Thermodynamics of the hydrolysis reactions of adenosine 3′,5′-(cyclic)phosphate(aq) and phosphoenolpyruvate(aq); the standard molar formation properties of 3′,5′-(cyclic)phosphate(aq) and phosphoenolpyruvate(aq)

Article abstract of DOI:10.1016/j.jct.2003.08.002

Molar calorimetric enthalpy changes Δ_rH_m(cal) have been measured for the biochemical reactions {cAMP(aq) + H₂O(l) = AMP(aq)} and {PEP(aq) + H₂O(l) = pyruvate(aq) + phosphate(aq)}. The reactions were catalyzed, respectively, by phosphodiesterase 3prime;,5prime;-cyclic nucleotide and by alkaline phosphatase. The results were analyzed by using a chemical equilibrium model to obtain values of standard molar enthalpies of reaction Δ_rH_m^o for the respective reference reactions {cAMp^-(aq) + H₂O(l) = HAMP^-(aq)} and {PEP^3-(aq) + H₂O(l) = pyruvate^-(aq) + HPO₄^2-(aq)}. Literature values of the apparent equilibrium constants K′ for the reactions {ATP(aq) = cAMP(aq) + pyrophosphate(aq)K {ATP(aq) + pyruvate(aq) = ADP(aq) + PEP(aq)}, and {ATP(aq) + pyruvate(aq) + phosphate(aq) = AMP(aq) + PEP(aq) + pyrophosphate(aq)} were also analyzed by using the chemical equilibrium model. These calculations yielded values of the equilibrium constants K and standard molar Gibbs free energy changes Δ_rG_mo for ionic reference reactions that correspond to the overall biochemical reactions. Combination of the standard molar reaction property values (K, Δ_rH _m^o, and Δ_rG_m^o) with the standard molar formation properties of the AMP, ADP, ATP, pyrophosphate, and pyruvate species led to values of the standard molar enthalpy Δ_fH_m^o, and Gibbs free energy of formation Δ_fG_m^o and the standard partial molar entropy S_m^o of the cAMP and PEP species. The thermochemical network appears to be reasonably well reinforced and thus lends some confidence to the accuracy of the calculated property values of the variety of species involved in the several reactions considered herein. Published by Elsevier Ltd.

Full text of DOI:10.1016/j.jct.2003.08.002

J. Chem. Thermodynamics 35 (2003) 1809–1830
www.elsevier.com/locate/jct
Thermodynamics of the hydrolysis reactions
0
0
of adenosine 3 ,5 -(cyclic)phosphate(aq) and
phosphoenolpyruvate(aq); the standard
molar formation properties of
0
0
3
,5 -(cyclic)phosphate(aq) and
phosphoenolpyruvate(aq)
*
Robert N. Goldberg , Yadu B. Tewari
Biotechnology Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
Received 24 June 2003; accepted 6 August 2003
Abstract
Molar calorimetric enthalpy changes D
actions {cAMP(aq) + H
r
m
H (cal) have been measured for the biochemical re-
2
O(l) ¼ AMP(aq)} and {PEP(aq) + H O(l) ¼ pyruvate(aq) + phos-
2
0 0
phate(aq)}. The reactions were catalyzed, respectively, by phosphodiesterase 3 ,5 -cyclic
nucleotide and by alkaline phosphatase. The results were analyzed by using a chemical equi-
ꢀ
3ꢁ
librium model to obtain values of standard molar enthalpies of reaction D
r
H
for the respec-
O(l) ¼
m
ꢁ
ꢁ
tive reference reactions {cAMP (aq) + H
ꢁ
2
O(l) ¼ HAMP (aq)} and {PEP (aq) + H
2
2ꢁ
0
pyruvate (aq) + HPO (aq)}. Literature values of the apparent equilibrium constants K for
4
the reactions {ATP(aq) ¼ cAMP(aq) + pyrophosphate(aq)}, {ATP(aq) + pyruvate(aq) ¼
ADP(aq) + PEP(aq)}, and {ATP(aq) + pyruvate(aq) + phosphate(aq) ¼ AMP(aq) + PEP(aq) +
pyrophosphate(aq)} were also analyzed by using the chemical equilibrium model. These
0
0
Abbreviations: ADP, adenosine 5 -diphosphate; AMP, adenosine 5 -monophosphate; ATP, adenosine
-triphosphate; cAMP, adenosine 3 ,5 -(cyclic)phosphate; PEP, phosphoenolpyruvate; GlyGly, glycylgly-
0
0 0
5
0
0
cine; Hepes, N-(2-hydroxyethyl)piperazine-N -2-ethanesulfonic acid; Pipes, piperazine-N,N -bis(2-ethane-
sulfonic acid); TAPS, N-[tris(hydroxymethyl)methyl-3-amino]propanesulfonic acid; Tricine,
N-tris(hydroxymethyl)methylglycine; TEA, triethanolamine; Tris, 2-amino-2-hydroxymethylpropane-1,3
diol.
*
Corresponding author. Tel.: +1-301-975-2584; fax: +1-301-975-5449.
E-mail addresses: robert.goldberg@nist.gov (R.N. Goldberg), yadu.tewari@nist.gov (Y.B. Tewari).
0021-9614/$ - see front matter. Published by Elsevier Ltd.
doi:10.1016/j.jct.2003.08.002

1810
R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
calculations yielded values of the equilibrium constants K and standard molar Gibbs free en-
ꢀ
ergy changes D
r
G
for ionic reference reactions that correspond to the overall biochemical re-
ꢀ
m
ꢀ
actions. Combination of the standard molar reaction property values (K, D
with the standard molar formation properties of the AMP, ADP, ATP, pyrophosphate, and
r
H , and D G )
r
m
m
ꢀ
pyruvate species led to values of the standard molar enthalpy D
f
H
and Gibbs free energy
m
ꢀ
ꢀ
of formation D G and the standard partial molar entropy Sm of the cAMP and PEP species.
f
m
The thermochemical network appears to be reasonably well reinforced and thus lends some
confidence to the accuracy of the calculated property values of the variety of species involved
in the several reactions considered herein.
Published by Elsevier Ltd.
0
0
Keywords: Adenosine 3 ,5 -(cyclic)phosphate; Alkaline phosphatase; Calorimetry; Chemical thermody-
0
0
namics; Enthalpy; Entropy; Gibbs free energy; Phosphodiesterase 3 ,5 -cyclic nucleotide; Phosphoenolpy-
ruvate
1
. Introduction
This study reports results of experiments and calculations that lead to the thermo-
0
0
dynamic properties of adenosine 3 ,5 -(cyclic)phosphate and phosphoenolpyruvate
(
see figure 1) that play important roles in biochemistry and in physiology. Adenosine
0
0
3
,5 -(cyclic)phosphate or cAMP, is frequently referred to as the ‘‘second messenger’’.
It is synthesized from ATP by the catalytic action of adenylate cyclase and its break-
down to AMP is brought about by the action of a phosphodiesterase that has spec-
ificity for cAMP. The two respective biochemical reactions are:
NH2
N
H N
2
N
N
H
N
O
H
N
N
N
O
+
H O
2
O
N
OPO3H2
HO
P
O
OH
HO
OH
O
adenosine 3',5'-(cyclic)phosphate
adenosine 5'-monophosphate
CH2
O
O
OH
P
OH
O
+
H O
2
+
H PO
3 4
HO
O
O
OH
phospho(enol)pyruvate
pyruvate
FIGURE 1. Structures of the substances in reactions (1) and (2). The neutral forms of the species are
shown.

R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
1811
ATPðaqÞ ¼ cAMPðaqÞ þ pyrophosphateðaqÞ;
ð1Þ
ð2Þ
cAMPðaqÞ þ H OðlÞ ¼ AMPðaqÞ:
2
The physiological importance of cAMP arises from the fact that hormones work at
cell surfaces to stimulate adenylate cyclase. This serves to increase the concentration of
cAMP which then acts inside the cell as the intracellular mediator of the hormonal mes-
sage (i.e., as the ‘‘second messenger’’). The physiological effects of cAMP are, in gen-
eral, exerted through the activation of specific protein kinases. Thus, cAMP is an
essential element of control in many biological processes [1,2]. Several toxins operate
by disrupting the delicate balance(s) required for the proper operation of cAMP.
Phosphoenolpyruvate or PEP has often been referred to as a ‘‘high-energy’’ com-
pound because of the very negative standard molar transformed Gibbs free energy
0ꢀ
change D
r
G for the hydrolysis reaction:
m
PEPðaqÞ þ H
The PEP is formed during the breakdown of glucose to lactic acid. It then donates
2
OðlÞ ¼ pyruvateðaqÞ þ phosphateðaqÞ:
ð3Þ
a phosphate to ADP by means of the following reaction:
PEPðaqÞ þ ADPðaqÞ ¼ pyruvateðaqÞ þ ATPðaqÞ:
The PEP plays similar and important energy transfer roles in many biochemical
processes, e.g., the Hatch–Slack (C ) pathway for CO fixation in plants, in the syn-
ð4Þ
4
2
thesis of the cell-walls of bacteria, in the initiation of the chorismate metabolic path-
way, and in the operation of the heart [1,2].
In this study, we have used calorimetry to determine molar enthalpy changes for re-
actions (2) and (3). These results are then used in a chemical equilibrium model [3,4] to
ꢀ
calculate standard molar enthalpy changes D
r
H for chemical reference reactions that
m
correspond to the overall biochemical reactions (2) and (3). These results, together with
equilibrium data and formation properties from the literature, are then used to calcu-
late the standard molar formation properties of the cAMP and PEP aqueous species. It
will be seen that the results form a reasonably well reinforced thermochemical network
that lends confidence to the accuracy of the calculated property values.
2
. Experimental
2
.1. Materials
1
Pertinent information on the substances used in this study is given in table 1.
The mass fraction of water in each of these samples was determined by means of
Karl Fischer titration [5]. The sample of PEP had been characterized by high-perfor-
1
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 (NIST), nor is it intended to imply
that the materials or equipment identified are necessarily the best available for the purpose.

