988 and 1993) Quantities, Units and Symbols in Physical Chemistry, Blackwell Scientific Publications, Oxford.

4. Alberty, R. A. (1992) Biophys. Chem. 42, 117-131.

5. Alberty, R. A. (1992) Biophys. Chem. 43, 239-254.

6. Clarke, E. C. W., and D. N. Glew, D. N. (1966) Trans. Faraday Soc. 62, 539-547.

7. Alberty, R. A., and Goldberg, R. N. (1992) Biochemistry 31, 10610-10615.

8. Wilhoit, R. C. (1969) Thermodynamic Properties of Biochemical Substances, in Biochemical Microcalorimetry, H. D. Brown, ed., Academic Press, New York.

9. Alberty, R. A. (1969) J. Biol. Chem. 244, 3290-3302.

10. Alberty, R. A. (1992) J. Phys. Chem. 96, 9614-9621.

11. Alberty, R. A., and Goldberg, R. N. (1993) Biophys. Chem. 47, 213-223.

12. Teague, W. E., and Dobson, G. P. (1992) J. Biol. Chem. 267, 14084-14093.

13. Webb, E. C. (1992) Enzyme Nomenclature, Academic Press, San Diego.

14. Alberty, R. A., and Cornish-Bowden, A. (1993) Trends Biochem. Sci. 18, 288-291.

15. Cech, T. R., Herschlag, D., Piccirilli, J. A., and Pyle, J. A. (1992) J. Biol. Chem. 256, 17479-82.

16. Blackburn, G. M., Kang, A. S., Kingsbury, G. A., and Burton, D. R. (1989) Biochem. J. 262, 381-391.

17. Pike, V. W. (1987) in Biotechnology (H.-J. Rehm and G. Reed, eds.), vol. 7a, 466-485, Verlag-Chemie.

18. "A Guide to the Procedures for the Publication of Thermodynamic Data", (1972) PureAppl. Chem. 289, 399-408. (Prepared by the IUPAC Commission on Thermodynamics and Thermochemistry.)

19. "Guide for the Presentation in the Primary Literature of Numerical Data Derived from Experiments". (February 1974) Prepared by a CODATA Task Group. Published in National Standard Reference Data System News.

20. Alberty, R. A., and Oppenheim, I. (1988) J. Chem. Phys. 89, 3689-3693.

21. Alberty, R. A., and Oppenheim, I. (1992) J. Chem. Phys. 96, 9050-9054.

22. Wyman, J., and Gill, S. J. (1990) Binding and Linkage, University Science Books, Mill Valley, CA.

23. Smith, W. R., and Missen, R. W. (1982) Chemical Reaction Equilibrium Analysis: Theory and Algorithms, Wiley-Interscience, New York.

24. Alberty, R. A. (1983) I & EC Fund. 22, 318-321.

25. Goldberg, R. N., and Tewari, Y. B. (1989) J. Phys. Chem. Ref. Data 18, 809-880.

26. Larson, J. W., Tewari, Y. B., and Goldberg, R. N. (1993) J. Chem. Thermodyn. 25, 73-90.

27. Goldberg, R. N., and Tewari, Y. B. (1991) Biophys. Chem. 40, 241-261.

28. Clarke, E. C. W., and Glew, D. N. (1980) J. Chem. Soc., Faraday Trans. 1 76, 1911-1916.

29. Pitzer, K. S. (1991) Ion Interaction Approach: Theory and Data Correlation, in Activity Coefficients in Electrolyte Solutions, 2nd Edition, K. S. Pitzer, editor, CRC Press, Boca Raton, Fla.

30. Record, M. T., Anderson, C. F., and Lohman, T. M. (1978) Q. Rev. Biophys. 11, 2.

31. Anderson, C. F., and Record, M. T. (1993) J. Phys. Chem. 97, 7116-7126.

32. Alberty, R. A. (1993) Pure Appl. Chem. 65, 883-888.

33. Guynn, R. W., and Veech, R. L. (1973) J. Biol. Chem. 248, 6966-6972.

34. Alberty, R. A. (1991) J. Chem. Educ. 68, 984.

35. Alberty, R. A. (1992) J. Chem. Educ. 69, 493.

36. Alberty, R. A. (1994) Biophys. Chem. 49, 251-261.

9. APPENDIX: SURVEY OF CURRENT BIOCHEMICAL THERMODYNAMIC TABLES
(The reader is cautioned on distinguishing chemical reactions from biochemical reactions.)

