New ultrahigh affinity host-guest complexes of cucurbit[7]uril with bicyclo[2.2.2]octane and adamantane guests: Thermodynamic analysis and evaluation of M2 affinity calculations

Article abstract of DOI:10.1021/ja109904u

A dicationic ferrocene derivative has previously been shown to bind cucurbit[7]uril (CB[7]) in water with ultrahigh affinity (ΔG^o= -21 kcal/mol). Here, we describe new compounds that bind aqueous CB[7] equally well, validating our prior suggestion that they, too, would be ultrahigh affinity CB[7] guests. The present guests, which are based upon either a bicyclo[2.2.2]octane or adamantane core, have no metal atoms, so these results also confirm that the remarkably high affinities of the ferrocene-based guest need not be attributed to metal-specific interactions. Because we used the M2 method to compute the affinities of several of the new host-guest systems prior to synthesizing them, the present results also provide for the first blinded evaluation of this computational method. The blinded calculations agree reasonably well with experiment and successfully reproduce the observation that the new adamantane-based guests achieve extremely high affinities, despite the fact that they position a cationic substituent at only one electronegative portal of the CB[7] host. However, there are also significant deviations from experiment, and these lead to the correction of a procedural error and an instructive evaluation of the sensitivity of the calculations to physically reasonable variations in molecular energy parameters. The new experimental and computational results presented here bear on the physical mechanisms of molecular recognition, the accuracy of the M2 method, and the usefulness of host-guest systems as test-beds for computational methods.

Full text of DOI:10.1021/ja109904u

ARTICLE
pubs.acs.org/JACS
New Ultrahigh Affinity Host-Guest Complexes of Cucurbit[7]uril with
Bicyclo[2.2.2]octane and Adamantane Guests: Thermodynamic
Analysis and Evaluation of M2 Affinity Calculations
Sarvin Moghaddam,† Cheng Yang,‡ Mikhail Rekharsky,‡ Young Ho Ko,§ Kimoon Kim,§ Yoshihisa Inoue,*,‡
and Michael K. Gilson*,z,†
†Center for Advanced Research in Biotechnology, University of Maryland Biotechnology Institute, 9600 Gudelsky Drive, Rockville,
Maryland 20850, United States
‡PRESTO (JST) and Department of Applied Chemistry, Osaka University, Yamada-oka, Suita 565-0871, Japan
§National Creative Research Initiative Center for Smart Supramolecules, Department of Chemistry, and Division of Advanced Materials
Science, Pohang University of Science and Technology, San 31 Hyojadong, Pohang 790-784, Republic of Korea
S Supporting Information
b
ABSTRACT: A dicationic ferrocene derivative has previously been
shown to bind cucurbit[7]uril (CB[7]) in water with ultrahigh affinity
(ΔGo = -21 kcal/mol). Here, we describe new compounds that bind
aqueous CB[7] equally well, validating our prior suggestion that they,
too, would be ultrahigh affinity CB[7] guests. The present guests, which
are based upon either a bicyclo[2.2.2]octane or adamantane core, have
no metal atoms, so these results also confirm that the remarkably high
affinities of the ferrocene-based guest need not be attributed to metal-
specific interactions. Because we used the M2 method to compute the
affinities of several of the new host-guest systems prior to synthesizing them, the present results also provide for the first blinded
evaluation of this computational method. The blinded calculations agree reasonably well with experiment and successfully
reproduce the observation that the new adamantane-based guests achieve extremely high affinities, despite the fact that they position
a cationic substituent at only one electronegative portal of the CB[7] host. However, there are also significant deviations from
experiment, and these lead to the correction of a procedural error and an instructive evaluation of the sensitivity of the calculations to
physically reasonable variations in molecular energy parameters. The new experimental and computational results presented here
bear on the physical mechanisms of molecular recognition, the accuracy of the M2 method, and the usefulness of host-guest
systems as test-beds for computational methods.
’ INTRODUCTION
a truly blinded prediction mode; that is, without prior knowledge
The synthetic host cucurbit[7]uril (CB[7])1,2 (Figure 1)
binds certain cationic guests from aqueous solution with affinities
surpassing those of most protein-small molecule pairs.3,4 The
highest CB[7] affinity to date, -21 kcal/mol, is achieved by a
ferrocene outfitted with ammonium groups, one on each cyclo-
pentadienyl ring. The ferrocene core, which is hydrophobic,
binds in the cavity of CB[7], while one ammonium sits at each
portal, interacting with the electronegative carbonyl oxygens.4
Experiment and calculation indicate that the extremely high
affinity of this host-guest pair results from the favorable
energetic interactions, coupled with disproportionately low en-
tropic penalties.4 The computations, carried out with the second
generation Mining Minima (M2) method,5,6 also yielded en-
couragingly good agreement with experiment, suggesting that
M2 calculations might be useful as a tool to guide the design of
new host-guest pairs. On the other hand, the M2 calculations
were carried out with prior knowledge of the measured affinities,
and it is known that computational methods are best evaluated in
of the experimental results.
Recently, we proposed a new series of molecules as candidate high-
affinity guests of CB[7].7 These designed compounds essentially
replace the ferrocene moiety with a bicyclo[2.2.2]octane moiety,
which is similar to ferrocene in its size and hydrophobic character.
Calculations with the M2 method supported our expectation that this
class of compounds would bind CB[7] with affinities similar to those
of analogous ferrocene derivatives. The calculations were carried out
and published before the guests were synthesized, allowing for a
rigorous prospective test of the calculations.
We now describe the synthesis of three of these compounds
(Figure 2) and report that they do, in fact, reach the extremely
high binding affinities with CB[7] previously observed for the
ferrocene-based guests (Figure 3). We furthermore report the
synthesis of an additional set of guests (Figure 4) comprising a
nonpolar adamantyl core decorated with one cationic substituent,
Received: November 4, 2010
Published: February 22, 2011
r
2011 American Chemical Society
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Figure 1. Cucurbit[7]uril, shown as a chemical drawing (left) and in 3-dimensional representations. Side view (center) highlights the repeating
glycouril unit. Top view (right) highlights the circular shape of this host. Three-dimensional graphics here and in other figures were generated with the
program VMD.33.
derivatives were synthesized as described in the Supporting Information.
Adamantane derivatives were purchased from Aldrich or TCI and used as
received.
Microcalorimetric titration experiments were carried out in an
isothermal titration calorimeter VP-ITC (MicroCal) by consecutively
injecting a fixed volume (3-10 μL) of guest solution into the micro-
calorimetric reaction cell (1.4 mL) charged with a CB[7] solution. The
multistep competitive titration technique was employed to determine
the extraordinarily large binding constants ranging from 109 to 1015 M-1
.
Thus, the stepwise titration runs were performed employing two series
of appropriate competitive guests, each of which possesses an affinity of
approximately 3 orders of magnitude smaller than that of the target
guest.4 We chose cyclopentanone, L-phenylalanine, spermine, 1,6-hex-
anediamine, aminomethylcyclohexane, and N,N0-bis(aminoethyl)-1,6-
hexanediamine as competitors, which possess the binding constants of
4.2 ꢀ 105, 1.8 ꢀ 106, 4.8 ꢀ 108, 2.1 ꢀ 109, 1.3 ꢀ 1011, and 1.7 ꢀ 1011
M-1, respectively.
