Thermodynamics of the oxidation-reduction reaction {2 glutathione red(aq) + NADPox(aq) = glutathioneox(aq) + NADPred(aq)}

Article abstract of DOI:10.1016/S0021-9614(03)00111-3

Microcalorimetry, spectrophotometry and high performance liquid chromatography were used to conduct a thermodynamic investigation of the glutathione reductase catalyzed reaction. The reaction involves the breaking of a disulfide bond and is useful in the repair of enzymes. The results of the equilibrium and calorimetric measurements were analyzed in terms of a chemical equilibrium model that accounts for the multiplicity of ionic states of the reactants and products.

Full text of DOI:10.1016/S0021-9614(03)00111-3

J. Chem. Thermodynamics 35 (2003) 1361–1381
www.elsevier.com/locate/jct
Thermodynamics of the oxidation–reduction
reaction {2 glutathionered(aq) + NADPox(aq) ¼
glutathioneox(aq) + NADPred(aq)}
*
Yadu B. Tewari, Robert N. Goldberg
Biotechnology Division, Mail stop 8312, National Institute of Standards and Technology,
Gaithersburg, MD 20899, USA
Received 11 February 2003; accepted 28 April 2003
Abstract
Microcalorimetry, spectrophotometry, and high-performance liquid chromatography
(h.p.l.c.) have been used to conduct a thermodynamic investigation of the glutathione reductase
catalyzed reaction {2 glutathionered(aq) + NADPox(aq) ¼ glutathioneox(aq) + NADPred(aq)}.
The reaction involves the breaking of a disulfide bond and is of particular importance because
of the role glutathionered plays in the repair of enzymes. The measured values of the apparent
equilibrium constant K0 for this reaction ranged from 0.5 to 69 and were measured over a range
of temperature (288.15 K to 303.15 K), pH (6.58 to 8.68), and ionic strength Im (0.091 mol Á kgÀ1
to 0.90 mol Á kgÀ1). The results of the equilibrium and calorimetric measurements were analyzed
in terms of a chemical equilibrium model that accounts for the multiplicity of ionic states of the
reactants and products. These calculations led to values of thermodynamic quantities at
T ¼ 298:15 K and Im ¼ 0 for a chemical reference reaction that involves specific ionic forms.
3À
2À
4À
red
Thus, for the reaction {2 glutathioneÀred(aq) + NADP (aq) ¼ glutathione (aq) + NADP
ox
ox
(aq) + Hþ(aq)}, the equilibrium constant K ¼ ð6:5 Æ 4:4Þ Á 10À11, the standard molar enthalpy
of reaction DrHmo ¼ ð6:9 Æ 3:0Þ kJ Á molÀ1, the standard molar Gibbs free energy change
DrGom ¼ ð58:1 Æ 1:7Þ kJ Á molÀ1, and the standard molar entropy change DrSmo ¼ Àð172 Æ 12Þ
J Á KÀ1 Á molÀ1. Under approximately physiological conditions (T ¼ 311:15 K, pH ¼ 7.0, and
Im ¼ 0:25 mol Á kgÀ1 the apparent equilibrium constant K0 ꢀ 0:013. The results of the several
studies of this reaction from the literature have also been examined and analyzed using the
chemical equilibrium model. It was found that much of the literature is in agreement with
the results of this study. Use of our results together with a value from the literature for the stan-
dard electromotive force Eo for the NADP redox reaction leads to Eo ¼ 0:166 V (T ¼ 298:15 K
* Corresponding author. Tel.: 1-301-975-2584.
E-mail addresses: yadu.tewari@nist.gov (Y.B. Tewari), robert.goldberg@nist.gov (R.N. Goldberg).
0021-9614/$ - see front matter. Published by Elsevier Science Ltd.
doi:10.1016/S0021-9614(03)00111-3

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Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 35 (2003) 1361–1381
2À
and I ¼ 0) for the glutathione redox reaction {glutathione (aq) + 2 Hþ(aq) + 2 eÀ ¼ 2 glutathi-
ox
oneÀred(aq)}. The thermodynamic results obtained in this study also permit the calculation of the
standard apparent electromotive force E0o for the biochemical redox reaction {glutathi-
oneox(aq) + 2 eÀ ¼ 2 glutathionered(aq)} over a wide range of temperature, pH, and ionic
strength. At T ¼ 298:15 K, I ¼ 0:25 mol Á kgÀ1, and pH ¼ 7.0, the calculated value of E0o
is )0.265 V.
Published by Elsevier Science Ltd.
Keywords: Apparent equilibrium constant; Chemical thermodynamics; Enthalpy; Entropy; Gibbs free
energy; Glutathione reductase; NADP; b-Nicotinamide adenine dinucleotide phosphate
1. Introduction
Glutathione reductase is an NADP1 dependent enzyme that catalyzes the follow-
ing oxidation–reduction reaction (also see figure 1):
2 glutathioneredðaqÞ þ NADPoxðaqÞ ¼ glutathioneoxðaqÞ þ NADPredðaqÞ:
ð1Þ
The physiological function of glutathionered appears to be that of an intercellular
reducing agent [1]. As a very important example, enzymes that have become inactive
due to sulfide oxidation can sometimes be reactivated by means of (non-enzymatic)
disulfide exchange with glutathionered. Two factors that serve to aid this repair
mechanism are that the total glutathione concentration c in animal tissues is fairly
high (c ꢀ 0:005 mol Á dmÀ3) and that the position of equilibrium of reaction (1) lies
far to the left. Thus, the living system has available a good supply of a substance
(glutathionered) that can make necessary repairs to enzymes. This helps enzymes
maintain their active conformations and thereby catalyze reactions needed to
maintain physiological function. Both the three-dimensional structure of glutathione
reductase [2,3] and the mechanism of reaction (1) [4,5] are known.
In an early study, Rall and Lehninger [6] were unable to detect the reversibility of
reaction (1). However, later studies [7–12] reported values of the apparent equilibrium
constants K0 [13] for this reaction. The experiments, which were performed over a wide
range of temperatures and pHs, led to values of K0 that differed by as much as three
orders of magnitude. Also, a calorimetrically determined value of the molar enthalpy
change for this reaction has been reported [14]. However, the study of the thermody-
namics of reaction (1) is complicated by the fact that its position of equilibrium lies
very far in the direction of the formation of {glutathionered(aq) + NADPox(aq)}. Ad-
ditionally, dissolved oxygen brings about the oxidation of two of the reactants
(NADPred and glutathionered). In physiological studies [11], it is difficult to measure
the concentration of glutathioneox. Thus, even though it is not known if reaction (1)
1
Chemical abbreviations used in this paper are: EDTA, ethylene diaminetetraacetic acid; NADPox
b-nicotinamide adenine
dinucleotide phosphate reduced form; and Tris, 2-amino-2-hydroxymethyl-propane-1,3 diol.
,
b-nicotinamide adenine dinucleotide phosphate oxidized form; NADPred
,

FIGURE 1. Structures of the substances in reaction (1). The neutral forms of the species are shown.

