Chemical double mutant cycles for the quantification of cooperativity in H-bonded complexes

Article abstract of DOI:10.1021/ja9083495

Chemical double mutant cycles have been used in conjunction with new H-bonding motifs for the quantification of chelate cooperativity in multiply H-bonded complexes. The double mutant cycle approach specifically deals with the effects of substituents, sec

Full text of DOI:10.1021/ja9083495

Published on Web 11/30/2009
Chemical Double Mutant Cycles for the Quantification of
Cooperativity in H-Bonded Complexes
Amaya Camara-Campos, Daniele Musumeci, Christopher A. Hunter,* and
Simon Turega
Krebs Institute, Department of Chemistry, UniVersity of Sheffield,
Sheffield S3 7HF, United Kingdom
Received October 1, 2009; E-mail: c.hunter@sheffield.ac.uk
Abstract: Chemical double mutant cycles have been used in conjunction with new H-bonding motifs for
the quantification of chelate cooperativity in multiply H-bonded complexes. The double mutant cycle approach
specifically deals with the effects of substituents, secondary interactions, and allosteric cooperativity on
the free energy contributions from individual H-bond sites and allows dissection of the free energy contribution
due to chelate cooperativity associated with the formation of intramolecular noncovalent interactions. Two
different doubly H-bonded motifs were investigated in carbon tetrachloride, chloroform, 1,1,2,2-tetrachlo-
roethane, and cyclohexane, and the results were similar in all cases, with effective molarities of 3-33 M
for formation of intramolecular H-bonds. This corresponds to a free energy penalty of 3-9 kJ mol-1 for
formation of a bimolecular complex in solution, which is consistent with previous estimates of 6 kJ mol-1
.
This result can be used in conjunction with the H-bond parameters, R and ꢀ, to make a reasonable estimate
of the stability constant for formation of a multiply H-bonded complex between two perfectly complementary
partners, or to place an upper limit on the stability constant expected for a less complementary system.
Introduction
systems, such as the DNA base-pair type H-bonded complexes
that have been extensively studied, a straightforward separation
The development of a quantitative understanding of molecular
interactions is the key to harnessing the potential of molecular
recognition in areas of molecular engineering such as nano-
technology and drug design.1 At the level of simple functional
group interactions in nonpolar solvents, the principles are
reasonably well-established: the more polar are the functional
groups, the stronger are the interactions.1,2 However, in systems
that feature multiple interaction sites, it is more difficult to make
predictions. In general, the more interactions there are, the more
stable is the complex, but the extent to which cooperativity
between multiple interaction sites is expressed is not well-
understood at a quantitative level.3 This type of chelate
cooperativity is experimentally quantified by the effective
molarity, EM, which is a measure of the increased probability
of intramolecular contacts relative to intermolecular contacts.4
However, estimates of effective molarities for noncovalent
intramolecular interactions span over 10 orders of magnitude,
so it is hazardous to try to make quantitative predictions of the
binding properties of cooperative systems that are common in,
for example, supramolecular self-assembly, macromolecular, and
biomolecular structures.5
of the contributions to binding is not possible: there are
secondary electrostatic interactions between the H-bonding
functional groups that are very close in space, and this
contribution is difficult to measure directly; there are through-
bond polarization effects that make it practically impossible to
identify a good reference system, where a single isolated H-bond
can be characterized; if an appropriate reference complex that
makes only one H-bond can be identified, the stability of this
complex is unlikely to be sufficient to allow accurate determi-
nation of the association constant.6 These problems can be
avoided in carefully designed systems that feature very strong
binding interactions located at well-defined and well-separated
sites, and so chelate cooperativity can be quantified more
(3) (a) Shinkai, S.; Ikeda, M.; Sugasaki, A.; Takeuchi, M. Acc. Chem.
Res. 2001, 34, 494–503. (b) Badjic, J. D.; Nelson, A.; Cantrill, S. J.;
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10, 1023–1032. (l) Tobey, S. L.; Anslyn, E. V. J. Am. Chem. Soc.
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Schmidtchen, F. P. Org. Lett. 2006, 8, 2329–2332.
One of the problems with experimental quantification of
chelate cooperativity is that it is necessarily found in relatively
complex systems, where there are multiple noncovalent interac-
tions that are difficult to dissect. Even for apparently simple
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18518 J. AM. CHEM. SOC. 2009, 131, 18518–18524
10.1021/ja9083495  2009 American Chemical Society

Quantification of Cooperativity in H-Bonded Complexes
A R T I C L E S
Figure 1. Proposed structures of complexes for studying H-bond cooperativity: (a) ANAN ·DD and (b) AOAO ·DD (R ) 2-ethylhexyl). Two views of the
molecular mechanics structures obtained by energy minimization using the OPLS force-field in Macromodel are also shown.10
routinely in complexes that are bound via metal-ligand
interactions.7 Here, we describe a new H-bond motif that is
designed to allow accurate quantification of chelate cooperativity
in a H-bonded complex using chemical double mutant cycles.
changes in conformational entropy on binding.9 The separation
of the H-bond acceptor sites on 1,8-diazabiphenylene and the
bisamide differs slightly, and molecular mechanics calculations
suggest that there are differences between the complementarity
of the two AA·DD H-bonding motifs. 1,8-Diazabiphenylene
can make two H-bonds with resorcinol in a planar complex
(Figure 1a), whereas the bisamide has to adopt a tilted geometry
to make two interactions (Figure 1b). In addition, the bisamide
has more conformational flexibility than 1,8-diazabiphenylene,
which could affect cooperativity between the two binding sites.
