Two-component dendritic chain reactions: experiment and theory

Article abstract of DOI:10.1021/ja910839n

New analytical diagnostic techniques that are based on signal-amplification mechanisms could significantly improve the sensitivity of detection of various analytes. We have developed a new approach to achieving exponential amplification of a diagnostic signal through a two-component dendritic chain reaction. The chain reaction generated the analyte of interest and thereby initiated additional diagnostic cycles. The system was designed for the detection of hydrogen peroxide and produced significantly larger intensity of diagnostic signal than a classic probe. In addition, a mathematical model that simulates the disassembly kinetics of one-component and two-component reactions was developed and shown to correlate well with the observed experimental data. The modularity and flexibility of a two-component detection system should allow extension to the detection of other analytes.

Full text of DOI:10.1021/ja910839n

Published on Web 03/01/2010
Two-Component Dendritic Chain Reactions: Experiment and
Theory
Eran Sella,† Ariel Lubelski,‡ Joseph Klafter,‡ and Doron Shabat*,†
Department of Organic Chemistry and Department of Chemical Physics, School of Chemistry,
Raymond and BeVerly Sackler Faculty of Exact Sciences, Tel AViV UniVersity,
Ramat AViV, Tel AViV 69978, Israel
Received December 23, 2009; E-mail: chdoron@post.tau.ac.il
Abstract: New analytical diagnostic techniques that are based on signal-amplification mechanisms could
significantly improve the sensitivity of detection of various analytes. We have developed a new approach
to achieving exponential amplification of a diagnostic signal through a two-component dendritic chain
reaction. The chain reaction generated the analyte of interest and thereby initiated additional diagnostic
cycles. The system was designed for the detection of hydrogen peroxide and produced significantly larger
intensity of diagnostic signal than a classic probe. In addition, a mathematical model that simulates the
disassembly kinetics of one-component and two-component reactions was developed and shown to correlate
well with the observed experimental data. The modularity and flexibility of a two-component detection system
should allow extension to the detection of other analytes.
leading to exponential growth of the diagnostic signal.8 The
DCR probe used in our report was based on an AB3 self-
Introduction
The autoamplification mechanism is a well-known approach
to achieving exponential growth of a desired target. Thus far,
there are only a few examples of the use of exponential
amplification methods to produce multiple copies of a target
molecule. The most familiar is the polymerase chain reaction
(PCR); this technique is utilized in molecular biology to amplify
DNA exponentially by making copies of a specific region of a
nucleic acid target.1 Other examples include PCR-based tech-
niques such as immuno-PCR,2,3 the amplification of an enan-
tiomeric excess of chiral molecules,4 and self-replicating sys-
tems.5 Recently, two novel related approaches to achieving
exponential amplification of diagnostic signals for the detection
of specific analytes were reported in the literature. The first,
developed by the Mirkin group, uses a cascade reaction
involving a supramolecular allosteric catalyst that generates the
analyte of interest.6 The generated analyte initiates additional
reaction cycles and, consequently, produces exponential progress.
The second approach, developed by our group, applies a
distinctive dendritic chain reaction (DCR) that releases several
reagent molecules upon reaction with an analyte.7 When the
reagent molecules are free, they acquire the chemical reactivity
of the analyte and therefore initiate additional reaction cycles
immolative dendron, which is equipped with a trigger, one
reporter, and two reagent end groups (Figure 1). Cleavage of
the trigger by the analyte generates the release of one chro-
mogenic reporter and two reagent molecules. The two free
reagents then activate two additional dendrons by cleavage of
their triggers. The process progresses exponentially until all
dendrons have been disassembled. The preparation of the DCR
probe demanded multistep synthesis with selective incorporation
of the reagent units and the reporter on the dendritic platform.
A simpler option to obtaining DCR amplification would be
to use the reagent component and the reporter component in
the form of two different molecules (Figure 2). The first
component (I) is based on an AB2 self-immolative dendron9
equipped with two reagent units and a trigger designed to react
with a specific analyte. The second component (II) is a probe
composed of the same trigger attached to a reporter. The AB2
self-immolative dendron acts as an amplifier moiety, and the
other component acts as a probe that releases a chromogenic
molecule to produce a diagnostic signal. The two-component
dendritic chain reaction (2CDCR) mode of action is illustrated
in Figure 2. An analyte molecule activates the trigger of the
AB2 self-immolative dendron component to release two reagent
units. As a consequence of their release, the free reagents gain
the chemical reactivity of the analyte of interest. Some of the
reagent molecules now activate the triggers of additional AB2
self-immolative dendrons, and some react with probe compo-
nents to release reporter units. The process will progress until
all of the dendritic molecules are disassembled. If more than
two reagent units are released per molecule of analyte, then the
signal obtained by the free reporter will grow exponentially.
