Thermodynamics of Enzyme-Catalyzed Reactions

It is the aim of this project to provide a compilation of data on the thermodynamics of enzyme-catalyzed reactions. The data presented herein is limited to direct equilibrium and calorimetric measurements performed on these reactions under in vitro conditions. This is the principal thermodynamic information that is needed to determine the position of equilibrium of a given reaction.

The following information is given for each entry in this database: the reference for the data; the reaction studied; the name of the enzyme used and its Enzyme Commission number; the method of measurement; the conditions of measurement (temperature, pH, ionic strength, and the buffer(s) and cofactor(s) used); the data and an evaluation of it; and, sometimes, commentary on the data and on any corrections which have been applied to it. The absence of a piece of information indicates that it was not found in the paper cited.

While the above scheme is a useful way to order the thermodynamic data on enzyme-catalyzed reactions, one possible complication is that a given reaction can sometimes be catalyzed by more than one enzyme. Also, we have generally relied upon the author(s) of a given study for the identification of the enzyme. The user of these tables is therefore advised, when looking for data on a given reaction, to also look in these tables under those enzymes that catalyze reactions that are closely related to the one sought.

The complete evaluation of the data contained in these tables would involve the adjustment of the results obtained for each reaction to a common standard state followed by thermochemical cycle calculations to determine how well the data for the various reactions fit together. The adjustment to a standard state generally requires thermodynamic data on hydrogen and metal ion binding to the substrates involved in the reaction as well as information on the activity coefficients of the species in the solution.¹³ This is beyond the scope of this database. It is our belief that this complete evaluation would have great value in the organization and systematization of these data. However, such evaluations have been performed only for a limited set of biochemical substances and reactions (see refs. 6, 9, and 10). These evaluations, which involved a solution of thermochemical networks, also included thermodynamic data on the condensed phases and, in some cases, electrochemical potentials. Thus, third law entropies and enthalpies of combustion, enthalpies of solution, solubilities, and activity coefficients were also included to make the necessary thermodynamic ties to the condensed phases.

It is highly desirable that equilibrium be approached from both directions in any equilibrium investigation. The failure of some investigators to do this is a serious oversight in the experimental work and is a primary source of systematic error in much of the "equilibrium" data reported in the literature. Another source of systematic error in many of these studies is sample impurity. As an example, Miller and Smith-Magowan¹⁰ have pointed out that samples of nicotinamide-adenine dinucleotide (NAD) and nicotinamide-adenine dinucleotide phosphate (NADP) can also contain the respective -isomers. Since, most enzymes are specific for the -isomer, the presence of an unrecognized amount of the -isomer can be a source of systematic error in equilibrium or calorimetric measurements. Occasionally, we have performed calculations on the data given in the papers or extracted values from figures in the papers. For example, we have sometimes been able to calculate an equilibrium constant where none has previously been calculated, e.g. if the investigator(s) have given results in terms of per cent conversion for a reaction of the type A = B.

ATP(aq) + H₂O(l) = ADP(aq) + orthophosphate(aq). (1)

The apparent equilibrium constant for the overall biochemical reaction (1) is

K_c' = c(ADP)c(orthophosphate)/{c(ATP)c^o}. (2)

The ATP, ADP, and orthophosphate each exist in several different ionized and metal bound forms: e.g. ATP^4-, HATP^3-, H₂ATP^2-, MgATP^2-, MgHATP^-, etc. Thus, ATP has often been denoted in the literature as ATP or as (ATP)_tot. When it is clear that one is dealing with total amounts of substances, it is not necessary to use either the or "tot" and these designations can be dispensed with. This has been done throughout the tables of data. In the above equation, c^o is 1 mol dm^-3; it is included to make the apparent equilibrium constant dimensionless. The subscript c has been attached to the apparent equilibrium constant to indicate that it is based on the concentration (molarity) scale.

The apparent equilibrium constant can be used to calculate the standard transformed Gibbs energy of reaction _rG'^o at specified conditions of temperature T, pressure p, ionic strength (I_m when the units are mol kg^-1 and I_c when the units are mol dm^-3), pH, and pMg:

_rG'^o = -RT lnK'. (3)

The gas constant R is equal to 8.31451 J K^-1 mol^-1. Either _rG'^oor the apparent equilibrium constant K' can be used to determine the position of equilibrium of biochemical reactions.^14,15

It is also possible to choose a reference reaction involving selected solute species:

ATP^4-(aq) + H₂O(l) = ADP^3-(aq) + HPO₄^2-(aq) + H⁺(aq). (4)

The equilibrium constant for this reference reaction is

K_c(ref) = c(ADP^3-)c(HPO₄^2-)c(H⁺)/{c(ATP^4-)(c^o)²}. (5)

Equations which relate these two different types of equilibrium constants have been derived.^16,17 To calculate the equilibrium constant K_c(ref) from the apparent equilibrium constant K, or vice versa, one needs the equilibrium constants for the binding of hydrogen and metal ions to ATP^4-, ADP^3-, and HPO₄^2-.