The chelate cooperativity in these systems can be quantified
by comparing the stability of the doubly H-bonded complexes
with a set of reference complexes that feature only single point
binding interactions. Pyridine (designated AN), monoamide (AO),
and 4-t-butylphenol (D) were used as monofunctional reference
compounds for 1,8-diazabiphenylene (ANAN), bisamide (AOAO),
and resorcinol (DD), respectively (Figure 2). Compounds D,
DD, AN, and ANAN are commercially available, and the amides
were synthesized in one-step reactions (see Supporting Informa-
tion). The chemical double mutant cycle in Figure 3 illustrates
the use of the reference compounds to determine the free energy
contribution associated with the intramolecularity of the second
H-bond in the doubly H-bonded complexes.11 Changing the
substituents on the aromatic rings affects the H-bonding
properties of the key functional groups. For example, t-butyl
substituents are known to perturb the H-bond properties of
Results and Discussion
Approach. Two different types of complex were chosen for
investigation (Figure 1). By using a DD·AA H-bonding motif
and molecules that contain no additional H-bonding sites,
complications associated with self-interaction are minimized.
Although the oxygen of phenol is a H-bond acceptor, it is not
a very good one (ꢀ ) 2.7),8 so self-association is negligible at
millimolar concentrations. Phenol is one of the strongest H-bond
donor functional groups (R ≈ 4), and amides and pyridines are
very good H-bond acceptors (ꢀ ≈ 8 and 7, respectively), which
ensures that reference complexes featuring a single H-bond will
be sufficiently stable to measure accurate association constants.2
The complexes in Figure 1 both feature two H-bonding
interactions that are separated by sufficient distance to ensure
that the secondary electrostatic interactions that usually com-
plicate the analysis of multiply H-bonded complexes are
minimized.6 The components of the complexes all have limited
torsional flexibility, which should minimize contributions from
(5) (a) Page, M. I.; Jencks, W. P. Proc. Natl. Acad. Sci. U.S.A. 1971, 68,
1678–1683. (b) Bo¨hm, H.-J. J. Comput.-Aided Mol. Des. 1994, 8, 243–
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H.-J. Chem.-Eur. J. 1996, 2, 1446–1452. (d) Beijer, F. H.; Sijbesma,
R. P.; Kooijman, H.; Spek, A. L.; Meijer, E. W. J. Am. Chem. Soc.
1998, 120, 6761–6769.
(9) Searle, M. S.; Williams, D. H. J. Am. Chem. Soc. 1992, 114, 10690–
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(10) Mohamadi, F.; Richard, N. G. J.; Guida, W. C.; Liskamp, R.; Lipton,
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Chem. 1990, 11, 440.
(11) (a) Cockroft, S. L.; Hunter, C. A. Chem. Soc. ReV. 2007, 36, 172–
188. (b) Carver, F. J.; Hunter, C. A.; Jones, P. S.; Livingstone, D. J.;
McCabe, J. F.; Seward, E. M.; Tiger, P.; Spey, S. E. Chem.-Eur. J.
2001, 7, 4854–4862. (c) Carver, F. J.; Hunter, C. A.; Livingstone,
D. J.; McCabe, J. F.; Seward, E. M. Chem.-Eur. J. 2002, 8, 2848–
2859. (d) Hunter, C. A.; Low, C. M. R.; Rotger, C.; Vinter, J. G.;
Zonta, C. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 4873–4876. (e)
Cockroft, S. L.; Hunter, C. A.; Lawson, K. R.; Perkins, J.; Urch, C. J.
J. Am. Chem. Soc. 2005, 127, 8594–8595. (f) Cockroft, S. L.; Perkins,
J.; Zonta, C.; Adams, H.; Spey, S. E.; Low, C. M. R.; Vinter, J. G.;
Lawson, K. R.; Urch, C. J.; Hunter, C. A. Org. Biomol. Chem. 2007,
5, 1062–1080.
(7) (a) Taylor, P. N.; Anderson, H. L. J. Am. Chem. Soc. 1999, 121, 11538–
11545. (b) Screen, T. E. O.; Thorne, J. R. G.; Denning, R. G.; Bucknall,
D. G.; Anderson, H. L. J. Mater. Chem. 2003, 13, 2796–2808. (c)
Camara-Campos, A.; Hunter, C. A.; Tomas, S. Proc. Natl. Acad. Sci.