Here we report a simple approach to exponential signal
† Department of Organic Chemistry.
‡ Department of Chemical Physics.
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(9) Erez, R.; Shabat, D. Org. Biomol. Chem. 2008, 6, 2669–2672.
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A R T I C L E S
Sella et al.
Figure 1. Amplification cycle produced by a dendritic chain reaction with an AB3 self-immolative dendron.
Figure 2. Graphical illustration of a two-component dendritic chain reaction.
amplification based on a two-component dendritic chain reaction
and describe a mathematical model of the kinetic disassembly
behavior observed.
1 and probe 2 is illustrated in Figure 3. Cleavage of the trigger
of dendron 1 by a hydrogen peroxide molecule will generate
the release of the two choline molecules. The two free choline
units will be oxidized by choline oxidase (COX) present in
solution to produce four molecules of hydrogen peroxide that
then activate two AB2 dendrons and two probe molecules.
Choline is initially oxidized to betain aldehyde and then to
betain; each step produces one molecule of hydrogen peroxide.
The rate of disassembly should exponentially increase until all
of the reporter molecules have been released. The signal can
be detected with a spectrophotometer by monitoring the yellow
color of the released 5-amino-2-nitrobenzoic acid.
Results
On the basis of the above illustration, we designed self-
immolative AB2 dendron 1 to detect the analyte, hydrogen
peroxide, and probe 2 containing a reporter unit (Figure 3).
Dendron 1 was composed of two choline units and phenylbo-
ronic acid as a trigger, which is cleaved upon reaction with
hydrogen peroxide.10 Probe 2 is composed of the 5-amino-2-
nitrobenzoic acid reporter attached to the phenylboronic acid
trigger. The two-component DCR amplification cycle of dendron
Self-immolative AB2 dendron 1 was synthesized as described
in Scheme 1. Phenolic dendritic core 1b was prepared as
(10) Lo, L.-C.; Chu, C.-Y. Chem. Commun. 2003, 2728–2729.
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A R T I C L E S
Figure 3. Two-component DCR system to detect hydrogen peroxide. The choline reagent units and 5-amino-2-nitrobenzoic acid reporter are indicated.
Scheme 1. Chemical Synthesis of Dendron 1
previously described.11 Etherification of the phenol group of
1b by benzyliodide 1a and potassium carbonate generated ether
1c. The latter was deprotected with p-TsOH to give diol 1d,
which was further treated with 2 equiv of p-nitrophenyl-choline
carbonate in the presence of DMAP to afford dendron 1.
The synthesis of probe 2 was performed using the synthesis
strategy shown in Scheme 2. Commercially available 5-amino-
2-nitrobenzoic acid was protected with allyl alcohol to give ester
2a. The reaction of 2a with triphosgene generated the isocyanate
derivative, which was immediately reacted with alcohol 2b to
afford carbamate 2c. Deprotection of the allyl ester by Pd(PPh3)4
in the presence of benzylamine produced desired probe 2.
To evaluate the two-component DCR technique, dendron 1
and probe 2 were incubated with various amounts of hydrogen
peroxide in the presence of COX, and the release of the 5-amino-
2-nitro-benzoic acid reporter was monitored at a wavelength
of 405 nm (Figure 4).
When 1.0 equiv of hydrogen peroxide (vs dendron 1) was
used, the system reached complete disassembly within 30 min.
As expected, disassembly was slower when less hydrogen
peroxide was used (Figure 4). The exponential progress of the
system disassembly is demonstrated by the sigmoidal plots
obtained for reaction with various equivalents of H2O2. The
background signal obtained because of spontaneous hydrolysis
is also amplified; therefore, the sensitivity of this system is
limited, and detection of the analyte can be observed down to
5 µM H2O2.
