Chelate cooperativity and spacer length effects on the assembly thermodynamics and kinetics of divalent pseudorotaxanes

Article abstract of DOI:10.1021/ja2107096

Homo- and heterodivalent crown-ammonium pseudorotaxanes with different spacers connecting the two axle ammonium binding sites have been synthesized and characterized by NMR spectroscopy and ESI mass spectrometry. The homodivalent pseudorotaxanes are investigated with respect to the thermodynamics of divalent binding and to chelate cooperativity. The shortest spacer exhibits a chelate cooperativity much stronger than that of the longer spacers. On the basis of crystal structure, this can be explained by a noninnocent spacer, which contributes to the binding strength in addition to the two binding sites. Already very subtle changes in the spacer length, i.e., the introduction of an additional methylene group, cause substantial changes in the magnitude of cooperative binding as expressed in the large differences in effective molarity. With a similar series of heterodivalent pseudorotaxanes, the spacer effects on the barrier for the intramolecular threading step has been examined with the result that the shortest spacer causes a strained transition structure and thus the second binding event occurs slower than that of the longer spacers. The activation enthalpies and entropies show clear trends. While the longer spacers reduce the enthalpic strain that is present in the transition state for the shortest member of the series, the longer spacers become entropically slightly more unfavorable because of conformational fixation of the spacer chain during the second binding event. These results clearly show the noninnocent spacers to complicate the analysis of multivalent binding. An approximate description which considers the binding sites to be connected just by a flexible chain turns out to be more a rough approximation than a good model. The second conclusion from the results presented here is that multivalency is expressed in both the thermodynamics and the kinetics in different ways. A spacer optimized for strong binding is suboptimal for fast pseudorotaxane formation.

Full text of DOI:10.1021/ja2107096

Article
pubs.acs.org/JACS
Chelate Cooperativity and Spacer Length Effects on the Assembly
Thermodynamics and Kinetics of Divalent Pseudorotaxanes
Wei Jiang,†,§ Karol Nowosinski,† Nora L. Low,† Egor V. Dzyuba,† Fabian Klautzsch,† Andreas Schafer,†
̈
̈
Juhani Huuskonen,‡ Kari Rissanen,‡ and Christoph A. Schalley*,†
†Institut fur Chemie und Biochemie, Freie Universitat Berlin, Takustrasse 3, 14195 Berlin, Germany
̈
̈
‡Department of Chemistry, Nanoscience Center, University of Jyvaskyla, P.O. Box 35, 40014 Jyvaskyla, Finland
̈
̈
̈
̈
S
* Supporting Information
ABSTRACT: Homo- and heterodivalent crown-ammonium
pseudorotaxanes with different spacers connecting the two axle
ammonium binding sites have been synthesized and charac-
terized by NMR spectroscopy and ESI mass spectrometry. The
homodivalent pseudorotaxanes are investigated with respect
to the thermodynamics of divalent binding and to chelate
cooperativity. The shortest spacer exhibits a chelate cooper-
ativity much stronger than that of the longer spacers. On the
basis of crystal structure, this can be explained by a noninnocent spacer, which contributes to the binding strength in addition to
the two binding sites. Already very subtle changes in the spacer length, i.e., the introduction of an additional methylene group,
cause substantial changes in the magnitude of cooperative binding as expressed in the large differences in effective molarity. With
a similar series of heterodivalent pseudorotaxanes, the spacer effects on the barrier for the intramolecular threading step has been
examined with the result that the shortest spacer causes a strained transition structure and thus the second binding event occurs
slower than that of the longer spacers. The activation enthalpies and entropies show clear trends. While the longer spacers reduce
the enthalpic strain that is present in the transition state for the shortest member of the series, the longer spacers become
entropically slightly more unfavorable because of conformational fixation of the spacer chain during the second binding event.
These results clearly show the noninnocent spacers to complicate the analysis of multivalent binding. An approximate description
which considers the binding sites to be connected just by a flexible chain turns out to be more a rough approximation than a
good model. The second conclusion from the results presented here is that multivalency is expressed in both the thermo-
dynamics and the kinetics in different ways. A spacer optimized for strong binding is suboptimal for fast pseudorotaxane
formation.
were also observed in a study of intramolecular binding of
covalently linked ligands to human carbonic anhydrase.6 This
study arrives at the conclusion that flexible spacers longer
than the optimal distance between the binding sites will still be
effective, though not optimal.
INTRODUCTION
■
Multivalency describes molecular recognition phenomena
between the two binding partners involving multiple binding
sites separated by spacers. This is widely observed in bio-
chemistry.1 Quite significant interaction energy increases have
been found for example for pentavalent Shiga-like toxins when
compared to the monovalent one.2 Also, multivalent carbohy-
drate interactions have been examined quite extensively.3 In
a seminal paper on the activation of cGMP-gated membrane
channels in vertebrate photoreceptors and olfactory neurons,
Kramer and Karpen4 reported an up to 1000-fold activity in-
crease of polymer-linked cGMP dimers over monovalent ones.
