Origin of the dendritic effect in multivalent enzyme-like catalysts

Article abstract of DOI:10.1021/ja7113213

Functionalization of multivalent structures such as dendrimers and monolayer passivated nanoparticles with catalytically active groups results in very potent catalysts, a phenomenon described as the positive dendritic effect. Here, we describe a series of

Full text of DOI:10.1021/ja7113213

Published on Web 04/10/2008
Origin of the Dendritic Effect in Multivalent Enzyme-Like
Catalysts
Giovanni Zaupa, Paolo Scrimin,* and Leonard J. Prins*
Department of Chemical Sciences, UniVersity of PadoVa, and ITM-CNR PadoVa section,
Via Marzolo 1, 35131 PadoVa, Italy
Received December 21, 2007; E-mail: leonard.prins@unipd.it; paolo.scrimin@unipd.it
Abstract: Functionalization of multivalent structures such as dendrimers and monolayer passivated
nanoparticles with catalytically active groups results in very potent catalysts, a phenomenon described as
the positive dendritic effect. Here, we describe a series of peptide dendrons and dendrimers of increasing
generation functionalized at the periphery with triazacyclononane, a ligand able to form a strong complex
with ZnII. Kinetic studies show that these metallodendrimers very efficiently catalyze the cleavage of the
RNA model compound HPNPP, with dendrimer D32 exhibiting a rate acceleration of around 80 000 (kcat
uncat) operating at a concentration of 600 nM. A theoretical model was developed to explain the positive
/
k
dendritic effect displayed by multivalent catalysts in general. A detailed analysis of the saturation profile
and the Michaelis–Menten parameters kcat and KM shows that it is not necessary to ascribe the positive
dendritic effect to, for instance, changes in the catalytic site, increased substrate binding constant, or changes
in the microenvironment. Rather it appears that the efficient catalytic behavior of multivalent catalysts is
mainly determined by two factors: the number of catalytic sites occupied by substrate molecules under
saturation conditions, and the efficiency of the multivalent system to generate catalytic sites in which multiple
catalytic units act cooperatively on the substrate.
1. Introduction
or markers is now rapidly leading toward new applications. In
addition, theoretical studies start to unravel the fundamental
aspects of multivalent interactions, and parameters are being
developed to describe them.16–18
Our main interest is in developing multivalent enzyme-like
catalysts, in which multivalent scaffolds are used to rapidly
create multiple catalytic sites in which different functional
groups can act in a cooperative manner on a substrate. So far,
our attention has been devoted mainly to tripodal scaffold
Multivalency is becoming a key concept in the fields of
(bio)recognition,1–4 catalysis,5,6 supramolecular chemistry,7 and
nanotechnology.8,9 The interest in multivalent structures, i.e.,
structures able to develop multiple single interactions with a
target, originates from the awareness that multivalent interactions
play a fundamental role in numerous biological processes.10,11
The functionalization of multivalent molecular architectures,
such as small tripodal scaffolds,12 dendrimers,13 polymers,14 and
surfaces,15 with recognition and sensing elements, catalytic units,
(13) (a) For illustrative examples, see: Prinzen, L.; Miserus, R. J. H. M.;
Dirksen, A.; Hackeng, T. M.; Decker, N.; Bitsch, N. J.; Megens,
R. T. A.; Douma, K.; Heemskerk, J. W.; Kooi, M. E.; Frederik, P. M.;
Slaaf, D. W.; Van Zandvoort, M. A. M. J.; Reutelingsperger, C. P. M.
Nano Lett. 2007, 7, 93–100. (b) Kostiainen, M. A.; Szilvay, G. R.;
Smith, D. K.; Linder, M. B.; Ikkala, O. Angew. Chem., Int. Ed. 2006,
45, 3538–3542. (c) Rameshwer, R.; Thomas, T. P.; Peters, J.; Kotlyar,
A.; Myc, A.; Baker, J. R. J., Jr. Chem. Commun. 2005, 573, 9–5741.
(d) Chang, T.; Rozkiewicz, D. I.; Ravoo, B. J.; Meijer, E. W.;
Reinhoudt, D. N. Nano Lett 2007, 7, 978–980.
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A R T I C L E S
Zaupa et al.
molecules19–21 and self-assembled monolayers on Au nano-
particles,22–25 but recently we have also started to exploit
dendrimers as multivalent scaffolds.26 Dendrimers are mono-
dispersed, hyperbranched polymers which have the advantage
over nanoparticles and polymers that they are molecularly
defined, which facilitates analysis.27–30 Dendrimers have been
extensively used in catalysis taking advantage of various
dendrimer properties such as an ease of separation from the
reaction mixture, the ability to create a specific microenviron-
ment, or the induction of steric effects.5,31–34 The similarity in
size and molecular weight of dendrimers and proteins has led
toward the development of dendrimers as artificial enzymes.35–37
In seminal contributions, Reymond et al. showed that the
screening of combinatorial libraries of peptide dendrimers can
lead toward very potent catalysts displaying enzyme-like
behavior.38,39 It has been often observed that the potency of
dendrimer catalysts dramatically increases with their valency,
which is commonly referred to as a positive dendritic effect
and ascribed to various chemical causes such as an altered pKa
of the active unit, changes in polarity, or increased substrate
binding.28,40–45 Here, we observe a similar positive dendritic
effect in metallodendrimers of various generations which are
very active in the catalytic cleavage of HPNPP, a model
compound for RNA. Based on a theoretical model, we propose
that the dendritic effect in this kind of multivalent system is
related to the number of substrate molecules bound at saturation
and the efficiency of the dendrimers in generating catalytic sites
composed of two individual triazacyclononane-ZnII complexes.
Previously, we have shown that a DAB (poly(propylene
imine)) dendrimer functionalized at the periphery with 16
triazacyclononane (TACN) macrocycles in the presence of ZnII
very efficiently catalyzes the cleavage of 2-hydroxypropyl-p-
nitrophenyl phosphate (HPNPP), which is the standard model
of an RNA-phosphodiester.26 Very importantly, by studying the
catalytic activity of third generation dendrimers with different
mole fractions of TACN-ligands at the periphery we were able
to demonstrate that the catalytic activity results from the
simultaneous action of two ZnII metal ions on the substrate. In
other words, dendrimer functionalization results in the formation
of catalytic sites composed of two TACN-ZnII complexes. We
were interested to find out to which extent the formation of
such catalytic sites depended on the dendrimer generation and
set out to prepare a series of dendrimers of increasing generation
fully covered at the periphery with TACN-ligands.
2. Results and Discussion
2.1. Synthesis of Dendrons d2-d16 and Dendrimers D4-D32.
Solution-phase functionalization of DAB dendrimers is rather
cumbersome, especially for the higher generations, because of
difficulties in driving reactions to completion and in product
purification. To avoid these problems we decided to switch to
the use of the very frequently used MAP dendrimers, which
have a branched backbone composed of Lys residues (Chart 1).46,47
These dendrimers can be readily synthesized and functionalized
on a solid support using conventional peptide chemistry.