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Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 35 (2003) 1361–1381
is at equilibrium in vivo, a knowledge of K0 for this reaction under physiological
conditions still provides a basis for estimating the concentration of this important
metabolite.
This study was undertaken in light of the importance of this reaction as well as the
significant range in the values of K0 that have been reported in the literature. By us-
ing a chemical equilibrium model that assesses the contributions of the various ionic
species to the measured values of K0 for reaction (1), we have analyzed both the re-
sults of the current study and from the literature to obtain values of the equilibrium
constant and the standard molar enthalpy change of a chemical (ionic) reference re-
action under a standard set of conditions. This, in turn, allows for the prediction of
K0 over a wide range of conditions. Finally, by using a value of the standard electro-
motive force Eo for the NADP redox reaction, we have also obtained Eo for the glu-
tathione redox reaction.
2. Experimental
2.1. Materials
Pertinent information on the substances used in this study is given in table 1.2
High-performance liquid chromatography (h.p.l.c.) (see below) was used to assess
the purity of the samples of NADPox, NADPred, glutathioneox, and glutathionered
.
The mass fraction of water in each of these four samples was determined by means
of Karl–Fischer titration [15]. Gas chromatographic analysis was also used to mea-
sure the amounts of methanol (done by vendor) and ethanol in the samples of
NADPox and NADPred, respectively. The glutathione reductase was present at a
mass fraction of 0.0068 in a solution containing {(NH4)2SO4 (concentration
c ¼ 3:6 mol Á dmÀ3) + dithiothreitol (c ¼ 1:0 Á 10À4 mol Á dmÀ3)} at pH ¼ 7.0. It was
stored at T ꢀ 278 K.
2.2. Chromatography
Chromatographic method 1 used an Agilent model 1100 h.p.l.c. equipped with a
u.v. detector. This was the principal instrument used in this study. Also, while two
different wavelengths (k ¼ 210 nm and k ¼ 260 nm) were used for characterization
of materials, the wavelength k ¼ 210 nm was used exclusively in the equilibrium
and calorimetric measurements. A Macherey–Nagel Nucleogen DEAE column
(4.0 mm i.d., 125 mm long) was used for the separations. The mobile phases were:
(A) KH2PO4 (c ¼ 0:05 mol Á dmÀ3, pH ¼ 2.9) and (B) K2HPO4 (c ¼ 0:25 mol Á dmÀ3
,
pH ¼ 7.3). The volume fractions / and flow rates qV of these mobile phases were:
2
Certain commercial equipment, instruments, or materials are identified in this paper to specify the
experimental procedures adequately. Such identification is not intended to imply recommendation or
endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the
materials or equipment identified are necessarily the best available for the purpose.

TABLE 1
Principal substances used in this study with their Chemical Abstracts Service (CAS) registry numbers, empirical formulae, relative molecular masses Mr,
mass fraction moisture contents w determined by Karl–Fischer analysis, suppliers {B, Biocatalytics (Roche); F, Fisher; L, LabChem; M, Mallinckrodt;
and S, Sigma}, estimated mole fraction purities x and method(s) used to determine x
Substance
CAS no.
Formula
Mr
w
Supplier
x
Method(s)
EDTA (ethylene diaminetetraacetic acid)
-Glutathione, oxidized form
-Glutathione, reduced form
60-00-4
27025-41-8
70-18-8
C10H16N2O8
C20H32N6O12S2
C10H17N3O6S
292.24
612.63
307.33
S
S
S
S
L
B
L
0.0497
0.0464
0.99a
0.99b
h.p.l.c.
h.p.l.c.
L
Glutathione reductase (NAD(P)H), EC No. 1.6.4.2
Hydrochloric acid
5.16 Á 104
53-26-45
24292-60-2
HCl
C
36.461
787.37
NADP, oxidized form (b-nicotinamide adenine
dinucleotide phosphate oxidized, disodium salt)
NADP, reduced form (b-nicotinamide adenine
dinucleotide phosphate reduced, tetrasodium salt)
Phosphoric acid
21H26N7O17P3Na2
0.0407
0.0641
0.95c
h.p.l.c.
and g.c.
h.p.l.c.
and g.c.
2646-71-1
C21H26N7O17P3Na4
833.35
B
0.963d
7664-38-2
7758-11-4
77-86-1
H3PO4
K2HPO4
C4H11NO3
97.995
174.16
121.14
M
S
Potassium phosphate, dibasic
Tris(2-amino-2-hydroxymethyl-propane-1,3-diol)
F
The estimated mole fraction purities are exclusive of the amounts of water and any organic solvents that may be in the samples. The chromatographic
methods used in our laboratory are described in the text (see Section 2).
a This sample was examined by using h.p.l.c. method 1 (DEAE column, k ¼ 210 nm) and h.p.l.c. method 2 (C18 column, k ¼ 210 nm and k ¼ 260 nm). The
estimated mole fraction purity x > 0:99. The vendor reported x > 0:99.
b This sample was examined by using h.p.l.c. method 1 (DEAE column, k ¼ 210 nm) and h.p.l.c. method 2 (C18 column, k ¼ 210 nm and k ¼ 260 nm). The
estimated mole fraction purity x > 0:99. The vendor reported 0:98 < x < 1:00.
c This sample was examined by using h.p.l.c. method 1 (DEAE column, k ¼ 210 nm and k ¼ 260 nm) and h.p.l.c. method 2 (C18 column, k ¼ 210 nm and
260 nm). The estimated mole fraction purities x ranged from 0.941 to 0.961 with hxi ¼ 0:954. The vendor reported x ¼ 0:97. The mass fraction of methanol in
the sample was determined by the vendor (g.c. analysis) to be 0.020.
d This sample was examined by using h.p.l.c. method 1 (DEAE column, k ¼ 210 nm). Three additional peaks were seen. One peak had the same retention
time as NADPox and the other two were not identified. Assuming that the identification of NADPox is correct, the mole fraction of this substance in the
NADPred sample is 0.0098. Also, if we assume that the unknown impurities had the same response factor as NADPox, the mole fraction purity of the NADPred
is 0.963 (excluding water and ethanol). The vendor reported a mole fraction purity of 0.97. The mass fraction of ethanol in the sample was determined to be
0.0015 using g.c.

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/ðAÞ ¼ 0:90, /ðBÞ ¼ 0:10, and qV ¼ 0:0167 cm3 Á sÀ1 at time t ¼ 0; /ðAÞ ¼ 0:80,
/ðBÞ ¼ 0:20, and qV ¼ 0:0167 cm3 Á sÀ1 at t ¼ 10:0 min; /ðAÞ ¼ 0:80, /ðBÞ ¼ 0:20,
and qV ¼ 0:020 cm3 Á sÀ1 at t ¼ 10:1 min; /ðAÞ ¼ 0:20, /ðBÞ ¼ 0:80, and qV ¼
0:020 cm3 Á sÀ1 at t ¼ 15 min; and /ðAÞ ¼ 0:20, /ðBÞ ¼ 0:80, and qV ¼ 0:020 cm3 Á sÀ1
at t ¼ 30 min. Typical retention times (k ¼ 210 nm) were: glutathionered, 2.1 min;
glutathioneox, 2.7 min, NADPox, 6.9 min; and NADPred, 13.9 min. Chromatographic
method 2 used an Agilent HP1050 h.p.l.c. equipped with a u.v. detector set at two
different wavelengths (k ¼ 210 nm and k ¼ 260 nm) and a Hypersil C18 column
(4.0 mm i.d., 250 mm long). The mobile phase consisted of KH2PO4 (c ¼ 0:05
mol Á dmÀ3, pH ¼ 2.9) and acetonitrile. The operation was isocratic with the respec-
tive volume fractions / ¼ 0:97 and / ¼ 0:03. This method was used to assess sample
purities (see table 1).
The analysis of the ethanol in NADPred and NADPox was carried out with an HP
5890 gas chromatograph equipped with a flame ionization detector and a fused silica
Phenomenex ZB-FFAP capillary column (0.53 mm i.d., 30 m long). The injector and
detector temperatures were 523 K and 543 K, respectively. The head pressure of the
helium carrier gas was 283 kPa. The initial column temperature of 308 K was held
for 5 min and then raised to 523 K at a rate of 0.5 K Á sÀ1 and held at 523 K for
10 min. The substance 1-butanol was used as an internal standard for the quantita-
tive analysis of ethanol.
2.3. Spectrophotometric measurements
Although the h.p.l.c. methods were satisfactory for most of our measurements,
the presence of interferences that we could not resolve led us to adopt a spectropho-
tometric method for the measurement of NADPred. Thus, a Beckman DU650 spec-
trophotometer was used to measure the molality of this substance. Holmium oxide
solutions {National Institute of Standards and Technology (NIST) Standard Refer-
ence Material (SRM) 2034} and NIST calibrated glass filters (SRM 930e) were used
for the calibrations of wavelength and absorbance, respectively. All spectrophoto-
metric measurements were done at k ¼ 340:0 nm and with a path length of 1.00 cm.
The use of the spectrophotometric method used to measure the molality of
NADPred requires a knowledge of the molar (decadic) absorption coefficient e of this
substance. Measurements of e were done with NADPred molalities m in the range
7.4 Á 10À5 mol Á kgÀ1 to 1.6 Á 10À4 mol Á kgÀ1. The buffer was Tris (m ¼ 0:098
mol Á kgÀ1) adjusted to pH ¼ 8.00 with HCl(aq). This buffer was degassed by first
using our in-house vacuum system and then by bubbling Ar(g) through the solution.
The solutions were kept in tightly capped bottles at all times. The cuvette used in the
spectrophotometer was also tightly capped and flushed with Ar(g) prior to use. Our
measurements led to a value of e ¼ 6:135 Á 104 dm2 Á molÀ1 for the molar (decadic)
absorption coefficient NADPred at k ¼ 340 nm. Conversion of our gravimetric result
(molal absorption coefficient em ¼ 6:043 Á 104 kg Á dmÀ1 Á molÀ1) to a concentration
basis was done by using a value for the apparent molar volume of aqueous
(Tris + HCl) [16]. Horecker and Kornberg [17] reported the value e ¼ 6:220 Á 104
dm2 Á molÀ1 for NADPred at k ¼ 340 nm. Ziegenhorn et al. [18] reported

Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 35 (2003) 1361–1381
1367
e ¼ 6:178 Á 104 dm2 Á molÀ1, albeit at k ¼ 334 nm. In obtaining our value for e, it was
necessary to assume an average molecular weight for the impurities in the sample of
NADPred. We assumed that this molecular weight was the same as NADPred. This as-
sumption by itself can cause an error as large as 0:02 Á e. Thus, the value of e obtained
in this study is in agreement with the values of e from the literature.
A similar procedure was used to measure em for NADPox. Here the result was
e ¼ 719 dm2 Á molÀ1 (em ¼ 708 kg Á dmÀ1 Á molÀ1) for a molality m(NADPox) ¼
0.00964 mol Á kgÀ1 at k ¼ 340:0 nm and T ¼ 298:15 K. The buffer was again Tris
(c ¼ 0:098 mol Á dmÀ3) adjusted to pH ¼ 8.00 with HCl(aq). Again, it was assumed
that the average molecular weight of the impurities in the sample of NADPox was
the same as that of NADPox.
2.4. Degradation studies
The possibility of degradation of several key substances is relevant to this study.
Therefore, studies of the instabilities of the pertinent substances were performed by
monitoring the changes with time of the chromatographic peak areas corresponding
to these substances. All studies were performed at T ¼ 298:15 K. With the relevant
substances dissolved in a phosphate buffer {c(K2HPO4) ¼ 0.10 mol Á dmÀ3 adjusted
to pH ¼ 7.30 with H3PO4}, the mole fraction changes with time x_ were found to
be: glutathioneox, <0.001 hÀ1; glutathionered, 0.079 hÀ1; NADPox, <0.001 hÀ1; and
NADPred, 0.037 hÀ1. Glutathionered was found to degrade to glutathioneox. However,
the degradation products for NADPred have not been identified. Nevertheless, it was
found that the stability of glutathionered was substantially improved and that of
NADPred was somewhat improved by adding EDTA (c ꢀ 0:001 mol Á dmÀ3) to the
solutions and by degassing the solutions with Ar(g) to minimize the oxidation of
these substrates. When these precautionary steps were taken, the degradation rates
were: x_ ¼ 0:008 hÀ1 for glutathionered and x_ ¼ 0:026 hÀ1 for NADPred. Because of
these improvements, the aforementioned precautionary steps were used in all mea-
surements. Additionally, all solutions were prepared immediately prior to use and
kept in an ice bath until needed.
2.5. Equilibrium measurements
As a very first step, the buffer with EDTA was placed in the spectrophotometer
cell (path length ¼ 1.00 cm) and the (decadic) absorbance A of the spectrophotometer
was set to A ¼ 0. The reaction mixture, consisting of (glutathionered + NADPox) dis-
solved either in a phosphate or in a (Tris + HCl) buffer containing EDTA, was then
prepared and its absorbance was measured. The enzyme (glutathione reductase) so-
lution was then added to the reaction mixture and ꢀ30 min was allowed for reaction.
All equilibrations were carried out using gentle lateral shaking (ꢀ60 shakes minÀ1 in
a thermostat set at the appropriate temperature. Injections of portions of the reaction
mixture were then made into the Agilent model 1100 h.p.l.c. (chromatographic meth-
od 1) and the molality of glutathioneox was measured. The calculation of this molal-
ity used a response factor obtained by using a stock solution of glutathioneox having

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approximately the same molality as that of the final reaction mixture. The measured
molalities of glutathioneox were constant and in agreement (within experimental er-
ror) with the result obtained from the first injection performed after 30 min following
the initiation of reaction. The reaction mixture was then transferred to the Beckman
DU650 spectrophotometer and the absorbance was measured. The molality of
NADPred was calculated by using the already known value of the molar absorption
coefficient (see above) and the difference between the absorbance of the final reaction
mixture and the absorbance of the reaction mixture prior to addition of the glutathi-
one reductase. A small correction was made for the addition of the enzyme (glutathi-
one reductase) solution. The molalities of glutathionered and NADPox were calculated
from the masses of these samples used to prepare the initial reaction mixture with
small corrections made for the formation of (glutathioneox + NADPred). Since the po-
sition of equilibrium of reaction (1) lies very far to the left, the aforementioned cal-
culation should give very accurate values of the molalities of glutathionered and
NADPox. The measured and calculated molalities of the reactants and products were
then used to calculate a value of the apparent reaction quotient Q0 for reaction (1)
2
Q0 ¼ mðglutathioneoxÞmðNADPredÞ Á mo=½fmðglutathioneredÞg Á mðNADPoxÞꢁ:
ð2Þ
The standard molality mo ¼ 1 mol Á kgÀ1 has been used to make Q0 dimensionless.
The final reaction mixture was then divided into two portions. Additional gluta-
thione reductase was added to one portion and an additional portion of the initially
prepared reaction mixture (glutathionered + NADPox) was added to the other por-
tion. After ꢀ30 min of equilibration time, three injections of portions of the ‘‘enzyme
addition’’ solution were made into the Agilent model 1100 h.p.l.c. (chromatographic
method 1). Then, three injections of the ‘‘substrate addition’’ solution were made.
These measurements allowed for the determination of the molality of glutathioneox
for both solutions. The absorbance of both of these solutions was then measured in
order to obtain the molality of NADPred. Values of Q0 for both the ‘‘enzyme addi-
tion’’ and ‘‘substrate addition’’ solutions were then calculated. This tactic looks to
see if the value of Q0 changes due to these additions. The absence of change (within
the experimental uncertainties) in the value of Q0 is good evidence that equilibrium
has been achieved.
2.6. Microcalorimetry
Descriptions of the microcalorimeters used in this study and their performance
characteristics, the data-acquisition system, and the computer programs used to treat
the results have been given by Steckler et al. [19,20]. These calorimeters were cali-
brated electrically by using a high stability d.c. power supply, calibrated digital volt-
meter, standard resistor, and time-interval counter. The electric potential differences
U of the thermopiles in the microcalorimeters are measured with Hewlett–Packard
model 34420A Nanovolt Meters. The values of U are then recorded on a microcom-
puter and the areas of the thermograms are calculated by numerical integration.

Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 35 (2003) 1361–1381
1369
The calorimetric sample vessels were fabricated from high-density polyethylene.
Each vessel had two compartments that held, respectively, ꢀ0.55 cm3 and ꢀ0.40
cm3 of solution. The substrate solutions were placed in the 0.55 cm3 compartment
and the enzyme solutions were placed in the 0.40 cm3 compartment. The substrate
solution contained (NADPred + glutathioneox) in a phosphate buffer. NADPred was
used as the limiting reagent. To minimize oxidation, a small amount of EDTA
was present and, as done above, Ar(g) was used to degas the solutions. The enzyme
solution consisted of glutathione reductase in the same phosphate buffer used to pre-
pare the substrate solution. Prior to use the glutathione reductase solution under-
went three exchanges with phosphate buffer {c ¼ 0:10 mol Á dmÀ3, adjusted to
pH ¼ 7.60 with H3PO4(aq)} by using a Millipore Ultrafree Centrifugal Filter {vol-
ume V ¼ 15 cm3, relative molecular mass cut-off ¼ 5000, centrifugation at 1400gn
(gn ¼ 9:80665 m Á sÀ2) and at T ¼ 277 K}.
The vessels and their contents were allowed to thermally equilibrate in the micro-
calorimeters for ꢀ60 min before the enzyme and substrate solutions were mixed. Af-
ter mixing, ꢀ50 min was allowed for reaction. Following reaction, the vessels were
removed from the microcalorimeters and chromatographic method 1 (see Section
2) was used for the analysis of the reaction mixtures. In all cases, it was found that
the mole fraction of unreacted NADPred was <0.004.
‘‘Blank’’ enthalpy changes DmixH were determined in control experiments. Thus,
for mixing of the substrate solution with the buffer, DmixH was )(0.17 Æ 0.8) mJ. For
the mixing of the enzyme solution with the buffer, DmixH was )(0.07 Æ 0.2) mJ. We
judge the total correction applied for the blank enthalpy changes to be uncertain by
ꢀÆ0.8 mJ. Since the measured reaction enthalpy changes were ꢀ)22 mJ, the uncer-
tainties in the blank enthalpy changes leads to uncertainties of ꢀ0:04 Á DrHm(cal) in
the final results. The quantity DrHm(cal) is the calorimetrically determined molar en-
thalpy of reaction pertinent to the actual experimental conditions.
Measurement of pH was done with an Orion Model 811 pH meter and a Radi-
ometer combination glass micro-electrode at the actual temperature at which ex-
periments were performed. The pH meter was calibrated with Radiometer
standard buffers that bracketed the pHs of the solutions used in this study. The
pHs of the reaction mixtures were calculated by using interpolation with the mea-
sured electric potential differences and the pHs of the standard buffers. The elec-
trode was thoroughly cleaned after use to minimize possible contamination of it
by glutathione.
3. Results and discussion
3.1. Thermodynamic formalism
The apparent equilibrium constant for reaction (1) is
2
K0 ¼ mðglutathioneoxÞ Á mðNADPredÞ Á mo=½fmðglutathioneredÞg Á mðNADPoxÞꢁ:
ð3Þ

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The molalities m in the above equations are the total molalities of the various
charged and uncharged species that are formed from the dissociation of the bio-
chemical substances in solution. The quantity mo (mo ¼ 1 mol Á kgÀ1) has been used
to make K0 dimensionless. Following our usual practice, we have selected a chemical
reference reaction that involves the predominant species present under the experi-
mental conditions used in our study. Thus, the selected reference reaction is
2 glutathionerÀedðaqÞ þ NADPo3Àx ðaqÞ ¼ glutathioneo2Àx ðaqÞþ
red
4À
NADP ðaqÞ þ HþðaqÞ:
ð4Þ
The equilibrium constant for this reference reaction is
K ¼ mðglutathione2oÀx Þ Á mðNADP4À Þ Á mðHþÞ=
red
2
½fmðglutathioneÀredÞg Á mðNADPo3Àx Þꢁ;
ð5Þ
In this study, the standard state for the solute is the hypothetical ideal solution of
unit molality (mo ¼ 1 mol Á kgÀ1) and the standard state of the solvent is the pure
solvent; the standard pressure po ¼ 0:1 MPa.
3.2. Results of experiments
The results of the equilibrium and calorimetric measurements on reaction (1) are
given in tables 2 and 3, respectively. In table 2, the average difference between the
measured molalities m of glutathioneox(aq) and NADPred(aq) is 0:20m. Since, by stoi-
chiometry, the values of these molalities should be equal, we take one-half of this av-
erage difference to represent an initial approximate estimate of the inaccuracy of our
chromatographic and spectrophotometric measurements. Also, in table 2, it is seen
that the values of K0 obtained with the ‘‘forward direction of reaction’’ experiments
differ, respectively, on the average by 0.09K0 and 0:08K0 from the values of K0 ob-
tained from the ‘‘enzyme addition’’ experiments and from the ‘‘substrate addition’’
experiments (see Section 2). Since these differences are less than the imprecision of
the measurements, we have evidence that equilibrium has been achieved. Therefore,
we identify (see column 12 in table 2) the measured quantities (reaction quotients) as
apparent equilibrium constants K0. The basis for the values of K for the reference re-
action (4) (right-most column in table 2) will follow the description of the equilib-
rium model (see below). The calorimetric experiments summarized in table 3 lead
to a molar enthalpy change DrHmðcalÞ ¼ ð4:2 Æ 0:3Þ kJ Á molÀ1 for reaction (1) car-
ried out in phosphate buffer at T ¼ 298:15 K, pH ¼ 7.41, and Im ¼ 0:35 mol Á kgÀ1
.
The uncertainties in the measured values of K0 and DrHm(cal) represent only the
random errors inherent in the measurements and do not reflect possible systematic er-
rors which are now considered. We judge that reasonable estimates of the standard
uncertainties [21] in the measured values of K0 for reaction (1) are 0:04K0 due to pos-
sible impurities in the samples of NADPox, NADPred, glutathioneox, and glutathionered
and 0:15K0 due to possible errors in the chromatographic and spectrophotometric
measurements. For the results leading to DrHm(cal) for reaction (1), the estimates of
possible systematic error are: 0:02DrHm(cal) due to possible impurities in the sample