Figure 2. New, designed guest molecules based on
bicyclo[2.2.2]octane core.
a
Computational Methods. The M2 computational method has
been previously described5,6,8 and also is currently available for down-
load at http://pharmacy.ucsd.edu/labs/gilson. It is therefore not de-
scribed in detail here. In brief, the standard free energies (or, more
properly, chemical potentials) of the free host and guest are computed
and subtracted from that of their complex. The free energies are
estimated as sums over local energy wells, where the energy is computed
as the sum of the potential energy provided by an empirical force field,
such as CHARMm9-11 and an implicit solvation free energy. A general-
ized Born (GB)12,13 solvation model is used during conformational
search and energy-minimization for the sake of computational tract-
ability, but the free energy of each energy well is corrected by subtracting
out the GB energy of its energy-minimum and adding back the solvation
estimated with a finite-difference solution of the linearized Poisson-
Boltzmann (PB) equation,14 plus a nonpolar term estimated as propor-
tional to the molecular surface area.15 Prior studies indicate that
substituting PB for GB energies improves accuracy.6,16 The free energy
of each energy well is estimated by the harmonic approximation/mode
scanning method,8 which allows the harmonic approximation to be
corrected for the most marked anharmonicities based upon scans of the
energy along the low-force-constant eigenvectors of the Hessian matrix.
The overall free energy GN of a set of N conformers with individual free
energies (chemical potentials) Gi is given by
Figure 3. Ferrocene-based guest molecules.
Figure 4. New, adamantane-based guest molecules.
rather than two. Intriguingly, these adamantane-based com-
pounds prove to bind CB[7] as tightly as the dicationic guests
with ferrocene and bicyclo[2.2.2]octane cores. The new experi-
mental results are compared with our previously published M2
results, and new M2 calculations are also reported and analyzed.
N
GN ¼ - RT ln½ ∑ e-G =ðRTÞꢁ
ð1Þ
i
i ¼1
The search for new energy wells uses the aggressive Tork algorithm17
and is iterated until the overall free energy changes by less than 0.1 kcal/
mol from one iteration to the next. Each successive iteration takes the six
most stable conformations found in the prior cycle as the starting point
of a new conformational search, so each iteration involves 6 parallel
’ METHODS
Experimental Materials and Methods. CB[7] was prepared
and purified according to the literature procedures.2 Bicyclo[2.2.2]octane
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ARTICLE
Table 1. Correspondences between Quanta Commercial
CHARMm Atom Types11 (Accelrys, Inc., San Diego, CA) and
Academic CHARMM Atom Types9,10 Used To Generate an
Alternate Set of Physically Reasonable Lennard-Jones Param-
eters for the Host-Guest Systems Studied Herea
Table 2. Experimental Standard Free Energy (ΔGoexpt), en-
thalpy (ΔHoexpt), and Entropy Changes (-TΔSoexpt) for
Complexation of Ferrocene (Figure 3), Bicyclo[2.2.2]octane
(Figure 2) and Adamantane (Figure 4) Guests with CB[7] in
H2O at T = 298.15 K, Reported in kcal/mola
commercial CHARMm
academic CHARMM Type
ΔGo
ΔHo
-ΤΔSo
K (Μ-1
)
expt
expt
expt
HA (nonpolar)
HA
ferrocene guestsb
HA (aromatic)
HP
F1
F2
F3
F6
-13.0 ( 0.1
-21.5 ( 0.5
-21.0 ( 0.5
-21.5 ( 0.5
-21.5 ( 0.2
8.6 ( 0.5
4.1 ( 0.5
4.3 ( 0.4
0.5 ( 0.5
(3.2 ( 0.5) ꢀ 109
(2.4 ( 0.8) ꢀ 1012
(4.1 ( 1.0) ꢀ 1012
(3.0 ( 1.0) ꢀ 1015
HC
HC
H
-16.9 ( 0.2
-17.2 ( 0.2
-21.1 ( 0.2
HO
CT (aliphatic SP3 in CH group)
CT1
CT2
CT3
CC
CT (aliphatic SP3 in CH2 group)
bicycle[2.2.2]octane guests
CT (aliphatic SP3 in CH3 group)
B2
-13.4 ( 0.1
-19.5 ( 0.2
-20.6 ( 0.4
-15.8 ( 0.2
-15.6 ( 0.4
-16.3 ( 0.4
2.4 ( 0.2
-3.9 ( 0.5
-4.3 ( 0.5
(6.1 ( 0.5) ꢀ 109
(2.0 ( 0.5) ꢀ 1014
(1.2 ( 0.5) ꢀ 1015
C (carbonyl)
C5R
B5
CA
B11
NT (ammonium)
NT (amide)
NT (peptide)
NX
NH3
NH2
NH1
NH2
FE
adamantane guests
A1
A2
A3c
A4c
A5
-14.1 ( 0.2
-19.4 ( 0.1
-20.3
-19.0 ( 0.4
-19.3 ( 0.4
-21.9 ( 0.4
-20.1 ( 0.4
-19.5 ( 0.4
4.9 ( 0.4
-0.1 ( 0.5
1.7
(2.3 ( 0.8) ꢀ 1010
(1.7 ( 0.8) ꢀ 1014
7.7 ꢀ 1014
MFE
-21.5
-1.4
5 ꢀ 1015
OT
OH1
-19.1 ( 0.2
0.4 ( 0.5
(1.0 ( 0.3) ꢀ 1014
O
O
a All thermodynamic data are averages of three independent experi-
mental runs, unless stated otherwise; see Table S1 in the Supporting
a In the academic set, we also used CT1 parameters for an aliphatic
carbon with no hydrogens. The academic atom types and parameters are
drawn from parameter set toppar_c35b2_c36A3, file par_all27_prot_-
na.prm, obtained at http://mackerell.umaryland.edu/CHARMM_ff_-
params.html.
Information for full details. b Reference 4. Due to the extremely slow
c
equilibrium, the ΔGoexpt value was determined by the NMR competition
technique, in which the error was not determined.
carried out with the program UHBD,20 with interior and exterior
dielectric constants set to 1 and 80, respectively. The boundary of the
low-dielectric interior was defined by the Richards molecular surface21
with a 1.4 Å probe radius. Each atom’s dielectric cavity radius was set to
the Rmin value for its Lennard-Jones parameter, except that hydrogen
radii were set to 1.2 Å. Initial structures of the host-guest complexes
were generated with the program Vdock.22,23
Analysis of Solvation Thermodynamics. Combining mea-
sured calorimetric data with the results of M2 calculations permits us
to draw inferences about solvation thermodynamics, within the limits of
experimental and computational accuracy. Thus, the change in total
entropy on binding, as obtained calorimetrically, can be rigorously
decomposed into a change in configurational entropy, which is asso-
ciated only with motions of the host and guest, and a change in solvation
entropy, which is associated only with motions of the solvent (but is
Boltzmann-averaged over conformations of the host and guest);24 that
is, ΔSexpt = ΔScfg þ ΔSsolv. (The first two terms depend on the choice of
standard concentration, Co, here taken as 1 M as is customary.) Because
we have the first term from experiment and the second from calculation,
we can compute the third, the solvation entropy, as the difference
between the first two. In addition, since our implicit solvation model
gives us the change in the mean solvation free energy on binding, ΔW,
we can also obtain the change in the mean internal energy of the solvent
on binding ΔUsolv. That is, combining calculation and experiment gives
the following estimates of solvation thermodynamics:
searches from different starting points. For the present systems, each
iteration generated on the order of 1000-2000 local energy minima.
