The Thermodynamics of the Krebs Cycle and Related Compounds

Cite as: Journal of Physical and Chemical Reference Data 19, 1049 (1990); https:// doi.org/10.1063/1.555878 Submitted: 16 June 1988 . Published Online: 15 October 2009

Stanley L. Miller, and David Smith-Magowan

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Journal of Physical and Chemical Reference Data 19, 1049 (1990); https://doi.org/10.1063/1.555878 19, 1049

© 1990 American Institute of Physics for the National Institute of Standards and Technology. The Thermodynamics of the Krebs Cycle and Related Compounds

Stanley L. Miller Department of Chemistry (B-017), University of California San Diego, La Jolla. California 92093

and

David Smith-Magowana Chemical Thermodynamics Division. National Bureau of Standards. Gaithersburg. Maryland 20899

Received June 16, 1988; revised manuscript received March 20, 1990

A survey is made of the enthalpies of formation, third law entropies and Gibbs energies available for Krebs cycle and related compounds. These include formate, acetate, succinate, fumarate, glycine, alanine, aspartate and glutamate. The poten­ tial of the NAD+/NADH couple is recalculated based on lhe;; e;;tbanul/acetalde­ hyde and· isopropanol/acetone equilibria. The reported enzyme catalyzed equilibrium constants of the Krebs cycle reactions are evaluated with estimated errors. These 28 equilibria form a network of reactions that is solved hy a lea.qt squares regression procedure giving Gibbs energies of formation for 21 Krebs cycle and related compounds. They appear to be accurate to ± 0.4 kJ.mol- 1 for some compounds but ± 1 kJ·mol-1 in less favorable cases. This procedure indicates which third law 11,6 and enzyme equilibria are inaccurate, and allows very accu­ rate ArG to be determined for compounds related to the Krebs cycle by measuring enzyme equilibrium constants.

Keywords: enthalpy; entropy; enzyme equilibrium constants; Gibbs energies of formation; Krebs cycle compounds; NAD+INADH potential; thermodynamic network.

Contents

1. Introduction ...... 1050 7. Glossary of Symbols and Terminology ..... 1067 2. The Network and Its Analysis ...... 1050 8. Acknowledgements ...... 1068 2.1. Conventions ...... 1051 9. References...... 1068 2.2. Optically Active and Racemic Com- pounds ...... '.. 1051 List of Tables 3. Third Law Calculations and Ancillary Data. 1052 3.1. Succinate and Fumarate ...... 1052 1. CODATA values for elements and inor- 3.2. Glycine, Alanine, Aspartic Acid and ganic compounds ...... 1052 Glutamic Acid ...... 1052 2. Thermodynamic quantities for succinic acid 3.3. Citrate ...... 1053 and fumaric acid ...... 1053 3.4. Formate ...... 1053 3. Thermodynamic data for several amino 3.5. Acetate ...... 1055 acids ...... 1054 3.6. Other Krebs Cycle Acids ...... 1056 4. Selected third law ArG, ArH and So for 3.7. Ionization Data ...... 1056 formic and acetic acids ...... 1055 3.8. Gibbs Energies and Potentials for the 5. ArB and ASIl/l of some Krebs cycle acids ... 1056 NAD+/NADH and NADP+/ 6. Ionization data for some Krebs cycle com- NADPH systems ...... 1058 pounds ...... 1057 4. Evaluated Equilibria ...... 1061 7. Calculation of the NAD+ /NADH and 5. Results and Discussion ...... 1065 NADP+/NADPH potentials from the 6. Extensions and Improvements ...... 1066 ethanol/acetaldehyde and isopropanol/ acetone equilibria ...... 1059 8. Potentials of the pyridine nucleotide couples 3 -Deceased December 24, 1986. at 25 °C, pH 0 and 7 and 1=0.1 mol dm- • 1060 9. Thermochemical network analysis of the ©1990 by the U.S. Secretary of Commerce on behalf of the United- States. This copyright is assigned to the American Institute of Physics Krebs cycle network ...... 1066 1 and the American Chemical Society. 10. Gibbs energies of formation in kJ.mol- of Reprints available from ACS; see Reprints List at back of issue. Krebs cycle compounds ...... 1067

0047-2689/90/041049-25/$06.00 1049 J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 1050 S. L. MILLER ANDD. SMITH-MAGOWAN

List of Figures KRE] Wilhoit [69WIL], and Johnson [60JOH]. Thauer et aL [77THA/JUN] presented a review of energy conser­ 1. Krebs cycle interconnections...... 1051 vation in chemotrophic anaerobes which included exten­ sive tables of formation Gibbs energies and Gibbs energies for numerous reactions relevant to metabolic 1. Introduction activity. These were largely revisions of the data pre­ sented by Burton [57BUR]. There is also a recent book The Krebs cycle or citric acid cycle is the major path­ Thermodynamic Data for Biochemistry and Biotechnology way in aerobic organisms for the oxidation of sugars, [86HIN] that has a number of compilations.. fatty acids and some amino acids. The Krebs cycle pro­ Values for some species can also be found in the NBS duces NADH and FADH2 from these compounds, Tables of Chemical Thermodynamic Properties (Techni­ which are oxidized by O2 through the electron transport cal Note 270-3) [68WAG/EVA] and a revised edition system producing ATP. [82W AG/EVA]. Other compilations include gas phase In anaerobic organisms the Krebs cycle does not oper­ data of Stull, Westrum and Sinke [69STUIWES], heats ate in this manner unless there is a terminal electron ac­ of formation by Cox and Pilcher [70COX/PIL] and Do­ ceptor to oxidize the NADH and FADH2. Anerobic malski [72DOM], and heat capacities and entropies of organisms still have the Krebs cycle enzymes, but the condensed phases [84DOM/EVAI85WIL/CHA]. cycle is run in reverse and is used to synthesize alanine, aspartic acid and glutamic acid and amino acids derived 2. The Network and Its Analysis from these. The cycle is believed to have originated as a synthetic cycle in primitive anaerobic bacteria [76 BRO]. The regression procedure employed is the "CATCH" In addition to amino acid synthesis, there is the gly­ system used at the National Institute of Standards and oxylate bypass which is a modified Krebs cycle in cer­ Technology. It is described by Garvin et 01. [76GAR/ tain microorganisms that permits the oxidation of acetate PARa][76GAR/PARb] and Wagman et 01. [77WAGI and the regeneration of the oxalacetate which is re­ SCH], and is based on procedures developed by Pedley moved for amino acid synthesis and which is lost by and coworkers [69GUE/PED]. Some complications decarboxylation. have been discussed by Barnes et 01. [78BAR/PED]. These reactions form a network of interconnecting re­ The procedure has been designed to provide solution actions, most of which are reversible, that can be used to sets of thermochemical formation properties (Gibbs en­ determine the Gibbs energies of formation of these or­ ergies, enthalpies and entropies) based on input data sets ganic compounds. The usual method of calculating drawn from the full spectrum of thermochemical mea­ Gibbs energies of formation uses the enthalpy of forma­ surements. As described earlier, the present study is lim­ tion from the enthalpy of combustion and the entropy ited to a set of measured equilibrium constants that is from the third law and the measured heat capacities. solved for a set of formation free energies. This has not been particularly successful in practice to The regression process takes place in two discreet obtain accurate values of arG of organic compounds, steps. The frrst is an equally weighted least-sums solution usually because of the errors in the enthalpy of forma­ of the entire system of equations to assess the overall tion. A more accurate procedure would be to measure consistency. The least sums basis is less sensitive to out­ the equilibrium constants for a set of reactions, and com­ lying values that the least-squares. The second step is a bine these with a few third law arG's to obtain accurate least squares solution in which each of the input data is values of arG for the remaining compounds. An equi­ weighted by a factor called the "average fit". This aver­ librium constant measured to an accuracy of 4% corre­ age fit factor is simply the arithmetic average of the un­ sponds to an error of 0.1 kJ in the I1tG. There are few certainty aSSigned to the original data value and the arG available with an accuracy of 0.1 kJ, yet an accu­ residual (observed - calculated) obtained from the least racy of 4% on an equilibrium constant is not difficult to sums. This weighting scheme has been found to achieve obtain in many cases. Thus a large number of very accu­ a reasonable balance between the intrinsic uncertainty in rate arG can be obtained by determining equilibrium the data and their consistency with other data in the net­ constants' of an appropriately connected series of reac­ work. tions. The network of reactions treated in this study is out­ This is not a new idea. Lewis and Randall [23 LEWI lined schematically in Fig. 1. The metabolites for which RAN] discussed it many years ago and used it to deter­ the network was solved are connected by arrows with mine the arG of urea and related compounds. Burton the inorganic species omitted as well as NAD+ and [53BURIKRE], [57BUR] employed it to a limited extent NADP+. The transamination reactions are also omitted for some biochemical compounds. However, the Krebs but are equivalent to an amino acid dehydrogenase .. cycle is a more favorable case on which to apply this Some of the species e.g., acetate, appear several times to principle. avoid crossing arrows. The direction of the arrows is not There are several sources for compiled reference val­ significant but is generally in the favorable direction or ues for the formation energies of the species in the Krebs in the direction of reduction. More complete discussion cycle, including Burton and Krebs [57BUR], [53BURI of individual reactions will follow below.

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 THE THERMODYNAMICS OF THE KREBS CYCLE AND RELATED COMPOUNDS 1051

Citrate 2.cis -Aconitate ..!. Isocitrate .!. Succinate + Glyoxylate

9 Acetate ~~ 1y <>·Hydroxyglutarate 23 h _ 14 I Pyruvate ~ Oxaloacetate a-Ket09,:tarate 1 8 ~ Glut!:~e

p-Metnylaspartate 4 1 2 la:l ~~ J:: Fumarate..L Succinate t26 3 +4 t Mesaconate Glyoxylate + Acetate Aspartate ~C +27 1011' to Citramalate Glycolate Glycine Oxaloacetate

Acetate + Pyruvate

FIG. 1. Krebs cycle interconnections. NAD+, NAOH, C02, H20 not shown. The numbers refer to the reaction as listed in Table 9.

2.1. Conventions (Standard States The activity coefficients for neutral molecules will be and Activity Coefficients) taken as 1.00. There are considerable data available on the salting out properties of various salts which are well The gas constant employed is 8.31441 11(mol K) and approximated by the Sechenov equation [52LON/. the Faraday is taken to be 96487 (C/mol). The In­ MCD]. terunion Commission on Biothermodynamics [76INT] has recommended that measurements of enzyme equi­ logh / h O = km libria be made at 25 °C with the ionic strength brought to 0.1 M (0.1 Molar) with KCl at the lowest effective buffer where /; is the fugacity in the salt solution, /;0 is the concentration. The unit of concentration recommended fugacity in pure water, m is the molal salt concentration, is mol dm-3; for convenience, a solution of concentration and k is the Sechenov constant. The fl.G of transfer from 0.1 mol dm-3 (for example) may be referred to as a 0.1 M water to a 0.1 molal KCl solution would rarely amount solution. This is recommended even though mo~t mam­ to as much as 0.1 kl. and so this effect will be omitted. mals are at 37 0 and an ionic strength of 0.16 M. We follow these recommendations except for use where in­ 2.2. Optically Active and Racemic Compounds dicated of molal concentration (mol/kg of water). Note that a solution of molality 0.1 mollkg of water is referred It is evident that the Gibbs energies, enthalpies and to as a 0.1 m solution. entropies of D- and L-isomers of the same compound The standard state of pure water is taken as unit activ­ must be equal. The enthalpy of formation of a racemic ity, and water will be left out of the equilibrium constant mixture in solution at infInite dilution will also equal that equations. The standard state of 0.1 M KCl has a fl.!) of the D- or L-isomer. The enthalpy of the solid racemic lower by 0.01 kJ·mol-1 than pure water, but this differ­ compound will be the same as the isolated isomer only if ence will be neglected. it is a conglomerate (i.e., a mixture of the D- and L­ The Gibbs energies of formation can be corrected to crystals). Examples of conglomerates are sodium ammo­ zero ionic strength by using the activity coefficients in nium tartrate and glutamic acid. In many cases, the Table 6. These are single ion activity coefficients. There racemic mixture forms a DL-crystal, and this racemic is a dispute as to whether these are meaningful, but the crystal may have physical properties considerably differ­ approximations used here are sufficiently accurate for a ent from the D- or L- crystal. Examples are proline and Gibbs energy table. A table of single ion activity coeffi­ serine where the L-isomers are about ten times more sol­ cients is given by Kielland [37K1E]. Unless otherwise uble than the DL-crystals. indicated, the values of "I ± are taken from Robinson and The entropy of the D- and L- compounds in the crys­ Stokes [59ROB/STO]. . tal or in solution are the same. For the DL mixture in We will take "1+ = "1- = 'Y± for a 1:1 salt. For a 2:1 solution the entropy differs from that for the isolated salt (e.g., Na2 succinate) 'Y± = (Y+'Y- )1/3 and we approx­ isomers by the symmetry factor: imate the single ion activity coefficients as "1+ = 'Y!f2 and "1- = 'Y~.