TABLE 1
r
Principal substances used in this study with their Chemical Abstracts Service (CAS) registry numbers, empirical formulae, relative molecular masses M , mass
fraction moisture contents w determined by Karl Fischer analysis, suppliers (A, Aldrich; M, Mallinckrodt; and S, Sigma), estimated mole fraction purities x
and method(s) used to determine x
Substance
CAS No.
60-92-4
Formula
M
r
w
Supplier
S
x
Method(s)
h.p.l.c.
0
Adenosine 3 ,
0
C
C
10
H
11
N
N
5
5
NaO
6
7
P
P
351.188
369.203
0.078
ꢂ0.994
5 -(cyclic)phosphate,
sodium salt
Adenosine
0
149022-20-8
10
H
13
NaO
S
5 -monophosphate,
sodium salt
a
4
4
Alkaline phosphatase
Imidazole
Magnesium chloride
4.697 ꢃ 10
68.077
95.210
S
A
S
S
h.p.l.c.
288-32-4
7786-30-3
9040-59-9
C
3
H
MgCl
4
N
2
2
0
Phosphodiesterase 3 ,
0
1.714 ꢃ 10
b
5
-cyclic nucleotide
Phosphoenolpyruvate,
potassium salt
Phosphoric acid
Potassium phosphate,
dibasic
4267-07-0
C
3
H
4
KO
6
P
206.132
0.014
S
ꢂ0.992
7664-38-2
7758-11-4
H
K
3
2
PO
HPO
4
97.995
174.16
M
S
4
Pyruvic acid
127-17-3
C
3
H
4
O
3
88.062
S
The estimated mole fraction purities are exclusive of the amounts of water in the samples. The h.p.l.c. methods used in our laboratory are described in the
text (see Section 2.2).
a
Lyophilized powder; EC number 3.1.3.1.
Lyophilized powder; EC number 3.1.4.17.
b

R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
1813
mance liquid chromatography (h.p.l.c.) (u.v. detector) in an earlier study [5]; the
finding was that the mole fraction x(impurities) was <0.01. We also examined the
purity of the PEP by using an alternative h.p.l.c. method (see Section 2.2.2 below)
and in this case x(impurities) was found to be <0.005. Similarly we used two different
h.p.l.c. methods (see Section 2.2 below) to examine the purity of the cAMP: method
1
gave x(impurities) <0.007 and method 2 gave x(impurities) <0.005. The cAMP
and PEP were stored at T ꢂ 250 K until ready for use.
2
2
.2. Chromatography
.2.1. H.p.l.c. method 1
The separation of the cAMP and AMP was done with an Agilent 1100 h.p.l.c.
equipped with a u.v. detector set at the wavelength k ¼ 260 nm and an Alltech Inert-
sil ODS-2 column (4.6 mm i.d., 150 mm long) thermostatted at T ¼ 308 K. The mo-
bile phase was a gradient made from (I) {tetra butylammonium bromide
ꢁ
3
ꢁ3
(
(
concentration c ¼ 0:005 mol ꢃ dm ) + KH PO (c ¼ 20 mol ꢃ dm ), pH ¼ 3.5} and
2
4
II)
a solution that consisted of {solution (I) at the volume fraction
/
ðIÞ ¼ 0:40 + acetonitrile at / ¼ 0:60}. The following gradient of these two mobile
phases was formed: /ðIÞ ¼ 0:90 and /ðIIÞ ¼ 0:10 at time t ¼ 0; and /ðIÞ ¼ 0:20
3
ꢁ1
and /ðIIÞ ¼ 0:80 at t ¼ 25 min. The flow rate was 0.0167 cm ꢃ s . The approximate
retention times were 5.9 min and 9.3 min for AMP and cAMP, respectively. The lim-
it of detection of cAMP was found to be ꢂ6 ꢃ 10ꢁ mol ꢃ kgꢁ1.
7
2
.2.2. H.p.l.c. method 2
The separation of PEP from phosphate was done with a Dionex DX 500 Ion
Chromatograph with an ED50 conductivity detector (cell set at T ¼ 308 K; temper-
ꢁ
1
ature compensation ¼ 1.7 K ; self-regenerating suppressor current i ¼ 300 mA) and
a Dionex AS11 anion exchange separation column (4 mm i.d., 250 mm long) with an
AG11 guard column (4 mm i.d., 50 mm long). Both the column and the guard col-
umn were thermostatted in an LC25 chromatography oven at T ¼ 308 K. The mo-
ꢁ
3
bile phase consisted of (III) water and (IV) KOH in water (c ¼ 0:10 mol ꢃ dm ). The
KOH was generated by a Dionex EG-40 eluant generator cartridge. The following
step-gradient of these two mobile phases was formed: /ðIIIÞ ¼ 0:90 and
/
/
ðIVÞ ¼ 0:10 at t ¼ 0 min; /ðIIIÞ ¼ 0:90 and /ðIVÞ ¼ 0:10 at t ¼ 1:0 min;
ðIIIÞ ¼ 0:60 and /ðIVÞ ¼ 0:40 at t ¼ 10:0 min; /ðIIIÞ ¼ 0:60 and /ðIVÞ ¼ 0:40 at
t ¼ 14:0 min; /ðIIIÞ ¼ 0:10 and /ðIVÞ ¼ 0:90 at t ¼ 17:0 min; /ðIIIÞ ¼ 0:10 and
3
ꢁ1
/
ðIVÞ ¼ 0:90 at t ¼ 20:0 min. The flow rate was 0.0167 cm ꢃ s . The approximate
retention times were 7.8 min and 10.2 min for phosphate and pyrophosphate, respec-
tively. The limit of detection of PEP was found to be ꢂ2 ꢃ 10ꢁ mol ꢃ kgꢁ1.
6
2
.3. Degradation studies
Since the possibility of degradation of cAMP and PEP can affect the accuracy of
the calorimetric results, studies of the instabilities of these two substances were
performed by dissolving these two substances in the respective buffers used in the

1814
R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
calorimetric experiments and allowing these solutions to equilibrate at T ¼ 298:15 K.
The changes with time of their respective chromatographic peak areas were deter-
mined by using the h.p.l.c. methods described above. It was found that over a period
of 2 h, the mole fraction changes with time for both substances were zero within the
experimental error (ꢄ0.002 ꢃ x for cAMP and ꢄ0.005 ꢃ x for PEP).
2
.4. Extent of reaction measurements
0
Attempts were made to measure the apparent equilibrium constants K [6] of re-
actions (2) and (3). These studies used h.p.l.c methods 1 and 2, respectively. For re-
action (2), the solution used for the forward direction of reaction consisted of [cAMP
ꢁ
1
ꢁ1
(
m ¼ 0:0049 mol ꢃ kg ) in phosphate buffer {m(K
2
HPO
) ¼ 0.0138 mol ꢃ kg } + imidazole (m ¼ 5:2 ꢃ 10
4
ꢁ4
) ¼ 0.101 mol ꢃ kg
+
ꢁ
1
ꢁ1
m(H PO
3
4
mol ꢃ kg ) + MgCl
2
(
m ¼ 0:00107) at pH ¼ 7.53]. The reaction mixture used for the reverse direction of
ꢁ1
reaction consisted of [AMP (m ¼ 0:0050 mol ꢃ kg ) in phosphate buffer
ꢁ
1
ꢁ1
{
5
m(K HPO ) ¼ 0.101 mol ꢃ kg + m(H PO ) ¼ 0.0138 mol ꢃ kg } + imidazole (m ¼
ꢁ4 ꢁ1
2
2
4
3
4
.2 ꢃ 10 mol ꢃ kg ) + MgCl (m ¼ 0:00107) at pH ¼ 7.53]. The mass fraction of
0
0
phosphodiesterase 3 ,5 -cyclic nucleotide in the respective reaction mixtures was
ꢂ0.0014. The forward and reverse reactions were allowed to proceed with gentle lat-
ꢁ
1
eral shaking (ꢂ30 shakes min ) at T ¼ 298:15 K for 1 h and 4 h, respectively. For
reaction (3), the solution used for the forward direction of reaction consisted of [PEP
ꢁ
1
ꢁ1
+
(
m ¼ 0:0042 mol ꢃ kg ) in phosphate buffer {m(K HPO ) ¼ 0.102 mol ꢃ kg
2
4
ꢁ
1
m(H PO ) ¼ 0.0141 mol ꢃ kg } at pH ¼ 7.62]. The reaction mixture used for the re-
3
4
ꢁ
1
verse direction of reaction consisted of [pyruvic acid (m ¼ 0.0089 mol ꢃ kg ) in phos-
ꢁ
1
ꢁ1
phate buffer {m(K
2
HPO
4
) ¼ 0.102 mol ꢃ kg + m(H
3
PO
4
) ¼ 0.0141 mol ꢃ kg } at
pH ¼ 7.62]. The mass fraction of alkaline phosphatase in the respective reaction
ꢁ
4
mixtures was ꢂ4 ꢃ 10 . The forward and reverse reactions were allowed to proceed
ꢁ
1
with gentle lateral shaking (ꢂ30 shakes min ) at T ¼ 298:15 K for 1 h and 4 h,
respectively.
2
.5. Calorimetry
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. [7,8]. These calorimeters were calibrated
electrically by using a high stability d.c. power supply, calibrated digital voltmeter,
standard resistor, and time-interval counter. The electric potential differences U of
the thermopiles in the microcalorimeters are measured with Agilent model 34420A
Nanovolt Meters. The values of U are then recorded on a microcomputer and the
areas of the thermograms are calculated by numerical integration.
The calorimetric sample vessels were fabricated from high-density polyethylene.
3
3
Each vessel had two compartments that held, respectively, ꢂ0.55 cm and ꢂ0.40 cm
3
of solution. The substrate solutions were placed in the 0.55 cm compartment and
3
the enzyme solutions were placed in the 0.40 cm compartment. The substrate solu-
tion contained either cAMP or PEP in a phosphate buffer. In the case of cAMP, the