Next, we evaluated the 2CDCR system disassembly using
various ratios of dendron 1 versus probe 2. The results are
presented in Figure 5. When a high ratio of dendron 1 versus
probe 2 was used (2:1), system disassembly occurred rapidly
(11) Haba, K.; Popkov, M.; Shamis, M.; Lerner, R. A.; Barbas, C. F., III;
Shabat, D. Angew. Chem., Int. Ed. 2005, 44, 716–720.
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Scheme 2. Chemical Synthesis of Probe 2
(within 60 min). At ratios of dendron 1 versus probe 2 of 1:1
and 1:2, disassembly was slower (100 and 200 min, respec-
tively).
hydrogen peroxide, probe 4 releases free 7-hydroxycoumarin
that can be detected using fluorescence spectroscopy (Scheme
3).
The diagnostic activity of probe 2 is based on the release of
a chromogenic molecule. In principle, it is possible to use other
probes in the 2CDCR technique that have different modes of
action. As a representative example, we tested a fluorogenic
probe composed of phenylboronic acid (as a trigger for hydrogen
peroxide) linked to 7-hydroxycoumarin 4a. Upon reaction with
Probe 4 was evaluated together with dendron 1 in the 2CDCR
assay for the detection of hydrogen peroxide. An exponential
increase in the fluorogenic signal was observed in a manner
similar to that obtained with probe 2 (data not shown). The
increased sensitivity of the 2CDCR technique is best demon-
strated when the background noise is subtracted from the
measured signal. In Figure 6, we presented this data for probes
2 and 4. The net signal obtained using the 2CDCR approach
with probes 2 and 4 (for 0.01 equiv of hydrogen peroxide per
probe) in the presence of dendron 1 is significantly larger than
that observed in the absence of dendron 1.
Figure 4. Release of 5-amino-2-nitrobenzoic acid from probe 2 (500 µM)
in the presence of dendron 1 (500 µM) and choline oxidase (0.3 mg/mL)
in PBS (pH 7.4) upon addition of buffer only (background) or the indicated
equivalents of H2O2. The reaction progress was monitored at 405 nm for
the indicated time period.
Figure 6. Comparison of signals measured (at a time point of 50 min) in
the presence of dendron 1 (green) vs signals measured in the absence of
dendron 1 (blue). The background signal observed at 50 min was subtracted
from the measured values.
Theoretical Studies
To analyze the one-component DCR and the two-component
DCR disassembly behavior, we composed mathematical equations
that describe the kinetics of both systems. Figure 7 shows the
chemical structure of dendron 3, used in the DCR, and the chemical
structures of dendron 1 and probe 2, used in 2CDCR approach.
Initially, we modeled the kinetics of the one-component
dendritic chain reaction obtained by the disassembly of mol-
ecules such as dendron 3
H2O2 + AB2X f nDH2O2 + X
(1)
Figure 5. Release of 5-amino-2-nitrobenzoic acid from probe 2 in the
presence of choline oxidase upon addition of H2O2 (0.01 equiv vs probe 2)
when various ratios of dendron 1 and probe 2 are applied. The reaction
progress was monitored at 405 nm for the indicated time period.
where AB2X is the dendritic molecule that produces the chain
reaction, X is the reporter molecule whose concentration can
be measured using a spectrophotometer, B is the reagent
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A R T I C L E S
Scheme 3. Activation of Probe 4 by Hydrogen Peroxide to Release a Fluorogenic Molecule
molecule (in our case, the choline molecule), and nD is the
number of hydrogen peroxide molecules that are generated per
one molecule of dendron 3. DCR probe 3 is composed of two
choline molecules, a reporter molecule, and a trigger that reacts
with hydrogen peroxide. This reaction imitates the disassembly
of the dendritic molecule. The chemical reaction in eq 1
represents the net reaction equation (the whole process involving
the reaction of choline with the COX enzyme that generates
two hydrogen peroxide molecules).
eq 7 combined with eq 3, we obtain the concentration of the
released reporter molecule as a function of time:
H2O2
[X] ) [AB2X]0 - [AB2X]0 +
×
(
)
nD - 1
[AB2X]0
[H2O2]0
nD - 1
(8)
[AB X] +
exp(Kbt)
(
)
2
0
We described the reaction in eq 1 as a simple first-order
reaction:
The signal that we obtained in the experiment is the normalized
reporter concentration percentage, meaning the reporter con-
centration from eq 8 divided by the reporter concentration at
very long times multiplied by 100. This limit of long reaction
time can be easily obtained from eq 8, where the reporter
concentration reaches [X] ) [AB2X]0 and the experimental
signal takes the form
d[AB2X]
) -K[AB2X][H2O2]
(2)
dt
The relatively complicated reaction sequence is simplified
and characterized by a single kinetic constant (K) because
the oxidation step by COX is relatively fast and thus does
not affect the reaction between the dendritic probe and
hydrogen peroxide.