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 1052 S. L. MILLER AND D. SMITH-MAGOWAN

The entropy of the DL-compound in solution is TABLE 1. CODATA Il.fH and So values for elements and inorganic higher than that for the isolated isomers and the opti­ compounds. 1l.,G values calculated from these Il.rH and So. 3 cally active isomer will spontaneously convert to the The aqueous ions and aqueous gases refer to 1 mol dm- • The gases refer to 1 atm. These values are for 1=0 and not DL-mixture if a kinetic pathway is available. The Gibbs 3 1=0.1 mol dm- • energy of the D- and L-compounds in the crystal and in solution are also the same. The 11.0 of the DL mixture in Compound 1l.,G0 Il.rHo So solution differs from the isolated isomers by the entropy kJ·mol-1 kJ.mol -I J·mol-I K-1 difference: H2(g) 0 0 130.57 H2(aq) 17.73B -4.04B 57.571 C(grapbite) 0 0 5.74 N2(g) 0 0 191.50 The tables give the 11.0 and So for only the L-isomer, as O2(g) 0 0 205.04 this is usually the naturally occurring isomer. 02(aq) 16.52b -12.06b 109.20b H20 (1) -237.19 -285.83 69.95 H+(aq) 0 0 0 3. Third Law Calculations OH-(aq) -157.27 -230.02 -10.90 and Ancillary Data CO(g) -137.15 -110.53 197.55 C02 (g) -394.37 -393.51 213.68 In solving the network for the formation Gibbs ener­ CO2(aq) -386.00 -413.26 119.36 gies for individual metabolites, the data for the various HCOr(aq) -586.93 -689.93 98.4 COi-(aq) -527.98 -675.23 -50.0 equilibria have been supplemented by formation proper­ NH3 (g) -16.49 -45.94 192.66 ties for inorganic species and independent estimates of NH3(aq) -26.66° -81.04° 109.29° formation energies for several key compounds via third NH.+(aq) -79.46 -133.26 111.17 law calculations. These calculations include formate and Na+(aq) -242.47 -240.34 58.45 acetate which are included in the NBS Tables. The NBS K+(aq) -263.03 -252.14 101.20 evaluation for these compounds, however is over twenty 'From CODATA values for H2(g) and 1l.",,}G, ll.""tH, Il."",$ [77WIL/ years old and considerable new data exists for obtaining BAT]. the formation properties for the anions in aqueous solu­ bFrom CODATA values for 02(g) and 1l.",,}G, Il.wtH, Il."",$ [77WIL/ tion. BAT]. Data for the inorganic compounds needed to supple­ CProm CODATA values for NH.+ and ll.iaaG, Il.iool/, ll.ior!S [76CHRI HAN]. ment the network are listed in Table 1. They are taken from the CODATA compilation [89COXIWAG], and The data for fumaric acid on the other hand are con­ are generally the same as values tabulated in the NBS siderably less reliable. The combustion enthalpy has been Tables with a few exceptions. evaluated by Cox and Pilcher [7OCOX/PIL] and more The compounds for which estimates have been made recently by Pedley et al. [86PEDINAY] with the two via third law calculation are fumarate, succinate, evaluations differing by 0.7 kJ·mol- I. The absolute en­ glycine, alanine, aspartic acid and glutamic acid. Discus­ tropy is based upon heat capacity measurements that sions for each of these follow. have been extrapolated below 90 K [30P AR/HUFF], and the values for the enthalpy of solution and solubility 3.1. Succinate and Fumarate are somewhat uncertain. The solubility and activity coef­ ficients are discussed in the footnotes of Table 2. The The data necessary for third law calculations for suc­ acid dissociation constants have been subject to some cinate and fumarate are listed in Table 2. disagreement. Robinson and Stokes [59ROB/STO] gave The enthalpy of combustion of succinic acid is known values of pKI = 3.019 and pK2 = 4.3H4 while measure­ quite reliably (it is nearly a calorimetric standard) with ments by Bada and Miller [68 BAD/MIL] yielded values 3 recent determinations [72VAN/MANa] and [70ZAI/ of pKI = 2.94 and pK2 = 4.10 at I = 0.1 mol dm- • NAZ] in exoellent agreement with evaluated values Martell and Smith [74MAR/SMI] selected values ofpKI [70COX/PIL], [77PED/RYL] and [86PEDINAY]. The = 2.94 and pK2 = 4.109 at I = 0.1 mol dm-3 in good absolute entropy has been calculated from heat capacity agreement with the measurements of Bada and Miller. measurements [70VANIWES] from 5 to 328 K remov­ More accurate measurements for the properties of fu­ ing uncertainty associated with the extrapolation from 90 maric acid are highly desirable as it is probably the best to 0 K [30PARIHUF] which gave the value of So too choice for a key value upon which to base the entire high by 8.4 j·K-I.mol-I. network by virtue of the large number of compounds in The enthalpy of solution of succinic acid and the acid the network to which it is connected. dissociation constants are also known quite reliably. Vanderzee et al. [72VAN/MANb] have made a careful 3.2. Glycine, Alanine, AspartiC ACid, study of the enthalpy of solution, while the dissociation and Glutamic Acid constants have been evaluated by Martell and Smith [74MAR/SMI]. The solubility and activity coefficients The data for these compounds are listed in Table 3 for are given in the footnotes of Table 2. the L- isomers. Modern values for the absolute entropies

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 THE THERMODYNAMICS OF THE KREBS CYCLE 'AND RELATED COMPOUNDS 1059

TABLE 2. Third law calculation of thermodynamic data for succinic 3.3.-Citrate acid and fumaric acid. The values of 4.G and lUI are given 1 I in kJ.mol- and I>.S in J·mol-1.K- . The molality and ionic 1 strength (1) are given in mol kg-I. A good I1rB = -1837.6 ± 0.4 kJ·mol- for citric acid monohydrate is available [70COX/PIL], and but only a 1 Succinic Acid Ref Fumaric Acid Ref poor I1rH = -1544 ± 5 kJ·mol- for anhydrous citric acid has been determined. The third law entropy w~ 4.rH(cr) -94O.81±0.42 a -810.98±0.63 a determined by Evans et ale [62EVA/HOA] and they cal­ 28.70±0.04 b 35.8±0.5 c 4.IOIH culated the I1solG based on the data of Levien [55LEV]. 4.fH(aq) -912.11±0.42 -775. 18±0.80 Evans et ale give 4.ion H 2.73 h -2.39 h 4.fH (aq ion-~ -909.37 -777.57 1 SO(cr) 167.3±0.2 d 166.1±4.0 e I1rG (monohydrate, cr) -1472.8 ± 1.2 kJ·mol- 4.rS(cr) -657.43 -528.08 I1rG (citric acid, aq) = -1243.4 ± 1.2 kJ·mol-1 mlAt 0.699 f 0.0456 g 'Y1At 1.0 f 1.0 g I1rG (citrate-3, aq) = -1161.8 ± 1.4 kJ·mol-1 4.IOI S +93.30 +94.40 So (aq acid) +260.62 +260.45 4ion S -119.1 h -1~2.2 h The single ion activity cot:fficit:nUi are difficult to esti­ So (aq ion2-) +81.5 +108.3 mate, since the 'Y of the Na+ or K + salts have not been 4.rG (cr) -744.80 -653.54 measured. Using Kielland's value of 'Y -3 = 0.18 [37KiE] 4.101 G +0.89 +7.66 gives drG(aq acid) -743.92 -64'.88 4.ion G +56.15 h +43.93 h 2 1 4.r G (ion -, 1=0) -687.77 -601.95 I1rG (citrate, aq) = -1166.1 ± 2.5 kJ.mol- 'Y-2 0.40 0.36 3 f.J.fG (iori2-,I=O.1) -690.03.LO.44 -604.S0±1.S1 I = 0.10 mol dm-

An alternative procedure is to use the apparent pK's of -[7OCOX/PIL] Later values for succinic acid are -94O.35±0.54 citric acid to estimate the single ion activity coefficients. [72VAN/MANa] and -94O.19±0.21 [70ZAI/NAZ]. Using the data of Rajan and Martell [65RAJ/MAR] (PKI b[72bVAN/MANb]. CProm [69WIL]. The International Critical Tables give 8.90 kcal. = 2.79, pK2 = 4.30 and pK3= 5.65) we have 'Y-I Wasserman gives 7.98 kcal [30WAS]. 0.346, 'Y-2 = 0.179, 'Y-3= 0.0284, and d[70V AN/WES]. 130PARJHUF] The Cp was extrapolated from 90 K. I1rG (citrate, aq) = -1170.6 ± 2.5 kJ·mol-1 rSolubilityat 25 ° is 0.706 mol dm-3 [58LIN/SEI], which corrected for ionization of 6.94% gives 0.699 mol dm-3 for the undissociated acid. I =.0.1 mol dm -3 (KN03) 'Y taken as 1.0. S'fhe solubility is given only by formula in [30LAN/SIN] as 0.0521 mol 3 Using the data of Tate etal. [65TAT/GRZ]pKI = 2.88, dm- • The fumaric acid is 12.5% dissociated, so m = 0.0456 mol dm -3 for the undissociated acid. 'Y taken as 1.0. An earlier value of pK2 = 4.36, pK3= 5.85) we have 'Y-l = 0.565, 'Y-2 = this solubility is m = 0.0603mol dm-3 [23WEIIDOW]. 0.224 and 'Y -3 = 0.0623, giving 1Yfhese are for both ionizations. See Table 6 for pK values, 4H and I>.S of ionization. I1rG(citrate, aq) = -1168.7 ± 2.5 kJ·mol-1 iPor succinate Kielland [37KIE] gives 'Y-2 = 0.38 at 1= 0.1 mol dm-3 and Komar et ale [67KOMlMUS] aive 'Y-2 = 0.469 with 0.1 mol I = 0.1 mol dm-3 [(CH3)4NC1] dm-3 KCl and 'Y = 0.334 with 0.1 mol dm-3 NaCI. For sodium fu­ marate Robinson and Stokes give by interpolation 'Y::I: = 0.6OQ at I = The 'Y's are in the expected direction since K + is known 0.1 mol dm-3 (m = 0.033), which gives 'Y-2 = 'Y;= 0.360. Komar et ale [72KOMlTKHl give 'Y = 0.382 with 0.1 mol dm-3 KCI and 'Y = to be complexed by citrate. We will use the 'Y -3 for the 3 0.331 with 0.1 mol dm- NaCl. KN03 solutions, recognizing the low activity coefficient is probably due to complexing. Since KCl is frequently used for enzyme solutions, it is simpler to include the complexing ill the 1l.,G rather than correcting for it. The difficulty in determining the 'Y for a - 3 ion, as demonstrated by the large variation in the calculated values, suggest that citrate is a poor compound to use in the network. Therefore, its third law I1rG has been left are available for glycine and the L-isomers. The en­ out of all the network calculations. thalpies of combustion are fairly reliable but can always be improved. The enthalpy of formation of the DL- ala­ nine in solution COnfIrmS the value adopted for the L-iso­ 3.4. Formate mer as it is nearly identical. The enthalpies of solution for aspartic acid and glutamic acid are weak because it is There are several thermochemical cycles by which not clear whether the corrections were made for ioniza­ the Gibbs energy of formation of the formate anion can tion at high dilution. The activity coefficients at satura­ be calculated, a comparison of which will give some idea tion for aspartic and glutamic acids may also be in error. of the reliability of the estimated value.

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 1064 S. L. MILLER AND D. SMITH-MAGOWAN

1 1 TABLE 3. Third law calculation of thermodynamic data for several amino acids./lH and Il.G in kJ·mol- and So in J.mol-I.K- • The molality and ionic strength (I) are in mol kg-I.

