Computational and experimental studies of (2,2)-Bis(indol-1-yl- methyl)acetate suggest the importance of the hydrophobic effect in aromatic stacking interactions

Article abstract of DOI:10.1021/ja9828410

To understand the driving forces of aromatic stacking interactions in water, we have performed conformational searches, molecular dynamics simulations, potential of mean force (PMF) and free energy perturbation (FEP) calculations, syntheses, and NMR studies on sodium (2,2)-bis(indol-1-yl- methyl)acetate (1), sodium 3-indol-1-yl-2-methyl-propionate (2), and sodium 3-indol-1-yl-propionate (3). The conformational searches on 1 revealed that the isobutyric acid linker of 1 allows the molecule to adopt the tilted T- shaped stacked, off-center stacked, face-to-face stacked, and nonstacked conformations in a vacuum. The PMF and FEP calculations suggested that the most thermodynamically stable conformers in water are the tilted T-shaped stacked and nonstacked conformers. Independent NMR spectroscopic studies of 1-3 revealed that both the tilted T-shaped stacked and nonstacked conformers are populated in D₂O and in d₆-DMSO, and they are in a rapid equilibrium. Furthermore, the NMR studies found (i) a larger population of the tilted T, shaped stacked conformation of 1 at 22 °C in D₂O than in d₆-DMSO and (ii) more different populated stacked conformations of 1 at 60 °C in D₂O than in d₆-DMSO. One would expect larger populations of the stacked conformations in d₆-DMSO, whose dielectric constant is smaller than that of water, if the electrostatic interaction were the only driving force of the aromatic stacking interactions. The results, therefore, suggest that the hydrophobic effect plays an important role in the stacking interaction of 1 in water.

Full text of DOI:10.1021/ja9828410

J. Am. Chem. Soc. 1999, 121, 1717-1725
1717
Computational and Experimental Studies of
(2,2)-Bis(indol-1-yl-methyl)acetate Suggest the Importance of the
Hydrophobic Effect in Aromatic Stacking Interactions
†
‡
Yuan-Ping Pang, Jennifer L. Miller, and Peter A. Kollman*
Contribution from the Department of Pharmaceutical Chemistry, School of Pharmacy,
UniVersity of California, San Francisco, California 94143
ReceiVed August 10, 1998
Abstract: To understand the driving forces of aromatic stacking interactions in water, we have performed
conformational searches, molecular dynamics simulations, potential of mean force (PMF) and free energy
perturbation (FEP) calculations, syntheses, and NMR studies on sodium (2,2)-bis(indol-1-yl-methyl)acetate
(1), sodium 3-indol-1-yl-2-methyl-propionate (2), and sodium 3-indol-1-yl-propionate (3). The conformational
searches on 1 revealed that the isobutyric acid linker of 1 allows the molecule to adopt the tilted T-shaped
stacked, off-center stacked, face-to-face stacked, and nonstacked conformations in a vacuum. The PMF and
FEP calculations suggested that the most thermodynamically stable conformers in water are the tilted T-shaped
stacked and nonstacked conformers. Independent NMR spectroscopic studies of 1-3 revealed that both the
tilted T-shaped stacked and nonstacked conformers are populated in D2O and in d6-DMSO, and they are in a
rapid equilibrium. Furthermore, the NMR studies found (i) a larger population of the tilted T-shaped stacked
conformation of 1 at 22 °C in D2O than in d6-DMSO and (ii) more different populated stacked conformations
of 1 at 60 °C in D2O than in d6-DMSO. One would expect larger populations of the stacked conformations in
d6-DMSO, whose dielectric constant is smaller than that of water, if the electrostatic interaction were the only
driving force of the aromatic stacking interactions. The results, therefore, suggest that the hydrophobic effect
plays an important role in the stacking interaction of 1 in water.
-11
Introduction
interactions between heterocycles.9 Inspired by the literature
work of using propylene- or isobutyric acid-linked bis-hetero-
cycles to probe the interactions between aromatic groups,9
we have carried out computational and experimental studies of
stacking interactions of a novel molecular probe, sodium (2,2)-
bis(indol-1-yl-methyl)acetate (1, Figure 1) in water and in
DMSO to investigate the role of the hydrophobic effect in
aromatic stacking interactions.
Interactions between aromatic functional groups play a role
-20
1,2
in folding and complexation of biopolymers. In particular,
aromatic interactions are closely associated with the stabilization
of nucleic acid structures and the intercalation of drugs into
DNA and RNA. The stacking interactions of aromatic hydro-
carbons such as benzene in water are usually attributed to the
hydrophobic effect, namely, water’s preference for interacting
with itself relative to interacting with the aromatic hydrocar-
3
Strategy
bons. Similarly, the aromatic stacking interactions of hetero-
cycles such as adenine in water have been suggested to be due
to the hydrophobic effect, dispersion attractions, and attractive
interactions between the partial charges on heterocycles. On
the other hand, it has been suggested that the aromatic stacking
interactions stem exclusively from the attractive electrostatic
We wanted to answer three questions through conformational
searches, molecular dynamics (MD) simulations, potential of
mean force (PMF) and free energy perturbation (FEP) calcula-
tions, syntheses, and NMR studies of 1 and its monomeric
4
-8
*
To whom correspondence and reprint requests should be addressed.
On sabbatical leave from Neurochemistry Research, Mayo Foundation
(9) Newcomb, L. F.; Gellman, S. H. J. Am. Chem. Soc. 1994, 116, 4993-
4994.
†
for Medical Education and Research, 4500 San Pablo Rd., Jacksonville,
FL 32224. Current address: Department of Pharmacology, Mayo Foundation
for Medical Education and Research, 200 First St. SW, Rochester, MN
(10) Newcomb, L. F.; Haque, T. S.; Gellman, S. H. J. Am. Chem. Soc.
1995, 117, 6509-6519.
(11) Gellman, S. H.; Haque, T. S.; Newcomb, L. F. Biophys. J. 1996,
71, 3523-3525.
5
5905.
‡
Current address: CombiChem North, 1804 Embarcadero Rd., Suite
01, Palo Alto, CA 94303.
(12) Browne, D. T.; Eisinger, J.; Leonard, N. J. J. Am. Chem. Soc. 1968,
90, 7302-7323.
2
(
1) Burley, S. K.; Petsko, G. A. AdV. Protein Chem. 1988, 39, 125.
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(14) Leonard, N. J.; Ito, K. J. Am. Chem. Soc. 1973, 95, 4010-4016.
(15) Leonard, N. J. Acc. Chem. Res. 1979, 12, 423.
(16) Constant, J. F.; Laugaa, P.; Roques, B. P.; Lhomme, J. Biochemistry
1988, 27, 3997-4003.
(2) Saenger, W. Principles of Nucleic Acid Structure; Springer-Verlag:
New York, 1984.
3) Muller, N. Acc. Chem. Res. 1990, 23, 23.
P. O. P., Ed.; Academic Press: New York, 1974; Vol. I.
(17) Mutai, K.; Gruber, B. A.; Leonard, N. J. J. Am. Chem. Soc. 1975,
97, 4095-4104.
(
5) Crothers, D. M.; Ratner, D. I. Biochemistry 1968, 7, 1823.
(6) Ts’o, P. O. P.; Kondo, N. S.; Robins, R. K.; Broom, A. D. J. Am.
(18) Voet, D. J. Am. Chem. Soc. 1980, 102, 2071-2074.
(19) Ishida, T.; Shibata, M.; Fujii, K.; Inoue, M. Biochemistry 1983, 22,
3571-3581.
Chem. Soc. 1969, 91, 5625.
(
(
7) Tazawa, I.; Koike, T.; Inoue, Y. Eur. J. Biochem. 1980, 109, 33.
8) Friedman, R. A.; Honig, B. Biophys. J. 1995, 69, 1528-1535.
