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:
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3
3
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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
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(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
structure of the catalytic F1 unit in a vanadate-induced transition-like
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13783.
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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´
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