Glycine Ref L-Alanine Ref L-Aspartic Ref L-Glutamic Ref

Il.rH(cr) -528.52±0.50 a,f - 561.24±0.63 b,f -973.32±0.92 a -1005.25± 1.26 b,g /lH(soln) + 14. 16±0.01 e +7.49±0.03 i,h +25.82±0.10 +24.53±0.10 j Il.rH(aq) -514.36±0.50 -553.75±0.63 -947.50±0.93 -980.72± 1.27 SO(cr) +103.51 c 129.21 c + 170.12 c +188.20 c Il.rS(cr) -535.19 c -645.80 c -815.67 c -933.90 c msat 3.33 c 1.862 c 0.0375 c 0.0586 c 'Ysat 0.729 c 1.045 c 1.0 c 1.0 c Il.wtS +54.94 +30.59 +59.37 +58.70 SO(aq) +158.45 +159.80 +229.49 +246.90 Il.rG(cr) -368.98 -368.74 -730.19 -726.87 ll.oolG -2.22±0.04 c -1.63±0.04 c +8.12±0.08 c + 7.03 ±0.02 c I:J.rG(I=O) - 371.20±0.60 -370.37±0.70 -722.07 ±0.93 -719.84±1.27 'Y+ - or 'Yo+- 0.97 0.95 0.95 0.95 ~ra(I=O.l) -371.33 -310.'0 -122.20 -119.91 ll.ionG +22.26 k +24.39 k Il.rG+-+(I=O) -699.94 -695.59 'Y-+-(1 =0.1) 0.73 k 0.73 k ~rG-""-(I--O.l) -700.72 -696.37 ll.ioJ! +4.64 k +1.56 k Il.rH-+-(aq) -942.86 -979.16

B(7OCOX/PIL]. b[7OCOX/PIL]. This is for D-alanine and D-glutamic acid. The values for the L-isomers seem to be in error. 'l76HUT][84DOM/EVA]. d[43COH/EDS], p. 198 & 219 't75SPI/WAD]. !More recent values are Il.rH(glycine) = -528.61 ± 0.21 kJ·mol-1 and I:J.rH(L-alanine) = -559.48 ± 0.46 kJ·mol-1 [77NGA/SAB]. Values are also given by Kamaguchi et al. [75KAM/SAT] for Il.rH(L-alanine) = -561.08± 0.71 kJ.mol-', Il.rH(D-alanine) = -560.06 ± 0.76 kJ.mol-t, l Il.rH(DL-alanine) = -562.35 ± 0.65 kJ.mol- • SLater values are Il.rH(L-glutamic) = -1003.32 ± 1.17 kJ·mol-1 and I:J.rH(D-glutamic) = -1002.47± 0.97 kJ·mol-1 [75SAK/SEK]. hAnother value can be obtained from DL-alanine. Il.rH = -563.58±0.63kJ·mol-1 [7OCOX/PIL] and I:J.wJI = 9.13±0.03 kJ·mol-1 [82ABAlSHE]. This gives -554.45±0.64 kJ·mol-1 for the aqueous DL-alanine. i82ABAISHE. jL-Aspartic acid [82VAS/KOC], L-glutamic acid [80MAT / AMA]. It is not clear whether the corrections for ionization on disolution were made. The data of Rodante and Tocci [85ROD/TOC] are close to these values. Earlier values are given in [76HUT]. kSee Table 6.

Standard enthalpies of formation for the pure liquid culate due to complications from dimerization. Kaye and and gas phases have been evaluated by Cox and Pilcher Parks [34KAY/PAR] reported Patm/m = 1.91 X 10-4 [7OCOX/PIL], Pedley and Rylance [77PED/RYL], and atm (mol/kg) -1 while Campbell and Campbell Pedley et al. [86PED/NAY]. We will use the values [34CAM/CAM] obtained a value of Patm/m = 1.71 X given by Cox and Pilcher which are -425.0±0.4 10-4 atm (mol/kg)-l. These yield respectively, asolG = 1 kJ·mol- for the liquid and -378.9±0.6 kJ·mol-1 for the 21.21 and 21.50 kJ·mol-l . Taking the average of these gas monomer. The enthalpy of solution has been deter­ two values yields arG(HCOOH,aq) = - 372.38 1 l 1 mined [71KONIWAD] to be -0.678±0.OOI kJ.mol- , kJ·mol- • Taking Il.rH = -425.7 kJ.mol- for the yielding a value for arH(HCOOH(aq)) of -425.7±0.4 aqueous acid gives Il.rS = -178.84 and So = 162.72 l 1 kJ ·mol- . The third law entropy of the liquid has been ].K-1·mol- . 1 1 given as 129.59 ]·K- ·mol- [85WIL/CHA] from the The third law entropy of NaHC02 (24.80 cal heat capacity data of Stout and Fisher [41STO/FIS]. K-1.mol-1) has been measured [60WES/CHA]. The en­ This gives apS = 211.97 ]·K-1·mol-1 and Il.rG = thalpy of solution will be taken as +0.74±0.03 ]·mol-1 -361.80 kJ·mol-1 for the liquid. The difficulty is to ob­ [75CHA/AHL, 82CHO/AHL]. The value of +1.13 tain the Il.solG at 25 °C, and there seems to be no accurate [70SNE/GRE] may be too high because the fmal con­ data on the water-formic acid phase diagram. centration was too high. Bonner has recently measured 1 An alternative is to use the gas phase data and the Il.G msat = 14.7 mol kg- and 'Ysat = 0.877 [88BON]. of solution from the gas. Chao and Zwolinski [78CHA/ ZWO] give the ideal gas entropy of the formic acid 1 1 1 monomer as So = 248.86 ]·mol- K- and Il.rG = Il.solH/T + 2Rln msat + 2Rln 'Ysat = 45.00 ].K-1·mol- 1 l -351.00 kJ·mol- and Il.rH = -378.57 kJ·mol- • The Gibbs energy and entropy of solution are difficult to cal-

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 THE THERMODYNAMICS~OF;THE KREBS CYCLE AND RELATED COMPOUNDS 1055

This gives SO = 148.76 J·K-1.mol-1 for aqueous sodium hydrogenlyase equilibrium and So from sodium formate formate, and combined with So = 58.45 J·K-1·mol-1 for differs by only 0.4 kJ from the value selected for the 1 aqueous Na+ gives So 90.31 J·K-1·mol- for aqueous liquid by Cox and Pilcher combined with I:1sotlI. formate. The selected values are given in Table 4. They are The entropy of ionization of formic acid is 71.67 close to the NBS values for aqueous formic acid of Il.tG J·K-I·mol-t [76CHR/HAN], so for aqueous formic acid = -372.3 JoK-t'moI-I, ArH = -42:5.4 J·K-I·morl and 1 l So = 161.98 J.K-1.mol- and a,s = -179.37 So = 163 J K-1·mol- • The NBS values for formate are l I I J.K-1·mol- . This gives I:1tG -425.7 + 53.48 = I:1tG = -351.0 J.K-l.mol- , arB = -425.6 J.K-I.mol- -372.2 kJ·mol-1 for the aqueous acid using the third law and So = 92 J.K-1 mol-1 [68WAG/EVA][82WAG/ entropy for sodium formate. EVA]. The Gibbs energy of formation of formate can also be calculated from the formic hydrogenlyase equilibrium: TABLE 4. Selected third law A,.G, ArH and So for formic and acetic acids. Ionic strength (1) is in mol kg-l.

A;a ArH So which involves only formate and substances already kJ·mol-1 kJ.mol-1 J·mol-1·K-l adopted from the CODATA key values. The equi­ librium constant was measured by Woods [36WOO] Formic acid (aq) -371.79±0.20 -42S.3±0.4 162.0 yielding the valueR of ArG = -0.715 kJ.rno]-l and A., H Formate (aq) -350.37±0.20 -425.2±0.4 90.3 l Formate (aq, /=0.1) -3S0.99±0.20 -42S.8±0.4 90.3 = -22.64 kJ·mol- • The enthalpy is somewhat unreli­ Acetic acid (aq) -396.1±0.4 -48S.S±0.3 177.8 able as it was estimated from equilibrium determinations Acetate (aq) -369.0±0.4 -486.0±0.3 85.3 at only 25 and 38 °C. The resultant value of Acetate (aq, 1=0.1) -369.6±0.4 -480.6±0.3 85.3 I:1tG(formate,aq) = -350.37 kJ·mol-1 and I:1tG(formic l acid, aq) = -371.79 kJ·mol- . Using the arH = -425.7 kJ.mol-1 for the aqueous acid gives 1:1,s = -180.8 and So _ 160.7 J·K-l·mol-1• Alternatively, the non-enzymatic decomposition of 3.5. Acetate formate via the equilibrium: The thermodynamic properties of aqueous acetic acid HCOOH(aq) = H2(g) + CO2(g) and the acetate anion present difficulties in obtaining a reliable value for b.S of solution because of the formation will also yield a formation energy for the formate anion of dimers in the gas phase as in the case of formic acid. based only on the CODATA values. This equilibrium There are two modem enthalpies of combustion given was measured by Bredig et 01. [29BRE/CAR] from 20 to in Cox and Pilcher -115.71±0.10 and -115.79±0.09 90 °C, but at pressures of 60 to 100 atm. The fugacity kcal mol-1 with a selected value of -115.75±0.07 correction~ were di~Cll~~ed hy Waring [52WA R] who leea1 mol-1 = -4R4.3±O.3 ld.rnol-1 [70COX/PIL]. We calculated a value for ap(formic acid, aq) =" -371.66 take the enthalpy of solution as -1.176±0.004 kJ·mol-1 and -370.28 kJ.mol-1 (corrected and uncorrected, re­ [71KONIWAD] giving arH = -485.5±0.3 kJ·mol-1 spectively). This is in good agreement with the value for the aqueous acid. obtained from the hydrogenIyase equilibrium and third The pKa = 4.756 is reliably known. There have been a law calculations, but the reliability of the fugacity cor­ number of calorimetric determinations of the I:1H of ion­ rection is less than satisfactory for this application. ization in the range -0.07 to -0.137 kcal mol-1 with The decomposition of aqueous formic acid to carbon A.H from the temperature dependence of pKa in the monoxide and water has also been examined by Branch range -0.098 to -0.112 [77CHRIHAN].We select [15BRA] at temperatures of 156 and 219 °C and can also aioJ! = -0.112 kcal = -0.47 kJ and ll.ionS = -22.11 be used to obtain the formation Gibbs energy of aqueous cal K-1.mol-1 = -92.5 JK-1·mol-1 [52EVEILAN]. formic acid. This analysis has been discussed by Lewis This gives I:1rH = -486.0±0.3 kJ·mol-1 for the aqueous and Randall [23LEW/RAN] and Waring [52WAR] who ion. give values of I:1rG(formic acid, aq) = -373.25 kJ.mol-1 There are three direct methods of obtaining the en­ and -374.0:5 kJ·mol- t respectively. These agree well tropy of the aqueous acid and anion. They are from a) with the estimates by other means but are less reliable the entropy of the liquid, b )the entropy of the gaseous because of the large temperature correction. monomer, and c) the entropy of the sodium salt. There is We select atG from the formic hydrogenlyase reaction a modem entropy for the liquid of So = 37.76 cal and the entropy from the sodium formate. We also use K-1.mol-1 = 158.0 J·K-1·mol-1 [82MAR/AND] which pKa = 3.751, aioJ! = +0.04 ± 0.20 kJ·mol-1 and replaces the Parks and Kelly value of So = 38.2 cal l 1 l:1ionS = -71.67 ± 0.71, J·K-J·mol- and "'I = 0.778 K-1'mol- based on extrapolation of Cp below 90 K [59ROB/STO]. The lowering of Il.tG of formate from [29PARlKEL]. The entropy of solution (liq---ll*lm aq) the activity coefficient is arbitrarily put into the Il.rH. can be calculated from the 'Y = 3.20 at X2 = 0 given by The arB for aq formic acid obtained from the formic Hansen et 01. [55HANIMIL].

