Gated molecular recognition and dynamic discrimination of guests

Article abstract of DOI:10.1021/ja908436c

Some highly efficient enzymes, e.g., acetylcholinesterase, use gating as a tool for controlling the rate by which substrates access their active site to direct product formation. Mastering gated molecular encapsulation could therefore be important for manipulating reactivity in artificial environments, albeit quantitative relationships that describe these processes are unknown. In this work, we examined the interdependence between the thermodynamics (ΔG° ) and the kinetics (ΔG_in? and ΔG_out?) of encapsulation as mediated by gated molecular basket 1. For a series of isosteric guests (2-6, 106-107 A3) entering/ exiting 1, we found a linear correlation between the host-guest affinities (ΔG° ) and the free energies of the activation (ΔG _in? and ΔG_out?), which was fit to the following equation: ΔG? = ρΔG° + δ. Markedly, the kinetics for the entrapment of smaller guest 7 (93 A3) and bigger guest 8 (121 A3) did not follow the free energy trends observed for 2-6. Thus, it appears that the kinetics of the gated encapsulation mediated by 1 is a function of the encapsulation's favorability (ΔG° ) and the guest's profile. When the size/shape of guests is kept constant, a linear dependence between the encapsulation potential (ΔG° ) and the rate of guests' entering/departing basket (ΔG_in/out?) holds. However, when the potential (ΔG° ) is fixed, the basket discriminates guests on the basis of their size/shape via dynamic modulation of the binding site's access.

Full text of DOI:10.1021/ja908436c

Published on Web 12/28/2009
Gated Molecular Recognition and Dynamic Discrimination of
Guests
Stephen Rieth, Xiaoguang Bao, Bao-Yu Wang, Christopher M. Hadad, and
Jovica D. Badjic´*
Department of Chemistry, The Ohio State UniVersity, 100 West 18th AVenue, Columbus, Ohio 43210
Received October 4, 2009; E-mail: badjic@chemistry.ohio-state.edu
Abstract: Some highly efficient enzymes, e.g., acetylcholinesterase, use gating as a tool for controlling
the rate by which substrates access their active site to direct product formation. Mastering gated molecular
encapsulation could therefore be important for manipulating reactivity in artificial environments, albeit
quantitative relationships that describe these processes are unknown. In this work, we examined the
interdependence between the thermodynamics (∆G°) and the kinetics (∆Gin‡ and ∆Gout‡) of encapsulation
as mediated by gated molecular basket 1. For a series of isosteric guests (2-6, 106-107 Å3) entering/
exiting 1, we found a linear correlation between the host-guest affinities (∆G°) and the free energies of
the activation (∆Gin and ∆Gout‡), which was fit to the following equation: ∆G‡ ) F∆G°+ δ. Markedly, the
‡
kinetics for the entrapment of smaller guest 7 (93 Å3) and bigger guest 8 (121 Å3) did not follow the free
energy trends observed for 2-6. Thus, it appears that the kinetics of the gated encapsulation mediated by
1 is a function of the encapsulation’s favorability (∆G°) and the guest’s profile. When the size/shape of
guests is kept constant, a linear dependence between the encapsulation potential (∆G°) and the rate of
guests’ entering/departing basket (∆Gin/out ‡) holds. However, when the potential (∆G°) is fixed, the basket
discriminates guests on the basis of their size/shape via dynamic modulation of the binding site’s access.
quantitatiVe relationships6 that guide the recognition’s kinetics.
A high thermodynamic bias (∆G°) for a chemical process, e.g.,
Introduction
Mechanistic details about the formation of host-guest
encapsulation complexes are obtained from kinetic measure-
ments1 and are critical for designing synthetic receptors2 with
a mode of action resembling biological molecules. The exchange
of guests has thus been found to occur via: (a) a full or partial
dissociation of the host’s subunits;3 (b) an “expansion” of the
host’s apertures;4 and (c) a conformational change in the host’s
shell.5 All of these insightful findings, however, do not disclose
molecular recognition, can lead to a low activation barrier (∆G‡)
and an early transition state (according to Hammond’s postulate),
although the relationship does depend upon context.7 Precise
control over the kinetics of the encapsulation5,8 presents a
challenge, thereby providing an opportunity for directing
chemical reactivity9,10 and sequestration.11 Interestingly, some
very efficient enzymes, such as acetylcholinesterase, promote
a dynamic selection of guests via stochastic motion of aromatic
residues (gates) located along a pathway leading to the active
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10.1021/ja908436c  2010 American Chemical Society
J. AM. CHEM. SOC. 2010, 132, 773–776 773

A R T I C L E S
Rieth et al.