Formally in terms of dendrimer terminology, cleavage from resin
gives dendrons with a functional group at the focal point. In
analogy with systems reported by Reymond et al. we decided
to start the peptide synthesis with a small spacer (GlyCys) at
the focal point for the following reasons (Scheme 1).37,48 A small
spacer separates the growing dendrimer backbone (Lys residues)
from the resin which facilitates dendrimer growth. The Cys
residue is of importance, first, because it allows dimerization
of two dendrons to give a dendrimer via disulfide formation
(Chart 1c) and, second, because the thiol residue can be used
to quantify unambiguously the concentration of dendron in a
solution using Ellman’s reagent.
(20) Scarso, A.; Zaupa, G.; Bodar Houillon, F.; Prins, L. J.; Scrimin, P. J.
Org. Chem. 2007, 72, 376–385.
(21) Zaupa, G.; Martin, M.; Prins, L. J.; Scrimin, P. New J. Chem. 2006,
30, 1493–1497.
(22) Pasquato, L.; Pengo, P.; Scrimin, P. J. Mater. Chem. 2004, 14, 3481–
3487.
(23) Pengo, P.; Baltzer, L.; Pasquato, L.; Scrimin, P. Angew. Chem., Int.
Ed. 2007, 46, 400–404.
(24) Manea, F.; Bodar-Houillon, F.; Pasquato, L.; Scrimin, P. Angew.
Chem., Int. Ed. 2004, 43, 6165–6169.
(25) Pengo, P.; Polizzi, S.; Pasquato, L.; Scrimin, P. J. Am. Chem. Soc.
2005, 127, 1616–1617.
(26) Martin, M.; Manea, F.; Fiammengo, R.; Prins, L. J.; Pasquato, L.;
Scrimin, P. J. Am. Chem. Soc. 2007, 129, 6982–6983.
(27) Tomalia, D. A.; Naylor, A. M.; Goddard, W. A. Angew. Chem., Int.
Ed. Engl. 1990, 29, 138–175.
(28) Fréchet, J. M. J. Science 1994, 263, 1710–1715.
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(30) Bosman, A. W.; Janssen, H. M.; Meijer, E. W. Chem. ReV. 1999, 99,
1665–1688.
The synthesis of dendrons d2-d8 was performed on Rink AM
resin with an initial loading of 0.65 mmol/g. The largest dendron
d
16 was synthesized on Tentagel RAM with a reduced loading
(31) Chow, H.-F.; Leung, C.-F.; Wang, G.-X.; Yang, Y.-Y. C. R. Chimie
2003, 6, 735–745.
of 0.35 mmol/g, because the addition of the last Lys generation
could not be driven to completion on the original resin.
Quantitative coupling of each new Lys generation was in all
cases confirmed by a negative Kaiser test and a doubling of the
amount of dibenzofulvene-piperidine adduct liberated upon
Fmoc deprotection. The TACN macrocycle was introduced as
reported before using an acetate functionalized with diBOC-
protected triazacyclononane.26 Cleavage from resin yielded
dendrons d2-d16 which were purified by RP HPLC and
characterized by MALDI-TOF or ESI-MS analysis. Stock
solutions of the respective dendrons were prepared in a 1:1
mixture of H2O/CH3CN, the concentration of which was
determined using Ellman’s reagent. Before using these dendrons
in catalysis, the thiol unit was deactivated via reaction with 1
(32) Helms, B.; Fréchet, J. M. J. AdV. Synth. Catal. 2006, 348, 1125–1148.
(33) Twyman, L. J.; King, A. S. H.; Martin, I. K. Chem. Soc. ReV. 2002,
31, 69–82.
(34) Hecht, S.; Fréchet, J. M. J. Angew. Chem., Int. Ed. 2001, 40, 74–91.
(35) Liang, C.; Fréchet, J. M. J. Prog. Polym. Sci. 2005, 30, 385–402.
(36) Darbre, T.; Reymond, J.-L. Acc. Chem. Res. 2006, 39, 925–934.
(37) Esposito, A.; Delort, E.; Lagnoux, D.; Djojo, F.; Reymond, J.-L.
Angew. Chem., Int. Ed. 2003, 42, 1381–1383.
(38) Clouet, A.; Darbre, T.; Reymond, J.-L. Angew. Chem., Int. Ed. 2004,
43, 4612–4615.
(39) Javor, S.; Delort, E.; Darbre, T.; Reymond, J. L. J. Am. Chem. Soc.
2007, 129, 13238–13247.
(40) Delort, E.; Darbre, T.; Reymond, J.-L. J. Am. Chem. Soc. 2004, 126,
15642–15643.
(41) Dahan, A.; Portnoy, M. Org. Lett. 2003, 5, 1197–1200.
(42) Ribourdouille, Y.; Engel, G. D.; Richard-Plouet, M.; Gade, L. H. Chem.
Commun. 2003, 1228–1229.
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Chem.Commun. 2001, 361–362.
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(47) Crespo, L.; Sanclimens, G.; Pons, M.; Giralt, E.; Royo, M.; Albericio,
F. Chem. ReV. 2005, 105, 1663–1681.
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Koten, G. Angew. Chem., Int. Ed. 2000, 39, 176–178.
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Dendritic Effect in Multivalent Enzyme-Like Catalysts
A R T I C L E S
Chart 1a
a (a) Dendrons d2-d16, (b) the ligand triazacyclononane TACN, and (c) formation of dendrimers D4-D32 by dimerization of the respective dendrons.
Scheme 1. Synthesis of TACN-Functionalized Dendrons on Solid Support
equiv of N-ethylmaleimide. The quantitative reaction was
confirmed by a negative Ellman’s test. Dimerization of dendrons
to give dendrimers D4-D32 was performed by bubbling air
through a solution of the dendron in a 1:1 mixture of H2O
basified at pH 10 with NaOH and CH3CN. Also in this case,
quantitative dimerization was confirmed by a complete absence
of any signal indicating free thiol using Ellman’s reagent and
the presence of a single new peak in the HPLC spectrum.
2.2. Catalytic Cleavage of HPNPP. In analogy with our
previous studies,26 it was decided that the catalytic activity of
all dendrons d2-d16 and dendrimers D4-D32 was to be studied
at a constant concentration of TACN rather than at a constant
dendrimer concentration. Thus, any changes in catalytic activity
can be directly related to the valency of the dendrimer.
Consequently, at a constant TACN concentration of 20 µM this
implies that dendrimer D32 is present at a 600 nM concentration.
First, the catalytic activity of all multivalent catalysts in the
cleavage of HPNPP (Figure 1a) was studied in the presence of
increasing amounts of ZnII in a 7:3 H2O/CH3CN mixture
buffered at pH 7.5 at 40 °C. Plots of the initial rate as a function
of the number of equivalents of ZnII (per TACN) in all cases
clearly show a sigmoidal increase in activity up to 1 equiv of
ZnII, after which the catalytic activity remains constant (Figure
1b,c). This behavior is identical to that observed previously with
the DAB dendrimers26 and confirms that also here the 1:1
complex TACN-ZnII is the catalytically active unit. The fact
that all curves level off at constant values also indicates that
the contribution of free ZnII to catalysis can be neglected.