R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
1815
buffer also contained the cofactors MgCl
the hydrolysis reaction occur with sufficient rapidity for a precise calorimetric mea-
2
and imidazole which were needed to make
0
0
surement. The respective enzyme solutions consisted of phosphodiesterase 3 ,5 -cy-
clic nucleotide and alkaline phosphatase in the same phosphate buffer used to
prepare the substrate solution.
The vessels and their contents were allowed to thermally equilibrate in the micro-
calorimeters for ꢂ60 min before the enzyme and substrate solutions were mixed. Af-
ter mixing, ꢂ40 min was allowed for reaction (2) and ꢂ22 min for reaction (3).
Following reaction, the vessels were removed from the microcalorimeters and chro-
matographic methods 1 and 2 (see Section 2.2) were used for the analysis of the final
solutions from reactions (2) and (3), respectively. In all cases, it was found that the
ꢁ
4
mole fraction of unreacted cAMP was 65 ꢃ 10 ; small corrections to the amount of
reacted cAMP were made for incomplete reaction. In the case of reaction (3), the
chromatograms showed that, in all cases, no PEP remained. Based on the limit of
ꢁ
4
detection of PEP, the mole fraction of unreacted PEP was 67 ꢃ 10 .
‘
‘Blank’’ enthalpy changes DmixH were determined in control experiments. Thus,
for reaction (2), DmixH was )(1.0 ꢄ 0.1) mJ for the mixing of the substrate solution
with the buffer and DmixH was )(0.5 ꢄ 0.1) mJ for the mixing of the enzyme solution
with the buffer. For reaction (3), DmixH was (0.1 ꢄ 0.7) mJ for the mixing of the sub-
strate solution with the buffer and DmixH was (0.1 ꢄ 0.4) mJ for the mixing of the en-
zyme solution with the buffer. We judge the total corrections applied for the blank
enthalpy changes to be uncertain by ꢂꢄ0:2 mJ and ꢂꢄ0:8 mJ for reactions (2)
and (3), respectively. Since the measured reaction enthalpy changes were, respec-
tively, ꢂ)140 mJ and ꢂ)80 mJ for reactions (2) and (3), the uncertainties in
the blank enthalpy changes lead to uncertainties of ꢂ0:002 ꢃ D
ꢂ0:010 ꢃ D
(cal) is the calorimetrically determined molar enthalpy of reaction pertinent to
the actual experimental conditions.
r
H
m
(cal) and
r
H
m
(cal) in the final results for these two respective reactions. The quantity
D
r
H
m
2
.6. Measurement of pH
Measurement of pH was done with an Orion Model 811 pH meter and a Radiom-
eter combination glass micro-electrode at the temperature at which experiments 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 mix-
tures were calculated by using interpolation with the measured electric potential dif-
ferences and the pHs of the standard buffers.
3
. Results and discussion
3
.1. Thermodynamic formalism
The apparent equilibrium constants for reactions (2) and (3) are, respectively
0
K ¼ mðAMPÞ=mðcAMPÞ;
ð5Þ

1816
R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
0
ꢀ
K ¼ mðpyruvateÞ ꢃ mðphosphateÞ=fmðPEPÞ ꢃ m g:
ð6Þ
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 biochem-
ꢀ
ꢀ
ꢁ1
ical substances in solution. The quantity m (m ¼ 1 mol ꢃ kg ) has been used in
0
equation (6) to make K dimensionless. Following our usual practice, we have se-
lected chemical reference reactions that involved the predominant species present un-
der the experimental conditions used in our study. Thus, the selected reference
reactions that correspond to the overall biochemical reactions (2) and (3) are, respec-
tively
ꢁ
ꢁ
cAMP ðaqÞ þ H OðlÞ ¼ HAMP ðaqÞ;
ð7Þ
ð8Þ
2
3ꢁ
ꢁ
2ꢁ
4
PEP ðaqÞ þ H OðlÞ ¼ pyruvate ðaqÞ þ HPO ðaqÞ:
2
The equilibrium constants for these reference reactions are, respectively
ꢁ
ꢁ
K ¼ mðHAMP Þ=mðcAMP Þ;
ð9Þ
ꢁ
2ꢁ
3ꢁ
ꢀ
K ¼ mðpyruvate Þ ꢃ mðHPO Þ=fmðPEP Þ ꢃ m g:
In this study, the standard state for the solute is the hypothetical ideal solution of
ð10Þ
4
ꢀ
ꢁ1
unit molality (m ¼ 1 mol ꢃ kg ) and the standard state of the solvent is the pure sol-
ꢀ
vent; the standard pressure p ¼ 0:1 MPa.
3
.2. Results of experiments
The results of the extent of reaction measurements were that there were no mea-
surable amounts of either cAMP or PEP in the reaction mixtures following the
h.p.l.c. procedures described above (see Section 2.2). Based upon the lower limits
of the amounts of these substances detectable with our h.p.l.c. instruments, it is pos-
sible to set lower limits for the values of the apparent equilibrium constants. Thus for
0
3
ꢁ1
reaction (2) K > 8 ꢃ 10 (T ¼ 298:15 K, ionic strength I
m
¼ 0:32 mol ꢃ kg ,
0
pH ¼ 7.53, pMg ¼ 4.20) and for reaction (3) K > 450 (T ¼ 298:15 K, I
m
¼ 0:33
ꢁ
1
mol ꢃ kg , pH ¼ 7.62). Such values are far outside the limits of our measurement ca-
pability. However, later in this paper, we will use thermochemical cycle calculations
to establish the values of the equilibrium constants for these two reactions.
The results of the calorimetric measurements are (see tables 2 and 3): for reaction
(
ꢁ
2), the calorimetrically determined molar enthalpy of reaction D H ðcalÞ ¼
r
m
ꢁ
1
ꢁ1
ð56:32 ꢄ 0:25Þ kJ ꢃ mol at pH ¼ 7.53, I
m
¼ 0:32 mol ꢃ kg , and pMg ¼ 4.20 and
ꢁ
1
for reaction (3),
ꢁ
D
r
H
m
ðcalÞ ¼ ꢁð32:36 ꢄ 0:16Þ kJ ꢃ mol at pH ¼ 7.62 and
1
I
m
¼ 0:33 mol ꢃ kg . The uncertainties given here are equal to two estimated stan-
dard deviations of the mean. We judge that reasonable estimates of possible system-
atic error in the values of D (cal) due to
(cal) for reaction (2) are: 0:003 ꢃ D
impurities in the sample of cAMP; 0:002 ꢃ D (cal) due to possible calorimetric er-
rors; 0:001 ꢃ D H (cal) due to possible decomposition of cAMP prior to reaction; and
r
H
m
r
H
m
r
H
m
r
m
0
:0003 ꢃ D H (cal) due to a possible error in the extent of reaction. Similarly, we
r
m
judge that reasonable estimates of possible systematic error in the values of

TABLE 2
Results of the calorimetric measurements for reaction (2) {cAMP(aq) + H
1
2
O(l) ¼ AMP(aq)} in phosphate buffer at T ¼ 298:15 K, pH ¼ 7.53, a calculated ionic
strength I
m
¼ 0:32 mol ꢃ kgꢁ , and calculated pMg ¼ 4.20
3
4
3
Experiment
mðK HPO Þ
mðH PO Þ
10 ꢃ mðMgCl Þ
10 ꢃ mðImidazoleÞ
10 ꢃ mðcAMPÞ
D H ðcalÞ
2
4
3
4
2
r
m
ðmol ꢃ kgꢁ
1
Þ
ðmol ꢃ kgꢁ1Þ
ðmol ꢃ kg
ꢁ1
Þ
ðmol ꢃ kg
ꢁ1
Þ
ðmol ꢃ kg
ꢁ1
Þ
ðkJ ꢃ molꢁ1Þ
1
2
3
4
5
6
0.1001
0.1001
0.1001
0.1001
0.1001
0.1001
0.0138
0.0138
0.0138
0.0138
0.0138
0.0138
1.07
1.07
1.07
1.07
1.07
1.07
5.23
5.23
5.23
5.23
5.23
5.23
2.945
2.822
2.987
2.948
2.804
2.761
)56.10
)56.87
)56.45
)56.25
)56.08
)56.12
ðcalÞi ¼ ꢁð56:32 ꢄ 0:25Þ kJ ꢃ molꢁ
1
hD H
r m
0
0
Imidazole is C
3
H
4
N
2
and cAMP is the monosodium salt of adenosine 3 ,5 -(cyclic)phosphate (C10
H
13
N
5
NaO
7
P). The molalities m in columns 2 to 6
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
0
0
the indicated substances in their various ionic forms. The mass fraction w of the enzyme phosphodiesterase 3 ,5 -cyclic nucleotide was ꢂ0.0014. D
r
H
m
(cal) is the
calorimetrically determined molar enthalpy of reaction. The uncertainty in the average value of D H (cal) is equal to two estimated standard deviations of the
r m
mean.