Figure 1. (A) Reaction coordinate diagram showing an equilibrium with guests 2-6 (CBr4 is displayed) entering (kin) and departing (kout) gated molecular basket
1 (internal volume: 220 Å3). Solvent molecules (CD2Cl2, right) occupy basket 1 devoid of external guests. (B) Top view of 1A and 1B enantiomeric baskets that
interconvert by 180° rotation of their gates. (C) Energy minimized structures (B3LYP/3-21G) of guests 2-8 and their corresponding volumes (Å3).
site: the rate of trafficking of a bigger guest is hindered as
compared to a slightly smaller analogue.9a Accordingly, the
present study addresses the potential of synthetic baskets (Figure
1) to dynamically distinguish guests on the basis of gating. The
encapsulation kinetics has been found to follow a free-energy
relationship, suggesting important principles that might govern
recognition in artificial and gated environments.12
Results and Discussion
Gated molecular baskets13 were originally designed and
synthesized in our laboratory. These hosts have a bowl-shaped
platform with three pyridine-based gates, linked via a seam of
intramolecular hydrogen bonds (HBs) to occlude space and form
a dynamic and gated environment (Figure 1). The interconver-
sion of two C3 symmetric enantiomers, 1A and 1B, each
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774 J. AM. CHEM. SOC. VOL. 132, NO. 2, 2010

Recognition and Discrimination of Guests
A R T I C L E S
Table 1. Activation Parameters for the Trafficking of Guests 2-8 (2D EXSY NMR, CD2Cl2, 250.0 ( 0.1 K) In (kin, ∆Gin‡) and Out (kout
,
∆Gout‡) from Basket 1 and the 1A/B Interconversion (∆GA/B‡) as well as Thermodynamic Stabilities (∆G°, 250.0 ( 0.1 K) of [1 ⊂ 2-8]
Encapsulation Complexes
entry
guest
kin (M-1s-1
kout (s-1
)
∆Gin (kcal/mol)
∆Gout (kcal/mol)
∆GA/B (kcal/mol)a
∆G° (kcal/mol)
b
)
b
‡
‡
‡
2
3
4
5
6
7
8
(CH3)4C
1100 ( 115
1161 ( 134
1525 ( 200
2460 ( 251
8500 ( 3010
8040 ( 873
480 ( 48
30.3 ( 0.9
16.2 ( 0.8
3.41 ( 0.23
0.48 ( 0.01
0.10 ( 0.03
22.8 ( 0.8
14.4 ( 0.5
11.03 ( 0.05
11.00 ( 0.06
10.87 ( 0.07
10.63 ( 0.05
10.02 ( 0.18
10.04 ( 0.05
11.44 ( 0.05
12.81 ( 0.01
13.12 ( 0.02
13.89 ( 0.03
14.86 ( 0.01
15.63 ( 0.15
12.95 ( 0.02
13.17 ( 0.02
11.5 ( 0.1
11.8 ( 0.1
11.9 ( 0.1
12.3 ( 0.1
12.6 ( 0.1
11.6 ( 0.1
12.5 ( 0.1
-1.77 ( 0.05
-2.11 ( 0.06
-3.02 ( 0.07
-4.23 ( 0.05
-5.6 ( 0.1
-2.90 ( 0.06
-1.73 ( 0.06
(CH3)3CBr
(CH3)2CBr2
(CH3)CBr3
CBr4
(CH3)CCl3
(CH3)4Si
a Error margins were obtained on the basis of four independent measurements. b Each measurement was repeated twice.16
containing HBs displayed in a clockwise or counter-clockwise
orientation, has been verified from the NMR exchange of the
“hinge” Ha/b resonances appearing as a singlet at high and an
AB quartet at low temperatures (Figure 1B). Furthermore, the
polar (inductive and field) and steric characteristics of the R
amido units were shown14 to have an effect on the in/out rate
of the guest exchange: the guest trafficking was predominantly
a function of the rate by which the gates revolve. For guests
entering/exiting baskets, another question arises: is there a
relationship between the thermodynamic potential (∆G°) and
the activation energy (∆G‡) for the encapsulation?