TABLE 2
Results of equilibrium measurements for reaction (1): {2 glutathionered(aq) + NADPox(aq) ¼ glutathioneox(aq) + NADPred(aq)} at various temperatures and pHs
T/K
pH
K0 Á 103 K(calc) Á 1012
Type of
m(K2HPO4)
m(H3PO4)
m{(NH4)2SO4)}
m(Glutred
)
m(NADPox)
105 Á m(Glutox
)
105 Á m(NADPred
)
Im
experiment
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
Phosphate buffer
298.15
298.15
298.15
298.15
298.15
298.15
6.66
6.58
6.60
6.93
6.85
6.90
F
0.0955
0.0945
0.0955
0.0957
0.0954
0.0957
0.0140
0.0139
0.0140
0.0141
0.0140
0.0141
0.131
0.204
0.129
0.117
0.139
0.116
0.0204
0.00983
0.00973
0.00983
0.00895
0.00892
0.00894
5.51
4.25
6.58
7.26
6.95
9.18
5.06
4.32
4.35
7.10
6.98
7.13
0.69
0.90
0.68
0.67
0.73
0.67
0.69
0.46
0.70
1.6
3.8
2.5
4.7
4.8
5.1
6.8
EA
SA
F
0.0202
0.0204
0.0188
0.0188
0.0188
EA
SA
1.5
2.1
T/K
pH
Type of
m(Tris)
m(HCl)
m{(NH4)2SO4)}
m(Glutred
)
m(NADPox
)
105 Á m(Glutox
)
105 Á m(NADPred
)
Im
K0 Á 103 K(calc) Á 1012
experiment
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(Tris + HCl) buffer
0.0156
298.15
298.15
298.15
298.15
298.15
298.15
298.15
298.15
298.15
288.15
288.15
288.15
293.15
293.15
293.15
303.15
303.15
303.15
8.23
8.21
8.25
8.33
8.34
8.34
8.61
8.62
8.59
8.66
8.68
8.67
8.47
8.44
8.46
8.33
8.35
8.38
F
0.0984
0.0984
0.0984
0.100
0.100
0.100
0.100
0.0985
0.100
0.100
0.0988
0.100
0.100
0.0991
0.100
0.100
0.0988
0.100
0.0159
0.0159
0.0159
0.0161
0.0160
0.0161
0.0161
0.0159
0.0161
0.0161
0.0159
0.0161
0.0161
0.0160
0.0162
0.0161
0.0159
0.0161
0
0.00717
0.00710
0.00718
0.00891
0.00888
0.00889
0.00750
0.00742
0.00750
0.00727
0.00719
0.00725
0.00676
0.00668
0.00674
0.00694
0.00688
0.00694
34.2
34.1
33.8
36.9
36.2
43.4
32.2
32.2
35.1
36.3
36.4
38.5
28.8
25.8
31.7
35.5
35.7
36.3
23.8
23.4
24.0
37.0
35.5
35.3
38.1
37.0
35.6
24.6
24.5
25.0
25.0
24.6
24.9
25.0
25.1
25.0
0.091
0.091
0.091
0.42
0.50
0.42
0.48
0.71
0.47
0.44
0.65
0.43
0.32
0.59
0.31
0.48
0.64
0.48
46.8
47.3
46.5
43.2
41.0
48.7
67.2
67.5
68.6
45.2
46.6
48.9
49.2
44.8
54.1
49.4
51.1
50.8
46.4
48.5
44.8
12.3
10.1
13.8
13.7
10.4
14.2
7.5
EA
SA
F
0
0.0154
0.0156
0.0188
0.0188
0.0188
0.0156
0.0154
0.0156
0.0165
0.0163
0.0165
0.0147
0.0146
0.0147
0.0161
0.0159
0.0161
0
0.103
0.130
0.102
0.126
0.202
0.125
0.112
0.184
0.111
0.075
0.165
0.073
0.130
0.182
0.129
EA
SA
F
EA
SA
F
EA
SA
F
5.8
8.1
13.6
8.2
EA
SA
F
15.4
13.6
11.2
13.4
EA
SA
The three different types of equilibrium measurements described in the text (see Section 2) are: F, the measurement from the forward direction of reaction; EA, the experiment involving the addition of
enzyme (glutathione reductase) to the reaction mixture; and SA, the experiment involving the addition of (additional) substrate reaction mixture (glutathionered + NADPox) to the reaction mixture. The molalities
m in columns 4 to 10 are those measured following equilibration (see Section 2). All molalities are equal to the sums of the molalities of the indicated substances in their various ionic forms. The values of the ionic
strength Im (column 11) are calculated. Abbreviations used in this table are: NADPox, b-nicotinamide adenine dinucleotide phosphate oxidized form; NADPred, b-nicotinamide adenine dinucleotide phosphate
reduced form; Glutox, oxidized form of glutathione; Glutred, reduced form of glutathione; and Tris, (2-amino-2-hydroxymethyl-propane-1,3-diol). Ethylene diaminetetraacetic acid (EDTA) and ())-1,4-dithio-L-
threitol (DTT) were present at the respective approximate molalities 0.0010 mol Á kgÀ1 and 3 Á 10À6 mol Á kgÀ1. The mass fraction w of glutathione reductase was ꢀ3 Á 10À4. The molalities of glutathionered(aq) and
NADPox(aq) were calculated by using the known initial molalities of glutathionered(aq) and NADPox(aq) with a correction made for the extent of reaction n. The values of n were obtained for each experiment as
the average of the measured molalities of glutathioneox and NADPred. The measured values of the apparent equilibrium constant K0 for reaction (1) are given in column 12. The calculated values of the
equilibrium constant K(calc) for the chemical reference reaction (4) at the specified temperature and at a nominal I ¼ 0 are given in column 13.

1372
Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 35 (2003) 1361–1381
TABLE 3
Results of the calorimetric measurements for the reaction {glutathioneox(aq) + NADPred(aq) ¼ 2 glutathi-
onered(aq) + NADPox(aq)} in phosphate buffer at T ¼ 298:15 K, pH ¼ 7.41, and a calculated ionic strength
Im ¼ 0:35 mol Á kgÀ1
Experiment
m(K2HPO4) m(H3PO4)
103 Á m(glutathioneox
)
103 Á m(NADPred
)
DrHm(cal)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(mol Á kgÀ1
)
(kJ Á molÀ1
)
1
2
3
4
5
6
0.102
0.102
0.102
0.102
0.102
0.102
0.0105
0.0105
0.0105
0.0105
0.0105
0.0105
7.02
6.80
7.01
7.12
5.99
6.94
5.53
5.35
5.73
5.81
4.99
5.77
)4.40
)4.37
)3.99
)3.75
)4.44
)4.42
hDrHmðcalÞi ¼ Àð4:2 Æ 0:3Þ kJ Á molÀ1
The molalities m in columns 2 to 5 are those obtained after mixing of the enzyme and substrate
solutions and prior to any reaction. All molalities are equal to the sums of the molalities of the indicated
substances in their various ionic forms. NADPred is the reduced form of b-nicotinamide adenine dinu-
cleotide. The solution also contained some EDTA (m ꢀ 0:001 mol Á kgÀ1). The mass fraction w of gluta-
thione reductase was ꢀ3 Á 10À4. Since the measured molar enthalpy changes DrHm(cal) were negative
(exothermic), the value of DrHm(cal) for reaction (1) is positive (endothermic) and equal to (4.2 Æ 0.3)
kJ Á molÀ1. The uncertainty in the average value of DrHm(cal) given below is equal to two estimated
standard deviations of the mean.
of NADPred; 0:04DrHm(cal) due to possible errors in the calorimetric measurements;
and 0:01DrHm(cal) due to possible errors in the measured extents of reaction. These
estimates of possible systematic error are combined in quadrature together with the
statistical uncertainties in the measured values of K0 and DrHm(cal), expressed as
one estimated standard deviations of the mean, to obtain combined standard uncer-
tainties [21]. These combined standard uncertainties are then multiplied by two to ar-
rive at the final uncertainties in the measured quantities. Thus, the values of K0 are
believed to be uncertain by Æ0:33K0 and the value of DrHm(cal) is judged to be uncer-
tain by Æ 0.5 kJ Á molÀ1
.
3.3. Equilibrium modeling calculations
The pKs and standard molar enthalpy changes for the Hþ dissociation reactions
of the reactants and products are needed to relate the experimental results for reac-
tion (1) to thermodynamic quantities for the reference reaction (4). The values se-
lected for this purpose are given in table 4. The pKs and standard molar enthalpy
changes DrHmo for the ionization of the glutathionered and glutathioneox aqueous spe-
cies are based on the values selected by Martell et al. [22]. The pK value for
NADP2oÀx (aq) is based on the result of Briggs and Stuehr [23]. We have estimated
a value of DrHmo for this ionization reaction by assuming that the value of the stan-
dard molar entropy change DrSmo is equal to that of H2PO4À(aq). In the absence of
values for the pK and DrHmo for the ionization of NADPr3eÀd, we assume that these val-
2À
ues are the same as those of NADP (aq). This assumption seems reasonable in light
ox
of the structural similarity of these substances. The pK and DrHmo values for

Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 35 (2003) 1361–1381
1373
TABLE 4
The pKs and standard molar enthalpy changes DrHmo at T ¼ 298:15 K and I ¼ 0 for the aqueous ionization
reactions of substances pertinent to this study and to the analysis of results from the literature
DrHmo
Reaction
pK
(kJ Á molÀ1
)
Glutathionered ¼ glutathioneÀred + Hþ
red
3.69
ꢀ9
ꢀ32
ꢀ33
ꢀ4
2À
GlutathioneÀred ¼ glutathione + Hþ
9.07
10.15
4.26
2À
3À
2À
Glutathione ¼ glutathione + Hþ
ox
red
red
GlutathioneÀox ¼ glutathione3À+ Hþ
2À
Glutathione ¼ glutathioneo4Àx + Hþ
9.49
10.67
6.90
6.90a
7.198
8.072
6.993
ꢀ38
ꢀ34
ꢀ2a
ꢀ2a
3.6
ox
3À
Glutathione ¼ glutathioneox + Hþ
ox
NADP ¼ NADP4À + Hþ
2À
3À
ox
ox
NADP3À ¼ NADPred + Hþ
H2POÀ4 re¼d HPO42À + Hþ
Tris Á Hþ ¼ Tris + Hþ
47.45
36.64
Imidazoleþ ¼ imidazole + Hþ
See Section 3 for the basis of these values.
a Estimated.
H2POÀ4 (aq), Tris Á Hþ(aq), and imidazoleþ(aq) are from a recent review [24]. The val-
ues for imidazoleþ(aq) will be used for the analysis of some results from the litera-
ture. The pK and DrHmo values given in table 4 were adjusted, where necessary, to
ionic strength I ¼ 0. The adjustments for ionic strength were done by using the
€
extended Debye–Huckel equation [13,25] with the ‘‘ion-size’’ parameter set at
1.6 kg1=2 Á molÀ1=2
.
The equilibrium model used for the calculation of the equilibrium constants K
and standard molar enthalpies DrHmo for the reference reactions from the measured
values of K0 and DrHm(cal) has been described [25,26]. The calculations include cor-
rections for non-ideality and are made self-consistent with regard to the ionic
€
strength. The non-ideality corrections are based on the extended Debye–Huckel
equation in which the ‘‘ion-size’’ parameter has been set at 1.6 kg1=2 Á molÀ1=2. Use
of the equilibrium model with the experimental results for K0 and with the thermo-
dynamic quantities given in table 4, leads to the values of K(calc) for the reference
reaction (4) that are given in the right-most column in table 2. Note that these values
pertain to the actual temperature at which a measurement was performed and, nom-
inally, to the ionic strength I ¼ 0. However, it was found that the values of lg K(calc)
showed a linear dependence on the ionic strength of the solutions used for the mea-
surements. A linear fit to these results (see figure 2) leads to the value
K ¼ ð6:3 Æ 0:8Þ Á 10À11 for reaction (4). A plot of lg K as a function of I1=2 showed
a fair amount of curvature and was found to be unsatisfactory for purposes of ex-
trapolation even when an additional term in the first power of I was used in the
fit. However, a plot of K as a function of I1=2 yielded the value K ¼ ð6:6 Æ
0:7Þ Á 10À11. The uncertainties in the values of K are based solely on the fit and are
equal to two estimated standard deviations of the mean. We adopt the value
K ¼ 6:5 Á 10À11 as the final value of K for the reference reaction (4) at T ¼ 298:15
K and I ¼ 0. We also used the slope obtained in the least-squares fit of lg K vs I

1374
Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 35 (2003) 1361–1381
FIGURE 2. Plot of lg K(calc) against square root of ionic strength I at T ¼ 298:15 K and at a nominal
3À
2À
ox
I ¼ 0 for the reference reaction (4): {2 glutathioneÀred(aq) + NADP (aq) ¼ glutathione (aq) +
ox
NADP4reÀd(aq) + Hþ(aq)} for the solutions used in the respective measurements of the apparent equilibrium
constants K0 and from which the values of K(calc) were obtained. Only the results obtained at T ¼ 298:15
K are shown in this plot. The straight line is the least squares fit to the values. The intercept is )10.1975
and the slope is )1.52 kg Á molÀ1. The intercept yields the value of the equilibrium constant for the refer-
ence reaction (4) at T ¼ 298:15 K and I ¼ 0.
to adjust to I ¼ 0 the values of K(calc) given in table 2 (right-most column) and that
pertain to temperatures other than T ¼ 298:15 K. The results were: K ¼ 4:2 Á 10À11 at
T ¼ 288:15 K; K ¼ 5:0 Á 10À11 at T ¼ 293:15 K; and K ¼ 8:3 Á 10À11 at T ¼ 303:15 K.
From the temperature dependence of these values, we calculate DrHmo ꢀ 33 kJ Á molÀ1
for the reference reaction (4) at T ¼ 298:15 K and I ¼ 0. Similarly, using the slope
from the fit of K vs I1=2, the extrapolated values were: K ¼ 5:9 Á 10À11 at
T ¼ 288:15 K; K ¼ 5:9 Á 10À11 at T ¼ 293:15 K; and K ¼ 6:7 Á 10À11 at T ¼ 303:15
K. These values lead to DrHmo ꢀ 7 kJ Á molÀ1 for the reference reaction (4) at
T ¼ 298:15 K and I ¼ 0. We consider these values of DrHmo to be approximate be-
cause of the uncertainties in the extrapolations and also because these values are de-
rivative quantities.
Similarly, we used the equilibrium model and the experimentally determined value
of DrHm(cal) to calculate DrHmo ¼ ð6:9 Æ 0:5Þ kJ Á molÀ1 for the reference reaction (4)
at T ¼ 298:15 K and I ¼ 0. This value is in excellent and most likely fortuitous agree-
ment with the value of DrHmo obtained from the temperature dependence of the equi-
librium constants and that was based on the extrapolation of K vs I1=2 – but is

Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 35 (2003) 1361–1381
1375
substantially more precise. The equilibrium model was also used to calculate the
change in binding DrNðHþÞ of the hydrogen ion. Thus, for reaction (1) at
T ¼ 298:15 K, pH ¼ 7.41, and Im ¼ 0:35 mol Á kgÀ1, DrNðHþÞ ¼ À0:95. This calcu-
lated change in binding was used in making the buffer protonation correction [27].
The uncertainties in the calculated values of K and DrHmo are based on the respec-
tive uncertainties in the experimentally determined values of K0 and DrHm(cal). How-
ever, there is also a component of uncertainty due to possible errors in the
parameters used in the equilibrium model. This latter component of uncertainty
was estimated by perturbing each of the pertinent quantities in the model with an
assumed possible error. Thus, the pK values were perturbed as follows: Æ0.2 for
2À
glutathionered(aq); Æ0.2 for glutathioneÀred(aq); Æ0.2 for glutathione (aq); Æ0.2
red
for glutathioneoÀx(aq); Æ0.2 for glutathione (aq); Æ0.2 for glutathione (aq); Æ0.2
2À
3À
ox
ox
for NADP2oÀx (aq); Æ0.2 for NADP (aq); Æ0.003 for H2POÀ4 (aq); Æ0.003 for
3À
red
Tris Á Hþ(aq). The values of DrHmo /(kJ Á molÀ1) for the dissociation reactions were also
perturbed: Æ3.0 for glutathioneÀred(aq); Æ3.0 for glutathione (aq); Æ3.0 for glutathi-
2À
red
oneÀox(aq); Æ3.0 for glutathione (aq); Æ3.0 for glutathione (aq); Æ5.0 for
2À
3À
ox
ox
NADP2oÀx (aq); Æ5.0 for NADP (aq); Æ0.3 for H2POÀ(aq); Æ0.3 for Tris Á Hþ(aq).
3À
Finally, the ‘‘ion-size’’ parameter was perturbed by Æ04 .3 kg1=2 Á molÀ1=2. The effects
of these perturbations on the results for the experiments performed at pH values
of 6.58, 8.21, and 8.62 (see table 2) showed that approximate uncertainties in the val-
ues of K(calc) due to the aforementioned perturbations in the model were
Æ0.44K(calc), Æ0.30K(calc), and Æ0.93K(calc) for the respective pHs 6.58, 8.21,
and 8.62. An average value of Æ0.55K(calc) will be used in the propagation of error
analysis. Uncertainty in the ‘‘ion-size’’ parameter was the major factor contributing
to the uncertainty in the value of K(calc) for the experiment performed at pH ¼ 6.58.
At the higher pHs the uncertainty in the pK for glutathioneÀred(aq) was the predom-
inant factor. The effect of these perturbations on the calculated value of DrHmo was
Æ2.2 kJ Á molÀ1. Here the major contribÀuting factors were the uncertainties in the
pKs of glutathione2oÀx (aq) and glutathionered(aq). Additional estimates of possible sys-
tematic error (Æ0.2K and Æ2 kJ Á molÀ1) were also allowed for the respective extrap-
olations of the values of K(calc) and DrHmo to I ¼ 0. The final uncertainties in the
values of the thermodynamic quantities for the reference reaction (4) were obtained
by combining, in quadrature, the experimental uncertainties with the estimated un-
certainties attributable to the model. Thus, the final results with expanded uncertain-
ties [21] are: K ¼ ð6:5 Æ 4:4Þ Á 10À11 and DrHmo ¼ ð6:9 Æ 3:0Þ kJ Á molÀ1 for reaction
(4). The standard molar Gibbs free energy and entropy changes for reaction
(4) are, respectively, DrGmo ¼ ð58:1 Æ 1:7Þ kJ Á molÀ1 and DrSmo ¼ Àð172 Æ 12Þ
J Á KÀ1 Á molÀ1. These values all pertain to T ¼ 298:15 K and I ¼ 0.
red
3.4. Comparison with previous results
The results of equilibrium measurements from the literature that lead to values of
K for reaction (4) are summarized in table 5. All of these studies are based on studies
of reaction (1) with the exception of that of Rost and Rapoport [9] who reported the
value K0 ¼ 0:001 at T ¼ 311:15 K for the overall biochemical reaction