A clear-cut correlation of spacer length with channel activation
was observed: Too short spacers bind in a monovalent fashion
and have effects comparable to those of cGMP. With spacers
able to bridge the distance between binding sites and causing
some strain, the effect increases until the optimal binding situa-
tion is realized. Longer spacers suffer from additional entropic
penalties for conformational restrictions and lose some of their
potency with increasing length. Diestler and Knapp5 simulated
these binding events with statistical mechanics calculations whose
trends compare well with these experimental data. Similar trends
The multivalency concept has been transferred to synthetic
supramolecules and was utilized for the construction of more
complex architecture from suitably programmed building
blocks.7 Besides binding energy increases, multivalency also
contributes to controlling the geometry of the complex through
multipoint attachment between host and guest. It therefore
represents an important concept in supramolecular synthesis
besides templation,8 self-assembly,9 and self-sorting.10 For
example, multivalent calixarene11 and cyclodextrin complexes7b,12
have been investigated, multivalent (pseudo)rotaxanes have
been constructed,13 and adamantyl−cyclodextrin interactions
on surfaces were extensively studied.12b,14 A recent study by
Urbach et al.15 reported thermodynamic data for di- and tri-
valent interactions between two peptides, one of which carried
Received: November 14, 2011
Published: December 16, 2011
© 2011 American Chemical Society
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Figure 1. Mono- and divalent axles 1-H·PF6−4e-2H·2PF6, crown ether monomers and dimers 5−7, and pseudorotaxanes 8-H·PF6−14-4H·4PF6
assembled from them. Axle and crown ether protons are labeled with letters and numbers, respectively, to facilitate NMR signal assignment below.
tryptophan side chains, and the other was equipped with
methylviologen/cucurbit[8]uril complexes. An up to 280-fold
increase in binding constants was observed, but the thermo-
dynamic data revealed the entropic costs of conformational fixa-
tion to diminish the total binding energy significantly.
the two identical binding sites, homodivalent pseudorotaxanes
11a-2H·2PF6−11f-2H·2PF6 facilitate the thermodynamic anal-
ysis (Figure 2, left). Using the benzyl ammonium/24-crown-8
motif is advantageous, because it combines sufficiently fast
threading−dethreading equilibria for isothermal titration calorim-
etry (ITC) experiments with a substantial binding energy.18
Instead, the kinetics of the last threading step can be easily stud-
ied in heterodivalent pseudorotaxanes 13a-2H·2PF6−13e-2H·
2PF6, because the threading of the “green” hydroxypentyl
ammonium part through the 21-crown-7 ether is much slower
than the preceding threading of the axle through the larger
24-crown-8 moiety.10e−g With all building blocks available, the
12a-2H·2PF6−12e-2H·2PF6 pseudorotaxanes serve as the links
between the other two series. Monovalent building blocks 1
and 5 are needed to acquire thermodynamic data for 8-H·PF6,
9-2H·2PF6, and 10a-H·PF6−10d-H·PF6, without which a
detailed analysis of the chelate cooperativity is not possible.
Axle 3-2H·2PF6 is too short to span both crown ethers in 6 or 7
and thus forms quadruply threaded complexes 14-4H·4PF6.
Because only the spacer length changes between four and ten
Besides affecting the thermodynamic stability of multivalent
complexes, the spacer linking the binding sites can also cause
quite substantial kinetic effects. One of Stoddart’s trivalent
pseudorotaxanes16 with a rigid spacer exhibited two fast thread-
ing steps followed by a third step which took days for comple-
tion. Consequently, spacers are not necessarily independent
spectators but can alter the binding behavior significantly and
may even actively participate in the multivalent binding event.
The present study investigates the chelate cooperativity and
spacer-length dependence of the thermodynamic stabilities and
assembly kinetics of divalent crown ether/secondary ammonium
pseudorotaxanes17 (Figure 1). Figure 2 illustrates the concept:
The thermodynamic (binding constants) and kinetic (guest ex-
change half-lives) stabilities of three previously reported mono-
valent pseudorotaxanes are summarized in the center.10e Due to
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Figure 2. Center: Trends of thermodynamic and kinetic stabilities in three previously reported monovalent monovalent pseudorotaxanes (CD3Cl :
CD3CN = 2:1).10e Because the phenyl group of the “blue” axle is too bulky to thread through the 21-crown-7 ether, no pseudorotaxane forms from
the blue axle and 21-crown-7 ethers. Left: Thermodynamic model for divalent binding. Right: Kinetic path selection and the different time scales of
the three threading steps permit separate analysis of the final threading event.