Neopentane 2 and four homologous haloalkanes 3-6 were
chosen as guests (Figure 1C). These molecules have identical
profiles with van der Waals volumes of Br and CH3 groups
contributing to uniform size (106-107 Å3) and spherical shape
across the series. Basket 1 (Figure 1) was used in the study,
and its affinity (∆G°) toward guests 2-6 was more favorable
(more exoergic) as the number of CH3 units decreased (Table
1). As elucidated in an earlier study,13c the encapsulation limits
the rotational and vibrational degrees of freedom of CH3 groups,
which obstructs the binding via an unfavorable entropy (∆S° <
Figure 2. Activation energies for guests 2-6 (106-107 Å3) entering (∆G‡
)
in
0). Notably, the range of binding energies ∆G° (250 K, Table
1) spans ∼4 kcal/mol for these very similar guests, thereby
allowing a critical evaluation of the possible linear free energy
relationships (LFER).
and departing (∆G‡out) basket 1 were found to be a linear function of the
corresponding binding energies (∆G°, 250.0 ( 0.1 K). The kinetic behavior
of smaller 7 (93 Å3) and bigger 8 (121 Å3) deviates from the observed linear
free energy relationships (∆G‡ ) F∆G° + δ). The activation energies
characterizing the revolving of gates (∆G°A/B) also exhibit a LFER.
Kinetics and LFERs. Two-dimensional 1H-1H and 13C-13C
NMR magnetization transfer measurements (EXSY)15 were
completed to obtain the rate coefficients for guests 2-6 entering
(kin) and departing (kout) basket 1 in CD2Cl2 at 250.0 ( 0.1 K
(Table 1).16 The encapsulation (Figure 1A) was in accord with
an associative mechanism1a (Figure S10 of the Supporting
Information) whereby the association was first order in the guest
(Vin ) kin [guest][basket]) while the dissociation process was
zeroth order in the guest (Vout ) kout [basket ⊂ guest]).16
After the host-guest affinities (∆G° ) kin/kout) were plotted
against the corresponding free energies of activation (∆Gin/out ‡),
well-correlated linear relationships were observed (Figure 2);
note that the binding energies ∆G° from the EXSY measure-
denote as F,17 correspond to the susceptibility by which the free
energies of activation respond to the change in the thermody-
namic affinity of guests 2-6 toward molecular basket 1. For
the values of F, the ingress of guests generates a smaller slope
(Fin ) 0.25), while the egress has a larger magnitude of its slope
(|Fout| ) 0.74, Figure 2). An early transition state would suggest
that the guest entrapment (∆Gin ‡) would be less responsive to
∆G° than ∆Gout ‡, as is observed. The intercept of the fitted lines,
which we denote as δ, represents the activation barrier (∆G‡)
for the encapsulation of a guest having a binding energy of ∆G°
‡
) 0; note that under this circumstance, δ ) ∆Gin ‡ ) ∆Gout
)
11.56 ( 0.14 kcal/mol. One should note that the δ might also
correlate to the binding energy of the solvent (CH2Cl2) as a
competitive guest with basket 1.
1
ments match those obtained by the integration of H NMR
signals.16 Evidently, there exists quantitative relationships
between the thermodynamic potential for the encapsulation and
the free energy of activation for guests 2-6 entering/exiting
basket 1 in competition with the solvent (CD2Cl2). We ana-
lyzed these relationships with the following equation
∆G‡ ) F∆G° + δ. The slopes of the fitted lines, which we
First-order rate constants (kA/B, Figure 1B) for the intercon-
version of dynamic enantiomers 1A and 1B were obtained by
completing NMR line-shape simulations of the coalescence of
diastereotopic Ha/b resonances at variable temperatures (220-270
K, Table 1).16 After the data were placed into the free energy
correlation plot (Figure 2), the activation energies for 1A/B
interconversion (∆GA/B‡) were shown as well to be a linear
(14) Wang, B.-Y.; Rieth, S.; Badjic´, J. D. J. Am. Chem. Soc. 2009, 131,
7250–7252.
(15) (a) Jeener, J.; Meier, B. H.; Bachmann, P.; Ernst, R. R. J. Chem. Phys.
1979, 71, 4546–4553. (b) Perrin, C. L.; Dwyer, T. J. Chem. ReV. 1990,
90, 935–967.
(17) The slope F is akin to the Hammond-Leffler R value (R ) δ∆G‡/
δ∆G°). See: (a) Leffler, J. E. Science 1953, 117, 340–341. (b)
Hammond, G. S. J. Am. Chem. Soc. 1955, 77, 334–338.
(16) See Supporting Information for more details.
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A R T I C L E S
Rieth et al.