Importantly, although performed at a constant concentration
of TACN, the ZnII titration studies also clearly indicate an
increase in catalytic activity upon an increase of the dendron
and dendrimer valency. The catalytic performance of these
systems was studied in detail by measuring the initial rates in
the presence of increasing amounts of substrate HPNPP, i.e.,
under turnover conditions, in the presence of 1 equiv of ZnII
per TACN unit (Figure 2). All catalysts display enzyme-like
saturation behavior with multiple turnovers, and the Michaelis–
Menten parameters kcat and KM were determined for each catalyst
by fitting the saturation curves to the Michaelis–Menten equation
Vinit ) kcat[E][S]/(KM + [S]). It should be emphasized that the
Figure 1. Initial rates for (a) the cleavage of HPNPP by (b) dendrons d2
(9), d4 (0), d6 (b), and d8 (O) and (c) dendrimers D4 (9), D8 (0), D16 (b),
and D32 (O), as a function of the equivalents of ZnII added with respect to
[TACN]. The solid lines are trendlines. Conditions: [TACN] ) 2 × 10-5
M, [HPNPP] ) 2 × 10-4 M, [HEPES] ) 1 × 10-2 M, pH ) 7.5, T ) 40
°C, H2O/CH3CN ) 7:3.
Figure 2. Initial rates for the cleavage of HPNPP by (a) dendrons d2 (9),
d4 (0), d6 (b), and d8 (O) and (b) dendrimers D4 (9), D8 (0), D16 (b), and
D32 (O), as a function of substrate concentration. Conditions: [TACN] ) 2
× 10-5 M, [ZnII] ) 2 × 10-5 M, [HEPES] ) 1 × 10-2 M, pH ) 7.5, T
) 40 °C, H2O/CH3CN ) 7:3. Solid lines indicate the best fits to the
Michaelis–Menten equation.
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A R T I C L E S
Zaupa et al.
Table 1. Michaelis-Menten Parameters for Dendrons d2-d16 and
is enough to generate an extremely powerful catalyst. This
“dendritic” effect appears very general, since we have observed
similar behavior now for a wide variety of multivalent scaffolds,
including small tripodal structures,19,20 SAMs on Au nanopar-
ticles,24 and the DAB dendrimers26 reported before. This general
trend, also evidenced by related systems reported in the
literature, raised two questions which will be addressed here:
(a) what is the origin of the dendritic effect and (b) what is the
significance of the reported Michaelis–Menten parameters for
multivalent catalysts.
a
Dendrimers D4-D32
no.
kcat,den
kcat,unit
(×104 s-1
KM
kcat,den/KM
b
kcat,den/kuncat
TACN (×103 s-1
)
)
(×103 M) (L·mol-1 ·s-1
)
d2
D4
d4
D8
d8
D16
d16
D32
2
4
4
8
8
16
16
32
0.6
1.3
1.6
4.8
3.3
9.6
6.7
15.6
3.2
3.4
4.1
6.0
4.1
6.0
4.2
4.9
2.8
4.0
1.0
1.9
0.9
1.2
0.7
0.8
0.2
0.3
1.6
2.5
3.8
8.4
9.5
19.0
3190
6710
8120
24000
16600
48000
33400
78200
2.3. Theoretical Model and Simulations. Although a very
common approach, the fitting of the saturation curves obtained
for multivalent catalysts to the Michaelis–Menten equation is
not correct. The Michaelis–Menten equation specifically de-
scribes the situation in which one substrate molecule, S, binds
to the single catalytic site in an enzyme, E, with a dissociation
constant KM, after which it is transformed into product, P, with
a first-order rate constant kcat.53 However, multivalent catalysts
as studied by us and others are intrinsically different from
enzymes in the sense that they contain a multitude of catalytic
sites. Consequently, under saturation conditions multiple sub-
strate molecules are bound to the catalyst resulting in a
multicomponent complex ESn (with n depending on the number
of catalytic sites present). Fitting of the saturation curve of such
a system using the Michaelis–Menten equation gives composite
values for KM and kcat, which incorporate all the separate binding
and catalytic events that occur. We were interested in finding
the relation between these “averaged” parameters and the
individual parameters of a catalytic site. For that purpose a
theoretical model was developed taking into account all separate
binding and catalytic events that occur in a multivalent catalyst.
The model is schematically depicted in Figure 4.
The starting point is a multivalent catalyst En, in which n
denotes the number of catalytic units. Catalysis occurs either
by a single catalytic unit (single site catalysis) or by the
simultaneous action of two catalytic units (double site catalysis),
each of them characterized by different binding (Kmo, Kdi) and
rate (kmo, kdi) constants. The maximum number of substrate
molecules, S, bound to a multivalent catalyst, En, equals n in
case the catalytic site is composed of a single catalytic unit.
When the catalytic site is composed of two catalytic units, the
maximum number of bound substrate molecules is equal to n/2
or (n - 1)/2 in case n is an odd number. In the model, statistical
coefficients (see Supporting Information) affect the association
constants between binding site and substrate, and therefore the
equilibrium constants in this model define association, which
is opposite to the Michaelis–Menten parameter, KM, which is
generally defined as a dissociation constant. It should be noted
that this model bears a strong resemblance to a model recently
used by Huskens and Reinhoudt et al. to describe the interaction
of a multivalent guest with a multivalent monolayer of hosts.16
The model is based on the following assumptions/criteria:
• All binding events are noncooperative. In other words,
binding of a substrate has no effect on the binding constant of
the subsequent substrate molecule.
b
a Conditions as given in the legend of Figure 2. kuncat ) 2 × 10-7
s-1 26
.
Figure 3. Dendritic effect of dendrons d2-d16 (0) and dendrimers D4-D32
(9) in the cleavage of HPNPP.
value of kcat depends on what is considered the catalyst
concentration [E]. Generally,37,38,50 the dendron/dendrimer
concentration is taken as a reference, which gives a kcat,den value
describing the overall performance of the multivalent catalyst.
Alternatively, by taking the concentration of TACN as reference,
the kcat,unit value is the rate constant corrected for the number
of ligands present in the multivalent catalyst (kcat,den ) kcat,unit
× no. of catalyst units). The difference between these parameters
will be discussed extensively later. For the moment, in line with
the general interpretation of multivalent catalysts of this
type,35–37,50 the overall parameter kcat,den will be used. Table 1
lists all parameters including the rate acceleration (kcat,den/kuncat
)
with respect to the uncatalyzed reaction (kuncat ) 2 × 10-7
s-1).26
The obtained Michaelis–Menten parameters are clearly
indicative of a strong dendritic effect. The data of Table 1 and
the plot of Figure 3 indicate that the combination of a
continuously increasing kcat,den and decreasing KM values causes
an exponential growth of the second-order rate constant kcat,den
/
KM as a function of the catalyst valency. Dendrimer D32, present
in submicromolar concentrations, induces a rate enhancement
of around 80 000 with respect to the uncatalyzed cleavage of
HPNPP, which ranks it among the most potent catalysts reported
so far.49–52,24
These data indicate that the clustering of multiple copies of
a simple TACN-ligand on the surface of a multivalent dendrimer
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• The binding and rate constants for the catalytic sites
composed of one (Kmo, kmo) or two (Kdi, kdi) units are constant
and independent of the size of the multivalent catalyst.
• In this theoretical model statistical coefficients account for
all the possible modes in which a specific complex between
substrate and catalytic site can be formed. No cut-offs in terms
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(53) Kirby, A. J. Angew. Chem., Int. Ed. Engl. 1996, 35, 707–724.