atoms connecting the two axle phenyl groups within each series
protons in 13a-2H·2PF6 experience similar signal shifts: i and m
both shift by Δδ ∼ 0.8 ppm and j and l by Δδ ∼ 1.7 ppm. These
large upfield shifts can only be explained when these spacer
protons are located directly above the anthracene unit connecting
the two crown ethers. Upon divalent binding, this is the case, while
monovalent binding or the formation of oligomers would not fix
these protons above the anthracene. No signals are observed for
free axle and crown binding sites so that we conclude the divalent
pseudorotaxanes to be the by far dominating species in solu-
tion. The other less prominent complexation-induced signal
shifts are in good agreement with this interpretation, which also
holds for the other pseudorotaxanes under study (Supporting
Information). Also, ESI mass spectrometry supports the
formation of divalent pseudorotaxanes (Supporting Informa-
tion). For each pseudorotaxane, clean mass spectra are obtained
in which the only significant signal corresponds to the doubly
charged pseudorotaxane ions [11a-2H] 2+ (m/z 781) and [13a-
2H]2+ (m/z 757).19
Double Mutant Cycles for the Analysis of Chelate
Cooperativity. A detailed thermodynamic description of the
binding in our divalent pseudorotaxanes requires the analysis of
chelate cooperativity, which was examined earlier for other
systems by Anderson et al.,20 Ercolani et al.,21 Hunter et al.,22
and others.2b,12a,23 Here, we use the double mutant cycle con-
cept22d,g shown in Figure 4 for the analysis of the (always
positive)21c chelate cooperativity in the divalent pseudorotax-
anes under study. This cycle is derived from the disproportiona-
tion equilibria in eq 1.
of axles 2a-2H·2PF −2f-2H·2PF6 and 4a-2H·2PF6−4e-2H·2PF6,
6
the influence of the spacers on the thermodynamic and kinetic
properties of the divalent pseudorotaxanes can be directly analyzed.
RESULTS AND DISCUSSION
■
Synthesis and Characterization of Axles, Crown Ethers,
and Pseudorotaxanes. The syntheses and analytical data
of new building blocks and pseudorotaxanes are reported in
detail in the Supporting Information. Consequently, we restrict
ourselves to a few remarks and the discussion of one homo- and
one heterodivalent pseudorotaxane here. The 24-crown-8
homodimer bears quinoxaline groups, which facilitate the
dimerization of 5 with two molecules of butanal under strongly
acidic conditions (82% H2SO4).10f If for example dibenzo-24-
crown-8 was used, this reaction could occur on both sides and
oligomerization would not only reduce the yield but would also
render product isolation difficult.10a With the quinoxaline, one
side is blocked and the dimerization can only occur with the
benzo moiety.
The exclusive formation of homo- and heterodivalent pseudoro-
taxanes 11a-2H·2PF6−13e-2H·2PF6 from the corresponding
axles and wheels is supported by typical10f complexation-induced
10e,19
1
shifts in the H NMR and by ESI-MS experiments.
Signal
assignment was performed from the H,1H COSY NMR spectra
1
(see Supporting Information). As representative examples, the 1H
NMR spectra of 11a-2H·2PF and 13a-2H·2PF6 (Figures 3b,e)
6
are compared with those of the corresponding axles (Figures 3a,d)
and wheels (Figures 3c,f). In the spectra of 11a-2H·2PF6,
substantial signal shifts to higher field are observed for protons
g (Δδ = 0.78 ppm) and h (Δδ = 1.71 ppm). The corresponding
9‐2H·2PF + 10‐2H·2PF ⥂11‐2H·2PF + 2 8‐H·PF
6
(1)
6
6
6
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binding strengths. Because two copies of the monovalent and
one copy of the divalent crown ethers appear on each side of
eq 1, this effect cancels. Similarly, connecting two axle benzyl
groups by aryl ethers certainly makes the two aromatic rings
more electron-rich and has an effect on their π−π stacking
abilities and their C−H···O hydrogen bonding24 capabilities.
Again, this effect cancels for analogous reasons, like all others
that are not due to chelate cooperativity. All binding constants,
B
B
C
C
i.e. KA, K1 , K2 (and thus KB), K1 , K2 (and with them KC),
Kmono and with it KD, can be determined by assembling the
different mono- and divalent components of the pseudoro-
taxanes in four separate experiments corresponding to those
shown in Figure 4A−D.
For the equilibrium in eq 1, the free enthalpy change ΔΔG
can be described as the difference of the contributions of the
individual complexes involved (eq 2) and the equilibrium con-
stant as in eq 3.