The standard or thermodynamic equilibrium constant for reaction (4) is written in terms of activities a:

K(ref) = a(ADP^3-)a(HPO₄^2-)a(H⁺)/{a(ATP^4-)a(H₂O)}. (6)

The determination of K(ref) requires either a knowledge of both K_c(ref) at a single ionic strength and of the appropriate ratio of activity coefficients or an extrapolation of values of K_c(ref), determined at several ionic strengths, to I = 0. The distinction between the equilibrium constant K_c(ref), as given in Eq. (5), and the apparent equilibrium constant K, as given in Eq. (2), will be maintained throughout this database. Where possible, we have also included calculated values of standard equilibrium constants which were given in the various papers examined.

To avoid confusion between these different types of equilibrium constants and to avoid ambiguity about whether specific species or sums of species are intended, ammonia, for example rather than NH₃ or NH₄⁺, will be written when we mean total ammonia. The chemical formulas will be used when we mean one of these specific species. Other substances such as carbon dioxide (CO₂, HCO₃^-, and CO₃^2-), and orthophosphate (H₂PO₄^-, HPO₄^2-, and PO₄^3-) will be treated in the same manner. Exceptions will be made for water which will always be written as H₂O and for gaseous hydrogen and oxygen which will be written as H₂(g) and O₂(g), respectively.

A similar situation exists for enthalpies of reaction. Thus, the standard transformed enthalpy change for a biochemical reaction (e.g. reaction (1) above) at specified conditions of temperature, pressure, pH, pMg, and ionic strength will be designated as _rH'^o and the enthalpy change for a reference reaction (e.g. reaction (4) above) as _rH^o(ref). Enthalpy changes for a reference reaction which have been adjusted to a standard state will be designated as _rH^o(ref) at I = 0. The standard transformed enthalpy of reaction _rH'^o can be calculated with the van't Hoff equation from apparent equilibrium constants which have been determined as a function of temperature. Unless indicated otherwise, we have assumed that _rH'^o is independent of temperature (i.e. _rC_p^'o = 0) when performing this calculation. An enthalpy of reaction which has been determined calorimetrically will be designated as _rH(cal). To obtain either _rH'^o or _rH^o(ref) from calorimetric data requires that corrections be made for heat effects due to possible changes in pH, pMg, ionic strength, and for the protonation of the buffer. In the case where the solutions are well buffered and the changes in pH, pMg, and ionic strength are small, the major correction is for the enthalpy of protonation of the buffer by any protons released (or absorbed) as a consequence of the reaction. Thus,

_rH'^o = _rH(cal) - _rN(H⁺)_rH^o(buff) (7)

where _rN(H⁺) is the change in the binding of H⁺(aq) accompanying the biochemical reaction and _rH^o(buff) is the enthalpy of ionization of the buffer. Since this correction can be substantial, it will always be noted in these tables whether or not calorimetric results have been corrected for the enthalpy of protonation of the buffer. Unless indicated otherwise, we have relied upon the correction(s) made by the actual investigators. Enthalpies of reaction calculated from equilibrium constants measured at several temperatures require no such correction.

In this database, all units of energy are given in terms of the joule with conversions from results in calories based upon 1 cal = 4.184 J. The equilibrium and calorimetric results summarized in this database were all done at atmospheric pressure ( 0.101325 MPa). The standard pressure for thermodynamic results is 0.1 MPa.

Occasionally, some investigators have calculated apparent equilibrium constants where the concentration of water was included. Thus, for the above example involving ATP hydrolysis, the apparent equilibrium constant might be written as

K_c' = c(ADP)c(orthophosphate)/{c(ATP)c(H₂O)}. (8)

Where this has been done, we have adjusted the reported values of K to the usual convention represented by Eq. (2). At low solute concentrations, the concentration of water c(H₂O) is 55.35 mol dm^-3 at 298.15 K and 55.14 mol dm^-3 at 310.15 K.