1818
R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
TABLE 3
Results of the calorimetric measurements for reaction (3) {PEP(aq) + H
2
O(l) ¼ pyruvate(aq) + phos-
m
phate(aq)} in phosphate buffer at T ¼ 298:15 K, pH ¼ 7.62, and a calculated ionic strength I
¼ 0:33
mol ꢃ kgꢁ
1
3
Experiment
mðK HPO Þ
mðH PO Þ
10 ꢃ mðPEPÞ
D H ðcalÞ
2
4
3
4
r
m
ðmol ꢃ kgꢁ
1
Þ
ðmol ꢃ kgꢁ1Þ
ðmol ꢃ kg
ꢁ1
Þ
ðkJ ꢃ molꢁ1Þ
1
2
3
4
5
0.1017
0.1017
0.1017
0.1017
0.1017
0.0141
0.0141
0.0141
0.0141
0.0141
2.752
2.740
2.784
2.853
2.824
)32.68
)32.23
)32.32
)32.37
)32.22
ðcalÞi ¼ ꢁð32:36 ꢄ 0:16Þ kJ ꢃ molꢁ
1
hD H
r m
PEP is the monopotassium salt of phosphoenolpyruvate (C
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.
(cal) is the calorimetrically determined molar enthalpy of reaction. The mass fraction w of the
3 4 6
H KO P). The molalities m in columns 2 to
4
r m
D H
ꢁ4
enzyme alkaline phosphatase was ꢂ4 ꢃ 10 . The uncertainty in the average value of D
r m
H (cal) is equal to
two estimated standard deviations of the mean.
D
r
H
m
(cal) for reaction (3) are: 0:004 ꢃ D
PEP; 0:005 ꢃ D (cal) due to possible calorimetric errors; 0:003 ꢃ D
m
r
H
m
(cal) due to impurities in the sample of
(cal) due to
(cal) due to a
r
H
m
r
H
m
possible decomposition of PEP prior to reaction; and 0:0004 ꢃ D
r
H
possible error in the extent of reaction. These estimates of systematic error are com-
bined in quadrature together with the statistical uncertainties in the measured values
of D H (cal) expressed as one estimated standard deviation of the mean, to obtain
r
m
combined standard uncertainties [9]. These combined standard uncertainties were
then multiplied by two to arrive at the final results (phosphate buffer and
ꢁ
1
T ¼ 298:15 K): D
r
H
m
ðcalÞ ¼ ꢁð56:32 ꢄ 0:48Þ kJ ꢃ mol for reaction (2) at pH ¼
ꢁ1
r m
7
.53, I
m
¼ 0:32 mol ꢃ kg , and pMg ¼ 4.20 and D
H
ðcalÞ ¼ ꢁð32:36 ꢄ 0:48Þ
ꢁ
1
ꢁ1
kJ ꢃ mol for reaction (3) at pH ¼ 7.62 and I
m
¼ 0:33 mol ꢃ kg .
3
.3. Equilibrium model
ꢀ
m
þ
3
.3.1. Selected values of pK and D H for H (aq) and metal ion dissociation reactions
r
ꢀ
m
þ
The pKs and standard molar enthalpy D H changes for a variety of H (aq) and
r
metal ion dissociation reactions for the reactants and for the buffers are needed to
relate the experimental results for reactions (2) and (3) to thermodynamic quantities
for the respective reference reactions (7) and (8). The reactions for which these quan-
tities are needed are given in table 4 along with the selected values. Several of these
reactions have been included because they are pertinent to the analysis of results
from the literature. The basis of the selected values is now discussed. Where neces-
ꢀ
sary, adjustment of pK and D H values to ionic strength I ¼ 0 was done by using
r
m
m
the extended Debye–H u€ ckel equation [3] with the ‘‘ion-size’’ parameter set at
1=2
ꢁ1=2
1
.6 kg ꢃ mol
. The reaction property values for reaction (11) and (52) are based
¼ 0. The
on the values selected by Martell et al. [10] which we have adjusted to I
m

R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
1819
TABLE 4
The pKs and standard molar enthalpy changes D
metal ion dissociation reactions of substances pertinent to this study and to the analysis of results from the
ꢀ
þ
r
H
m
at T ¼ 298:15 K and I ¼ 0 for the aqueous H and
m
literature
ꢀ
Reaction
pK
r
D H
m
ðkJ ꢃ molꢁ
1
Þ
Pyruvic acid ¼ H þ pyruvateꢁ
0
þ
ð11Þ
ð12Þ
ð13Þ
ð14Þ
ð15Þ
ð16Þ
ð17Þ
ð18Þ
ð19Þ
ð20Þ
ð21Þ
ð22Þ
ð23Þ
ð24Þ
ð25Þ
ð26Þ
ð27Þ
ð28Þ
ð29Þ
ð30Þ
ð31Þ
ð32Þ
ð33Þ
ð34Þ
ð35Þ
ð36Þ
ð37Þ
ð38Þ
ð39Þ
ð40Þ
ð41Þ
2.48
12.1
ꢁ
þ
2ꢁ
a
H
2
PEP ¼ H þ HPEP
3.83
6.99
3.45
)27
2ꢁ
þ
3ꢁ
)16a
)22a
18a
HPEP ¼ H þ PEP
MgPEP ¼ Mg þ PEP3ꢁ
ꢁ
2þ
þ
ꢁ
H ꢃ cAMP ¼ H þ cAMP
ꢂ3.9
Mg ꢃ cAMPþ ¼ Mg þ cAMPꢁ
2þ
a
)21a
18.1
1.15
3.99
6.73
2.79
4.36
7.18
4.65
2.50
4.68
7.60
6.18
3.63
2.69
2.71
4.52
7.20
3.91
2.90
H
2
AMP ¼ H þ HAMPꢁ
þ
HAMP ¼ Hþ þ AMP
ꢁ
2ꢁ
)5.4
)11.3
17.6
2þ
2ꢁ
MgAMP ¼ Mg þ AMP
ꢁ
þ
2ꢁ
H
2
ADP ¼ H þ HADP
2
ꢁ
þ
3ꢁ
HADP ¼ H þ ADP
)5.6
)19.0
)12.5
15.0
MgADP ¼ Mg þ ADP3ꢁ
ꢁ
2þ
2
þ
2ꢁ
MgHADP ¼ Mg þ HADP
2
ꢁ
þ
3ꢁ
H
2
ATP ¼ H þ HATP
3
ꢁ
þ
4ꢁ
HATP ¼ H þ ATP
)6.3
)22.9
)16.9
)10.8
)12.2
)11.8a
)13.3
)3.8a
)11.1a
)8.0
3.6
MgATP ¼ Mg2þ þ ATP4ꢁ
2
ꢁ
ꢁ
2þ
3ꢁ
MgHATP ¼ Mg þ HATP
Mg ATP ¼ Mg þ MgATP
MgHPO ¼ Mg þ HPO4
MgHP O ¼ Mg þ HP
2þ
2ꢁ
2
2þ
2ꢁ
4
ꢁ
2þ
3ꢁ
2
O
7
2
7
2
7
ꢁ
2þ
4ꢁ
MgP O ¼ Mg þ P
2
O
2
7
2þ
2ꢁ
Mg P
2
2
O
7
¼ Mg þ MgP O
2
7
MgH P
2
2
O
7
¼ Mg þ þ H
PO
2
2 2
P O
2ꢁ
7
H
H
3
2
PO
4
¼ Hþ þ H
2
ꢁ
2.148
7.198
12.35
2.26
4
ꢁ
þ
2ꢁ
PO ¼ H þ HPO
4
4
2
4
ꢁ
þ
3ꢁ
HPO ¼ H þ PO4
16.0
ꢁ
¼ Hþ þ H
2ꢁ
H
3
P
2
O
2
P
2
O
)5.0
0.5
7
7
2
7
ꢁ
þ
3ꢁ
H
2
P
2
O
¼ H þ HP
2
O
6.72
7
3
7
ꢁ
þ
4ꢁ
HP
2
O
¼ H þ P
2
O
9.46
1.4
7
þ
ꢁ
H
2
CO
3
¼ H þ HCO
6.351
10.329
9.15
3
ꢁ
þ
2ꢁ
HCO3 ¼ H þ CO3
14.70

1820
R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
Table 4 (continued)
ꢀ
r
D H
m
Reaction
pK
ðkJ ꢃ molꢁ
1
Þ
þ
H
2
ꢃ GlyGlyþ ¼ H þ H ꢃ GlyGlyꢄ
ð42Þ
ð43Þ
ð44Þ
ð45Þ
ð46Þ
ð47Þ
ð48Þ
ð49Þ
ð50Þ
ð51Þ
ð52Þ
ð53Þ
ð54Þ
3.140
8.265
7.564
6.993
7.141
8.44
0.11
H ꢃ GlyGlyꢄ ¼ H þ GlyGly
þ
ꢁ
43.4
H ꢃ Hepesꢄ ¼ H þ Hepes
þ
ꢁ
20.4
þ
þ
H ꢃ Imidazole ¼ H þ Imidazole
36.64
11.2
H ꢃ PIPES ¼ H þ PIPESꢁ
ꢄ
þ
H ꢃ TAPSꢄ ¼ H þ TAPS
þ
ꢁ
40.4
þ
H
2
ꢃ Tricineþ ¼ H þ H ꢃ Tricineꢄ
2.023
8.135
7.762
8.072
3.25
5.85
H ꢃ Tricineꢄ ¼ H þ Tricineꢁ
þ
31.37
33.6
þ
þ
H ꢃ TEA ¼ H þ TEA
H ꢃ Trisþ ¼ H þ Tris
þ
47.45
)11.7
)7.3a
)20.1
MnAMP ¼ Mn þ AMP2ꢁ
2þ
2þ
2ꢁ
MnHPO
4
¼ Mn þ HPO
MgSO ¼ Mg þ SO 24 ꢁ
3.49
4
2
þ
2.26
4
See Section 3.3.1 for the basis of these values.
Estimated.
Where names and/or abbreviations have been used in this table, the chemical names and formulas of
a
b
0
these substances are: GlyGly ¼ Glycylglycine ¼ C
ethanesulfonic acid ¼ C S; Imidazole ¼ C
acid) ¼ C ; pyruvic acid ¼ C
sulfonic acid ¼ C S; Tricine ¼ N-tris(hydroxymethyl)methylglycine ¼ C
anolamine ¼ C ; and Tris ¼ 2-amino-2-hydroxymethylpropane-1,3 diol ¼ C
4
H
7
N
2
O
3
; HEPES ¼ N-(2-hydroxyethyl)piperazine-N -2-
0
8
H
17
N
2
O
4
3
H
4
N
2
; PIPES ¼ piperazine-N,N -bis(2-ethanesulfonic
8
H
17
N
2
O
6
S
2
3
H
4
O
3
; TAPS ¼ N-[tris(hydroxymethyl)methyl-3-amino]propane-
; TEA ¼ Trieth-
7
H16NO
6
6
H
12NO
5
6
H
15NO
3
4
H
11NO .
3
ꢀ
m
value of the pK for reaction (53) is also from Martell et al. [10]. The value of D H
r
ꢀ
for this reaction was obtained by using the standard molar entropy change D S for
r
m
reaction (29) together with the known pK value for reaction (53). The basis of the
values used for reactions (12) and (13) has been given previously [5]. The value of
the pK for reaction (14) is based on the result of Wold and Ballou [11] following ad-
ꢀ
justment to I
m
¼ 0. We have estimated the value of D
r
H for reaction (14) by taking
m
ꢀ
ꢀ
D
r
S for reaction (14) to be the average of the values of D
r
S for reactions (22) and
m
m
(
27). The value of the pK for reaction (15) is based on the result of Tate [12] follow-
ꢀ
ing adjustment to I ¼ 0. The value of D H for reaction (15) was estimated by tak-
m
r
m
ꢀ
ꢀ
r
m
ing D S for reaction (15) to be the same value as D S for reaction (17). The value of
r
m
the pK for reaction (16) is estimated from the result of Fan et al. [13] in which
2
þ
2þ
ꢀ
for this reaction was
Mn (aq) was used rather than Mg (aq). The value of D
r
H
m
ꢀ
obtained by using the standard molar entropy change D
with the estimated pK value for reaction (16). The values of pK and D H for reac-
tion (54) were calculated from the standard molar formation properties given by
r
S for reaction (19) together
m
ꢀ
r
m
Wagman et al. [14]. The values of the thermodynamic quantities in the remainder