However, many of these conformations are deleted because they are
repeats, based upon a comparison of all conformations with each other,
using an algorithm that accounts for molecular symmetries.18 The large
fraction of repeats reflects the modest number of flexible degrees of
freedom in the systems studied here. Occasional conformers with
implausible puckered conformations of the host or with the guest
outside the binding cavity also were discarded. The present calculations
required 2-7 iterations to converge, and yielded an average of about 80
distinct conformers per free guest or complex, with fewer for simpler
guests (e.g., 18 for B5) and more for the larger complexes (e.g., 159 for
B11 bound to CB[7]). When the final sets of conformers are sorted from
lowest to highest free energy and the cumulative free energy is computed
as a function of the number of conformers included, it is found that the
few most stable conformers suffice to converge the overall free energy to
within 1 kcal/mol of the value obtained from all conformers together.
For example, even for the largest system, B11 bound to CB[7], the three
most stable conformers yield a free energy within 1 kcal/mol of the full
value, the 10 most stable conformers yield a free energy within 0.5 of the
full value, and the least stable 100 conformers contribute only 0.03 kcal/
mol to the overall stability.
The parameters of the ferrocene derivatives were assigned as pre-
viously described.4 For the other molecules, initial bonded and Lennard-
Jones parameters were assigned from the commercial CHARMm force
field11 with the program Quanta (Accelrys, Inc., San Diego, CA). Partial
atomic charges were assigned with the program Vcharge with the VC/
2004 parameter set.19 Additional calculations were done in which the
Lennard-Jones parameters from the commercial CHARMm force field
were replaced with corresponding parameters from a recent version of
the academic CHARMM force.10 Table 1 lists the atom-type substitu-
tions used for this purpose. Poisson-Boltzmann calculations were
ΔSsolv ¼ ΔSexpt - ΔScfg
ΔUsolv ¼ ΔW þ TΔSsolv
ð2aÞ
ð2bÞ
where we have used the fact that Δ(PV) is negligible for an aqueous
binding reaction at 1 atm pressure.25 Note that ΔUsolv includes both
solvent-solvent and solute-solvent interactions.
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Table 3. Experimental (ΔGoexpt) and Computed (ΔGocalcd) Binding Free Energies for CB[7] with Bicyclo[2.2.2]octane Guests,
along with Computed Free Energy Breakdownsa
mean energy changes
ΔGo
ΔGo
Δ(U þ W)
-TΔSo
cfg
ΔUvdW
ΔUC
ΔWel
ΔEel
ΔUval
ΔWnp
expt
calcd
published
B2
-13.4
-19.5
-20.6
-12.8
-25.6
-19.9
-29.6
-37.6
-41.4
16.8
12.0
21.5
-34.6
-31.8
-42.0
-8.1
-162.1
-241.1
14.3
155.3
232.0
6.2
-6.8
-9.1
1.4
3.8
-2.7
-2.7
-3.8
B5
B11
13.5
corrected
B2
-13.4
-19.5
-20.6
-12.0
-23.1
-22.4
-29.4
-37.6
-38.2
17.4
14.5
15.7
-34.3
-31.3
-37.6
-8.2
-163.3
-227.5
14.5
156.7
226.4
6.3
-6.6
-1.1
1.2
3.0
3.9
-2.6
-2.7
-3.2
B5
B11
academic vdW
B2
-13.4
-12.4
-23.7
-22.9
-29.6
-38.5
-38.7
17.2
14.8
15.8
-32.9
-30.3
-35.7
-8.2
-155.1
-219.2
14.1
146.9
216.2
5.9
-8.2
-3.0
0.2
2.8
3.3
-2.7
-2.8
-3.2
B5
-19.5
-20.6
B11
academic vdW/commercial radii
B2
-13.4
-19.5
-20.6
-11.9
-17.8
-16.1
-28.0
-31.5
-30.0
16.1
13.7
14.0
-33.0
-30.6
-35.7
-7.2
-153.3
-219.2
14.7
152.9
225.9
7.5
-0.4
6.8
0.2
2.2
2.1
-2.7
-2.8
-3.2
B5
B11
a Published, our prior calculations; corrected, current calculations with corrected (finer) finite-difference Poisson-Boltzmann (FDPB) grids; academic
vdW, current calculations with corrected FDPB grids and academic Lennard-Jones parameters (see text); academic vdW/commercial radii, current
calculations with corrected FDPB grids, academic Lennard-Jones parameters, and dielectric cavity radii based upon commercial Lennard-Jones σ values;
Δ(U þ W), change in Boltzmann-averaged total potential and solvation energy; -TΔSocfg, configurational entropy contribution to binding free energy.
Mean energy changes, Boltzmann-averaged energy contributions from the various potential and solvation energy contributions, as follows: ΔUvdW, van
der Waals energy; ΔUC, Coulombic energy; ΔWel, electrostatic (PB) solvation energy; ΔEel, sum of ΔUC and ΔWel; ΔUval, valence (bond-stretch,
angle-bend, and dihedral) energy; ΔWnp, nonpolar solvation energy.
’ RESULTS AND DISCUSSION
not be ascribed to any subtlety in the electronic structure of the
ferrocene moiety, with its central iron atom and its aromatic
cyclopentadiene rings. Rather, van der Waals, electrostatic, and
solvent interactions apparently suffice, since these are the main
interactions accessible to the bicyclo[2.2.2]octane series with its
similarly high affinities.
Measured Affinities of Bicyclooctane and Adamantane
Guests with Cucurbit[7]uril. Despite extensive efforts to dis-
cover artificial host-guest systems with affinities rivaling that
of biotin and avidin, such an ultrahigh affinity has hitherto
been achieved only by one CB[7]-ferrocene couple, F6
(Figure 3, Table 2). The strikingly high affinity in this case
has been ascribed to the perfect size/shape complementarity
of the two molecules, combined with their rigidity, which
minimizes entropic losses.1,2,22 As a logical extension of this
idea, we have synthesized and tested a small series of bi-
cyclo[2.2.2]octane and adamantane molecules designed to
further probe the high-affinity binding regime of CB[7]
binding.
The binding free energies of the designed bicyclo[2.2.2]octane
guests with aqueous CB[7] range from -13.4 to -20.6 kcal/mol
(Table 2). These affinities are extraordinarily high for such small
host-guest systems,7,26 yet are commensurate with the CB[7]
affinities previously reported for the ferrocene-based guests1,2
which inspired these designs. Much as previously observed for
the ferrocenes2 (see Table 2), the neutral bicyclo[2.2.2]octane
guest, B2, has a binding free energy near -13 kcal/mol, while
adding two ammonium groups positioned to enable close polar
interactions with the carbonyls at the CB[7] portal, increases the
affinity by approximately 7 kcal/mol, as shown for B5 and B11.
