Evaluation of multivalent dendrimers based on melamine: Kinetics of thiol-disulfide exchange depends on the structure of the dendrimer

Article abstract of DOI:10.1021/ja0210906

The rate of thiol-disulfide exchange of dansyl groups mediated by dithiothreitol depends on the structure of the dendrimer. In general, the rate of exchange decreases as the size of the dendrimer increases. Dendrimers with disulfides attached near the core undergo exchange more slowly than dendrimers with disulfides near the periphery. Exchange is a bimolecular (noncooperative) process between dansyl-linked disulfides and dithiothreitol. No evidence for intramolecular macrocylization (cooperative) exchange is observed. Mass spectrometry is used to follow exchange in two dendrimers, providing qualitative and quantitative information about this process. Mathematical models suggest that the rates for exchange for all disulfides of a dendrimer are similar, but increase as the exchange reaction progresses.

Full text of DOI:10.1021/ja0210906

Published on Web 04/05/2003
Evaluation of Multivalent Dendrimers Based on Melamine:
Kinetics of Thiol-Disulfide Exchange Depends on the
Structure of the Dendrimer
Wen Zhang, Shane E. Tichy, Lisa M. Pe´rez, Gheorghe C. Maria,†,‡
Paul A. Lindahl, and Eric E. Simanek*
Contribution from the Department of Chemistry, Texas A&M UniVersity,
College Station, Texas 77843, and Laboratory of Chemical and Biochemical Reaction
Engineering, UniVersity Politechnica, Bucharest, Romania
Received August 15, 2002; E-mail: simanek@tamu.edu
Abstract: The rate of thiol-disulfide exchange of dansyl groups mediated by dithiothreitol depends on the
structure of the dendrimer. In general, the rate of exchange decreases as the size of the dendrimer increases.
Dendrimers with disulfides attached near the core undergo exchange more slowly than dendrimers with
disulfides near the periphery. Exchange is a bimolecular (noncooperative) process between dansyl-linked
disulfides and dithiothreitol. No evidence for intramolecular macrocylization (cooperative) exchange is
observed. Mass spectrometry is used to follow exchange in two dendrimers, providing qualitative and
quantitative information about this process. Mathematical models suggest that the rates for exchange for
all disulfides of a dendrimer are similar, but increase as the exchange reaction progresses.
Introduction
chosen as models of drugs because they offer a convenient
spectrophotometric probe for monitoring the kinetics of ex-
Thiol-disulfide exchange offers both a convenient method
for the attachment of ligands to multivalent macromolecules
and an opportunity to exploit “programmable release” of these
ligands upon exposure to a reducing environment. Accordingly,
disulfides have been employed to conjugate small molecules
to soluble scaffolds including proteins and synthetic polymers
for drug delivery.1-3 These disulfides are biolabile. Thiols
including glutathione, cysteine, and homocysteine appear in
human plasma at low concentrations, 10, 5, >1 µM, respec-
tively, while intracellular concentrations of these reducing agents
are significantly (>100×) higher.4-6 Here, we explore whether
the globular nature of dendrimers offers an opportunity to
manipulate the kinetics of thiol-disulfide exchange through the
placement of the disulfides within the globular architecture. This
manipulation is facilitated by control over atomic connectivity,
and not by any ability to exercise precise control over the shape
of these macromolecules in three dimensions. Here, we describe
five dendrimers, 1-5, that differ in size, valency, and placement
of disulfide-linked dansyl groups (Chart 1). Dansyl groups were
change processes and are sufficiently hydrophobic so that a rapid
extraction step could be used to quantify the extent of exchange.
The globular nature of the dendrimer provides a high density
of disulfide groups that in the presence of a single molecule of
glutathione (GSH) or other endogenous thiol could undergo
thiol-disulfide exchange to rapidly shed all ligands of interest
from the dendrimer. Such an event could be beneficial for drug
delivery applications. One pathway for this process (Scheme
1) arises from phase partitioning and local concentration effects.
The covalent architecture is shown with solid lines and the
hydrophobic environment (dendritic phase) with a dotted circle
to distinguish it from bulk solution. While not described here,
we envision that thiol-disulfide exchange reactions could be
used to replace a group, RS (i.e., thiopyridine), with the ligands,
LSH, of interest.7 When this conjugate is introduced to
physiological conditions, a single molecule of glutathione, GSH,
could mediate thiol-disulfide exchange, leading to a free thiol
on the dendrimer. Intramolecular reaction of this thiol to form
the macrocycle releases a second ligand LSH. If the ligand is
hydrophobic and preferentially partitions in the dendrimer phase
instead of water, further reaction can take place until all ligands
are released as shown. The formation of the dendritic poly-
(macrocycle) could further alter the hydrophobic environment
leading, to changes in the rates of exchange.