U.S.A. 2006, 103, 3034–3038. (d) Baldini, L.; Ballester, P.; Casnati,
A.; Gomila, R. M.; Hunter, C. A.; Sansone, F.; Ungaro, R. J. Am.
Chem. Soc. 2003, 125, 14181–14189. (e) Chi, X. L.; Guerin, A. J.;
Haycock, R. A.; Hunter, C. A.; Sarson, L. D. Chem. Commun. 1995,
2563–2565.
(8) Abraham, M. H.; Grellier, P. L.; Prior, D. V.; Morris, J. J.; Taylor,
P. J. J. Chem. Soc., Perkin Trans. 2 1990, 521–529.
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A R T I C L E S
Camara-Campos et al.
This double mutant cycle differs from those that we have
used previously to quantify functional group interactions. Here,
the chemical mutations correspond to removal of the covalent
connectivity between interaction sites rather than removal of
the interactions sites themselves. Thus, the double mutant state
D is two unconnected 1:1 complexes rather than a single
complex (Figure 3), and the free energy of state D, ∆G°D, is
twice the free energy for formation of the singly H-bonded A·D
complex, 2∆G°(A·D). The double mutant cycle measurement
of cooperativity, ∆∆G°, is given by eq 1.11
∆∆Go ) ∆GoA - ∆GBo - ∆GCo + ∆GDo
) ∆Go(AA·DD) - ∆Go(AA·D2) - ∆Go(A2·DD) +
(1)
2∆Go(A·D)
The number of functional group interactions in each of the
states A, B, C, and D in Figure 3 is the same, but the
stoichiometries differ, and so ∆∆G° is actually a measure of
the effective molarity (EM) for the intramolecular interaction
in the doubly H-bonded complex, rather than the strength of
the intramolecular H-bond. Equation 1 can be rewritten in terms
of association constants for the four different states, A, B, C,
and D in Figure 3, to give eq 2, which we can recognize as the
conventional definition of EM.4
1
Figure 2. Compound used in H NMR titrations and the proton labeling
scheme.
K(AA·DD)K2(A·D)
K(AA·D2)K(A2·DD)
KAKD
o
2EM )
)
) e-∆∆G /RT (2)
KBKC
where KD is K2(A·D), because there are two 1:1 complexes in
this state, and the statistical factor of 2 is applied to the effective
molarity to account for the degeneracy of the two interactions
in the AA·DD complex.
Binding Studies in Carbon Tetrachloride. The stability
constants for all eight complexes were measured in carbon
Figure 3. Chemical double mutant cycle to quantify the free energy benefit
associated with the intramolecularity of the second H-bond in the AA·DD
complex, state A.
1
1
tetrachloride using H NMR titration experiments. H NMR
dilution experiments indicated that self-association is not
significant at the concentrations used in these experiments for
any of the compounds. For the A·D and AA·DD complexes,
the titration data fit well to a 1:1 binding isotherm. The behavior
of the A2 ·DD and AA·D2 complexes is more complicated, but
the data could be fit to a 2:1 binding isotherm in all cases. The
association constants and limiting complexation-induced changes
phenols: for phenol R ) 3.8, for 4-t-butylphenol R ) 3.6, and
for 2-t-butylphenol R ) 3.4.12 The reference complexes allow
us to quantify these effects in the system of interest and thereby
measure their contribution to the observed stability of the
AA·DD complex. Thus, the difference between the stabilities
of complexes A·D and A2 ·DD can be used to measure the
difference between the H-bond donor properties of the phenol
and resorcinol. The difference between the stabilities of
complexes AO ·D and AOAO ·D2 can be used to measure the
difference between the H-bond acceptor properties of the mono-
and bisamide. These comparisons also quantify any allosteric
cooperativity present in the complexes (see ref 13 for a
discussion of the differences between allosteric and chelate
cooperativity).4 For example, binding at one hydroxyl on
resorcinol (DD) may polarize the other hydroxyl group and
cause changes in the strength of the second H-bond. The
magnitude of this allosteric effect is a contribution to the
difference between the stability of A·D and AA·D2, and so it
does not perturb the measurement of chelate cooperativity. The
double mutant cycle in Figure 3 quantifies and eliminates all
of these secondary and allosteric effects to obtain a direct
measurement of the free energy benefit associated with a
cooperative intramolecular H-bond interaction.
1
in H NMR chemical shift (∆δ) are presented in Table 1. The
amide and pyridine complexes exhibited quite different behavior
and will be discussed separately.