Thus, the new bicyclo[2.2.2]octane compounds display CB[7]
affinities and affinity-trends strikingly similar to those previously
observed for the ferrocene series of CB[7] guests. This observa-
tion substantiates the suggestion,7 based on M2 calculations, that
the ultrahigh affinity of the cationic ferrocenes for CB[7] need
The adamantane derivatives also achieve high measured
affinities for CB[7] (Table 2). The binding free energy of
the neutral adamantane derivative A1 is already quite strong, at
-14.1 kcal/mol, and the affinities become even greater, by -5 to
-7 kcal/mol, upon adding either a mono- (A2, A3, A5) or
di- (A4) cationic substituent positioned to interact with one of
the electronegative portals of the CB[7] host. The resulting
binding free energies reach a maximum of -21.5 kcal/mol, for
A4, corresponding to a binding constant 5 ꢀ 1015 M-1, in the
case of A4 (Table 2). These high affinities are particularly striking
given that these compounds have only one cationic substituent to
interact with the two electronegative portals of CB[7]. In
contrast, the highest-affinity ferrocenyl and bicyclo[2.2.2]octyl
compounds have two cationic substituents, and their variants
with only one cationic substituent display considerably lower
affinities.4 It is also interesting to examine the consequences
of going from A2, with its single monocationic substituent, to
A4, whose extended substituent includes a second ammonium
group: adding this second þ1 charge strengthens the affinity by
about -2 kcal/mol. This may be compared with the similar
change from B5 to B11 among the bicyclooctane derivatives,
where adding a second ammonium group, now to two R groups,
increases the affinity by only -1 kcal/mol. This comparatively
modest increment, despite a larger charge increment, presumably
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A smaller binding free energy, -17.4 kcal/mol rather than the
present -19.4 kcal/mol, was previously reported for A2 with
CB[7].3 The difference presumably results, at least in part, from
the difference in salt concentrations. The prior measurements
were done in (perdeuterated) 50 mM sodium acetate (pD 4.74),
while the present measurements were done in essentially pure
water, and it is known that the affinities of CB[7] for cationic
guests is strongly salt-dependent.27 If the neutral acetic acid
component of the sodium acetate buffer binds within the host’s
cavity, as previously observed in the case of CB[6],27,28 the
resulting competition between acetic acid and the guest mole-
cules could also have played a role in lowering their apparent
binding affinities.
Comparison of Calculation with Experiment. Comparison
of previously reported M2 calculations7 with the new experimental
data for the bicyclooctaneguests (Table 3, published) show that the
calculations were correct to within 1 kcal/mol for guests B2 and
B11 but overestimated the affinity of guest B5 by about 6 kcal/mol.
They thus succeeded in capturing the fact that these are remarkably
high affinity host-guest systems but were less reliable in detail than
hoped. We therefore reexamined the calculations for possible
sources of error and discovered that the finite difference Pois-
son-Boltzmann (FDPB) calculations, which had been incorpo-
rated into an automated procedure, had used fine finite difference
grids with spacings of 0.2-0.5 Å, with the coarser grids for the
larger molecules and complexes. Grid spacings less than ∼0.3 Å are
needed for properly converged results,14,29 and we modified
the FDPB procedure accordingly. When the calculations are
redone with FDPB grid spacings of 0.1-0.2 Å (Table 3,
corrected), the computed binding free energies shift by up to
2.5 kcal/mol, and the deviation from experiment increases for B2
and B11 but decreases to 3.6 kcal/mol for B5. The overall
deviation from experiment, summarized as the root-mean-square
deviation (rmsd), falls from 3.56 to 2.46 kcal/mol. The only
striking change we observed for the preferred conformations of
these systems, on going to finer FDPB grids, was that the CB[7]-
B11 complex is now predicted to prefer a more hydrated
conformation with the guest’s chain extending into solution
rather than lying on the CB[7] portal (Figure 5). This con-
formational change is associated with physically reasonable shifts
in multiple free energy contributions, indicating weaker Cou-
lombic interactions, greater electrostatic solvation, lower valence
strain (presumably due to more favored dihedral angles), and a
lower configurational entropy penalty. (Here, configurational
entropy indicates the component of the entropy associated with
the conformational fluctuations of just the host and guest; the full
entropy would include a contribution from solvent fluctuations.24)
Because the coarse FDPB grid spacings also affected prior
calculations for the ferrocenyl guests7 (Table 4, published), we reran
these calculations as well (Table 4, corrected). For this series, the
finer FDPB grids yield consistently weaker computed affinities,
underestimating the experimental affinities and leading to greater
deviations from experiment, with the overall rmsd rising from 2.11 to
3.93. Nonetheless, the new calculations still reproduce the basic trend
in this series, as a linear regression of calculation with experiment
yields a slope of 0.93, y-intercept of 2.7, and R2 of 0.9.
Figure 5. (a) Most stable computed conformation of compound B11
complexed with CB[7], from published calculations with overly coarse
finite difference Poisson-Boltzmann grid spacings (ref 7). (b) Most
stable computed conformation of compound B11 complexed with
CB[7], from new calculations with corrected (fine) finite difference
Poisson-Boltzmann grid spacings and original (commercial) CHARMm
parameters (see text.).
traces to the fact that the dicationic bicyclo substituents have
three methylenes between the ammonium groups (Figure 2),
whereas the ammonium substituent has two (Figure 4). In
addition, the bicyclooctane and adamantyl cores presumably
position the cationic substituents somewhat differently relative to
the CB[7] portal, and the adamantyl geometry may facilitate
favorable interactions of the terminal ammonium group of A4
with the host.
M2 calculations for the adamantane series with the improved
FDPB grid spacings (Table 5, corrected) significantly overshoot
the measured binding affinities, much as observed for B5. The
computed adamantyl binding free energies range from -24.1
to -29.7 kcal/mol, rather than -19.1 to -21.5 kcal/mol, as seen
experimentally. The rmsd is 5.97 kcal/mol. On one hand, these
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Table 4. Experimental (ΔGoexpt) and Computed (ΔGocalcd) Binding Free Energies for CB[7] with Ferrocene Guests, along with
Computed Free Energy Breakdownsa
mean energy changes
ΔGo
ΔGo
Δ(U þ W)
-TΔSo
cfg
ΔUvdW
ΔUC
ΔWel
ΔEel
ΔUval
ΔWnp
expt
calcd
published
F1
-12.9
-16.8
-17.2
-21.0
-10.5
-14.6
-14.5
-21.0
-25.3
-32.5
-31.1
-38.8
14.8
17.9
16.6
17.8
-27.0
-29.9
-33.0
-39.2
-17.0
-77.9
-70.2
-133.2
19.8
75.8
2.8
-2.0
4.6
1.5
2.3
0.2
0.8
-2.6
-2.9
-3.0
-3.4
F2
F3
74.8
F6
136.2
3.0
corrected
F1
-12.9
-16.8
-17.2
-21.0
-10.2
-12.4
-12.2
-17.8
-24.3
-30.6
-28.8
-37.7
14.1
18.2
16.6
19.9
-27.3
-29.8
-32.7
-39.2
-16.1
-77.8
-70.3
-134.0
19.1
77.6
3.0
-0.1
6.0
2.6
2.2
0.8
0.5
-2.6
-2.9
-3.0
-3.4
F2
F3
76.2
F6
138.4
4.4
academic vdW
F1
F2
F3
F6
-12.9
-11.3
-14.7
-15.5
-27.3
-29.6
-33.5
-33.3
-45.4
18.4
18.7
17.8
18.1
-29.5
-32.1
-34.8
-42.0
-18.3
-72.6
-67.3
-129.7
17.9
71.4
-0.4
-1.2
2.3
2.9
2.8
2.2
1.1
-2.6
-2.9
-3.0
-3.6
-16.8
-17.2
-21.0
69.6
128.8
-1.0
academic vdW/commercial Radii
F1
F2
F3
F6
-12.9
-16.8
-17.2
-21.0
-9.5
-12.5
-12.2
-22.6
-26.4
-29.0
-32.8
-41.7
16.9
16.5
20.5
19.2
-29.8
-31.8
-35.6
-41.9
-13.9
-71.8
-67.0
-132.2
17.2
74.4
3.3
2.6
5.9
4.0
2.7
3.1
-2.7
-2.9
-3.0
-3.5
72.9
-0.2
-0.3
136.2
a See caption of Table 3 for details.
