Energetic effects of magnesium in the recognition of adenosine nucleotides by the F1-ATPase β subunit

Article abstract of DOI:10.1021/bi1006767

Nucleotide-induced conformational changes of the catalytic β subunits play a crucial role in the rotary mechanism of F₁-ATPase. To gain insights into the energetic bases that govern the recognition of nucleotides by the isolated β subunit from thermophilic Bacillus PS3 (Tβ), the binding of this monomer to Mg(II)-free and Mg(II)-bound adenosine nucleotides was characterized using high-precision isothermal titration calorimetry. The interactions of Mg(II) with free ATP or ADP were also measured calorimetrically. A model that considers simultaneously the interactions of Tβ with Mg·ATP or with ATP and in which ATP is able to bind two Mg(II) atoms sequentially was used to determine the formation parameters of the Tβ-Mg·ATP complex from calorimetric data. This analysis yielded significantly different ΔH_b and ΔS_b values in relation to those obtained using a single-binding site model, while ΔG_b was almost unchanged. Published calorimetric data for the titration of Tβ with Mg·ADP [Perez-Hernandez, G., et al. (2002) Arch. Biochem. Biophys. 408, 177-183] were reanalyzed with the ternary model to determine the corresponding true binding parameters. Interactions of Tβ with Mg·ATP, ATP, Mg·ADP, or ADP were enthalpically driven. Larger differences in thermodynamic properties were observed between Tβ-Mg·ATP and Tβ-ATP complexes than between Tβ-Mg·ADP and Tβ-ADP complexes or between Tβ-Mg·ATP and Tβ-Mg·ADP complexes. These binding data, in conjunction with those for the association of Mg(II) with free nucleotides, allowed for a determination of the energetic effects of the metal ion on the recognition of adenosine nucleotides by Tβ [i.e., Tβ·AT(D)P + Mg(II) ? Tβ·AT(D)P-Mg]. Because of a more favorable binding enthalpy, Mg(II) is recognized more avidly by the Tβ·ATP complex, indicating better stereochemical complementarity than in the Tβ·ADP complex. Furthermore, a structural-energetic analysis suggests that Tβ adopts a more closed conformation when it is bound to Mg·ATP than to ATP or Mg·ADP, in agreement with recently published NMR data [Yagi, H., et al. (2009) J. Biol. Chem. 284, 2374-2382]. Using published binding data, a similar analysis of Mg(II) energetic effects was performed for the free energy change of F₁ catalytic sites, in the framework of bi- or tri-site binding models.

Full text of DOI:10.1021/bi1006767

5258 Biochemistry 2010, 49, 5258–5268
DOI: 10.1021/bi1006767
Energetic Effects of Magnesium in the Recognition of Adenosine Nucleotides
by the F1-ATPase β Subunit†
‡
‡
§
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ~
Nancy O. Pulido, Guillermo Salcedo, Ge^rardo Perez-Hernandez, Concepcion Jose-Nunez,
,‡
ꢀ
ꢀ
ꢀ
Adrian Velazquez-Campoy, and Enrique Garcıa-Hernandez*
´
‡
§
Instituto de Quımica, and Instituto de Fisiologıa Celular, Universidad Nacional Autonoma de Mexico, Circuito Exterior,
´
´
ꢀ
ꢀ
Ciudad Universitaria, Mexico 04510, D.F., Mexico, Departamento de Ciencias Naturales, Universidad Autonoma
ꢀ
Metropolitana-Cuajimalpa, Pedro Antonio de los Santos 84, San Miguel Chapultepec, Miguel Hidalgo, Mexico 11850,
ꢀ
ꢀ
Mexico, and ^Institute of Biocomputation and Physics of Complex Systems (BIFI), Universidad de Zaragoza, Zaragoza,
ꢀ
ꢀ
Spain, and Fundacion ARAID, Diputacion General de Aragon, Zaragoza, Spain
ꢀ
Received April 30, 2010
ABSTRACT: Nucleotide-induced conformational changes of the catalytic β subunits play a crucial role in the rotary
mechanism of F1-ATPase. To gain insights into the energetic bases that govern the recognition of nucleotides by the
isolated β subunit from thermophilic Bacillus PS3 (Tβ), the binding of this monomer to Mg(II)-free and Mg(II)-
bound adenosine nucleotides was characterized using high-precision isothermal titration calorimetry. The interac-
tions of Mg(II) with free ATP or ADP were also measured calorimetrically. A model that considers simultaneously
the interactions of Tβ with Mg ATP or with ATP and in which ATP is able to bind two Mg(II) atoms sequentially
3
was used to determine the formation parameters of the Tβ-Mg ATP complex from calorimetric data. This analysis
3
yielded significantly different ΔHb and ΔSb values in relation to those obtained using a single-binding site
model, while ΔGb was almost unchanged. Published calorimetric data for the titration of Tβ with Mg ADP
3
ꢀ
ꢀ
[Perez-Hernandez, G., etal. (2002) Arch. Biochem. Biophys. 408, 177-183] were reanalyzed with the ternary model to
determine the corresponding true binding parameters. Interactions of Tβ with Mg ATP, ATP, Mg ADP, or ADP
3
3
were enthalpically driven. Larger differences in thermodynamic properties were observed between Tβ-Mg ATP
3
and Tβ-ATP complexes than between Tβ-Mg ADP and Tβ-ADP complexes or between Tβ-Mg ATP and
3
3
Tβ-Mg ADP complexes. These binding data, in conjunction with those for the association of Mg(II) with free
3
nucleotides, allowed for a determination of the energetic effects of the metal ion on the recognition of adenosine
nucleotides by Tβ [i.e., Tβ AT(D)P þ Mg(II) h Tβ AT(D)P-Mg]. Because of a more favorable binding enthalpy,
3
3
Mg(II) is recognized more avidly by the Tβ ATP complex, indicating better stereochemical complementarity than in
3
the Tβ ADP complex. Furthermore, a structural-energetic analysis suggests that Tβ adopts a more closed
conformation when it is bound to Mg ATP than to ATP or Mg ADP, in agreement with recently published NMR
data [Yagi, H., et al. (2009) J. Biol. Chem. 284, 2374-2382]. Using published binding data, a similar analysis of
Mg(II) energetic effects was performed for the free energy change of F1 catalytic sites, in the framework of bi- or
tri-site binding models.
3
3
3
F0F1-ATP synthase occupies a prominent place in the reper-
tory of proteins that specialize in the interconversion of mechan-
ical and chemical energies. Through a sophisticated mechanism
involving internal rotary movements, this multimeric enzyme
couples the electrochemical potential of protons across mem-
branes to the endergonic synthesis of ATP from ADP and Pi.1
The water-soluble F1 sector (R3β3γδε) carries the enzymatic
machinery. In this subcomplex, three R subunits and three β
subunits are arranged alternately, forming a hexagonal ring that
encloses part of the elongated γ subunit structure (1). The three
catalytic sites of the enzyme are positioned at R-β subunit
interfaces, with a large preponderance of β subunit residues.
The R3β3γ oligomer is the minimal construction that preserves
normal rotational and hydrolytic activities (2-4), while the R3β3
oligomer retains some ATPase activity (5). Dissociation of the
R3β3 oligomer yields nativelike structured monomeric subunits
1Abbreviations: Mg(II), free magnesium ion; AMPPNP, adenylyl
50-imidodiphosphate; Pi, inorganic phosphate; EDTA, ethylenedi-
aminetetraacetic acid; Tris, 2-amino-2-(hydroxymethyl)propane-1,3-
diol; MgCl2, magnesium chloride; NaOH, sodium hydroxide; ATPase,
adenosine 50-triphosphatase; Tβ, isolated β subunit from thermophilic
Bacillus PS3; TF1, F1 sector from Bacillus PS3; EF1, F1 sector from
Escherichia coli; S1-S3, high-, medium-, and low-affinity β subunit sites
in F1, respectively; βDP and βTP, β subunits in the crystal structure of F1
bound to Mg ADP and Mg AMPPNP, respectively; ITC, isothermal
3
3
titration calorimetry; NMR, nuclear magnetic resonance; Kb, equili-
brium binding constant; ΔHb, binding enthalpy; ΔGb, Gibbs binding
free energy; ΔSb, binding entropy; ΔCpb, binding heat capacity; Kb1 and
Kb2, stepwise association constants for the interaction of ATP with
†This work was supported in part by DGAPA, UNAM (PAPIIT,
IN204609), and CONACyT (Grant 47097). N.O.P. and G.S. received
fellowships from CONACyT and DGAPA.