Equilibrium constants should be expressed as dimensionless quantities. However, the numerical value obtained for the equilibrium constant of an unsymmetrical reaction will depend upon the measure of composition and standard concentration selected for the reactants and products. Thus, for the chemical reaction

A(aq) = B(aq) + C(aq), (9)

K_c = c(B)c(C)/{c(A)c^o}, K_m = m(B)m(C)/{m(A)m^o}, and K_x = x(B)x(C)/x(A). Here, m and x are, respectively, molality and mole fraction and m^o = 1 mol kg^-1. The equilibrium constant expressed in terms of mole fractions is automatically dimensionless. In this database, the various types of equilibrium constants for unsymmetrical reactions are denoted by their appropriate subscripts; no subscript is needed for a symmetrical reaction. When necessary, results have been adjusted to units of mol dm^-3 to obtain the numerical value(s) of K_c given in these tables.

The density of the solution enters into the conversion of equilibrium constants which have been determined on a concentration basis, namely K_c to K_m, or K_c to K_x. This causes a slight complication in the calculation of the enthalpy of reaction from the derivative of K_c with respect to temperature since the derivative of the density of the solution with respect to temperature enters into this calculation. Fortunately, this is a small effect that can be neglected except for the most precise and accurate data. Also, this is not a problem for symmetrical reactions where the equilibrium constants are the same for any standard state concentration. Enthalpies of reaction calculated from the temperature derivatives of equilibrium constants which are on a molality or mole fraction basis are identical to calorimetrically determined enthalpies of reaction which have been corrected for the enthalpy of buffer protonation.

Alcohol dehydrogenase (EC 1.1.1.1) catalyzes the NAD/NADH coupled conversion of ethanol to acetaldehyde:

NAD(aq) + ethanol(aq) = NADH(aq) + acetaldehyde(aq). (10)

The apparent equilibrium constant for the overall biochemical reaction (9) is

K' = c(NADH)c(acetaldehyde)/{c(NAD)c(ethanol)}. (11)

The reference reaction corresponding to reaction (9) is:

NAD^-(aq) + ethanol(aq) = NADH^2-(aq) + acetaldehyde(aq) + H⁺(aq). (12)

The equilibrium constant for this reference reaction is:

K_c(ref) = c(NADH^2-)c(acetaldehyde)c(H⁺)/{c(NAD^-)c(ethanol)c^o}. (13)

In some cases, however, investigators have written:

NAD(aq) + ethanol(aq) = NADH(aq) + acetaldehyde(aq) + H⁺(aq). (14)

This is neither a chemical reference reaction nor an (overall) biochemical reaction. It is an incorrect representation because it implies that exactly one hydrogen ion was produced in the reaction. This may not always be the situation. Secondly, the equation is not electrically balanced (it would only appear to be balanced if one were to write NAD⁺ instead of NAD). In papers where this reaction has been written as in Eq. (14), the investigators have often given the quantity [c(NADH)c(acetaldehyde)c(H⁺)/{c(NAD)c(ethanol)c^o}] which is equal to [K'c(H⁺)/c^o]. Since this quantity is not an apparent equilibrium constant, the standard transformed Gibbs energy of reaction should not be calculated from it. Thus, when investigators have given numerical values of the apparent equilibrium constant K according to Eq. (11), we have included the results in these tables. However, when the only result reported is K'c(H⁺)/c^o, it is also given in these tables along with the pH range over which the measurements were performed. However, we have rewritten the reaction and, when possible, calculated the apparent equilibrium constant in accord with Eq. (10). The oxidized form of nicotinamide-adenine dinucleotide, which is generally written as NAD⁺ in the literature, does not have an electrical charge of +1 and, for this reason, a superscript + has not been attached to the NAD. The charges attached to the NAD and NADH in reaction (12) are those that would be expected for the predominant ionic forms at pH = 7. The assignment of these charges is based upon an examination of the structures of these substances and a knowledge of the acidity constants of the reactants and products (see below).

