Probing multivalent interactions in a synthetic host-guest complex by dynamic force spectroscopy

Article abstract of DOI:10.1021/ja2016125

Multivalency is present in many biological and synthetic systems. Successful application of multivalency depends on a correct understanding of the thermodynamics and kinetics of this phenomenon. In this Article, we address the stability and strength of mu

Full text of DOI:10.1021/ja2016125

ARTICLE
pubs.acs.org/JACS
Probing Multivalent Interactions in a Synthetic HostꢀGuest Complex
by Dynamic Force Spectroscopy
Alberto Gomez-Casado, Henk H. Dam, M. Deniz Yilmaz, Daniel Florea, Pascal Jonkheijm,* and
Jurriaan Huskens*
Molecular Nanofabrication Group, MESAþ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500AE Enschede,
The Netherlands
S Supporting Information
b
ABSTRACT: Multivalency is present in many biological and synthetic
systems. Successful application of multivalency depends on a correct
understanding of the thermodynamics and kinetics of this phenomen-
on. In this Article, we address the stability and strength of multivalent
bonds with force spectroscopy techniques employing a synthetic
adamantane/β-cyclodextrin model system. Comparing the experimen-
tal findings to theoretical predictions for the rupture force and the
kinetic off-rate, we find that when the valency of the complex is
increased from mono- to di- to trivalent, there is a transition from
quasi-equilibrium, with a constant rupture force of 99 pN, to a
kinetically dependent state, with loading-rate-dependent rupture forces from 140 to 184 pN (divalent) and 175 to 210 pN
(trivalent). Additional binding geometries, parallel monovalent ruptures, single-bound divalent ruptures, and single- and double-
bound trivalent ruptures are identified. The experimental kinetic off-rates of the multivalent complexes show that the stability of
the complexes is significantly enhanced with the number of bonds, in agreement with the predictions of a noncooperative
multivalent model.
or the folding of the Parkinson-involved protein R-synuclein8
1. INTRODUCTION
have been examined as well using force spectroscopy. Moreover,
Multivalency describes the interaction between multivalent
receptors and ligands. It plays a pivotal role in biochemistry,
governing many interactions between proteins and small mole-
cules, between proteins or antibodies and cell membranes,
modifications of this technique allow the construction of recog-
nition maps on cellular membranes9 or study the effect of
mechanical stress on chemical reactions.10
To our knowledge, only three studies probing multivalency at
between viruses and cells, etc.1 At interfaces in particular, multi-
the single molecule level by means of DFS have been reported
valency is poorly understood in a quantitative sense. Under-
before.11 The complexes used for these studies were biological
standing of multivalent interactions at interfaces thus constitutes
(concanavalinAꢀmannose,11a MUC1 antigenꢀantibody11b
)
a way to better understand and control biological recogni-
tion events2 and provides a tool to develop supramolecular nano-
materials.3
and synthetic (C60ꢀporphyrin tweezers11c). Both studies using
biomolecules concluded that the force of a multivalent bond
scaled sublinearly with the number of bonds, whereas the
C60ꢀporphyrin system yielded a divalent rupture force stronger
than 2 times the monovalent rupture force. Presumably, this
discrepancy could originate from the fact that the binding of C60
to porphyrin tweezers is likely to be not only multivalent but also
strongly cooperative,12 which would make the complex stronger
than a purely multivalent attachment. On the other hand, the
experiments using MUC1 antigenꢀantibody studied ruptures of
parallel bonds, which have been predicted to break at reduced
forces if the linkers connecting them are of different length.13 In
the case of the concanavalinAꢀmannose, conformational changes
in the protein upon binding could change the affinity for successive
In principle, the usage of single-molecule techniques allows
more detailed insight in the study of molecular interactions, in
comparison with the traditional ensemble methods, such as
calorimetry or NMR, on the macroscopic scale. Methods based
on atomic force microscopy (AFM) and optical tweezers are more
suited to register individual binding events and are employed to
observe covalent and noncovalent bonds under controlled stress.4 In
particular, dynamic force spectroscopy (DFS) enables the deter-
mination of kinetic dissociation rate constants by analyzing the
studied bond rupture at different loading rates, that is, how fast
the bond is loaded with the external force.5 Lifetimes of molecular
complexes and even a detailed description of the energy land-
scape for some biological systems have been deduced using this
technique.6 Besides the study of complexes, the structure and
unfolding pathways of proteins and mutant analogues such as titin7
Received: February 21, 2011
Published: May 26, 2011
r
2011 American Chemical Society
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Scheme 1. Compounds Used in This Studya
a Ad, adamantane; EG, ethyleneglycol; PEG, polyethyleneglycol.