100[H2O2]0(1 + exp(-Kbt))
[H2O2]0 + (nD - 1)[AB2X]0 exp(-Kbt)
SD(t) )
(9)
The following equations are valid at all times during the
course of the reaction
[AB2X] + [X] ) [AB2X]0
(3)
(4)
Figure 8 shows the obtained correlations between the calculated
signal function from eq 9 to the experimental data for various
concentrations of hydrogen peroxide.
[H2O2] ) [H2O2]0 + (nD - 1)([AB2X]0 - [AB2X])
where [H2O2]0 and [AB2X]0 are the initial concentrations of
hydrogen peroxide and the dendritic probe, respectively, and
[AB2X], [X], and [H2O2] are the concentrations of the
dendritic probe, the reporter molecule, and hydrogen perox-
ide, respectively, as functions of time.
Next we modeled the kinetics of the two-component dendritic
chain reaction, which can be described by the following pair of
chemical equations
AB2 + H2O2 f P + nTH2O2
(10)
We substitute eq 4 into eq 2 to obtain a simple differential
equation
AX + H2O2 f P + X
where AB2 is >a dendritic molecule composed of a trigger and
a reagent molecule (choline) such as compound 1, AX is a
molecule composed of a trigger and a reporter part such as probe
2, nT is the number of hydrogen peroxide molecules that are
generated per molecule of AB2 using the two-component
dendritic system, and P represents all the other products
irrelevant to the kinetic model. Here, as in the previous case,
we can write an equation that describes the dependency among
the concentrations:
d[AB2X]
) -K[AB2X]([H2O2]0 + (nD - 1)([AB2X]0 -
dt
[AB2X])) (5)
that can be rewritten as
d[AB2X]
) -K[AB2X](b - a[AB2X])
(6)
dt
where a ) nD - 1 and b ) [H2O2]0 + (nD - 1)[AB2X]0. By
integrating eq 6, we obtain the following result:
[H2O2] - [H2O2]0 ) (nT - 1)([AB2]0 - [AB2]) -
([AX]0 - [AX]) (11)
[H2O2]0
[AB2X] ) [AB2X]0 +
×
We rewrite this equation to obtain the concentration of hydrogen
peroxide
(
)
nD - 1
[AB2X]0
[H2O2]0
(7)
[H2O2] ) a + [AX] - (nT - 1)[AB2]
where a contains all of the constants:
(12)
[AB X] +
exp(Kbt)
(
)
2
0
nD - 1
This result is valid only for circumstances when the initial
concentration of hydrogen peroxide ([H2O2]0) is not zero. From
a ) (nT - 1)[AB2]0 - [AX]0 + [H2O2]0
(13)
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A R T I C L E S
Sella et al.
Figure 7. Chemical structures of DCR probe dendron 3, dendron 1, and probe 2.
We substitute eq 12 into eq 15 and obtain
d([AX] - (nT - 1)[AB2])
) -K([AX] -
dt
(nT - 1)[AB2])(a + [AX] - (nT - 1)[AB2]) (16)
By marking
y ) [AX] - (nT - 1)[AB2]
(17)
and substituting it into eq 16, we obtain a simple differential
equation
dy
dt
) -Ky(a + y)
(18)
Figure 8. Release of 4-nitroaniline from probe 3 under DCR conditions.