J. Phys. Chern. Ref. Data, Vol. 19, No.4, 1990 1056 s. L MILLER AND D. SMITH-MAGOWAN

Aw~ = Awl!lT - Rln 'Y + Rln 55.51 malic acid, pyruvic acid, a-ketoglutaric acid, and ox­ aloacetic acid. Even if the So of the crystal were known, This gives Aw~ = 19.79 J.K-I.mol-I, So = 177.8 the AS of solution will be difficult to measure. Ox­ J·K-I·mol-I for the aqueous acid, and So = 85.3 aloacetic acid decarboxylates relatively rapidly. The oth­ J.K-I.mol -I for acetate anion. ers are very soluble, but more significantly the hydroxy The statistical entropy of the gas phase monomer has acids form polyesters in concentrated solution and the been calculated a number of times and reviewed by Chao keto acids may dimerize, thereby making osmotic coeffi­ etal. [86CHAIHAL] who give So = 283.36J·K-I·mol-1 cient measurements difficult. The alkali metal salts all at 1 atm for the gaseous monomer. There are many data seem to be very soluble. on the volatility of of acetic acid-water solutions, which The ArB of the aqueous acid can be obtained from the gives Aw1G, but Awl! of the monomer is difficult to esti­ enthalpy of combustion and Il.wl!. In some cases it may mate. This will be taken up in a subsequent paper. be advantageous to measure enthalpy of combustion and The third law entropy of anhydrous sodium acetate solution of the ammonium salt. Isocitric acid forms a has been measured [83FRA/PLA] as 138.10 lactone easily so the best approach would be to measure J·K-I·mol-I. The enthalpies of solution include the enthalpy of combustion of the lactone and the AwP -17.32±O.21 kJ·mol-1 [6SPAR], -16.59 kJ·mol-1 in NaOH to get A.rH of isocitrate. [75CHOIAHL], -17.46 kJ·mol-1 [82CHOIAHL], and Table 5 gives the available enthalpies of formation of -16.88 kJ·mol-l from the extrapolation of the data of the Krebs cycle acids. . Snell and Greyson [70SNE/GRE] using enthalpies of di­ lution of Parker [65PAR]. We select an an average value of -17.03 J.K-l·mol-I. It is to be noted that the Awl! TABLE 5. A H and Aso! H of some Krebs cycle acids. measured is very sensitive to water in the sodium ac­ f etate. Thus if 1 % of the sodium acetate is hydrated after Acid AfH Il.H saln Af H (aq acid) weighing, the Il.wl! measured would be -16.16 kJ in­ kJ·mol-1 kJ·mol- 1 kJ·mol-1 stead of -17.03 kJ. Bonner has recently measured msat = 15.20 mol kg-I = Glycolic -664.0±4.0· + 15.94a -651.0±4.5 and 'Ysat 2.786 [88BON]. These are super saturated so­ b lutions since the trihydrate of sodium acetate is soluble L-Lactic -694.0± 1.0 +7.82c -686.2±1.0 L-Malic -110l.6b e to only 6.16 m. However, sodium acetate solutions are DL-Malic -1105.66±O.63 b 21.85 -1083.81±O.64 well known for their tendency to supersaturate. We have a·Hydroxyglutaric Glyoxylic d Awl!lT + 2 Rln msat + 2Rln 'Ysat Pyruvic -584.5±6.0 -19.10f -603.7 Oxaloacetic -984.5±4.0s a-Ketoglutaric -1026.2±O.9b + 15.17 = So (NaAc,aq) -S°(NaAc,cr) Isocitric b h ciS·Aconitic -1224.7±7.5 • This gives So = 143.27 JK-1·mol-1 for aqueous sodium trans-Aconitic -1232.7±2.5b acetate, and So = 143.27 - 58.42 = 84.85 J·K-I·mol-I for the acetate anion. &(68WAG/EVA] error estimated. b[7OCOXIPIL] This is in good agreement with the So = 85.3 159SAV /GUN] J·K-I·morl from the acetic acid route, but alternative 11(69STUIWES] error estimated. choices of the Awl! would give less satisfactory ~esults er86APE] (86.3 for Awl! = -16.59 and 83.4 for AsoP = -17.46). ~25BLA] We select A.,H from the enthalpy of combustion of the &(69WIL] error estimated IIciS-Aconitric acid is the Krebs cycle intermediate, but it is unstable liquid, So from the third law entropy of the liquid, and with respect to the trans-isomer. pK = 4.756 and 'Y = 0.791 from Robinson and Stokes [59ROB/STO]. The selected values are given in Table 4. These can be compared with the NBS values [68WAG/EVA] [82WAG/EV A]. For aqueous unionized acetic acid ArG 3.7. Ionization Data 1 = -396.6 kJ.mol- , ArB = -485.8 kJ.mol-t, So = 178.6 J·K-I·mol-I. For acetate ion Il.rG = -369.4 The values of pKau ll.ioJ! and AiowS used in this paper l kJ.mol-I, ArB = -485.76 kJ.mol- , S~ = 86.6 are listed in Table 6, together with the single ion activity I 3 J·K-I·mol- . coefficient data and the pK at 1=0.1 mol dm- • This is not intended to be complete since exten-sive compila­ tions are available [64SILIMAR] [71SILIMAR] 3.6. Other Krebs Cycle Acids [74MARISMI] [76CHRIHAN] [79PER], but the data used are stated because a considerable number of values It will be difficult to obtain third law entropy values are available in the literature. The blank spaces in the for a number of Krebs cycle acids such as lactic acid, table are evident, and such data would be useful.

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 THE THERMODYNAMICS OF THE KREBS CYCLE AND RELATED COMPOUNDS 1057

TABLE 6. Ionization data for some Krebs compounds. Min kJ·mol-1 and AS in ].mol-1·K-1.

Acid pKa Ref 11mB Ref l1iorJS "10 "1- Ref pK' (1=0.1)

Fomnc b +0.04 b -71.7 1.00 0.778 c Acetic 4.756 a -0.42 b -92.5 1.00 0.796 c 4.66 Succinic pKl 4.207 a +3.18 b -69.9 1.00 0.762 c 4.09 Succinic pK2 5.636 a -0.45 b -109.2 0.762 0.40 d 5.37 Fumaric pKl 3.095 b,f +0.46 b -57.7 1.00 0.762 d 2.98 Fumaric pK2 4.602 b,f -2.85 b -97.5 0.762 0.40 d 4.32 Glycolic 3.831 b +0.46 b -72.0 1.00 0.740 d 3.70 Lactic 3.858 b -0.43 b -75.3 1.00 0.76 d 3.74 Malic pKl 3.458 b +2.95 b -56.1 1.00 0.70 d 3.30 Malic pK2 5.097 b -1.18 b -101.3 0.70 0.35 d 4.80 a-Hydroxyglutaric pKl 3.59 j 1.00 0.70 d 3.44 a-Hydroxyglutaric pK2 5.14 j 0.70 0.35 d 4.84 Glyoxylic 3.46 b +2.22 b -58.8 1.00 0.60 d 3.24 Pyruvic 2.490 k +12.13 b -7.1 1.00 0.50 k 2.26 Oxaloacetic pKl 2.S55 k 1.00 0.57 k 2.31 Oxaloacetic pK2 4.370 k 0.57 0.19 k 3.89 a-Ketoglutaric pKl 2.26 I 1.00 0.70 d 2.11 a-Ketoglutaric pKa 4.80 1 0.70 0.40 d 4.56 Citric pKl 3.128 b +4.17 b -46.0 1.00 0.346 e 2.79 Citric pK2 4.761 b +2.44 b -82.8 0.346 0.179 e 4.30 Citric pK3 6.396 b -3.36 b -133.9 0.179 0.0284 e 5.65 Isocitric pKl 3.287 1.000 0.612 d 3.07 Isocitric pK2 4.714 0.612 0.246 d 4.32 Isocitric pK3 6.396 0.246 0.062 d 5.80 CIS-Aconitic pKl 1.9 m 1.00 0.61 d 1.7 cIS-Aconitic pK2 4.3 m 0.61 0.25 d 3.9 ci3-Acouiuc pK3 6.4 ill 0.25 0.062 d 5.8

Acid pKa Ref l1ioJl Ref l1itJ~ Ref "10 "1- Ref pK' (1= 0.1)

Olycine+o pKl 2.350 b +4.01 b -31.5 b 0.73 0.97 g 2.47 Glycine+- pK2 9.780 b +44.1 b -39.2 b 0.97 0.7l g 9.66

Alanine+ o pKl 2.340 b +3.01 b -34.7 b 0.73 0.95 d 2.45 Alanine+- pK2 9.870 b +45.23 b -37.2 b 0.95 0.73 d 9.76

Aspartico +o pKl 1.990 b +7.46 b -13.0 b 0.73 0.95 d 2.10 Aspartico +- pKz 3.900 b +4.60 b -59.4 b 0.95 0.73 d 3.79 Aspartic-+- pK3 10.002 b +37.76 'b -64.9 b 0.73 0.40 d 9.74

Glutamico+o pKl 2.162 b -0.27 b -42.3 b 0.73 0.95 d 2.28 GlutamicO +- pKz 4.272 b +L56 b -76.6 b 0.95 0.73 d 4.16 Olutamic-+- pK3 9.93 h +40.07 b -44.8 b 0.73 0.40 d 9.67

164SIL/MAR] and [79PER] b[77CHRlHAN] 't59ROB/STO] dEstimated from "I ± of similar compounds. 'See discussion under citrate third law data. 'Bada and Miller [68BADIMIL] give pKl = 2.937 and pK2 = 4.172 at 1=0.1 mol dm-3 measured with a glass electrode. pKI = 3.019 and pK2 = 4.384 are given in Robinson and Stokes. pKl = 3.095 and pK2 = 4.602 are given by Dahlgren and Long [6ODAHILON]. 'Cohn and Edsall [43COHIEDS] give "I = 0.970 and "I = 0.954 for glycine in 0.1 mol dm-3 KCI and 0.1 mol dm-3 NaCl respectively. hThe pK3= 9.371 given by Llapis and Ordonez [63LLAlORD] is inconsistent with a considerable number of alass electrode values. We therefore use pK = 9.67 at 0.1 mol dm-3 K.CI [53LUM/MAR] and calculate pK = 9.93 at I = 0 mol dm-3 using the activity coefficients. ~58HIT] .iEstimated k[52PED] t69JENIKNO] 1II(84SCHlEMP]

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 1058 S~·'L. MILLER AND D. SMITH-MACOWAN

3.8. Gibbs Energy and Potential for the NAD+ I calculated disagrees substantially with the measurements NADH and NADP+ INADPH Systems of the equilibrium constant reported by Happel et al. The disparity appears to stem from the values tabulated The two nicotinamide redox couples, NAD+/NADH for the enthalpies of formation of ethanol and acetalde­ (nicotinamide adenine dinucleotide, formerly referred to hyde. There are also differences in the Il.salG and Il.saP of as DPN or diphosphopyridine nucleotide) and NADP/ .solution between our calculation and Burton's. NADPH (nicotinamide adenine dinucleotide phosphate, The thermodynamic data for the dehydrogenation of formerly referred to as TPN or triphosphopyridine nu­ isopropanol are less variable. Burton employed the val­ cleotide) are centrally important energy mediators in all ues reported by Stull et al_ for the gas phase formation biological systems and have been widely studied for free energies. The equilibrium in the gas phase was mea­ many years. NADH is also a principal product of the sured directly by Buckley and Herington [65BUCIHER] Krebs cycle. at several temperatures. Their enthalpy was in good The reduction potentials (or Gibbs energy change) for agreement with that reported by Stull et al., although these two systems have been measured directly by po­ the entropies adopted were slightly different. The Il.salG tentiometry and from equilibrium constants of several for acetone is significantly different, however. reactions in which they participate. The principal diffi­ There is a consistency in Table 7 in that the values of culty with potentiometric determinations is that NAD+ the aqueous reaction and NADH themselves do not react with the electrode, so dyes that are reversible to the electrode must be used ethanol + acetone = acetaldehyde + isopropanol as mediators. It is very difficult to prove that the NAD/ dye/electrode system is completely reversible. The ma­ can be obtained from the difference of aqueous dehydro­ jor problem with calculations from equilibrium constants genation of ethanol and isopropanol (Il.G = 17.7, t:JI = 1 is the accuracy of the ancillary data needed to derive the 5.1 kJ.mol- ) and from the NAD+ lethanol and NADt I 1 reduction potential. isopropanol reactions (Il.G = 17.4, lUI = 4.3 kJ.mol- ). Clark [6OCLA] presented an extensive evaluation of However, it is apparent from the footnotes that a suitable these potentials, based on the data available at the time. choice of Il.salG and Il.saP can get the numbers to agree The best potentiometric measurements were those of much better. One would have expected that the free en­ Rodkey for NAD+ /NADH [55ROD][59ROD] and ergies and enthalpies of solution of such common com­ NADP+/NADPH [59RODIDON] who gave EO = pounds would be more accurately known, but this is not -0.1042V pH 0 and EO' = 0.3113V pH 7 for NAD+/ the case. Particularly uncertain are the Il.salG and Il.saP NADH. The alcohol dehydrogenase measurements used for acetaldehyde. were those of Burton and Wilson [53BURIWIL] with These 6.G values for NAD+/NADH can be con­ isopropanol/acetone and of Backlin [58BAC] with verted to potentials at pH 0 and pH 7 and I =0.1 mol ethanol/acetaldehyde. However, later measurements by dm-3 by Burton [74BUR] of equilibria catalyzed by yeast alcohol dehydrogenase and measurements by Happel et al. [74HAP/CHA] of the ethanol/acetaldehyde hydrogena­ tion equilibrium, that have been reported in the interven­ ing years, warrant some reconsideration of Clark's results. The reactions and associated data from various The values are given in Table 8. We select the average of sources that have been employed to evaluate the poten­ the ethanol, isopropanol and potentiometric values giv­ tials for both couples are summarized in Table 7. The ing footnotes to the table give the source of the data as well as some, but not all, of the alternative values in the liter­ EO = -0.1042 ± 0.0005 V pH 0 ature. Burton [74BUR] measured the equilibrium constants EO = -0.3113 ± 0.0005 V pH 7 for the reactions NAD+/ethanol and NAD+ /iso­ propanol with yeast alcohol dehydrogenase enzyme, ob­ taining results that agree very well with previous The agreement of the potentiometric potential and the determinations by Burton and Wilson [53BURIWIL]. two equilibria are now excellent and removes the dis­ The potentials for NAD+ and NADP+ were obtained crepancy that so troubled Clark [60CLA]. However this using thermodynamic data for the gas phase and aqueous agreement may well be fortuitous. phase equilibria for the dehydrogenations of ethanol and The potential of the NADP+/NADPH has been mea­ isopropanol. sured at 30°C (-0.3178 V) [59RODIDON] and can be In the case of gas phase dehydrogenation of ethanol, corrected to 25°C by dEo/dT = -1.31 X 10-3 V K-1 the Gibbs free energy of reaction was calculated from [59ROD] to give -0.3104 V at 25°C. This is very close enthalpies of formation and entropies tabulated by Stull, to the potentiometric NAD+/NADPH potential of Westrum and Sinke [69STUIWES]. However, the value -0.3113 V.