(20) Friedman, R. A.; Honig, B. Biophys. J. 1996, 71, 3525-3526.
1
0.1021/ja9828410 CCC: $18.00 © 1999 American Chemical Society
Published on Web 02/10/1999

1718 J. Am. Chem. Soc., Vol. 121, No. 8, 1999
Pang et al.
Table 1. Definition of the Six Torsions that Determine the
Conformations of 1
torsion
atom ID of 1a
T1
T2
T3
T4
T5
T6
14-15-16-19
15-16-19-24
28-27-24-19
27-24-19-16
27-24-19-21
24-19-21-22
a
For atom IDs, see Figure 4.
the relative conformational stabilities of 1 in water at 25 °C,
we carried out PMF calculations, which compute the potential
of mean force, characterizing conformational change as a
function of the first four torsions specified in Table 1 with
2
5
holonomic internal constraints. To effectively evaluate the
conformational stabilities of two conformers generated by
exchanging the carboxylate group and the methine hydrogen
2
2
Figure 1. Chemical structures of 1-5.
atom of 1, we used FEP calculations, which compute the free
-
energy difference between the two by perturbing the CO2 and
analogues (2 and 3, Figure 1). First, can 1 adopt the tilted
H groups to one another. Use of the FEP calculations rather
than the more computing-intensive PMF approach also simpli-
fied the conformational analysis of 1 because the relative
orientations of the carboxylate group were no longer of concern.
Both PMF and FEP calculations employing MD simulations
were performed in a box of explicit water molecules (TIP3P)26
with periodic boundary conditions, and thus they include the
solvent and entropy effects on conformational stability. Such
calculations are computing intensive and yet most appropriate,
since the stacking interactions involve considerable enthalpy-
entropy compensation. Evaluation with just potential energies
of different conformations would omit the solvent and entropy
effects and, therefore, not be able to assess the contribution of
the hydrophobic effect.
21
T-shaped, off-center, and face-to-face stacked conformations?
Second, which stacked conformation(s) is preferred in water if
adopts a stacked conformation(s)? Third, does the hydrophobic
1
effect play a role in the stacked conformations of 1?
The reasons to investigate 1 are as follows: First, concerning
the partial charges on the indole ring, 1 can be viewed as a
hybrid of a heterocycle 4 (Figure 1) and an aromatic hydro-
carbon 5 (Figure 1), which were found to adopt parallel stacked
9
-11,20
and nonstacked conformations in water, respectively.
Knowledge of stacking or nonstacking behavior of 1 in water
can yield insights into the hydrophobic effect in aromatic
stacking interactions. Second, 1 is readily synthetically acces-
sible. Third, the seven proton signals of the indole ring are
generally distinguishable in the NMR spectrum. This permits
an analysis of upfield or downfield shifts of the indole protons
that can yield crucial experimental evidence about the stacking
or nonstacking behavior of 1 in water. Fourth, 1 can later be
theoretically mutated to heterocycle 4 through steps, at each of
which one carbon (or hydrogen) atom is changed to a nitrogen
atom by employing a single-topology-based free energy per-
turbation approach.22 This permits an investigation on which
part of the partial charges on the adenine group plays a role in
the aromatic stacking interactions of 4. Although the aromatic
hydrocarbon 5 can also be theoretically mutated to 4 using a
dual-topology-based free energy perturbation approach for
investigation of the charge contribution, it is more efficient to
work with perturbations of 1 using the single-topology-based
approach.2
We then launched synthesis and NMR spectroscopic studies
on 1-3 to detect the populated conformations of 1 in water
and in DMSO. The NMR studies were focused on (i) chemical
shifts of the aromatic protons, which can provide information
about the stacking and nonstacking interactions, (ii) coupling
constants of the methylene protons, which can offer insights
into determination of which conformations are not likely in water
on the basis of torsions calculated from the observed coupling
2
7
constants by the Karplus equation, and (iii) symmetry infor-
mation contained in the spectra, which provides insights into
the conformational dynamics.
Results
Accuracy of the Computational Approach. The reliability
2-24
and accuracy of our computational approach rely mainly on
To answer the three questions, we first performed confor-
mational analysis of 1 to investigate if the commonly observed
tilted T-shaped, off-center, and face-to-face stacked conforma-
22
force field and sampling in the MD simulations. For the force
field, we used a well-balanced, second-generation AMBER force
28
field. This force field was developed specifically for the
2
1
tions are available to the isobutyric acid linked bis-indole 1.
simulations in solution (TIP3P water molecules) and is most
appropriate to the present work. Furthermore, Chipot et al. have
reported a study of benzene stacking interaction in water by
means of free energy calculations with the second-generation
We then carried out MD simulations of 1 in water. This study
did not provide information on relative conformational stability,
and yet it yielded information on interconversions among
different conformers derived from conformational searches. This
information was later used in PMF calculations. To estimate
29
AMBER force field. According to their calculations, the
(
25) Tobias, D. J.; Brooks, C. L. J. Chem. Phys. 1988, 89, 5115-5127.
(
21) Hunter, C. A.; Sanders, K. M. J. Am. Chem. Soc. 1990, 112, 5525-
(26) Jorgensen, W. L.; Chandreskhar, J.; Madura, J. D.; Impey, R. W.;
Klein, M. L. J. Chem. Phys. 1982, 79, 926-935.
(27) Silverstein, R. M.; Bassler, G. C.; Morill, T. C. Spectroscopic
Identification of Organic Compounds, 5th ed.; Wiley: New York, 1991; p
196.
5
534.
(
(
22) Kollman, P. Chem. ReV. 1993, 93, 2395-2417.
23) Pearlman, D. A.; Case, D. A.; Caldwell, J. W.; Ross, W. S.;
Cheatham III, T. E.; Debolt, S.; Ferguson, D.; Seibel, G.; Kollman, P. A.
Comput. Phys. Commun. 1995, 91, 1-41.
(28) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K.
M., Jr.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.;
Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 5179-5197.
(
24) Sun, Y. C.; Veenstra, D. L.; Kollman, P. A. Protein Eng. 1996, 9,
2
73-281.

Hydrophobic Effect in Aromatic Stacking Interactions
J. Am. Chem. Soc., Vol. 121, No. 8, 1999 1719
Table 2. Torsions (Deg of Arc) of the 12 Different Conformations
of 1
conformera
description
T1
T2
T3
T4
T5
T6
1
1
1
1
1
1
1
1
1
1
1
1
N1
N2
F3
S4
T5
nonstacked
nonstacked
92 -179 -96 177 -59 -61
104 -58
94 -170
65 -148
indolyl ring stacked
phenyl ring stacked
T-shaped stacked
nonstacked
T-shaped stacked
nonstacked
nonstacked
pyrrolyl ring stacked -66 -67 -122
off-center stacked
119 -74 -121
53 -80
0
46
42
118 -41 128 -55 177
72
63
90 -175
62
N6
T7
-98 -174 -94 177 -60 130
-104
67
93 -174
63
60
43
70
N8
N9
S10
O11
F12
-97 177 -167 -176
94
65 -93
169 -66 152
72 -165 120
Figure 2. Conversion between the two mirror images through the PMF
and FEP calculations.
71
65
60 -123
50 -78
95
63
indolyl ring stacked
78 -63 -58 179
parallel stacked benzene dimer has a contact and a solvent-
separated minimum with corresponding free energies of as-
sociation of -0.47 and -0.43 kcal/mol, respectively; the
T-shaped benzene dimer has corresponding energies of -1.94
and -0.74 kcal/mol. These results are consistent with the report
of other studies using an ab initio potential, which found free
energies of -0.1 and -0.74 kcal/mol for the contact and the
solvent-separated minima of the parallel benzene dimer, and
a
The letters N, F, S, T, and O indicate the nonstacked, face-to-face
stacked, partial face-to-face stacked, tilted T-shaped stacked and off-
center stacked conformations, respectively. For definitions of T1-T6,
see Table 1 and Figure 4.