† University Politechnica.
‡ Current address: Department of Chemistry, Texas A&M University,
College Station TX 77843.
(1) Huang S. Y.; Pooyan S.; Wang J.; Choudhury I.; Leibowitz M. J.; Stein S.
Bioconjugate Chem. 1998, 9, 612-617.
(2) Trimble, S. P.; Marquardt, D.; Anderson, D. C. Bioconjugate Chem. 1997,
8, 416-423.
(3) Trail, P. A.; Willner. D.; Knipe., J.; Henderson, A. J.; Lasch, S. J.; Zoeckler,
M. E.; Trailsmith, M. D.; Doyle, T. W.; King, H. D.; Casazza, A. M.;
Braslawsky, G. R.; Brown, J.; Hofstread, S. J.; Greenfiled, R. S.; Firestone,
R. A.; Mosure, K.; Kadow, K. F.; Yang, M. B.; Hellstroem, K. R.;
Hellstroem, I. Cancer Res. 1997, 57, 100-105.
A number of observations suggested that the cooperative
pathway described by Scheme 1 might be accessible. First, there
are many reports of sequestration of hydrophobic molecules by
(4) Araki, A.; Sako, Y. J. Chromatogr. 1987, 422, 43-52.
(5) Burgunder, J. M.; Nelles, J.; Bilzer, M.; Lauterburg, B. H. Eur. J. Clin.
InVest. 1988, 18, 420-424.
(7) By using dendrimers displaying thiopyridine groups, both captopril and
cysteine-containing peptides can be incorporated onto dendrimers. Umali,
A.; Simanek, E. E. Org. Lett. 2003. In press.
(6) Meister, A. Pharmacol. Ther. 1991, 51, 155-194.
9
5086
J. AM. CHEM. SOC. 2003, 125, 5086-5094
10.1021/ja0210906 CCC: $25.00 © 2003 American Chemical Society

Kinetics of Thiol−Disulfide Exchange in Dendimers
A R T I C L E S
Chart 1
Scheme 1 . Hypothetical Reaction with Glutathione (GSH) Can
cooperative release of ligands from the dendrimer. Second,
intramolecular thiol-disulfide exchange to form large macro-
cycles has been reported.19-22 Notably, Rabenstein has observed
that the single disulfide of somatostatin (RSSR),which has
undergone thiol-disulfide exchange with glutathione (GSH) to
yield the mixed thiol-disulfide, reacts intramolecularly to form
a 38-atom macrocycle faster than intermolercularly with a
second equivalent of glutathione.19 Arginine vasopressin and
oxytocin follow similar trends, forming 20-membered rings.20,21
Zhang and Snyder have reported on the cyclization of dipeptides
containing two cysteine residues separated by up to five amino
acids mediated by oxidized glutathione.22 Third, the mechanism
for thiol-disulfide exchange has been investigated and involves
the SN2 reaction of thiol or the more reactive thiolate anion.23-25
Given that our dendrimers comprise basic triazines, opportunities
for thiolate generation or enhanced nucleophilicity of the thiols
is also possible.
Mediate Exchange through Bimolecular or Cooperative Processesa
a Dotted line represents the dendritic phase. The multivalent scaffold
can be prepared by exchange groups (RS) with ligands (LS) of interest.
dendrimers.8-18 Most notable is Meijer’s “dendritic box” which
sequesters hydrophobic guests as a function of the peripheral
group.16-18 Such sequestration in our system could lead to
Dithiothreitol (DTT) was chosen to mediate exchange instead
of glutathione to simplify analysis. While glutathione is physi-
ologically relevant and introduces interesting questions including
the role of charge and additional steric bulk on thiol-disulfide
exchange, its use complicates interpretation of data resulting
from the transient formation of dendrimer-glutathione mixed
disulfides. These complications lead us to save such inquiries
for other studies of advanced architectures with established
biocompatibility.26 However, equilibrium constants between
GSH/DTT redox pairs have been determined.27
(8) Newkome, G. R. Moorefield, C. N.; Baker, G. R.; Johnson, A. L.; Behera,
R. K. Angew. Chem., Int. Ed. Engl. 1991, 30, 1176-1178.
(9) Newkome, G. R.; Moorefield, C. N.; Baker, G. R.; Saunders, M. J.;
Grossman, S. H. Angew. Chem., Int. Ed. Engl. 1991, 30, 1178-1180.
(10) Hawker, C. J.; Wooley, K. L.; Fre´chet, J. M. J. J. Chem. Soc., Perkin Trans.