Scheme 2. Tip Functionalization with Mono-Ad, Di-Ad, or Tri-Ad Using PEG3000 Linkera
a Ad, adamantane; PEG, polyethyleneglycol; NHS, N-hydroxysuccinimide; DIPEA, N,N-diisopropylethyleneamine; rt, room temperature.
bindings. In this study, we use a synthetic hostꢀguest system
aiming to avoid the potential problems described above. The
binding sites that are physically different molecules ensure that
the affinities for the second and successive bonds are unaffected
by the first, and the geometry of the multivalent guests is such
that only one linker is pulled.
In our laboratory, we use the adamantane/β-cyclodextrin
(βCD) supramolecular complex as a model system to study
multivalency.14 βCD is an oligosaccharide consisting of seven
glucose units connected in a ring shape. The inner cavity of
this ring is hydrophobic and can accommodate a wide variety
of guest molecules.15 This hostꢀguest couple has been used
by us for fabricating various nanostructures, and detailed SPR
work in combination with thermodynamic models has pro-
vided insight in the multivalent characteristics of this
interaction.16 Previously, employing DFS we reported the
rupture force between a series of monovalent guests bound to
an AFM tip and surface-bound βCD. The notion of thermo-
dynamic equilibrium allowed correlating quantitatively the
measured pull-off force values with free binding energy of the
complexes.17
Here, we provide a comprehensive thermodynamic and
kinetic analysis of the binding of mono-, di-, and trivalent guests
to self-assembled monolayers of βCD host. The interactions
between single pairs of βCD and adamantane as well as between
divalent and trivalent assemblies of these molecules were studied
using DFS to study their binding forces and kinetic off-rates. A
theoretical model for the multivalent assembly is used to
compare the measured multivalent off-rates with the expected
monovalent off-rate.
2. RESULTS AND DISCUSSION
2.1. Monovalent Guest. In a typical force spectroscopy (FS)
experiment, several force curves are acquired using a functiona-
lized AFM tip and/or substrate. Thus, βCD and adamantyl-
functionalized molecules (Scheme 1) need to be immobilized in
a convenient manner, one over the surface of the AFM tip and the
other on a supporting substrate. We followed a well-known
procedure to create a densely packed monolayer of βCD over a
gold substrate, also known as the molecular printboard.18 These
printboards expose the hydrophobic cavities of βCD in a
hexagonal lattice with a lattice constant of ca. 2 nm to the
medium, effectively acting as a surface-bound multivalent recep-
tor. The adamantyl (Ad) guests are readily attached to gold-
coated AFM tips using thiol groups, either in a single-step
procedure, when using short linkers, or successively connecting
amine-reactive linkers and amino-functionalized guest moieties
to a cysteamine monolayer (Scheme 2 and see the Experimental
Section for a detailed description of the procedures for functio-
nalizing the tip and substrate). For the study of multivalent
guests, the spacers between the two Ad moieties must be chosen
to be long enough to allow for multivalent complexation on the
molecular printboard.19 The functionalized tip and supporting
substrate are installed in the AFM setup for the DFS experiment.
A laser is employed to monitor the deflection of a soft cantilever
connected to the tip. The distance between the base of this
cantilever and the substrate is controlled by means of a piezo-
electric crystal. Starting from a situation where the tip and substrate
are not in contact, the distance between them is reduced (approach)
until a positive deflection is detected. After a chosen delay during
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which tip and surface remain in contact, the separation between
substrate and cantilever base is progressively increased (retract).
During this step, a negative deflection can be observed, which is
related to an interaction between the tip and surface. When the
energy accumulated in the bent cantilever is enough to break this
interaction, the measured maximum deflection can be multiplied
by the cantilever spring constant to give the unbinding force of
the studied interaction. On a typical curve like the ones shown in
Figure 1A, the retraction starts at the far left, and interactions
with the surface are being broken until achieving the flat zero-
force region, representing a relaxed cantilever.