Mg(II); KP1 and KP2, association constants for ATP and Mg ATP,
3
respectively, binding to Tβ; ΔHint, intrinsic binding enthalpy; ΔHdsolv
,
desolvation enthalpy; ΔSconf, ΔSsolv, and ΔSr-t, conformational, solva-
tion, and roto-translational entropy changes, respectively; ΔA, sur-
face area change; Δcpi, specific heat capacity for the surface area of the
type i; R, cooperative heterotropic association constant; Δh, cooperative
enthalpy; Δs, cooperative entropy.
*To whom correspondence should be addressed: Instituto de Quımica,
´
ꢀ
ꢀ
Universidad Nacional Autonoma de Mexico, Circuito Exterior, Ciudad
ꢀ
Universitaria, Mexico 04510, D.F., Mexico. Telephone: þ52 55 56 22 44 24.
Fax: þ52 55 56 16 22 03. E-mail: egarciah@unam.mx.
r
pubs.acs.org/Biochemistry
Published on Web 05/18/2010
2010 American Chemical Society

Article
Biochemistry, Vol. 49, No. 25, 2010 5259
which, although catalytically inactive, bind nucleotides with
considerable affinity (6-12).
Expression and Purification of the Tβ Subunit. Mono-
meric Tβ was expressed in Escherichia coli strain DK 8 (8), which
lacks the genes for F1F0, and purified to homogenity as pre-
viously described (30).
According to the binding change mechanism (2), the three
catalytic sites act in a concerted manner, alternating sequentially
through three different conformations (tight, loose, and open)
with vastly different substrate affinities [high (S1), medium (S2),
and low (S3) affinity]. These sites exhibit strong positive and
negative cooperativity in catalysis and binding, respectively (13).
High-resolution crystal structures of F1 have yielded invaluable
information for unveiling key molecular elements of the binding
change mechanism (1, 14-22). The structure of bovine mito-
chondrial F1 bound to Mg nucleotides (the Mg ADP-inhibited
All experiments were performed at pH 8.0 in a 0.05 M Tris-HCl
buffer solution supplemented with 0.1 M NaCl to prevent protein
aggregation. Purified Tβ was thoroughly dialyzed against the buffer
solution prior to calorimetric measurements. After degassification,
the protein concentration was determined spectrophotometrically,
using an extinction coefficient of 15360 M-1 cm-1 at 280 nm. For
ADP and ATP, an extinction coefficient of 15600 M-1 cm-1 at
259 nm was used. MgCl2 and nucleotides (sodium salts) were dis-
solved into the buffer solution obtained from the last dialysis. The
solution’s pH was readjusted to 8.0 using NaOH when necessary.
Isothermal Titration Calorimetry. ITC determinations
were performed using the high-precision VP-ITC microcalori-
3
3
F1 state) obtained by Abrahams et al. (1) revealed the three
β subunits in different conformations. One β subunit (βE) shows
an open conformation and has an empty catalytic site. The other
two β subunits are in the closed conformation, one binding
Mg ADP (βDP) and the other binding Mg AMPPNP (βTP).
meter (MicroCal, Inc.). Binding of Tβ to Mg ATP or ATP was
3
3
3
assessed in the temperature range of 15-30 ꢀC. The Tβ con-
centration was typically 0.05-0.07 mM, while the ligand con-
centration in the syringe was 2.0-2.5 mM. In the titration of Tβ
with the Mg(II)-free nucleotide, ligand and protein solutions
were supplemented with 2 mM EDTA to sequester any residual
trace of Mg(II) in the solution. The titration schedule consisted of
20-30 consecutive injections of 3-8 μL with a 6 min interval
between injections. The dilution heat of the ligand was obtained
via addition of the ligand to a buffer solution under identical
conditions and the injection schedule used with the protein
sample. In the case of the titration of Tβ with Mg(II)-free
nucleotide, the binding constant (Kb), the enthalpy change
(ΔHb), and the stoichiometry (n) were determined by nonlinear
fitting of normalized titration data using an identical and
Noninhibited structures of bovine and yeast mitochondrial F1
have also been determined (20, 21). In these structures, the βDP
catalytic site is occupied by Mg AMPPNP.
3
In spite of the impressive advances in establishing the mole-
cular bases of the function of F0F1-ATP synthase and its dif-
ferent subcomplexes, many key aspects remain to be unveiled.
In particular, knowledge of the energetic principles that drive
substrate recognition and intersubunit communication is still
rudimentary. The energetic contribution of Mg(II) in this enzyme
is also poorly understood (2). Besides its role as a cofactor
required for stabilization of the transition state (23), Mg(II) has
been implicated as being crucial in determining the binding
asymmetry and cooperativity between catalytic sites (24, 25).
However, recent studies have challenged that conclusion, indi-
cating that heterogeneity in β subunit affinities is an inherent
property of nucleotide-free F1 (22, 26, 27). As far as we know,
no systematic characterization of the energetic contribution of
Mg(II) in the recognition of nucleotides by F1 or by the isolated
subunits has been conducted.
independent binding site model (31):
2
nMTΔHbV0
XT
1
4
Q ¼
1 þ
þ
2
nMT nKbMT
3
5
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ꢀ
ꢁ
2
Nucleotide-induced conformational changes in β subunits are
considered to be the essential driving force for rotational catalysis
in F1 (1, 3, 4, 11, 12, 28, 29). Saliently, the isolated β subunit
undergoes conformational changes that resemble those between
open and closed β subunit conformations in F1 crystal
structures (6, 7, 10-12, 30). Therefore, the isolated β subunit
provides an excellent opportunity to study issues that are difficult
to address in larger F0F1-ATP synthase subcomponents. In this
work, we have aimed to gain new insights into the energetic bases
of the recognition of adenosine nucleotides by the monomeric β
subunit from thermophilic Bacillus PS3 (Tβ). For this purpose,
XT
1
4XT
-
1 þ
þ
-
nMT nKbMT
nMT
where Q is the normalized differential heat evolved per mole of
ligand, after correction for the heats of dilution of the ligand, V0 is
the working volume of the cell, and XT and MT are the ligand and
macromolecule concentrations, respectively. For the titration of
Tβ with Mg(II)-bound ATP, both the ligand and protein
solutions contained 5 mM MgCl2. The resulting binding iso-
therms were analyzed using a ternary model in which Tβ may
bind ATP or Mg ATP, while ATP may also be in the form of
3
the binding of Tβ to ATP and Mg ATP was characterized as a
Mg2 ATP (see Appendix). In the fitting of this model, formation
3
3
function of temperature using high-precision isothermal titration
calorimetry. The associaton of Mg(II) with free ATP was also
characterized calorimetrically. The binding data of these com-
plexes allowed the determination of the energetic contribution of
Mg(II) in the recognition of ATP by Tβ. A similar analysis was
performed for ADP as the ligand, and the properties of the two
nucleotide complexes were compared. Finally, the energetic
effects of Mg(II) in F1 catalytic sites were explored using affinity
constants available in the literature.
parameter values for Tβ ATP, Mg ATP, and Mg2 ATP
(determined in independent experiments) were kept fixed, while
3
3
3
those for the Tβ-Mg ATP complex were the fitting parameters.
3
Titration of ATP with MgCl2 was performed in the tempera-
ture range of 15-30 ꢀC. The reaction cell contained 1.5 mM
ATP, and the syringe contained 80 mM MgCl2. Each titration
consisted of a series of 35 consecutive injections of 2-15 μL with
a 10 min interval between injections. The binding isotherms were
analyzed using a model in which two Mg(II) ions bind sequen-
tially to ATP (32):
MATERIALS AND METHODS
2
Q ¼ ð½ATPꢀTV0Þf½Kb1½MgꢀΔHb1 þ Kb1Kb2½Mgꢀ ðΔHb1
Materials. All chemicals, including ATP and ADP sodium
salts, were from Sigma Chemical Co.