A
D
B
C
(2)
ΔΔG = ΔG + ΔG − ΔG − ΔG
KAKD
KBKC
K =
(3)
Inserting the expressions for KA to KD from Figure 4A−D
yields the effective molarity EM (eq 4). Thus, from the binding
constant accessible by experiments, the effective molarity can
be calculated providing a measure to judge the magnitude of
chelate cooperativity in the pseudorotaxanes under study.22c,d
1
Figure 3. H NMR spectra (500 MHz, 298 K, CDCl3:CD3CN = 5:1,
2.0 mM) of (a) axle 2a-2H·2PF6, (b) pseudorotaxane 11a-2H·2PF6,
(c) crown ether homodimer 6, (d) axle 4a-2H·2PF6, (e) pseudoro-
taxane 13a-2H·2PF6, and (f) crown ether heterodimer 7. Dotted lines
indicate complexation-induced signal shifts. Signal assignments are
based on 1H,1H COSY NMR experiments. Labels refer to those shown
in Figure 1. Asterisk = residual solvent. The corresponding ESI mass
spectra are shown in the Supporting Information.
2
2
A
D
2K
EMK
K K
mono
mono
K =
= 2EM or EM =
2
2
B
C
K
K
2K K
(4)
mono mono
Spacer Effects on the Thermodynamic Binding Data
from Isothermal Titration Calorimetry (ITC). The thermo-
dynamic binding data for the mono- and divalent pseudorotax-
anes under study are summarized in Table 1 as obtained from
ITC experiments. It is widely accepted that ITC measurements
provide accurate data for systems, in which the so-called
Wiseman c value25 (eq 5) is between 10 and 1000. In this equa-
tion, n represents the number of binding sites, Ka the binding
constant, and [H]tot the total host concentration. Wiseman
If the formation of the divalent pseudorotaxane occurs with
strongly positive cooperativity, the equilibrium shifts far to the
product side (eq 1). Double mutant cycles eradicate all effects
that are not due to chelate cooperativity. For example, connect-
ing two monovalent crown ethers by the anthracene spacer
might change the electronic properties of the aromatic system
attached to the crowns and thus may have an effect on their
Figure 4. Double mutant cycle for the disproportionation equilibrium in eq 1. Divalent pseudorotaxanes exhibiting strong positive chelate
cooperativity shift this equilibrium further (large negative ΔΔG and high EM values) to the product side than that of weakly cooperative systems
(small negative ΔΔG and low EM values).
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Table 1. Thermodynamic Binding Data As Obtained from ITC Titrations (CHCl3/CH3CN = 2.2:1, 298 K)
a
a
b
Ka [M−1]
ΔG [kJ mol−1]
ΔH [kJ mol−1]
−TΔS [kJ mol−1]
EM [mM]
8-H·PF6
9-2H·2PF6
420 50
735 90
−15.0 0.3
−16.4 0.3
−12.3 0.4
−16.3 0.3
−13.3 0.4
−25.1 0.3
−17.4 0.2
−16.2 0.2
−15.7 0.2
−16.0 0.3
−15.3 0.3
−61.3
−48.0
−75.2
+2.9
+46.3
+31.7
+62.8
−19.2
−9.4
+46.2
+49.1
+52.7
+53.5
+50.7
+51.9
K1
K2
K1
K2
145 20
10a-2H·2PF6
714 90
220 30
−3.9
11a-2H·2PF6
11b-2H·2PF6
11c-2H·2PF6
11d-2H·2PF6
11e-2H·2PF6
11f-2H·2PF6
25,000 2,500
1,100 100
700 60
−71.3
−66.5
−68.9
−69.2
−66.7
−67.2
132
5.8
3.7
3.0
560 50
630 60
480 50
a
b
ΔH and ΔS values have larger errors than those of ΔG and should be regarded as estimates rather than precise values. The EM values were
B
B
C
C
2
calculated using the experimentally determined KA, K1 , K2 , K1 K2 , and KD = Kmono values.
c values within this range are often difficult to achieve for
low affinity systems, because the low binding constant would
require high concentrations for compensation that result in
solubility problems. For the pseudorotaxanes discussed here,
the c values are in the range of 2 (11f-2H·2PF6) to 100 (11a-
2H·2PF6).
effective molarity is particularly high for 11a-2H·2PF6 and then
drastically drops to less than 10 mM for the other divalent
pseudorotaxanes. Consequently, chelate cooperativity is partic-
ularly pronounced for the pseudorotaxane bearing a C2-spacer
between the two axle phenols.
In their essay on cooperativity,22f Anderson and Hunter
use the dimensionless quantity KmonoEM as a measure of
cooperativity. If KmonoEM ≫ 1, the system exhibits positive
cooperativity, if KmonoEM ≪ 1, the system prefers the partially
bound state. For 11a-2H·2PF6, we calculate KmonoEM to be 40,
clearly indicating a highly positive cooperativity for this system.