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 THE THERMODYNAMICS OF THE KREBS CYCLE AND RELATED COMPOUNDS 1069

TABLE 7. Calculation of the NAD+/NADH and NADP+/NADPH potentials from the ethanoVacetaldehyde and isopropanoVacetone equi­ libria. The standard state for H2 is 1 atm. The standard state for NAD+, NADH, NADP+, NADPH and H+ is 1 m aqueous at an ionic strength of 0.1 m. The values in parenthesis are those used by Burton [74BUR].

A.Go I:Jr kJ·mol-1 kJ.mol-1

CH3CH2OH(g) CH3CHO(g) + Hz 36.4(35.0) _ 69.8(68.4) b CH3CHzOH(aq) CH3CH2OH(g) 13.0(13.4) C 52.6(52.8) d CH3CHO(aq) CH3CHO(g) 6.0(6.1)e 43.3(43.7) f CH3CH2OH(aq) CH3CHO(aq) + H2 43.4(41.6) 79.0(77.4)

NAD+ + CH3CHzOH(aq) NADH + CH3CHO(aq) + H+ 63.3(63.3) m 46.9(46.9) m NAD+ + Hz NADH + H+ 20.0(21.8) -32.1( -30.6)

CH3CHOHCH3(g) CH3COCH3(g) + Hz 21.4(20.5) , 55.6(55.0) h CH3CHOHCH3(aq) CH3CHOHCH3(g) 12.0(12.0) i S8.6(S7.4)j CH3COCH3(aq) CH3COCH3(g) 7.7(8.4)k 41.0(40.9) 1 CH3CHOHCH3(aq) CH3COCH3(aq) + H2 25.7(24.4) 73.3(71.4)

NAD+ + CH3CHOHCH3(aq) NADH+ CH3COCH3(aq) + H+ 45.9(45.9) m 42.6(42.6) m NAD+ + H2 NADH+ H+ 20.2(21.7) - 30. 7( - 28.8)

NAD+ + NADPH NADH + NADP+ -1.0( - 3.0) D 04.0(4.0)D NADP+ + H2 NADPH + H+ 21.1(2S.1)D -26.7( -25.3) D

-Prom measured equilibria by Happel et al. [74HAP/CHA] by our third law analysis. bA calorimetric value of +70.1 kJ was obtained at 82 ° by Kistiakowsky and coworkers [38DOL/GRE] and corrected to +69.1 kJ at 25 0. cProm A..o1G(g-aq) = A.solG(l-aq) + R11n po, where po is the vapor pressure of the liquid. This A.fKJ1G is from [70DAVISIL]. Burton used [3SBUT/RAU]. Other values include 13.2 [68WAGIEVA], 12.9 kJ·mol-1 [78PEM/MAS]. dprom A.fKJtH(liq-aq) = -10.2 kJ.mol-1and A.vap1I = 42.4 [73WIL/ZWO]. Other values of A.fKJtH(liq-aq) include -10.6 [68WAG/EVA], -10.10 [69ALEIHIL1 -10.18 [69ARNIKUV], and -10.4 kJ·mol-1 [S2ROSIWAG] used by Burton. eprom Kurz [67KUR] and used by Burton. Other values include +5.9 kJ·mol-1[36WUR!FIL], +6.4 [70DAVISIL], +6.7 kJ·mol-1 [69BUT/LIN]. i'prom A.vap1I = 25.8 kJ·mol-1 [49COL/DEV] and A.fKJtH(l-aq) = -17.5 [67KUR]. Other values for A.vap1I are 27.2 [SOCOLIPOP] and 26.1 kJ·mol-1 [68WAG/EVA]. Other values for A..otH are -18.4 kJ [69WAG/EVA], -18.4 [S2BEL/CLU] and -17.2 by extrapolation [83FER/ MAR], -17.9 kJ·mol-1 [69RAG/CAV] used by Burton. 'Average of A.rG = 21.SkJ·mol-1 from a third law analysis by us of the measured equilibria of Buckley and Herington [6SBUC/HER1 and A.rG = 21.8 kJ·mol-1 is from the second law analysis. The data of Kolb & Burwell [4SKOLIBUR] give a third law analysis of A.rG = +20.6 and a second law analysis of A.rG = +21.3 kJ·mol-1 [69STUIWES]. hAverage of A.rG = 56.0 kJ from a third law analysis by us of the Buckley & Herington data [6SBUC/HER] and A.rG = 55.2 kJ·mol-1 of their second law analysis. The direct calorimetric measurement of the heat of hydrogenation is + 55.8 at 82°C [38DOLIBRE] and corrected to 55.4

kJ.mol-1 at 25 0. iprom Rytting et al. [78RYT/HUS]. Other values include 12.0 kJ·mol-1 [3SBUTIRAM] used by Burton, and 12.8 [6SHINIWEI]. jProm A.fKJtH(l-aq) = -13.07 kJ·mol-1 [69ARNIKOV] and A.vap1I = 45.5 [73WIL/ZWO]. Other values include -11.8 [SIDIM/LAN] used by Burton, .-13.0 [69ALE/HILl and -13.1 kJ.mol-1 [81ROU/SOM]. kprom [73COX/PAR]. Other values include +8.4 kJ·mol-1 [30BEAlMCV] used by Burton, +8.0 [69BUT/LIN], and +8.8 kJ.mol-1 [31HAR]. lprom A.fKJtH = -10.0 kJ.mol-1 [73COX/PAR] and A.vapH = 31.0 [77CHAIWIL]. Other values of A.KltH include -10.2 and -9.9 [72ARNI BUR],-10.2 [81DEL/STR1 and -9.7 [83BEN/CIL]. Burton used -9.9 kJ·mol-1 without citing a source. mBurton aives K = 6.91 ~ 10-12 and AG = 63.7 kJ.mnl-1 ~t 1 = O.Ol:\mol dm-3 for the ethanol reaction and K - 7.71 X 10-9 and AG - 46.5 kJ at 1 = 0.013 mol dm-3 for the. isopropanol reaction. These can be converted to 1 = 0 and 1 = 0.1 by Backlin's equation [S8BAK110g K = log K (1 =0) + 0.315 Vi, giving K = 6.36 X 10-12 (1 =0 mol dm-3) and 8.01 X 10-12 (1 =0.1 mol dm-3), A.G = 63.9 kJ (1 =0) and 63.3(1 =0.1 mol dm-3). Using the same ionic strength dependence for the isopropanol reaction converts K = 7.71 X 10-9 at 1 = 0.013 to K = 7.10 X 10-9 (1=0) and 8.93 X 10-9 (1=0.1 mol dm-l). A.G = 46.5 (1=0) and A.G = 45.9 (1=0.1 mo1 dm-3). DThis is the.difference of the NAD+ reduction and the tfanshydrogenase equilibrium. The NAD+ reduction values are the average of the ethyl alcohol and isopropanol equilibria. The /:Jl is given in [74BUR].

J. Phy•• Chem. Ref. Data, Vol. 19, No.4, 1990 1060 S. L MILLER AND D. SMITH-MAGOWAN

TABLE 8. Potentials of the pyridine nucleotide couples at 25 0 pH 0 and 7 and I = 0.1 mol dm-3. The I::..G is in kJ.mol-1 at pH O.

NAD+ /NADH

19.96 -0.1034 -0.3105 From ethanol/acetaldehyde (This calc) 21.75 -0.1127 -0.3198 From ethanol/acetaldehyde [74BUR] 20.25 -0.1049 -0.3120 From isopropanol/acetone (This calc) 21.54 -0.1116 -0.3187 From isopropanol/acetone [74BUR] 20.11 -0.1042 -0.3113 Potentiometric [55ROD] 20.11 -0.1042 -0.3113 Value selected

NAnp+ /NAnPH

19.34 -0.1033 -0.3104 Potentiometric [59ROD/DON] 21.13 -0.1095 -0.3166 Transhydroaenase K = 1.50 21.13 -0.1095 -0.3166 Value selected

The NADP+ /NADPH potential can be obtained been found to contain variable amounts of the a-isomer. from the NAD+ /NADH potential and the transhydro­ As the enzymes react mainly with the natural p-isomer, genase equilibrium the presence of 5-20% a-isomer, as is found in some commercial preparations [60KAP], would lead to a com­ NAD+ NADPH = NADH NADP+ + + mensurate error in the measured equilibrium constant. This has been measured directly [53KAP/COL] as K = The problem should be more acute with NAD+ than 1.43 at 37°C but should be nearly the same at 25 °C. with NADP+, as the latter is typically synthesized enzy­ There are two measurements of the glutamate dehydro­ matically from NAD+, so that the product would only genase equilibrium with both NAD+ and NADP+ consist of the p-isomer. Even then the conversion of the P to a-isomer is acid catalyzed and fast (t1/2 is a few glutamate + NAD+ + H2 0 = hours at pH 5) so that initially pure preparations may a-ketoglutarate + NH.. + + NADH + H+ become contaminated [750PP/KAP][87KAM/MAL]. It is evident that a more accurate value of the NAD+ glutamate + NADPH+ + H2 0 = and NADP+ potentials awaits attention to the a-isomer a-ketoglutarate + ~ + + NADPH + H+ problem, as well as using a system whose potential is more accurately known than ethanol/acetaldehyde or the difference being the transhydrogenase reaction. isopropanoVaeetone. The best system would seem to be Olsen and Anfmsen [530LS/ANF] gave K = 1.466 and the formate/bicarbonate system, although the potential Engel and Dalziel [67ENG/DAL] gave 1.60. Burton difference is rather large for an equilibrium measure­ f74BUR1 uses a figure of 3.32 from Engel and Dalziel but ment. Approximate equilibrium measurements have been this is apparently the value at I =0 instead of I =0.1 mol made at 10°C [76RUS/MUL] and at 55 ° [83YAM/SAl] 3 dm- • The average of the three transhydrogenase equi­ which are in fair agreement with those calculated from libria is 1.50 and I::..G = -1.00 kJ. We take for the the 1::..,0 values, but measurements at 25°C are needed. NADP+/NADPH potential for I = 0.1 mol dm-3 Even more accurate would be a potentiometric value whose reversibility could be demonstrated. The poten­ EO = -0.1095 ± 0.0040 V pH 0 tiometric measurement could be for NAD+/NADH or for some organic system that can be directly coupled to EO = -0.3166 ± 0.0040 V pH 7 NAD+ (e.g., lactate/pyruvate or ethanol/acetaldehyde). The enthalpy of reduction of NAD+ by H2 and for­ The error is higher in this case because of the differences mate was measured by calorimetry [79REKlEGO] between the potentiometric determination and the trans­ [81REKIEGO][86REK/GAL] with respective values of 1 hydrogenation equilibrium. -27.2±1.7 and -27.6±1.7 kJ·mol- • These are less There is an additional source of error potentially negative by nearly 5 kJ·mol-1 than the value of -32.1 present in all NAD+ equilibrium measurements. Since kJ·mol- 1 given in Table 7. An attempt to resolve this the time when many of the measurements cited were discrepancy will not be made here, since this study deals performed, commercial preparations of NAD+ have mainly with Gibbs energies.