Typically in FS studies the moieties of interest are not directly
connected to the AFM tip surface; instead, a flexible linker is
introduced between them to allow some translational and
rotational freedom for complexation. In addition, this linker, if
long enough, allows the rupture of the specific interaction pair to
happen when the tip is several nanometers away from the surface
and any nonspecific interactions between tip and surface have
been already overcome. Furthermore, the characteristic non-
linear elasticity of the linker can be used as an internal check of
the measurements. A force curve measured using such linkers
shows multiple ruptures. The first rupture event, a sudden
change in the measured force, usually originates from unspecific
short-range interactions between the tip and substrate. Subse-
quent events originate from the studied moieties being ruptured
and should show a nonlinear region, characteristic of the
particular linker in use, prior to the rupture. The slope of this
curve immediately before the rupture is the instantaneous
loading rate that is being applied to the bond (Figure 1C). Thus,
the choice of a linker between an AFM tip and the guest
molecules largely influenced the availability of rate data in our
previous DFS studies,17 where we used short linkers (alkyl chains
of 7ꢀ18 carbons). Moreover, achieving and proving that the
ruptures originate from a single hostꢀguest pair is much more
difficult with such sort linkers. Therefore, we decided to explore
here the use of longer tethers between the monovalent guest and
the tip surface. We chose three different water-soluble ethyle-
neglycol (EG) based linkers, that is, a short tetraethyleneglycol
(Scheme 1A, EG4) linker, an EG13 (Scheme 1A) linker of
intermediate length, and a long linker containing a polyethyle-
neglycol (PEG) chain of Mw 3000 g/mol (Scheme 1A, PEG
3000, approximately 68 ethyleneglycol units). In aqueous
media,20 we examined forceꢀdistance curves, selecting only
those events that represent a polymer stretch region matching
the expected single PEG chain behavior, which we used as an
internal check of our measurements. A curve for each of these
linkers is shown in Figure 1A, where it can be clearly seen how the
separation between the first and final ruptures increases with the
linker length. In addition, only in the case of the longest linker did
we unequivocally observe nonlinear stretching behavior that
could be reliably fitted to a worm-like chain (WLC) model21
to obtain instantaneous loading rates, whereas in the case of the
shorter linkers the transition in stiffness occurs too fast yielding
too few data points for a reliable fitting procedure. With these
results in hand, in the remainder of this study we employed the
PEG 3000 linker (Figure 1B).
Figure 1. (A) Characteristic forceꢀseparation curves (offset in force
axis for clarity) for monovalent adamantyl guests linked to the AFM tip
by a short tetra ethylene glycol linker (EG4, top), linker with 13 EG units
(EG13, middle), or a long linker of ca. 68 EG units (PEG3000, bottom).
(B) Characteristic forceꢀseparation curves (offset in force axis for
clarity) for mono-, di-, and trivalent adamantyl guests linked to the
AFM tip by a long PEG3000 linker. (C) Example of a curve with
highlighted rupture force and WLC (worm-like chain) fit to the data.
The slope of this fit at the rupture point quantifies the stiffness of the
polymer, and together with the retraction speed allows the calculation of
the instantaneous loading rate.
The collected forceꢀdistance curves, obtained from experi-
ments where the monovalent adamantyl guest was linked to the
tip via the PEG 3000 linker, were fitted to a WLC polymer model,
where the contour length was the fitting parameter and the
persistence length was fixed at a value of 3.5 Å, corresponding to
one-half of the Kuhn length of 7 Å.22 The fitted contour length
(typically between 10 and 50 nm) was reasonably close to the
expected value for a PEG chain of 3000 g/mol (average 25 nm),
considering the polydispersity of the linker and the fact that we
selected the last rupture event, which relates to the longest
available linker on the tip. Next, the instantaneous loading rate
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Figure 2. Analysis of DFS data of the monovalent guest (Mono-Ad) using PEG3000 linker. (A) Pairs of force and loading rate obtained from the
collected curves and (B,C) kernel smoothened densities of probability constructed from them (the ticks indicate individual occurrences). Data
corresponding to the main peaks of force and loading rate are assigned to monovalent binding, and the data corresponding to the high-force, high-rate
tails of the distributions correspond to monovalent (parallel) binding. (D) Combined results from different retracting speeds; the dotted line is the
averaged rupture force of a monovalent complex.