2
þ ΔHb2Þꢀ=ð1 þ Kb1½Mgꢀ þ Kb1Kb2½Mgꢀ Þg

5260 Biochemistry, Vol. 49, No. 25, 2010
Pulido et al.
where Q is the cumulative heat effect, subscripts 1 and 2 stand for
the binding of the first and second Mg(II), respectively, [ATP]T is
the total ATP concentration, and [Mg] is the free Mg(II)
concentration.
Changes in Solvent-Accessible Surface Area. Surface area
calculations were conducted with NACCSESS [Hubbard, S. J.,
and Thornton, J. M. (1993) NACCESS, Department of Bio-
chemistry and Molecular Biology, University College, London],
using a probe radius of 1.4 A and a slice width of 0.1 A. Changes
in solvent-accessible surface areas (ΔA) were estimated from the
difference between the complex and the sum of the free molecules.
ΔA-Based Calculations of ΔCpb. To estimate ΔCpb from
structural data, we used the semiempirical relationship
X
ΔCpb
¼
ΔcpiΔAi
where Δcpi is the specific heat capacity contribution per unit of
surface area of type i. Parameters for protein’s apolar (carbon
and sulfur atoms) and polar (oxygen and nitrogen atoms)
surfaces, obtained from data of cyclic dipeptides for the transfer
from the solid state to water, were taken from ref 33. These
parameters were also used for the adenine surfaces. A recently
published sugar-specific parametrizarion was used for the ribose
moiety in the nucleotide (34). For Mg(II) and phosphate surfaces,
we derived corresponding specific parameters. Heat capacity
changes accompanying the transfer of magnesium and inorganic
phosphate from the gas phase to an aqueous solution were taken
from ref 35. These magnitudes (-41 and -81 cal mol-1 K-1 for
magnesium and inorganic phosphate, respectively) were then
corrected for expansion effects by adding to them R, the universal
constant of ideal gases (36), and normalized by the corresponding
total surface area (113 and 188 A2 for magnesium and inorganic
phosphate, respectively).
F
IGURE 1: Calorimetric isotherms for the formation of Tβ-ATP,
Tβ-Mg ATP, Mg-ATP, and Mg2-ATP complexes at 25 ꢀC, in a
3
0.05 M Tris-HCl buffer solution supplemented with 0.1 M NaCl
(pH 8.0). Solid lines correspond to the best fitting curves. In the
titration of ATP with Mg(II), the experimental data were best fitted
by a sequential binding two-site model. For the Tβ-ATP complex,
an identical and independent binding site model was used. In the case
of the Tβ-Mg ATP complex, a coupled equilibrium model was used
which considers the binding of Tβ to ATP or Mg ATP and the
binding of ATP to one or two magnesium ions.
3
3
RESULTS
Thermodynamics of Mg(II) Binding to Free ATP. At pH
8, ATP is completely unprotonated (ATP4-). Therefore, it is able
to bind two Mg(II) ions in a stepwise manner:
and Kb values available in the literature, ΔCpb values are still
scarce. Alberty (39) reported a value of 30 cal mol-1 K-1 for the
Mg-ATP complex, which is similar to that obtained in this
study. In contrast, Wang et al. (40), using isothermal flow
calorimetric data in the temperature range of 50-125 ꢀC,
obtained significantly larger values for the two Mg(II)-bound
ATP complexes (121 and 50 cal mol-1 K-1 for Mg-ATP and
Mg2-ATP complexes, respectively).
ATP þ MgðIIÞ h Mg- ATP þ MgðIIÞ h Mg2- ATP
Consistent with this, binding isotherms obtained for the titration
of ATP with MgCl2 were best described with a sequential binding
site model (Figure 1). Results from calorimetric measurements
performed at different temperatures are summarized in Table 1.
ATP binds the first Mg(II) with an ∼400-fold avidity in relation
to the second one. Both binding events are entropically driven,
with the enthalpic component being more unfavorable for the
formation of the mono-Mg(II) species. Assuming ΔCpb is
temperature-independent, a linear regression analysis of ΔHb
data versus temperature in Table 1 gives values of 37 ( 10 and
20 ( 10 cal mol-1 K-1 for Mg-ATP and Mg2-ATP complexes,
respectively (Figure 2). The ΔHb1 and Kb1 values obtained here
are similar to those recommended by Smith et al. (37) (T = 25 ꢀC,
ΔHb = 4.49 kcal mol-1, and Kb = 35500 M-1), who compiled
and critically examined a large set of published binding data for
the Mg-ATP complex. As far as we know, only one ITC study of
the interaction of Mg(II) with ATP has been reported (38). Data
in that study (28 ꢀC) were analyzed using a single-site model,
yielding a similar enthalpy change (ΔHb = 4.2 kcal/mol), but a
somewhat smaller binding constant (Kb = 9600 M-1) compared
to those listed in Table 1. In contrast to the large number of ΔHb
Thermodynamics of ATP and Mg ATP Binding to
3
Isolated Tβ. Figure 1 shows examples of binding isotherms
obtained for Tβ-ATP and Tβ-Mg ATP complexes.2 The
3
binding isotherms for the Tβ-ATP complex were well fitted
using a single-site binding model. For the titration of Tβ with
Mg(II)-bound ATP, the calorimetric data were fitted using a
model in which ATP and Mg ATP compete for Tβ’s binding site,
3
and the equilibria among the ATP, Mg ATP, and Mg2 ATP
3
3
species are taken into account (see Appendix).
Table 2 summarizes the calorimetric results obtained for
Tβ-ATP and Tβ-Mg ATP complexes at different tempera-
3
tures. For both binding events, calorimetric data consistently
yielded an ∼1:1 stoichiometry. The two complexes differ signi-
ficantly from each other in their thermodynamic properties.
2The new noncovalent bond formed in the considered binding
reaction is indicated by a dash. In the formation of a ternary complex,
the noncovalent contact in the preformed binary complex is indicated by
a center dot.

Article
Biochemistry, Vol. 49, No. 25, 2010 5261
Table 1: Thermodynamic Parameters for the Binding of Mg(II) to ATP at Different Temperaturesa
Mg-ATP
Mg2-ATP
temp
Kb1
(ꢁ10-4 M-1
ΔGb1
(kcal/mol)
ΔHb1
(kcal/mol)
TΔSb1
(kcal/mol)
Kb2
(M-1
ΔGb2
(kcal/mol)
ΔHb2
(kcal/mol)
TΔSb2
(kcal/mol)
(ꢀC)
)
)
15
20
25
30
2.2 ( 0.2
3.0 ( 0.0
3.6 ( 0.1
4.0 ( 0.1
-5.7
-6.0
-6.2
-6.4
3.9 ( 0.1
4.2 ( 0.1
4.4 ( 0.2
4.6 ( 0.1
9.6
10.2
10.6
11.0
49 ( 21
63 ( 7
98 ( 15
101 ( 17
-2.2
-2.4
-2.7
-2.8
1.5 ( 0.2
1.5 ( 0.1
1.7 ( 0.2
1.8 ( 0.1
3.7
3.9
4.4
4.6
aEquilibrium constants correspond to stepwise association constants. Values are means of three independent experiments at each temperature.
Table 2: Thermodynamic Parameters for the Binding of Mg ATP or ATP
3
to Tβ at Different Temperatures
temp
Kb
ΔGb
ΔHb
TΔSb
(ꢀC) (ꢁ10-5 M-1
)
(kcal/mol) (kcal/mol) (kcal/mol)
n
Tβ-Mg ATP
3
15
20
25
30
1.8 ( 0.1
1.3 ( 0.1
1.0 ( 0.1
0.73 ( 0.1
-6.9
-9.6 ( 0.2
-9.9 ( 0.1
-10.4 ( 0.2
-11.8 ( 0.2
-2.7
-3.0
-3.6
-5.1
1.02 ( 0.01
0.98 ( 0.01
0.99 ( 0.01
0.95 ( 0.02
-6.9
-6.8
-6.7
Tβ-ATP
15
20
25
30
0.25 ( 0.01
0.19 ( 0.00
0.13 ( 0.01
0.12 ( 0.01
-5.8
-5.7
-5.6
-5.6
-2.4 ( 0.2
-3.1 ( 0.2
-3.4 ( 0.1
-4.3 ( 0.5
3.4
2.7
2.2
1.3
0.98 ( 0.09
1.01 ( 0.05
1.05 ( 0.05
1.02 ( 0.10
Table 3: Thermodynamic Cooperativity Parameters for the Heterotropic
F
IGURE 2: Binding enthalpies as a function of temperature for the
Interaction in the Binding of Mg(II) and Nucleotides to Tβ at 25 ꢀC
Tβ-ATP, Tβ-Mg ATP, Mg-ATP, and Mg2-ATP complexes in
3
a 0.05 M Tris-HCl buffer solution supplemented with 0.1 M NaCl
(pH 8.0). Dashed lines correspond to the least-squares linear fittings
of the Kirchoff equation (∂ΔHb/∂T = ΔCp) to the calorimetric data,
assuming ΔCp is independent of temperature.
