Thermodynamics of reactions catalyzed by l-iditol 2-dehydrogenase: The xylose assimilation pathway

Article abstract of DOI:10.1006/jcht.1996.0099

Apparent equilibrium constants and calorimetric enthalpies of reaction have been measured for the following enzyme catalyzed (L-iditol 2-dehydrogenase) biochemical reactions in phosphate buffer at pHs near 7.5 and at the temperature 298.15 K D-sorbitol(aq) + NAD_ox(aq) = D-fructose(aq) + NAD_red(aq), L-iditol(aq) + NAD_ox(aq) = L-sorbose(aq) + NAD_red(aq), xylitol(aq) + NADox(aq) = D-xylulose(aq) + NAD_red(aq). Here, NAD_ox is β-nicotinamide-adenine dinucleotide (oxidized form) and NAD_red is β-nicotinamide-adenine dinucleotide (reduced form). The results are used to calculate equilibrium constants and standard molar enthalpies, entropies, and Gibbs free energies for reference reactions involving specific species. Standard formation properties and standard transformed formation properties of the biochemical reactants are also calculated. The thermodynamics of the xylose assimilation pathway is summarized.

Full text of DOI:10.1006/jcht.1996.0099

J. Chem. Thermodynamics 1996, 28, 1127–1144
Thermodynamics of reactions catalyzed by
L-iditol 2-dehydrogenase: the xylose assimilation
pathway
Yadu B. Tewari and Robert N. Goldberg
Biotechnology Division, National Institute of Standards and Technology,
Gaithersburg, MD 20899, U.S.A.
Apparent equilibrium constants and calorimetric enthalpies of reaction have been measured for
the following enzyme catalyzed (L-iditol 2-dehydrogenase) biochemical reactions in phosphate
buffer at pHs near 7.5 and at the temperature 298.15 K
D-sorbitol(aq) + NADox(aq) = D-fructose(aq) + NADred(aq),
L-iditol(aq) + NADox(aq) = L-sorbose(aq) + NADred(aq),
xylitol(aq) + NADox(aq) = D-xylulose(aq) + NADred(aq).
Here, NADox is b-nicotinamide-adenine dinucleotide (oxidized form) and NADred is
b-nicotinamide-adenine dinucleotide (reduced form). The results are used to calculate
equilibrium constants and standard molar enthalpies, entropies, and Gibbs free energies for
reference reactions involving specific species. Standard formation properties and standard
transformed formation properties of the biochemical reactants are also calculated. The
thermodynamics of the xylose assimilation pathway is summarized. 7 1996 Academic Press Limited
1. Introduction
The enzyme L-iditol 2-dehydrogenase (Enzyme Commission number 1.1.1.14),(1) also
known as sorbitol dehydrogenase, catalyzes the following reactions in bacteria and
mammals:†
D-sorbitol(aq) + NADox(aq) = D-fructose(aq) + NADred(aq),
L-iditol(aq) + NADox(aq) = L-sorbose(aq) + NADred(aq),
xylitol(aq) + NADox(aq) = D-xylulose(aq) + NADred(aq).
(1)
(2)
(3)
Reaction (3) is of importance to the conversion of hemicellulosic materials (a
significant component of plants) to ethanol. In this application, the hemicellulose
† Abbreviations used in this paper follow. For species in chemical reference reactions: NAD−, oxidized
form of b-nicotinamide-adenine dinucleotide; NADH2−
,
reduced form of b-nicotinamide-adenine
dinucleotide; NADP3−, oxidized form of b-nicotinamide-adenine dinucleotide phosphate; and NADPH4−
,
reduced form of b-nicotinamide-adenine dinucleotide phosphate. For reactants in overall biochemical
reactions: ATP, adenosine 5'-triphosphate; ADP, adenosine 5'-diphosphate; NADox, b-nicotinamide-
adenine dinucleotide (oxidized form); NADred, b-nicotinamide-adenine dinucleotide (reduced form);
NADPox, b-nicotinamide-adenine dinucleotide phosphate (oxidized form); NADPred, b-nicotinamide-
adenine dinucleotide phosphate (reduced form). Tris is tris(hydroxymethyl)aminomethane.
0021–9614/96/101127 + 18 $18.00/0
7 1996 Academic Press Limited

1128
Y. B. Tewari and R. N. Goldberg
is first broken down into D-xylose, which then enters the xylose assimilation
pathway.(2,3)
L-iditol 2-dehydrogenase also participates in the polyol pathway.(4) This is normally
a minor metabolic pathway. However, in certain disease states, particularly diabetic
hyperglycemia, this pathway assumes increased importance. Thus, intermediates
such as D-sorbitol can accumulate in cells and cause a serious osmotic imbalance and
consequent pathology in nerves and in tissues. One such example is the formation
of cataracts.(5)
The principal aim of this study is to determine apparent equilibrium constants
and calorimetric enthalpies for reactions (1), (2), and (3). These results are then used
to calculate equilibrium constants and standard molar enthalpies for reference
reactions that involve specific species. These quantities can be used to calculate the
position of equilibrium of the corresponding biochemical reactions as a function of
temperature, pH, and ionic strength. Standard formation properties and standard
transformed formation properties(6) for these various substances are also obtained.
These results are used in conjunction with results from the literature to gain insight
into the operation of the xylose assimilation pathway.
2. Experimental
Pertinent information on the substances used in this study is given in table 1.
Estimates of the purities of the D-fructose, L-iditol, D-sorbitol, L-sorbose, and xylitol
were obtained chromatographically with a Dionex Bio-LC (see below). The use of
this method for D-xylulose was not possible because D-xylulose appeared as a very
broad peak on the chromatograms. However, the mole fraction purity
of the D-xylulose was estimated by using L-iditol 2-dehydrogenase to catalyse the
reaction of the D-xylulose with excess NADred. The chromatogram of this reaction
mixture obtained with the Dionex BioLC showed that the reaction was complete
(Q0.005 mole fraction D-xylulose remained). The amount of xylitol formed in this
reaction was also measured chromatographically and the result used to calculate a
mole fraction purity of (0.919 2 0.005) for the D-xylulose sample. This does not
include the water in the sample, the mass fraction of which was determined by
Karl Fischer titration. The supplier used g.c. to determine a mole fraction purity of
1 0.95 for this D-xylulose sample. The uncertainty given above for the D-xylulose
mole fraction purity is based on three replicate measurements and is equal to two
estimated standard deviations of the mean. Because the method used depends upon
a knowledge of the purity of the xylitol, and is also subject to possible interferences,
we believe that a more realistic estimate of the uncertainty is 20.03. This brings our
result for the D-xylulose mole fraction purity into agreement with the approximate
result of the analysis performed by g.c.
A Hewlett-Packard h.p.l.c. (see below) was used to obtain estimates of the
mole fraction purities of the NADox and NADred. In addition, the supplier used
the following methods to characterize several of these substances: thin-layer
chromatography for L-iditol and L-sorbose; enzymatic and spectrophotometric
assays for the NADox and NADred; and g.c. for the L-sorbose, D-sorbitol, and