When the data of the monovalent guest were plotted in this
way (open symbols in Figure 2D), a zero slope was observed in
the explored loading rate range, indicating that the complex can
be considered in thermodynamic equilibrium for our experi-
mental conditions, in agreement with our previous studies on
monovalent guests17,24 and other systems.25 In addition, the
most apparent rupture force in the case of the monovalent
adamantane guest, 97 ( 19 pN, closely matches our previous
results obtained for short tethers (102 ( 15 pN).17 This loading
rate-independent behavior can be explained by the fact that the
binding and unbinding rate constants for the cyclodex-
trinꢀadamantane system (kon is diffusion limited, on the order
was calculated from the slope of the WLC fit at the rupture point
(Figure 1C) to give pairs of forceꢀloading rate values. For these
forces and loading rates, an estimated density of probability was
constructed. Such density graphs (Figures 2B,C) show what
forces and loading rates were observed for each set of pulling
conditions. On some of the force probability densities a long
high-force tail or even a well-defined secondary peak was found
(Figure 2C). Crossing these data with the loading rate data,
where also a long tail was present, we found that data points can
be grouped into two quadrants (Figure 2A). One group consists
of low force/low rate data points, which relate to monovalent
force, and another group consists of high force/high rate data points,
which we tentatively attribute to the parallel rupture of two mono-
valent hostꢀguest pairs. In this latter case, the rupture force value
has been predicted to vary with the difference in length of the
chains that link the two guests, being lower when the two pairs
are linked by chains of different lengths as compared to the
situation when both chains are of identical length.13
To perform further analysis on the monovalent data, we
made use of a theory developed by Evans et al.5 based on
previous work by Bell,23 which predicts linear scaling of the
rupture force f to the logarithm of the loading rate r, where kB
is the Boltzmann constant, T is the temperature, Δx is the
width of the energy barrier, and koff is the intrinsic dissociation
rate (the dissociation rate constant when the bond is not
loaded by an external force).
of 108 Mꢀ1 sꢀ1 26
,
and koff estimated to be 2 ꢁ 103 sꢀ1 for a
measured equilibrium constant,16a Keq = 4.6 ꢁ 104 Mꢀ1
)
represent a very rapid equilibration as compared to the time
scale of the AFM measurements. The monovalent guest probed
under these conditions can be considered at thermodynamic
equilibrium, and thus no kinetic effects such as the unbinding
force dependence on loading rate are expected to show up in the
measurements. This aspect could be confirmed by implementing
a model27 that predicts the transition from equilibrium to a
dynamic regime. The estimated potential of the adamantaneꢀ
cyclodextrin interaction was introduced in such model (see the
Supporting Information), obtaining an equilibrium rupture force
of 90 pN and an unforced off-rate of 2 ꢁ 103 sꢀ1, which are
very close to the values presented above. The loading rate
required to observe the characteristic logarithmic increase of
rupture forces is estimated as 107ꢀ108 pN/s, well beyond the
range of AFM-based DFS. Loading rate dependence could not
ꢀ
ꢁ
kBT
rΔx
f ¼
ln
ð1Þ
Δx
k
off kBT
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Figure 3. Analysis of DFS data of the divalent guest (Di-Ad) using PEG3000 linker. (A) Pairs of force and loading rate obtained from the collected
curves. (B,C) Kernel smoothened densities of probability constructed from them (the ticks indicate individual occurrences). The main peak on the force
distribution is assigned to divalent force (divalent-double, filled symbols), and the secondary peak at lower force (when present) is assigned to pull-offs
were only a single adamantane was bound in the instant of rupture (divalent-single, open symbols). Data corresponding to the high-force, high-rate tails
originate from several possible situations were more than one divalent hostꢀguest complex was ruptured. Notice that because only one linker is involved
in divalent-single and divalent-double ruptures, both fall in the same band of loading rates. (D) Combined results from different retracting speeds; the
dashed line is a logarithmic fit as a guide to the eye.
be assessed for the parallel monovalent unbinding events (filled
symbols in Figure 2D), because all ruptures occurred at similar
loading rates.
been previously reported that the difference in length between
two linkers in a parallel rupture will lead to lower rupture
forces.13 In the case of probing two hostꢀguest complexes, the
maximum rupture force will be measured when the linkers are
loaded under identical conditions at the moment of the rupture.
This implies that both chains are of the same length, which is not
likely when using long polymeric linkers, and their attachments
points are such that both distances to the surface are equal. The
geometry of our divalent guest is the optimal approach to achieve
simultaneous and equal loading, because the two hostꢀguest
pairs are connected by a single linker and branch out only at the
very end. The measured higher rupture forces in the case of the
divalent guest (approximately 170 pN at 30 nN/s) when
compared to parallel monovalent guests (approximately 140
pN at 30 nN/s) confirm the prediction that linking the guest
moieties through a single tether is the optimal approach to
measure multivalent interactions.