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Figure 4. Theoretical model describing all separate binding and catalytic events that occur in a multivalent catalyst En. Within the multivalent catalyst
binding and catalysis can occur via a single catalytic unit (Kmo, kmo) or via the cooperative action of two catalytic units (Kdi, kdi). In the model, the equilibrium
constants Kmo and Kdi are used as association constants.
of distance between catalytic units are present. The validity of
this assumption will be discussed later.
Using this model the catalytic behavior of a series of
multivalent catalysts E2-E8 with 2 up to 8 catalytic units (n )
2–8) was evaluated.54 Values for association and rate constants
were arbitrarily set to values that resemble our experimental
data. We were interested in simulating the saturation curves for
these multivalent catalysts under three different conditions,
representing limiting cases:
• Catalysis only occurs via a single catalytic unit (Kmo ) 500
M-1, kmo ) 1 × 10-4 s-1). Catalytic sites composed of two
units are not considered. In the model (Figure 4) this implies
that only the first row is taken into consideration.
• Catalysis occurs either by a single catalytic unit (Kmo
)
500 M-1, kmo ) 1 × 10-4 s-1) or by the simultaneous action
of two catalytic units (Kdi ) 750 M-1, kdi ) 1 × 10-3 s-1).
The catalytic site composed of two units is characterized by
stronger binding and a higher rate constant.
Figure 5. Calculated saturation behavior of multivalent catalyst models
E2-E8 for situations in which catalysis results (a) only from single catalytic
units (all models give an identical curve), (b) from both single and double
site catalysis, and (c,d) from only double site catalysis in which the curves
for the catalysts containing an even (c) or an odd (d) number of catalytic
units are separated. The symbols denote E2 (0), E3 (9), E4 ()), E5 (*), E6
(b), E7 (O), and E8 (2).
• The catalytic activity of the multivalent catalyst originates
only from double site catalysis (Kdi ) 750 M-1, kdi ) 1 × 10-3
s-1), whereas the activity of the single catalytic units is ignored.
In the model (Figure 4) this implies that only the first column
is taken into consideration.
In accordance with our experimental data, all simulations were
performed at a constant concentration of catalytic units (20 µM),
calculating for each multivalent catalyst E2-E8 the initial rate
(Vinit) as a function of the initial substrate concentration ([S]0).
The calculated saturation curves are shown in Figure 5a-d.
2.3.1. Single Site Catalysis (Kmo ) 500 M-1, kmo ) 1 × 10-4
s-1). Under these conditions all multivalent catalysts E2-E8 have
an identical saturation profile, which is identical to the saturation
(54) The models for E2-E8 were implemented in MicroMath Scientist for
WindowsTM, version 2.01. For details, see the Supporting Information.
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profile of the monomeric catalytic site (Figure 5a). The identical
behavior of the models confirms the validity of the statistical
coefficients used in the model.
2.3.2. Both Single and Double Site Catalysis (Kmo ) 500
M-1, kmo ) 1 × 10-4 s-1, Kdi ) 750 M -1, kdi ) 1 × 10-3 s-1).
A different situation is observed in case also two catalytic units
can simultaneously act on a substrate. Analyzing the simulated
saturation curves, a first observation is that all curves go through
a maximum after which the initial rate drops (Figure 5b). The
reason is that initially the substrate binds to two catalytic units,
(Kdi > Kmo), and is transformed at a higher rate (kdi > kmo).
Subsequently, the substrate saturates the multivalent catalyst
leading to a situation (which is not yet reached in the
simulations) in which each catalytic unit has one substrate
molecule bound (EnSn). A second observation is that the
maximum value of Vinit increases with the number of catalytic
sites in the multivalent system with a concomitant steeper slope
for low substrate concentrations.
2.3.3. Double Site Catalysis (Kdi ) 750 M-1, kdi ) 1 × 10-3
s-1). For these conditions, multivalent models containing an
even or odd number of catalytic units exhibit a different
saturation behavior (Figures 5c and d, respectively). Models with
an “even” number all saturate at the same Vinit, but this maximum
level is reached at lower substrate concentrations when the
valency of the system increases. The “odd” models saturate at
lower Vinit values, which depend on the number of catalytic units
present. As the valency increases the difference between the
saturation of the “odd” and “even” models becomes smaller.
As will be discussed later, the difference between “odd” and
“even” models is of importance, since it gives an explanation
for the experimentally observed difference between dendrons
and dendrimers.
2.4. Analysis of the Simulations. The simulations clearly
demonstrate that the saturation behavior of a multivalent catalyst
strongly depends on its valency, keeping constant the Michaelis–
Menten parameters for the individual catalytic sites and exclud-
ing any cooperative effect. This means that the observation of
a change in saturation profile for dendrimer catalysts of different
generations does not necessarily indicate an increased cooper-
ativity or a higher catalytic efficiency. This will become more
clear from the following analysis. We were curious as to what
would happen if we used the calculated saturation curves (Figure
5) as “experimental” input for the classical Michaelis–Menten
equation, since this is exactly how the saturation profiles of
multivalent catalysts are commonly analyzed. This analysis was
performed on the third set of simulations (only double site
catalysis) for the simple reason that this situation bears the most
resemblance to the experimental observations. The first simula-
tion (only single site catalysis) is not interesting. Since only
single catalytic units are involved, obviously there is no reason
to gain any benefit from incorporating multiple units in a
multivalent system. In the type of enzyme-like multivalent
catalysts studied here, the dendritic effect originates from the
fact that catalysis involves the simultaneous action of two
catalytic units in the chemical transformation. The second
simulation takes into account both single and double site
catalysis, but in most experimental cases the catalytic activity
of a single unit can be neglected with respect to double site
catalysis (kmo << kdi). Additionally, to the best of our
knowledge, no example of a saturation profile for a multivalent
catalyst in which Vinit goes through a maximum has been
reported. This indicates that generally the affinity of the substrate
for the double sites is much higher than that for the single site
Figure 6. Michaelis–Menten parameters (a) kcat,den, (b) KM, and (c) kcat,den
KM for models E2-E8 obtained by fitting the calculated saturation curves
from Figure 5c and d (9: “even” models, 0: “odd” models).
/
(Kdi >> Kmo).55 The third simulation, therefore, bears the most
relevance to the behavior of these multivalent catalysts.56
Accordingly, the simulated saturation curves of Figure 5c and
d were fitted using the Michaelis–Menten equation Vinit
)
(kcat,den[E][S])/(KM + [S]). In order to stay in line with common
enzyme terminology and enzyme model analysis, the Michaelis–
Menten parameter KM, describing dissociation, will be used from
now on. Figure 6a-c give the Michaelis–Menten parameters
that are generally used to describe the catalytic efficiency of
multivalent catalyst, i.e., kcat,den, KM, and the second-order rate
constant kcat,den/KM. The results for the “odd” and “even” models
are indicated separately. Both series display very similar trends
for all parameters, but between them a very interesting difference
exists. The analysis will be initially focused on the “even”
models, bearing in mind that the discussion is valid also for
the “odd” models.
The outcome of this “retro”-fitting gives very surprising
results. As expected, the first-order rate constant kcat,den as a
function of valency always increases accounting for the nu-
merical increase of catalytic units present in the model.
Remarkably, the “overall” dissociation constant KM decreases
(55) A study of the saturation behavior of the single TACN-ZnII complex
under the same experimental conditions as those for the dendrimers
give a strictly linear behavior between Vinit and [HPNPP] (see
Supporting Information), indicating indeed a very low binding constant
between the single TACN-ZnII complex and HPNPP. This supports
our assumption to ignore single site catalysis.