R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
1821
of the table are from Alberty and Goldberg [15] {reactions (17) to (29)}, Goldberg
and Tewari [16] {reactions (30) to (33)}, and Goldberg et al. [17] {reactions (34)
to (51)}.
3
.3.2. Calculations
With the thermodynamic quantities given in table 4 it is now possible to use
ꢀ
our previously described [3,4] equilibrium model to calculate values of D H
r
m
(
T ¼ 298:15 K and I ¼ 0) for the reference reactions (7) and (8) from the exper-
m
imentally determined values of D
D
respectively. The calculated values of D
accompanying the biochemical reactions (2) and (3), are )0.947 and 0.0774, re-
r m
H
(cal). The results of these calculations are
ꢁ1
ꢀ
ꢁ1
ꢀ
r
H ¼ ꢁ47:8 kJ ꢃ mol and D
m
r
H ¼ ꢁ29:78 kJ ꢃ mol for reactions (7) and (8),
m
þ
þ
r
NðH Þ, the changes in binding of H (aq)
2þ
spectively. For reaction (2), the calculated value of D
r
NðMg Þ, the change in
þ
ꢁ4
binding of Mg (aq), is 5.6 ꢃ 10 . The ionic strengths of the reaction mixtures
and the value pMg ¼ 4.20 for reaction (2) were also calculated by using the equi-
librium model.
ꢀ
The uncertainties in the calculated values of D
r
H
for the reference reactions
m
have two components: the experimental uncertainties in the measured values of
(cal) (see Section 3.3) and possible errors in the quantities used in the equilib-
D
r
H
m
rium model. This latter component of uncertainty was examined by perturbing each
of the pertinent quantities in the model by an assumed possible error in its value.
The perturbations used for the pK values of the various species are: ꢄ0.2 for
H ꢃ cAMP(aq); ꢄ0.2 for Mg ꢃ cAMP(aq); ꢄ0.05 for H AMP(aq); ꢄ0.05 for
2
ꢁ
ꢁ
2ꢁ
HAMP (aq); ꢄ0.1 for MgAMP(aq); ꢄ0.1 for H PEP (aq); ꢄ0.1 for HPEP (aq);
2
ꢁ
ꢄ0.03 for pyruvic acid (aq); ꢄ0.003 for H
3
PO
(aq); and ꢄ0.003 for H ꢃ imidazole (aq). The
4
(aq); ꢄ0.003 for H
2
PO (aq); ꢄ0.03
4
2
4
ꢁ
þ
for HPO (aq); ꢄ0.005 for MgHPO
4
ꢀ
ꢁ1
perturbations used for the values of D
r
H /(kJ ꢃ mol ) are: ꢄ6 for H ꢃ cAMP(aq);
m
ꢁ
ꢄ8 for Mg ꢃ cAMP(aq); ꢄ2 for H
2
AMP(aq); ꢄ2 for HAMP (aq); ꢄ4 for MgAM-
ꢁ
2ꢁ
P(aq); ꢄ7 for H
2
PEP (aq); ꢄ5 for HPEP (aq); ꢄ2 for pyruvic acid(aq); ꢄ0.2 for
ꢁ
2ꢁ
4
H PO (aq); ꢄ0.2 for H PO (aq); ꢄ2 for HPO (aq); ꢄ0.4 for MgHPO (aq); and
3
4
2
4
4
þ
ꢄ0.2 for H ꢃ imidazole (aq). The ‘‘ion-size’’ parameter used in the activity coefficient
model was also perturbed by ꢄ0.3 kg ꢃ mol . The combined effects of these per-
1=2
ꢁ1=2
ꢁ
1
ꢁ1
ꢀ
turbations were ꢄ1.9 kJ ꢃ mol and ꢄ0.3 kJ ꢃ mol in the calculated values of D
r
H
m
for the reference reactions (7) and (8), respectively. In the calculation of the uncer-
ꢀ
tainty in D
value of D
r
H for reaction (7), the most significant factor was the uncertainty in the
H for the ionization of HAMP (aq) {reaction (18)}. In the calculation
m
ꢀ
ꢁ
r
m
ꢀ
of the uncertainty in D
uncertainties in the values of the pK and D H for the ionization of HPEP (aq)
r
H
for reaction (8), the most significant factors were the
ꢀ
m
2ꢁ
r
m
{
reaction (13)}. These estimated uncertainties were combined in quadrature with
ꢁ
1
the final experimental uncertainties of ꢄ0.48 kJ ꢃ mol for both reactions (2) and
ꢀ
ꢁ1
ꢀ
(
3) to obtain the final results: D
r
H ¼ ꢁð47:8 ꢄ 2:0Þ kJ ꢃ mol
and D
r
H ¼
m
m
ꢁ
1
)
(29.78 ꢄ 0.55) kJ ꢃ mol for reactions (7) and (8), respectively, at T ¼ 298:15 K
ꢀ
ꢁ1
and I
in all future discussions.
m
¼ 0. The latter value will be rounded to D
r
H ¼ ꢁð29:8 ꢄ 0:6Þ kJ ꢃ mol
m

1822
R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
3
.4. Comparisons with previous results
There have been three previous calorimetric studies of reaction (2) [18–20] and two
earlier calorimetric studies of reaction (3) [21,22]. The results of these studies are given
in table 5. The early result of Greengard et al. [18] is clearly in error and was essentially
acknowledged to be so by Gerlt et al. [20]. More importantly, there is a good agreement
of our result with that obtained by Gerlt et al. [20]. The previous studies [21,22] of re-
action (3) gave few details concerning the conditions of measurement. Indeed, George
ꢀ
ꢁ1
et al. [22] reported only the value D
r
H ¼ ꢁ25:1 kJ ꢃ mol for the reference reaction (8)
m
and gave no other details. In any case, it is likely that there is agreement between our
result and the very early result of Meyerhof and Schulz [21].
3
.5. Standard molar formation properties
A thermochemical pathway to the standard molar enthalpies of formation D H ,
ꢀ
m
f
ꢀ
standard molar Gibbs free energies of formation D G , and standard partial molar
entropies S of the cAMP(aq) and PEP(aq) species is now described. The pathway
uses measured thermodynamic quantities {K , D
transformed enthalpy change D H } for reaction (1) and for the following biochem-
f
m
ꢀ
m
0
r
m
H (cal), and the standard molar
0
ꢀ
r
m
ical reactions:
ATPðaqÞ þ pyruvateðaqÞ ¼ ADPðaqÞ þ PEPðaqÞ;
ð55Þ
ð56Þ
ATPðaqÞ þ pyruvateðaqÞ þ phosphateðaqÞ ¼
AMPðaqÞ þ PEPðaqÞ þ pyrophosphateðaqÞ:
The selected reference reactions corresponding to the above biochemical reactions
are, respectively
4
ꢁ
ꢁ
3ꢁ
7
ATP ðaqÞ ¼ cAMP ðaqÞ þ HP O ðaqÞ;
ð57Þ
ð58Þ
2
4ꢁ
ꢁ
3ꢁ
3ꢁ
þ
ATP ðaqÞ þ pyruvate ðaqÞ ¼ ADP ðaqÞ þ PEP ðaqÞ þ H ðaqÞ;
4
ꢁ
ꢁ
2ꢁ
ATP ðaqÞ þ pyruvate ðaqÞ þ HPO ðaqÞ ¼
4
2ꢁ
3ꢁ
3ꢁ
þ
AMP ðaqÞ þ PEP ðaqÞ þ HP O ðaqÞ þ H ðaqÞ:
ð59Þ
2
7
0
Using the equilibrium model [3,4] with the experimental results {K and
ꢀ
D H (cal)} for reactions (1), (55), and (56) and with the pK and D H values given
r
m
r
m
ꢀ
ꢀ
in table 4, we have calculated values of D
r
H , K, and D G for the reference reactions
r
m
m
(
57) to (59). The results of these calculations are given in table 6. Auxiliary property
ꢀ
ꢀ
ꢀ
values (D
f
H , D G , and S ) are also needed for several additional species in order to
f
m
m m
calculate the formation properties. The sources of these values are: Cox et al. [36] for
H O(l), HPO (aq), and Mg (aq); Tewari and Goldberg [37] for pyruvate (aq);
2
2
4
ꢁ 2þ ꢁ
3
7
ꢁ
Goldberg and Tewari [16] for HP
ꢁ
2
O (aq), and Boerio-Goates et al. [38] for
4ꢁ
2ꢁ
3ꢁ
AMP (aq), HAMP (aq), ADP (aq), and ATP (aq). The results of the calcula-
tions (see table 7) that follow pertain to T ¼ 298:15 K and I ¼ 0.
m