Nicotinamide-adenine dinucleotide reactions
1129
xylitol. The estimates of the mole fraction purities obtained by the supplier with
these methods were in agreement with the purities obtained in this laboratory
with the aforementioned chromatographic techniques. The mass fractions of
water in the substances (see table 1) were measured with a Metrohm Model
633 automatic Karl Fischer titrator. Information on the optical rotations
a (l = 589.3 nm, T = 273.15 K, mass concentration g, path length = 10 cm) of these
samples that was obtained from the vendors follows: D-fructose (g = 1 g·dm−3),
a = −92.4·p/180; L-iditol (g = 0.3 g·dm−3), a = −3.3·p/180; L-sorbose (g =
1.2 g·dm−3), a = −43.8·p/180; and D-xylulose (g = 0.1 g·dm−3), a = −29·p/180.
Analyses for NADox and NADred were done with a Hewlett-Packard h.p.l.c., a
Serva DEAE Si 100 column thermostatted at T = 311 K, and a diode array detector
set at a wavelength of 254 nm. Solutions I and II were used for the mobile phase:
I, 0.02 mol·dm−3 KH2PO4 at pH = 4.7; and II, 0.25 mol·dm−3 K2HPO4 at pH = 7.47.
The following linear gradient was used: solution I (volume fraction f = 1.00) at
time t = 0; at t = 15 min the mobile phase consisted of solution I (f = 0.50) and
TABLE 1. Chemical Abstracts Services (CAS) registry numbers, empirical formulas, molar masses M, suppliers, mass
fraction of water contents w determined by Karl Fischer analysis, and mole fraction purities x for the principal
substances used in this study. The mole fraction purities do not include the water, or, for NADred, the ethanol in the
sample
CAS
registry
number
M
Substance
Formula
K2HPO4
Supplier a
w b,c
x
kg·mol−1
dipotassium hydrogen
phosphate
D-fructose
7758-11-4
0.174176
S
0.995
57-48-7
488-45-9
C6H12O6
C6H14O6
0.180158
0.182174
1 41 e
F
S
S
S
S
B
S
S
S
S
0.0026 2 0.0008 q0.99
0.0047 2 0.0002 q0.99
L-iditol
L-iditol 2-dehydrogenase d 9028-21-1
NADox
NADred
phosphoric acid
D-sorbitol
L-sorbose
xylitol
53-84-9
606-68-8 C21H27N7O14P2Na2
7664-38-2
50-70-4
87-79-6
87-99-0
551-84-8
C21H27N7O14P2
0.663431
0.709411
0.97995
0.0659 2 0.0005
0.99
0.99
q0.999
0.98
f
H3PO4
C6H14O6
C6H12O6
C5H12O5
C5H10O5
0.182174
0.180158
0.152147
0.150131
0.0058 2 0.0009
0.0003 2 0.0001 q0.99
0.0020 2 0.0001
0.109 2 0.005
0.991
D-xylulose
0.919 g
a B = Baker, F = Fisher, and S = Sigma. Certain commercial materials and products are identified in this paper to
specify adequately the experimental procedure. Such identification does not imply recommendation or endorsement by
the National Institute of Standards and Technology.
b All uncertainties given in this paper are, unless indicated otherwise, equal to two estimated standard deviations of
the mean.
c The mass fraction moisture contents of dipotassium hydrogen phosphate and L-iditol 2-dehydrogenase were not
measured. The phosphoric acid was a solution of known concentration.
d Lyophilized powder obtained from sheep liver.
e This approximate molar mass is based upon the structural information given by Eklund et al.(7)
f Two different samples of NADred were used. The mass fraction water contents were (0.0621 2 0.0007) and
(0.0616 2 0.0008). These respective NADred samples were reported by the vendor to contain mass fractions of ethanol
equal to 0.035 and 0.028.
g This mole fraction purity is based upon the measurement of the amount of xylitol formed by reaction of the
D-xylulose sample with excess NADred
.

1130
Y. B. Tewari and R. N. Goldberg
solution II (f = 0.50). The flow rate was 0.0167 cm3·s−1. Typical retention times of
NADox and NADred were 9.3 min and 15.9 min, respectively.
A Dionex Bio-LC with a pulsed amperometric detector, a Dionex MA1 column,
and a 1.0 mol·dm−3 NaOH mobile aqueous phase at a flow rate of 0.005 cm3·s−1 was
used for the analyses of the sugars and sugar alcohols. Typical retention times were:
17.1 min and 23.0 min, respectively, for D-sorbitol and D-fructose; 15.7 min and
21.3 min, respectively, for L-iditol and L-sorbose; and 14.4 min and 1 29 min,
respectively, for xylitol and D-xylulose. The peaks corresponding to D-xylulose were
very broad and could not be integrated reliably.
A Beckman DU-70 spectrophotometer was used to measure the changes in the
(decadic) absorbances A of the reaction mixtures. At the temperature T = 298.15 K
and a wavelength l = 340 nm, the molar (decadic) absorption coefficient o of
NADred is 6.292·104 dm2·mol−1, while o of NADox is Q25 dm2·mol−1.(8) The remaining
reactants, i.e. the sugars and sugar alcohols, do not absorb at l = 340 nm. Thus, any
change in the absorbance of a reaction mixture is attributed to a change in the
concentration of NADred. The cuvettes placed in this spectrophotometer
had a nominal pathlength of 1.00 cm and were thermostatted at T = 298.15 K.
The accuracy of the thermostat was confirmed by measuring the temperature inside
a cuvette in the spectrophotometer with a thermistor that, in turn, had been
calibrated with a National Institute of Standards and Technology (NIST) calibrated
standard platinum resistance thermometer. The spectrophotometer was also
calibrated with NIST standard reference materials no. 2031 (calibrated glass filters
for absorbance) and no. 2034 (holmium oxide solution for l).
The pHs of the reaction mixtures were measured with a combination glass
micro-electrode and an Orion Model 811 pH meter. All pH measurements
were made at the temperature at which the reactions occurred. Calibration of the
pH meter was performed with a standard buffer prepared from KH2PO4
(m = 0.009695 mol·kg−1) and Na2HPO4 (m = 0.03043 mol·kg−1). These phosphates
are standard reference materials 186-Id and 186-IId, respectively, from the National
Institute of Standards and Technology. Intercomparisons of this ‘‘physiological’’
buffer against Fisher buffers certified at pH = 7.00, 8.00, and 9.00 were also
done with agreement to within 20.03.
The method used for the equilibrium measurements is now described. First, a
series of solutions was prepared in Teflon stoppered glass bottles. These solutions
contained all four reactants (D-sorbitol, NADred, D-fructose, and NADox) at
molalities that resulted in apparent reaction quotients Q' close to the estimated
value of the apparent equilibrium constant K' under the conditions of measurement.
The initial absorbances (l = 340 nm, T = 298.15 K) of these reaction mixtures
were then measured. Following addition of a solution containing the enzyme (L-iditol
2-dehydrogenase), the absorbances were again measured. A suitable period of time
for reaction was allowed, and the reaction mixtures were judged to be at equilibrium
when the changes in the absorbances with time were comparable with that observed
for the change in the absorbance of an (NADred + buffer) solution at the
same T and pH. On this basis, the reaction(s) reached equilibrium within
1 2 h.