Δg
Δh
TΔs
complex
Tβ-Mg ATP
R
(kcal/mol)
(kcal/mol)
(kcal/mol)
7.7
1.1
-1.2
-0.1
-7.0
-3.4
-5.8
-3.3
3
Tβ-Mg ADP
3
The 7-fold association constant value obtained for the
Tβ-Mg ATP complex arises from significant, although partially
3
parameters, the cooperativity association constant, R, and the
cooperativity enthalpy, Δh, can be calculated from the thermo-
dynamic parameters for the binding of the nucleotide and Mg-
bound nucleotide to Tβ, and they reflect the reciprocal effect of
each ligand on the binding to Tβ [R = KP2/KP1 = Kb1*/Kb1, and
Δh = ΔHP2 - ΔHP1 = ΔHb1* - ΔHb1 (see Appendix)].
counterbalanced, variations in enthalpy and entropy. At all
temperatures sampled, Tβ binding to Mg ATP was around
3
2-fold more exothermic than that to ATP. In contrast, the
binding entropy was more favorable for the Tβ-ATP complex.
Also using ITC, Odaka et al. (8) measured Tβ-Mg ATP
3
binding energetics at a single temperature (21 ꢀC). Data obtained
in that study (ΔHb = -12 kcal/mol, TΔSb = -5.5 kcal/mol, and
Kb = 66000 M-1) are somewhat different from those in Table 2.
These differences are in part due to the use of different binding
models. In fact, if our binding isotherms were analyzed using a
simple 1:1 binding model, values closer to those of Odaka et al.
would be obtained (for instance, at 20 ꢀC, ΔHb and TΔSb would be
-10.7 and -4.1 kcal/mol, respectively). These contrasting results
illustrate the importance of taking into account the coupled
equilibria occurring during the titration of Tβ with Mg(II)-bound
DISCUSSION
The elucidation of the molecular bases that govern the
formation of noncovalent protein adducts requires a quantitative
knowledge of the forces that drive the recognition process. In
what follows, a structural-energetic analysis is presented for the
formation of the Tβ complexes studied here, simultaneously
considering the full set of thermodynamic functions.
Tβ-Mg ATP and Tβ-Mg ADP Complexes Differ
3
3
from Each Other Energetically and Structurally. Figure 3
compares the thermodynamic signatures for the Tβ-Mg ATP
ATP (i.e., that Tβ is able to bind Mg ATP or ATP, and that ATP is
3
able to bind one or two magnesium ions) for the determination of
3
and Tβ-Mg ADP complexes. For the last complex, the calori-
the true formation parameters of the Tβ-Mg ATP complex.
3
3
metric data obtained previously (30) were fitted using the ternary
binding model depicted in Appendix. For that purpose, the
formation parameters of the Mg-ADP and Tβ-ADP complexes
were also measured calorimetrically (see below). As seen in
Figure 3, the presence of the γ-phosphate moiety makes the
Analysis of the thermal dependence of ΔHb yields ΔCpb values of
-150 ( 20 and -96 ( 17 cal mol-1 K-1 for Tβ-Mg ATP and
3
Tβ-ATP complexes, respectively (Figure 2).
Table 3 shows the cooperativity parameters for the hetero-
tropic interaction between magnesium and nucleotides. These

5262 Biochemistry, Vol. 49, No. 25, 2010
Pulido et al.
Table 4: Surface Area Changes and Structure-Based Estimations of ΔCpb
for the Formation of Tβ-Mg ADP and Tβ-Mg ATP Complexesa
3
3
ΔA (A2)
Tβ-Mg
ADP
Tβ-Mg
ATP
Δcpi
3
3
surface
(cal mol-1 K-1 A-2
)
protein
polar
-9
-240
-61
-384
-0.27b
apolar
0.45b
nucleotide
magnesium
-72
-143
-34
-19
-32
-59
-203
-39
-15
-29
-0.36c
-0.43c
0.10d
phosphate
hydroxyl (ribose)
no-ring carbon (ribose)
ring carbon (ribose)
nitrogen (adenine)
carbon (adenine)
0.36d
0.09d
-107
-84
-106
-80
-0.27b
0.45b
ΔA-based calculation
ΔCpcalc (cal mol-1 K-1
)
-40
-36
-67
-150
ΔCpexp (cal mol-1 K-1
)
aThe atomic coordinates of the three β subunits were extracted from the
X-ray structure of MF1 [Protein Data Bank entry 1bmf (1)] and used to
calculate ΔA values for the binding of the isolated free β subunit (βE) to
Mg ADP (βDP) and Mg ATP (βTP). bFrom ref 33. cObtained from
F
IGURE 3: Thermodynamic signatures of Tβ-Mg ATP and Tβ-
3
3
Mg ADP complexes at 25 ꢀC as determined by isothermal titration
calorimetry. See the legend of Figure 1 for the experimental condi-
tions.
3
3
hydration heat capacities reported in ref 35. dFrom ref 34.
affinity slightly higher for Mg ATP compared to that of
3
Mg ADP, with a binding enthalpy similar to that of Mg ADP
3
3
entry 1bmf) indicates that the two catalytic sites in closed
conformation share similar residual hydration. Six and five water
molecules are seen at the βDP and βTP sites, respectively, bridging
the contact between the protein and the Mg-bound nucleotide
(e3.5 A cutoff). Thus, it seems that residual hydration effects
(factor 3) are also not significant in the determination of the
(ΔΔHb = -0.1 kcal/mol), while the binding entropy becomes
slightly less unfavorable [Δ(TΔSb) = 0.3 kcal/mol]. In contrast,
TF1 catalytic sites exhibit a slightly stronger preference for
Mg ADP over Mg ATP, indicating the importance of the
oligomeric environment for substrate recognition (41). This
preference is even more dramatic in the whole F0F1-ATP
synthase, where the presence of the transmembranal proton
3
3
difference in ΔCpb between Tβ-Mg ADP and Tβ-Mg ATP
3
3
complexes.
gradient decreases the affinity for Mg ATP by more than 6
orders of magnitude (42).
3
A previous structural-energetic analysis showed that the small
ΔCpb (-36 cal mol-1 K-1) observed for the Tβ-Mg ADP
3
Figure 3 also compares ΔCpb values for Tβ-Mg ADP and
3
complex can be explained satisfactorily on the basis of desolva-
Tβ-Mg ATP complexes. The binding of Mg ATP to Tβ elicits a
3
3
tion of the protein binding site and ligand surfaces (30). In that
significantly larger decrease in heat capacity in relation to
analysis, the coordinates of the empty and the Mg ADP-filled
3
Mg ADP. Although exceptions can be found (34), typically the
3
β subunits, extracted from the X-ray structure of inhibited
MF1 (1), were used for calculation of the changes in solvent
accessibility of surface areas (ΔA) accompanying the formation
of the complex. The large structural rearrangement involved in
the transition from βE to βDP elicits extensive exposition and
burying of surface areas at opposite zones of the protein. This
strong compensatory effect yields a marginal net protein ΔA,
explaining why a small ΔCpb value is observed experimentally.