1 1993, 1287-1297.
(11) Liu, M.; Kono, K.; Fre´chet, J. M. J. J. Controlled Release 2000, 65, 121-
131.
(12) Pistolis, G.; Malliaris, A.; Paleos, C. M.; Tsiourvas, D. Langmuir 1997,
13, 5870-5875.
(13) Pistolis, G.; Malliaris, A.; Tsiourvas, D.; Paleos, C. M. Chem.-Eur. J. 1999,
5, 1440-1444.
(14) Heise, A.; Hedrick, J. L.; Frank, C. W.; Miller, R. D. J. Am. Chem. Soc.
1999, 121, 8647-8648.
(15) Jansen, J. F. G. A.; Peerlings, H. W. I.; Van Hest, J. C. M.; Meijer, E. W.;
De Brabander van den Berg, E. M. M. NATO Advanced Study Institute
Series C; Plenum: New York, 1997; Vol. 499, pp 371-384.
(16) Jansen, J. F. G. A.; de Brabander van den Berg, E. M. M.; Meijer, E. W.
Science 1994, 266, 1226-1229.
(19) Rabenstein, D. L.; Weaver, K. H. J. Org. Chem. 1996, 61, 7391-7397.
(20) Rabenstein, D. L.; Yeo, P. L. J. Org. Chem. 1994, 59, 4223-4229.
(21) Rabenstein, D. L.; Yeo, P. L. Bioorg. Chem. 1995, 23, 109-118.
(22) Zhang, R.; Snyder, G. H. J. Biol. Chem. 1989, 264, 18472-18479.
(23) Wilson, J. M.; Bayer, R. J.; Hupe, D. J. J. Am. Chem. Soc. 1977, 99, 7922-
7926.
(17) Jansen, J. F. G. A.; Meijer, E. W.; de Brabander-van den Berg, E. M. M.
J. Am. Chem. Soc. 1995, 117, 4417-4418.
(24) Szajewski, R. P.; Whitesides, G. M. J. Am. Chem. Soc. 1980, 102, 2011-
(18) Zhang, X.; Wilhelm, M.; Klein, J.; Pfaadt, M.; Meijer, E. W. Langmuir
2000, 16, 3884-3892.
2026.
(25) Houk, J.; Whitesides, G. M. J. Am. Chem. Soc. 1987, 109, 6825-6836.
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A R T I C L E S
Zhang et al.
Table 1. Molecular Weight Data for 1-5 and Protected Precursors Including MALDI-TOF, Dynamic Light Scattering (DLS), and Size
Exclusion Chromatography (SEC) (the structures of the Protected Dendrimers (8, 11, 14, 17, 20) are given in Supporting Information)
deprotected
protected
DLS
dendrimers
MALDI
dendrimers
MALDI calc, (obsd)
SEC
1
2
3
4
5
1891.62 (1890.40)
3167.98 (3167.85)
4333.85 (4333.39)
9219.61 (9219.12)
6887.80 (6888.30)
8
11
14
17
20
2290.83 (2290.86)
3968.78 (3968.20)
5134.43 (5133.57)
10824.03 (10820.91)
8526.24 (8490.15)
2.50 kDa 2.36 nm
4.22 kDa 3.18 nm
5.52 kDa 3.70 nm
12.70 kDa 5.90 nm
9.35 kDa 4.98 nm
Mn 2217, Mw 2290, Mw/Mn 1.03
Mn 3724, Mw 3766, Mw/Mn 1.01
Mn 4255, Mw 4335, Mw/Mn 1.02
Mn 6055, Mw 6268, Mw/Mn 1.03
Mn 5369. Mw 5572, Mw/Mn 1.03
ecules, respectively. Fragment ions at 4316.43 and 4299.37 were also
observed. The total analyte response was taken to be the total area of
these five peaks. The areas of peaks of interest were calculated using
the automatic integration function included with the Voyager (Data
Explorer) software package.30
Experimental Section
Release Studies. Thiol-disulfide exchange was monitored in 20
mM phosphate buffer at pH 7.5. To perform a single exchange
experiment, multiple (10-15) reaction vials were prepared containing
degassed buffer. Dendrimer was added to each from a stock solution.
Upon addition of DTT (from a stock solution) to each reaction vial,
the vials were placed on a shaker table to ensure adequate mixing to
reduce artifacts arising from mass transport. At a given time, a vial
was removed from the shaker plate. One milliliter of chloroform was
added and the mixture shaken to extract the chromophore. Molecules
1-5 are soluble in water and only sparingly soluble in chloroform over
almost the entire concentration range of these solutions. The phases
were separated with the aide of a quick centrifugation step. An aliquot
(0.5 mL) of the organic phase was removed via syringe, and the
fluorescence of the resulting solution was determined. Mass spectral
analysis of the organic phase revealed no disulfides of the dansyl
chromophore, only free thiols. Addition of acetic acid to quench the
reaction did not appear to affect the measurement. Analyses were
performed in duplicate to estimate the magnitude of experimental error.