Nicotinamide-adenine dinucleotide reactions
1131
All solutions were prepared gravimetrically. Appropriate corrections were
applied for loss of solution following the initial determinations of the absorbances
of the reaction mixtures and the return of these solutions from the cuvettes to
the bottles in which the solutions had been prepared and to which the enzyme
was subsequently added. Also, the (numbered) cuvettes were rinsed with distilled
water and air-dried following the initial determination of the absorbances of the
reaction mixtures. Appropriate corrections, based upon separate control
experiments, were applied for the absorbance of the enzyme solution and for
the observed change in absorbance of the NADred with time (NADred drift).
The correction to the absorbances of the reaction mixtures due to the absorption
of the enzyme was 1 −0.0043. The correction for the NADred drift was
2.5·10−6·A·s−1. Since these experiments lasted 1 7.2·103 s, the drift corrections were
1 0.02·A.
The apparent reaction quotients Q' were selected so that Q' (min) Q K' Q Q' (max),
where K' is the presumed value of the apparent equilibrium constant and Q' (min)
and Q' (max) are, respectively, the minimum and maximum values of the apparent
equilibrium quotient used in the experiments. The experimental results were
then used to construct a plot of Q' as a function of the change in absorbance
DA. In such a plot, or in a numerical fit of Q' against DA, the value of Q'
corresponding to DA = 0 is K'. This method presupposes a knowledge of an
approximate value of K', and it will not work if the presumed value of K' is not in
the aforementioned range. In this study, approximate values of K' were obtained
from results in the literature as well as from preliminary experiments in which
equilibrium was approached from both extreme ends of the reaction. However, even
if the condition Q' (min) Q K' Q Q' (max) is not met, the results of an unsuccessful
experiment will lead to a better estimate of K' and, very likely, to a successful next
experiment.
The reaction mixtures having the smallest absolute value of DA for a given
reaction were analysed with the h.p.l.c. methods described above. Here, solutions
for the determination of the response factors were prepared from the same
stock solutions of reagents used for the preparation of the reaction mixtures in the
spectrophotometric measurements. Values of the apparent equilibrium constants K'
were calculated from the chromatographically determined molalities. However, the
molalities of NADox and D-xylulose in reaction (3) could not be measured with
the h.p.l.c. for the following reasons. The detector was saturated at the molality
of the NADox used in this set of experiments and the D-xylulose chromatographic
peak was very broad and could not be integrated reliably. Thus, for reaction (3), the
initial molalities of NADox and D-xylulose and the extent of reaction, as determined
from the measured changes in the molalities of NADred and xylitol, were used to
calculate K' from the h.p.l.c. results.
Three heat-conduction microcalorimeters were used for enthalpy of reaction
measurements. They were calibrated electrically with a high stability d.c. power
supply, calibrated digital voltmeter, standard resistor, and time-interval counter.
Descriptions of the calorimeters and their performance characteristics, the
data-acquisition system, and the computer programs used to treat the results are

1132
Y. B. Tewari and R. N. Goldberg
given in references 9 and 10. The sample vessels, fabricated from high-density
polyethylene, contained two compartments that held 1 0.55 cm3 and 1 0.45 cm3 of
solution. A stock solution III consisting of phosphate buffer and NADred was
made before the preparation of the other solutions used in the calorimetric
experiments. The substrate solution (placed in the 0.55 cm3 compartment) consisted
of a sugar (D-fructose, L-sorbose, or D-xylulose) dissolved in solution III. The enzyme
solution (placed in the 0.45 cm3 compartment) consisted of L-iditol 2-dehydrogenase
dissolved in a separate portion of solution III. The molality of the NADred in these
solutions was in excess of the amount required for complete reaction of the respective
sugar.
The vessels and their contents were allowed to equilibrate in the calorimeters for
1 h before the enzyme and substrate solutions were mixed. Following reaction
in the calorimeter for 60 min to 90 min, the reaction vessels were removed from
the calorimeters and their contents were promptly analysed with the Dionex
h.p.l.c. Thus, it was found that the mole fractions of unreacted D-fructose, L-sorbose,
and D-xylulose were, respectively, 0.147, 0.200, and Q0.005. Appropriate corrections
were applied for incomplete reaction. The ‘‘blank’’ enthalpy changes for the mixing
of the substrate solutions with solution III ranged from 0.29 mJ to 0.96 mJ; for
the mixing of the enzyme solutions with solution III they ranged from −0.13 mJ
to −0.60 mJ. These ‘‘blank’’ enthalpies of mixing were also applied as corrections
to the measured enthalpy changes which were approximately −125 mJ, −78 mJ,
and −304 mJ for the respective reactions involving D-fructose, L-sorbose, and
D-xylulose. There were changes in the pHs of the reaction mixtures as a consequence
of the reactions. Thus, for the reactions involving D-fructose, L-sorbose, and
D-xylulose, {pH(final) - pH(initial)} was 0.17, 0.13, and 0.16, respectively. The
positive signs indicate that protons were absorbed as a consequence of the reaction.
3. Results and discussion
The apparent equilibrium constants corresponding to the overall biochemical
reactions (1), (2), and (3) are, respectively
K' = m(D-fructose)·m(NADred)/{m(D-sorbitol)·m(NADox)},
K' = m(L-sorbose)·m(NADred)/{m(L-iditol)·m(NADox)},
K' = m(D-xylulose)·m(NADred)/{m(xylitol)·m(NADox)}.
(4)
(5)
(6)
The molalities m in equations (4), (5), and (6) are the total molalities of the various
charged and uncharged species that are formed from the dissociation of the various
substances in solution. As D-fructose, L-sorbose, D-xylulose, D-sorbitol, L-iditol, and
xylitol do not ionize except in extremely alkaline solutions, the only dissociations of
concern are those involving NADox and NADred. These dissociations are dealt with
below.