Following the same approach, area changes were calculated for
desolvation of polar surfaces increases the heat capacity, due to
the liberation of water molecules that undergo a net gain of soft
vibration modes upon return to the bulk solvent (43). In the case
of phosphate groups, gas-to-water transfer data indicate that
their desolvation yields positive heat capacity changes (35), which
is consistent with the calorimetric results for the Mg-ATP and
Mg2-ATP complexes (Figure 2). Thus, the more negative ΔCpb
value observed for the Tβ-Mg ATP complex cannot be ex-
3
plained on the basis of γ-phosphate desolvation, suggesting the
occurrence of additional molecular events.
the binding of Mg ATP to the isolated β subunit, using the
3
isolated structures of MF1’s βE and βTP. Table 4 lists ΔA values
Besides desolvation effects, a number of factors can contribute
significantly to the heat capacity of biomolecular complexes,
namely, (1) (de)protonation effects, (2) exchange of counter-
ions, (3) sequestration or liberation of structural water molecules,
for this complex and compares them with those for the
Mg ADP-bound complex. For this analysis, recently published
3
sugar-specific parameters were used for ribose surfaces in the
nucleotides (34). Furthermore, we derived specific heat capacity
parameters for Mg(II) and phosphate surfaces, by using hydra-
tion data available in the literature (35). As shown in Table 4, the
use of this refined set of parameters yields an excellent estimation
and (4) conformational changes (43-45). For the Tβ-Mg ADP
3
complex, very similar binding values were obtained using Tris or
cacodylate buffers (30). These buffers differ from each other
largely in their ionization enthalpies (ΔΔHion = 12 kcal/mol) and
in the electrical charge of their unprotonated bases (neutral for
Tris and negative for cacodylate). Therefore, it seems that factors
1 and 2 can be ruled out as major contributors to ΔCpb in the
formation of Tβ-nucleotide complexes. On the other hand,
scrutiny of the inhibited-state MF1 structure (Protein Data Bank
of ΔCpb for the Tβ-Mg ADP complex. In contrast, in the case of
3
the Tβ-Mg ATP complex, the estimated value is approximately
3
half of that measured calorimetrically, suggesting that the MF1’s
βTP conformation is not as a good model as MF1’s βDP for the
corresponding nucleotide-bound conformation of isolated Tβ.

Article
Biochemistry, Vol. 49, No. 25, 2010 5263
Yagi et al. (10) measured the influence of nucleotides on the
NMR signals of the 12 Tβ tyrosine residues. The NMR spectra for
Tβ bound to ADP, Mg ADP, and ATP were very similar to each
Table 5A shows calculations according to Scheme 2 using the
thermodynamic data in Tables 1 and 2. Mg(II) binding is favored
by ∼7 kcal/mol of Gibbs free energy, versus the ∼1 kcal/mol
3
other, while the Tβ-Mg ATP complex exhibited a dissimilar
obtained from the difference between Tβ-Mg ATP and Tβ-
3
3
spectrum. More recently, Yagi et al. (12) performed a more detailed
NMR analysis of the nucleotide-induced conformational changes
in Tβ. By using segmental isotope labeling, they found that the
ATP complexes. Mg(II) sequestration by the Tβ ATP complex is
3
both enthalpically and entropically driven. In contrast, the
straight difference between Tβ-Mg ATP and Tβ-ATP com-
3
relative orientation of the C-terminal domain in Mg ATP-bound
plexes would lead to a different picture, i.e., that Mg(II) binding is
enthalpically driven and entropically unfavored. The same results
as those calculated considering Scheme 2 are obtained if the
parameters for Mg(II) binding to the Tβ-nucleotide complex
are calculated using the binding parameters for Mg(II) bind-
ing to ATP and the cooperativity parameters [Kb1* = RKb1, and
ΔHb1* = ΔHb1 þ Δh (see Appendix)]. In fact, this is another way
of applying Hess’ law.
3
and Mg ADP-bound Tβ complexes differs by 10ꢀ. These studies
3
indicate that the monomeric Tβ subunit adopts a closer conforma-
tion when bound to Mg ATP. Thus, the more negative ΔCpb value
3
of the Tβ-Mg ATP complex might be explained on the basis of a
3
greater burial of protein surface area, elicited by a larger con-
formational change compared to that observed in MF1’s βTP (1).
Energetic Effects of Mg(II) in the Recognition of Nucleotides
by Isolated Tβ. According to Hess’ law, the difference between
To explore the molecular features of the incorporation of
Tβ-Mg ATP and Tβ-ATP complexes corresponds to the
Mg(II) into the Tβ ATP adduct, the theoretical ΔCpb was
calculated for this binding event. In the structure of βTP bound
3
3
transfer of Mg(II) from ATP to the Tβ ATP preformed complex:
3
to Mg AMPPNP extracted from the inhibited MF1 crystal
3
Scheme 1
structure, the Mg(II) atom is completely inaccessible to the
solvent. Removing Mg(II) from the complex yields virtually no
surface area changes (<1 A2) in either the nucleotide or the
protein. Thus, in the case of a rigid body-like association between
Mg(II) and Tβ ATP, the heat capacity effect would correspond
3
entirely to desolvation of the Mg(II) ion. The complete desolva-
tion of an Mg(II) ion elicits a heat capacity increase of 39 cal
mol-1 K-1, once corrected for expansion effects (36). This value
is significantly different from the negative ΔCpb value obtained
from calorimetric data for the sequestration of Mg(II) by
To determine the “pure” Mg(II) binding contribution
Tβ ATP þ MgðIIÞ h Tβ ATP- Mg ꢂ Tβ- Mg ATP
3
3
3
Tβ ATP (Table 5A). Overall, these results indicate that some
3
the association between the metal ion and free ATP needs to be
conformational rearrangements occur in the Tβ ATP complex
3
taken into account:
upon Mg(II) binding. This picture is consistent with the con-
formational variations between Tβ ATP and Tβ-Mg ATP
Scheme 2
3
3
complexes evidenced from NMR data (10, 12).
The Mg(II) contribution in the Tβ-Mg ADP complex was also
3
determined in this work. For that purpose, the formation para-
meters of the Tβ-ADP and Mg-ADP complexes were measured
calorimetrically (Table 5B). Similar to that observed with the
Mg-ATP complex, binding of Mg(II) to free ADP is entropically
driven and enthalpically unfavored, although with a binding con-
stant that is 1 order of magnitude smaller (Kb = 2455 ( 108 M-1).
In the case of the Tβ-ADP complex, the interaction is both more
stable (Kb = 60000 M-1) and more exothermic (∼2-fold more
Table 5: Thermodynamic Parameters for the Binding of Mg(II)a
(A) Tβ ATP
3
ΔGb (kcal/mol)
ΔHb (kcal/mol)
TΔSb (kcal/mol)
ΔCpb (cal mol-1 K-1
)
Tβ þ Mg ATP h Tβ-Mg ATP
-6.8
5.6
-10.4
3.4
-3.6
-2.2
10.6
4.8
-150
99
3
3
Tβ-ATP h Tβ þ ATP
Mg(II) þ ATP h Mg-ATP
-6.2
-7.4
4.4
37
Tβ ATP þ Mg(II) h Tβ ATP-Mg
-2.6
-14
3
3
(B) Tβ ADP
3
ΔGb (kcal/mol)
ΔHb (kcal/mol)
TΔSb (kcal/mol)
Tβ þ Mg ADP h Tβ-Mg ADP
-6.6
6.5
-10.5
7.1
-3.9
0.6
3
3
Tβ ADP h Tβ þ ADP
3
Mg(II) þ ADP h Mg-ADP
-4.6
-4.7
3.7
8.3
Tβ ADP þ Mg(II) h Tβ ADP-Mg
0.3
5.0
3
3
aAll data obtained at 25 ꢀC.

5264 Biochemistry, Vol. 49, No. 25, 2010
Pulido et al.
negative) than that of the Tβ-ATP complex. With the Tβ-ADP
and Mg-ADP complex formation parameters determined, the
Mg(II) simultaneously, but the binding of a second Mg(II)
excludes the binding of ATP].
It is interesting to note that while the difference in the enthalpy
calorimetric data reported previously for the Tβ-Mg ADP com-
3
plex (30) were reanalyzed using the ternary model described in
Appendix (Table 2). Since there was no evidence of the formation of
the Mg2-ADP complex, Kb2 and ΔHb2 were set to zero in the fitting
analysis.
of formation between Tβ-Mg ATP and Tβ-Mg ADP (ΔΔHb =
3
3
-0.1 kcal/mol) complexes is very similar to that between
Mg-ATP and Mg-ADP complexes (ΔΔHb = -0.3 kcal/mol),
the difference in the entropy of formation between the protein
adducts is significantly smaller [Δ(TΔSb) of 0.3 kcal/mol vs
Δ(TΔSb) of 2.3 kcal/mol] (Table 5B). The net change in the
number of degrees of freedom upon molecular association is
determined by three major contributions, namely
As shown in Table 5B, there are some differences in the
binding energetics of the two nucleotides to Tβ. The interaction
of Tβ with Mg ATP is energetically similar to that of Mg ADP.