Correlation between calculated values obtained from eq 9 (solid line) and
experimental data observed by the disassembly behavior of DCR probe 3
(dotted plot). Concentrations were 350 µM for probe 3 and 0.3 mg/mL for
choline oxidase in PBS (pH 7.4). Hydrogen peroxide concentrations were
350, 35, 3.5, and 0 µM. From these correlations, we obtained the kinetic
constant (K). Xi is a measure of the fit (square deviation). The background
experiment was correlated numerically using a different procedure than the
correlation to eq 9 because eq 9 is valid only for an initial hydrogen peroxide
concentration other than zero.
that resembles eq 6. By solving this equation, we obtain
ay0 exp(-Kat)
y0 + a - y0 exp(-Kat)
(19)
y(t) ) [AX] - (nT - 1)[AB2] )
The next step is to obtain the concentrations of [AX] and [AB2]
as functions of time. We return to kinetic eq 14 and divide each
equation by [AX] and [AB2], respectively, to obtain
We then formulate simple kinetic equations for the two
reactants (AB2 and AX):
d[AB2]
) -K[H2O2] dt
[AB2]
(20)
d[AB2]
d[AX]
) -K[AB2][H2O2]
) -K[H2O2] dt
AX
dt
(14)
d[AX]
) -K[AX][H2O2]
dt
By integrating these two equations, we obtain
[AB2]
It is important to note that these two equations use the same
kinetic constant (K) because the reaction of hydrogen peroxide
with the trigger is identical. (The relatively fast enzymatic step
that is included in the first reaction is assumed not to change
the kinetic constant.) By multiplying the first equation by (nT
- 1) and subtracting the second equation from the first, we
obtain the following equation:
log
) - t K[H O ] dt
∫
2
2
(
)
0
[AB2]0
[AX]
(21)
(22)
log
) - t K[H O ] dt
∫
2
2
(
)
0
[AX]0
From eq 21, we observe that
[AB2]
[AX]
[AX]0
d([AX] - (nT - 1)[AB2])
)
[AB2]0
) -K([AX] -
dt
(nT - 1)[AB2])[H2O2] (15)
We rewrite eq 22 as
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Two-Component Dendritic Chain Reactions
A R T I C L E S
[AB ]
[AB2] )
2 0[AX]
(23)
[AX]0
By substituting eq 23 into eq 19, we obtain
((nT - 1)[AB2]0 - [AX]0 + [H2O2]0)[AX]0 exp(-Kat)
[AX] )
[H2O2]0 - ([AX]0 - (nT - 1)[AB2]0) exp(-Kat)
(24)
The next step is to calculate the reporter concentration as a
function of time. We use the following equation, which is valid
at all times:
[AX] + [X] ) [AX]0
(25)
By combining with eq 24, dividing by the reporter concentration
at long times, and multiplying by 100, we finally obtain the signal
value, which is the normalized concentration of the reporter:
Figure 9. Correlations among calculated values obtained from eq 26 (solid
line) and the experimentally measured disassembly behavior of dendron 1
and probe 2 (dotted plot) for various ratios of dendron 1 vs probe 2. The
various correlations provided the kinetic constant (K). Xi is the value of
the fit quality (square deviation).
100[H2O2]0(1 - exp(-Kat))
ST(t) )
[H2O2]0 - ([AX]0 - (nT - 1)[AB2]0) exp(-Kat)
(26)
signal upon its release. Another important feature of the
2CDCR system is the option to use various ratios of the two
components. This option allows control of the amplification
rate as demonstrated by our experiments using different ratios
of dendron 1 and probe 2 (Figure 5).
Figure 9 shows correlations of the calculated signals obtained from
eq 26 versus the measured experimental data for different ratios
of dendron 1 and probe 2.
Discussion
The two-component DCR approach offers considerable
advantages compared to diagnostic assays based on the sto-
ichiometric reaction between the analyte and the probe. In the
reaction demonstrated in this study, analyte, hydrogen peroxide,
and a phenylboronic acid-based probe react stoichiometrically.
As demonstrated in Figure 6, the net signal obtained for the
two-component DCR assay is significantly larger than the signal
produced by analogous classic probe behavior.