Nicotinamide-adenine dinucleotide reactions
1133
In discussing the thermodynamics of these reactions, it is useful to introduce the
reference reactions:
D-sorbitol(aq) + NAD−(aq) = D-fructose(aq) + NADH2−(aq) + H+(aq), (7)
L-iditol(aq) + NAD−(aq) = L-sorbose(aq) + NADH2−(aq) + H+(aq),
xylitol(aq) + NAD−(aq) = D-xylulose(aq) + NADH2−(aq) + H+(aq).
The equilibrium constants for reactions (7), (8), and (9) are
(8)
(9)
Km = m(D-fructose)·m(NADH2−)·m(H+)/{m(D-sorbitol)·m(NAD−)·m°}, (10)
Km = m(L-sorbose)·m(NADH2−)·m(H+)/{m(L-iditol)·m(NAD−)·m°},
Km = m(D-xylulose)·m(NADH2−)·m(H+)/{m(xylitol)·m(NAD−)·m°}.
(11)
(12)
Here the molalities refer to specific species. Note that all species without
charge numbers in reactions (7) to (9) and equations (10) to (12) are neutral. Since
reactions (1), (2), and (3) are symmetric, the values of the corresponding apparent
equilibrium constants are independent of the choice of standard state. However,
reactions (7), (8), and (9) are not symmetric and the values of the corresponding
equilibrium constants depend on the choice of standard state. The standard state
of the solute used herein is the hypothetical ideal solution of unit molality
(m° = 1 mol·kg−1); the standard pressure p° is 0.1 MPa. The quantity m° has been
placed in the denominators of equations (10), (11), and (12) to make the equilibrium
constants dimensionless.
The results obtained with the various reaction mixtures and which correspond to
reactions (1), (2), and (3) are given in table 2. Polynomial fits of Q' as a function
of the change in absorbance DA with terms to (DA)3 were found to represent
the results adequately. The value of Q' which corresponds to DA = 0 is equal to
the apparent equilibrium constant K'. Thus, the first term in the polynomial fit
for each set of results and its standard deviation yielded the following results:
K' = (0.092 2 0.003), K' = (0.180 2 0.005), and K' = (1.22 2 0.02)·10−3 for
reactions (1), (2), and (3), respectively. Here the uncertainties are equal to two
standard deviations. However, we believe that these uncertainties should be increased
because the correction for the absorbance of the enzyme and for the ‘‘NADred drift’’
(see Experimental section) could be uncertain by as much as 20 per cent. This leads
to an additional uncertainty of 20.001 in K' for reactions (1) and (2), and 20.02
in K' for reaction (3). Thus, the results obtained with the spectrophotometric method
are: K' = (0.092 2 0.004), K' = (0.180 2 0.006), and K' = (1.22 2 0.04)·10−3 for
reactions (1), (2), and (3), respectively.
The following results were obtained from the h.p.l.c. measurements: K' =
(0.102 2 0.009), K' = (0.199 2 0.009), and K' = (1.21 2 0.05)·10−3 for reactions
(1), (2), and (3), respectively. These two standard deviation uncertainties were
obtained from the standard deviations of the molalities of the reactants as determined
by h.p.l.c. and of the response factors used to calculate these molalities. It is seen
that the spectrophotometric and h.p.l.c. results for reactions (1) and (3) are in

1134
Y. B. Tewari and R. N. Goldberg
TABLE 2. Molalities of substances m in reaction mixtures, pHs, apparent reaction quotients Q', and measured changes in absorbance
DA. All molalities are equal to the sums of the molalities of the indicated substances in their various ionic forms. The changes in
absorbance have been corrected for the absorbance of added enzyme (L-iditol 2-dehydrogenase) and for drift in the absorbance of NADred
.
The mass fraction of the lyophilized enzyme in these solutions was 1 0.0013. The calculated ionic strengths Im for the reaction mixtures
for biochemical reactions (1), (2), and (3) are, respectively, 0.197 mol·kg−1, 0.191 mol·kg−1, and 0.189 mol·kg−1. Uncertainties are
discussed in the text
Biochemical reaction (1): NADox(aq) + D-sorbitol(aq) = NADred(aq) + D-fructose(aq)
m(K2HPO4) m(H3PO4) 104·m(NADox
)
104·m(D-sorbitol) 104·m(NADred
)
104·m(D-fructose)
pH
Q'
DA
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
7.63
7.64
7.63
7.63
7.62
7.61
0.09860
0.09861
0.09861
0.09862
0.09863
0.09864
0.01047
0.01047
0.01047
0.01048
0.01048
0.01048
4.271
5.382
6.268
7.185
9.140
10.55
8.314
7.837
7.515
7.133
6.582
6.083
1.706
1.631
1.582
1.557
1.400
1.316
4.362
4.256
4.121
3.902
3.632
3.409
0.2096
0.1646
0.1384
0.1185
0.08453
0.06987
−0.3787
−0.2840
−0.1998
−0.1348
0.0444
0.1371
Biochemical reaction (2): NADox (aq) + L-iditol (aq) = NADred (aq) + L-sorbose (aq)
m(K2HPO4) m(H3PO4) 104·m(NADox
)
104·m(L-iditol)
104·m(NADred
)
104·m(L-sorbose)
pH
Q'
DA
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
7.58
7.58
7.57
7.57
7.58
7.57
0.09591
0.09592
0.09592
0.09593
0.09594
0.09595
0.01115
0.01115
0.01115
0.01115
0.01116
0.01116
3.575
4.912
6.422
7.437
10.45
12.48
9.180
8.917
8.403
7.873
6.992
6.468
1.726
1.639
1.513
1.517
1.333
1.212
8.440
7.994
7.719
7.305
6.408
5.618
0.4440
0.2992
0.2164
0.1892
0.1169
0.08432
−0.4665
−0.2820
−0.1017
−0.0235
0.2554
0.4280
Biochemical reaction (3): xylitol(aq) + NADox (aq) = D-xylulose(aq) + NADred(aq)
m(K2HPO4) m(H3PO4) 103·m(NADox
)
103·m(xylitol)
104·m(NADred
)
105·mD-xylulose)
pH
103·Q'
DA
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
7.56
7.53
7.51
7.50
7.48
0.09526
0.09533
0.09536
0.09540
0.09545
0.01107
0.01108
0.01108
0.01108
0.01109
1.252
2.492
3.024
3.727
4.524
3.374
3.006
2.860
2.687
2.392
1.722
1.576
1.493
1.407
1.263
8.898
8.006
7.614
6.898
6.487
3.628
1.684
1.315
0.969
0.757
−0.2039
−0.0683
−0.0198
0.0802
0.1980
agreement, but that the spectrophotometric and h.p.l.c. results for reaction (2)
differ by an amount (0.004) that is slightly outside the stated uncertainties. In any
case, we calculate a weighted average of the spectrophotometric and h.p.l.c.
results: K' = (0.094 2 0.004), K' = (0.186 2 0.005), and K' = (1.22 2 0.03)·10−3
for reactions (1), (2), and (3), respectively. However, we judge that impurities in the
biochemicals used in this study could cause errors as large as 0.03·K' for reactions
(1) and (2) and 0.05·K' for reaction (3). On this basis, we increase the uncertainties
and arrive at the final set of results: K' = (0.094 2 0.005), K' = (0.186 2 0.008), and
K' = (1.22 2 0.07)·10−3 for reactions (1), (2), and (3), respectively.
Results for the calorimetrically determined molar enthalpies DrHm(cal) for
the reverse of reactions (1), (2), and (3) are given in table 3. We believe that the
statistical uncertainties for reactions (1) and (2) given in this table are sufficiently
large to encompass possible systematic errors in the measurements. However,
we judge that a reasonable uncertainty in DrHm(cal) due to the uncertainty in the