3
0,31
-1.9 and -0.4 kcal/mol for the T-shaped benzene dimer.
They have also shown good agreement for isolated benzene-
benzene interactions between the molecular mechanics calcula-
tions with the new AMBER force field and high-level ab initio
calculations.29 Chipot’s results suggest that the new AMBER
force field is reliable for prediction of aromatic interactions of
1
, which is structurally analogous to the benzene dimer. For
the sampling, we carried out nanosecond scale MD simulations
with two dedicated SGI supercomputers (Power Challenge with
4
×R10K processors and Origin 2000 with 8×R10K processors),
which allowed us to evaluate the convergence of the simulations.
To assess the inherent accuracy of the PMF and FEP methods,
we performed a perturbation of one conformation of bis-indole
1
(1N6), through a large conformational change, to its thermo-
dynamically identical mirror image (1N6′) by employing a PMF
calculation to change the conformation of the linker (1N6′int),
followed by a FEP calculation to exchange the carboxylate and
methine proton (1N6′) (Figure 2). Using the combined PMF
and FEP strategy, we found that the calculated free energy
difference between the two mirror images was 0.4 ( 0.7 kcal/
mol (see Materials and Methods). This result suggests that the
combined PMF and FEP approach would be reliable in
predicting preference of two conformers whose free energy
difference is greater than 0.4 ( 0.7 kcal/mol.
The reliability of the free energy perturbation studies will be
demonstrated later (i) by the closed thermodynamic cycle
constructed by the calculated free energy changes (see PMF
Calculations) and (ii) by the consistent, independent NMR
results (see Populated Tilted T-Shaped Stacked Conformations
and Populated Nonstacked Conformations).
Conformational Analysis. A total of 12 different conformers
of 1 was identified from a conformational search of this
molecule. Six torsions that define the 12 conformers are listed
in Table 2. There are two tilted T-shaped conformers, two face-
to-face stacked conformers, three off-center stacked conformers,
and five nonstacked conformers (see Figure 3). According to
the conformational search, the isobutyric acid linker does not
prevent 1 from adopting the tilted T-shaped and other two
parallel stacked conformations in a vacuum.
Figure 3. Conformations of 1 identified from the conformational search
6
7
(H atoms, except for H and H in the tilted T-shaped conformers, are
not displayed, for clarity).
Table 3. Relative Free Energies (G) of the 15 Conformers at 25
°
C in Water, Assuming That the Relative Free Energy of 1T5 is 0
conformer
T5
1T7
1N8
G (kcal/mol)
conformer
G (kcal/mol)
1N9ba
1
0
3.7 ( 1.2
4.0 ( 0.6
4.9 ( 0.9
5.5 ( 0.5
6.1 ( 1.1
7.3 ( 0.8
9.2 ( 1.4
0.3 ( 0.4
0.7 ( 0.2
1.0 ( 0.8
1.3 ( 0.1
2.2 ( 1.0
2.4 ( 0.3
2.7 ( 0.9
1F3ba
1S10
1O11
1F12
1S4
1
1
1
1
1
N1
N6 a
N2b
N2
1F3
N9
a
See FEP Calculations for Definitions of 1Xb.
(
29) Chipot, C.; Jaffe, R.; Maigret, B.; Pearlman, D. A.; Kollman, P. A.
Conformational Stability. The relative free energies of the
5 conformers calculated by the PMF and FEP methods are
listed in Table 3. On the basis of the computational study alone,
it is predictable that both the tilted T-shaped stacked and
J. Am. Chem. Soc. 1996, 118, 11217-11224.
1
(
30) Linse, P. J. Am. Chem. Soc. 1992, 114, 4366.
(31) Hobza, P.; Selzle, H. L.; Schlag, E. W. J. Am. Chem. Soc. 1994,
1
16, 3500-3506.

1720 J. Am. Chem. Soc., Vol. 121, No. 8, 1999
Pang et al.
6
7
5
Scheme 1. Syntheses of Compounds 1-3 (Free Acids)
of H and H , but the downfield shift of H was not observed
in the spectra of 1, 2, and 3 (Table 4 and Figure 5). Therefore,
6
7
the observation of just the upfield shifts of H and H suggested
that the tilted T-shaped conformations (1T5 and/or 1T7) are
populated in D2O and in d6-DMSO, whereas the parallel stacked
conformations are not populated.
Populated Nonstacked Conformations. In the NMR spectra
of 1 in D2O and in d6-DMSO, there are (i) one set of indole
proton resonances, (ii) two methylene proton resonances (Ha
and Hb), and (iii) a pair of different coupling constants Jac (9 to
nonstacked conformations (1T5, 1T7, 1N8, 1N1, and 1N6) are
significantly populated in water at 25 °C. Interestingly, according
to the inherent accuracy of the PMF and FEP methods, the data
suggest that the parallel stacked conformations (1F12, 1F3b,
8
Hz) and Jbc (6 Hz) (Figures 5 and 6 and Table 5). To account
for the symmetry of the spectra, the asymmetric conformer 1T7
1T5) must rapidly interchange to its enantiomeric conformer
T7′ (1T5′) by and only by interchange of 1T7 through a
symmetric “intermediate” 1N1 (or 1T5 through a symmetric
intermediate” 1N6) (Figure 6). In this way, the two indole rings
1
S10, 1S4, and 1F3) are not populated. This prompted us to
(
1
launch experimental studies on 1 to confirm the computational
finding.
Synthesis. Compounds 1-3 (free acids) were synthesized in
low yields (20-30%) by the standard N-alkylation method
outlined in Scheme 1. The yields encountered were low mainly
because elimination of the acidic R proton of the substituted
“
over time will experience the same environment; axial proton
Ha′ (Ha′′) in 1T7 (1T5) will interchange to equatorial proton
Hb′′ (Hb′) in 1T7′ (1T5′) through a 120° rotation of bond T4 (a
120° rotation of bond T2), and it will then interchange to equa-
torial proton Hb′′ (Hb′) in 1T7 and/or 1T5 through mirror in-
version of 1T7′ (1T5′) to 1T7 (1T5), consequently reducing
four distinct methylene protons in asymmetric 1T7 (1T5) to
two distinct methylene protons of Ha (an average of Ha′ and
Hb′′) and Hb (an average of Hb′ and Ha′′). However, interchanges
of Ha′ to Hb′′ and Hb′ to Ha′′ would result in Jac ) Jbc, since Jac
propionate changed, under basic condition, the SN2 reaction to
the low-yield Michael addition.32 In making 2 and 3, the
retention times of the ester intermediates of 2 and 3 were found
identical to that of starting material indole, which caused a
purification problem. This problem was avoided by hydrolyzing
a mixture of indole and its N-substituted ester analogue, followed
by extracting the desired acid product with basic solution.
Because the NMR spectroscopic studies required only mil-
ligrams of the materials, no efforts were made to improve the
synthetic yields.
Stacked Interaction in 1. All the aromatic protons of 1-3
in D2O or d6-DMSO are distinguishable and readily assigned
according to Aldrich’s proton NMR spectra of different methyl-
substituted indole derivatives.33 The changes in chemical shift
of the indole protons of 1-3 are listed in Table 4 and depicted
in Figure 5. The indole regions of the proton NMR spectra of
)
(Ja′c + Jb′′c)/2, Jbc ) (Jb′c + Ja′′c)/2, Ja′c ) Ja′′c, and Jb′′c )
Jb′c. This contradicts the observation of Jac ) 9 to 8 Hz and Jbc
6 Hz. Therefore, 1T5 and 1T5′ and/or 1T7 and 1T7′ cannot
)
be the only populated conformers. To account for the different
Jac and Jbc, the symmetric “intermediate” 1N1 and/or 1N6 must
also be populated so that the observed axial and equatorial
protons become approximately (Ha′ + Hb′′ + Ha′′′)/3 and (Hb′
+
Ha′′ + Hb′′′)/3, respectively (Figure 6b). Accordingly, Jac
approximately equals (Ja′c + Jb′′c + Ja′′′c)/3 ) (9 + 5 + 9)/3 )
1.0 mM 2 and 1.0 mM 3 are essentially identical. The chemical
8
6
Hz and Jbc is about (Jb′c + Ja′′c + Jb′′′c)/3 ) (5 + 9 + 5)/3 )
shifts of the aromatic protons of 1 and 2 are independent of
concentration over the ranges of 0.01-20 mM and 0.1-40 mM,
respectively (Table 4b). Solutions of concentrations higher than
Hz, which are now consistent with (i) the upfield chemical
6
7
shifts of H and H, (ii) the symmetry of the spectra, and (iii)
the well-differentiated Jac and Jbc. Therefore, the observations
of one set of indole proton resonances and two methylene proton
resonances and yet a pair of different Jac and Jbc suggest that
1N6 and/or 1N1 is also populated in water and in DMSO.