For reaction (10) and many similar reactions, the quantity K'c(H⁺)/c^o has frequently been found to be independent of pH. The reason for this is that NAD has a pK of 3.88,^18,19 NADH a pK of 4.46,¹⁹ and the ethanol and acetaldehyde are not ionized unless placed in extremely alkaline solutions. Thus, at neutral pH, the predominant species in aqueous solution are NAD^-, NADH^2-, ethanol⁰, and acetaldehyde⁰. These same species should also be predominant for 5 < pH < 10. Because of this, the quantity [c(NADH)c(acetaldehyde)c(H⁺)/{c(NAD)c(ethanol)c^o}] = [K'c(H⁺)/c^o] is very nearly equal to K_c(ref). The situation for NADP/NADPH coupled reactions is similar to that for NAD/NADH reactions. The only difference is that NADP also has a pK at 6.1 due to the ionization of the phosphate group attached at the 2'-hydroxyl position in the adenosine.²⁰ On the basis of structure, one would expect the pKs for the ionization of this phosphate group to be nearly equal for both NADP and NADPH. Thus, the statements made above regarding the thermodynamics of NAD/NADH coupled reactions should also be true for NADP/NADPH coupled reactions.

The review of Miller and Smith-Magowan¹⁰ contains a discussion of some thermodynamic pathways leading to the standard Gibbs energy and enthalpy changes for the following reactions:

NAD^-(aq) + H₂(g) = NADH^2-(aq) + H⁺(aq), (15)

NADP^3-(aq) + H₂(g) = NADPH^4-(aq) + H⁺(aq). (16)

For reaction (15) at T = 298.15 K and I_m = 0.1 mol kg^-1, Miller and Smith-Magowan¹⁰ give _rG^o = 20.0 kJ mol^-1 and _rH^o = -32.1 kJ mol^-1. For reaction (16) at T = 298.15 K and I_m = 0.1 mol kg^-1, they¹⁰ give _rG^o = 21.1 kJ mol^-1 and _rH^o = -26.7 kJ mol^-1. Here, we have rewritten the corresponding equations in Miller and Smith-Magowan's Table 7 in accordance with the preceding discussion concerning the notation for NAD and NADP type species. For additional information related to the thermodynamics of these two important reactions, the reader is also referred to the study by Burton²¹ and the review by Rekharsky et al.²²

Apparent equilibrium constants obtained from studies of in vitro systems can also be used to calculate the position of equilibrium in metabolic processes involving several reactions. Glycolysis is probably the best example of a situation where data are available and for which such calculations have been performed.^14,23 The results of these calculations can then be compared with information on the concentrations of the various substrates obtained from the analysis of in vivo systems. This comparison can provide valuable insight into the chemical machinery of living systems.

For many biochemical reactions, the apparent equilibrium constant is a function of temperature, pH, pX, and ionic strength. Thus, when performing Hess' Law and thermochemical cycle calculations, it is necessary that the data for all of the reactions in such a calculation refer to the same set of conditions. The dependencies of apparent equilibrium constants and standard transformed enthalpies of reaction on the conditions of reaction can be very complex and the reduction of such results to a common standard state generally requires auxiliary information on the binding of protons and metal ions to the various reactants as well as information on or assumptions about the activity coefficients of the species in solution. Calculations of this type have been performed by Kuby and Noltmann,²⁴ Alberty,^25,26 Guynn, Gelberg, and Veech,²⁷ Langer et al.,²⁸ Goldberg and Tewari,¹³ and others.

Tables of standard formation properties²⁹ have proven to be a useful way of generalizing upon and presenting thermodynamic data for many chemical substances. However, tables of this type have been prepared for only limited classes of biochemical substances.^6,10,30 It has recently been shown³¹ how it is possible to prepare tables of standard transformed formation properties for biochemical reactants (i.e. sums of species) as distinct from standard formation properties for individual biochemical species. The adenosine 5'-triphosphate series was used as a prototype for this purpose. Thus, it appears likely and desirable that several different types of thermodynamic tables will eventually appear in the literature. Clearly, the larger the scope of such tables, the more useful they are for calculating thermodynamic quantities for reactions which have not been the subject of a direct investigation.

2. M. R. Atkinson and R. K. Morton, in "Comparative Biochemistry", edited by M. Florkin and H. S. Mason (Academic Press, New York, 1960), Vol. 2; pp. 1-95.

3. T. E. Barman, "Enzyme Handbook" (Springer-Verlag, New York, 1969), Vols. I and II.

4. T. E. Barman, "Enzyme Handbook" (Springer-Verlag, New York, 1974), Supplement I.

5. H. D. Brown, in "Biochemical Microcalorimetry", edited by H. D. Brown (Academic Press, New York, 1969); pp. 149-164.

6. R. C. Wilhoit, in "Biochemical Microcalorimetry", edited by H. D. Brown (Academic Press, New York, 1969); pp. 33-81, 305-317.