For the amide system, the H-bond acceptor was titrated into
the H-bond donor (which was the fixed concentration host),
except in the case of the AOAO ·D2 complex, where the solubility
of phenol is sufficient to be used as the titrant (or guest). The
limiting ∆δ values for both host and guest were obtained by
extrapolation of the binding isotherm, and these data provide
experimental evidence for the structures of the complexes in
solution. In all cases, there is a large downfield change in the
chemical shift of the signal due to the OH protons (>+1 ppm)
indicative of H-bonding interactions. The signals due to the
aromatic protons on the amide ring show relatively small
changes in chemical shift, while the ∆δ values for the aromatic
protons of D and DD are small and negative. In complex
AOAO ·DD, proton o shows a particularly large change in
chemical shift, which may be due to the constrained geometry
enforced by the formation of two H-bonds leading to larger
aromatic ring current shifts. The three-dimensional solution
structure of this complex was determined using the experimental
∆δ values and the program Shifty that we have described
(12) Abraham, M. H.; Grellier, P. L.; Prior, D. V.; Duce, P. P.; Morris,
J. J.; Taylor, P. J. J. Chem. Soc., Perkin Trans. 2 1989, 699–711.
(13) Hunter, C. A.; Anderson, H. L. Angew. Chem., Int. Ed. 2009, 40, 2678–
2686.
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Quantification of Cooperativity in H-Bonded Complexes
A R T I C L E S
a
1
Table 1. Association Constants and Limiting Complexation-Induced Changes in Chemical Shift from H NMR Titrations in CCl4 at 295 K
global
microscopic
∆δ (ppm)
complex
∆G° (kJ mol-1
)
K
K1
K2
OH
o
m
c
a
b
AO ·D
-11.3 ( 0.3
-7.9 ( 0.6
-16.1 ( 0.6
-18.6 ( 0.3
-13.5 ( 0.6
-17.2 ( 0.6
-9.4 ( 0.3
-9.5 ( 0.6
-18.7 ( 0.6
-19.5 ( 0.3
-7.6 ( 0.6
-15.2 ( 0.6
100 M-1
50 M-1
100 M-1
25 M-1
3.7
3.7
2.3
2.4
1.5
3.8
2.7
0.5
1.4
3.2
3.6
4.4
-0.1
-0.2
-0.2
-0.6
-0.2
0.2
-0.1
0.0
-0.7
0.7
0.2
-0.2
-0.2
-0.2
-0.2
-0.1
-0.3
-0.1
-0.0
-0.8
-0.1
0.0
0.0
0.1
0.0
0.0
0.1
0.3
0.2
0.0
0.1
0.1
0.1
-0.1
0.0
0.1
0.0
0.2
AOAO ·D
AOAO ·D2
AOAO ·DD
AO ·DD
0.1
0.1
0.3
710 M-2
1950 M-1
500 M-1
1100 M-2
47 M-1
27 M-1
4 M-1
1950 M-1
250 M-1
AO2 ·DD
AN ·D
47 M-1
48 M-1
0.2
0.0
0.1
0.2
0.3
0.0
ANAN ·D
ANAN ·D2
ANAN ·DD
AN ·DD
96 M-1
2050 M-2
2850 M-1
44 M-1
43 M-1
22 M-1
2850 M-1
22 M-1
0.2
0.2
-0.3
0.2
0.2
-0.4
AN2 ·DD
490 M-2
0.3
-0.1
a All titrations were repeated at least three times. K is the global association constant for formation of the complex from its components. For systems
that can form both 1:1 and 2:1 complexes, K1 is the statistically corrected microscopic association constant for formation of the 1:1 complex from its
components, and K2 is the statistically corrected microscopic association constant for formation of the 2:1 complex from the 1:1 complex. The global
association constants for complexes AOAO ·D, AO ·DD, ANAN ·D, and AN ·DD are quoted as macroscopic values that have not been statistically
corrected, that is, 2K1. For these complexes, free energies are quoted using the statistically corrected microscopic association constants K1. Errors in the
∆δ values for the host are (0.1 ppm, but the errors for the guest signals are larger (values in italics).
Figure 4. (a) Structure of the AOAO ·DD complex obtained from Shifty
using the experimental complexation-induced changes in 1H NMR chemical
Figure 5. (a) Changes in the 1H NMR chemical shift of the signal due to
shift. The experimental ∆δ values are shown with the calculated values
proton o in DD on addition of AO. The line shows the best fit to a 2:1
from the structure optimization in brackets. The intermolecular orientation
binding isotherm. (b) Changes in the 1H NMR chemical shift of the signals
and position and the two torsion angles indicated were allowed to vary
due to protons c (black), a (blue), and b (red) in AOAO on addition of D.
during the structure optimization process.14 (b) Overlay of the structures
The lines show the best fit to a 2:1 binding isotherm.