Figure 3. Snapshots of CBr4 departing 1, along a force vector aligned with the basket’s side aperture, obtained from steered molecular dynamics (SMD)
simulations of the process (0, 440, and 1000 ps; top). The variation of intramolecular N---H distances (assigned as I, II, and III) in basket 1 as a function
of time during the SMD simulation (bottom).
function (R2 ) 0.972) of the thermodynamic stability of 1/2-6
complexes. The slope of the fitted line is small (|FA/B| ) 0.26)
while the intercept (11.13 ( 0.09 kcal/mol) is very similar to
the δ value above (11.56 ( 0.14 kcal/mol, Figure 2). The
existing LFER corroborates the synergy between the internal
dynamics of the gates and the thermodynamic stability of guests
bound in the cavity of host 1. Furthermore, the energy required
for revolving the gates at ∆G° ) 0 is almost equal to the
Å3) was, however, found to access/leave the basket’s cavity at
a rate slower than expected on the basis of the LFER in Figure
2. The results of the kinetic measurements for 7 and 8 can be
interpreted by considering the mechanism of conformational
gating in acetylcholinesterase (AChE).9b A guest will make
repeated attempts to access the cavity of dynamic [1-CD2Cl2]
via Brownian motion. The gates switch between open and closed
states and when an attempt coincides with the open state, the
encapsulation happens (Figure 3). The likelihood that the gates
open wide enough to admit a substrate is evidently related to
the substrate’s size. Hence, larger substrate 8 has a lower
probability while smaller substrate 7 has a higher probability
for entering “the transient aperture” created by the gates.
‡
‡
constrictive binding (∆Gin ) ∆Gout ) 11.56 ( 0.14 kcal/
mol)-physical barrier that a guest encounters in escaping the
basket.18 The host’s conformational change, i.e., gating, is
evidently controlling the uptake/release of guest molecules.
Mechanistic Considerations. The departure of sizable CBr4
(or for that matter 2-5), via a trajectory along the side aperture
of the basket, was computed using steered molecular dynamics
(SMD)19 and the AMBER program.16 Importantly, a simulta-
neous cleavage of all three N-H---N hydrogen bonds is required
for a guest (106-107 Å3) to leave the basket’s cavity (Figure
3).16 Furthermore, the results of the SMD simulation indicated
that smaller CHCl3 (75 Å3) can enter and exit 1, without
considerably perturbing the position of the gates.16 If the
trafficking of smaller guests does not require a considerable
perturbation of the gates, then one could expect a faster 1A/B
interconversion (Figure 1B) on the account of greater effective
space available to the revolving gates and weaker (distance-
dependent) basket-to-guest electrostatic interactions. Indeed, our
experimental studies suggested a more rapid rotation of gates
in [1-CD2Cl2]: ∆G‡ ) 9.2 ( 0.1 kcal/mol at 250.0 K.16
On the Observed LFERs. The relationships described in
Figure 2 pertain to guests (2-6) that have the same size and
shape. Will guest molecules, having profiles slightly different
from 2-6, obey the ∆G°/∆G‡ linear correlations?
Conclusions
Quantitative relationships that describe the kinetic discrimina-
tion of guests in artificial gated receptors have been studied.
Our experimental results suggest that the encapsulation kinetics,
mediated by gated basket 1, is governed by the guest’s profile
and the host/guest interaction potential (∆G°).20 Thus, when
the size/shape of guests is kept constant, the encapsulation
potential (∆G°) is a linear function of the rate by which they
enter/depart basket 1 (∆Gin/out ‡). However, when the potential
is fixed (project a vertical line for 7 and 8 in Figure 2), basket
1 discriminates guests on the basis of their size/shape via
dynamic modulation of the binding site’s access, thereby
resembling enzymes.9 A more complete understanding of the
kinetic selection will benefit from studying a broader scope of
guest molecules and baskets, and such research is in progress.
Acknowledgment. This work was financially supported with
funds from the Ohio State University and the National Science
Foundation under CHE-0716355. Generous computational resources
were provided by the Ohio Supercomputer Center.
Guests 7 and 8 were chosen to examine this aspect (Figure
1C). 1,1,1-Trichloroethane 7 is a nonspherical compound and
is smaller (93 Å3) than guests 2-6 (∼107 Å3). Interestingly, 7
entered/departed basket 1 faster than one would predict on the
basis of the LFER in Figure 2. Larger tetramethylsilane 8 (120
Supporting Information Available: Detailed description of
experimental and computational methods. This material is
available free of charge via the Internet at http://pubs.acs.org.
(18) Cram, D. J.; Blanda, M. T.; Paek, K.; Knobler, C. B. J. Am. Chem.
Soc. 1992, 114, 7765–7773.
JA908436C
(19) Izrailev, S.; Stepaniants, S.; Balsera, M.; Oono, Y.; Schulten, K.
Biophys. J. 1997, 72, 1568–1581.
(20) Northrup, S. H.; Hynes, J. T. J. Chem. Phys. 1979, 71, 871–883.
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776 J. AM. CHEM. SOC. VOL. 132, NO. 2, 2010