7. R. K. Thauer, K. Jungermann, and K. Decker, Bacteriol. Rev. 41, 100 (1977).

8. M. V. Rekharsky, A. M. Egorov, G. L. Gal'chenko, and I. V. Berezin, Thermochim. Acta 46, 89 (1981).

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

10. S. L. Miller and D. Smith-Magowan, J. Phys. Chem. Ref. Data 19, 1049 (1990).

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

12. E. S. Domalski, W. H. Evans, and E. D. Hearing, "Heat Capacities and Entropies of Organic Compounds in the Condensed Phase," J. Phys. Chem. Ref. Data 13, Suppl. 1 (1984).

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

14. R. A. Alberty, Biophys. Chem. 42, 117 (1992).

15. R. A. Alberty, Biophys. Chem. 43, 239 (1992).

16. R. A. Alberty, J. Biol. Chem. 243, 1337 (1968).

17. R. C. Phillips, P. George, and R. J. Rutman, J. Biol. Chem. 244, 3330 (1969).

18. C. E. Moore, Jr. and A. L. Underwood, Analyt. Biochem. 29, 149 (1969).

19. W. T. Yap, B. F. Howell, and R. Schaffer, National Institute of Standards and Technology, unpublished results.

20. R. M. C. Dawson, D. C. Elliot, W. H. Elliot, and K. M. Jones, "Data for Biochemical Research" (Oxford University Press, Oxford, 1986)

21. K. Burton, Biochem. J. 143, 365 (1974).

22. M. V. Rekharsky, G. L. Gal'chenko, A. M. Egorov, and I. V. Berezin, in "Thermodynamic Data for Biochemistry and Biotechnology", edited by H. J. Hinz ( Springer-Verlag, Berlin, 1986); pp. 431-444.

23. S. Minakami and H. Yoshikawa, J. Biochem. (Tokyo) 59, 139 (1966).

24. S. A. Kuby and E. A. Noltmann in "The Enzymes", Volume 6, edited by P. D. Boyer, H. Lardy, and K. Myrbäck (Academic Press, New York, 1962) pp. 515 - 603.

25. R. A. Alberty, J. Biol. Chem., 244, 3290 (1969).

26. R. A. Alberty, Proc. Natl. Acad. Sci. U.S.A. 88, 3268 (1991).

27. R. W. Guynn, H. J. Gelberg, and R. L. Veech, J. Biol. Chem. 248, 6957 (1973).

28. R. S. Langer, C. R. Gardner, B. K. Hamilton, and C. K. Colton, AIChE J. 23, 1 (1977).

29. D. D. Wagman, W. H. Evans, V. B. Parker, R. H. Schumm, I. Halow, S. M. Bailey, K. L. Churney, and R. L. Nuttall, "The NBS Tables of Chemical Thermodynamic Properties", J. Phys. Chem. Ref. Data, 11, Supplement No. 2 (1982).

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

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

32. R. N. Goldberg, Y. B. Tewari, D. Bell, K. Fazio, and E. Anderson, "Thermodynamics of enzyme-catalyzed reactions: Part 1. Oxidoreductases," J. Phys. Chem. Ref. Data, 22, 515 (1993).

33. R. N. Goldberg and Y. B. Tewari, "Thermodynamics of enzyme-catalyzed reactions: Part 2. Transferases," J. Phys. Chem. Ref. Data, 23, 547 (1994).

34. R. N. Goldberg and Y. B. Tewari, "Thermodynamics of enzyme-catalyzed reactions: Part 3. Hydrolases," J. Phys. Chem. Ref. Data, 23, 1035 (1994).

35. R. N. Goldberg and Y. B. Tewari, "Thermodynamics of enzyme-catalyzed reactions: Part 4. Lyases," J. Phys. Chem. Ref. Data, 24, 1669 (1995).

36. R. N. Goldberg and Y. B. Tewari, "Thermodynamics of enzyme-catalyzed reactions: Part 5. Isomerases and ligases," J. Phys. Chem. Ref. Data, 24, 1765 (1995).

37. R. N. Goldberg, "Thermodynamics of enzyme-catalyzed reactions: Part 6 - 1999 update," J. Phys. Chem. Ref. Data, 28, 931 (1999).

38. T. N. Bhat, "Migration from Static to Dynamic Web Interface - Enzyme Thermodynamics Database as an Example," Proceedings of the The 9th World Multi-Conference on Systemics, Cybernetics and Informatics (WMSCI2005), July 10-13 Orlando, Florida, USA, 69 - 74.

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