When more than one weak moiety is attached in a multivalent
fashion, the dissociation rate constant is expected to decrease several
orders of magnitude,16b,29 opening the possibility to probe the
complex in an out-of-equilibrium regime. This is confirmed here
by measuring rupture forces for divalent-double cyclodextrinꢀ
adamantane complexes, which presented a defined loading rate
dependency.
2.2. Divalent Guest. Following the same attachment proce-
dure using the PEG 3000 linker to the AFM tip, we collected and
analyzed forceꢀdistance curves for the divalent guest (Figure 3A).
In strong contrast to the monovalent guest, the most probable
rupture force was found to be dependent on the loading rate,
ranging from 140 ( 15 pN (probe retraction speed 260 nm sꢀ1
)
to 184 ( 25 pN (probe retraction speed 1160 nm sꢀ1). The
rupture forces for divalent guests were in all cases smaller than
twice the rupture force for monovalent guests, in agreement with
theoretical predictions28 and experimental studies.11a,b,13 How-
ever, when crossing the distributions of rupture force and loading
rate (Figure 3), we clearly distinguish three regions. The most
probable loading rate comprised two characteristic rupture force
peaks. The lower of these two peaks indicates a rupture force
matching the values of the previously determined monovalent
unbinding force and can be interpreted as events where only one
of the adamantyl moieties was bound at the moment of rupture
(named as divalent-single in the rest of this Article). The higher
and most probable force corresponds to divalent ruptures
(divalent-double). Finally, a third region consists of high-force,
high-loading rate events, which we attribute to parallel unbinding
of two (or more) divalent guests. Because these data can originate
from several binding situations (doubleþdouble, singleþsingle,
and singleþdouble bound for two parallel divalent guests),
further analysis was not performed.
2.3. Trivalent Guest. Experiments using the trivalent guest
were performed in the same manner as described above. The
density of probability of measured rupture forces showed multiple
peaks over a large range of forces (see the Supporting Informa-
tion). We discussed above that high force peaks originate from
parallel ruptures. In the case of two trivalent guests rupturing
One important aspect revealed by these experiments is the
difference between multivalent and parallel arrangements. It has
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Figure 5. Comparison of AFM-DFS data of mono-, di-, and tri-
adamantyl guests. Different attachment geometries are assigned, single
bound mono-, di-, and trivalent (open symbols), double bound di- and
trivalent (filled symbols), and triple bound trivalent (stars). The lines are
least-squares fits to the Evans model for the double and triple bound
data, and the average rupture force for the single bound data.
Table 1. Parameters Obtained by Fitting FS Data to
BellꢀEvans Modela
bond
monovalent
valency
(estimated)
double
triple
Δx (nm)
0.2ꢀ0.3 0.24 ( 0.09
200031
0.27 ( 0.10
0.004 (0.0003ꢀ0.05)
koff (sꢀ1
)
0.2 (0.01ꢀ3.5)
Figure 4. Results from the analysis of DFS data of trivalent guest
(Tri-Ad) using PEG3000 linker. (A) Kernel smoothened density of
probability of rupture forces corresponding to the main peak of the
loading rate distribution (the ticks indicate individual occurrences). The
three different peaks are assigned (from lower to higher force) to
ruptures of trivalent-single (open symbols), -double (filled symbols),
and -triple (stars) bound guest. (B) Combined results from different
retracting speeds; the dotted lines are logarithmic fits for the second and
third peaks as a guide to the eye.
a For koff, a confidence interval is given in parentheses.
the middle peak compare well to the values and trend of the
divalent-double ruptures (Figure 5), which confirms our inter-
pretation of the force density graphs for the trivalent guest. The
rupture force of a fully bound trivalent complex showed a
stronger dependence on the loading rate, with values ranging
from 175 ( 18 pN (probe retraction speed 581 nm sꢀ1) to 210 (
20 pN (probe retraction speed 2620 nm sꢀ1), when compared to
the measured forces for the divalent complex at similar
loading rates.