TABLE 5
Results of equilibrium measurements for reaction (1), {2 glutathione(aq) + NADPox(aq) ¼ glutathione(aq) + NADPred(aq)}, from the literature
T/K
pH
K0
1011 Á K(calc)(T)
Reference
Ic
1011 Á K(calc)a
(T ¼ 298:15 K)
1011 Á Kb
(T ¼ 298:15 K)
(mol Á dmÀ3
)
293.15
293.15
293.15
293.15
283.15
298.15
313.15
311.15
298.15
311.15
311.15
298.15
298.15
298.15
298.15
7.40
7.40
8.30
9.30
6.80
6.80
6.80
7.00
6.90
6.90
7.00
7.00
7.82
8.00
8.47
0.27
0.29
0.34
0.40
0.40
0.40
0.40
0.37
0.25
0.25
0.25
0.35
0.51
0.52
0.54
1.4 Á 10À5
1.6 Á 10À4
1.2 Á 10À4
3.2 Á 10À4
0.00644
0.00644
0.0595
0.0010
0.0242
0.0156
0.0198
0.0053
0.0373
0.049
0.0032
0.0034
0.0039
0.0044
4.4
0.0033
0.0036
0.0041
0.0046
5.1
Mapson and Isherwood (1963)
Mapson and Isherwood (1963)
Mapson and Isherwood (1963)
Mapson and Isherwood (1963)
Scott et al. (1963)
9.8
8.8
7.7
4.9
22
4.1
3.5
4.1
3.0
Scott et al. (1963)
Scott et al. (1963)
Rost and Rapoport (1964)c
Veech (1968)
–
18
0.36
18
9.7
11
11
13
13
Veech (1968)
Veech et al. (1969)
9.7
2.3
2.3
2.0
6.7
7.3
7.2
8.0
Gorin et al. (1975)
Gorin et al. (1975)
2.0
1.9
1.9
2.6
Gorin et al. (1975)
Gorin et al. (1975)
0.138
2.6
The thermodynamic temperature T, pH, molar ionic strength Ic, and the reported values (column 4) of the apparent equilibrium constant K0 are given for
each study. We used the reported results together with the equilibrium model (see Section 3) to calculate values of the equilibrium constant K(calc) (column 5)
at the specified temperature T and at a nominal I ¼ 0 for the chemical reference reaction (4). The value of the standard molar enthalpy change for reaction (1)
obtained in this study (DrHmo ¼ 6:9 kJ Á molÀ1) was used, where necessary, to adjust the values of K(calc) in column 5 to T ¼ 298:15 K. These adjusted values
are given in column 6. The values of K in column 7 were obtained by making a final adjustment for ionic strength. This adjustment was done by using the slope
obtained from a linear least-squares fit to our results (see Section 3 and figure 1). The results of Mapson and Isherwood [7] are discordant and no adjustment
was made to their results. The value K ¼ ð6:5 Æ 2:2Þ Á 10À11 for the reference reaction (4) at T ¼ 298:15 K and I ¼ 0 was obtained in this study.
a Calculated with the equilibrium model. See Section 3.
b Calculated by using the values of K(calc) at T ¼ 298:15 K (column 6) with a final adjustment for ionic strength (see above and Section 3).
c Rost and Rapoport [9] studied the reaction {2 glutathione(aq) + NADox(aq) ¼ glutathione(aq) + NADred(aq)}. Their results were used in a thermochemical
cycle (see Section 3) to obtain the value of K(calc) for reaction (4) given in this table.

Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 35 (2003) 1361–1381
1377
2 glutathioneredðaqÞ þ NADoxðaqÞ ¼ glutathioneoxðaqÞ þ NADredðaqÞ:
ð6Þ
Rost and Rapoport [9] gave very few experimental details in this preliminary report
and there was no follow-up publication by them on their result(s). Also, and more
importantly, since glutathione reductase appears to be specific for NADPox [28], one
questions how these investigators were able to use this enzyme to carry out reaction
(6). Nevertheless, we have used their result [9] together with our equilibrium model to
calculate the value K(T ¼ 298:15 K and I ¼ 0) ¼ 1.5 Á 10À11 for the reference reaction
2 glutathionerÀedðaqÞ þ NADoÀxðaqÞ ¼ glutathione2oÀx ðaqÞ þ NADr2eÀdðaqÞ:
ð7Þ
In the equilibrium modeling calculations, we used the value DrHmo ¼ 6:9 kJ Á molÀ1
for reaction (6) {i.e., DrHmo (7) was assumed to be the same as the value obtained in
this study for reaction (4)} as well as the value pK ¼ 3:88 [29] for the ionization
reaction of NADox(aq) to NADÀox(aq). On the basis of structural similarity, the pK
for NADÀred(aq) was assumed to have the same pK value as NADox(aq). We also used
the value DrGom ¼ À1:0 kJ Á molÀ1 (T ¼ 298:15 K and I ¼ 0:1 mol Á kgÀ1) given by
Miller and Smith-Magowan [30] (see their table 7) for the reaction
NADÀoxðaqÞ þ NADP4reÀdðaqÞ ¼ NADPo3Àx ðaqÞ þ NADr2eÀdðaqÞ:
ð8Þ
This value was adjusted to I ¼ 0 using the activity coefficient model described above.
These calculations lead to the value K(calc) ¼ 3.6 Á 10À12 for the reference reaction (4).
Approximate values for the ionic strengths of the reaction mixtures used in the
various studies were calculated from the information given by the workers on the
composition of their solutions. The significance of the ionic strength in the calcula-
tions emphasizes the importance of having reasonably complete information on the
composition of the solutions used in these studies. Unfortunately, this level of detail
is not available for these studies. Thus, in treating the earlier results, it was necessary
to make several assumptions regarding the ionic forms of the substances used in the
studies. For example, the fractions of the phosphate ion species in the initial reaction
mixture were calculated from the specified pH. These fractions were then used to cal-
culate the molality of the monovalent cation (Naþ or Kþ) needed to maintain elec-
troneutrality. Similarly, there is also uncertainty regarding the ionic forms of the
oxidized and reduced forms of glutathione and NADP used in these studies. In
any case, the equilibrium model was then used to calculate the values of K(calc)
for reaction (4) that are given in table 5. The final adjustments to I ¼ 0 were done
by using the slope s ¼ Àð7:4 Æ 1:0Þ Á 10À11 kg1=2 Á molÀ1=2 obtained from the linear
least squares fit K vs I1=2 to our results (see above). This adjustment was made for
all of the studies with the exception of that of Mapson and Isherwood [7]. It is im-
portant to recognize that both the equilibrium model used in these calculations and
the parameters in the model can change. However, sufficient details are given in the
experimental results so that the derived results can be recalculated should improved
models or parameters later become available.
The average values of K(T ¼ 298:15 K and I ¼ 0) for the reference reaction (4) ob-
tained from these studies are: Mapson and Isherwood [7], K ¼ ð3:9 Æ 0:6Þ Á 10À14
;
Scott et al. [8], K ¼ ð8:8 Æ 1:2Þ Á 10À11; Rost and Rapoport [9], K ꢀ 5 Á 10À11; Veech