(56) An additional analysis of Figure 5b, in which also single sites contribute
to catalysis, leads to the same conclusions. This is described in detail
in the Supporting Information. Summarizing, the presence of con-
comitant single and double site catalysis leads towards a less
pronounced dendritic effect and a disappearance of the “odd/even”
effect (see later).
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Figure 8. Effect of the clustering of catalytic units on the creation of
catalytic sites in multivalent models E2 and E4. Each catalytic unit is depicted
by a black circle (b), each catalytic site by a line connecting two catalytic
units (-).
Figure 7. (a) First-order rate constant per catalytic unit (kcat,unit ) kcat,den
/
n) and (b) the effect on kcat,unit/KM for “even” (9) and “odd” (0) models.
in an asymptotic manner as a function of the valency, suggesting
that substrate binding becomes stronger as the valency of the
structure increases. As a result of these effects, the second-order
rate constant kcat,den/KM exponentially increases as a function
of valency, which in the literature has been described as a strong
positiVe dendritic effect.32,40,41 It should be explicitly remem-
bered, though, that the Michaelis–Menten parameters for the
individual catalytic site and the concentration of catalytic units
were kept identical for all models E2-E8. Apparently, the strong
dendritic effect is a phenomenon that is not necessarily related
to a change in either the catalytic (kdi) or binding constant (Kdi)
of the individual catalytic site. In order to discover the true origin
of the dendritic effect the two parameters kcat,den and KM will
be discussed separately.
2.4.1. Catalytic Constant kcat,den. The numerical increase of
the number of catalytic units upon increasing valency automati-
cally generates a higher value for kcat,den for each successive
generation. In fact, corrected for the number of catalytic sites,
a new constant kcat,unit (kcat,den/n) can be defined which is now
indeed constant for the “even” models (Figure 7a). Removing
the numerical effect of kcat,den obviously also affects the second-
order rate constant kcat,unit/KM which now increases linearly with
the valency (Figure 7b). However, albeit no longer exponential,
the increase of kcat,unit/KM is still an important dendritic effect,
which is entirely due to changes in KM.
2.4.2. Dissociation Constant KM. The dendritic effect clearly
originates from a decrease in the overall KM upon an increase
in valency, notwithstanding the fact that the KM for a single
catalytic site was kept constant. The reason for this particular
behavior is exemplified for binding of substrate molecules to
multivalent models E2 and E4. The clustering of 12 catalytic
units in a divalent system (E2) generates 6 catalytic sites (Figure
8, top left). However, clustering of the same number of catalytic
units in a tetravalent system (E4) generates 18 catalytic sites
(Figure 8, top right). Increasing the valency of the system causes
an exponential growth of the number of potential catalytic sites.
This is visualized by plotting the number of available (double)
binding sites for the first substrate molecule against valency
(Figure 9, 9). As comparison, also the (linear) increase in single
Figure 9. Number of potential catalytic sites for binding of the first
substrate to models E2-E8 (b: single binding sites, 9: double binding sites,
0: double binding sites corrected).
binding sites is depicted (Figure 9, b). Obviously, similar
statistical effects are also present for the binding of subsequent
substrate molecules. Interestingly, however, at saturation both
models E2 and E4 have an identical number of 6 substrate
molecules bound (Figure 8, bottom), which explains that under
these conditions no difference in catalytic activity is observed
between them (since kcat,unit is constant). This analysis shows
that the clustering of catalytic units in a multivalent system
causes an increase in the “apparent” concentration of catalytic
sites, resulting in an higher “apparent” substrate binding. It
appears that this is the main origin for the dendritic effect.
The extent of the dendritic effect is determined by the number
of catalytic sites that are formed upon clustering catalytic units
in a multivalent system. As indicated before, in setting up the
theoretical model it was assumed that in models E2-E8 all
possible combinations of single catalytic units can form a double
binding site. In practice, this may be true for catalysts with a
low valency (3,4) but is rather unlikely for real multivalent
systems in which spatial distances may prevent the cooperative
action of two catalytic units on a substrate. In order to perform
simulations that more closely resemble such an experimental
situation, the statistical coefficients were altered. It was assumed
that starting from dendrimer E3 each subsequent generation loses
10% of the potential binding sites composed of two catalytic
units for binding of the first (and also subsequent) substrate
molecules. As an example, the new coefficients for binding of
the first substrate are shown in Figure 9 (0). For dendrimer
model E8 the number of accessible binding sites for the first
substrate is reduced by 50%. The number of possibilities to bind
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Figure 10. Effect of reduced statistical coefficients on (a) KM and (b) kcat,unit/KM for “even” dendrimers (9: maximized coefficients, O: reduced coefficients).
four substrates (E8S4) is reduced by almost 70%. Using these
new coefficients new saturation profiles were calculated (as-
suming only double site catalysis) and “retro”-fitted using the
Michaelis–Menten equation. Obviously, the statistical coef-
ficients do not affect the saturation level of each dendrimer,
and consequently the newly obtained kcat,unit values are identical
to those shown in Figure 7a. The changes in KM and kcat,unit/KM
are given in Figure 10a and 10b together with those obtained
from the first set of simulations. For reasons of clarity only those
for the “even” models are shown (a same trend is observed for
the “odd” models). For the models with high valency the effect
Figure 11. Plot of the number of substrate molecules bound at saturation
of reducing the available binding sites results, as expected, in
divided by the number of isomers for the saturated complex against the
dendrimer valency.
a less pronounced decrease in KM and, as a consequence, a
smaller increase in kcat,unit/KM. However, considering the fact
that for E8 up to 50% of the potential sites for the first substrate
molecule has been removed, the effect on these parameters is
surprisingly small. This is a clear indication that the observed
phenomenon is not just a theoretical possibility but also a very
plausible explanation for experimental observations. That this
is indeed the case will be shown next, when our own
experimental data are analyzed. However, before doing that,
the difference between “odd” and “even” models is addressed,
since this is of relevance for our experimentally observed
difference between dendrons and dendrimers.
2.5. “Odd–Even” Effect: Importance of Saturation in
Multivalent Catalysts. The “odd” and “even” models are
analogous multivalent systems in the sense that both contain
identical catalytic sites (composed of two units) with identical
Michaelis–Menten parameters kdi and Kdi. However, the simula-
tions and the “retro”-fitting using the Michaelis–Menten equation
show some peculiar differences between the two series.
Importantly, although the “odd” models have identical
catalytic sites compared to the “even” models, the resulting
kcat,unit values are lower (Figure 7a) and are not constant. The
reason is that complete saturation of all catalytic units is not
possible for the “odd” models since the catalytic site is
composed of two units. The abundance of the single catalytic
unit that does not contribute to catalysis at saturation makes
the system appear less active. Obviously, this becomes less
important when the valency increases and, in fact, kcat,unit for
the “odd” models asymptotically reaches the level of the “even”
models. The observed difference in kcat,unit between “odd” and
“even” models is important, since it illustrates that the kcat,unit
value depends on the extent to which a multivalent system can
be saturated and not necessarily reflects the efficiency of the
catalytic site. This is of practical relevance in case the saturation
behavior of two structurally related, but different, multivalent
series is compared (for instance, dendrons d2-d16 and dendri-
mers D4-D32).