2.4. Kinetic Analysis. The monovalent adamantylꢀβCD
system appears to be at equilibrium under the accessible condi-
tions for loading rate and acquisition bandwidth. Therefore, the
BellꢀEvans model (eq 1), developed for dissociations occurring
out-of-equilibrium, can not be applied to our data to obtain a
value for koff for the monovalent system based on force spec-
troscopy. However, the experimental data from divalent and
trivalent guests show a pronounced loading rate dependence of
the rupture forces, making them suitable for a fit. The values of
Δx and koff for ruptures of double (from divalent-double and
trivalent-double data) and triple (from trivalent-triple data)
attachments are presented in Table 1. From these data, an
increased stability of the complex is clearly observed upon
increasing the valency, with lifetimes extended 100- to 10 000-
fold per each extra bond. Such enhanced stability is a general
feature of multivalent complexes and responsible for multivalent
strategies serving as design criteria for novel (macro)molecules
for biomedical applications.30
simultaneously, the forces cannot only be relatively high (tripleþ
triple, tripleþdouble, doubleþdouble) but also appear in a range
of forces very near divalent characteristic forces (singleþsingle)
and between divalent and trivalent forces (singleþdouble). We
have shown that parallel ruptures are characterized by higher
instantaneous loading rates as compared to ruptures where only a
single linker is being stretched. This fact enables us to filter out
the FS data collected using trivalent guests by selecting only the
data corresponding to the main loading rate peak to discard these
parallel ruptures (see Figure S5 in the Supporting Information).
After such a procedure, the rupture forces of the remaining events
were used to construct density graphs where three distinct force
peaks could be resolved (Figure 4). A straightforward explanation
for the meaning of these three characteristic forces is to consider
that the lower, middle, and higher force peaks originate from
ruptures where one (trivalent-single), two (trivalent-double), or
three (trivalent-triple) adamantyl moieties, respectively, were
bound. Moreover, the rupture forces determined by the lower
force peak compare well to the unbinding force of a monovalent
complex of ca. 100 pN, while the rupture forces determined by
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Scheme 3. Diagram of Multivalent Equilibrium and Stepwise Kinetics
2.5. Comparison of DFS Results with Theoretical Model
for Multivalent Dissociation. A model predicting the thermo-
dynamics and kinetics of multivalent assemblies has been
proposed16b and validated for divalent hostꢀguest systems like
the one in our study.16a The multivalent binding/unbinding
process can be described in a stepwise manner as depicted in
Scheme 3; an intermolecular binding is followed by successive
intramolecular steps where the intrinsic binding affinity is un-
changed. This model explains the enhanced binding affinity by a
high local effective concentration (Ceff) of the host that is
available for the divalent guest molecule when it is bound
through only one of its guest moieties (divalent-single). Thus,
no cooperativity in the sense of an increase of intrinsic binding
affinity from the first to the second binding is assumed.12 The
expected equilibrium constant for a multivalent complex can be
related to the corresponding monovalent constant according to
this scheme. For clarity, the trivalent rates and equilibrium
constants are here given the subscript “T” and their monovalent
and divalent counterparts the subscripts “M” and “D”, respec-
tively. In the case of a divalent complex, we have:
The values for Keq-M (4.6 ꢁ 104 Mꢀ1) and Ceff (0.2 M) were
determined in previous studies16a using the same βCD and
adamantyl hostꢀguest system. In particular, the value of Ceff
indicates that the second guest moiety is only able to complex
with the (approximately 6) host cavities directly near the already
occupied cavity. Thus, we can estimate the value for the unforced
off-rate of a monovalent guest:
kon-M
koff-MðestimatedÞ
¼
¼ 2 ꢁ 103 sꢀ1
Keq-M
Substituting this value in eq 5 for a model-based estimation of
the unforced off-rate of a divalent guest gives:
2 koff-MðestimatedÞ
3
koff-DðestimatedÞ
¼
¼ 0:47 sꢀ1
Keq-MCeff
This estimated value for the divalent off-rate is remarkably
close to the value (0.2 sꢀ1) found after fitting the Evans model to
our DFS data. The strong agreement between these two values
for koff-D confirms that the enhanced unbinding force for a
double-bound guest can be fully attributed to multivalency
effects, which was our main aim when designing the structure
of the guest molecules.
2kon-M kon-MCeff
¼ Ke2q-MCeff
ð2Þ
3
Keq-D
¼
koff-M 2koff-M
3
A similar derivation can be done for the trivalent guest; in this
case, we introduce in the last step (Scheme 3) the parameter
C0eff = Ceff /3, because there are only two accessible cavities for
the third guest moiety once a double bond has been established.