2
0 mM for 1 and 40 mM for 2 became turbid. These results
indicate that intermolecular interactions are insignificant at 0.5
mM 1 and at 1.0 mM 2. However, the resonances of protons
6
7
H and H of 0.5 mM 1 in D2O at 22 °C are significantly shifted
On the basis of the NMR study alone (i.e., independent of
the calculated free energies), it is clear that both the tilted
T-shaped stacked and nonstacked conformers are populated in
water and in DMSO at 22 °C, and they exist in a rapid
equilibrium. Although the NMR study provides no insight into
the possibility that 1N8 may or may not be populated in water,
the experimental study does confirm the computational findings
of all other populated conformations (1T5, 1T7, 1N1, and 1N6).
upfield by 0.08 and 0.28 ppm, respectively, relative to those of
1
)
.0 mM 2 at the same condition. A smaller upfield shift (∆δH7
-0.16 ppm) was also observed in d6-DMSO at 22 °C. These
results revealed the stacking interaction between the two indole
rings of 1 in D2O and in d6-DMSO.
Populated Tilted T-Shaped Stacked Conformations. Fur-
6
7
thermore, the upfield shifts indicate that protons H and H
experience electron shielding. Examination of the Dreiding
stereomodel of 1 (page T391, 1997 Aldrich Catalog, 1001 W.
St. Paul Ave., Milwaukee, WI 53233) revealed that only the
tilted T-shaped stacked conformations (1T5 and 1T7) permit
7
Hydrophobic Effect. At 22 °C, the upfield shift of H of
0.5 mM 1 in d6-DMSO was found to be 0.12 ppm less than the
corresponding shift in water (Table 4), indicating that population
of the nonstacked conformations is larger in d6-DMSO than in
water. This result suggests that the stacking interaction of 1 is
weak, but it is stronger in water than in DMSO, consistent with
the role expected from the hydrophobic effect. One would
observe a larger population of the stacked conformation in d6-
DMSO, whose dielectric constant is smaller than that of water,
if the electrostatic interaction were the only driving force of
the aromatic stacking interactions. To further support the role
of the hydrophobic effect, the NMR studies were carried out at
varied temperatures. Interestingly, at 60 °C, only the broadened
6
7
spatial arrangements in which H and H are located above the
inner region of one indole ring, therefore experiencing electron
shielding. The off-center stacked conformers could also render
6
7
a spatial arrangement in which H and H experience electron
shielding. However, this conformation would inevitably result
5
5
in a downfield shift of H , due to the location of H over the
outer region of the same indole ring that causes the upfield shifts
(
32) Doebel, K. J.; Wasley, J. W. F. J. Med. Chem. 1972, 15, 1081-
082.
33) Pouchert, C. J.; Behnke, J. The Aldrich library of 13C and 1H FT-
NMR spectra; Aldrich Chemical: Milwaukee, WI, 1992.
1
(
7
signal of H of 0.5 mM 1 in water was found shifted upfield by

Hydrophobic Effect in Aromatic Stacking Interactions
J. Am. Chem. Soc., Vol. 121, No. 8, 1999 1721
in 1 or 3 - δ in 2) and (b) Chemical Shifts of the Aromatic
Table 4. Changes in Chemical Shift (ppm) of the Indole Protons (∆δ
Protons of 1 and 2 versus Concentration in D O at 22 °C
2
H
) δ
H
H
(a) ∆δ
H
of Indole Protons
solvent
T (°C)
∆δH2
∆δH3
∆δH4
∆δH5
∆δH6
∆δH7
3
3
1
1
1
1
1
relative to 2
relative to 2
relative to 2
relative to 2
relative to 2
relative to 2
relative to 2
D
2
O
22
22
22
60
22
60
100
-0.01
-0.02
-0.02
-0.06
-0.01
0
0.01
0.01
0.01
-0.01
0.02
0.02
0.02
0
0
0
0.01
0
0
0
d
6
-DMSO
O
O
-DMSO
-DMSO
-DMSO
-0.01
-0.01
-0.03
0.01
D
D
2
0
-0.02
0
0.01
0
-0.08
-0.10
-0.04
-0.05
-0.06
-0.28
-0.38
-0.16
-0.19
-0.17
2
d
d
d
6
6
6
0
-0.01
-0.01
(b) Chemical Shifts of the Aromatic Protons of 1 and 2 versus Concentration in D
2
O at 22 °C
4
2
7
6
5
3
H (ppm)
H (ppm)
H (ppm)
H (ppm)
H (ppm)
H (ppm)
1
1
1
1
1
2
2
2
2
2
(20 mM)
(2.0 mM)
(1.0 mM)
(0.1 mM)
(0.01 mM)
(40 mM)
(20 mM)
(2 mM)
7.54
7.54
7.55
7.55
7.55
7.54
7.54
7.55
7.55
7.55
7.14
7.16
7.16
7.16
7.17
7.17
7.17
7.18
7.18
7.18
7.11
7.11
7.11
7.11
7.13
7.41
7.41
7.43
7.43
7.43
7.05
7.06
7.04
7.06
7.07
7.13
7.14
7.14
7.14
7.14
6.99
6.99
7.00
7.00
7.02
7.00
7.00
7.00
7.00
7.01
6.41
6.42
6.43
6.42
6.43
6.40
6.40
6.41
6.41
6.42
(1 mM)
(0.1 mM)
Figure 4. Specifications of the atom identifications of 1.
.10 ppm relative to the corresponding sharp signal of H in
7
0
water at 22 °C (Table 4 and Figures 5 and 7). Other chemical
shift changes of 1 are insignificant in comparison with the
chemical shift differences between 2 and 3 (Table 4). Signal
6
7
broadening occurred only to H and H in water at 60 °C. In
7
contrast, a further upfield shift and broadening of H were not
observed in d6-DMSO at 60 °C and even at 100 °C (Table 4
and Figure 7). Such observations indicated that a temperature
of 60 °C is not high enough to reduce or abolish the hydrophobic
effect of 1 in water. The results, therefore, suggest that stacked
conformers such as 1T5 and 1T7 become more populated at
6
0 °C in water. Clearly, elevating the temperature to 60 °C
increased the stacked conformations in water and not in d6-
DMSO. This further suggests that the hydrophobic effect plays
a role in the stacking interaction of 1.
Discussion
In an attempt to provide additional links between the NMR
experimental results and the computational predictions, we back-
calculated the chemical shifts of 2 and 3 using the ab initio
method with the B3LYP/6-31G*//B3LYP/6-31G* function,
employing the Gaussian 94 program (see Materials and Meth-
ods).34 The calculated chemical shifts of relatively large and
flexible structures 2 and 3 are in good agreement with
experimentally measured values (Table 6). However, the dif-
Figure 5. Comparison of the chemical shifts of the aromatic protons
among 1 (0.5 mM), 2 (1.0 mM), and 3 (1.0 mM) in D O (top) and
-DMSO (bottom) at 22 °C.