Table 5. Experimental (ΔGoexpt) and Computed (ΔGocalcd) Binding Free Energies for CB[7] with Adamantane Guests, along with
Computed Free Energy Breakdownsa
mean energy changes
ΔGo
ΔGo
Δ(U þ W)
-TΔSo
cfg
ΔUvdW
ΔUC
ΔWel
ΔEel
ΔUval
ΔWnp
expt
calcd
corrected
A1
-14.1
-19.4
-20.4
-21.5
-19.1
-18.2
-25.9
-25.6
-29.7
-24.1
-30.8
-37.7
-38.9
-45.4
-36.7
12.6
11.8
13.3
15.7
12.5
-35.7
-35.5
-35.1
-38.1
-35.6
-1.8
-77.2
-77.0
-145.4
-75.6
9.1
76.1
7.2
-1.1
-2.0
-7.0
0.4
0.0
1.5
0.9
2.5
1.1
-2.4
-2.5
-2.6
-2.8
-2.5
A2
A3
75.0
A4
138.5
76.0
A5
academic vdW
A1
A2
A3
A4
A5
-14.1
-15.1
-21.4
-22.5
-22.4
-21.0
-30.8
-36.8
-38.6
-39.9
-35.3
15.7
15.4
16.1
17.5
14.3
-31.4
-31.2
-30.9
-33.2
-30.6
-6.2
-74.7
-75.4
-137.2
-73.8
8.7
70.7
2.4
-4.0
-6.4
-5.2
-3.3
0.7
0.9
1.4
1.3
1.1
-2.5
-2.5
-2.7
-2.9
-2.6
-19.4
-20.4
-21.5
-19.1
68.9
132.1
70.5
academic vdW/commercial radii
A1
A2
A3
A4
A5
-14.1
-19.4
-20.4
-21.5
-19.1
-14.3
-18.2
-19.3
-17.2
-17.1
-29.1
-33.8
-34.3
-31.9
-31.8
14.8
15.7
15.0
14.7
14.8
-31.3
-31.2
-31.0
-32.9
-30.6
-4.4
-74.3
-74.4
-133.3
-73.3
8.7
73.9
4.3
-0.3
-1.9
1.8
0.4
0.2
1.3
1.9
0.5
-2.5
-2.5
-2.6
-2.8
-2.5
72.5
135.3
74.1
0.8
a See caption of Table 3 for details. The published set is absent from this table as we have not previously published calculations for these compounds.
deviations are considerably greater than hoped. On the other
hand, it is arguably a success that the computed binding affinities
of the adamantyl compounds A2 and A3 are very similar to that
of B5, even though they have only one cationic substituent,
whereas B5 has two. Indeed, on the basis of the computed results
for monocationic ferrocene derivatives, one might have expected
that the computed affinities of the monocationic adamantanes
would be closer to -12 kcal/mol. The basis for this outcome may
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Table 6. Comparison of Lennard-Jones Parameters for Key
Atom Types in the Commercial CHARMm and Academic
CHARMM Force Fielda
force field used here are larger for aliphatic carbons than
those of corresponding atom types in the academic
CHARMM force field, as summarized in Table 6. Therefore,
switching from CHARMm to CHARMM parameters might
be expected to weaken the van der Waals attractions com-
puted for the adamantanes and bicyclooctanes. On the other
hand, the aromatic atom types used for the cyclopentadiene
moieties of ferrocene are assigned somewhat smaller values
of ε in CHARMm than CHARMM, so switching to the
academic parameter set should not strengthen ferrocenes
van der Waals terms. These considerations suggested that
replacing the CHARMm Lennard-Jones parameters with
those from CHARMM might improve agreement with
experiment.
Tables 3-5 thus present the results of new M2 calculations
with academic Lennard-Jones parameters substituted for the
initial commercial ones for all atoms (see Table 6), while leaving
all other force-field parameters (e.g., bond-stretches, partial
charges) unchanged at their commercial values. Table 7 then
compares the accuracy of these calculations with the original
ones. The purpose of this analysis is to examine the sensitivity of
the calculations to these parameters, not to suggest general
application of such a mixed parameter set. Switching to the
academic parameters does improve the agreement with experi-
ment: the rmsd of the computed binding free energies relative to
experiment, across all compounds, falls from 4.64 to 2.7 kcal/
mol. In addition, the correlation coefficient R2 rises from 0.61 to
0.87 for a free linear regression, and from 0.54 to 0.78 for a linear
regression constrained to pass through (0,0). The improved
accuracy traces entirely to improved results for the adamantanes,
their rmsd falling from 5.97 to 1.66 kcal/mol, with little change in
accuracy for the ferrocenes (rmsd 3.93 falling to 3.52 kcal/mol)
and some worsening for the bicyclooctanes (rmsd 2.46 rising to
2.82 kcal/mol).
The improvement in accuracy for the adamantanes results
from weaker computed affinities, which, in turn, result largely
from changes in the van der Waals terms (Table 5). Inter-
estingly, however, the weakening of the computed van der
Waals attractions for the adamantanes is accompanied by an
increased entropic penalty, which further reduces the com-
puted affinity. We conjecture that this increase in the
entropic penalty for the adamantanes on going to academic
Lennard-Jones parameters stems from the generally greater
atomic radii (Lennard-Jones σ parameters) in the academic
parameter set (Table 6). The rationale is that adamantane,
being bulkier than bicyclo[2.2.2]octane, fits more snugly into
the cavity of CB[7], so that increasing the atomic radii leads
to a more significant loss of flexibility, and hence entropy, in
the bound complex. A similar pattern is seen for the ada-
mantane and bicyclooctane cores on their own (R = H in
Figures 2 and 4), as shown in Table 8. This observation is
consistent with the suggested attribution of these energy and
entropy shifts to the interactions of the cores with the cavity
of CB[7].
There are also changes in the electrostatic terms on going from
the commercial to academic parameters, with a tendency toward
weaker Coulombic attractions, ΔUC, and smaller Poisson-
Boltzmann desolvation penalties, ΔWel. These two changes
prove to be rather balanced, so that the changes in the total
electrostatic energy, ΔEel = ΔUC þ ΔWel, are smaller in
magnitude than the changes in the individual terms. These
electrostatic changes appear to be attributable to the fact that
commercial
academic
name
ε
σ
name
ε
σ
Ferrocenes
cyclopentadiene C C5R 0.0500 2.040 CA
cyclopentadiene H HA 0.0420 1.330 HP
0.0700 1.9924
0.0300 1.3582
ammonium N
ammonium C
ammonium H
NT 0.1500 1.650 NH1/NH2/NH3 0.2000 1.850
CT
0.0903 1.800 CT3
0.0800 2.060
0.0220 1.320
HA 0.0420 1.330 HA
Bicyclooctanes and Adamantanes
C
CT
0.0903 1.800 CT1
CT2
0.0200, 2.275,
0.0550 2.175
0.0220 1.320
0.2000 1.850
0.0460 0.2245
aliphatic H
N
ammonium H
HA 0.0420 1.330 HA
NT 0.1500 1.650 NH3
HC 0.0498 0.600 HC
CB[7]
carbonyl O
carbonyl C
N
O
C
0.1591 1.550
0.1410 1.870 CC
O
0.1200 1.700
0.0700 2.000
NX 0.0999 1.830 NH1/NH2/NH3 0.2000 1.850
other Cs
CT
0.0903 1.800 CT1
CT2
0.0200 2.275
0.0550 2.175
0.0220 1.320
H
HA 0.042 1.330 HA
a See caption of Table 1 for details. Note that the academic parameters
are the same for the NH1, NH2 and NH3 atom types, as indicated in the
table, and that the commercial CT atom type maps to academic CT1 if
the carbon has one hydrogen and to CT2 if it has two hydrogens. We
also used CT1 parameters for an aliphatic carbon with no hydrogens.