3
3
However, the thermodynamic differences between the Tβ-Mg
3
ATP and Tβ-ATP complexes are significantly larger than those
between the corresponding ADP complexes, indicating a very
different effect of the metal ion in both types of nucleotide-Tβ
ΔSb ¼ ΔSconf þ ΔSsolv þ ΔSr-t
complexes. According to Scheme 2, the Tβ ATP complex binds
where ΔSconf, ΔSsolv, and ΔSr-t stand for the conforma-
tional, solvation, and roto-translational entropy changes, respec-
tively (33). It is well established that the formation of bimolecular
complexes involves a constant loss of ΔSr-t, regardless of the size
of the interacting molecules (49). On the other hand, the presence
3
to Mg(II) with significantly more avidity. This improved affinity
is mainly due to a favorable enthalpic contribution, while the
binding entropies of both complexes are approximately the same
size. The binding enthalpy is a measure of the strength of the
interaction between the molecular partners (ΔHint) relative to the
energy penalty paid by desolvation (ΔHdsolv) of the contact
surfaces:
of the γ-phosphate of ATP should yield a more favorable ΔSsolv
,
since a larger surface area becomes buried upon binding to the
protein. Therefore, the smaller entropy difference between
Tβ-Mg ATP and Tβ-Mg ADP complexes in relation to that
between Mg-ATP and Mg-ADP complexes may be interpreted
in terms of a more unfavorable ΔSconf for the formation of the
3
3
ΔHb ¼ ΔHint þ ΔHdsolv
Examples can be found in the literature of exothermic
(ΔHint < -ΔHdsolv) or exothermic (ΔHint > -ΔHdsolv) recogni-
tion of metal ions by proteins (46). Accordingly, it is clear that the
Tβ-Mg ATP complex, i.e., the freezing of a larger number of
3
protein rotatable bonds.
Overall, the analysis given above indicates that the Tβ ATP
adduct provides a better site for Mg(II) anchoring than the
Tβ ATP adduct provides a better stereochemical environment
3
3
for Mg(II) anchoring than the Tβ ADP adduct. In fact,
3
Tβ ADP adduct. Furthermore, entropy and heat capacity
mutational studies have shown that the complete octahedral
coordination of Mg(II) in F1 closed catalytic sites requires the
presence of the γ-phosphate of ATP (24). The β-phosphate
of ATP and four β subunit residues (three of them linked
via structural water molecules) complement the coordination
of the metal ion. Furthermore, since no R subunit residue is
involved in the binding to Mg(II) in F1, in principle the full
coordination of the metal ion can be achieved in the isolated
β subunit.
3
changes are consistent with the catalytic subunit adopting a more
closed conformation when it is bound to Mg ATP than when it is
3
bound to ATP or Mg ADP. These results confirm and comple-
3
ment in energetic terms the conclusions reached recently by
Yagi et al. (12), who found that in the presence of Mg(II), the
γ-phosphate elicits a structural rearrangement at the catalytic site
that follows the overall bending motion, a rearrangement that is
not seen upon ADP or Mg ADP binding.
3
Energetic Role of Mg(II) in the Recognition of ATP by
Catalytic Sites in F1. In spite of the wealth of available
information about the catalytic and binding properties of F1,
there is still a debate regarding whether the occupancy of
two (2, 26, 27, 50) or three catalytic sites (41, 51, 52) is sufficient
to achieve rapid ATPase activity. Furthermore, binding and
kinetic data of ATP synthase and its different subcomplexes have
proven to be difficult to analyze and interpret. For instance,
although F1 catalytic sites exhibit strong negative binding
cooperativity (13, 53), experimental data have been just as well-
described using sequential or independent site models (26, 41).
Needless to say, settlement of these mechanistic aspects is
essential for the correct determination of F1 binding para-
meters. Studies based on either bi- or tri-site models have been
conducted for measurement of the association constants of both
Mg(II)-free and Mg(II)-bound nucleotides. Thus, just as with the
isolated Tβ subunit, the Gibbs free energy contributions of
Mg(II) in F1 catalytic sites were determined using both bi- and
tri-site binding data. It is worth recalling that, according to the
analysis presented above for isolated Tβ, the determination of
the true thermodynamic parameters for the recognition of the
Mg(II)-bound nucleotide requires the simultaneous considera-
tion of the association parameters of the free nucleotide with Tβ
Another way to look at the effect of Mg(II) in the recognition
of nucleotides by Tβ is through the cooperative hetero-
tropic association constant (R), which is calculated as the ratio
between the Tβ-Mg ATP and Tβ-ATP binding constants (see
3
Appendix) (47, 48). According to the data listed in Table 3, the
binding of ATP and Mg(II) to Tβ is highly cooperative (R = 7.7),
while Mg(II) has virtually no effect in the case of ADP (R = 1.1).
Similarly, the cooperative enthalpy (Δh) is given by the enthalpy
difference between the Mg(II)-bound and Mg(II)-free nucleotide-
Tβ complexes. For ATP recognition, Δh is -7.0 kcal/mol,
whereas for ADP, Δh is -3.4 kcal/mol. The cooperative entropic
term for ATP (Δs) is -5.8 cal mol-1 K-1, whereas for ADP it is
-3.3 cal mol-1 K-1. In the case of ADP, the cooperative
enthalpy and entropy cancel out, giving rise to a negligible
cooperative Gibbs energy. Besides, both enthalpic and entropic
terms for ATP are smaller (approximately 2-fold) than those
for ADP. Wirh regard to the binding cooperativity in the
Tβ-Mg ADP ternary system, from a formal point of view it is
3
interesting to point out that, considering ATP as the reference
binding molecule, this system represents an example of coupling
between a cooperative homotropic interaction [ATP may bind
one or two Mg(II) ions] and cooperative heterotropic interaction
[ATP may bind Tβ, may bind Mg(II), or may bind both Tβ and

Article
Biochemistry, Vol. 49, No. 25, 2010 5265
Table 6: Binding Energetics of F1 Catalytic Sitesa
b
(A) Tri-site Data for EF1
ΔGb(S1)
ΔGb(S2)
ΔGb(S3)
ΔGb(S1) = ΔGb(S2) = ΔGb(S3)
ΔGb(S1)
ΔGb(S2)
ΔGb(S3)
ref
EF1β þ Mg ATP
EF1β þ ATP
-5.79
EF1β ATP þ Mg(II)
3
3
-10.43
-10.02
-7.93
-6.17
-6.04
-10.84
-10.29
-8.36
-6.50
-5.80
54
54
EF1β þ Mg ADP
EF1β þ ADP
EF1β ADP þ Mg(II)
3
3
-7.78
-5.53
-8.05
b
(B) Bi-site Data for EF1
ΔGb(S1)
-10.80
ΔGb(S2)
ΔGb(S1)
-9.95
ΔGb(S2)
ΔGb(S1)
ΔGb(S2)
ref
EF1β þ Mg ADP
EF1β þ ADP
EF1β ADP þ Mg(II)
3
3
-6.88
-5.99
-6.91
-6.95
27
c
(C) Tri-site Data for TF1
ΔGb(S2)
ΔGb(S3)
ΔGb(S2)
ΔGb(S3)
ΔGb(S2)
ΔGb(S3)
ref
TF1β þ Mg ATP
TF1β þ ATP
TF1β þ ADP
TF1β ATP þ Mg(II)
3
3
-9.00
-9.11
-6.26
-6.37
-6.91
-7.85
-5.60
-6.19
-8.28
-6.71
35, 55
35, 55
TF1β þ Mg ADP
TF1β ADP þ Mg(II)
3
3
-5.88
-4.80
aΔGb values are given in kilocalories per mole. bData obtained at 23 ꢀC. cData obtained at 25 ꢀC.
or Mg(II). Nevertheless, in the case of Tβ, the consideration of all
the different coupled equilibria simultaneously yields only minor
differences in the ΔHb and ΔSb values (<2 kcal/mol) determined
using either a simple binary binding model or a complex ternary
model, while the differences in ΔGb were negligible (<0.2 kcal/mol).