7
2
ference (0.76 ppm) in the calculated chemical shift of H
d
6
between 2 and 3 is larger than the observed change (0.28 ppm)
7
of H in 1 caused by electron shielding in the conformations
Back-calculation of NOE spectra of 1 in different conformations
may also, in theory, provide a link between the experiments
and the calculations. However, the NOE back-calculation was
not pursued because of the symmetrical nature of the observed
with intra-aromatic interactions. This result, unfortunately,
precludes a meaningful analysis of the chemical shifts in 1.
(34) Gaussian 92 and 94; Gaussian, Inc.: Pittsburgh, PA 1992.

1722 J. Am. Chem. Soc., Vol. 121, No. 8, 1999
Pang et al.
Figure 6. (a) Conformational interconversions of 1T7 to 1N1 and 1T5
to 1N6. (b) Schematic representation of the conformational intercon-
versions that interchange Ha′ to Hb′′ and Hb′ to Ha′′, and yet
differentiate Jac from Jbc
.
Table 5. Coupling Constants of the Methylene Protons in 0.5 mM
and 1.0 mM 2
1
structure
solvent
T (°C)
J
ac (Hz)
J
bc (Hz)
6
na
J
ab (Hz)
1
1
1
1
1
2
2
2
2
D
D
2
O
O
22
60
22
60
100
22
60
22
60
9
8
9
8
8
8
7
7
7
14
14
14
14
14
14
14
14
14
a
2
d
d
d
6
-DMSO
-DMSO
-DMSO
6
6
7
7
6
6
D
D
2
O
O
a
2
na
d
d
6
-DMSO
-DMSO
7
7
6
Figure 7. Comparison of the chemical shifts of the aromatic protons
a
Not available because the signal was overlapped by the solvent
among 1 (0.5 mM) and 2 (1.0 mM) in D
2 6
O at 60 °C (top) and in d -
signal.
DMSO at 60 °C (middle), and in d -DMSO at 100 °C (bottom).
6
spectrum of 1. In practice, the molecular symmetry of 1 causes
the complication in distinguishing the NOE signals between two
aromatic protons in one indole ring from the ones between two
protons in two indole rings in the experimentally measured
spectra and also the complication in averaging the NOE signals
in the back-calculation.
Table 6. Observed and Calculated Chemical Shifts of the
Aromatic Protons in 2 and 3
chemical shift (ppm)
H2
H3
H4
H5
H6
H7
Structure 2
6.40
6.38
observed in DMSO
observed in D
B3LYP/6-31G*//
7.31
7.15
7.67
7.52
7.51
6.91
6.99
6.98
6.50
7.11
7.12
6.62
7.47
7.39
7.83
There are a large number of structural precedents for hetero-
2
O
1
2,13,17,19
cycles to adopt parallel stacked conformations.
well known that the nucleotide bases tend to adopt parallel
It is also
5.69
B3LYP/6-31G*
3
5
stacked conformations in ordered DNA and RNA structures.
Structure 3
6.39
6.37
The tilted T-shaped stacked conformations are reportedly seen
only in aromatic hydrocarbons.21,36-38 We found from both
computational and experimental studies that the parallel stacked
conformations of bis-indole 1 are not populated in water, but
rather, the molecule is in an equilibrium between the tilted
T-shaped stacked and nonstacked conformations. This unprec-
edented observation does not imply that nucleotide bases tend
to adopt the tilted T-shaped conformation, because the charges
observed in DMSO
7.33
7.16
7.71
7.52
7.51
6.96
7.00
6.98
6.71
7.11
7.11
6.60
7.47
7.39
7.07
observed in D
2
O
B3LYP/6-31G*//
5.67
B3LYP/6-31G*
of the indole ring are different from those of nucleotide bases
and, more importantly, because the linker of 1 is different from
those used to restrain the nucleotide bases in DNA and RNA.
In addition, the driving force to form parallel stacked nucleotide
bases in DNA and RNA is not necessarily the same as the one
to adopt the tilted T-shaped stacked indole pair in 1. The
hydrophobic effect simply arises from stronger solvent-solvent
than solvent-solute interactions. This effect on aromatic stack-
ing interactions needs careful evaluation. In the present study,
examining the chemical shift changes alone would lead to a
(
35) Bugg, C. E.; Thomas, J. M.; Sundaralingam, M.; Rao, S. T.
Biopolymers 1971, 10, 175-219.
36) Janda, K. C.; Hemminger, J. C.; Winn, J. S.; Novick, S. E.; Harris,
S. J.; Klemperer, W. J. Chem. Phys. 1975, 63, 1419.
37) Cox, E. G.; Cruikshank, D. W. J.; Smith, J. A. C. Proc. R. Soc.
London 1958, A247, 1.
38) Paliwal, S.; Geib, S.; Wilcox, C. S. J. Am. Chem. Soc. 1994, 116,
497-4498.
(
(
(
4

Hydrophobic Effect in Aromatic Stacking Interactions
J. Am. Chem. Soc., Vol. 121, No. 8, 1999 1723
(m, 1 H); 13C NMR (CDCl
) δ 177.9, 135.7, 128.6, 127.8, 122.0, 121.2,
conclusion that only the stacked conformation(s) is populated
in D2O as well as in d6-DMSO, since the changes of chemical
shifts provide no indication of whether the nonstacked confor-
mations are also populated. This would lead to a wrong
conclusion that the hydrophobic effect has nothing to do with
stacking interactions. However, combining the chemical shift
changes with the calculated free energies of various conforma-
tions in water at 25 °C (Table 3), the symmetry of the NMR
spectra, and the observed and back-calculated coupling constants
led to the interpretation that both the tilted T-shaped stacked
and nonstacked conformations are populated in D2O and in d6-
DMSO, and they are in a rapid equilibrium. Given the fact that
both the tilted T-shaped and nonstacked conformations are
populated in both D2O and d6-DMSO, it is clear that the stacking
interaction in 1 is weak. Nevertheless, the importance of the
hydrophobic effect in the weak stacking interactions of 1 is
supported by the facts that the percentage of the stacked
conformation of 1 in water is higher than that in organic solvent
at 22 °C, and that the percentage difference is magnified at 60
3
1
C
19.9, 108.9, 102.4, 47.2, and 45.2; HRMS (ESI), m/z calcd for
+
20
H
19
N
2
O
2
(M + H ): 319.1446, found 319.1446.
3-Indol-1-yl-2-methylpropionic Acid. A mixture of indole (500 mg)
and powdered 85% KOH (350 mg) in 6.0 mL of dry DMSO was stirred
at RT for 2 h under argon. Methyl 3-bromo-2-methylpropionate (680
µL) was then added dropwise to the bluish solution at RT. The reaction
was quenched after 20 h of stirring at RT. The extract of CH
washed with saturated aqueous NH Cl and dried over MgSO
column chromatography on silica gel using 10% EtOAc in hexane as
eluent gave a mixture of the desired intermediate and indole. KOH
(4.5 N, 8 mL) was added dropwise at RT to a solution of 400 mg of
the mixture of the propionate intermediate and indole in 10 mL of
MeOH and 8 mL of EtOH. After 12 h of refluxing under argon, the
desired acid product as a yellowish solid (326 mg, 30% yield) was
isolated by a procedure similar to that used in isolating (2,2)-bis(indol-
2
Cl
2
was
4
4
. Flash
1
2
-yl-methyl)acetic acid: mp 59-61 °C; IR (CDCl
940, 2882, 1707, 1452, 1314, 1236, 1204, and 741 cm ; H NMR
) δ 11.94 (s, 1 H), 7.60 (d, J ) 9.0 Hz, 1 H), 7.28 (d, J ) 6.0
3
) 3098, 3054, 2978,
-
1 1
(CDCl
3
Hz, 1H), 7.19-7.14 (m, 1 H), 7.10-6.99 (m, 2 H), 6.45 (d, J ) 3.0
Hz, 1 H), 4.38 (dd, J ) 6.0, 12.0 Hz, 1 H), 4.00 (dd, J ) 9.0, 15.0 Hz,
1 H), 3.00-2.93 (m, 1 H), and 1.21 (d, J ) 6.0 Hz, 3 H); C NMR
(CDCl ) δ 180.9, 135.9, 128.6, 128.2, 121.6, 121.0, 119.5, 109.2, 101.6,
48.4, 40.4, and 14.9; HRMS (ESI), m/z calcd for C12
H ) 204.1024, found 204.1020.