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 THE THERMODVNAMICS OF THE KREBS CYCLE AND RELATED COMPOUNDS 1061

4. Evaluated Equilibria aGO = -13.70 ± 0.04 kJ·mol-1

Reaction 1. Succinate Dehydrogenase This is based on the measurements of K = 3.98 X 10-3 at 1=0.1 mol dm-3 by Goldberg et ale [86GOL/ fumarate + H2 = succinate GAJ]. The equilibrium was investigated at temperatures between 13°C and 43 °C and ionic strengths between AGo -84.43 ± 0.19 kJ·mol-1 = 0.066 and 0.366 mol kg-I. There is a slight systematic This is based on the potential measured by Borsook difference between these results and those of Bada and 3 3 and Schott [31 BOR/SCHa,b] using succinate dehydro­ Miller (K = 4.64 X 10- at 1=0.1 mol dm- ) [68BAD/ genase, methylene blue mediator, and a platinum elec­ MIL], who investigated the enzyme-catalyzed reaction trode. from 5 to 36°C and compared the results with non-enzy­ matic attainment of equilibrium at temperatures of fumarate + 2e- + 2H+ = succinate 118°C and 136 °e. The difference may be due to the use of KCl as background electrolyte in one case [86GOL/ EO +0.4375 ± 0.0010 pH 0 = GAJ] and NaCl in the other [68BADIMIL]. EO' = +0.0234.L 0.0010 pH 7 Reaction 4. Malate Synthetase The Gibbs energy is given by AGO = -nFEo. An acetate + glyoxylate = L-malate error of 0.0010 V corresponds to 0.20 kJ·mol-1 in aG. Since the ratio of activity coefficients should be about 1, aGO = -14.6 ± 2.0 kJ·mol-1 the ionic strength dependence should be small. Potential measurements of enzyme equilibrium have always been Hersh [73HER] determined the equilibrium constant difficult and prone to large errors. However, this deter­ for the reaction : mination is one of the few that seems accurate. The AG acetyl-CoA + glyoxylate = malyl-CoA value is conflmled by A,E'/ AT (between 18 and 30°C) giving!:JI = -124.9 kJ·mol-1 that can be compared to obtaining a value of K = 330 at 30°C or aGo = -14.6 1 l thermal data yielding Ml = -131.8 kJ·mol- (Table 2). kJ·mol- • Assuming that the free energies of hydrolysis Borsook and Schott calculated the AG for this reaction of acetyl- and malyl-CoA are the same, as seems to be from the heats of combustion and third law entropies the case for acetyl CoA and succinyl CoA [78LYN/ and obtained remarkably good agreement, -20.14 kcal Guy], and neglecting the dependence on temperature, mol-l from the potential measurements compared to leaves this as the value for reaction 4. The approxima­ -20.46 kcal mol-l from the third law calculation. This tions made should be within the stated uncertainty. paper was widely cited as evidence that thermodynamics is applicable to biological systems [81SLA]. The excel­ Reaction 5. Isocitrase lent agreement of the two ArG is apparently the result of succinate glyoxylate = isocitrate a cancellation of errors. The error in the entropy of suc­ + l 1 cinate (2.0 cal K-1.mol- ) by itself would result in an aGo = -16.0 ± 2.0 kJ.mol- error in ArG of 0.60 kcal mol-I, and the errors in the arB of succinic and fumaric acids were comparable. The active isomer is threo Ds (+) isocitrate [62VIC] but will be referred to here as isocitrate. Williams et al. Reaction 2. Fumarase [71WIL/ROC] reported K = 430 for direct determina­ tion of the equilibrium at 27°C, (the range was 320 and fumarate H 0 = L-malate + 2 630). They calculated K = 630 from the ratio of forward aGo = -3.57 ± 0.04 kI·mol-1 and reverse rate constants. These measurements were 3 obtained at pH 7.7 and 1= 0.1 mol dm- , corresponding This is based on Krebs determination, at 1=0.1 mol to aG = 15.0 kI and -16.0 kI, respectively. The av­ 3 dm- , of K =4.32 [53KREa] and is in close agreement erage is -15.5 kJ, for 27°C. However, at 25 °C the equi­ with Bok and Alberty'S value of 4.26 [53BOK/ALB]. librium should be slightly more to the right, so we have Recent determinations by Goldberg et ale [85GAJ/ assigned a value of -16.0 kJ for this reaction. GOL] at several ionic strengths lead to a value of 4.20 ± This is a difficult equilibrium to measure. For example, 0.05 which is also in very good agreement. It is con­ a previous study [57SMI/GUN] reported a value of K = flmled by high temperature non-enzymatic, base cata­ 34, but this was in error because the reaction mixtures lyzed reaction [59ERI/ALB]. It is in agreement with the contained cysteine which binds to glyoxylate. This is one value of 4.25 ±0.08 given by Cook et ale [80COO/ of the more useful equilibria in the Krebs cycle. BLA]. Reaction 6. Citrate-oxaloacetate Lyase Reaction 3. Aspartase acetate + oxaloacetate = citrate 1 fumarate + ~ + = L-aspartate AGO = -2.43 ±0.59 kJ·mol-

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 1062 S. L MILLER AND"O. SMITH-MAGOWAN

This is based on the value reported by Tate and Datta kcal is due primarily to the uncertainty in this potential. [65TAT/DAT] of K =3.08 ± 0.72 for 25°C, 1=0.1 Cook et ale [80COO/BLA] give Keq for dissolved COz mol dm-3 and oxaloacetate in the keto form. For as 1.04±0.18 M which becomes 30.4 for COz gas. aqueous oxaloacetate this becomes K =2.65±0.72. Reaction 10. Glycolate Dehydrogenase These measurements are complicated by complexing with magnesium ions, and the above has been corrected glycolate + NAD+ = by extrapolation to Mg+z = O. Harvey and Collins [63HAR/COL] report a value of 15.7 at 30°C but the glyoxylate + NADH + H+ equilibrium was measured only from the cleavage direc­ tion. Guynn et al. [73GUY/GEL] report a value of AGO = +84.35 ± 0.67 kJ·mol-1 3 K =0.94 ±0.07 at 38°C and 1=0.25 mol dm- ; however a reliable correction to 25°C and 1=0.1 mol dm-3 is not This is based on Zelitch's measurement [55ZEL] of 15 feasible because AJI is not known and the 'Y corrections K = 1.65±0.43 X 10- • Later measurements [68KOH/ are large. JAKb][70KOH/WAR] gave values of 2.61 X 10-15 and 15 2.90 X 10- • The systematic shift towards glyoxylate Reaction 7. Aconitase may be due to the presence of Tris buffer, which can complex the glyoxylate. The value of 6 X 10-18 of cis -aconitate + H20 = citrate Cartwright and Hullin [66CAR/HUL] seems to be too low. Other problems suggest that the equilibrium should AGO = -8.49±0.04 kJ.mol-1 be reinvestigated to obtain a more reliable value.

Reaction 11. Lactate Dehydrogenase This is based on measurements of the amount of aconi­ L-Iactate + NAD+ = tate in equilibrium with citrate and isocitrate. There is an equivalent equilibrium of cis -aconitate + H20 = isoci­ pyruvate + NADH + H+ trate, but the difference between these AG values is that AGO = 65.98 ± 0.42 kJ·mol-1 for isocitrate = citrate. There are several values for K of about 20 in the literature [43KRE/EGG] [66THO/ We have selectedK = 2.76 X 10-12 which is the value NAN], and several around 30 [43MAR/LEO][53KREa]. reported by Hakala et al. [56HAK/GLA]. They also We will use Krebs value of 30.7 [53KREa]. measured the temperature coefficient, obtaining a value of!::JI = 43.1±0.8 kJ·mol-1 which is in agreement with Reaction 8. Aconitase an early calorimetric value of tJl = 44.4±1.1 kJ·mol-1 [55KAT] but not with later values of tJl = 61.9±1.3 isocitrate = citrate kJ·mol-1 [75DON/BAR] and !:JI = 55.8±1.1 kJ·mol-1 [79SCH/HIN]. Cook et 01. [8OCOO/BLA] reported an 1 12 AGO = -6.11 ± 0.20 kJ·mol- equilibrium constant of K = 2.19±0.08 X 10- • There is a direct potentiometric measurement for the reaction This is based on the results of Blair [69 BLA] at 1=0.1 Labeyrie [60LAB/NAS]. mol dm-3 and 25°C. The Mgz+ was extrapolated to zero with the ionic strength maintained at 0.1 M by Na +, pyruvate + 2e- + 2H+ = lactate giving K = 11.73. With tetramethylammonium as cation, 3 the value of Kwas 9.31 at 1=0.1 mol dm- • Other values of EO = -0.188±0.OO3 V at 25°C and pH 7 (corrected include 14.7 [53KREa] and 7.8 [67ENG/DEN] The from -0.190 V at 27 U). If the NAD"T INAUH potential value of 11.73 is adopted here. is taken as -0.320 V at 25°C and pH 7, then K = 3.4 X 10-12 and AG = 65.4 kJ.mol-t, but the agreement is Reaction 9. Isoeitrate Dehydrogenase mueh less if the NAD+INADH potential is taken as -0.311V. Earlier measurements of Barron and Hastings isocitrate + NADP+ = [34BARIHAS] and of Wumiser [33WUR/MAY] gave EO values of -0.158 V. These may be correctable to a-ketoglutarate + NADPH + COz(g) -0.167 V if they used DL-Iactate instead of L-lactate, but -0.167 V is still in disagreement with the measure­ AGO = -8.0±1.2 kJ.mol- 1 ments of Labeyrie et al. An accurate potential for lac­ tate/pyruvate would be most useful. This is based on the measurements of Londesborough Reaction 12. Malate Dehydrogenase and Dalziel [68LON/DAL] at 25°C and 1=0.1 mol 3 dm- , who gave K = 25.6. The effect of ionic strength L-malate + NAD+ = and Mg2+ was small, but there is considerable uncer­ oxaloacetate + NADH + H+ tainty in the potential of the NADP/NADPH redox couple as discussed above. The assigned error of 0.30 AG = +68.37 ± 0.41 kJ·mol-1

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 THE THERMODYNAMICS OF THE KREBS CYCLE AND RELATED COMPOUNDS 1063

This is based on Burton and Wilson's [53 BUR/WIL] Reaction 16. Malate-lactate Transhydrogenase value of K = 1.05 X 10-12 for the reaction at I = 0.1 mol dm-3 (K =0.6 X 10-12 at I =0). Later results have been L-Iactate + oxaloacetate = pyruvate + L-malate in .very good agreement with this value. These include K = 1.28 X 10-12 [68KOH/JAKa], 0.79 X 10-12 I1GO = -1.46±0.60 kJ·mol-1 [65YOS], K = 1.03 X 10-12 [62RAV /WOL], K = 0.59 X 10-12 [75SCHIRIF] and K = 0.71 X 10-12 [80COOI The equilibrium constant for this reaction is given in BLA]. Guynn et 01. [73GUY/GEL] give K=1.02 ±.03 Methods of Enzymology [69ALL] as K = 1.8±0.4. The X 10-12 at I =0.25, which corrects to K = 0.73 X 10-12 temperature is not specified but is assumed to be 25°C. at I =0.1 mol dm-3 using the ionic strength dependence given by Burton and Wilson [53BUR/WIL]. A calori­ Reaction 17. Isocitrate-pyruvate Transcarboxylase metric measurement gave till = 89.5±0.8 kJ·mol-1 [76JES]. pyruvate + isocitrate =

Reaction 13. Malic Enzyme L-malate + a-ketoglutarate

L-malate + NADP+ = I1GO = -6.69±0.80 kJ·mol-1

pyruvate + C01(g) +. NADPH + H+ This is not a single enzyme, but rather a combination of aG = +1.00±1.20kJmol-1 the malic enzyme and isocitrate dehydrogenase. Ochoa [53HARIKOR] [500CHIVEI] gives a value of (-15 for Ochoa and coworkers [53HARlKOR] measured this the equilibrium constant. Since this is a directly mea­ equilibrium at pH = 7.4 and 22-25 °C, yielding sured equilibrium which does not require a potential for NADP, the uncertainty is taken to be ±0.8 kJ. K [malate] [NADP+] - 19 6 = [pyruvate][C02 (aq)][NADPH] - . Reaction 18. Glutamate Dehydrogenase

Schimerlik and Cleland [77SCH/CLE] give values of K = 83 and 22 as determined from ratios of rate con­ a-ketoglutarate + NH. + + NADH + H+ stants and a value of K = 33.0±2.0 determined from a directly measured equilibrium constant. Using the value aGO = + 74.80±0.80 kJ mol-1 of K = 19.6± 10 for this reaction and the value given in 1 Table 1 for CO2(g) = CO2(aq) (I1Go = +8.37 kJ.mol- ) yields the value given above. Bngel and Dalziel [67BNG/DAL] measured this equi­ librium using both NAD+ and NADP+, obtaining values Reaction 14. Oxaloacetate Decarboxylase atI = 0.1 mol dm-3 of K = 8.17 X 10-14 andK = 5.10 X 10-14 respectively. Olsen and Anfmsen [530LSI oxaloacetate + H 20 = pyruvate + HC03- ANF) also measured these two systems and obtained val­ ues of K = 14.4 X 10-14 (NAD) and 8.9 X 10-14 I1Go = -25.94±1.25 kJ·mol-1 (NADP). However, the ionic strength in this case was 3 0.47 mol dm- • Several investigators have made determi· The value selected is that reported by Wood et al. nations using only NADP. Cook, et al. [8OCOO/BLA] [66WOO/DAV]. It is based on a complicated set of equi­ obtained the value K = 4.4 ± 0.1 X 10-14 at an ionic 3 lihria involving phosphoenol pyruvate and A TP hydrol­ strength of apparently 0.1 mol dm- • Subramanian ysis. It is difficult to evaluate, but it is consistent with the [78SUB] obtained a value of K = 7.3 X 10-14 at I = malic enzyme and malic dehydrogenase equilibria. The 0.305 mol dm-3 which becomes K = 4.1 X 10-14 at uncertainty assigned is estimated. I =0.1 mol dm-3 using the ionic strength dependence of Engel and Dalziel. The value for NADP relative to that Reaction 15. a-Hydroxyglutarate Dehydrogenase for NAD, as determined by Engel and Dalziel, has been used in estimating the NADP/NADPH potential. These L-a-hydroxyglutarate + NAD+ = subsequent measurements using the NADP reaction give values that are consistent with the choice of K 8.17 X a-ketoglutarate + NADH + H+ = 10-14 for the equilibrium with NAD. A value of Il.H = aG = +67.53 ± 0.21 kJ mol-1 73.2 kJ.mol- 1 was obtained from the temperature dependence of the equilibrium constant [67ENG/DAL] This equilibrium was measured by Buckel & Miller and till = 64.6±1.2 kJ.mol-1 by calorimetry [87BUCIMIL]. [78SUB][79 SUB].