Nicotinamide-adenine dinucleotide reactions
1135
TABLE 3. Results of calorimetric measurements for the reverse of biochemical reactions (1), (2), and (3) in phosphate
buffer at T = 298.15 K. The molalities m 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. DrHm(cal) is the calorimetrically determined molar enthalpy of reaction. The ionic strengths Im
are calculated. The mass fraction of the L-iditol dehydrogenase in the final solutions was 10.0004. The uncertainties
are equal to two estimated standard deviations of the mean
Reverse of biochemical reaction (1):
D-fructose(aq) + NADred(aq) = D-sorbitol(aq) + NADox(aq)
m(K2HPO4)
m(H3PO4)
m(D-fructose)
m(NADred
)
Im
DrHm(cal)
Experiment
pH
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
kJ·mol−1
1
2
3
4
5
7.55
7.55
7.55
7.55
7.55
0.0994
0.0994
0.0994
0.0994
0.0994
0.0167
0.0167
0.0167
0.0167
0.0167
0.00893
0.00872
0.00856
0.00908
0.00865
0.0132
0.0132
0.0132
0.0132
0.0132
0.217
0.217
0.217
0.217
0.217
−17.32
−17.19
−17.35
−16.77
−16.77
ꢀDrHm(cal)ꢁ = − (17.1 2 0.3) kJ·mol−1
Reverse of biochemical reaction (2):
L-sorbose(aq) + NADred(aq) = L-iditol(aq) + NADox(aq)
m(K2HPO4)
m(H3PO4)
m(L-sorbose)
m(NADred
)
Im
DrHm(cal)
Experiment
pH
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
kJ·mol−1
1
2
3
4
5
6
7.39
7.39
7.39
7.39
7.39
7.39
0.102
0.102
0.102
0.102
0.102
0.102
0.0191
0.0191
0.0191
0.0191
0.0191
0.0191
0.00945
0.00955
0.00929
0.00886
0.00899
0.00885
0.0125
0.0125
0.0125
0.0125
0.0125
0.0125
0.215
0.215
0.215
0.215
0.215
0.215
−10.20
−9.67
−11.52
−10.21
−10.79
−10.42
ꢀDrHm(cal)ꢁ = − (10.5 2 0.5) kJ·mol−1
Reverse of biochemical reaction (3):
D-xylulose(aq) + NADred(aq) = xylitol(aq) + NADox(aq)
m(K2HPO4)
m(H3PO4)
m(D-xylulose)
m(NADred
)
Im
DrHm(cal)
Experiment
pH
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
kJ·mol−1
1
2
3
4
5
6
7.43
7.43
7.43
7.43
7.43
7.43
0.102
0.102
0.102
0.102
0.102
0.102
0.0191
0.0191
0.0191
0.0191
0.0191
0.0191
0.00868
0.00917
0.00866
0.00881
0.00910
0.00918
0.0127
0.0127
0.0127
0.0127
0.0127
0.0127
0.218
0.218
0.218
0.218
0.218
0.218
−35.12
−34.89
−35.63
−35.06
−35.12
−35.32
ꢀDrHm(cal)ꢁ = − (35.2 2 0.2) kJ·mol−1
purity of the D-xylulose sample is 1 0.03·DrHm(cal) 1 1.1 kJ·mol−1. Thus,
for the reaction conditions given in table 3, DrHm(cal) = (17.1 2 0.3) kJ·mol−1,
DrHm(cal) = (10.5 2 0.5) kJ·mol−1, and DrHm(cal) = (35.2 2 1.1) kJ·mol−1 for
reactions (1), (2), and (3), respectively.
Information on the dissociation constants of the reactants is needed to relate
the results for the reactions (1), (2), and (3), expressed in terms of apparent

1136
Y. B. Tewari and R. N. Goldberg
equilibrium constants involving sums of molalities of species, to the reference
reactions (7), (8), and (9) that involve specific species. Moore and Underwood(11)
performed a potentiometric titration of NADox and obtained pK = (3.88 2 0.02) for
the dissociation of NAD0(aq) to NAD−(aq) at T = 298.15 K and ionic strength I = 0.
We estimate pK 1 3.9 for the dissociation of NADH−(aq) to NADH2−(aq) at
T = 298.15 K and I = 0 on the basis of the structural similarity of NADox and
NADred. At the pHs used in this study, the predominant species (mole fraction
x q 0.999) of NADox and NADred have charge numbers of −1 and −2, respectively.
Since D-fructose, L-sorbose, D-xylulose, D-sorbitol, L-iditol, and xylitol do not ionize
except in extremely alkaline solutions, the predominant forms of these substances are
the neutral species. In summary, the predominant species at the pHs used in this
study are those shown in the reference reactions (7), (8), and (9). On the basis of
stoichiometry, the change in binding of the hydrogen ion DrN(H+) = −1.00 for
reactions (1), (2), and (3) at the pHs used in this study. Thermodynamic quantities
for the dissociation of the phosphate buffer are also needed for the equilibrium
calculations to follow. We have used Km = 6.23·10−8 and DrHm° = 4.2 kJ·mol−1 at
T = 298.15 K and I = 0 for the dissociation of H2PO4− (aq):
H2PO4− (aq) = HPO24 − (aq) + H+(aq).
(13)
These values were calculated from the standard formation properties given in
reference 12.
The results given in tables 2 and 3 can be used together with the above
thermodynamic quantities for the dissociation constants and standard molar
enthalpies of dissociation and a previously described(13) equilibrium model to obtain
thermodynamic quantities for the reference reactions (7), (8), and (9). This
calculation is particularly simple since there is one predominant reaction in each
case and, at a fixed ionic strength, Km(ref) = Km'·m(H+). However, it is still necessary
to make adjustments to various quantities for ionic strength. To do this, we have
used an estimated ‘‘ion-size’’ parameter of 1.6 kg1/2·mol−1/2 in the extended
Debye-Huckel equation to estimate the activity coefficients of the aqueous species
in solution.
From these equilibrium calculations, we obtain Km = (9.0 2 0.8)·10−10
,
Km = (20.2 2 1.8)·10−10, and Km = (0.153 2 0.015)·10−10 for the reference reactions
(7), (8), and (9), respectively, at T = 298.15 K and I = 0. Similarly, from the
results given in table 3, we calculate DrHm°
=
(21.3 2 0.3) kJ·mol−1,
DrHm° = (14.7 2 0.5) kJ·mol−1, and DrHm° = (39.4 2 1.1) kJ·mol−1 for the reference
reactions (7), (8), and (9), respectively, at T = 298.15 K and I = 0. The uncertainties
in these thermodynamic quantities have two components: possible errors in the
measurement of the apparent equilibrium constants and calorimetric enthalpies of
reaction, and possible errors in the quantities used in the equilibrium model. The
uncertainty in the activity coefficient model is the major factor in the equilibrium
model component. The effects of these possible errors on the calculated
thermodynamic quantities were determined by perturbing both the measured
apparent equilibrium constants and calorimetric enthalpies of reaction and the