For longer spacer lengths, the KmonoEM values are around 1
to 2 so that the cooperativity of binding is not significantly
positive here.
c = nK [H]
(5)
a
tot
A recent report by Turnbull and Daranas26 showed, however,
that accurate data can also be obtained for small c values.
Because the curvatures of our titration curves are well-defined,
the binding constants Ka and with them the free enthalpies of
binding ΔG can be obtained by curve fitting with errors of
about 10%. Instead, the errors of ΔH and ΔS are likely larger,
because the titration curves do not have the typical sigmoidal
shape which defines the step size and with it provides a precise
value for ΔH. As a control experiment for the accuracy of the
A Rationalization of the Pronounced Chelate Coop-
erativity of 11a-2H·2PF6 Based on its Crystal Structure.29
The addition of a single methylene group drastically decreases
the effective molarity between 11a-2H·2PF6 and 11b-2H·2PF6.
Because only the spacer is varied, the question arises: why such
a significant change in cooperativity? This finding clearly
points to noninnocent spacers, which contribute to the overall
free binding enthalpies. A view of the crystal structure of
11a-2H·2PF6 (Figure 5) provides further insight. Not unexpect-
edly,30 the binding between the axle ammonium groups and
the crown ethers are mediated by two moderate N−H···O hy-
drogen bonds at each ammonium cation31 and weak C−H···O
hydrogen bonds involving the polarized methylene groups next
to the ammonium cations.32 The C2 spacer in the axle center
almost exactly spans the two axle phenols placing them directly
above the anthracene spacer between the two crown ethers.
The plane-to-plane distances33 nicely match that expected for
π-stacked complexes. Consequently, a complex forms in which
the two axle phenols are perfectly preorganized for π−π stack-
ing interactions with the anthracene. The addition of one or more
methylene groups in the axle center necessarily induces deviations
of the two phenols from this close-to-perfect arrangement. In view
of the double mutant cycle shown above, it should be noted that
the preorganizing effect of the C2 spacer modulates the π−π
interactions. It is this modulation, not the absolute π−π stacking
interaction, which causes the pronounced chelate cooperativity.
The longer spacers cannot arrange the two phenols in such a
nearly perfect geometry. Consequently, the modulation of the
π−π interactions decreases and no such pronounced cooperativity
effect is observed for these pseudorotaxanes.
1
ΔG values, we performed H NMR competition experiments
and offered two different axles to the crown dimer in a 3:3:2
ratio (Supporting Information). The pseudorotaxane axle pro-
tons g are not superimposed by any other signal, while their
positions differ depending on the spacer length. Consequently,
their integrations could easily be evaluated to obtain ΔΔG
values for couples of pseudorotaxanes. These experiments result
in a trend, which closely parallels the binding energy differences
obtained from the ITC experiments. Together with the argu-
ments put forward by Turnbull and Daranas,27 we therefore
conclude that the free binding enthalpies ΔG in Table 1 are
sufficiently precise to evaluate the chelate cooperativity of the
pseudorotaxanes under study.
The binding constant of Kmono = 420 M−1 for pseudorotaxane
8-H·PF6 describes the monovalent binding event. The
formation of 9-2H·2PF6 should proceed in two steps. Including
statistical factors,27 the first binding constant K1 should be twice
Kmono, and the second one, K2, a half Kmono. The two constants
measured for 9-2H·2PF6 are close to these expected values, as
are K1 and K2 for 10a-2H·2PF6. Because the values for these
two complexes are very similar, we can, in agreement with a
recent literature report,28 safely assume those of 10b−f-2H·
2PF6 to be in the same ranges. Consequently, the values for
10a-2H·2PF6 were used for all EM calculations.
The binding constants for the divalent pseudorotaxanes
11a−f-2H·2PF6 significantly depend on the spacer length with
a sharp drop from 25 000 M−1 for 11a-2H·2PF6 (C2-spacer)
to 1100 M−1 for 11b-2H·2PF6 (C3-spacer). For even longer
spacers, the decrease in Ka is less drastic. With 132 mM, the
Kinetics: Heterodivalent Pseudorotaxanes. The diva-
lent pseudorotaxanes above form through two threading steps.
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1
by H NMR spectroscopy. To prepare the kinetics study, the
following two experiments were performed:
(i) To make sure that the thermodynamic trends remain
unaltered with the unsymmetrical axles 4a−e-2H·PF6, 1H NMR
competition experiments like those discussed above were per-
formed with pseudorotaxanes 12a−e-2H·2PF6 and 13a−e-2H·
2PF6 (see Supporting Information). The same trends were ob-
tained so that we conclude the transition from axles 2a−e-2H·
PF6 to 4a−e-2H·PF6 to likely alter the absolute, but not the
relative, spacer-induced stabilities.
(ii) Figure 6 shows the temporal development of a 1:1:1 mixture
of axles 4a-2H·PF6 and 4b-2H·PF6 with crown heterodimer 7.