-Indol-1-yl-propionic Acid. A procedure similar to that employed
in the synthesis of 3-indol-1-yl-2-methylpropionic acid yielded the
desired product (30%) as a yellowish solid: mp 87-88 °C; IR (CDCl
1
3
°C, which is consistent with the fact that the hydrophobic effect
is often an entropy-driven process. In contrast, refs 9-11
suggested that 4 was parallel stacked and 5 nonstacked based
on the NMR studies and concluded that the hydrophobic effect
3
H14NO
2
(M +
+
3
does not play a role in aromatic stacking, since the polar 4
stacked and the nonpolar 5 did not.9
-11
Our preliminary free
3
)
energy calculations mutating 1 to 4 suggest that the tilted
T-shaped stacking conformations should be considered in the
interpretation of experimental data on 4, but these are not yet
definitive. In any case, our results on 1 stand on their own in
showing the importance of the hydrophobic effect on aromatic
association in water and suggesting that caution should be used
in design of simplified molecular probes to study the structures
and functions of complicated proteins and nucleic acids.
-
1
1
3
052, 2915, 1715, 1462, 1316, 1238, 1179, 928, and 746 cm ; H
NMR (CDCl ) δ 11.04 (s, 1 H), 7.58 (d, J ) 6.0 Hz, 1 H), 7.21-7.03
m, 3 H), 6.96 (d, J ) 3.0 Hz, 1 H), 6.42 (d, J ) 3.0 Hz, 1 H), 4.19
3
(
(
13
3
t, J ) 6.0 Hz, 2 H), and 2.64 (t, J ) 9.0 Hz, 2 H); C NMR (CDCl )
δ 177.6, 135.5, 128.6, 127.7, 121.6, 121.0, 119.5, 108.9, 101.6, 41.1,
+
and 34.4; HRMS (ESI), m/z calcd for C11
found 190.0861.
H12NO
2
(M + H ) 190.0868,
General Description of the Computational Studies. All the
calculations were performed by employing the AMBER 4.1 program
(
various minor revisions made from October 1994 to March 1997) with
Materials and Methods
the Cornell et al. all-atom force field and by using the Gaussian 92
program.2
SHAKE procedure for all bonds of the system, (ii) a time step of 1.0
fs, (iii) a dielectric constant ꢀ ) 1.0, (iv) a cutoff distance of 9.0 Å
3,28,34
All the MD, PMF, and FEP calculations used (i) the
Synthesis. Methyl (2,2)-Bis(indol-1-yl-methyl)acetate. A mixture
of indole (500 mg) and powdered 85% KOH (350 mg) in dry DMSO
39
(6.0 mL) was stirred at room temperature (RT) for 2 h under argon.
0
Methyl 3-bromo-2-(bromomethyl)propionate (300 µL) was then added
dropwise to the bluish solution at RT. The reaction was quenched after
for calculating nonbonded interactions, (v) a rectangular periodic
boundary condition with the constant temperature (T ) 298 K and
TAUTP ) 0.3) and constant pressure (P ) 1 atm and TAUP ) 0.3)
algorithm, (vi) the Berendsen coupling algorithm (NTT ) 1), and
(vii) a flag (IFTRES ) 0) to calculate all solute-solute nonbonded
interactions. The nonbonded list was updated every 25 steps in the
MD simulations and the PMF calculations.
2
0 h of stirring at RT. The extract of CH
aqueous NH Cl and dried over MgSO . Flash column chromatography
on silica gel using 10% EtOAc in hexane as eluent gave 140 mg (20%)
of the ester product as a yellowish oil: R ) 0.47 (20% EtOAc in
hexane); IR (CDCl ) 3054, 2951, 1732, 1514, 1454, 1314, 1263, 1213,
2 2
Cl was washed with saturated
4
0
4
4
f
3
-
1 1
1
7
9
4
1
1
177, and 741 cm ; H NMR (CDCl
3
) δ 7.62 (d, J ) 9.0 Hz, 2 H),
Structure 1 was built with two MEN (1-methyleneindole) residues
-
.15-7.02 (m, 8 H), 6.50 (dd, J ) 3.0, 6.0 Hz, 2 H), 4.51 (dd, J )
.0, 15.0, 2 H), 4.18 (dd, J ) 6.0, 15.0 Hz, 2 H), and 3.57-3.48 (m,
and one ACT (CHCO
2
) residues with the PREP, LINK, EDIT, and
PARM modules of the AMBER program. For all the MD and PMF
calculations, one negatively charged molecule 1 and one sodium
counterion were solvated by the TIP3P water molecules in a periodic
boundary box (DISO ) 2.2, DISH ) 2.0, NCUBE ) 4, CUTX )
1
3
H); C NMR (CDCl
3
) δ 172.5, 135.8, 128.7, 127.9, 122.0, 121.2,
+
19.8, 109.0, 102.2, 52.3, 47.3, and 45.7; MS (70 eV) m/z 332 (M ),
70, 130, 103, 77, and 63; HRMS (ESI), m/z calcd for C21
H ) 333.1603, found 333.1600.
H
21
N
2
O
2
(M
+
+
10.0, CUTY ) 13.0, CUTZ ) 14.0, generally a box size of 32 × 33
3
×
35 Å with about 1050 water molecules; note that the number of
(2,2)-Bis(indol-1-yl-methyl)acetic Acid. KOH (4.5 N, 8 mL) was
water molecules varies with conformations of 1). The resulting system
was slowly heated to 298 K (1 K per 100 steps) by coupling to different
heat baths with constant NTV simulation and then equilibrated with
constant NTP simulation for 50 ps at 298 K and 1 atm.
added dropwise at RT to a solution of methyl (2,2)-bis(indol-1-yl-
methyl)acetate (500 mg) in 10 mL of MeOH and 8 mL of EtOH. The
resulting solution was refluxed under argon for 12 h and poured into
5
0 mL of water. The alcohol in the resulting mixture was removed by
For all the FEP and PMF calculations, (i) the thermodynamic
integration approach was used; (ii) the reported free energy change of
a perturbation or a subperturbation was a mean of the free energy
changes calculated in forward and reverse runs plus and minus the
standard deviation of the mean; (iii) the reported free energy change
of a perturbation which was broken into several subperturbations was
rotary vaporation under reduced pressure. The aqueous solution was
first washed with EtOAc and then adjusted to pH 5 with 2 N HCl. The
product was extracted with EtOAc and dried over MgSO . Flash column
4
chromatography on silica gel using first 30% EtOAc in hexane as eluent
to remove impurities and then EtOAc as eluent yielded 450 mg (94%)
of the acid product as a reddish solid: mp 132-133 °C; IR (CDCl
3
)
;
3
063, 2928, 1715, 1516, 1458, 1317, 1227, 1177, 907, and 733 cm-1
(
39) Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J. Comput. Phys.
1
H NMR (CDCl
3
) δ 10.38 (s, 1 H), 7.63-7.57 (m, 2 H), 7.11-7.05
1
977, 23, 327-341.
(40) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Di
(
m, 4 H), 6.79-6.93 (m, 4 H), 6.48 (d, J ) 3.0 Hz, 2 H), 4.39 (dd, J
)
6.0, 15.0 Hz, 2 H), 4.04 (dd, J ) 6.0, 15.0 Hz, 2 H), and 3.50-3.42
Nola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684-3690.