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et al. [10,11], K ꢀ 16 Á 10À11; Gorin et al. [12], K ¼ ð7:3 Æ 0:6Þ Á 10À11. The result of our
study K ¼ ð6:5 Æ 2:2Þ Á 10À11 (the experimental uncertainty is used for purpose of
comparison with the earlier results) is in agreement with the results obtained from
the study of Scott et al. [8], Rost and Rapoport [9], and Gorin et al. [12]. The result(s)
of Veech and coworkers [10,11] lies higher than the values obtained from the other
studies. The results of Mapson and Isherwood [7] are clearly discordant with all of
the studies. Their [7] values are almost certainly in error, possibly because of contam-
ination of the glutathione sample [10].
Pau [14] used a titration calorimeter {imidazole buffer (Ic ¼ 0:1 mol Á dmÀ3
,
pH ¼ 6.8)} to measure the calorimetric molar enthalpy change DrHmðcalÞ ¼ À33:1
kJ Á molÀ1 for reaction (1) at T ¼ 298:15 K. Use of our equilibrium model and the
values given in table 4 leads to the value DrHmo ¼ 3:2 kJ Á molÀ1 for the reference re-
action (4) at T ¼ 298:15 K and I ¼ 0. Pau [14] did not assign an uncertainty to this
value. This result, however, relies on a very large correction [27] for the enthalpy
change due to the protonation of the imidazole buffer. The use of phosphate buffer
(our study) serves to keep this correction much smaller. This fact and possible impu-
rities in the samples used by Pau [14] might explain the difference (3.7 kJ Á molÀ1
)
between the value obtained from his study [14] and the value DrHmo ¼ ð6:9 Æ 0:5Þ
kJ Á molÀ1 obtained in our study. As done above in the comparison of the equilibrium
values, only the experimental uncertainty in our result was used for purpose of com-
parison with the result of Pau [14]. From the temperature dependence of the values
of K obtained from the study of Scott et al. [8], we calculate the value DrHmo ¼
Àð5:8 Æ 2:7Þ kJ Á molÀ1 for reaction (4) at T ¼ 298:15 K and I ¼ 0; the uncertainty
is equal to two estimated standard deviations of the mean. We note that the sign
of this value of DrHmo is opposite from both our calorimetric result and that of
Pau [14] as well as the value of DrHmo calculated from the temperature dependence
of the equilibrium constant in our own study. Additionally, there was agreement
between the vanÕt Hoff value of DrHmo (our study) and the value of this quantity
obtained via calorimetry. For these reasons, we believe that the temperature depen-
dence of the values of K reported by Scott et al. [8] is in error.
3.5. Standard electromotive force for the glutathione redox reaction
In their review of the literature, Miller and Smith-Magowan [30] (see their table 7
and also note that they [30] did not write charge numbers for the NADP species) se-
lected the value DrGom ¼ 21:13 kJ Á molÀ1 (T ¼ 298:15 K, I ¼ 0:1 mol Á kgÀ1) for the
reaction
NADP3oÀx ðaqÞ þ H2ðgÞ ¼ NADP4À ðaqÞ þ HþðaqÞ:
ð9Þ
red
Use of the activity coefficient model described above leads to DrGom ¼ 26:0 kJ Á molÀ1
for reaction (9) at T ¼ 298:15 K and I ¼ 0. Combination of this value of DrGom with
our result DrGom ¼ 58:1 kJ Á molÀ1 for reaction (4) leads to DrGmo ¼ DrGomð9ÞÀ
DrGomð4Þ ¼ À32:1 kJ Á molÀ1 for the reaction
glutathione2oÀx ðaqÞ þ H2ðgÞ ¼ 2 glutathioneÀ ðaqÞ:
ð10Þ
red

Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 35 (2003) 1361–1381
1379
Alternative ways of writing the redox reactions (9) and (10), respectively, are
NADP3ÀðaqÞ þ HþðaqÞ þ 2eÀ ¼ NADP4reÀdðaqÞ;
glutathioneo2Àx ðaqÞ þ 2 HþðaqÞ þ 2 eÀ ¼ 2 glutathioneÀredðaqÞ:
ð11Þ
ð12Þ
ox
The values of the standard electromotive force for reactions (11) and (12), respec-
tively, are Eo ¼ À0:135 V and Eo ¼ þ0:166 V. These values pertain to T ¼ 298:15 K,
I ¼ 0, and a standard pressure po ¼ 0:1 MPa. It should be recognized that the value
of DrGom for reaction (12) can be used to calculate the difference in the standard molar
Gibbs free energies of formation [Df Gom{glutathione2oÀx (aq)} ) Df Gom{glutathi-
oneÀred(aq)}].
The standard thermodynamic quantities obtained in this study serve as a basis for
the calculation of values of the standard apparent electromotive force E0o for the
(overall) biochemical redox reaction
glutathioneoxðaqÞ þ 2 eÀ ¼ 2 glutathioneredðaqÞ:
ð13Þ
The quantity E0o is a function of temperature, pH, and ionic strength. A convenient
method for calculating values of E0o from standard formation properties has been
described by Alberty [31–33] and applied to a number of redox reactions. This
method uses standard transformed molar Gibbs free energies of formation Df Gm0o
which are calculated from values of Df Gmo for the pertinent species. Using AlbertyÕs
approach we calculate E0o ¼ À0:265 V for the biochemical redox reaction (13) at
T ¼ 298:15 K, I ¼ 0:25 mol Á kgÀ1, and pH ¼ 7.0. At the same temperature and pH,
but with I ¼ 0:10 mol Á kgÀ1, E0o ¼ À0:260 V. The values of the standard electro-
motive forces for reactions (12) and (13) rely on Miller and Smith-MagowanÕs [30]
selected value of DrGom for reaction (9) and our value of DrGom for reaction (4).
Unfortunately, Miller and Smith-Magowan [30] did not assign any uncertainty to
their selected value. Our result of DrGom for reaction (9) is estimated to be uncertain
by Æ 1.7 kJ Á molÀ1. This leads to a minimal uncertainty of Æ 0.009 V in the values of
Eo and E0o for reactions (12) and (13).
Gorin et al. [12] have summarized values of E0o (T ¼ 298:15 K, pH ¼ 7.0, ionic
strength not specified) obtained from 10 studies in the literature. The values range
from +0.04 V to )0.37 V. Three of the E0o values rely on the NADP or NAD couples,
four rely on the cystine couple, and the remaining three studies used either indicators
or potentiometric methods. The average of the values cited is )0.27 V. Considering
the scatter and uncertainties associated with the values in the literature, the value E0o
(T ¼ 298:15 K, pH ¼ 7.0) ¼ )0.27 V that is calculated from our results and the value
of DrGom for reaction (9) selected by Miller and Smith-Magowan [30] is remarkably
consistent with the literature.
3.6. Apparent equilibrium constant under approximately physiological conditions
It is desirable to have a value of the apparent equilibrium constant for reaction (1)
under approximately physiological conditions which are taken to be [34] T ¼ 311:15
K, pH ¼ 7.0, and Im ¼ 0:25 mol Á kgÀ1. By using the equilibrium model and with our

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Y.B. Tewari, R.N. Goldberg / J. Chem. Thermodynamics 35 (2003) 1361–1381
final values of K and DrHmo we calculate the value K0 ¼ 0:013 for reaction (1) under
these conditions. The corresponding value of the standard molar transformed Gibbs
free energy change is DrG0mo ¼ 11:2 kJ Á molÀ1. However, Mg2þ(aq) is present under
physiological conditions at an approximate concentration c ꢀ 10À3 mol Á dmÀ33À[34].
Since Mg2þ(aq) very likely will bind to the negatively charged anions NADPox (aq)
and NADP4reÀd(aq), the calculated value of K0 for physiological conditions might be
in error due to the neglect of these bindings in the calculation. Thus, the above cal-
culated values of K0 and DrG0mo for reaction (1) under approximately physiological
conditions {i.e., with Mg2þ(aq) present} should be considered to be approximate.
The predominant structural feature of reactions (12) and (13) is the breaking of a
disulfide bond. For this reason, the thermodynamic quantities for these reactions are
of significance to workers concerned with the molecular biology of molecules that
undergo this very important type of transformation.
Acknowledgements
We thank Dr. Vytas Reipa for his suggestion regarding the use of Ar(g) to min-
imize the oxidation of the reactants.
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JCT 03/023