be analyzed by comparing the free energy breakdowns for B5
vs the monocationic adamantanes, A2, A3, and A5 (Tables 3
and 5). Not surprisingly, the net electrostatic driving force
for binding (the sum of the Coulombic and FDPB terms) is
more favorable for B5 (around -7.0 kcal/mol vs -2.0 to 0.40
kcal/mol). However, this electrostatic advantage is balanced
by countervailing differences in the mean van der Waals and
valence energies and in the configurational entropy. The
valence and entropic differences likely stem from the fact that
the adamantane guests have fewer rotatable bonds. The more
favorable van der Waals terms for the adamantanes may
result from the fact that the adamantane core has 10 aliphatic
carbons interacting with the CB[7] cavity, while the bicyclo-
[2.2.2] core has only eight.
Calculations with Alternative Molecular Parameters. We
conjectured that the marked affinity overestimates for the
adamantanes might trace to overly strong attractive van der
Waals interactions between the adamantane core and the
CB[7] cavity. This explanation would be consistent with the
observation that the bicyclooctane affinities are not over-
estimated as much, given that the bicyclooctane core is
somewhat smaller than the adamantyl core, so its van der
Waals contacts with the host are less intimate. Here, van der
Waals interactions are modeled with the Lennard-Jones
expression
!
ꢀ ꢁ
ꢀ ꢁ
12
6
σ
σ
ELJ ¼ ε
-
r
r
so we examined the Lennard-Jones terms more closely and
observed that the values of ε from the commercial CHARMm
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Table 7. Analysis of Deviations between Calculated and Measured Binding Free Energies (kcal/mol) for Merged Ferrocene,
Bicyclo[2.2.2]octane, and Adamantane Data Setsa
standard
intercept
forced through (0,0)
rmsd
slope
R2
slope
R2
corrected FDPB
4.64
2.7
1.67
1.55
1.01
10.7
8.7
0.61
0.87
0.7
1.1
0.54
0.78
0.68
corrected FDPB, academic LJ
corrected FDPB, academic LJ, commercial radii
1.08
0.88
3.00
2.5
a RMSD, root-mean-square deviation; standard, unconstrained linear regression results; forced through (0,0), results of a linear regression forced
through the origin.
Table 8. Computed (ΔGocalcd) Binding Free Energies for CB[7] with Plain Bicyclo[2.2.2]octane and Adamantane (R = H), along
with Computed Free Energy Breakdownsa
mean energy changes
ΔGo
Δ(U þ W)
-TΔSo
ΔUvdW
ΔUC
ΔWel
ΔEel
ΔUval
ΔWnp
calcd
cfg
bicyclo[2.2.2]octane
commercial CHARMm
academic CHARMM
adamantane
-13.4
-11.3
-23.5
-24.1
10.1
12.8
-28.9
-28.1
0.9
7.3
9.6
8.2
6.7
-0.5
-0.4
-2.3
-2.3
-2.8
commercial CHARMm
-15.7
-10.5
-29.1
-29.3
13.4
18.8
-34.8
-30.9
-0.2
-4.8
9.0
9.0
8.8
4.2
-0.7
-0.2
-2.4
-2.4
academic CHARMM
a See caption of Table 2 for details. Experimental data are not available for these guest compounds.
modifies the electrostatic solvation energies because the di-
electric cavity radius, ri, assigned to each atom, i, is computed
from its Lennard-Jones σi parameter, as 21/6/2, except that all
hydrogens are assigned a dielectric cavity radius of 1.2 Å.
Increasing these dielectric cavity radii leads to somewhat smaller
electrostatic desolvation penalties on binding on going from the
commercial to academic parameters. As this was not part of our
originally intended parameter adjustment, we reran the affinity
calculations a third time, using the academic Lennard-Jones
parameters but now forcing the dielectric cavity radii to those
associated with the original calculations with the commercial
Lennard-Jones parameters. The results, presented in Tables 3-5
and again compared with experiment in Table 7, are more
accurate (rmsd, 3.0 kcal/mol) than the original calculations with
commercial Lennard-Jones parameters (rmsd, 4.64 kcal/mol),
but not quite as accurate as the calculations with academic
Lennard-Jones parameters and corresponding dielectric cavity
radii (rmsd, 2.7 kcal/mol).
Thermodynamic Analysis. Calorimetric Measurements.
The calorimetry experiments used to obtain the host-guest
binding free energies reported here also provide changes in
enthalpy and entropy. The thermodynamic decompositions are
presented numerically in Table 2 and graphically in Figure 6 in
the form of an entropy-enthalpy scatter plot. By way of
comparison, Figure 6 also displays entropy-enthalpy data for
the binding of native and modified cyclodextrins with a variety of
guest molecules,30 along with lines of constant ΔGo for values
of -2 and -20 kcal/mol. The data points for all three of the
CB[7] host-guest series studied here lie below (or, equivalently,
to the left of) the cyclodextrins in the scatter plot. In this sense,
the high-affinity CB[7] overcomes the enthalpy-entropy com-
pensation trend clearly evident in the cyclodextrin data. This
observation is consistent with and extends a similar prior
observation for the ferrocene guests.4 The data in Figure 6
Figure 6. Calorimetric entropic vs enthalpic contributions to binding
free energy for CB[7] host-guest systems, with cyclodextrin data as
reference: red circles, ferrocenes (Table 2); green squares, adamantanes
(Table 4); black triangles, bicyclo[2.2.2]octanes (Table 3); blue dia-
monds, compiled cyclodextrin data from multiple sources.30 Lines of
constant binding free energy, at -2 and -20 kcal/mol, are also
provided. Entropy values are for 1 M standard concentration.
the values of σ in the academic parameters tend to be somewhat
larger than those in the commercial parameters (Table 6).
Increasing σ weakens the Coulombic attractions between the
ammonium groups of the guests and the carbonyls of the host,
because it increases the distance between these groups at
equilibrium (data not shown). Increasing σ simultaneously
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suggest that one may attribute the unusually high affinities of the
present CB[7] systems to their ability to overcome the usual
pattern of enthalpy-entropy compensation.
Indeed, entropy-enthalpy compensation is not evident even
within each of the three series of guests (ferrocenes, bicyclooc-
tanes, adamantanes). Instead, within each series, the enthalpy
changes are rather uniform, at -21.4 ( 0.3 kcal/mol for the
ferrocenes, -15.9 ( 0.4 kcal/mol for the bicyclooctanes, and -
20.0 ( 1.2 for the adamantanes, and the differences in -ΔG°
result chiefly from larger variations in the entropic contributions
(-TΔS°): -4.4 ( 3.3 for the ferrocenes, -1.9 ( 3.8 for the
bicyclooctanes, and 1.1 ( 2.4 for the adamantanes. The chemical
changes within each series of guests correspond primarily to
changes in the number of cationic groups, and it is perhaps
surprising that such changes in charge generate free energy
contributions that are almost entirely entropic in nature. One
may speculate that the negative enthalpic contributions of
cation-host interactions are largely balanced by the positive
enthalpic costs of stripping hydrating water from the interacting
groups. The role of entropy in these systems is highlighted by the
fact that a linear regression of their binding free energies against
the entropic contributions to their binding free energies has a
slope of 0.95 with a correlation coefficient R2 = 0.61. In contrast, a
linear regression of binding free energy against binding enthalpy
shows no correlation (slope, 0.050; R2 = 0.004).