obtained from Shifty (gray) and from molecular mechanics calculations using
the OPLS force-field in Macromodel (blue).10
the bisamide AOAO, and this is the reason for the large negative
∆δ value for this proton. The structures of the other complexes
were also investigated using this method, but the singly
previously.14 The calculation converged to a well-defined
structure, and the results are shown in Figure 4. The experi-
mental structure is in close agreement with the structure
H-bonded complexes are less constrained, and a large number
calculated using molecular mechanics. The tilted geometry
of different H-bonded structures are consistent with the experi-
mental data in all cases.
means that proton o of DD is located over the aromatic ring of
For the 2:1 complexes formed by the amide systems, the
(14) (a) Hunter, C. A.; Packer, M. J. Chem.-Eur. J. 1999, 5, 1891–1897.
titration data show clear evidence that the two binding events
(b) Packer, M. J.; Zonta, C.; Hunter, C. A. J. Magn. Reson. 2003,
are different (Figure 5). The changes in chemical shift for the
162, 102–112. (c) Gardner, M.; Guerin, A. J.; Hunter, C. A.;
signal due to proton o in DD suggest a difference in structure
between AO ·DD and AO2 ·DD. At the beginning of the titration,
the signal moves upfield, which is consistent with the behavior
of this signal in all of the other complexes (Table 1), but in the
second phase of the titration, the signal moves downfield (Figure
Michelsen, U.; Rotger, C. New J. Chem. 1999, 309–316. (d) Hunter,
C. A.; Low, C. M. R.; Packer, M. J.; Spey, S. E.; Vinter, J. G.;
Vysotsky, M. O.; Zonta, C. Angew. Chem., Int. Ed. 2001, 40, 2678–
2686. (e) Spitaleri, A.; Hunter, C. A.; McCabe, J. F.; Packer, M. J.;
Cockroft, S. L. CrystEngComm 2004, 6, 489–493. (f) Hunter, C. A.;
Spitaleri, A.; Tomas, S. Chem. Commun. 2005, 3691–3693.
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A R T I C L E S
Camara-Campos et al.
Table 2. Calculated and Experimental Association Constants for
quantify these effects and eliminate any contribution to the value
of EM obtained using eq 2.
Formation of H-Bonded Complexes in CCl4 at 295 K
a
complex
R
ꢀb
log Kpred
log Kexpt
The behavior of the pyridine system was much simpler.
Titrations were carried out with the H-bond acceptor as the host,
except in the case of the AN2 ·DD complex. No biphasic behavior
was observed in any of the titrations, and systems with a 2:1
stoichiometry gave simple binding isotherms with similar
microscopic association constants for the first and second
binding event. The OH signal shows large downfield shifts in
all of the complexes, indicative of H-bonding interactions. The
stability constants in Table 1 show that there are no significant
substituent effects on the H-bond interactions in complexes
involving ANAN. The microscopic association constants for
formation of ANAN ·D from ANAN and D (48 M-1) and for
formation of ANAN ·D2 from ANAN ·D and D (43 M-1) are the
same as the association constant for formation of the reference
AN ·D complex (47 M-1). The microscopic association constants
for formation of AN ·DD from AN and DD (22 M-1) and for
formation of AN2 ·DD from AN and AN ·DD (22 M-1) are 2-fold
lower than the association constant for formation of the reference
AN ·D complex (47 M-1). This substituent effect is very similar
to that observed for DD in the amide complexes. These systems
therefore provide ideal cases for the determination of EM using
the double mutant cycle in Figure 3 and eq 2, which corrects
for the small substituent effects on the H-bond properties of
the functional groups involved.