Taking this into account, we estimated the off-rate of a trivalent
guest to be:
Because the association rate in this system is diffusion limited,
we propose kon = 108 Mꢀ1 sꢀ1 in the case of the monovalent
adamantyl/βCD system. In the case of the divalent guest, a
statistical factor 2 is introduced.
kon-D ¼ 2kon-M
ð3Þ
9 koff-MðestimatedÞ
ðKeq-MCeff Þ
3
koff-TðestimatedÞ
¼
¼ 2 ꢁ 10ꢀ4 sꢀ1
2
kon-D
Keq-D
¼
koff-D
ð4Þ
This theoretical value and the experimentally observed koff-T
(4 ꢁ 10ꢀ3 sꢀ1) agree remarkably, and we tentatively ascribe the
small discrepancy to the conformational difference of the ethy-
leneglycol linkers in a fully bound trivalent and a fully bound
divalent complex (see the Supporting Information). The intro-
duction of an additional bond significantly stabilizes the trivalent
We can combine eqs 2ꢀ4 to obtain a relationship between the
monovalent and divalent off-rate constants:
koff-M
1
2
¼
K
eq-MCeff
ð5Þ
koff-D
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complex over 100-fold as compared to the fully bound divalent
complex, confirming the characteristical binding of a multivalent
ligand onto independent binding sites.
2-mercaptoethanol (1 mM total thiol concentration) overnight. For the
Ad-EG13-SH functionalization, the cantilevers were immersed in an
ethanol solution of 25% Ad-EG13-SH and 75% 2-mercaptoethanol
(1 mM total thiol concentration) overnight. Finally, the cantilevers
were rinsed with ethanol and blown dry in a stream of nitrogen. For the
PEG 3000 functionalization, the cantilevers were cleaned as described
before and immersed in an ethanol solution of cystamine hydrochloride
(1 mM) for 3 h. After being rinsed with ethanol and dichloromethane,
the amine terminated cantilevers were incubated for 2 h in a 100:1
dichloromethane/DIPEA solution with PEG 3000 linker (NHS-PEG-
NHS, 5 mg/mL, ∼1 mM) and rinsed with dichloromethane. Finally,
they were immersed for 2 h in a solution of amino terminated mono-, di-,
or tri-adamantane guest (1 mM) in 100:1 dichloromethane/DIPEA,
rinsed with dichloromethane, and blown dry in a stream of nitrogen.
AFM Force Spectroscopy Measurements. All force measure-
ments were performed with a commercial Multimode Picoforce SPM
(Veeco, Digital Instruments, U.S.) using a liquid cell (Veeco) and stock
PBS buffer (B. Braun Melsungen AG, Germany). The spring constants
of the cantilevers were calibrated using the built-in thermal tune soft-
ware. Forceꢀdistance curves were acquired by approaching and retract-
ing the tip at speeds ranging from 10 to 103 nm/s. The tip was laterally
displaced over the substrate between each approachꢀretraction cycle,
covering 1 μm2, and the maximum force applied to the surface was kept
under 500 pN. Two different cantilevers were used for each guest. We
could obtain up to 5000 curves per cantilever, limited by the appearance
of high adhesion between the tip and surface and a large decrease in the
chance of observing polymer stretching. This we attribute to deteriora-
tion of the monolayers due to the repeated contact or adsorption of
contamination on the tip.
Data Analysis. We selected relevant force curves using our own
plug-in script developed for Hooke.32 Each curve was examined for
sudden changes in force (rupture events), and then the data prior to the
last rupture (the unbinding event happening farthest away from the
surface) were fitted using a WLC model with fixed persistence length
3.5 Å. Rupture events were rejected or kept for further analysis based on
the quality of the fit, which was assessed visually and numerically by
comparing the averaged force difference from each data point to the
corresponding fitted force dD-F with the standard deviation of the
measured force in the noncontact area σNC (see more details in the
Supporting Information). If the ratio of these two parameters is close
to 1, the difference between the fit and data can be explained by thermal
noise. Pairs of rupture force and instantaneous loading rate were
obtained from the valid events, and an estimation of the rupture force
and loading rate probability densities was obtained with the help of
the statistical package R,33 by using kernel density estimation with
Epanechnikov kernels and a fixed bandwidth of 10 pN in the case of
force or an automatically selected bandwidth (Sheather and Jones
algorithm)34 in the case of loading rate and contour length.
3. CONCLUSIONS
We measured rupture forces of mono-, di-, and trivalent com-
plexes of the β-cyclodextrinꢀadamantyl hostꢀguest pair. The
monovalent complex was probed at equilibrium, while the divalent
and trivalent showed a significant loading rate dependency. The
rupture forces of the fully bound divalent and trivalent complexes
were found to be less than twice and thrice, respectively, that of the
monovalent complex. However, the transition between the equilib-
rium regime (monovalent) and the kinetic regime (divalent and
trivalent) so far prevents a more meaningful comparison of these
rupture forces to further confirm a particular scaling law.