1. Burton, K., Appendix in Krebs, H. A., and Kornberg, H. L. (1957) Energy Transformations in Living Matter, Springer-Verlag, Berlin.

2. Atkinson, M. R., and R. K. Morton, R. K. (1960) in Comparative Biochemistry, Volume II, Free Energy and Biological Function, Florkin, M., and Mason, H. (eds.), Academic Press, New York.

3. Wilhoit, R. C. (1969) Thermodynamic Properties of Biochemical Substances, in Biochemical Microcalorimetry, H. D. Brown (ed.), Academic Press, New York. This article gives standard thermodynamic properties of a large number of species at zero ionic strength. In a separate table standard enthalpies and standard Gibbs energies of formation of adenosine phosphate species are given relative to H₂ADP^- at 298.15 K.

4. Thauer, R. K., Jungermann, K., and Decker, K. (1977) Bacteriological Reviews 41, 100-179. Standard Gibbs energies of formation of many species of biochemical interest at 298.15 K. Table of standard Gibbs energies of reaction corrected to pH 7 by adding mG ^o(H⁺), where m is the net number of protons in the reaction.

5. Goldberg, R. N. (1984) Compiled thermodynamic data sources for aqueous and biochemical systems: An annotated bibliography (1930-1983), National Bureau of Standards Special Publication 685, U. S. Government Printing Office, Washington, D. C. A general and relatively complete guide to compilations of thermodynamic data on biochemical and aqueous systems.

6. Rekharsky, M. V., Galchenko, G. L., Egorov, A. M., and Berezin, I. V. (1986) Thermodynamics of Enzymatic Reactions, in Thermodynamic Data for Biochemistry and Biotechnology, H.-J. Hinz (ed.), Springer-Verlag, Berlin. Tables of H ^o, G ^o, and S ^o at pH 7 and 298.15 K, but the reactions are written in terms of ionic species so that there is a question about the interpretation of the parameters.

7. Goldberg, R. N., and Tewari, Y. B. (1989) Thermodynamic and Transport Properties of Carbohydrates and their Monophosphates: The Pentoses and Hexoses, J. Phys. Chem. Ref. Data 18, 809-880 . Values on a very large number of reactions at 298.15 K carefully extrapolated to zero ionic strength. H ^o and G ^o for a large number of sugars and their phosphate esters.

8. Miller, S. L., and Smith-Magowan, D. (1990) The Thermodynamics of the Krebs Cycle and Related Compounds, J. Phys. Chem. Ref. Data 19, 1049-1073. A critical evaluation for a large number of reactions and properties of substances at 298.15 K.

9. Goldberg, R. N., and Tewari, Y. B. (1991) Thermodynamics of the Disproportionation of adenosine 5'-diphosphate to adenosine 5'-triphosphate and Adenosine 5'-monophosphate, Biophys. Chem. 40, 241-261. Very complete survey of data on this reaction and on the acid dissociation and magnesium complex dissociations involved.

10. Goldberg, R. N., Tewari, Y. B., Bell, D., Fazio, K., and Anderson, E. (1993) Thermodynamics of Enzyme-Catalyzed Reactions; Part 1. Oxidoreductases, J. Phys. Chem. Ref. Data, 22, 515-582. This review contains tables of apparent equilibrium constants and standard transformed molar enthalpies for the biochemical reactions catalyzed by the oxidoreductases.

11. Goldberg, R. N., and Tewari, Y. B. (1994) Thermodynamics of Enzyme-Catalyzed Reactions: Part 2. Transferases, J. Phys. Chem. Ref. Data 23, 547-617.

Standard Thermodynamic Tables

1. Wagman, D. D., Evans, W. H., Parker, V. B., Schumm, R. H., Halow, I., Bailey, S. M., Churney, K. L., and Nutall, R. L. (1982) The NBS Tables of Chemical Thermodynamic Properties, J. Phys. Chem. Ref. Data, 11, Suppl. 2.

2. Cox, J. D., Wagman, D. D., and Medvedev, M. V. (1989) CODATA Key Values for Thermodynamics, Hemisphere, Washington, D. C.