AO ·D
3.6
3.6
3.6
3.4
3.4
3.4
3.6
3.6
3.6
3.4
3.4
3.4
8.0
7.0
7.0
7.0
8.0
8.0
7.0
7.0
7.0
7.0
7.0
7.0
1.8
1.4
2.8
3.4
1.5
3.1
1.4
1.4
2.8
3.4
1.2
2.4
2.0
1.4
2.9
3.3
2.4
3.0
1.7
1.7
3.3
3.5
1.3
2.7
AOAO ·D
AOAO ·D2
AOAO ·DD
AO ·DD
AO2 ·DD
AN ·D
ANAN ·D
ANAN ·D2
ANAN ·DD
AN ·DD
AN2 ·DD
a
H
These values were derived from literature values of R2 using the
H
relationship R ) 4.1(R2 + 0.33). The value for D is based on the
literature data for this compound, and the value for DD is based on the
value for 2-t-butylphenol. The R values for phenol and 3-methoxyphenol
are identical, so we assume that the resorcinol hydroxyl groups have
little effect on each other.12 b These values were derived from literature
H
H
values of ꢀ2 using the relationship ꢀ ) 10.3 (ꢀ2 + 0.06). The value
for AO is based on the literature data for N,N-dicyclohexyl benzamide,
and the value for AOAO is based on the value for N,N-dicyclohexyl
4-nitrobenzamide, which probably exaggerates the substituent effect.12
The values for AN and ANAN are both based on the literature data for
pyridine.12 Data have not been reported for a suitable analogue of
ANAN, but the minimum on the AM1 molecular electrostatic potential
surface of ANAN is practically identical to that found for AN, which
suggests that the substituent effect is small in this compound. The
Evaluation of Cooperativity. Using eq 2, the value of EM
for the intramolecular interaction in the doubly H-bonded
complexes AA·DD can be estimated at 12 ( 5 and 3 ( 1 M
for the amide and pyridine systems, respectively. These values
correspond to a free energy contribution of -6 and -3 ((1) kJ
mol-1 arising from the intramolecular nature of the second
H-bond interaction. Despite the differences in structure shown
in Figure 1, the magnitude of the chelate cooperativity is similar
in the two systems and consistent with the value of 6 kJ mol-1
that we have proposed as the free energy penalty associated
with restricting biomolecular motion on formation of a 1:1
H-bonded complex.2 A free energy penalty of 6 kJ mol-1 for
an intermolecular interaction implies that for cooperative
intramolecular interactions in well-organized complementary
molecular assemblies the value of EM should be of the order
10 M, as observed in the complexes reported here.
experimental results in Table
1 confirm that the H-bond acceptor
properties of ANAN and AN are practically identical.
5a). The association constant for the first binding event (K1 )
250 M-1) is significantly larger than that for the second binding
event (K2 ) 4 M-1). The value K1 is also significantly larger
than K(AO ·D), which suggests that there are additional inter-
molecular interactions, for example, aromatic interactions, in
the AO ·DD complex that are lost again on formation of the
AO2 ·DD complex. This would account for the increase in K1
and decrease in K2. In the titration of AOAO with D, the signals
due to protons a and b first move downfield then upfield during
the titration, indicating that the AOAO · D and AOAO · D2
complexes also have different structural properties (Figure 5b).
However, in this case, there is no difference in the microscopic
association constants for the two binding events (K1 ≈ K2).
Although this behavior complicates analysis of the titration data,
the peculiarities in the behavior of the 1:1 complexes, AO ·DD
and AOAO ·D, do not affect the double mutant cycle and the
determination of EM, which depends only on the overall stability
of the 2:1 complexes, AO2 ·DD and AOAO ·D2 (Figure 3, eq 2).
The stability constants in Table 1 show that there are
significant substituent effects on the H-bond interactions in these
systems. The microscopic association constants for formation
of AOAO ·D from AOAO and D (25 M-1) and for formation of
AOAO ·D2 from AOAO ·D and D (27 M-1) are both 4-fold lower
than the association constant for formation of the reference
AO ·D complex (100 M-1). This is due to the electron-
withdrawing amide substituents that reduce the H-bond acceptor
ability of the carbonyl groups in AOAO as compared to AO. The
microscopic association constant for formation of each H-bond
in the AO2 ·DD complex (ꢀK ) 33 M-1) is 3-fold lower than
the association constant for formation of the reference AO ·D
complex (100 M-1). This substituent effect is consistent with
the experimentally measured H-bond donor properties of phenol
and 2-t-butyphenol, which indicate that DD is likely to be a
slightly poorer H-bond donor than D (see Table 2). However,
the double mutant cycle approach is specifically designed to
We have previously shown that the stability of an intermo-
lecular complex that contains a single H-bond interaction can
be estimated reasonably well by eq 3.15
∆Go ) -(R - RS)(ꢀ - ꢀS) + 6 kJ mol-1
(3)
where R and ꢀ are the H-bond parameters for the functional
groups that form the H-bond in the complex, and RS and ꢀS are
the corresponding parameters for the solvent.
The results for the doubly H-bonded complexes above suggest
that this equation can be extended in a straightforward way to
estimate the stability of a H-bonded complex that contains
multiple interaction sites (eq 4).
∆Go ) -
(R - R )(ꢀ - ꢀ ) + 6(N - 1) kJ mol-1
S S
∑
sites
(4)