Nicotinamide-adenine dinucleotide reactions
1137
‘‘ion-size’’ parameter used in the activity coefficient model by the final uncertainties
given in the discussion above. An uncertainty of 20.3 kg1/2·mol−1/2 was assumed
for the ‘‘ion-size’’ parameter in the activity coefficient model. The effects due to
these perturbations were then combined in quadrature to obtain the estimated
uncertainties assigned to the thermodynamic quantities for the reference reactions
(7), (8), and (9). It was found that the uncertainties in the equilibrium constants for
reference reactions (7), (8), and (9) due to perturbations of the ‘‘ion-size’’ parameter
by the aforementioned amount were 150 per cent larger than the components in the
uncertainties obtained from the perturbation where only the uncertainties in the
measured apparent equilibrium constants were used. Since reactions (7), (8), and (9)
are charge asymmetric, this is not unexpected. However, perturbation of
the ‘‘ion-size’’ parameter caused no change in the calculated standard molar
enthalpies for reactions (7), (8), and (9). The reason is that when, for example, the
reverse of reaction (7) is carried out in phosphate buffer, the change in binding of
H+(aq), DrN(H+), is equal to 1.00, and this is compensated by the release of one
H+(aq) from the phosphate buffer. Thus, the net reaction is the sum of reaction (13)
and the reverse of reaction (7):
D-fructose(aq) + NADH2−(aq) + H2PO4− (aq) =
D-sorbitol(aq) + NAD−(aq) + HPO42 − (aq). (14)
Since this reaction is charge symmetric, {DrHm°(I) − DrHm°(I = 0)} = 0 within the
assumption of the Debye-Huckel model. The equilibrium constants and standard
molar enthalpies for the reference reactions were used to calculate the values of the
standard molar Gibbs free energies and standard molar entropies given in table 4.
Thermodynamic results from the literature are summarized in table 5. For
purposes of comparison, convenient quantities are the equilibrium constants
Km for the reference reactions (7), (8), and (9). The result Km = (9.0 2 0.8)·10−10
(T = 298.15 K and I = 0) obtained in the present study for reference reaction (7) is
in good agreement with the value 9.5·10−10 obtained by Chakravorty et al.(17)
The results obtained from the other studies(14–16,18,19) for reference reaction (7) range
TABLE 4. Equilibrium constants Km, standard molar enthalpies DrHm°, standard molar Gibbs free energies DrGm°,
and standard molar entropies DrSm° for reactions (7), (8), and (9) at T = 298.15 K and I = 0. The basis of the uncertainties
is discussed in the text
DrHm°
DrGm°
DrSm°
Reaction
1010·Km
kJ·mol−1
kJ·mol−1
J·K−1·mol−1
D-sorbitol(aq) + NAD−(aq) =
D-fructose(aq) + NADH2−(aq) + H+(aq) a
L-iditol(aq) + NAD−(aq) =
9.0 2 0.8
20.2 2 1.8
21.3 2 0.3
14.7 2 0.5
39.4 2 1.1
51.63 2 0.23
49.63 2 0.23
61.73 2 0.26
−101.7 2 0.4
−117.2 2 0.6
−74.9 2 1.2
L-sorbose(aq) + NADH2−(aq) + H+(aq)b
xylitol(aq) + NAD−(aq) =
D-xylulose(aq) + NADH2−(aq) + H+(aq) c
0.153 2 0.015
a Reaction (7). b Reaction (8). c Reaction (9).

1138
Y. B. Tewari and R. N. Goldberg
TABLE 5. Results from the literature for biochemical reactions (1), (2), and (3). The thermodynamic temperatures T, the pH, the buffers and
their concentrations, the MgCl2 concentrations c(MgCl2), and the apparent equilibrium constants K' are given for each study. Approximate
(concentration) ionic strengths Ic were calculated from the information given on the compositions of the solutions used in each study. We have
calculated the values of the equilibrium constants Km (column 7) for the respective reference reactions (7), (8), and (9) at T = 298.15 K and
I = 0
Biochemical reaction (1): D-sorbitol(aq) + NADox(aq) = D-fructose(aq) + NADred(aq)
T
K
c(MgCl2)
mol·dm
Ic
10
pH
8.0
Buffer
K' 10 ·Km
Reference
−3
−3
mol·dm
−3
(14)
293.15
phosphate (0.00432 mol·dm
)
0
0.012
?
0.057
0.006
0.22
0.22
0.24 a
20 b
Blakley
(15)
298.15 17.0 c
?
?
0.021 a
0.031 a
0.454 a
0.0058
0.032
120
Williams-Ashman and Banks
−3
(16)
298.15
296.15
298.15
298.15
7.87 d
8.6
7.0
Tris (0.05 mol·dm
)
0.008
2.3
Hollmann
−3
(17)
glycine (0.080 mol·dm ) + KOH
phosphate (0.1 mol·dm
phosphate (0.1 mol·dm
0
0
0
9.5 b
2.3
Chakravorty et al.
Schneider and Giffhorn
Schneider and Giffhorn
−3
(18)
)
)
−3
(19)
7.0
13
Biochemical reaction (2): L-iditol(aq) + NADox(aq) L-sorbose(aq) + NADred(aq)
T
K
c(MgCl2)
mol·dm
Ic
10
pH
Buffer
K' 10 ·Km
Reference
−3
−3
mol·dm
−3
a
(16)
298.15
7.87 d
Tris (0.05 mol·dm
)
0.008
0.057
0.031
2.3
Hollmann
Biochemical reaction (3): xylitol(aq) + NADox(aq) D-xylulose(aq) + NADred(aq)
T
K
c(MgCl2)
mol·dm
Ic
10
pH
Buffer
K'
10 ·Km
Reference
−3
−3
mol·dm
−3
(16)
298.15
296.15
298.15
298.15
298.15
7.87 d
8.6
9.5
7.0
7.0
Tris (0.05 mol·dm
)
0.008
0
0
0.005
0.050
0.057
0.006
0.011
0.071
0.20
0.0031 a
0.0215 a
0.23
0.47 b
0.14
10.2
0.28
Hollmann
−3
(17)
glycine (0.080 mol·dm ) + KOH
Chakravorty et al.
Sugai and Veiga
−3
(20)
glycine (0.030 mol·dm ) + NaOH
0.060
−3
−4
(21)
Tris (0.05 mol·dm
Tris (0.05 mol·dm
)
)
14·10
Ditzelmuller et al.
−3
−4
(22)
6.9·10
Rizzi et al.
−pH
a Calculated from reported value of K'·10
.
b Adjusted to T = 298.15 K with the appropriate standard molar enthalpy of reaction determined in this study.
(15)
c Williams-Ashman and Banks did not report the composition of the solution used in their measurements. The pH was assumed to be near
7.0.
d This is the average pH at which measurements were performed.
from 2.3·10−10 to 20·10−10 and have a mean value of 11·10−10, not far from the result
obtained in this study. Our result Km = (20.2 2 1.8)·10−10 for reference reaction
(8) differs by a factor of 10 from the result 2.3·10−10 obtained from the study
of Hollmann.(16) For reference reaction (9), the values of Km vary over a more
narrow range (1.4·10−11 to 4.7·10−11); the mean is 2.7·10−11. Our result, Km =
(1.53 2 0.5)·10−11, falls in the lower end of this range. There are several factors that
lend confidence to the results obtained in the present study: two different methods
of measurement (spectrophotometry and h.p.l.c.) were used; the materials were well
characterized; the biochemicals were present in solution for only a few hours, thus
minimizing the possibility of side reactions; and the position of equilibrium was
approached from two different directions. Of the studies cited in table 5, equilibrium
was approached from both directions of reaction only by Rizzi et al.(22)
The review of Miller and Smith-Magowan(23) gave DrGm° = 20.2 kJ·mol−1 and
DrHm° = −30.7 kJ·mol−1 at T = 298.15 K and Im = 0.1 mol·kg−1 for the reaction
NAD−(aq) + H2(g) = NADH2−(aq) + H+(aq).
(15)