Although all three series reach nearly the same maximal
binding free energy of about -20 kcal/mol (notably for F6,
B11, and A4), they display somewhat different enthalpy-
entropy breakdowns. In particular, guest F6 displays an excep-
tionally high enthalpic gain of -21.5 kcal/mol, while guests B11
and A4 combine large enthalpic gains (-16.3 and -20.1 kcal/
mol, respectively) with more modest entropic assists (-4.3
and -1.4 kcal/mol, respectively). One may speculate that the
obviously lower enthalpic gains for bicyclooctane guests result
from less efficient interfacial contact of the bicyclooctane core
with the CB[7] interior, leading to weaker van der Waals
interactions. However, these lower enthalpic gains are well
compensated by the less negative or even positive entropy
changes associated with this series. One may speculate that the
tighter fit of the slightly bulkier ferrocenes and adamantanes leads
to a greater entropic penalty. On the other hand, this idea is not
clearly supported by the computed configurational entropy
changes (next subsection), and such a solute-centric explanation
neglects the likelihood that the aqueous solvent, with its many
degrees of freedom, also plays a key role in determining the
observed thermodynamic breakdowns. The role of solvent is
considered in the following subsection.
Computational Analysis. The present M2 calculations allow
the computed binding free energies to be separated into the
change in potential energy (U) plus solvation energy (W), and
the change in configurational entropy (-TΔScfg). These free
energy components cannot be compared directly with calori-
metric enthalpy and entropy changes, however. This is because
the solvation part, W, is a free energy, which we are currently
unable to separate into its enthalpic and entropic components.
Nonetheless, the thermodynamic breakdown provided by M2 is
of interest in its own right, and can furthermore be combined
with the calorimetric data to provide at least a tentative look at
solvation thermodynamics, as now described.
Figure 7. Changes in configurational entropy (-TΔScfg, 1 M standard
concentration) on binding, versus changes in potential plus solvation
energy (U þ W), both computed with the M2 method (see text), in
kcal/mol. Prior calculations for other, lower-affinity host-guest systems
are included for reference. From top to bottom, results are presented for
corrected, academic VDW, and academic VDW/commercial radii para-
meters (Tables 2,3, and 4): red circles, ferrocenes (Table 2); green
squares, adamantanes (Table 4); black triangles, bicyclo[2.2.2]octanes
(Table 3); blue diamonds, compiled M2 results data from prior studies
of cyclodextrins6 (filled diamonds) and other hosts5,31 (hollow dia-
monds). Lines of constant binding free energy, -2 kcal/mol above and
-20 kcal/mol below, are also provided.
Figure 7 examines the relationship between the computed
energy (U þ W) and entropy (-TΔScfg) changes for the
CB[7] host-guest systems studied here, in the context of other
host-guest systems with more normal, lower affinities. Scatter
plots are provided for all three sets of molecular parameters
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Journal of the American Chemical Society
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Figure 9. Measured changes in entropy vs enthalpy for desolvation of
various cations,32 ranging from þ1 to þ3.
In contrast, the calorimetric results provide the total entropy
change, both configurational and solvent. Interestingly, and again
as seen in the calorimetric data (above), the computations
summarized in Figure 7 show no evident entropy-energy
correlation within each series of A, B, and F guests. Moreover,
whereas the measured total binding entropy was found to
correlate with measured binding free energy (above), the com-
puted entropic contribution to the binding free energy has little
correlation (R2 = 0.07) with the measured binding free energies,
indicating that the solvent entropy plays a significant role in
determining the binding free energy.
Solvation thermodynamics were computed from the com-
bined experimental and computational results, via eqs 2a and 2b.
The derived changes in solvation entropy and energy on binding
are displayed as scatter plots in Figure 8, for all three computa-
tional parameter sets. One striking result is that the solvent
potential energy is found to rise dramatically, by 18 to 235 kcal/
mol, on binding. This potentially surprising result is traceable
directly to similarly massive increases in the electrostatic solva-
tion free energy term obtained from the Poisson-Boltzmann
model (see ΔWel in Tables 3-5.) The physical picture is one
where powerful Coulombic attractions (ΔUC , 0) between the
ionized guests and the highly electronegative carbonyl portals of
CB[7] are quite precisely balanced by similarly large losses in
solvation energy (ΔWel . 0). Indeed, the values of ΔUC and
ΔWel are highly anticorrelated (data not shown), as previously
noted.31 Intuitively, as oppositely charged groups are brought
together, they cancel each other’s electrical fields more and more.
This in turn weakens the resulting polarization of the high
dielectric solvent and makes the net solvation free energy (and
potential energy) less negative.
Figure 8. Scatter plots of derived values for the changes in solvation
entropy and solvation potential energy on binding. From top to bottom,
results are presented for corrected, academic VDW and academic VDW/
commercial radii parameters (Tables 2, 3 and 4): red circles, ferrocenes
(Table 2); green squares, adamantanes (Table 4); black triangles,
bicyclo[2.2.2]octanes (Table 3).
(above). As previously noted for the ferrocene4,7 and
bicyclooctane7 guests, the ultrahigh affinity systems described
here fall below the customary energy-entropy correlation (blue
diamonds), indicating that the high affinities computed for these
systems result in part from their ability to overcome the typical
balance of binding forces, Δ(U þ W), and losses in configura-
tional entropy, -TΔScfg. This observation is broadly consistent
with the calorimetric observations regarding entropy-enthalpy
compensation (previous subsection), but is not precisely the
same because the configurational entropy is associated with the
motions of only the host and guest; it excludes solvent entropy.
The derived solvation entropies are much smaller in magni-
tude and range than the derived solvation energies (prior
paragraph and Figure 8). As a consequence, the slopes of linear
fits to the entropy-energy data in Figure 8 are on the order of
0.1, very different from the slopes of ∼1 commonly observed in
scatter plots for overall binding thermodynamics, for example,
Figures 6 and 7. We were initially concerned at this marked
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imbalance of solvation energy and solvation entropy and there-
fore sought a way to check its plausibility. Thus, recognizing that
most of the binding reactions studied here lead to partial
dehydration of cationic groups, we examined experimental data
on the complete dehydration of simple cations, through water to
gas-phase transfer.32 The relationship between solvation entropy
and enthalpy for these species, shown in Figure 9, is similar to our
derived results for host-guest binding (Figure 8), both in the
overall shape of the plots and in the fact that the solvation
energies are 20-30 times greater than the solvation entropies.
This similarity supports at least the qualitative validity of the
host-guest solvation thermodynamics derived here.
Both the experimental and computational thermodynamic
analyses of the systems studied here indicate that their remark-
ably high affinities are traceable in part to the fact that they lose an
unusually small amount of entropy on binding in proportion to
their energetic or enthalpic changes. Somewhat unexpectedly,
the measured binding free energies are found to correlate with
measured changes in entropy but not enthalpy. Combining the
experimental and computational results furthermore affords at
least a qualitative look at changes in solvation thermodynamics
on binding. We observe massive increases in the potential energy
associated with solvent-solute and solvent-solvent interactions
on binding, accompanied by smaller increases in solvent entropy.