where N is the number of molecules involved in the complex,
R and ꢀ are the functional group H-bond parameters for the
(15) Cook, J. L.; Hunter, C. A.; Low, C. M. R.; Perez-Velasco, A.; Vinter,
J. G. Angew. Chem., Int. Ed. 2007, 46, 3706–3709.
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18522 J. AM. CHEM. SOC. VOL. 131, NO. 51, 2009

Quantification of Cooperativity in H-Bonded Complexes
A R T I C L E S
Table 3. Association Constants and Cooperativity Parameters
a
1
from H NMR Titrations in Various Solvents at 295 K
solvent
complex
K
∆G° (kJ mol-1
)
∆∆G° (kJ mol-1
)
EM (M)
CCl4
AN ·D
47 M-1
-9.4 ( 0.3
ANAN ·DD 2850 M-1 -19.5 ( 0.3 -3 ( 1
3
AN2 ·DD
ANAN ·D2 2050 M-2 -18.7 ( 0.6
AN ·D 130 M-1 -11.9 ( 0.3
490 M-2 -15.2 ( 0.6
C6H12
ANAN ·DD 7400 M-1 -21.9 ( 0.4 -9 ( 1
33
12
20
AN2 ·DD
8500 M-2 -22.2 ( 0.5
220 M-2 -13.2 ( 0.4
ANAN ·D2
C2H2Cl4 AN ·D
24 M-1
-7.8 ( 0.3
ANAN ·DD 240 M-1 -13.4 ( 0.4 -6 ( 1
AN2 ·DD
ANAN ·D2
AN ·D
120 M-2 -11.7 ( 0.3
50 M-2
25 M-1
-9.6 ( 0.3
-7.8 ( 0.2
CHCl3
ANAN ·DD 410 M-1 -14.8 ( 0.5 -7 ( 1
Figure 6. Correlation between the association constant estimated using
eq 4 (Kpred) and the experimental values for the eight complexes in Table
1 (Kexpt), showing the data for the amide complexes in gray and the pyridine
complexes in black. The line corresponds to y ) x. Excluding the anomalous
AO ·DD complex, the correlation coefficient between the calculated and
experimental values of log K is r2 ) 0.96.
AN2 ·DD
90 M-2 -11.0 ( 0.3
67 M-2 -10.3 ( 0.3
ANAN ·D2
a All titrations were repeated at least three times. K is the global
association constant for formation of the complex from its components.
are generally larger in cyclohexane and smaller in tetrachloro-
ethane and chloroform. In most cases, there are small substituent
effects, which are corrected for in the double mutant cycle, but
in cyclohexane, the ANAN ·D2 complex showed an anomalously
low association constant as compared to the reference complex
AN ·D: the microscopic association constant for formation each
H-bond in the ANAN ·D2 complex (ꢀK ) 15 M-1) is 10-fold
lower than the association constant for formation of the reference
AN ·D complex (130 M-1). This result is responsible for the
higher value of EM found in cyclohexane. Although the values
of EM in Table 3 show some variation, they are similar in all
four solvents, and given the errors and assumptions involved
in these measurements, any further interpretation of the differ-
ences is not warranted. We conclude that for this range of
solvents, there are no substantial solvent effects on chelate
cooperativity, and the free energy benefit associated with the
interactions formed in the complex, RS and ꢀS are the corre-
sponding parameters for the solvent, and the sum represents
the sum over all intermolecular interaction sites.
In practice, factors that are known to impinge on effective
molarities are likely to reduce the observed stability of a
complex as compared to the theoretical value given by eq 4.
Thus, flexible molecules that lose conformational degrees of
freedom on complexation will form less stable complexes, as
will systems where there is conformational strain or a mismatch
in the geometry of the binding sites.16 Nevertheless, eq 4 serves
as a useful guide to the association constant that one can expect
to achieve in a well-designed system. The eight complexes
discussed above present different stoichiometries and numbers
of interaction sites and serve as a simple test of eq 4. The H-bond
parameters used for the functional groups involved are listed
in Table 2. As discussed above, there are substituent effects on
the H-bond properties of the functional groups, and so the
H-bond parameters quoted in Table 2 are based on analogous
literature compounds for which experimental data are available.
The agreement between the association constants estimated using
eq 4 and the experimental association constants is rather good
in most cases (Table 2, Figure 6). The only major outlier is the
AO ·DD complex, which is the system that displays anomalous
intramolecularity of a H-bond is between 3 and 9 kJ mol-1
.
Note that this free energy contribution, -RT ln(EM), is different
from the net free energy benefit associated with formation of
the intramolecular H-bond, -RT ln(K EM). For the systems
studied here, the complexes featuring intramolecular H-bonds
are 6-12 kJ mol-1 more stable than the corresponding singly
H-bonded complexes.
1
behavior in the H NMR titration, as discussed above (K1 .
Conclusions
K2). The experimental value of the association constant for this
complex is an order of magnitude larger than that predicted by
eq 4, which is indicative of the additional aromatic interactions
that stabilize this complex.
This article introduces the use of chemical double mutant
cycles for the quantification of chelate cooperativity in multiply
H-bonded complexes. The approach specifically deals with the
effects of substituents, secondary interactions, and allosteric
cooperativity on the free energy contributions from individual
H-bond sites and allows dissection of the free energy contribu-
tion due to chelate cooperativity associated with the formation
of intramolecular noncovalent interactions. Two different doubly
H-bonded motifs and four different organic solvents were
investigated, and the results were similar in all cases. The
effective molarity for formation of intramolecular H-bonds is
in the range 3-33 M for these systems. This corresponds to a
free energy penalty of 3-9 kJ mol-1 for formation a bimolecular
complex in solution, which is consistent with previous estimates
of 6 kJ mol-1.2 The H-bond motifs in this work were chosen,
because the molecular components are geometrically comple-
mentary and relatively rigid, which minimizes the effects of
geometric strain and loss of conformational entropy on binding.