Currently, the two factors that limit the detection sensitivity of
the 2CDCR assay are the minor amount of spontaneous hydrolysis
of dendritic compound 1 and its disassembly rate. To prepare an
ideal dendritic compound, one should design a molecule that is
very stable to spontaneous hydrolysis yet can undergo rapid
disassembly upon relation to the analyte. This assignment should
be possible because the 2CDCR system is modular. Various
reporter molecules may be used, as demonstrated, and any analyte
of interest that has a cleavage reactivity toward a specific trigger
could be incorporated. This modularity should allow the design of
an ideal system. Once an efficient system is in hand, the 2CDCR-
based assay could be extended to the detection of other analytes
and biocatalysts by coupling it with another probe activity. This
option was previously demonstrated with the one-component DCR
approach for the detection of the biocatalytic activity of enzyme
penicillin-G-amidase.7
Most signal-amplification methods are based on a linear
increase in a measurable signal.12-17 In contrast, the described
approach progresses through an exponential pathway. The
two-component DCR approach is based on disassembly
mechanisms of a dendritic amplifier moiety and a chromoge-
nic probe.18-21 Both are equipped with identical triggering
systems designed for activation by a specific analyte. The
amplifier component releases reagent units that acquire the
reactivity of the analyte, thereby initiating amplification
cycles, and the probe component generates a chromogenic
signal. The synthesis of this two-component amplification
system was rather simple in comparison with synthesis of
our initial DCR system. In addition, the two-component
system provides additional flexibility. Once the amplifier
component is in hand, the diagnostic assay can be performed
in combination with different types of probe molecules. We
demonstrated this versatility by the synthesis and use of two
different probe molecules. The first was based on the
chromogenic reporter, 5-amino-2-nitrobenzoic acid, which
generates a visible spectroscopic signal when its amine
functional group is free. The second probe contained 7-hy-
droxycoumarin, which produces a fluorogenic spectroscopic
(12) Masar, M. S., III; Gianneschi, N. C.; Oliveri, C. G.; Stern, C. L.;
Nguyen, S. T.; Mirkin, C. A. J. Am. Chem. Soc. 2007, 129, 10149–
10158.
We were able to develop simple mathematical equations that
model the kinetic behavior of the one-component and two-
component dendritic chain reactions. The calculated plots
obtained from the equations showed good to excellent correla-
tions with the experimental results. This mathematical model
should assist in predicting the kinetic disassembly of other DCR
systems once the individual constants are calculated and
introduced into the corresponding equations.
(13) Nam, J. M.; Thaxton, C. S.; Mirkin, C. A. Science 2003, 301, 1884–
1886.
(14) Sagi, A.; Weinstain, R.; Karton, N.; Shabat, D. J. Am. Chem. Soc.
2008, 130, 5434–5435.
(15) Thomas, S. W.; Joly, G. D.; Swager, T. M. Chem. ReV. 2007, 107,
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(16) Wu, Q.; Anslyn, E. V. J. Am. Chem. Soc. 2004, 126, 14682–14683.
(17) Zhu, L.; Anslyn, E. V. Angew. Chem., Int. Ed. 2006, 45, 1190–1196.
(18) Amir, R. J.; Pessah, N.; Shamis, M.; Shabat, D. Angew. Chem., Int.
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Conclusions
(19) Sagi, A.; Segal, E.; Satchi-Fainaro, R.; Shabat, D. Bioorg. Med. Chem.
2007, 15, 3720–3727.
We have demonstrated a new approach to achieving
exponential amplification of a diagnostic signal through a
two-component dendritic chain reaction. The amplification
(20) Sella, E.; Shabat, D. Chem. Commun. 2008, 5701–5703.
(21) Shamis, M.; Shabat, D. Chem.sEur. J. 2007, 13, 4523–4528.
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occurred through a distinctive chain reaction that generated
the analyte of interest, thereby initiating additional diagnostic
cycles. The system was designed for the detection of
hydrogen peroxide, and we demonstrated that it produced a
significantly higher diagnostic signal than a classic probe.
The versatility of the two-component amplification system
was exemplified by the use of two different spectroscopic
probes that generated either a chromogenic or a fluorogenic
signal. A mathematical model that simulates the disassembly
kinetics of the one-component and the two-component
systems was developed and was shown to correlate well with
the observed experimental data. Additional 2CDCR systems
with superior detection sensitivity for the identification of
other analytes are currently being developed and will be
reported in due course.
Acknowledgment. D.S. thanks the Israel Science Foundation
(ISF) and the Binational Science Foundation (BSF) for financial
support.
Supporting Information Available: Full experimental details,
characterization data of all new compounds, and spectroscopic
assay conditions. This material is available free of charge via
the Internet at http://pubs.acs.org.
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