A comparison with the thermodynamics of ion solvation indi-
cates that this pattern is consistent with the release of electrically
oriented waters on binding as these electrostatically complemen-
tary molecules come together. The combined computational and
experimental analysis points to a central role for solvent entropy
in determining the variations in binding free energy across the
systems studied here.
The new bicyclo[2.2.2]octane measurements also provided an
opportunity to test the accuracy of M2 mining minima affinity
calculations in a truly blind predictive mode, because the
compounds had not been synthesized when we did the first
calculations.7 Our original calculations provided reasonably good
overall agreement with experiment but deviated by 6 kcal/mol
for the binding free energy of one guest. This result prompted a
search for sources of error, which led to the discovery that the
prior M2 calculations7 used overly coarse grid spacings for the
finite difference Poisson-Boltzmann solvation model. Correct-
ing this procedural problem for the bicyclo[2.2.2]octane guests
improved the agreement between computation and experiment.
However, the calculations for several ferrocene-based guests
became less accurate with this correction, and calculations for
the new adamantane-based guests were found to overestimate
their binding affinities by 3-8 kcal/mol. On the other hand,
these initial calculations for the adamantanes were successful in
the sense that they correctly yielded ultrahigh affinities compar-
able to those of the bicyclooctanes and ferrocenes with two
cationic substituents, despite their having only one cationic
substituent.
Because the M2 calculations are physics-based and provide
breakdowns of the computed binding free energies into changes
in Boltzmann-averaged energy terms and configurational entropy,
analysis of the computational results can be informative. Here,
examination of the force field parameters and computed binding
energetics of the various guests with CB[7] led to a suggestion
that replacing the Lennard-Jones parameters from the commer-
cial CHARMm model with those from the academic model might
improve accuracy. This proved to be the case, as the somewhat
bulkier (larger σ) and less “sticky” (lower ε) academic Lennard-
Jones parameters particularly reduced the computed affinities of
the adamantanes, which had been significantly overestimated.
The present results suggest that the academic Lennard-Jones
parameters might be generally preferable, but the range of host-
guest systems studiedistoo limited to permit this conclusion to be
drawn with any certainty. Nonetheless, the present analysis
provides a helpful sense for the sensitivity of the calculations to
physically reasonable parameter variations and indicates a need
for further comparisons of calculation with experiment to further
assess and optimize the reliability of the method.
From a chemical standpoint as well, the solvation entropies
appear to be reasonable. In particular, the compounds fall into
chemically similar clusters. Thus, referring to the top scatter plot,
B11, with a charge of þ4, leads to a uniquely large solvation
entropy change on binding (about-20 kcal/mol); F6, B5, and A4,
with charges of þ2 lead to somewhat smaller entropy changes
(about -18 kcal/mol); F2, F3, A2, A3, andA5, with charges ofþ1,
generate yet smaller entropy changes (about -12 kcal/mol); and
F1 and A1, with one hydroxyl and a charge of 0, produce the
smallest solvation entropy changes (about -6 kcal/mol). The chief
surprise is B2, which, with two hydroxyls and a charge of 0, leads to
a solvation entropy change similar to those of the þ1 guests.
Perhaps the extra solvation entropy change results from the fact
that the second hydroxyl of B2 partly desolvates both portals of
CB[7], while the monocations chiefly affect only one portal.
These derived solvation entropy changes on binding correlate
with the measured binding free energies, with a regression slope
of 0.82 and a correlation coefficient R2 = 0.62. Mathematically,
this observation is a straightforward consequence of eq 1a and
the fact that the measured affinities correlate with the measured
entropies but not with the computed configurational entropies.
Physically, it suggests that the variations in binding affinity across
the various guest-CB[7] systems are attributable chiefly to
differences in their changes in solvation entropy upon binding.
It would appear that enthalpic changes due to changes in direct
host-guest Coulombic interactions are strongly canceled by
opposing changes in solvation enthalpy, leaving the changes in
solvation entropy as the dominating thermodynamic influence.
Accordingly, linear regression of the computed changes in
Coulombic interactions on binding, ΔUC, against the changes
in solvation energy (ΔUsolv from 2b) yields a slope of -1.002
with a correlation coefficient of R2 = 0.996.
’ CONCLUSIONS
We have described the synthesis and evaluation of new guest
molecules that bind CB[7] in water with affinities rivaling those of
the highest-affinity protein-small molecule systems. The new
guests are based upon rigid, aliphatic cores chosen to fit well into
the cavity of CB[7], outfitted with cationic groups positioned to
interact favorably with the carbonyl oxygens at one or both
portals. These compounds are metal-free, unlike previously
reported ultrahigh affinity CB[7] guests based upon a ferrocene
core.4 The present results thus are consistent with a prior
suggestion4,7 that the high affinities of the ferrocene-based guests
do not result from metal-specific interactions. The new adaman-
tane derivatives are of particular interest because, whereas boththe
ferrocene guests and the new bicyclo[2.2.2]octanes need charges
of þ2 to reach femtomolar dissociation constants, the adaman-
tanes reported here accomplish this with a charge of only þ1.
This work highlights the utility of host-guest systems as
intriguing and computationally tractable test cases for
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physics-based methods of computing binding affinities. We
suggest, in particular, that host-guest systems be used to test
methods of predicting protein-ligand binding affinities. Such
tests should be informative, since host-guest binding pre-
sumably operates on the same basic principles as protein-
small molecule binding. However, because host-guest sys-
tems are smaller than proteins, the calculations can be
completed in less time and with far less concern regarding
the adequacy of conformational sampling. By the same token,
it should also be feasible to carry out calculations with
relatively sophisticated energy models, such as ones that
account explicitly for electronic polarization. It is worth
noting that the types of chemical groups in many host-guest
systems fall within the range of those routinely incorporated
into candidate drug molecules, so no special parameter
assignment issues need arise. The cucurbiturils may be
particularly useful test systems in this regard, because they
afford a wide range of binding free energies for various guest
molecules in aqueous solution.
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Supporting Information. Complete ref 10; synthetic
b
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titration data for guests A2, B2, B5, and B11 with CB[7];
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and bound complexes. This material is available free of charge via
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’ AUTHOR INFORMATION
Corresponding Author
inoue@chem.eng.osaka-u.ac.jp; mgilson@ucsd.edu
Present Addresses
zSkaggs School of Pharmacy and Pharmaceutical Sciences, 9500
Gilman Drive, MC 0736, La Jolla, California, 92093, USA.
(27) Rekharsky, M. V.; Ko, Y. H.; Selvapalam, N.; Kim, K.; Inoue, Y.
Supramol. Chem. 2007, 19, 39.
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’ ACKNOWLEDGMENT
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M.K.G. thanks the National Institute of General Medical
Sciences for supporting this project through grants GM61300
and GM061300-S1. The content is solely the responsibility of
the authors and does not necessarily represent the official views
of the National Institute of General Medical Sciences or the
National Institutes of Health. Y.I. and C.Y. thank the Japan
Science and Technology Agency and the Japan Society for the
Promotion of Science for the financial support of this work. K.K.
thanks CRI and WCU (Project No. R31-2008-000-10059-0)
Programs of MOEST, Korea, for support.
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