Nicotinamide-adenine dinucleotide reactions
1139
Adjustment of these quantities for ionic strength as described above yields
DrGm° = 22.65 kJ·mol−1 and DrHm° = −31.94 kJ·mol−1 for reaction (15) at I = 0.
Combinations of reactions (7), (8), and (9) with the reverse of reaction (15) give the
following reactions:
D-sorbitol(aq) = D-fructose(aq) + H2(g).
L-iditol(aq) = L-sorbose(aq) + H2(g),
xylitol(aq) = D-xylulose(aq) + H2(g).
(16)
(17)
(18)
With this thermochemical pathway, the standard reaction quantities for reactions
(7), (8), and (9) determined in this study, the aforementioned values of DrHm° and
DrGm° for reaction (15), and the standard formation properties(24) of D-fructose(aq),
L-sorbose(aq), and D-xylulose can be used to calculate standard formation properties
and standard partial molar entropies for D-sorbitol(aq), L-iditol(aq), and xylitol(aq).
The results of these calculations are given in table 6. As the thermodynamic
properties of the pure D and L forms are equal, these designations have been removed
in table 6. Also, the values for these properties are given in table 6 to more significant
figures than they are known. This was done to ensure that there were sufficient
significant figures so that there would be no loss of accuracy in the calculation of
quantities for reactions. The values of the properties of sorbitol(aq), iditol(aq), and
xylitol(aq) given in table 6 appear to be the first reported. Also, while an enthalpy
of combustion has been reported(25) for xylitol(s), the literature does not appear to
contain values for similar quantities for the other two sugar alcohols. Nor do there
appear to be any determinations of the third law entropies, solubilities, or enthalpies
of solution that are needed to arrive at the formation properties of sorbitol(aq),
iditol(aq), and xylitol(aq) via a thermochemical pathway that starts with
the elements. However, it is possible to perform some comparisons
TABLE 6. Molar masses M, standard molar enthalpies of formation DfHm°, standard molar Gibbs
free energies of formation DfGm°, standard partial molar entropies Sm°, and standard partial molar heat
capacities C° of the substances pertinent to this study in aqueous solution at T = 298.15 K and at
p,m
p° = 0.1 MPa. For aqueous solutions, the standard state for the solute is the hypothetical ideal solution
(m = 1 mol·kg−1) and the standard state for the solvent is the pure solvent. The designations D and L have
been removed from these substances, since the thermodynamic properties of the pure forms are equal.
The properties of fructose, sorbose, xylose, and xylulose and the values for the standard partial molar
heat capacities C° are from reference 24. The properties of iditol, sorbitol, and xylitol were calculated
p,m
from results obtained in this study
M
DfHm°
DfGm°
Sm°
C°
p,m
Substance
Formula
kg·mol−1
kJ·mol−1
kJ·mol−1
J·K−1·mol−1
J·K−1·mol−1
fructose
iditol
sorbitol
sorbose
xylitol
xylose
xylulose
C6H12O6
C6H14O6
C6H14O6
C6H12O6
C5H12O5
C5H10O5
C5H10O5
0.180158
0.182174
0.182174
0.180158
0.152147
0.150131
0.150131
−1259.38
−1309.94
−1312.62
−1263.30
−1100.99
−1045.74
−1029.65
−915.51
−938.93
−944.49
−911.95
−785.23
−750.49
−746.15
279.7
319.4
328.9
254.6
265.8
203.9
243.3
369
279
319

1140
Y. B. Tewari and R. N. Goldberg
with thermochemical cycle calculations involving (NADPox + NADPred) coupled
reactions.
Apparent equilibrium constants have been measured(16,26–28) for the reactions:
xylitol(aq) + NADPox(aq) = L-xylulose(aq) + NADPred(aq),
xylitol(aq) + NADPox(aq) = D-xylose(aq) + NADPred(aq).
(19)
(20)
Reference reactions that correspond to these respective biochemical reactions are:
xylitol(aq) + NADP3−(aq) L-xylulose(aq) + NADPH4−(aq) + H+(aq), (21)
xylitol(aq) + NADP3−(aq) D-xylose(aq) + NADPH4−(aq) + H+(aq).
(22)
As done previously, comparison of results is in terms of calculated values of
the equilibrium constants for the reference reactions at T = 298.15 K and I = 0.
Adjustments for ionic strength were made with the extended Debye-Huckel equation
with an ‘‘ion-size’’ parameter of 1.6 kg1/2·mol−1/2. In performing these calculations, the
dissociation constants of the buffers used in these studies were taken from reference
29. Thus, from the results of Hollmann and Touster(26) and Hollmann(16) we calculate
respective values of Km = 2.0·10−11 and Km = 0.68·10−11 for the reference reaction (21)
at T = 298.15 K and I = 0. Similarly, from the results of Scher and Horecker(27) and
Ditzelmuller et al.(28) we calculate respective values of Km = 8.5·10−11 and
Km = 5.0·10−11 for the reference reaction (22) at T = 298.15 K and I = 0. We now
use the standard formation properties given in table 6 together with the standard
formation properties tabulated by Alberty(32) for NADP3−(aq) and for NADPH4−(aq)
to calculate Km = 4.0·10−12 for the reference reaction (21) and Km = 2.3·10−11 for the
reference reaction (22), both at T = 298.15 K and I = 0. Thus, Hollmann’s(16) most
recent result (probably preferable to his first(26)) is slightly larger than the value of
the equilibrium constant calculated from the formation properties. Similarly, the
values of the equilibrium constants calculated from the results of Scher and
Horecker(27) and of Ditzelmuller et al.(28) are all larger than the value of the
equilibrium constant calculated from the formation properties. While measurement
error in the apparent equilibrium constants for reactions (19) and (20) or in the
formation properties of NADP3−(aq) and NADPH4−(aq) is the most likely
explanation for these differences, another possible explanation could lie in the
adjustment of the results to I = 0. This problem is exacerbated by the fact that ions
with charge numbers of −3 and −4 are reactants in reactions (21) and (22).
Also, some of these earlier workers did not specify the compositions of their
solutions.
Standard transformed Gibbs free energies of formation DfGm'° and standard
transformed enthalpies of formation DfHm'° are useful properties for thermodynamic
calculations on (overall) biochemical reactions. Specifically, they can be used for
biochemical reactions analogous to the way standard formation properties for
species are used to calculate standard Gibbs free energies and standard enthalpies
of chemical reference reactions. The basis for the calculation of these transformed
formation properties has been discussed previously,(30) and the methodology has