TABLE 5
ꢀ
for the reference reactions (7)
m
Calorimetric results from the literature leading to values (column 8) of the standard molar enthalpy changes D
r
H
ꢁ
ꢁ
3ꢁ
ꢁ
2ꢁ
{
cAMP (aq) + H
¼ 0
Investigators
2
O(l) ¼ HAMP (aq)} and (8) {PEP (aq) + H
2
O(l) ¼ pyruvate (aq) + HPO (aq)} at the temperature T ¼ 298:15 K and the ionic strength
4
I
m
ꢀ
T/K
Buffer
pH
pMg
Im
D H ðcalÞ
D H
r
m
r
m
ðmol ꢃ kgꢁ
1
Þ
ðkJ ꢃ molꢁ1Þ
ðkJ ꢃ molꢁ1
Þ
Biochemical reaction (2): cAMP(aq) + H
ꢁ
2
O(l) ¼ AMP(aq)
ꢁ
Reference reaction (7): cAMP (aq) + H
2
O(l) ¼ HAMP (aq)
a
Greengard et al. (1969) [18]
b
298.15
298.15
298.15
298.15
phosphate
phosphate
phosphate
phosphate
7.3
7.8
7.3
7.53
3.89
b
0.10
0.15
0.10
0.32
)(63.0 ꢄ 1.4)
)(61.1 ꢄ 1.0)
)(54.8 ꢄ 0.6)
)(56.3 ꢄ 0.5)
)55.1
)52.4
)46.9
)(47.8 ꢄ 2.0)
Cheung et al. (1974) [19]
a
Gerlt et al. (1975) [20]
This study
3.89
4.20
Biochemical reaction (3): PEP(aq) + H
3
2
O(l) ¼ pyruvate(aq) + phosphate(aq)}
ꢁ
ꢁ
2ꢁ
Reference reaction (8): {PEP (aq) + H
2
O(l) ¼ pyruvate (aq) + HPO (aq)}
4
c
Meyerhof and Schulz (1935) [21] 293.15
d
phosphate
?
phosphate
?
?
?
)35.4
?
ꢂ)31
George et al. (1970) [22]
This study
298.15
298.15
?
7.62
?
e
?
0.33
)25.1
)(32.4 ꢄ 0.5)
)(29.8 ꢄ 0.6)
The calculated values of pMg and the ionic strength I
m
are given in columns 5 and 6, respectively; the values of the calorimetrically determined molar
enthalpy of reaction D (cal) corresponding to the overall biochemical reactions (2) and (3) are given in column 7. The basis of the uncertainties of our
r
H
m
results is given in the text (see Section 3). The uncertainties given for the results of the remaining investigations reflect only the statistical uncertainties based on
two estimated standard deviations of the mean.
a
0ꢀ
for reaction (2). The values of
Both Greengard et al. [18] and Gerlt et al. [20] reported values of the standard molar transformed enthalpy change D
r
H
and their reported values of the buffer protonation corrections.
m
0
ꢀ
D
r
H
m
(cal) given above were obtained by using both their [18,20] reported values of D
Cheung et al. [19] in their table 5 give values for the ‘‘enthalpy of hydrolysis of cAMP.’’ These values, however, were obtained ‘‘after correction for
r
H
m
b
ꢁ1
protonation of the phosphate buffer.’’ The value D
r
H
cAMP(aq) that were hydrolyzed. They [19] also used Mn (aq) as a cofactor. The calculated value of pMn for their experiments is 5.7.
m
(cal) ¼ )61.1 kJ ꢃ mol was obtained from their [19] reported enthalpies of reaction and the amounts of
2
þ
c
ꢀ
In the calculation of D
r
H
from Meyerhof and SchulzÕs [21] reported value of D
r
H
m
(cal), the following conditions were assumed: pH ¼ 7.0;
m
ꢁ1
ꢁ1
m(MgCl
d
2
) ¼ 0.001 mol ꢃ kg ; I
m
¼ 0:25 mol ꢃ kg . No correction was made to adjust the result to T ¼ 298:15 K.
ꢀ
George et al. [22] reported only the value of D
Magnesium was not used in these experiments.
r
H
at T ¼ 298:15 K and I ¼ 0. No other details were given.
m
e

TABLE 6
ꢀ
ꢀ
for the reference reactions
m
Values of the standard molar enthalpy change D
r
H , equilibrium constant K, and standard molar Gibbs free energy change D
r
G
m
(
57) to (59) at the temperature T ¼ 298:15 K and the ionic strength I
m
¼ 0
pMg
ꢀ
ꢀ
Investigators
T/K
Buffer
pH
Im
r
D H
K
r
D G
m
m
ðmol ꢃ kgꢁ
1
Þ
ðkJ ꢃ molꢁ1
Þ
ðkJ ꢃ molꢁ1
Þ
Biochemical reaction (1): ATP(aq) ¼ cAMP(aq) + pyrophosphate(aq)
4
ꢁ
ꢁ
3ꢁ
O
7
Reference reaction (57): ATP (aq) ¼ cAMP (aq) + HP
2
(aq)
Hayaishi et al. (1971)
a
298.15
Tris
7.3
2.80
0.11
0.47
1.87
[
23]
Takai et al. (1971) [24]a;b 306.15
Tris
HEPES
7.3
6.2 to 7.7
2.91 0.058
3.64 to 4.44 0.057 to 0.098 29.0
1.1
0.81 ꢄ 0.09
)0.23
0.52 ꢄ 0.25
Kurashina et al. (1974)
25]a;c
298.15
[
Biochemical reaction (55): ATP(aq) + pyruvate(aq) ¼ ADP(aq) + PEP(aq)
4
ꢁ
ꢁ
3ꢁ
3ꢁ
þ
Reference reaction (58): ATP (aq) + pyruvate (aq) ¼ ADP (aq) + PEP (aq) + H (aq)
10
Meyerhof and Oesper
d ;e
303.15
ꢂ7.6
ꢂ3 ꢃ 10ꢁ
ꢂ54.7
(
1949) [26]
Krimsky (1959) [27]e
McQuate and Utter
303.15
303.15
Tris
Tris
7.72 to 8.70 4.95
7.4 to 9.0
0.25
0.26
(6.3 ꢄ 1.7) ꢃ 10
(5.6 ꢄ 1.7) ꢃ 10
ꢁ12
12
63.9 ꢄ 0.7
64.2 ꢄ 0.7
ꢁ
4.43
(
1959) [28]e
Rao et al. (1979) [29]e
Cheer et al. (1980) [30]
288.15
298.15
HEPES
HEPES,
TEA, Tris
HEPES,
TAPS,
8.0
4.38
0.40
0.093 to 0.24 6.6
3.4 ꢃ 10ꢁ12
65.4
f
8.00 to 8.54 5.12
8.5 2.07
Redman-Furey (1982)
g
298.15
0.11 to 0.13
11.4
[
31]
glycylglycine,
Tris

Biochemical reaction (56): ATP(aq) + pyruvate(aq) + phosphate(aq) ¼ AMP(aq) + PEP(aq) + pyrophosphate(aq)
4
ꢁ
ꢁ
2ꢁ
2ꢁ
3ꢁ
3ꢁ
þ
Reference reaction (59): ATP (aq) + pyruvate (aq) + HPO (aq) ¼ AMP (aq) + PEP (aq) + HP
2
O
(aq) + H (aq)
63.3
4
7
12
Hatch and Slack (1968)
h
303.15
Tris
8.3
2.37
0.042
8.6 ꢃ 10ꢁ
[32]
Reeves et al. (1968) [33]
10
298.15
imidazole and 6.51 to 8.39 1.9 to 6.1
Tris
0.081 to 0.16
0.077
(4.7 ꢄ 3.0) ꢃ 10ꢁ
53.2 ꢄ 1.6
5.1 ꢃ 10ꢁ
10
53.1
Sugiyama (1973) [34]
298.15
Tris
7.24
4.99
ꢀ
ꢀ
The values of D
r
H , K, and D
r
G
(columns 7, 8, and 9, respectively) were calculated (see Section 3.5) from the reported values of the apparent equilibrium
(cal), and, in one case [25], values of the standard molar transformed enthalpy
m
m
0
constants K , calorimetrically determined molar enthalpies of reaction D
H for the (overall) biochemical reactions that correspond to the chemical reference reactions. The values of pMg and I were calculated by using
the equilibrium model and the reported solution compositions. The uncertainties reflect only the statistical uncertainties based on two estimated standard
r
H
m
0
ꢀ
change D
r
m
m
deviations of the mean.
a
The three equilibrium studies for reaction (1) cited here were carried out by Hayaishi et al. [23–25]. The final study [25], which was carried out in 1974, is
assumed to be the most definitive.
b
ꢀ
ꢁ1
0
A value of D
r
H
¼ 29:0 kJ ꢃ mol for reaction (57) at T ¼ 298:15 K and I ¼ 0 was used to adjust the result to T ¼ 298:15 K.
m
c
Kurashina et al. [25] measured K as a function of temperature at two different pHs (7.0 and 7.30) and reported the results in terms of a small graph which
0
ꢀ
that they calculated from these results. The value
does not allow an accurate recovery of the original values. However, they [25] did report the values of D
r
H
m
ꢀ
0
ꢀ
of D H given in column 7 for reaction (57) was calculated from their reported values of D H .
r
r
d
Burton and Krebs [35], based on a personal communication from Meyerhof, give a pH of ꢂ7.6 for this study. The buffer, pMg, and I
m
are not known.
e
f
ꢀ
ꢁ1
A value of D
r
H
¼ 9:3 kJ ꢃ mol for reaction (58) at T ¼ 298:15 K and I ¼ 0 was used to adjust the result to T ¼ 298:15 K.
m
Cheer et al. [30] used Hepes, triethanolamine (TEA), and Tris buffers in their study. Use of their [30] reported values of D
r
H
m
(cal) and our equilibrium
ꢀ
ꢁ1
model (see Section 3.3) leads to the following values for D
r
H /(kJ ꢃ mol ) obtained with the various buffers: Hepes, 5.6; TEA, 6.1; and Tris, 8.2
3
. These values
m
ꢁ1
ꢀ
ꢀ
¼ 6:6 kJ ꢃ molꢁ1 for the reference reaction (58) is given
are within ꢂ1 kJ ꢃ mol of the values of D
r
H
calculated by Cheer et al. [30]. The average value D
r
H
m
m
above.
g
ꢀ
ꢁ1
Use of Redman-FureyÕs [31] reported values of D
r
H
buffers she used: glycylglycine, 15.6; TAPS, 11.7; Tricine, 11.9; and Tris, 10.7. We have discarded the result obtained with glycylglycine buffer and, in this table,
m
(cal) and our equilibrium model leads to the following values for D
r
H /(kJ ꢃ mol ) with the various
m
ꢀ
ꢁ1
give the average of the remaining values, D
r
H
¼ 11:4 kJ ꢃ mol for the reference reaction (58) at T ¼ 298:15 K and I
m
¼ 0.
m
h
ꢀ
ꢁ1
A value of D
r
H
¼ 4:6 kJ ꢃ mol for reaction (59) at T ¼ 298:15 K and I ¼ 0 was used to adjust the result to T ¼ 298:15 K.
m