Solvent Effects. To investigate the influence of the solvent
on the cooperativity observed in the doubly H-bonded com-
plexes, a further set of experiments was carried out in cyclo-
hexane, 1,1,2,2-tetrachloroethane, and chloroform. Because of
the complications and structural complexity encountered in
titrations with the amide system in carbon tetrachloride, only
the pyridine system was studied. The behavior of the complexes
1
in the H NMR titrations was very similar to that observed in
carbon tetrachloride, and the results are collected in Table 3.
As compared to carbon tetrachloride, the association constants
(16) (a) Bruice, T. C.; Lightstone, F. C. Acc. Chem. Res. 1999, 32, 127–
136. (b) Cacciapaglia, R.; Di Stefano, S.; Mandolini, L. Acc. Chem.
Res. 2004, 37, 113–122. (c) Kirby, A. AdV. Phys. Org. Chem. 1980,
17, 183.
9
J. AM. CHEM. SOC. VOL. 131, NO. 51, 2009 18523

A R T I C L E S
Camara-Campos et al.
analyzed using purpose written software. This allowed calculation
of the association constant for all of the complexes. Dilution studies
in CCl4 indicated that aggregation was insignificant at the concen-
trations used. However, dimerization of D was taken into account
to fit the data for complex ANAN ·D2.18 Dimerization does not affect
the value of the association constant, but the chemical shift of the
OH proton changes dramatically at high concentrations, and this
affects the guest limiting changes in chemical shift.
NMR Structure Determination. NMR structure determinations
were carried out using the Shifty software described in detail
elsewhere.15 The molecules were built in XED 2.8 using standard
bond lengths and angles and were energy minimized.19 A genetic
algorithm was used to optimize the conformation of the complex
so that the calculated ∆δ values matched the experimental values
as closely as possible. The conformational search allowed inter-
molecular translations of (5 Å and intermolecular rotations of
(180°, as well as intramolecular torsional changes of (180° for
the bonds highlighted in Figure 4. The van der Waal clashes were
penalized at distances less than 2 Å for intermolecular clashes and
1 Å for intramolecular clashes for non-hydrogen atoms. In all cases,
20 different runs using random starting points were carried out.
All solutions with rmsd values less than 0.02 ppm were collected.
Each run was carried out in five steps, progressively reducing each
dimension of the search space by a factor of 2. For each step, the
population size was set to 500 and number of generations to 1000.
Each calculation (20 runs) took about 6 h on a DELL-Linux cluster
with 12 dual processor INTEL Pentium IV 3.0 GHz nodes.
In addition, the H-bonding sites are sufficiently well-separated
to avoid the complications of secondary electrostatic interactions.
Thus, the effective molarities for these systems are likely to be
close to the upper limit for multiply H-bonded architectures and
are significantly higher than the values that we reported recently
for some related but more flexible complexes.17 Used in
conjunction with the H-bond parameters, R and ꢀ, the free
energy penalty of 6 kJ mol-1 for formation of a bimolecular
complex for perfectly complementary intramolecular interactions
can be used to make a reasonable estimate of the stability
constant for formation of a multiply H-bonded complex.
Experimental Section
1
1H NMR Titrations. H NMR titrations were carried out by
preparing a 3 mL sample of the host at known concentration
(0.1-10 mM) in CCl4, cyclohexane, 1,1,2,2-tetrachloroethane-d2,
or chloroform-d. For the nondeuterated solvents, CCl4 and cyclo-
hexane, a capillary with D2O was used inside the NMR tube as a
lock signal, and a solvent suppression pulse sequence was used in
the cyclohexane experiments. 0.6 mL of the host solution was
1
removed, put in the NMR tube, and a H NMR spectrum was
recorded. An accurately weighed sample of the guest was dissolved
in 2 mL of the host solution (so that the concentration of host
remained constant during the titration). The concentration of guest
was 10-100 times larger than that of host. Aliquots of the guest
solution were added successively to the NMR tube containing the
1
host solution, and the H NMR spectrum was recorded after each
Acknowledgment. We thank the EPSRC for funding.
addition. Changes in chemical shift for the proton signals were
Supporting Information Available: Synthetic details. This
material is available free of charge via the Internet at http://
pubs.acs.org.
(17) Hunter, C. A.; Ihekwaba, N.; Misuraca, M. C.; Segarra-Maset, M. D.;
Turega, S. M. Chem. Commun. 2009, 3964–3966.
(18) Hunter, C. A.; Jones, P. S.; Tiger, P.; Tomas, S. Chem.-Eur. J. 2002,
8, 5435–5446.
(19) Vinter, J. G. J. Comput.-Aided Mol. Des. 1994, 8, 653–668.
JA9083495
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18524 J. AM. CHEM. SOC. VOL. 131, NO. 51, 2009