Nicotinamide-adenine dinucleotide reactions
1141
TABLE 7. Standard transformed molar enthalpies of formation DfHm'° and standard transformed molar
Gibbs free energies of formation DfGm'° of aqueous biochemical reactants at T = 298.15 K, p° = 0.1 MPa,
pH = 7.0, and Im = 0.25 mol·kg−1. These property values are based on the convention of making a
transformation for all of the hydrogen atoms in these substances. The values for NADox, NADred
,
NADPox, and NADPred are based on the convention DfGm° = DfHm° = 0 at I = 0 for the species NAD−(aq)
and NADP3−(aq)
DfHm'°
DfGm'°
Substance
kJ·mol−1
kJ·mol−1
fructose
iditol
sorbitol
sorbose
xylitol
−1264.30
−1315.68
−1318.36
−1268.22
−1105.91
−1049.84
−1033.75
−10.26
−41.38
−6.57
−33.28
−2981.79
−2000.19
−426.32
−368.32
−373.77
−422.76
−296.04
−342.83
−338.49
1059.10
1120.09
1011.86
1072.95
−2102.88
−1231.48
−1219.42
xylose
xylulose
a
NADox
NADred
a
a
NADPox
a
NADPred
ATP b,c
ADP b,c
xylulose 5-phosphate c,d
a The property values for this reactant are from Alberty.(32)
b The property values for this reactant are from Alberty and Goldberg.(31)
c The property values for this reactant pertain to pMg = 3.
d The calculation of a value of DfGm'° for this reactant involved the use of an estimated acidity constant
and magnesium ion binding constant for xylulose 5-phosphate2−(aq) (see text).
been applied to a number of biochemical reactants.(31–33) Following these earlier
papers and the convention(30) of making a transformation for all the hydrogen atoms
in these substances, we have used the formation properties given in table 6 to
calculate the values of DfHm'° and DfGm'° given in table 7. The values of the standard
transformed formation properties of the biochemical reactants xylose(aq) and
xylulose 5-phosphate(aq) in table 7 were calculated from the standard formation
properties of the species which were based on a thermochemical cycle calculation.(24)
In the absence of direct measurements, we estimated an acidity constant and Mg2+
binding constant for xylulose 5-phosphate2−(aq) from corresponding results(34,35) for
ribose 5-phosphate2−(aq). These constants were then used with a value(24) of DfGm° for
the species xylulose 5-phosphate2−(aq) to calculate the value of DfGm'° for the
biochemical reactant xylulose 5-phosphate(aq) given in table 7. Perturbation of both
of the aforementioned constants by 50 per cent of their estimated values led to a
maximum change of −0.42 kJ·mol−1 in the calculated value of DfGm'° for xylulose
5-phosphate(aq). Thus, we conclude that these estimates do not seriously affect the
resulting value of DfGm'°.
We now use the standard transformed formation properties given in table 7
to calculate standard transformed reaction quantities DrGm'°, DrHm'°, and DrSm'° at
T = 298.15 K, pH = 7.0, and I = 0.25 mol·kg−1 for the several reactions given in
table 8. In addition to reactions (1), (2), and (3), which were the subject of this

1142
Y. B. Tewari and R. N. Goldberg
TABLE 8. Standard transformed thermodynamic quantities for several biochemical reactions, including those in the
xylose assimilation pathway, at T = 298.15 K, pH = 7.0, and I = 0.25 mol·kg−1. The values of K' and DrGm'° for
biochemical reaction (25) pertain to pMg = 3. The values of the standard transformed thermodynamic quantities for
biochemical reactions (1), (2), (3), (23), and (24) should be satisfactory for these reactions carried out in solutions
containing Mg2+(aq)
DrHm'°
DrGm'°
DrSm'°
Biochemical reaction
K'
kJ·mol−1 kJ·mol−1 J·K−1·mol−1
D-sorbitol(aq) + NADox(aq) = D-fructose(aq) + NADred(aq) a
L-iditol(aq) + NADox(aq) = L-sorbose(aq) + NADred(aq) b
xylitol(aq) + NADox(aq) = D-xylulose(aq) + NADred(aq) c
D-xylose(aq) = D-xylulose(aq) d
0.033
0.071
5.7·10−4
0.17
22.9
16.3
41.0
16.1
−29.4
8.4
6.6
18.5
4.3
−14.3
−9.5
48.6
32.8
75.5
39.4
−50.5
D-xylose(aq) + NADPred(aq) = xylitol(aq) + NADPox(aq) e
0.0031
D-xylulose(aq) + ATP(aq) = D-xylulose 5-phosphate(aq) + ADP(aq) f 47
a Reaction (1). b Reaction (2). c Reaction (3). d Reaction (23). e Reaction (24). f Reaction (25).
investigation, reactions (23), (24), and (25) are included in table 8 as they are
pertinent to a discussion of the xylose assimilation pathway (see below).
The literature does not appear to contain dissociation constants for the magnesium
complexes of NAD−(aq), NADH2−(aq), NADP3−(aq), or NADPH4−(aq). Alberty,(32)
however, has noted that, on the basis of structural similarity, the values of these
dissociation constants should be the same for the respective oxidized and reduced
forms of these substances. Therefore, the effects due to binding of these substances
with Mg2+(aq) should cancel when the respective oxidized and reduced forms are on
opposite sides of a reaction. Thus, the use of the values of the standard transformed
thermodynamic quantities in table 7 for the calculation of the standard transformed
reaction quantities (see table 8) for reactions (1), (2), (3), and (24) is judged to be
satisfactory for these reactions carried out in solutions containing Mg2+(aq).
Reaction (23) involves neutral species which do not bind Mg2+(aq) and is predicted
to be independent of pMg, where pMg = − lg{c(Mg2+)/c°}. The values given in
table 8 for K' and DrGm'° for reaction (25) pertain to pMg=3.
The xylose assimilation pathway in bacteria usually proceeds via reactions (23) and
(25).(3) The sum of these two reactions is:
D-xylose(aq) + ATP(aq) = D-xylulose 5-phosphate(aq) + ADP(aq).
(26)
In yeast and fungi, the xylose assimilation pathway proceeds via reactions (24), (3),
and (25),(3) the sum of which is:
D-xylose(aq) + ATP(aq) + NADPred(aq) + NADox(aq) =
D-xylulose 5-phosphate(aq) + ADP(aq) + NADPox(aq) + NADred(aq). (27)
The D-xylulose 5-phosphate(aq) formed from both pathways then enters the pentose
phosphate pathway,(3) where further reactions occur. With the values of the standard
transformed reaction quantities given in table 8, we obtain, for T = 298.15 K,
pH = 7.0, pMg = 3.0, and I = 0.25 mol·kg−1, DrGm'° = −5.2 kJ·mol−1 for reaction
(26) (the bacterial pathway) and DrGm'° = −5.3 kJ·mol−1 for reaction (27) (the yeast
and fungal pathway). Interestingly, the values of DrGm'° under these near physiological

Nicotinamide-adenine dinucleotide reactions
1143
conditions are essentially the same for both pathways. It is also apparent from the
values of DrGm'° given in table 8 for reactions (3) and (24) that, in the absence of
reaction (25), xylitol will be the principal product formed in the yeast and fungal
pathway. The primary thermodynamic driving force for both pathways comes from
reaction (25) which, to operate properly, is dependent on the existence of an adequate
supply of ATP from other metabolic pathways. Clearly the actual operation of
the xylose assimilation pathway(s) also involves kinetic and other considerations such
as the existence of an adequate supply of cofactors (NADPred and NADox) and
adequate enzymatic activity.
We thank Dr Miral Dizdaroglu for the use of the Beckman DU-70
spectrophotometer. Support given to this study by the Offices of Industrial
Technologies and Transportation Technologies in the U.S. Department of Energy
is gratefully acknowledged.
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(Received 22 March 1996; in final form 15 April 1996)
WE-059