1826
R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
TABLE 7
ꢀ
ꢀ
m
Standard molar enthalpies of formation D
standard partial molar entropies S for the adenosine 3 ,5 -(cyclic)phosphate (cAMP) and phosphoenolpy-
f
H , standard molar Gibbs free energies of formation D
f
G , and
m
ꢀ
0
0
m
ruvate (PEP) aqueous species at T ¼ 298:15 K and I
m
¼ 0
D G
ꢀ
ꢀ
ꢀ
S
Species
Empirical formula
f
D H
Reference
m
f
m
m
ðkJ ꢃ molꢁ
1
Þ
ðkJ ꢃ molꢁ1
Þ
ðJ ꢃ Kꢁ1 ꢃ molꢁ1
304.5
Þ
a
a
H ꢃ cAMP
C
C
C
C
C
C
C
10
10
10
H
H
H
4
12
11
N
N
5
5
O
O
6
P
P
1314.3
)1296.3
)816.0
)793.7
)1255.7
This study
This study
This study
This study
This study
This study
This study
ꢁ
ꢁ
cAMP
Mg ꢃ cAMP
6
290.2
245.6a
325.6a
161.8a
)25.7
þ
ꢁ
a
a
11MgN
5
O
6
P
)1724.3
ꢁ
ꢁ
ꢁ
2ꢁ
3ꢁ
a
H
HPEP
2
PEP
3
3
3
3
H
O
6
O
6
O
6
P
P
P
)1534.4
)1333.1
)1311.3
)1271.4
)1746.5
2
a
H
3
2
2
)1561.4
3
ꢁ
PEP
MgPEP
H
H
)1577.4
)2022.4
ꢁ
ꢁ
a
a
MgO
6
P
)22.9
Auxiliary property values
H
HPO
2
O(l)
ꢁ
H
2
O
)285.83
)1299.0
)2294.87
)594.0
)1635.37
)1629.97
)2626.54
)3619.21
)467.00
)237.14
)1096.0
)1973.86
)473.6
)1040.45
)1078.86
)1906.13
)2768.10
)455.4
69.95
)33.5
)15.2
183
[36]
[36]
[16]
[37]
[38]
[38]
[38]
[38]
[36]
2
4
2ꢁ
4
HPO
3
7
ꢁ
3ꢁ
HP
2
O
2
HP O
7
ꢁ
ꢁ
pyruvate
AMP
HAMP
C
C
C
C
C
3
H
3
O
3
2ꢁ
2ꢁ
10
10
10
10
H
12
13
12
12
N
N
N
N
5
5
5
5
O
O
O
O
7
P
214.5
361.4
207.4
182.8
)137.0
ꢁ
ꢁ
H
H
H
7
P
3
ꢁ
ꢁ
3ꢁ
P
2
4ꢁ
P
3
ADP
ATP
10
13
4
2
þ
2þ
Mg
Mg
The auxiliary values used to calculate the formation properties of the cAMP and PEP species are also
0
0
given. Abbreviations are: AMP, adenosine 5 -monophosphate; ADP, adenosine 5 -diphosphate; and ATP,
0
adenosine 5 -triphosphate. The standard state is the hypothetical ideal solution of unit molality.
a
This value is based, in part, on an estimate.
ꢀ
ꢁ1
Our result, D
r
H ¼ ꢁ47:8 kJ ꢃ mol for reaction (7), is used in conjunction
m
ꢀ
ꢁ
ꢀ
with the values of D
f
H
for H
ꢁ
2
O(l) and for HAMP (aq) to calculate D
f
H ¼
m
m
ꢁ
1
ꢁ
1296:34 kJ ꢃ mol for cAMP (aq). Use of this value together with the values of
ꢀ
4ꢁ
3ꢁ
ꢀ
ꢁ1
D
f
H
for ATP (aq) and for HP
2
O (aq) leads to D
r
H ¼ 28:0 kJ ꢃ mol for reac-
m
7
m
ꢀ
m
ꢁ1
tion (57). This result is in excellent agreement with the value D H ¼ 29:0 kJ ꢃ mol
r
obtained from the study of Kurashina et al. [25] in which the temperature depen-
0
dence of K for reaction (1) was measured. Similarly, we use the value
ꢀ
ꢁ1
D
r
G ¼ 0:52 kJ ꢃ mol for reaction (57), which we calculated from the results of
m
ꢀ
4ꢁ
Kurashina et al. [25], together with the values of D
f
G
for ATP (aq) and for
ꢁ
m
3
7
ꢁ
ꢀ
ꢁ1
HP
2
O (aq) to calculate D
f
G ¼ ꢁ793:72 kJ ꢃ mol for cAMP (aq). The standard
m
ꢀ
ꢁ1
ꢁ1
ꢁ
partial molar entropy S ¼ 290:2 J ꢃ K ꢃ mol of cAMP (aq) is calculated by using
m
ꢀ
ꢀ
ꢀ
the values of D
r
H
ATP (aq) and for HP O (aq). As a first approximation, one could estimate
and D G for reaction (57) together with the values of S for
m m
r
m
4ꢁ
3ꢁ
2
7
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ1
ꢁ1
S {cAMP (aq)} ꢂ ðS {HAMP (aq)} ) S {H O(l)} ¼ 291 J ꢃ K ꢃ mol . The excel-
m
m
m
2
ꢀ
lent accord of the experimental result for S with this estimate combined with the
m
ꢀ
excellent agreement in the values of D
to the values of the standard molar formation properties of cAMP (aq) given in
table 7 and in the standard reaction quantities for reaction (57).
r
H
for reaction (57) lends some confidence
ꢁ
m
ꢀ
ꢁ1
3ꢁ
The value D
f
H ¼ ꢁ1577:37 kJ ꢃ mol for PEP (aq) is calculated by using our
m
ꢀ
ꢁ1
ꢀ
for
result D
r
H ¼ ꢁ29:8 kJ ꢃ mol for reaction (8) together the values of D
f
H
m
m

TABLE 8
ꢀ
ꢀ
m
Values of standard molar enthalpy changes D
for the several reference reactions considered herein
r
H , equilibrium constants K, and standard molar Gibbs free energy changes D
r
G
at T ¼ 298:15 K and I ¼ 0
m
m
ꢀ
ꢀ
r
D G
m
ꢀ
DrS
m
Reaction
r
D H
K
m
ðkJ ꢃ molꢁ
)47.8
1
Þ
ðkJ ꢃ molꢁ1
)48.0
Þ
ðJ ꢃ K ꢃ molꢁ1
Þ
1.3
ꢁ
ꢁ
cAMP ðaqÞ þ H
2
OðlÞ ¼ HAMP ðaqÞ
ð7Þ
ð8Þ
ð57Þ
ð58Þ
2.6 ꢃ 10
5.0 ꢃ 10
8
3
ꢁ
ꢁ
2ꢁ
10
PEP ðaqÞ þ H
2
OðlÞ ¼ pyruvate ðaqÞ þ HPO ðaqÞ
)29.8
)61.1
105.3
4
4
ꢁ
ꢁ
3ꢁ
ATP ðaqÞ ¼ cAMP ðaqÞ þ HP
2
O
ðaqÞ;
28.0
9.3
0.81
0.52
64.2
92.2
7
4
ꢁ
ꢁ
3ꢁ
5.7 ꢃ 10ꢁ12
ATP ðaqÞ þ pyruvate ðaqÞ ¼ ADP ðaqÞ þ
)184.1
3ꢁ
þ
PEP ðaqÞ þ H ðaqÞ;
ATP ðaqÞ þ pyruvate ðaqÞ þ HPO ðaqÞ ¼ AMP2ꢁðaqÞ þ
4
ꢁ
ꢁ
2ꢁ
ð58Þ
7.7 ꢃ 10ꢁ10
4.6
52.0
)158.7
4
3ꢁ
3ꢁ
þ
PEP ðaqÞ þ HP
2
O
ðaqÞ þ H ðaqÞ:
7
The standard state is the hypothetical ideal solution of unit molality.

