not only the symmetrically loaded capsule 10 but also 20-
0% (depending on the other components present) of an
K
D
to be 4. Six determinations with various mole fractions
4
of the azide and acetylene showed K ) 9 ( 3. The exchange
D
unsymmetrically filled capsule. This species was identified
by the addition of excess dioxane as a capsule containing
one acetylene and one dioxane molecule.
of these small guests is fast. They equilibrate on mixing;
the system is at a steady state. Perhaps the space in 11 is
better occupied or there is a weak attractive force between
the occupants. In any case, the preference for 11 is only a
few tenths of a kcal/mol.
At these concentrations, chosen for convenience of moni-
toring by NMR, the capsule is saturated. Increasing the
external concentrations of the reactants does not increase the
concentration of the heterocapsule, but it increases the rate
of the cycloaddition reaction outside. The rate inside is fixed
A new, unsymmetrical complex appeared when a mixture
of azide and acetylene were present, and it was the most
abundant species. Fortunately, its NH resonances were well
separated from those of the other capsule species (Figure 6)
and allowed clean integration and quantification of this
“
Michaelis complex.”7
at saturation, and comparing the kcat to the outside rate k
2
suffers all of the ambiguities that arise when a bimolecular
rate is compared to a unimolecular one.
The calculated concentrations inside are a matter of
3
volume: the capacity is ∼450 Å , and the two reactants enjoy
a 3.7 M engagement for a matter of seconds when they are
encapsulated. The rate inside, assuming the appropriate
-
8
orientation can be achieved, would then be ∼6 × 10
M
-
1
s , a figure larger than the initial rate actually observed.
One might well ask, why is the reaction not faster inside?
Perhaps they are positioned in a way that is not ideal for the
transition state; we have no reason to believe that the
transition state is bound better than the reactants. At these
concentrations the reaction outside the capsule is calculated
-
12
-1
to proceed at a rate of 5.4 × 10 M s , some 240 times
Figure 6. Encapsulated species in a solution of capsule 2, phenyl
azide, and phenylacetylene in mesitylene-d12. (a) NH resonances
of the capsule with acetylene and dioxane; (b) NH resonances of
capsule with azide and dioxane; (c) NH resonances of “Michaelis”
complex 11; (d) NH resonance of capsule complex 9; (e) NH
resonance of capsule complex 10; (f) NH resonances of product
complex 12; (g) ortho-protons of the phenyl rings of encapsulated
slower than inside the capsule.
The direct observation of the Michaelis complex is, to our
knowledge, unique to the case at hand. While it simplifies
the analysis, one thing is clear: the product is the best guest
in the system, gradually the capsule is filled with it, and the
reaction, slowed by product inhibition, grinds to a halt.
Overcoming the general problem of product inhibition
1,4-isomer 5 in complex 12 (see assignments in Figure 5). (A) At
t ) 0 incubating 3 (50 mM), 4 (25 mM), and capsule 2 (5 mM) in
8
remains a challenge for the future. In the meantime, the
exquisite selectivity for the extended regioisomer 5 augurs
mesitylene-d12. (B) t ) 8500 min for the same system as in (A).
(C) Encapsulation of authentic 1,4-isomer 5 with 2 in mesitylene-
well for controlling reactions within reversibly formed
d .
12
9
capsules.
Acknowledgment. We are grateful to the Skaggs Re-
search Foundation and the National Institutes of Health for
support. J.C. is a Skaggs Postdoctoral Fellow. Professors
Dmitry Rudkevich, JoAnne Stubbe, Jamie Williamson, and
Dr. Steffi K o¨ rner gave us invaluable advice.
We studied the disproportionation equilibrium of Figure
. A purely statistical distribution of the two guests predicts
5
twice as much heterocapsule 11 as either homocapsule, since
there are two ways to fill the former and only one way to
fill either of the latter (given the orientation preferences
discussed above). The effect of dioxane, the spectator guest,
was comparable on both homocapsules; i.e., no great
OL0168115
(8) For a discussion, see: Nakash, M.; Clyde-Watson, Z.; Feeder, N.;
preference for homocapsules exists. For the equilibrium K
D
Davies, J. E.; Teat, S. J.; Sanders, J. K. M. J. Am. Chem. Soc. 2000, 122,
5286-5293 and references therein.
2
)
[11] /[9][10], the statistical distribution would predict
(
9) For examples with metal-ligand capsules, see: Zeigler, M.; Brum-
aghim, J. L.; Raymond, K. N. Angew. Chem., Int. Ed. 2000, 39, 4119-
4121. Caulder, D. L.; Raymond, K. N. J. Chem. Soc., Dalton Trans. 1999,
1185-1200. Umemoto, K.; Yamaguchi, K.; Fujita, J. J. Am. Chem. Soc.
2000, 122, 7150-7151. Fujita, M.; Umemoto, K.; Yoshizawa, M.; Fujita,
N.; Kusukawa, T.; Biradha, K. Chem. Commun. 2001, 509-518.
(
7) Because both reactants form symmetrical complexes (e.g., 9 and 10)
the system shows substrate inhibition and does not obey Michaelis-Menten
kinetics; for a discussion, see: Fersht, A. Enzyme Structure and Mechanism,
nd ed.; W. H. Freeman: New York, 1985; p 114.
2
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