Figure 5. Crystal structure of pseudorotaxane 11a-2H·2PF6. (a) Cut-out of
one crown-axle binding motif: N−H···O and C−H···O hydrogen bonds
connecting the crown and the axle on one side of the divalent
pseudorotaxane. Note that the exact lengths and angles are somewhat
different for the second binding site (see text). (b) The whole complex and
plane-to-plane distances between axle phenyl rings and the anthracene
spacer of the crown ether dimer. (c) Space filling representation and view of
the packing of two neighboring complexes (axle: blue, crown dimer:
yellow). For more crystallographic details, see Supporting Information.
Figure 6. Temporal development of a 1:1:1 mixture of 4a-2H·2PF6,
4b-2H·2PF6, and 7 (500 MHz, 298 K, CDCl3:CD3CN = 2:1, 5.0 mM).
Reaction intervals are given on the right side, the evolution of integral
ratios on the left. m and i denote the axle protons ortho to the phenol
O atoms (Figure 1).
The kinetics of the first one should be more or less spacer-
independent, while the second threading event can be expected
to be affected by the spacer between the two ammonium ions.
To be able to compare the thermodynamic spacer effects with
the kinetic ones, it would thus be preferable if the second,
spacer-dependent threading step could be monitored inde-
pendently. For this reason, the heterodivalent pseudorotaxanes
13a−e-2H·2PF6 (Figure 1) were chosen, because they bear
orthogonal and thus clearly distinguishable binding sites.10e−g
The anthracene stopper of axles 4a−e-2H·2PF6 ensures
sequential threading to exclusively occur from one side of the
axle. As a consequence, threading now involves three steps
(Figure 2): (i) A fast threading of the 24-crown-8 moiety onto
the hydroxypentyl ammonium site occurs on a millisecond time
scale10e and yields 19a−e-2H·2PF6. This step happens more or
less exclusively, because the slipping of the smaller 21-crown-7
ether onto the axle is much slower. (ii) Migration of the 24-
crown-8 ether to the second, anthracenyl methyl ammonium
station proceeds on a second time scale10e and gives rise to
20a−e-2H·2PF6. (iii) Finally, threading of the smaller 21-
crown-7 ether onto the hydroxypentyl ammonium group requires
many minutes10e and completes the formation of the pseudoro-
taxanes 13a−e-2H·2PF6. Consequently, intermediates 20a−
e-2H·2PF6 accumulate before the last step occurs. Their
conversion to the final pseudorotaxane can thus be monitored
Protons i and m ortho to the phenol oxygen atoms are most
indicative of the formation of intermediates 20a-2H·PF6 and
20b-2H·PF6 and the final divalent pseudorotaxanes 13a-2H·PF6
and 13b-2H·PF6. From this experiment, four conclusions can
be drawn: First, the signals are all separate from each other so
that it is possible to follow the kinetics of pseudorotaxane for-
mation quantitatively. Second, intermediate 20b-2H·PF6 is con-
verted more quickly to 13b-2H·PF6 than 20a-2H·PF6 to 13a-
2H·PF6. Consequently, the shorter C2 spacer does not foster
the highest threading rate. Rather, the C3 spacer reacts through
the lower activation barrier. Although 20b-2H·PF6 vanishes
within the first few minutes at room temperature, it will still be
possible to quantitatively follow the kinetics at lower temper-
atures. The third conclusion is derived from the integrals: When
the sum of the integrals of 13a-2H·PF6 and 20a-2H·PF6 is
compared to the sum of 13b-2H·PF6 and 20b-2H·PF6, the ratio
is 1:1 and remains constant for about the first 40 min. At about
that time, the intermediates 20a-2H·PF6 and 20b-2H·PF6 have
been fully converted into the heterodivalent pseudorotaxane
products. A very slow error correction then leads to a decrease of
13b-2H·PF6 relative to 13a-2H·PF6 in line with the thermody-
namics discussed above for the homodivalent pseudorotaxanes.
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The constant 1:1 integral ratio observed at the beginning of the
experiment clearly indicates that the first two threading steps
giving rise to intermediates 20a,b-2H·PF6 do not depend
on the spacer, while the third threading event does (Figure 2,
right). The stabilities of the intermediates are independent of
the length of the spacers, and statistically a half of host 7 will
be consumed by 4a-2H·2PF6 and a half by 4b-2H·2PF6. Con-
sequently, it is possible to investigate the kinetics of the final
step independently from the preceding ones, and the model
depicted in Figure 2 (right) fits the experiments. Finally, the
back-reaction from intermediates 20a,b-2H·PF6 to the reactants
is significantly slower than the forward reaction to the final
pseudorotaxanes. Otherwise, the spectrum obtained after 40 min
would not show a 1:1 ratio of the two pseudorotaxanes. In addi-
tion, the dethreading of the green axle from 21-crown-7 is also
very slow compared to the forward threading step. Error-
correction, which starts to become visible after ca. 40 min, leads
to the thermodynamically predominant stable complex 13a-
2H·PF6 shown in Figure 6. This is important, because the last
threading step can then be treated with a simple quasi-irreversible
unimolecular kinetic model (eq 6). The activation parameters are
accessible by determining the rate constants at different tempera-
tures with the help of the Eyring equation (eq 7).