J. Phys. Chem. Ref. Data, Yol. 19, No.4, 1990 1064 s. L. MILLER AND D. SMITH-MAGOWAN

Reaction 19. Alanine Dehydrogenase is obtained as the sum of the pyruvate-formate lyase re­ action L-alanine + NAD+ + H20 = o o pyruvate + NIl.+ + NADH + H+ II II CH3 C 000- + HPO~- CH3 C PO~- + HCOl flGo = 75.15 ± 0.80 kJ·mol-1 aGO = - 7.7::1::3.0 kJ.mol 1 The equilibrium measured at pH 10 [600CO/HAL] 14 and the hydrolysis of acetylphosphate and corrected for ionization gives K = 3.85 X 10- , a Yoshida and Freese [65YOS/FRE] reported an equi­ II librium constant of K = 3.1 X 10-14, while Grimshaw CH3COPO~- + H20 and Cleland [81GRI/CLE] obtained a value of K = 6.8 o X 10-14 which is selected. II CH CO- HP04" H+ Reaction 20. Aspartate-glycine Transaminase 3 + + flGo = -43.1 kJ.mo~-1 (PH 7)

L-aspartate + glyoxylate = oxaloacetate + glycine t = -3.1 kJ·mol- (PH 0) 1 flGo 10.2±1.20 kJ.mol- , The ftrst reaction was measured by Tanaka and Johnson This is based on an equilibrium constant of K = 61 [71 TAN/JOM] as K = 23 at 37 ° with a substantial error determined by Gibbs and Morris [66GIB/MOR][7OGIB/ since the acetyl phosphate is unstable. The flG for the MaR]. The experiment was not well described in the hydrolysis of acetyl phosphate is Jenck's value [76JEN] reference so the error may be understated. In measuring Reactions 24-28. Glutamate to Acetate and Pyruvate this equilibrium, care should be taken to establish that the aspartate or other amino acid has not been racemized Reaction 24 is the overall reaction. since glyoiylate is a catalyst for this reaction. L-glutamate + H 20 = Reaction 21. Glutamate-alanine Transaminase acetate + pyruvate + ~ + L-glutamate + pyruvate = aGo = 8.70 ± 0.80 kJ.mol-1 a.-ketoglutarate + L-alaninc This is the sum of reactions 25-28 studied by Barker and 6..Go = -1.04±O.13kJ.mol-1 coworkers. The sequence of reactions is:

Krebs [53K.REb] has reported a carefully determined L-glutamate = L-threo-~-methyl aspartate value for the equilibrium constant of 1.52. The deviation flGo = +5.86±0.12 kJmol-1 (Reaction 25) between experimental values was no more than 9% and dp.tp.rmination~ l1~ing the racemic mixture yielded the L-threo-/3-methyl agpartate = mesaC'.onatp. + NH.. + same value as using the L-isomer. The experimental con­ flGO +3.56±0.42 kJ·mol-1 (Reaction 26) ditions were very close to the recommended values of = 3 25°C and 1=0.1 mol dm- • Values of K = 1.6 and K = mesaconate + H20 = L-citramalate 1.7 at 37 DC have been reported [62SBG/BBA][65MARJ 1 TER]. . flGo = -4.31±0.54 kJ.mol- (Reaction 27) L-citramalate acetate pyruvate Reaction 22. Glutamate-aspartate Transaminase = + flGo = +3.60±0.04 kJ·mol-1 (Reaction 28) L-glutamate + oxaloacetate = a-ketoglutarate + L-aspartate L-alutamate + H20 = acetate + pyruvate + NHt flGo = -4.73±0.12 kJ.mol-1 flGO = +8.70±0.80 kJ.mol-1 This is based on the value of 6.74 for the equilibrium Mesaconate is methyl fumarate and citramalate is a­ constant given by Krebs [~3KREb]. The deviation methyl malate. among reported values is only 4% (in K) and all precau­ tions against systematic errors appear to have been CH3 taken. -OQC CH3 \ / -OOC-CH2--t--COO­ Reaction 23. Pyruvate Formate Lyase C=C / \ I H COO- The equilibrium constant for the reaction OH

pyruvate + H20 = acetate + formate + H+ flGo = 10.8 ± 4.0 kJ

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 THE THERMODYNAMICS OF THE KREBS CYCLE AND RELATED COMPOUNDS 1065

Barker et al. [64BARIROO][69BARa] measured a-ketoglutarate + NAD+ +CoA =

(L-glutamate) succinyl-CoA + NADH + H+ + CO2(g) (L-threo-J3.methyl asparate) succinyl-CoA + GDP + Pi

10.7 0.4 at pH 8.2, 30 0 ± succinate + GTP

The correction to 25 0 should not be large. GTP = GOP + Pi

Barker et al. [59BAR/SMy] measured. The first reaction is probably reversible, but the K.eq ap­ parently has not been measured. This combined with I1G (mesaconate)(NHt) _ of hydrolysis of succinyl CoA would give a value of I1G (hthreo·,8-methyl asparate) - for reaction 9. 0.238 at pH 7.9 and 0.306 at pH 9.7 Reaction C. Glycine Dehydrogenase Barker et al. [69WANIBARa][69WANIBARb] mea­ glycine + NAD+ + H20 = sured glyoxylate + NH..+ +NADH + H+ L-citramalate) = 5.8 ± 1.0 (mesaconate) A value of the equilibrium constant of 2.3x 10-11 ha.~ been reported for this reaction [62GOLIWAG], but this The value was 4.6 in the forward direction and 7.0 in value is inconsistent with the transamination equilibria, the reverse direction. so this reaction has not been included in the analysis. Buckel and Miller [87BUCIMIL] measured Reaction D. Aspartate Dehydrogenase (acetate)(pyruvate) _ 0232 + 0008 (L-citramalate) -. _. . aspartate + NAO+ + H20 = oxaloacetate + NIl. + + NADH + H+ This differs from an earlier value [67BAR][69BARb]. There is no direct measurement of this equilibrium There are a number of reactions related to the Krebs 1 (110 --80 kJ.mol- ). However several transamination re­ cycle that have not been included because their equi­ actions can be manipulated to yield an equivalent reac­ librium constants are not known. These include: tion. Reaction A. Citrate Synthetase (or Condensing Enzyme) Reaction E. Pyruvate Decarboxylase acetyl CoA + oxaloacetate + H20 = Pyruvate + NAD+ + H20 = citrate + CoA + H+ Acetate + NADH + CO2 (g) + H+ I1G o --32.2 kJ.mol-1 This reaction is considered irreversible (I1G = -32 This equilibrium constant is K = 4.65 X 10' at 22°C kJ·mol-1 at pH 0 and -72 kJ·mol-1 at pH 7). However, and pH 7.2 (2.93 X 10-2 at pH 0) [52STE/OCH] ang K = the reaction is just measurable if the reaction is pulled to 2.24X 106 at 38°C and pH 7 (0.224 at pH 0) [63GUYI the left by reduction of the pyruvate to lactate. GEL]. This reaction is related to Reaction 6 by the hy­ drolysis of acetyl-CoA, and the network could be 5. Results and Discussion rermed if reliable measurements for this hydrolysis con­ stant were available. The published values for the Gibbs The results of the CATCH analysis of this Krebs cycle energy of hydrolysis, variously reported as -30.8, network are shown in Table 9. The differences between -36.4 and -34.5 kJ.mol-1 [55BUR] -31.5 [64JENI the experimental and calculated 110 of reaction are OIL] and -35.7 kJ·mol-1 [78LYN/Guy], are too dis­ mostly less than the uncertainty of the experimental data. parate to be used in the network. The ··succinate + acetate" results appear to be superior to the "all 3rd lawu calculation, even though one would Reaction B. a-Ketoglutarate Dehydrogenase expect superior results when the system is anchored with more third law data. However, it takes only one bad a-ketoglutarate + NAO+ + H 0 = 2 third law value to distort the results. The most probable succinate + NADH + H+ + CO2(g) compound with bad third law I1tG in this system is fu­ marate, where the uncertain entropy could result in a This reaction is irreversible as written (I1G = - 24.4 third law I1tG too low by 1 kJ·mol-1 or more. The 3rd kJ at pH 0 and -64.3 at pH 7) and is the sum of several law aspartic acid and glutamic acid values may also be in reactions in the Krebs cycle, i.e.; error, in this case from the enthalpy of combustion.

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 1066 S. L. MILLER AND D. SMITH-MAGOWAN

TABLE 9. CATCH analysis of the ,Krebs cycle network. The succinate + acetate calculation used only these third law Il.tG. The All 3rd law calculation used the Il.tG of fumarate, glycine, alanine, aspartic acid and glutamic acid in addition.

Il.rG/kJ.mol- 1

Reaction Expt Succinte All3rd + acetate law

01. Fumarate + Hz = Succinate -84.43 -84.46 -84.49 02. Fumarate + H20 = Malate -3.57 -3.34 -3.27 03. Fumarate + NHt = Aspartate -13.72 -13.77 -13.80 04. Acetate + Glyoxylate = Malate -14.39 -14.33 -14.30 05. Succinate + Glyoxylate = Isocitrate -15.98 -16.11 -15.93 06. Acetate + OXaloacetate = Citrate -2.43 -2.32 -2.36 07. Aconitate + H20 = Citrate -8.49 -8.49 -8.49 08. Isocitrate = Citrate -6.11 -6.15 -6.13 09. Isocitrate + NADP+ = a-Ketoglutarate + CO2(g) + NADPH -8.03 -7.86 -7.75 10. Oly~olate + NAD+ = OlyuAylatc:: + NADH + H+ 34.3' 34.3' 34.3' 11. Lactate + NAD+ = Pyruvate + NADH + H+ 65.98 66.35 66.35 12. Malate + NAD+ = Oxaloacetate + NADH + H+ 68.37 68.35 68.34 13. Malate + NADP+ = Pyruvate + C02(g) + NADPH + H+ 1.00 1.07 -0.24 14. OxaloacetAtc + 1120 Pyruvate + HCOl- -25.94 -25.89 -25.68 15. a-Hydroxyglutarate + NAD+ = a-Ketoglutarate + NADH + H+ 67.53 67.53 67.53 16. Lactate + Oxaloacetate = Pyruvate + Malate -1.46 -1.99 -1.99 17. Pyruvate + Isocitrate = Malate + a-Ketoglutarate -6.69 -6.79 -6.70 IS. Glutam.o.tc + NAD+ + H 20 ~ a-Ketoglutarate + NI~+ + NADII + 11+ 74.70 74.12 74.16 19. Alanine + NAD+ + H20 = Pyruvate + NII.+ + NADH + H+ 75.15 75.16 75.17 20. Aspartate + Glyoxylate = Oxaloacetate + Glycine -10.21 -10.21 -10.38 21. Glutamate + Pyruvate = a-Ketoglutarate + Alanine -1.05 -1.04 -1.01 22. Glutamate + Oxaloacetate = a-Ketoglutarate + Aspartate -4.73 -4.66 -4.72 23. Pyruvate + H20 = Acetate + Formate + H+ -10.92 -10.64 -10.85 24. Glutamate + H20 = Acetate + Pyruvate + ~ + 8.70 8.74 8.74 25. Glutamate = ~-Methylaspartate 5.86 5.86 5.86 26. ~-Methylaspartate = Mesaconate + NIl.+ 3.56 3.57 3.57 27. Mesaconate + H20 = Citramalate -4.31 -4.30 -4.30 28. Citramalate = Acetate + Pyruvate 3.60 3.61 3.61 29. NAD + H2 = NADH + H+ 20.12 19.92 20.00 30. NADP + H2 = NADPH + H+ 21.02 21.04 20.93 31. Elements = Formate -351.16 -351.17 -351.17 32. Elements = Succinate -690.07 -690.08 -689.84 33. Elements = Acetate -372.21 -371.55 -371.29 34. Elements = Fumarate -604.25 -605.63 -605.35 35. Elements = Glycine -371.29 -370.61 -370.74 36. Elements = Alanine -370.49 -371.40 -370.84 37. Elements = Aspartate -700.74 -698.87 -698.62 38. Elements = Glutamate -696.34 -697.45 -696.71

The IlrG of the compounds are given in Table 10. The equilibrium constants involving this compound are rela­ results of the two calculations are mostly within 0.5 tively uncertain. l l kJ·mol- and none differ by more than 1.0 kJ·mol- • The The Il.P's in Table 10 are self-constant. Care should differences with the third law Il.P is somewhat more but be taken in combining these values with those in other

still satisfactory. tables, since the combined errors in the Ilr G could be The errors given for IlP in Table 10 may be to small, quite large. since they are dependent on the input data and the rather arbitrary errors assigned to the enzyme equilibria. In 6. Extensions and Improvements cases where the compounds are involved in a number of reactions, (e.g., fumarate and alanine), the error esti­ There are a number of branches to the Krebs cycle mates are probably correct. The error estimates may be which can be put into this network. These include oxalic too low for compounds connected to the network by acid, fatty acids, alcohols, amines, other amino acids and only one reaction. Examples are glycolate, glycine, and even sugars. Equilibrium constants are not available for a-hydroxyglutarate. The IlP for glyoxylate may be in all the steps in these branches, so some experimental error by an amount greater than indicated because all the work will be required.