Senior and colleagues have thoroughly studied F1 from E. coli
(EF1) following the quenching of a Trp residue introduced at
position 331 in the β subunit (EF1βY331W) (24, 25, 42, 51, 54).
Binding data were analyzed using a model of three independent
sites (S1-S3). Table 6A shows Gibbs free energies for the binding
of EF1 catalytic sites to ADP and ATP, in the presence or absence
of Mg(II). In the presence of the metal ion, three different
affinities were observed. According to these data, EF1 exhibits
a somewhat stronger avidity for Mg ATP than for Mg ADP.
For both nucleotides, ΔGb(S1) is ∼2.5 kcal/mol more exergonic
than ΔGb(S2), which in turn is ∼1.7 kcal/mol more negative
than ΔGb(S3). In contrast, the three sites exhibited identical
affinities in the absence of Mg(II). This last result led to the
proposal that Mg(II) is essential for imparting asymmetric
binding properties in F1.
difference in affinity between S1 and S2 is not sensitive to the
presence or absence of Mg(II).
Allison and co-workers reported tri-site binding data for TF1
also using mutant β subunits, βY341W (41, 55). Table 6C lists
values for only catalytic sites S2 and S3, since under the
conditions used by the authors, only the upper limits for ΔGb(S1)
were inferred. ΔGb(S2) values for Mg(II)-bound nucleotides are
significantly more exergonic for TF1 than for EF1, while ΔGb(S3)
values are rather similar. For the binding of Mg(II)-free nucleo-
tides, three different affinities were observed for TF1, with
ΔGb(S3) being comparable to the single affinity value obtained
for the three EF1 catalytic sites.
Bi- or tri-site binding models lead to very different pictures of
the role of Mg(II) in stabilization in F1 (Table 5). Data inferred
from the tri-site model indicate that incorporation of the Mg(II)
ion depends strongly on the conformation of the catalytic site,
with the strength of the stabilization paralleling the affinity for
the Mg(II)-bound nucleotide. This conclusion remains the same,
regardless of whether the three catalytic sites are thought to have
different or identical affinities for Mg(II)-depleted nucleotides. In
the case of EF1, the difference between ΔGb(S1) and ΔGb(S2) is
larger than that between ΔGb(S2) and ΔGb(S3). Since βTP and
βDP are conformationally very similar to each other, it follows
that Mg(II) perceives in some way the asymmetric environment
provided by the adjacent R and γ subunits. In contrast, the bi-site
model leads to the conclusion that Mg(II) contributes similarly in
both catalytic sites. In other words, Mg(II) does not make any
contribution per se to the heterogeneity of the catalytic sites, at
least in terms of ΔGb. The idea that intersubunit interactions
alone induce nucleotide binding heterogeneity at catalytic sites
has recently received important support from the recently
determined crystal structure of nucleotide-free mitochondrial
F1, where the three β subunits present different conforma-
tions (22), as in the structure of nucleotide-bound MF1.
3
3
In a recent study, Bulygin and Milgrom (27) noted that sulfate
competes with adenosine nucleotides for catalytic sites in EF1,
similar to that observed previously for inorganic phosphate. This
observation is relevant, as a large body of data (including those
from Senior’s lab) has been obtained with sulfate as a cosolute.
Bulygin and Milgrom (27) obtained binding constants of sulfate-
free EF1βY331W for ADP, Mg ADP, and ATP considering two
3
independent binding sites, while Mg ATP was not measured in
3
that study. Therefore, Table 6B lists only bi-site binding data for
ADP and Mg ADP. Measurements performed in the absence
3
of sulfate revealed that EF1βY331W catalytic sites also exhibit
different affinities for Mg(II)-free nucleotides, an observation
that contradicts the view that the metal ion is the determinant for
the nucleotide binding asymmetry. For Mg ADP, the difference
3
Like those observed for isolated Tβ, available affinity
constants for F1 catalytic sites indicate that the stabilization
effects of Mg(II) depend significantly on the nucleotide
between ΔGb(S1) and ΔGb(S2) (∼4 kcal/mol) is significantly
larger than the difference between the same two sites in the tri-site
model (∼2.5 kcal/mol). Furthermore, in the bi-site model, the

5266 Biochemistry, Vol. 49, No. 25, 2010
Pulido et al.
involved. Furthermore, it has recently been suggested that
to liberate products efficiently, the ADP-releasing β subunit
in F1 should adopt a less closed conformation compared to that
of the ATP-bound subunit (12). Thus, the nucleotide-dependent
conformational and energetic behavior of the monomeric subunit
seems to have functional repercussions in F1. To further explore
the energetic bases that drive nucleotide recognition by F1 catalytic
sites, a calorimetric characterization of the binding of this oligomer
to Mg(II)-free and Mg(II)-bound nucleotides is currently being
undertaken in our lab.
association constants for ATP and Mg ATP binding to Tβ,
respectively, and Kb1* is the association constant for Mg(II)
binding toTβ-ATP.
The total concentrations of ATP, magnesium, and Tβ after
each calorimetric injection i are given by
3
"
#
ꢀ
ꢁ
i
v
½ATPꢀT ¼ ½ATPꢀ0 1 - 1 -
,
i
V0
½MgꢀT ¼ ½Mgꢀ0
,
i
ꢀ
ꢁ
i
v
½TβꢀT ¼ ½Tβꢀ0 1 -
,
i
ACKNOWLEDGMENT
V0
ꢀ
We thank M. in S. Virginia Gomez Vidales for her invaluable
where [ATP]0 is the concentration of ATP in the syringe, [Mg]0 is
the concentration of magnesium in the syringe and the cell, [Tβ]0
is the initial concentration of Tβ in the cell, v is the injection
volume, and V0 is the cell volume.
ꢀ
assistance in the ITC experiments and Drs. Armando Gomez-Puyou
ꢀ
and Marietta Tuena de Gomez-Puyou (IFC, UNAM) for their
critical reading of the manuscript prior to its submission.
The Newton-Raphson method can be used to solve numerically
the set of nonlinear equations for each titration point, thus, deter-
mining the free concentrations of ATP, magnesium, and Tβ after
each calorimetric injection. Using the association constants, the con-
centration of each complex after each injection can be calculated:
APPENDIX
We will consider a ternary system in which the Tβ subunit may
bind ATP or Mg ATP and, at the same time, ATP may bind one
or two magnesium ions (Scheme 3).