‘apparent’ stronger binding of substrates to “odd” models
compared to “even” ones. The origin of the difference between
“odd” and “even” models can also be traced back to statistics.
As example, consider “odd” model E3 which at saturation has
one substrate molecule bound (E3Sd1). The complex E3Sd1 can
be formed in three different ways, depending which catalytic
units are involved in substrate binding. On the other hand,
“even” model E4 has two substrate molecules bound at saturation
(E4Sd2). However, also for complex E4Sd2 only three isomeric
forms are possible, since binding of the first substrate molecule
defines the position of the second substrate molecule. As a
consequence, “retro”-fitting of the saturation profiles using the
Michaelis–Menten equation results in a lower “apparent” KM
value (indicating stronger binding) for “odd” model E3 compared
to “even” model E4. In fact, a plot of the number of substrate
molecules bound under saturation divided by the number of
possible isomers for the saturated complex against the number
of catalytic units (Figure 11) gives a trend that nicely corre-
sponds to the simulated behavior for KM (Figure 6b). Based on
this theoretical analysis, it appears that an experimental observa-
tion of such behavior for KM between two series of analogous
multivalent catalysts is indicative of a different level of
saturation for the two series. As will be discussed next, the series
of dendrons d2-d16 and dendrimers D4-D32 represent such a
case.
2.6. Interpretation of the Experimental Data. After this
theoretical analysis, the question is whether the conclusions are
also valid to explain experimental observations. From the
theoretical analysis it is clear that the critical parameters are
the first-order rate constant per catalytic unit (kcat,unit obtained
by dividing kcat,den by the number of catalytic sites) and the
dissociation constant (KM). These values are plotted in Figure
12a and b for dendrons d2-d16 and dendrimers D4-D32 as a
function of the number of catalytic units present. Figure 12c
reports the resulting second-order rate constant (kcat,unit/KM).
As a general observation, it becomes immediately clear that
the series of dendrons and dendrimers have quite different
Remarkably, the KM values show an opposite trend, being
much lower for “odd” models (Figure 6b). This indicates an
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Figure 12. Plots of (a) kcat,unit, (b) KM, and (c) kcat,unit/KM as a function of the number of catalytic units (TACN) present in dendrons d2-d16 (0) and
dendrimers D4-D32 (9).
characteristics, in terms of both kcat,unit and KM, although both
classes display a similar trend upon increasing the valency. The
origin of the difference between dendrons and dendrimers will
be discussed later. First, the general tendencies of kcat,unit and
KM will be discussed. Considering kcat,unit, the most important
observation is that for the dendron series kcat,unit increases
(slightly) from d2 to d4, after which it remains constant up to
d16. For the dendrimer series a jump in activity is observed from
D4 to D8, but after that also in this series the activity per catalytic
site remains constant (except for D32, which will be discussed
later). Apparently, upon reaching d4 for the dendron series and
D8 for the dendrimer series, the maximum dendritic effect in
terms of creating catalytic sites is reached. Any additional
increase in valency is of no releVance for the actiVity of the
indiVidual catalytic site. The observed increase in the “overall”
rate constant kcat,den is entirely numerical. In fact, although the
highest “overall” rate constant is observed for dendrimer D32
(kcat,den ) 15.6 × 103 s-1), analysis of kcat,unit shows that the
catalytic units in this dendrimer are in fact performing worse
than its smaller analogues D8 and D16.
Whereas the catalytic efficiency per unit is largely indepen-
dent of the dendron or dendrimer generation, the KM value for
both dendrons and dendrimers continuously decreases upon
increasing the generation. In analogy with other systems, this
would normally be ascribed to the formation of a microenvi-
ronment within the dendrimer which causes an enhanced
substrate binding. However, considering the fact that this trend
is identical to that predicted by the theoretical model based on
statistical possibilities of forming catalytic sites (Figure 6b), a
chemical explanation is not necessary at all. Increasing the
dendrimer generation simply increases the apparent concentra-
tion of catalytic sites which consequently automatically results
in an apparent stronger binding.
generations. This trend is identical to that simulated for a system
in which the maximum number of binding sites is not generated
upon the addition of a new dendrimer generation (Figure 10b).
The observation that the parameter kcat,unit/KM was only slightly
affected by even large changes in the statistical coefficients
indicates that from this perspective the multivalent catalysts
reported here, although very potent, behave rather poorly.57
Apparently, upon the addition of a new generation the number
of potential binding sites increases relatively little, especially
for the higher generations. This can be rationalized considering
the backbone structure of these structures, which are composed
of lysine residues. The asymmetric nature of this branching unit
results in a dispersion of the TACN-ligands in the dendrons
with some of them located at the periphery and others closer to
the core. This spatial difference becomes larger for each
generation added.
What remains is a discussion on the difference between the
dendrons and dendrimers. Both classes of multivalent catalysts
display a similar trend (constant kcat,unit and decreasing KM), but
the dendrimer series is characterized by a higher kcat,unit value
(higher activity), but also a higher KM (“apparent” weaker
binding). Generally, a higher kcat,unit would be ascribed to a
catalytic site with improved properties. However, considering
the structural similarities between dendrons and dendrimers this
does not seem very likely. The argument that dimerization
induces changes in the structure and, in so doing, optimizes
the catalytic site does not hold, since in that case also within
the dendron and dendrimer series kcat,unit should increase. This
is clearly not the case. Experimental evidence for the fact that
the catalytic sites in dendron d16 and dendrimer D16 are identical
was obtained by performing a “reversed” Michaelis–Menten
kinetics, i.e., increasing the amount of catalyst at a constant
substrate concentration. In such a case, at saturation a maximum
of one substrate molecule is bound to the multivalent catalyst
and thus provides a tool to probe a single catalytic site.50 The
A plot of kcat,unit/KM versus the number of catalytic units gives
an idea about the efficiency of these dendrimers in generating
catalytic sites. As illustrated in the theoretical analysis, a
maximum efficiency upon increasing dendrimer generation gives
a linear relation between kcat,unit/KM and the number of catalytic
units (Figure 7b). For dendrons d2-d16 and dendrimers D4-D32
the increase in the second-order rate constant kcat,unit/KM is
significantly lower and, in fact, seems to level off at high
(57) A linear relation between 1/KM and valency has been observed
40
experimentally by Reymond et al. for peptide-based dendrimer
catalysts. The impressive results of these multivalent catalysts in terms
of generating catalytic sites is probably caused by the presence of
catalytic histidine units in each generation, rather than only in the
periphery of the dendrimer.