1828
R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
ꢁ
2ꢁ
ꢀ
pyruvate (aq), HPO (aq), and H
2
O(l) given in table 7. Use of this value of D H for
f
4
m
3ꢁ
ꢀ
4ꢁ
3ꢁ
PEP (aq) together with the values of D
vate (aq) from table 7 leads to D
is in satisfactory agreement with the values (see table 6) of D
f
H
for ATP (aq), ADP (aq), and pyru-
m
ꢁ
ꢀ
ꢁ1
r
H ¼ 9.3 kJ ꢃ mol for reaction (58). This value
m
ꢀ
r
H
m
that range from
ꢁ
1
ꢁ1
6
.6 kJ ꢃ mol to 11.4 kJ ꢃ mol that we calculated from the calorimetric results of
Cheer et al. [30] and Redman-Furey [31]. The two routes to the formation properties
3
ꢁ
ꢀ
m
of PEP (aq) use values of D G (see table 6) for reactions (58) and (59) together
r
ꢀ
4ꢁ
3ꢁ
ꢁ
2ꢁ
with values of D G for ATP (aq), ADP (aq), pyruvate (aq), AMP (aq),
f
m
3
7
ꢁ
2ꢁ
ꢀ
HP
6
2
O (aq), and HPO (aq). For reaction (58), we adopt the value D
r
G ¼
4
m
ꢁ
1
4:2 kJ ꢃ mol based primarily on the study of McQuate and Utter [28]; this result
ꢀ
ꢁ1
3ꢁ
leads to D
the value D
f
G ¼ ꢁ1271:4 kJ ꢃ mol for PEP (aq). For reaction (59), we adopt
m
ꢀ
ꢁ1
r
G ¼ 53:2 kJ ꢃ mol based on the studies of Reeves et al. [33] and of
m
ꢀ
ꢁ1
3ꢁ
Sugiyama [34]; this result leads to D
ering the uncertainties of the several values that entered into the calculations, this is
judged to be a satisfactory agreement. Since reaction (58) appears to have been stud-
f
G ¼ ꢁ1270:2 kJ ꢃ mol for PEP (aq). Consid-
m
ied more thoroughly than reaction (59) and also because it relies on fewer auxiliary
ꢀ
values of D
f
G , the route that uses reaction (58) is preferred and we adopt the value
m
ꢀ
ꢁ1
3ꢁ
D
cAMP and PEP species (see table 7) are calculated from the values just obtained to-
f
G ¼ ꢁ1271:4 kJ ꢃ mol for PEP (aq). The remaining property values for the
m
ꢀ
gether with the auxiliary values given in table 7 and the appropriate pK and D H
values from table 4. The property values given in table 7 are now used to calculate
a set of ‘‘best’’ values of D H , K, D G , and D S for the five reference reactions
r
m
ꢀ
ꢀ
ꢀ
r
m
r
m
r
m
considered herein. These values are given in table 8.
3
.6. Apparent equilibrium constants under approximately physiological conditions
It is important to appreciate that the results given in tables 4, 7, and 8 provide the
0
essential property values needed to calculate K and the position of equilibrium of the
TABLE 9
Values of the apparent equilibrium constants K and standard molar transformed Gibbs free energy
0
0
ꢀ
¼ 0:25 mol ꢃ kgꢁ1 for the several
changes D
r
G
at T ¼ 311:15 K, pH ¼ 7.0, pMg ¼ 3.0, and I
m
¼ 0 and I
m
m
overall biochemical reactions considered herein
Reaction
0
ꢀ
m
Im
K
r
D G
ðmol ꢃ kgꢁ
1
Þ
ðkJ ꢃ molꢁ1
3.45
Þ
ATP(aq) ¼ cAMP(aq) + pyrophosphate(aq)
(1)
0
0
0
0
0
0.26
0.17
.25
.25
4.55
7
7
1
9
cAMP(aq) + H
2
O(l) ¼ AMP(aq)
(2)
5.2 ꢃ 10
8.6 ꢃ 10
1.5 ꢃ 10
8.9 ꢃ 10
7.7 ꢃ 10
1.6 ꢃ 10
4.7 ꢃ 10
1.2 ꢃ 10
)46.0
)47.3
)60.6
)59.3
30.5
0
PEP(aq) + H
phosphate(aq)
2
O(l) ¼ pyruvate(aq) +
(3)
0.25
0
ꢁ
ꢁ
ꢁ
ꢁ
6
5
4
3
ATP(aq) + pyruvate(aq) ¼
ADP(aq) + PEP(aq)
(55)
(56)
0.25
0
28.5
19.8
ATP(aq) + pyruvate(aq) +
phosphate(aq) ¼ AMP(aq) + PEP(aq) +
pyrophosphate(aq)
0.25
17.4

R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
1829
several biochemical reactions considered herein as a function of temperature, pH,
pMg, and ionic strength. These calculations can be performed either by using a
chemical equilibrium model [3,4] or by using the standard molar formation proper-
ties [15]. Of particular interest are the values of the apparent equilibrium constants
under approximately physiological conditions which are taken to be [39] T ¼ 311:15
ꢁ
1
K, pH ¼ 7.0, pMg ¼ 3.0, and I ¼ 0:25 mol ꢃ kg . By using the equilibrium model
m
with the property values given in tables 4 and 8, we have calculated the values of
0
0ꢀ
K and of the standard molar transformed Gibbs free energy change D G under
r
m
these conditions for the five overall biochemical reactions considered herein. These
values are given in table 9.
Acknowledgements
We thank Dr. Prasad Reddy (National Institute of Standards and Technology) for
helpful discussions regarding the biochemistry of the reaction that forms adenosine
0
0
3
,5 -(cyclic)phosphate from ATP.
References
[
[
[
[
[
1] D. Voet, J.G. Voet, Biochemistry, John Wiley & Sons, New York, 1990.
2] A.L. Lehninger, Biochemistry, second ed., Worth Publishers, New York, 1975.
3] R.N. Goldberg, Y.B. Tewari, Biophys. Chem. 40 (1991) 241–261.
4] D.L. Akers, R.N. Goldberg, Math. J. 8 (2001) 86–113.
5] Y.B. Tewari, N. Kishore, R. Bauerle, W.R. LaCourse, R.N. Goldberg, J. Chem. Thermodyn. 33
(2001) 1791–1805.
[
[
[
6] R.A. Alberty, A. Cornish-Bowden, Q.H. Gibson, R.N. Goldberg, G. Hammes, W. Jencks, K.F.
Tipton, R. Veech, H.V. Westerhoff, E.C. Webb, Pure Appl. Chem. 66 (1994) 1641–1666.
7] D.K. Steckler, R.N. Goldberg, Y.B. Tewari, T.J. Buckley, J. Res. Natl. Bur. Stand. (US) 91 (1986)
113–121.
8] D.K. Steckler, R.N. Goldberg, Y.B. Tewari, T.J. Buckley, Computer Software for the Acquisition
and Treatment of Calorimetric Data, Natl. Bur. Stand. (US) Tech. Note 1224, US Government
Printing Office, Washington, DC, 1986.
[
9] B.N. Taylor, C.E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST
Measurement Results, NIST Technical Note 1297, US Government Printing Office, Washington, DC,
1994.
[
10] A.E. Martell, R.M. Smith, R.J. Motekaitis, NIST critically selected stability constants of metal
complexes database, NIST Standard Reference Database 46, Version 6.0, National Institute of
Standards and Technology, Gaithersburg, MD, 2001.
[
[
[
[
11] F. Wold, C.E. Ballou, J. Biol. Chem. 227 (1957) 301–312.
12] M.E. Tate, Biochem. J. 195 (1981) 419–426.
13] S. Fan, A.C. Storer, G.G. Hammes, J. Am. Chem. Soc. 99 (1977) 8293–8298.
14] D.D. Wagman, W.H. Evans, V.B. Parker, R.H. Schumm, I. Halow, S.M. Bailey, K.L. Churney, R.L.
Nuttall, J. Phys. Chem. Ref. Data 11 (Suppl 2) (1982).
[
[
[
[
15] R.A. Alberty, R.N. Goldberg, Biochemistry 31 (1992) 10610–10615.
16] R.N. Goldberg, Y.B. Tewari, J. Chem. Thermodyn. 34 (2002) 821–839.
17] R.N. Goldberg, N. Kishore, R.M. Lennen, J. Phys. Chem. Ref. Data 31 (2002) 231–370.
18] P. Greengard, S.A. Rudolph, J.M. Sturtevant, J. Biol. Chem. 244 (1969) 4798–4800.

1830
R.N. Goldberg, Y.B. Tewari / J. Chem. Thermodynamics 35 (2003) 1809–1830
[
[
[
[
19] W.Y. Cheung, S.M. Patrick, S.N. Pennington, Int. J. Biochem. 5 (1974) 311–319.
20] J.A. Gerlt, F.H. Westheimer, J.M. Sturtevant, J. Biol. Chem. 250 (1975) 5059–5067.
21] O. Meyerhof, W. Schulz, Biochem. Z. 281 (1935) 292–305.
22] P. George, R.J. Witonsky, M. Trachtman, C. Wu, W. Dowart, L. Richman, W. Richman, F.
Shurayh, B. Lentz, Biochim. Biophys. Acta 226 (1970) 1–15.
[
[
23] O. Hayaishi, P. Greengard, S.P. Colowick, J. Biol. Chem. 246 (1971) 5840–5843.
24] K. Takai, Y. Kurashina, C. Suzuki, H. Okamoto, A. Ueki, O. Hayaishi, J. Biol. Chem. 246 (1971)
5
843–5845.
25] Y. Kurashina, K. Takai, C. Suzuki-Hori, H. Okamoto, O. Hayaishi, J. Biol. Chem. 249 (1974) 4824–
828.
[
4
[
[
[
[
[
[
26] O. Meyerhof, P. Oesper, J. Biol. Chem. 179 (1949) 1371–1385.
27] I. Krimsky, J. Biol. Chem. 234 (1959) 232–236.
28] J.T. McQuate, M.F. Utter, J. Biol. Chem. 234 (1959) 2151–2157.
29] B.D.N. Rao, F.J. Kayne, M. Cohn, J. Biol. Chem. 254 (1979) 2689–2696.
30] R.L. Cheer, G.R. Hedwig, I.D. Watson, Biophys. Chem. 12 (1980) 73–82.
31] N.L. Redman-Furey, Biochemical Thermodynamics and Analytical Enthalpimetry, Thesis, Pennsyl-
vania State University, 1982.
[
[
[
[
[
32] M.D. Hatch, C.R. Slack, Biochem. J. 106 (1968) 141–146.
33] R.E. Reeves, R.A. Menzies, D.S. Hsu, J. Biol. Chem. 243 (1968) 5486–5491.
34] T. Sugiyama, Biochemistry 12 (1973) 2862–2868.
35] K. Burton, H.A. Krebs, Biochem. J. 54 (1953) 94–105.
36] J.D. Cox, D.D. Wagman, V.A. Medvedev, CODATA Key Values for Thermodynamics, Hemisphere,
New York, 1989.
[
[
37] Y.B. Tewari, R.N. Goldberg, J. Solution Chem. 23 (1994) 167–184.
38] J.A. Boerio-Goates, M.R. Francis, R.N. Goldberg, M.A.V. Ribeiro da Silva, M.D.M.C. Ribeiro da
Silva, Y.B. Tewari, J. Chem. Thermodyn. 33 (2001) 929–947.
[
39] D. Veloso, R.W. Guynn, M. Oskarsson, R.L. Veech, J. Biol. Chem. 248 (2003) 4811–4819.
JCT 03-086