1724 J. Am. Chem. Soc., Vol. 121, No. 8, 1999
Pang et al.
Table 7. Observed Interconversions among the 12 Conformers in
the MD Simulations and Their Duration in Water at 25 °C
1
S10 (2 ps) f 1S4 (203 ps) f 1O11 (565 ps) f 1T7 (229 ps/stop)
S10′ (0 ps) f 1N2 (263 ps) f 1S10 (46 ps) f 1N9 (47 ps) f
1
1
N1 (39 ps) f 1N8 (17 ps) f 1N1 (209 ps) f 1N9 (94 ps) f
1N1 (183 ps) f 1N8 (2 ps) f 1N1 (6 ps) f 1N8 (15 ps) f
N2 (79 ps/stop)
Figure 8. Splicing scheme used for deriving the charges of 1.
1
a sum of the free energy changes of the subperturbations plus and minus
a sum of the corresponding standard deviations; and (iv) convergence
of each perturbation was checked by the criterion that the difference
in free energy change between a run and the run calculated with doubled
simulation time should not be greater than the standard deviation,
otherwise longer simulation was performed until the criterion was met.
RESP Charges. Using the RESP module of the AMBER program,
the RESP charges of 1 were derived by splicing the electrostatic
potentials of two 1-methylindole and one deprotonated acetic acid. A
two-stage fitting protocol was used. The Lagrange constraints were
used to set a net charge of the four extra protons outlined in boxes a
and b equal to zero, leaving a net charge of all atoms of 1 equal to -1
1T7 (213 ps) f 1N1 (311 ps) f 1T7 (171 ps) f 1N1 (305 ps/stop)
1
1
N2 (225 ps) f 1T5 (775 ps/stop)
N1 (17 ps) f 1N6 (522 ps) f 1N8 (7 ps) f 1N6 (30 ps) f
1
N8 (2 ps) f 1N6 (41 ps) f 1N2 (222 ps/stop)
1S4 (379 ps) f 1N2 (384 ps) f 1N9 (237 ps/stop)
1
F12 (7 ps) f 1S10 (52 ps) f 1N2 (50 ps) f 1N8 (1 ps) f
1N6 (7 ps) f 1N8 (41 ps) f 1N2 (331 ps) f
1T7 (511 ps/stop)
1
1
T7 (334 ps) f 1N6 (492 ps) f 1T5 (508 ps/stop)
F3 (0 ps) f 1O11 (353 ps) f 1T7 (65 ps) f 1N2 (58 ps) f
1
T5 (524 ps/stop)
2
8,41
(see Figure 8).
The electrostatic potentials of MEN and ACT were
1
1
N9 (388 ps) f 1O11 (48 ps) f 1T5 (463 ps) f 1N9 (101 ps/stop)
generated by the ab initio calculations with the RHF/6-31G*//RHF/6-
3
4
3
1G* function employing the Gaussian 92 program. The splicing
N8 (0 ps) f 1N6 (44 ps) f 1N8 (4 ps) f 1N6 (25 ps) f
1N8 (1 ps) f 1N6 (2 ps) f 1N8 (6 ps) f 1N6 (14 ps) f
1N8 (4 ps) f 1N6 (9 ps) f 1N8 (3 ps) f 1N6 (61 ps) f
approach was used to reduce the conformational influence on the charge
calculation.
1
1
1
1
1
1
1
N8 (12 ps) f 1N6 (15 ps) f 1N8 (13 ps) f 1N6 (1 ps) f
N8 (3 ps) f 1N6 (7 ps) f 1N8 (5 ps) f 1N6 (11pa) f
N8 (6 ps) f 1N6 (12 ps) f 1N8 (15 ps) f 1N6 (47 ps) f
N8 (4 ps) f 1N6 (3 ps) f 1N8 (8 ps) f 1N6 (91 ps) f
N8 (3 ps) f 1N6 (7 ps) f 1N8 (5 ps) f 1N6 (40 ps) f
N8 (2 ps) f 1N6 (1 ps) f 1N8 (4 ps) f 1N6 (7 ps) f
N8 (9 ps) f 1N6 (3 ps) f 1N8 (1 ps) f 1N6 (6 ps) f
Conformational Analysis. A total of 1296 different conformers were
generated by specifying all discrete possibilities at 60° of arc increment
in a range of 0-360° for the first four torsions (T1-T4) defined in
Table 1. Conformers were optimized without restraining any torsions
during the energy minimization by employing the Sander module.2
Based on the criterion that two conformers are different if the difference
of one of the four defined torsions between the two conformers is greater
than 30° of arc, conformational cluster analysis on the optimized
conformers resulted in 38 different conformers. Duplicated structures
and mirror images due to the symmetric nature of 1 were deleted by
visual inspection, which yielded 12 different conformers. The relative
orientation of the carboxylate group was not taken into account in order
to make use of FEP calculations.
MD Simulations. For all the 1.0 ns MD simulations, the first four
specified torsions of 1 (Table 1) were calculated from all the trajectories
saved at every 1.0-ps interval using the CARNAL module of the
AMBER program. A table of such torsions was analyzed to obtain
information about the conformational changes. One compares such
torsions with 38 sets of the torsions that were obtained initially from
the conformational search and designates one or none of the 12
conformers that is identical to the instantaneous conformer of 1 at 1.0-
ps intervals, according to the criterion that two conformers are identical
if the differences of the four torsions between the two conformers are
all less than 30° of arc.
3,28
1N8 (20 ps) f 1N6 (17 ps) f 1N8 (5 ps) f 1N6 (10 ps) f
1N8 (5 ps) f 1N6 (119 ps) f 1N8 (9 ps) f 1N1 (36 ps) f
1N8 (17 ps) f 1N6 (1 ps) f 1N8 (1 ps) f 1N6 (85 ps) f
1
T5 (161 ps/stop)
PMF Calculations. For effective sampling, the observed intercon-
versions among the 12 conformers in the MD simulations in water at
5 °C were used as conformational perturbation paths in the PMF
2
calculations. This is crucial to the PMF calculations. In theory, the
calculated free energy change does not depend on paths of perturbations
along which the calculation is performed. In practice, due to limitation
in sampling, such a calculation can often be path-dependent. The PMF
calculations with two arbitrarily selected conformers often yielded huge
hysteresis caused by close van der Waals contacts incurred during the
conformational change from one state to the other. Pilot studies showed
that using two conformers that were found to be directly interconvertible
in the MD simulation can minimize the problem of the close van der
Waals contacts. Electrostatic and van der Waals contributions were
simultaneously calculated with 100 windows. Each forward or reverse
run was calculated for at least 1.0 ns. All conformational perturbation
paths were visually inspected with the Midas Plus graphics program
of the UCSF Computer Graphics Lab to ensure that no close van der
Waals contacts incurred in the conformational changes. For a smooth
conformational transition, some of the PMF calculations listed in Table
Conformer 1S10 and its thermodynamically identical mirror image
1
S10′ were arbitrarily chosen in the first two simulations. Analysis of
all trajectories collected at 1.0-ps intervals during the 1.0-ns MD
simulation revealed that 1S10 was stable only for 2.0 ps and then
changed to 1S4, which was stable for 203.0 ps and then changed to
1
O11, which was stable for 565.0 ps and then changed to 1T7, which
was stable for 229.0 ps until the simulation stopped (see Table 7). In
the simulation with 1S10′, 1S10′ was immediately changed to “inter-
mediate” 1N2 and later to other “intermediates” (see Table 7).
Conformers 1T7 and 1N2, which appeared at the end of the first two
simulations, were then chosen in the next two simulations. The
simulation with the conformer that appeared at the end of the prior
simulation was iterated until a reasonably stable conformer such as
8
were broken into two subperturbations which change part of the four
torsions at the first step and the rest at the last step. The free energy
changes of 12 independent perturbations are listed in Table 8. The
convergence of the data in Table 8 is demonstrated by the fact that the
free energy difference (0.3 ( 0.4 kcal/mol) of the perturbation of 1T5
to 1T7 matches the free energy difference (0.4 ( 0.6 kcal/mol) of two
consecutive perturbations from 1T5 to 1T7 through 1N6.