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initial rate Vinit was measured at a constant HPNPP concentration
of 2 × 10-5 M and a concentration of TACN ranging from 1
× 10-5 to 4 × 10-4 M. Fitting of the obtained saturation curves
to the Michaelis–Menten equation gave kcat values of 8.6 × 10-5
s-1 and 8.4 × 10-5 s-1 for dendron d16 and dendrimer D16,
respectively, and KM values of 1.28 × 10-4 and 1.38 × 10-4
M, respectively. The almost identical values for kcat indicate
that the catalytic sites in dendron d16 and dendrimer D16 are
equally active. Assuming an identical catalytic activity for all
catalytic sites present in the multivalent structures, dividing the
rate constant kcat,unit obtained under substrate saturation condi-
tions by these newly obtained values yields the number of
catalytic sites in each structure.50,58 Interestingly, these calcula-
tions show that dendron d16 contains only 5 catalytic sites (4.17
× 10-4/8.6 × 10-5) against 7 (6.0 × 10-4/8.4 × 10-5) for
dendrimer D16. It is worth noticing that both structures can form
a maximum of 8 catalytic sites composed of two TACN-ZnII
complexes. Therefore, based on the theoretical analysis, we
postulate that the difference between kcat,unit values of the
dendrons and the dendrimers is caused by a different degree of
saturation. At saturation the dendrimer complex DxSm has a
higher stoichiometry than the corresponding dendron complex
dxSn (m > n, with x as the number of catalytic units). Upon
dimerization, catalytic sites are generated which are not present
within the dendron. However, the efficiency of creating these
additional sites strongly depends on the dendron generation.
Dimerization of dendron d2 to give dendrimer D4 has only a
small effect on kcat,unit (and KM) which must be related to the
small size of this dendron compared to the GlyCys spacer. Upon
dimerization the two parts do not sense each other. For larger
dendrimers “contact” between the two halves is established
resulting in additional catalytic sites (and thus a higher kcat,unit).
On the other hand, this jump in activity is not observed upon
dimerization of dendron d16 to give D32. Both catalysts have
nearly identical values for kcat,unit (Table 1), which indicates that
the newly created sites are no longer accessible for substrate
molecules. For dendrimer D32, steric crowding limits access of
substrate molecules to the catalytic sites buried inside the
dendrimer. The lower degree of saturation also explains why,
in terms of catalytic activity per unit (kcat,unit), dendrimer D32
behaves worse than its smaller analogues D8 and D16.
Interpretation of our own experimental data in view of the model
analysis showed that these multivalent catalysts are far from
being exceptional, despite the fact that their catalytic perfor-
mances at first appear outstanding in terms of rate acceleration
kcat,den/kuncat and second-order rate constant kcat,den/KM. The
maximum kcat,unit values are already reached at relatively low
generations and drop again for the structure with the highest
valency (Figure 12a). Additionally, the value of (kcat,unit/KM)
grows significantly less than linear as a function of valency
(Figure 12c), indicating that the formation of accessible catalytic
sites upon valency is not optimal.
Generally, the efficiency of multivalent catalysts is described
using the Michaelis–Menten parameters kcat,den and KM. How-
ever, our analysis suggests that these “averaged” parameters
by themselves are flawed indicators of catalytic efficiency, the
first one being numerically inflated, the second one being
compiled of all separate binding events that occur. The question
is how to use these parameters for the evaluation of multivalent
catalysts. It appears that the potency of a multivalent catalyst
depends largely on two issues: first, the extent to which the
multivalent catalyst can be saturated or, in other words, the
number of catalytic units that are effectively participating in
catalysis under saturation conditions; second, the efficiency of
the multivalent system in increasing the apparent concentration
of catalytic sites composed of two (or more) catalytic units.
This has the following consequences for the experimental
parameters kcat,unit and KM.
The value of kcat,unit in a given system appears to be
independent of its valency. A positive dendritic effect here
implies that kcat,unit increases as a function of valency.59 This
might result from the formation of a catalytic site composed of
two catalytic units at low valencies or also three units (at higher
valencies) which may lead toward mechanistically different
pathways. An increase in kcat,unit may also have a “chemical”
origin, for instance, a change in local pH or a conformational
change. Alternatively, a decrease in kcat,unit indicates that the
system loses efficiency because the steric size inhibits access
of the substrate to some catalytic sites, resulting in a decreased
level of saturation.
As for the value of KM, the observation of a linear correlation
between 1/KM and valency by itself is not an indication of a
positive dendritic effect. However, it is clear that a system
displaying such linear behavior is extremely efficient in creating
catalytic sites.40 Positive dendritic effects, for instance, due to
the formation of a hydrophobic microenvironment, are evident
only in case a plot of 1/KM against valency increases more than
linear. On the other hand, for a less efficient multivalent catalyst
the value of 1/KM will level off at higher valencies.
Intuitively, one would argue that an increase in the number
of catalytic sites would, for statistical reasons, have to result
also in a lower KM (stronger binding), but the analysis of the
“odd/even” models indicates that such an argumentation is not
correct when the saturation stoichiometry is different. In fact,
the striking resemblance between the experimental data for the
KM values of dendrons and dendrimers (Figure 12b) and the
simulated values for the “odd/even” models (Figure 6b) is in
strong support of our explanation that the difference between
dendrons and dendrimers is due to a different level of saturation.
In summary, this study of multivalent enzyme-like catalysts
sheds new light on the origin of the dendritic effect displayed
by these systems. The analysis of the model clearly shows that
the dendritic effect is an intrinsic consequence of clustering
catalytic units in a multivalent structure in case the catalytic
pathway involves two or more catalytic units. Obviously, this
does not exclude, as frequently reported, that the dendritic effect
is additionally induced by alterations of chemical parameters,
but this has to be specifically proven. Although here the attention
was focused on dendrimer catalysts it is clear that the discussion
is also valid for other multivalent systems, ranging from small,
tripodal catalysts to self-assembled monolayers on Au nano-
3. Conclusions
We have presented a series of multivalent dendritic structures
that show very high catalytic activity in the cleavage of HPNPP,
an RNA model compound. The observation that the activity
was strongly related to the valency of the structures and the
fact that we had previously observed similar behavior in related
multivalent structures prompted us to develop a theoretical
model in order to understand the origin of the dendritic effect.
(58) Hollfelder, F.; Kirby, A. J.; Tawfik, D. S. J. Am. Chem. Soc. 1997,
119, 9578–9579.
(59) Francavilla, C.; Drake, M. D.; Bright, F. V.; Detty, M. R. J. Am. Chem.
Soc. 2001, 123, 57–67.
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Dendritic Effect in Multivalent Enzyme-Like Catalysts
A R T I C L E S
4.7. Dimerization of Dendrons. 400 µL of a NaOH solution in
water at pH 10 and 400 µL of acetonitrile were added to 200 µL
of the stock solution of dendron; the solution was stirred by bubbling
air through the reaction mixture until the completion of disulfide
formation was confirmed by Ellman’s test (absence of thiols).
4.8. Kinetic Measurements. Kinetics were measured at 40 °C
in aqueous solution containing 30% of acetonitrile, buffered at pH
7.5 with HEPES 0.01 M. Reaction mixtures were prepared by
adding in order the solution of dendron or dendrimer, a solution of
Zn(NO3)2, and a solution of HPNPP in water. The experiments were
performed in 96-well plates (Greiner) in a volume of 250 µL; the
cleavage of the phosphodiester was monitored by measuring the
absorbance of p-nitrophenolate at 405 nm; the plates were sealed
with a cover to prevent evaporation. Initial velocities were calculated
by a linear fitting of the initial part of the kinetics (conversion
<10%).
4.9. Dendron d2. HPLC (Agilent Zorbax, C18, 300 Å (A: H2O
+ 0.1% TFA, B: CH3CN + 0.1% TFA; gradient: 5% B (0–5 min),
5–50% B (5–20min)): 13.8 min (100%). MS (ESI-(+), (H2O +
0.1% HCOOH)/(CH3CN + 0.1% HCOOH) ) 1:1): m/z 645.0 (calcd
(M + H)+: 644.4).