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 THE THERMODYNAMICS OF THE KREBS CYCLE AND RELATED COMPOUNDS 1067

TABLE 10. Gibbs energies of formation of Krebs cycle compounds. because of the metastability of the supersaturated The "succinate + acetate" and "all third law" columns solutions, even though the stable phase is the trihydrate. are as described in Table 9. The 11,0 of NAD+ and Third law entropies have been obtained for L-serine and NADP+ have been set at -418.40 kJ/mol and are not the actual values. L-proline, but the solid phases at saturation are hydrates. In addition the DL-amino acids are very much less solu­ ble in these two cases, and the activity coefficients have been measured nearly to saturation for these racemic succinate + acetate all3rd law amino acids. Modem enthalpies of solution for a number of amino acids are needed with aspartic acid, glutamic acid, as­ Formate -350.99 ± 0.20 - 350.99 ± 0.20 Acetate -371.57 ± 0.33 -371.33 ± 0.37 paragine and glutamine being prime candidates. Those Succinate -690.08 ± 0.29 -689.74 ± 0.35 planning to make measurements of AsaP should select Fumarate -605.61 ± 0.35 -605.24 ± 0.34 compounds with modem third law entropies and en­ Mesaconate -608.54 ± 0.68 -607.83 ± 0.61 thalpies of combustion. Glycolate - 523.68 ± 0.82 -523.75 ± 0.91 The problems of the NAD+ and NADP+ potentials L-Lactate -520.29 ± 0.52 -519.92 ± 0.48 L-Malate -846.14 ± 0.41 -845.91 ± 0.36 have been reviewed along with the problem of the a-iso­ L-Citramalate - 850.03 ± 0.67 -849.35 ± 0.61 mer. An accurate potentiometric measurement would be L-a-Hydroxyglutarate -848.58 ± 0.83 -847.90 ± 0.83 ideal. Although the potential at 1=0 mol dm-3 is good Glyoxylate -460.25 ± 0.44 -460.30 ± 0.44 to have, the real need is at I ...... O.l mol dm-3• The next Pyruvate -474.85 ± 0.46 -474.44 ± 0.44 most accurate way to obtain this potential is to measure Oxaloacetate - 798.71 ± 0.46 -798.40 ± 0.50 a-Ketoglutarate -801.97 ± 0.75 - 801.26 ± 0.72 the equilibrium constant for reaction with formate/bicar­ Glycine -370.60 ± 0.69 -370.77 ± 0.51 bonate at 25°C. This is an accurately known potential L-Alanine -371.38 ± 0.49 -370.88 ± 0.39 although the equilibrium lies far to the side of reduction L-Aspartate -698.85 ± 0.37 -698.52 ± 0.35 of NAD+. Even better would be the equilibrium using L-Threo-~-methylaspartate -691.57 ± 0.67 -690.83 ± 0.57 L-Glutamate -697.43 ± 0.67 -696.90 ± 0.55 Hz. Citrate -1172.59 ± 0.62 -1172.11 ± 0.62 The lyase reactions tie the Krebs cycle network D-Isocitrate -1166.44 ± 0.61 -1165.98 ± 0.61 tightly together, so that really accurate ArG for the cit­ cis-Aconitate -926.91 ± 0.75 -926.43 ± 0.80 rate, isocitrate and malate lyase reactions would be very NAD+ -418.40 ± 0.00 -418.40 ± 0.00 valuable. Several carboxylation reactions would be of NADH -397.48 ± 0.31 -397.51 ± 0.36 NADP+ -418.40 ± 0.00 -418.40 ± 0.00 interest, examples being acetate to pyruvate and succi­ NADPH -396.38 ± 0.36 - 396.53 ± 0.41 nate to a-ketoglutarate. These reactions are very unfa­ vorable at the level of the keto acid, but reduction to the amino acid or hydroxy acid would be measurable with a strongly reducing couple such as formate/bicarbonate. The present network can be improved in a number of Accurate equilibrium constants are usually easier to ways. Enthalpies of combustion can always be im­ measure with pH independent reactions than with those proved. It is recognized how difficult these measure­ involving NAD+/NADH. Examples are transamination ments are, but the data are badly needed. It is suggested and amination equilibria, e.g. that the enthalpies of combustion be measured on differ­ ent compounds of the same substance. Thus, to obtain alanine + a-ketoglutarate = pyruvate + glutamate better data on the acetate ion, it would be better to mea­ sure five samples of acetic acid and five of ammonium alanine + H20 = lactate + ~ + acetate instead of ~n 5alD.plc!i of acetic acid, which is difficult to obtain water free. It is necessary to have the These reactions are various sums of the alanine, gluta­ enthalpy of solution to compare the results, but AsaP are mate and lactate dehydrogenases, but more accurate data relatively easy to obtain accurately. Similarly it is hetter for the dehydrogenases should be obtainable using the to split the samples among D, Land DL-alanine instead transamination and amination equilibria combined with of using only L-alanine. one good dehydrogenase equilibrium, e.g., alanine dehy­ There are a number of third law entropies that would drogenase. be useful to have, with fumarate being the prime candi­ date since it is more central to the Krebs cycle than succinate. There seems little point in obtaining third law 7. Glossary of Symbols and Terminology entropies of compounds for which the entropy of solution is difficult to obtain. Examples are lactic acid, English pyruvic acid and isocitric acid, which are very soluble and which form polyesters, aldol products and a lactone. m concentration of solution expressed as molality The heat capacity should be measured on the compound (amount of solute per kg of water) which is in equilibrium at saturation. It was fortunate n moles of substance that the So of anhydrous sodium acetate was usable x mole fraction

J. Phy•• Chem. Ref. Data, Vol. 19, No.4, 1990 1068 S. L. MILLER AND D. SMITH-MAGOWAN

EO, Emf at pH 0 9. References EO' Emf at pH 7 15BRA Branch, G. E. K. (1915) The free energy of formation F Faraday (96487 C mol-I) of formic acid, J. Am. Chem. Soc. 37, 2316-2326. G Gibbs energy 23LEW/RAN Lewis, G. N., & Randall, M. (1923) Thermodynamics H enthalpy (McGraw Hill, New York), p. 584-585. 23WEI/DOW Weiss, J. M., & Downs, C. R. (1923) The physical I ionic strength properties of maleic, fumaric and malic acids, J. Am. K equilibrium constant Chem. Soc. 45, 1003-1008. M concentration of solution expressed as molarity 25BLA Blaschko, H. (1925) tiber die Verbrennungswanne der (amount of solute per 1000 cm30f solution) Brenztraubensiure und ihre Physiologische Bedeu­ P pressure (atm) tung, Biochem. Z. 158, 428-434. 29BRE/CAR Bredig, G., Carter, S. R., & Enderli, M. (1929) tiber R gas constant (8.31441 J·mol-I·K-I) das Gleichgewicht der Kohlendioxyd-Abspaltung aus S entropy Ameisensaure und ihr Potential, Monatsch. 54, 1023- T thermodynamic temperature 1030. V volts 29PAR/KEL Parks, O. S., Kelley, K. K., & Huffman, H. M. (1929) Thermal data on organic compounds. V. A revision of the entropies and free energies of nineteen organic NAD+ Nicotinamide adenine dinucleotide compounds, J. Am. Chem. Soc. 51, 1969-1973. NADH Reduced nicotinamide adenine dinucleotide 30BEAIMCV Beare, W. G., McVicar, G. A., & Ferguson, J: B. NADP+ Nicotinamide adenine dinucleotide phosphate (1930) The determination of vapour and liquid compo­ NADPH Reduced nicotinamide adenine dinucleotide sitions in binary systems. II. Acetone-water at 25 0, J. phosphate Phys. Chern. 34, 131{)-1318. CoA Coenzyme A 30LAN/SIN Lange, N. A., & Sinks, M. H. (1930) The solubility, specific gravity and index of refraction of aqueous s0- ATP Adenosine triphosphate lutions of fumaric, maleic and i-malic acids, J. Am. ADP Adenosine diphosphate Chem. Soc. 52, 2602-2604. AMP Adenosine monophosphate 30PAR/HUF Parks, G. S., & Huffman, H. M. (1930) Thermal data GTP Guanosine triphosphate on organic compounds. IX. A study of the effect of unsaturation on the heat capacities, entropies and free GDP GuannRine diJlhnRJlhate energies uf sume hydrocl:lrbu~ and uthcr cuwpuunWi, Inorganic orthophosphate J. Am. Chem. Soc. 52, 4381-4391. 30WAS Wassermann, A., (1930) Die zwischenmolekularen Greek: Bindungsfestigkeiten der Fumar- und Maleinsiure and wcr Diwcthyl~tcr. Z. Physik.. Chcw. A 146, 418- 445. "y activity coefficient 31BORJSCHa Borsook, H., & Schott, H. F. (1931) The role of the A change in a property enzym~ in the succinate-enzyme-fumarate equilibrium, J. BioI. Chem. 92, 535-557. Superscripts: 31BORJSCHb Borsook, H., & Schott, H. F. (1931) The free energy, heat, and entropy of formation of I-malic acid, J. BioI. standard state quantity Chem. 92, 559-567. 31HAR Hartley, G. S. (1931) Diffuaion IUld distribution in II solvent of graded composition, Trans. Faraday Soc. Subscripts: 27, 10-29. 33WUR/MAY Wurmser, M. R., & Mayer-Reich, M. N. (1933) f formation property L'Bquilibre entre 100 acidoo lactique et pyruvique, J. Chim. Phys. 30, 249-265. r reaction property 34BAR/HAS Barron, E. S. 0, & Hasting, A. B. (1934) Studies on sol solution property biological oxidations. III. The oxidation-reduction po­ ion ionization property tential of the system lactate-enzyme-pyruvate, J. BioI. Chem. 107,567-578. Physical States: 34CAM/CAM Campbell, A. N., & Campbell, A. J. R. (1934) The thermodynamics of binary liquid mixtures: formic acid and water, Tram. Faraday Soc. 30, 1109-1114. ao aqueous, standard state of the indicated species 34KAY/PAR Kaye, W. A., & Parks, G. S. (1934) The partial pres­ aq aqueous solution, concentration not specified sures of formic and acetic acids above some aqueous cr crystalline solid solutions; and their partial molal free energies at 1. 0 g gas molal conCAntrAtinn, 1. Chern. PhylOl. 2, 141-142. 35BUTIRAM Butler, J. A. V., Ramchandani, C. N., & Thomson, D. 1 liquid W. (1935) The solubility of non-electrolytes. Part I. The free energy of hydration of some aliphatic alco­ hols, J. Chem. Soc. 1935,280-285. 36WOO Woods, D. D. (1936) Hydrogenlyases. IV. The synthe­ 8. Acknowledgements sis of formic acid by bacteria, Biochem. J. 30,515-527. 36WUR/F1L Wurmser, R., & Filitti-Wurmser, S. (1936) Sur This work was supported by NBS Grant l"eauilibre entre l'alcool isopropyliQue et l'acetone 6ONANB6D0656 to one of us (SLM). We thank Drs. R. en presence d'alcooldeshydrase. Potential d'oxydore­ Goldberg, E. Domalski and M. Chase for helpful com­ duction du systeme -CHOH-~-CO- • J. Chim. ments, and L. Lane for manuscript preparation. Phys. 33, 577-584.

J. Phys. Chem. Ref. Data, Vol. 19, No.4, 1990 THE THERMODYNAMICS OF THE KREBS CYCLE AND RELATED COMPOUNDS 1069

37K.IE Kielland, J. (1937) Individual activity coefficients of 53BURIKRE Burton, K., & Krebs, H. A. (1953) The free-energy ions in aqueous solutions, J. Am. Chem. Soc. 59,1675- changes associated with the individual steps of the tri­ 1678. carboxylic acid cycle, glycolysis and alcoholic fer­ 38DOL/GRE Dolliver, M. A., Gresham, T. L., Kistiakowsky, G. B., mentation and with the hydrolysis of the Smith, B. A., & Vaughan, W. E. (1938) Heats of Of­ pyrophosphate groups of adenosinetriphosphate, ganic reactions. VI. Heats of hydrogenation of some Biochem. J. 54, 94-107. oxygen-containing compounds, J. Am. Chem. Soc. 60, 53BUR/WIL Burton, K., & Wilson, T. H. (1953) The free-energy 440-450. changes for the reduction of diphosphopyridine nucle­ 41STO/FIS Stout, J. W., & Fisher, L. H. (1941) The entropy of otide and the dehydrogenation of L-malate and L­ formic acid. The heat capacity from 15 to 300 OK. glycerol I-phosphate, Biochem. J. 54, 86-94. Heats of fusion and vaporization, J. Chem. 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