Additionally, we could identify events where two parallel
monovalent complexes were dissociating. Although the two
single binding moieties are chemically identical to the case of a
fully bound divalent complex, differences of length or load
between the two parallel tethers lowered the measured rupture
force with respect to the rupture force of a divalent complex. The
geometry of the multivalent guests employed in this study, with
only one tether pulling at the complex, allowed us to achieve a
situation equivalent to two or three equal parallel tethers, an
optimal condition for obtaining more reliable results when
studying multivalent interactions. Ruptures of lower force,
matching the forces of monovalent or divalent ruptures, were
observed in some of the experiments using multivalent guests.
This suggests that at the moment of rupturing, the multivalent
guests were partially bound to the CD printboard.
Finally, we found our initial assumption for our system,
noncooperative multivalency, confirmed by the kinetic off-rate
values obtained from the analysis of the DFS experiments
performed using multivalent adamantly guests.
4. EXPERIMENTAL SECTION
Materials. All solvents were purchased from commercial sources
and used as received. Cystamine hydrochloride, PEG 3000 (NHS-
terminated homobifunctional PEG, MW 3000), and 2-mercaptoethanol
were purchased from Sigma-Aldrich. βCD adsorbate was synthesized as
described previously.18 Detailed synthesis of compounds shown in
Scheme 1 can be found in the Supporting Information.
Cyclodextrin Monolayer. All glassware was cleaned to remove
organic contamination by using piranha solution (3:1 mixture of sulfuric acid
and hydrogen peroxide) and thoroughly rinsed with MQ water and ethanol.
Gold-coated (200 nm thickness) glass squares were purchased from
Arrandee (Arrandee, Germany). After being rinsed with chloroform,
they were annealed under a high purity hydrogen flame for about 5 min
and allowed to cool. CD adsorbate (1ꢀ2 mg) was dissolved in a 3:2
solution of chloroform and ethanol (total volume 50 mL). The gold
substrates were immersed in fresh piranha solution for 10ꢀ20 s to
remove any organic contamination, rinsed with MQ water and ethanol,
and immediately put into the CD solution. The samples were kept in this
solution overnight at 60 °C, rinsed sequentially with dichloromethane,
ethanol, and MQ water to remove any excess of adsorbed material, and
used immediately in the force spectroscopy experiments.
’ ASSOCIATED CONTENT
S
Supporting Information. Synthesis of compounds, de-
b
tails of the forceꢀdistance curve filtering procedure, density of
probability graphs of force, loading rate, and contour length for
mono-, di-, and trivalent guests, comparison of the monovalent
equilibrium rupture force with a theoretical model, and addi-
tional details about the stability of the fully bound trivalent guest.
This material is available free of charge via the Internet at http://
pubs.acs.org.
Functionalization of AFM Tips. Gold-coated V-shaped AFM
cantilevers with pyramidal tips (Veeco, Digital Instruments, U.S.) were
cleaned in piranha solution for 10 s, then carefully rinsed with MQ water
and ethanol. In the case of Ad-EG4-SH functionalization, the cantilevers
were immersed in an ethanol solution of 0.5% Ad-EG4-SH and 99.5%
’ AUTHOR INFORMATION
Corresponding Author
p.jonkheijm@utwente.nl; j.huskens@utwente.nl
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ARTICLE
’ ACKNOWLEDGMENT
van Hulst, N. F.; Reinhoudt, D. N. Small 2005, 1, 242–53. (b)
Thompson, D. Langmuir 2007, 23, 8441–51.
(20) Hinterdorfer, P.; Kienberger, F.; Raab, A.; Gruber, H. J.;
Baumgartner, W.; Kada, G.; Riener, C.; Wielert-Badt, S.; Borken, C.;
Schindler, H. Single Mol. 2000, 1, 99–103.
(21) Test fits of similar quality were obtained using the freely jointed
chain (FJC) model. WLC was preferred due to its availability in the
employed data analysis tool (Hooke, see ref 32).
(22) (a) Oesterhelt, F.; Rief, M.; Gaub, H. E. New J. Phys. 1999, 1,
1–11. (b) Thormann, E.; Hansen, P. L.; Simonsen, A. C.; Mouritsen,
O. G. Colloids Surf., B 2006, 53, 149–56.
We thank the Dutch nanotechnology network NanoNed
(Project No. TPC 6939) for financial support. P.J. thanks the
Dutch Science Council of the Chemical Sciences for a VENI
grant (700.57.401).
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