4.10. Dendron d4. HPLC (Agilent Zorbax, C18, 300 Å (A: H2O
+ 0.1% TFA, B: CH3CN + 0.1% TFA; gradient: 5% B (0–5 min),
5–50% B (5–20 min)): 14.8 min (100%). MS (ESI-(+), (H2O +
0.1% HCOOH)/(CH3CN+0.1% HCOOH) ) 1:1): m/z 1238.8 (calcd
(M + H)+: 1238.8), 620.0 (calcd (M + 2H)2+: 619.9), 413.7 (calcd
(M + 3H)3+: 413.6), 310.6 (calcd M + 4H)4+: 310.5).
4.11. Dendron d8. HPLC (Agilent Zorbax, C18, 300 Å (A: H2O
+ 0.1% TFA, B: CH3CN + 0.1% TFA; gradient: 5% B (0–5 min),
5–50% B (5–20 min)): 16.3 min (100%). MS (MALDI-TOF
Perseptive Biosystems Voyager-DE-PRO): 2430 (calcd (M + H)+:
2428)).
4.12. Dendron d16. HPLC (Agilent Zorbax, C18, 300 Å (A: H2O
+ 0.1% TFA, B: CH3CN + 0.1% TFA; gradient: 5% B (0–5 min),
5–50% B (5–20 min)): 17.0 min (100%). MS (MALDI-TOF
Perseptive Biosystems Voyager-DE-PRO): 4800 (calcd (M + H)+:
4804)).
4.13. Dendrimer D4. HPLC (Agilent Zorbax, C18, 300 Å (A:
H2O + 0.1% TFA, B: CH3CN + 0.1% TFA; gradient: 5% B (0–5
min), 5–50% B (5–20 min)): 13.1 min (100%). MS (ESI-(+), (H2O
+ 0.1% HCOOH)/(CH3CN + 0.1% HCOOH) ) 1:1): m/z 1286.0
(calcd (M + H)+: 1285.8).
4.14. Dendrimer D8. HPLC (Agilent Zorbax, C18, 300 Å (A:
H2O + 0.1%TFA, B: CH3CN + 0.1%TFA; gradient: 5% B (0–5
min), 5–50% B (5–20min)): 14.6 min (100%).
4.15. Dendrimer D16. HPLC (Agilent Zorbax, C18, 300 Å (A:
H2O + 0.1% TFA, B: CH3CN + 0.1%TFA; gradient: 5% B (0–5
min), 5–50% B (5–20 min)): 15.6 min (100%).
particles, polymers, and self-assembled structures. Our analysis
provides a better understanding of the origin of the dendritic
effect and indicates that a careful interpretation of the experi-
mental data is of importance for assessing the efficiency of
multivalent catalysts.
4. Experimental Section
Solvents and reagents were purchased from commercial sources
and used without further purification. The diBoc-TACN acetic acid
(2-(1-(4,7-bis(tert-butyloxycarbonyl)-1,4,7-triazacyclononane)-ace-
tic acid) was synthetized using a previously reported procedure.26
HPNPP (2-hydroxypropyl p-nitrophenyl phosphate) was synthetized
according to a literature procedure.60 Dendrons were synthesized
using standard peptide synthesis protocols (see below) following
the synthetic route depicted in Scheme 1.
4.1. Fmoc Removal. The resin was treated with a solution of
20% of piperidine in DMF for 10 min, filtered, and washed (2×
each) with DMF and CH2Cl2. The procedure was repeated.
4.2. Coupling of the First Amino Acid on Resin. The resin
was treated to remove the Fmoc group. Fmoc-Gly-OH (3 equiv)
was dissolved in DMF/CH2Cl2 1:1, and then HOBt (1-hydroxy-
benzotriazole, 4 equiv), EDC (N-(3-dimethylaminopropyl)-N′-
ethylcarbodiimide, 4 equiv), and DIPEA (N,N-diisopropylethy-
lamine, 20 equiv) were added. After 10 min the solution was added
to the resin, and the mixture was stirred for 2.5 h. The resin was
filtered and washed (3× each) with DMF and CH2Cl2. The
procedure was repeated, after which quantitative coupling was
checked with the Kaiser test.
4.3. Coupling of the Amino Acids on the Free Amines
(General Procedure). The amino acid (3 equiv relative to the free
NH2) was dissolved in a 1:1 mixture of DMF/CH2Cl2, after which
HBTU (O-(benzotriazol-1-yl)-N,N,N′,N′-tetramethyluronium hexaflu-
orophosphate, 4 equiv), HOBt (4 equiv), and N-methylmorpholine
(20 equiv) were added. After 10 min the solution was added to the
resin, and the mixture was stirred for 2 h 30 min. The resin was
filtered and washed (3× each) with DMF and CH2Cl2. The
procedure was repeated until the coupling was complete (Kaiser
test).
4.4. Cleavage. The resin was treated with the cleavage mixture
(CH2Cl2, triisoproylsilane, trifluoroacetic acid 1/1/8 plus one drop
of water) for 1.5 h. The resin was filtered, and the solution was
evaporated under vacuum. The peptide was precipitated from
methanol/diethyl ether and purified using RP HPLC (Agilent
Zorbax, C18, 300 Å (A: H2O + 0.1% TFA, B: CH3CN + 0.1%
TFA; gradient: 5% B (0–5 min), 5–50% B (5–20 min). A stock
solution of the dendrons was prepared dissolving the solids in a
1:1 mixture of H2O/CH3CN.
4.5. Quantification of Thiol Groups. The concentration of the
dendron in the stock solution was determined by the quantification
of the free thiols using the Ellmann’s reagent (DTNB, 5,5′-dithio-
bis(2-nitrobezoic acid)). 40 µL of stock solution of DTNB (2 mM
in sodium acetate 0,05 M) and 8 µL of stock solution of dendron
were added to 400 µL of a 0.1 M solution of phosphate buffer pH
7.0. The concentration of free thiol was determined measuring the
absorbance at 412 nm (ꢀ412 ) 13 470 L ·mol-1 ·cm-1 based on a
calibration curve obtained from Cys).
4.6. Blocking of Free Thiol in Dendrons. 200 µL of stock
solution of dendron were added to 800 µL of a 1:1 mixture of a
0.1 M phosphate buffer at pH 7.0 and acetonitrile, after which 1.5
equiv of N-ethylmaleimide (from a 0.05 M solution in methanol)
were added. The completion of the reaction was confirmed by a
negative Ellman’s test.
4.16. Dendrimer D32. HPLC (Agilent Zorbax, C18, 300 Å (A:
H2O + 0.1% TFA, B: CH3CN + 0.1% TFA; gradient: 5% B (0–5
min), 5–50% B (5–20 min)): 16.5 min (100%).
Acknowledgment. The authors thank the University of
Padova (CPDA054893) and MIUR (PRIN2006) for financial
support.
Supporting Information Available: Mathematical treatment
of model En, implementation of the models E2–E8 in the simula-
tion software,54 saturation profile of the TACN-ZnII complex,
theoretical analysis for both single- and double site catalysis.
This material is available free of charge via the Internet at http://
pubs.acs.org.
(60) Brown, D. M.; Usher, D. A. J. Chem. Soc. 1965, 6558–6564.
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