The concentration of the different complexes can be expressed
as a function of the concentrations of free species:
3
½Tβ ATPꢀi ¼ KP1½Tβꢀi½ATPꢀi
3
½Mg ATPꢀ ¼ Kb1½ATPꢀ½MgðIIÞꢀ
3
½Tβ Mg ATPꢀi ¼ KP2Kb1½Tβꢀ ½ATPꢀi½Mgꢀi
½Mg ATPꢀ ¼ Kb1½ATPꢀ ½Mgꢀ i
3
3
2
½Mg2 ATPꢀ ¼ Kb1Kb2½ATPꢀ½MgðIIÞꢀ
3
3
i
i
i
2
½Tβ ATPꢀ ¼ KP1½Tβꢀ½ATPꢀ
3
½Mg2 ATPꢀi ¼ Kb1Kb2½ATPꢀi½Mgꢀi
3
½Tβ Mg ATPꢀ ¼ KP2Kb1½Tβꢀ½ATPꢀ½MgðIIÞꢀ ¼
3
3
The heat effect associated with each injection, qi, can be
calculated from the change in concentration for each complex
after each calorimetric injection, and the enthalpy change asso-
ciated with formation of each complex:
K
P1Kb1 ꢃ ½Tβꢀ½ATPꢀ½MgðIIÞꢀ
Considering the mass conservation for each component [Tβ,
ATP, and Mg(II)]:
ꢄꢂ
ꢀ
ꢁꢃ
½ATPꢀT ¼ ½ATPꢀ þ ½Mg ATPꢀ þ ½Mg2 ATPꢀ þ ½Tβ ATPꢀ
v
3
3
3
qi ¼ V0 ½Tβ ATPꢀi - ½Tβ ATPꢀi - 1 1 -
ΔHP1
3
3
þ ½Tβ Mg ATPꢀ
V0
3
3
ꢂ
ꢀ
ꢁꢃ
½MgꢀT ¼ ½MgðIIÞꢀ þ ½Mg ATPꢀ þ 2½Mg2 ATPꢀ
3
3
v
þ ½Tβ Mg ATPꢀi - ½Tβ Mg ATPꢀi - 1 1 -
ðΔHP2 þ ΔHb1Þ
þ ½Tβ Mg ATPꢀ
3
3
3
3
3
3
3
V0
ꢂ
ꢀ
ꢁ
ꢃ
½TβꢀT ¼ ½Tβꢀ þ ½Tβ ATPꢀ þ ½Tβ Mg ATPꢀ
3
3
v
v
0V0
þ ½Mg ATPꢀi - ½Mg ATPꢀi - 1 1 -
- FMg ATP½ATPꢀ
ΔHb1
3
3
3
V0
Then, introducing the equilibrium constants for each complex,
we arrive at the following set of nonlinear equations:
ꢂ
ꢀ
ꢁ
v
þ ½Mg2 ATPꢀi - ½Mg2 ATPꢀi - 1 1 -
3
3
2
V0
½ATPꢀT ¼½ATPꢀ þ Kb1½ATPꢀ½MgðIIÞꢀ þ Kb1Kb2½ATPꢀ½MgðIIÞꢀ
ꢃ
ꢅ
v
0V0
þ KP1½Tβꢀ½ATPꢀ þ KP2Kb1½Tβꢀ½ATPꢀ½MgðIIÞꢀ
- FMg
½ATPꢀ
ðΔHb1 þ ΔHb2Þ
ATP
2
3
2
½MgꢀT ¼½MgðIIÞꢀ þ Kb1½ATPꢀ½MgðIIÞꢀ þ 2Kb1Kb2½ATPꢀ½MgðIIÞꢀ
þ KP2Kb1½Tβꢀ½ATPꢀ½MgðIIÞꢀ
½TβꢀT ¼½Tβꢀ þ KP1½Tβꢀ½ATPꢀ þ KP2Kb1½Tβꢀ½ATPꢀ½MgðIIÞꢀ
where ΔHP1 and ΔHP2 are the enthalpy changes associated with
the binding of ATP and Mg ATP to Tβ, respectively, and ΔHb1
and ΔHb2 are the enthalpy changes associated with the binding of
the first and second Mg(II) molecules to ATP, respectively. The
3
correction terms including FMg ATP and FMg ATP, the fractions
of ATP in the syringe with one and two magnesium atoms bound,
where Kb1 and Kb2 are the stepwise association constants for
the sequential binding of Mg(II) to ATP, KP1 and KP2 are the
2
3
3
Scheme 3

Article
Biochemistry, Vol. 49, No. 25, 2010 5267
respectively, reflect the amount of Mg ATP and Mg2 ATP
complexes introduced into the cell just by injection and not due
to equilibrium balance.
Finally, the heat effect is normalized considering the amount of
ligand injected:
6. Dunn, S. (1980) ATP causes a large change in the conformation of the
isolated β subunit of Escherichia coli F1 ATPase. J. Biol. Chem. 255,
11857–11860.
3
3
7. Hirano, M., Takeda, K., Kanazawa, H., and Futai, M. (1984)
Detection of ATP-dependent conformational change in the F1 por-
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linonaphthalene-1-sulfonate. Biochemistry 23, 1652–1656.
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Ogasahara, K., Yutani, K., and Yoshida, M. (1994) Tyr-341 of the
a subunit is a major Km-determining residue of TFl-ATPase: Parallel
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Akutsu, H. (1999) Functional conformation changes in the TF1-
ATPase subunit probed by 12 tyrosine residues. Biophys. J. 77, 2175–
2183.
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qi
Qi ¼
v½ATPꢀ0
In the experiments, Kb1, ΔHb1, Kb2, ΔHb2, KP1, and ΔHP1 were
determined directly from direct binary titrations. KP2 and ΔHP2
were determined from the ternary experiments, once the other
parameters had been previously determined.
The cooperativity in the binding of ATP and Mg(II) to Tβ is
contained in the values of KP2 and ΔHP2. If KP1 and KP2 are equal
and ΔHP1 and ΔHP2 are equal, the binding of Mg ATP to Tβ is
3
the same as that of ATP, and magnesium does not have any effect
on the ATP binding. If KP1 and KP2 are not equal and/or ΔHP1 and
ΔHP2 are not equal, the binding of Mg ATP to Tβ is different
3
from that of ATP, and magnesium has some effect on the ATP
binding. In that case, the cooperative heterotropic association
constant for ATP and magnesium binding to Tβ will be given by
13. Kayalar, C., Rosing, J., and Boyer, P. D. (1977) An alternating site
sequence for oxidative phosphorylation suggested by measurement of
substrate binding patterns and exchange reaction inhibitions. J. Biol.
Chem. 252, 2486–2491.
KP2
R ¼
KP1
14. Bianchet, M. A., Hullihen, J., Pedersen, P. L., and Amzel, L. M.
(1998) The 2.8-A structure of rat liver F1-ATPase: Configuration of a
critical intermediate in ATP synthesis/hydrolysis. Proc. Natl. Acad.
Sci. U.S.A. 95, 11065–11070.
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J. E. (2000) The structure of the central stalk in bovine F1-ATPase at
2.4 A resolution. Nat. Struct. Biol. 7, 1055–1061.
16. Rodgers, A. J. W., and Wilce, M. C. J. (2000) Structure of the
γ-ε complex of ATP synthase. Nat. Struct. Biol. 7, 1051–1054.
17. Braig, K., Menz, R. I., Montgomery, M. G., Leslie, A. G. W., and
Walker, J. E. (2000) Structure of bovine mitochondrial F1-ATPase
inhibited by Mg2þADP and aluminium fluoride. Structure 8, 567–573.
18. Menz, R. I., Walker, J. E., and Leslie, A. G. W. (2001) Structure of
bovine mitochondrial F1-ATPase. Cell 106, 331–341.
19. Chen, C., Saxena, A. K., Simcoke, W. N., Garboczi, D. N., Pedersen,
P. L., and Ko, Y. H. (2006) Mitochondrial ATP synthase. Crystal
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where an R of >1 indicates positive cooperativity, an R of <1
indicates negative cooperativity, and an R of 1 indicates no
cooperativity. Similarly, the cooperative enthalpy change for
ATP and magnesium binding to Tβ will be given by
Δh ¼ ΔHP2 - ΔHP1
The cooperative entropy change can be calculated as
TΔs ¼ Δh - Δg ¼ Δh þ RT ln R
Finally, we may conclude that the cooperative effect between
Mg(II) and ATP is reciprocal. From energy conservation (Hess’
law) applied to the formation of the Tβ Mg(II) ATP ternary
3
3
complex, we obtain
20. Kabaleeswaran, V., Puri, N., Walker, J. E., Leslie, A. G. W., and
Mueller, D. M. (2006) Novel features of the rotary catalytic mechan-
ism revealed in the structure of yeast F1 ATPase. EMBO J. 25, 5433–
5442.
Kb1KP2 ¼ KP1Kb1
ΔHb1 þ ΔHP2 ¼ ΔHP1 þ ΔHb1
ꢃ
ꢃ
then
21. Bowler, M. W., Montgomery, M. G., Leslie, A. G. W., and Walker,
J. E. (2007) Ground state structure of F1-ATPase from bovine heart
mitochondria at 1.9 A resolution. J. Biol. Chem. 282, 14238–14242.
22. Kabaleeswaran, V., Shen, H., Symersky, J., Walker, J. E., Leslie,
A. G. W., and Mueller, D. M. (2009) Asymmetric structure of the
yeast F1 ATPase in the absence of bound nucleotides. J. Biol. Chem.
284, 10546–10551.
23. Ko, Y. H., Hong, S., and Pedersen, P. L. (1999) Chemical mechanism
of ATP synthase. J. Biol. Chem. 274, 28853–28856.
24. Weber, J., Hammond, S. T., Wilke-Mounts, S., and Senior, A. E.
(1998) Mg2þ coordination in catalytic sites of F1-ATPase. Biochem-
istry 37, 608–614.
KP2
KP1
Kb1
ꢃ
R ¼
¼
Kb1
Δh ¼ ΔHP2 - ΔHP1 ¼ ΔHb1ꢃ - ΔHb1
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