FEP Calculations. All derivative conformers generated by exchang-
ing the carboxylate group with the methine proton (i.e., 1N2b, 1F3b,
and 1N9b, see Figure 9), excluding those whose potential energy is 5
kcal/mol higher than that of the corresponding parent conformers, were
then compared for free energy difference at 25 °C in water with their
parent conformers. This free energy difference was computed by the
FEP method.22
1
T5 was identified, or until the conformer that appeared at the end of
a simulation was identical to the conformers that appeared previously
in the same or other simulations. Other conformers, which did not
appear in the previous simulations, were arbitrarily chosen again in a
new simulation, followed by subsequent simulations with the conform-
ers that appeared at the end of the former simulations. This process
was repeated until all 12 conformers had appeared in the simulations.
(
41) Cieplak, P.; Cornell, W. D.; Bayly, C.; Kollman, P. A. J. Comput.
In the FEP calculation, the conformation of isobutyric acid was
restrained (rigidified) with a harmonic potential (IFCON ) CONS and
Chem. 1995, 16, 1357-1377.

Hydrophobic Effect in Aromatic Stacking Interactions
J. Am. Chem. Soc., Vol. 121, No. 8, 1999 1725
Table 8. Free Energy Differences between Different
Conformations at 25 °C in Water
Table 10. Effect of the Force Constant Used To Restrain the
Conformation of 1F3b on Free Energy at 25 °C in Water
perturbation
∆G (kcal/mol)
time (ns)
K (kcal/mol)
∆G (kcal/mol)
time (ns)
1N6 to 1N6′int
1T7 to 1N1
1T7 to 1T5
1N9 to 1O11
1T7 to 1O11
1S10 to 1S4
1S4 to 1O11
1N2 to 1N6
1N8 to 1N6
1N6 to 1T5
1S10 to 1F12
1T7 to 1F3b
1N6 to 1T7
4.8 ( 0.3
0.7 ( 0.4
8.0
8.2
6.0
2.0
2.0
2.0
2.0
4.4
3.2
4.0
2.0
2.0
4.0
800
8
-5.2 ( 0.8
-5.8 ( 0.6
8.0
1.2
-0.3 ( 0.4
2.8 ( 0.4
Table 11. Free Energy Changes of 1F3 to 1F3b Calculated with
Different Perturbation Approaches at 25 °C in Water
5.2 ( 0.07
2.4 ( 0.1
-1.8 ( 0.3
-1.1 ( 0.2
0.6 ( 0.07
-1.3 ( 0.07
1.2 ( 0.2
perturbation
∆G (kcal/mol)
time (ns)
approach 1
approach 2
-5.2 ( 0.8
-5.3 ( 0.8
8.0
6.0
3.7 ( 0.2
-0.9 ( 0.5
simultaneously (i) the charge of the methine proton to the charge of
carbonyl carbon, (ii) the charge of the carbonyl carbon to the charge
of the methine proton, and (iii) the charges of the two oxygen atoms
to zero. Second, the van der Waals run exchanged the carboxylate group
with the methine proton. Third, the electrostatic run introduced the
charges of the two oxygen atoms at the final state. The nonbonded list
was updated at every step in this path. The comparison of the free
energy changes calculated with the two approaches is listed in Table
11. To achieve a comparable standard deviation of the mean, the three-
step path requires less simulation time and is more efficient than the
two-step path.
Figure 9. Conformational derivation by exchanging the carboxylate
Chemical Shifts of 2 and 3. A total of 14 different conformations
for 2 were generated by the same procedure used to generate the
different conformations of 1, except that the orientation of the
carboxylate group was taken into account. Similarly, five conformations
for 3 were obtained from the conformational search. Optimization using
the Gaussian 94 program with the B3LYP/6-31G* function reduced
the numbers of different conformations of 2 and 3 to 10 and 3,
respectively. The chemical shifts in Table 6 are the average of the
chemical shifts of different conformations calculated with the B3LYP/
group with the methine proton.
Table 9. Free Energy Differences at 25 °C in Water between the
Parent and Derivative Conformers Restrained by the Force Constant
of 800 kcal/mol
perturbation
∆G (kcal/mol)
time (ns)
1N6′int to 1N6′
1N2 to 1N2b
1F3 to 1F3b
1N9 to 1N9b
-4.4 ( 0.4
-0.2 ( 0.7
-5.2 ( 0.8
1.0 ( 0.3
16.0
8.0
8.0
8.0
6
-31G*//B3LYP/6-31G* function and are relative to the absolute
shielding value of tetramethylsilane (32.184025 ppm) calculated with
the same function.
CONK ) 800 kcal/mol in PARM). The perturbation was broken into
two subperturbations in order to avoid calculation failure due to the
presence of two negatively charged intermediate carboxylate groups
in a one-step perturbation. The first subperturbation mutated the
carboxylate group to a methine proton. The second then changed the
other methine proton to a carboxylate group. Electrostatic and van der
Waals contributions were separately calculated with 1000 windows for
electrostatic and 50 windows for van der Waals. No counterion was
included, to avoid calculation failure when the counterion occasionally
moved out of the water box after removal of the charges of the
carboxylate group. The flag NCORC was set to 1 to calculate the
Acknowledgment. P.A.K. is pleased to acknowledge re-
search support from the NSF (CHE-9417458). Y.P.P. acknowl-
edges the support of the Mayo Foundation for Medical
Education and Research, the help of Drs. Bert E. Thomas IV,
Piotr Cieplak, and Christopher Chipot in the charge calculations,
and the assistance from the members of the Kollman group in
using the AMBER programs. We thank Professor Paul Carlier
of the Hong Kong University of Science and Technology for
comments on our NMR studies, M. Stacy of the Mayo
Foundation for the support of the computing resources at Mayo
Clinic Rochester, and L. Benson of the Mayo Foundation for
mass spectroscopic analysis. We are grateful to the UCSF
Computer Graphics Lab (RR-1081, T. Ferrin, P.I.) for graphics
support and to the San Diego and Pittsburgh Supercomputer
Center for computational support.
contributions to the free energy from any constraint whose equilibrium
value changed with λ.42 Each forward or reverse run was calculated
for at least 1.0 ns. The nonbonded list was updated at every five steps
in the FEP calculations.
The results of the FEP calculations are listed in Table 9. Exchange
of the carboxylate group with the methine proton makes 1N2 and 1F3
more stable in water by 0.2 ( 0.7 and 5.2 ( 0.8 kcal/mol, respectively.
To the contrary, the exchange of the carboxylate group makes the
nonstacked conformer 1N9 less stable in water by 1.0 ( 0.3 kcal/mol.
A calculation with different force constants used to restrain the
isobutyric acid linker was carried out to examine the effect of the force
constant on free energy. The results in Table 10 indicate that changing
the force constant from 800 to 8 kcal/mol does not significantly affect
the calculated free energy difference. To examine perturbation path
efficiency, a calculation with an alternative path was performed. This
path consisted of three steps: First, the electrostatic run mutated
Supporting Information Available: General description of
synthesis; NMR spectral data of 1-3 in D2O and d6-DMSO at
different temperatures; Tables I-V containing the atom types,
RESP charges, force field parameters of 1, and Tables VI and
VII containing the torsions that define the different conformers
of 2 and 3 and the corresponding conformational energies
calculated with the B3LYP/6-31G*//B3LYP/6-31G* function
(PDF). This material is available free of charge via the Internet
at http://pubs.acs.org.
(
42) Pearlman, D. A.; Kollman, P. A. J. Chem. Phys. 1991, 94, 4532-
4
545.
JA9828410