effect becomes. Entropically, the C2-spacer is thus favorable due
to the lower number of degrees of freedom that are fixed upon
the last threading effect. At chain lengths around C5, the third
threading event is not governed by strain (enthalpy) anymore
and the entropic effects originating from conformational fixation
take over. This leads to a slight increase of the activation barrier
for longer spacers. Kinetically, the fastest threading thus occurs
around this spacer length , and thus the kinetically optimum
spacer length clearly differs from the thermodynamic one.
CONCLUSIONS
■
The following conclusions can be drawn from the results discussed
above:
(i) Already quite subtle changes in the spacer length such as
the introduction of an additional methylene group in an
alkyl chain can cause substantial alterations in multivalent
binding. A model that describes multivalent binding by
just considering the binding sites as connected through
an innocent, flexible molecular thread can be too simple
for an accurate description when dealing with short spacers.
In the C2-spacer pseudorotaxane 11a-2H·2PF6, the spacer
participates in binding through a significant preorganization
effect which increases the binding strength and with it
causes strong positive chelate cooperativity.
(ii) Multivalency can be expressed thermochemically, i.e., in
binding constant variations, but it can also be expressed
kinetically. No direct correlation between the thermody-
namics and kinetics need to exist. In the examples discussed
here, the spacer optimal for strong binding is unfavorable
for the final threading step, because it induces strain in the
transition structure, which does not exist anymore in the
final product.
(iii) In view of the analysis of spacer length in the article by
Kramer and Karpen4 mentioned in the Introduction,
similar trends are found here: A too short spacer such as
the phenyl group in axle 3-2H·2PF6 can only undergo
monovalent binding with one host molecule. Conse-
quently, the remaining binding sites also bind, but the
system forms larger assemblies such as 14-4H·4PF6 to
maximize the binding energy.10e,f When the spacer be-
comes long enough to span both binding sites of the
host, divalent binding occurs through transition states
that are strained and thus enthalpically disfavored with
stoppers of intermediate length. Axles with even longer
spacers then react more quickly until the entropic penalty
for conformational fixation dictates higher barriers again.
(iv) In line with the analysis of entropy effects by Whitesides
et al.,6 the entropic effects of longer spacers are not very
pronounced so that significantly overlong, but flexible,
spacers still remain potent. With our study, we have shown
that similar trends govern divalent binding in both small
synthetic supramolecular systems and biological systems.
⎛
⎜
⎝
⎞
⎟
⎠
c
ln
= − kt
c
(6)
0
⧧
⧧
k
h
k
ΔH
R
1
T
ΔS
R
B
ln
= −
+
+ ln
(7)
T
Spacer Effects on the Activation Parameters of the
Final Threading Step. The rate constants for the final thread-
ing step have been measured at different temperatures for all
five pseudorotaxanes 13a−e-2H·2PF6 (Supporting Informa-
tion). The activation parameters are summarized in Table 2.
Table 2. Activation Parameters for the Final Intramolecular
Threading Step Converting 20a−e-2H·2PF6 into 13a−e-2H·2PF6
(determined on a 500 MHz NMR spectrometer
(CDCl3:CD3CN = 2:1, 5.0 mM)
ΔG⧧ (298 K)
ΔH⧧
−TΔS⧧ (298 K)
[kJ mol−1]
[kJ mol−1]
[kJ mol−1]
13a-2H·PF6
13b-2H·PF6
13c-2H·PF6
13d-2H·PF6
13e-2H·PF6
91.9 2.0
86.7 1.8
84.7 2.3
84.2 1.1
85.2 2.5
59.2 1.8
53.3 1.6
49.7 2.3
49.0 0.9
47.5 2.3
32.7 1.9
33.4 1.8
35.0 2.7
35.2 1.0
37.7 2.7
The free enthalpies of activation decrease with spacer length
from ca. 92 kJ mol−1 for the C2-spacer in 13a-2H·2PF6 to ca.
84 kJ mol−1 for the C5-spacer in 13d-2H·2PF6 and then slightly
increases again (though within experimental error) for 13e-2H·
2PF6. Consequently, the spacer giving rise to the maximum
binding strengths exhibits the highest activation barrier.
A closer look at the activation enthalpies and entropies
points to the reasons for this behavior. The activation enthalpy
for the formation of 13a-2H·2PF6 is particularly high, indicating
the presence of some strain in the transition state. With longer
spacers, the strain is released and the activation enthalpy de-
creases. All activation entropies are negative as expected for a
situation in which a freely mobile chain is fixed through intra-
molecular ring formation. The longer the spacer, the larger this
ASSOCIATED CONTENT
■
S
* Supporting Information
Synthetic procedures and characterization data for new com-
pounds; analytical data for pseudorotaxanes including 1D
NMR, 1H,1H COSY NMR, and ESI-FTICR mass spectra;
experimental details for 1H NMR competition experiments, ITC
titrations, and crystal structure determination; rate-constant
determination and Eyring plots. This material is available free of
charge via the Internet at http://pubs.acs.org.
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Article
J. Am. Chem. Soc. 2009, 131, 16544−16554. (j) Mukhopadhyay, P.; Wu,
A.; Isaacs, L. J. Org. Chem. 2004, 69, 6157−6164. (k) Rudzevich, Y.;
AUTHOR INFORMATION
Corresponding Author
christoph@schalley-lab.de
■
Rudzevich, V.; Klautzsch, F.; Schalley, C. A.; Bohmer, V. Angew. Chem.,
̈
Int. Ed. 2009, 48, 3867−3871. (l) Schmittel, M.; Mahata, K. Chem.
Commun. 2010, 46, 4163−4165. (m) Tomimasu, N.; Kanaya, A.;
Takashima, Y.; Yamaguchi, H.; Harada, A. J. Am. Chem. Soc. 2009, 131,
12339−12343. (n) Wu, A.; Isaacs, L. J. Am. Chem. Soc. 2003, 125, 4831−
4835. (o) Jiang, W.; Schalley, C. A. Beilstein J. Org. Chem. 2010, 6, no.
14. (p) Wang, F.; Han, C.; He, C.; Zhou, Q.; Zhang, J.; Wang, C.; Li,
N.; Huang, F. J. Am. Chem. Soc. 2008, 130, 11254−11255.
Present Address
§The Skaggs Institute for Chemical Biology, The Scripps
Research Institute, 10550 N. Torrey Pines Rd., La Jolla, CA
92037.
ACKNOWLEDGMENTS
■
(11) (a) Casnati, A.; Sansone, F.; Ungaro, R. Acc. Chem. Res. 2003,
36, 246−254. (b) Sansone, F.; Baldini, L.; Casnati, A.; Ungaro, R.
New J. Chem. 2010, 34, 2715−2728. (c) Wang, L.; Vysotsky, M. O.;
We are grateful to Prof. Christopher Hunter (University of
Sheffield) and Prof. Pablo Ballester (ICIQ Tarragona) for
valuable advice and thank Mr. Igor Linder, M.Sc., Mr. Abdullah
Abdulkader, Mr. Tobias Becherer, and Miss Sinaida Lel (FU
Berlin) for inspiring discussions and help with guest synthesis.
This research is financially supported by the Deutsche
Forschungsgemeinschaft (SFB 765), the Fonds der Chemischen
Industrie, German Academic Exchange Service (DAAD) and the
Academy of Finland (KR: grant no. 122350 and 140718). E.V.D.
thanks the Studienstiftung des deutschen Volkes for a Ph.D.
fellowship.
Bogdan, A.; Bolte, M; Bohmer, V. Science 2004, 304, 1312−1314.
̈
(12) (a) Huskens, J. Curr. Opin. Chem. Biol. 2006, 10, 537−543.
(b) Nijhuis, C. A.; Yu, F.; Knoll, W.; Huskens, J.; Reinhoudt, D. N.
Langmuir 2005, 21, 7866−7876. (c) Liu, Y.; Chen, Y. Acc. Chem. Res.
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Stoddart, J. F. Chem.Eur. J. 2004, 10, 1926−1935. (b) Badjic,
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(31) N-H···O hydrogen bond parameters: 2.14 Å (H78b···O10),
2.28 Å (H78a···O15) and 161.1° (N78−H78b−O10), 132.1° (N78−
H78a−O15) and 2.02 Å (H97a···O7), 2.61 Å (H97b···O2) and 170.7°
(N97−H97a−O7), 128.2° (N97−H97b−O2).
(32) C-H···O hydrogen bond parameters: 2.38 Å (H79a···O11),
2.55 Å (H77a···O14), and 2.59 Å (H77b···O11) and 140.2° (C77−
H79a−O11), 161.8° (C77−H77a−O14) and 135.6° (C77−H77b−
O11) and 2.38 Å (H96b···O3) and 155.9° (C96−H96a−O3).
(33) The normal from C90 to the plane through C2−C7 = 3.51 Å
and the normal from C83 to the plane of C9−C14 = 3.48 Å.
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