Fluorescence Quantification. Fluorescence spectra were recorded
on an SLM Instruments AMINCO spectrophotometer using an excita-
tion wavelength of 350 nm and monitoring emission at a wavelength
of 497 nm.
Mass Spectrometry Studies. Matrix-assisted laser desorption/
ionization time-of-flight (MALDI-TOF) spectra were recorded in linear
ion mode with an Applied Biosystems Voyager DE-STR mass
spectrometer (ABI, Framingham, MA). Positive ions were generated
by using a nitrogen laser pulse (λ ) 337 nm, 20 Hz) and accelerated
under 20 kV using delayed extraction (550 ns) before entering the time-
of-fight mass spectrometer. Laser strength was adjusted to provide
minimal fragmentation and optimal signal-to-noise ratio. An average
of 200 laser shots was used for each spectrum, and data were processed
with the accompanying Voyager software package.
Kinetic Modeling. Models were developed to fit the observed kinetic
data from a minimalist approach. Reaction order for dendrimer and
DTT were determined experimentally for 3 and 5. To compare the
statistical model with the experimental data, a standard deviation of σ
) 3.4 × 10-4 mM was used, corresponding to 1% of the initial
concentration of dendrimer 3.31 The computational strategy used to
identify the rate constants of these kinetic models has been described
for similar isothermal batch processes.32,33 Models used initial concen-
trations identical to those used experimentally and were solved by
numerical integration of differential mass balances under constant
system-volume conditions. All calculations were done in Matlab (2001)
on a Dell PC.34 Details are available in the Supporting Information.
Structural Modeling of Dendrimers. Computational models were
obtained using the Cerius2 4.6 suite of programs from Accelyrs, Inc.
Minimization and dynamics calculations were performed in the gas
phase with the open force field (OFF) program using the pcff second-
generation force field.35 The dendrimers were initially drawn and
minimized in the fully extended, open conformation before constant
volume and temperature (NVT) molecular dynamics calculations were
performed using simulated annealing. The simulation annealing was
carried out for 840 ps over a temperature range of 300-1000 K, with
∆T ) 50 K, using the Nose temperature thermostat, a relaxation time
of 0.1 ps, and a time step of 0.001 ps. The dendrimer was minimized
after each anneal cycle, resulting in 300 minimized energy structures.
1
Synthesis. Intermediates and targets provided satisfactory H and
13C NMR spectra and mass spectra. The synthesis of related molecules
has been described.36 The syntheses of 1-5 are fully described and
elaborated upon in the Supporting Information.
The exchange reactions were performed at approximately pH 4.5 to
retard the rates of reaction so that more data could be collected early
in the time course and errors that could result from delays in workup
or data acquisition could be avoided. An overlayer preparation which
has been described previously was used with 2,4,6-trihydroxyaceto-
phenone (THAP).28 A 1:1 mixture of the 1 µM dendrimer DTT solution
and 10 mg/mL THAP solution in methanol was spotted in 1 µL aliquots
on top of a 100 mg/mL THAP bed of matrix.29
The experimental conditions were optimized prior to the addition
of DTT and held constant throughout the monitoring of the experiment.
The MALDI mass spectra for 1-5 are straightforward to interpret. For
example, the mass spectrum of 3 shows peaks at m/z 4334.74, 4356.84,
and 4372.64 attributed to protonated, sodiated, and potassiated mol-
Results and Discussion
Evaluation of Molecular Weights. The molecular weights
of targets 1-5 and the corresponding protected precursors were
measured by MALDI-TOF mass spectrometry and are in
excellent agreement with expected values (Table 1). The
protected precursors were also evaluated by dynamic light
scattering and size exclusion chromatography. A strong cor-
relation between all these techniques for the smaller dendritic
(30) Koomen, J. M.; Russell, W. K.; Hettick, J. M.; Russell, D. H. Anal. Chem.
2000, 72, 3860-3866.
(31) To simplify the estimate statistical tests, a normal experimental noise with
a minimum level of σ˜ ) 3.4 × 10-4 mM was considered from experiments
and for all the observed species (see Appendix A of the Supporting
Information).
(26) Preliminary investigations have shown that triazine dendrimers do not show
any changes to liver or kidney function when administered to mice in single
bolus injections up to 10 mg/kg. Zhang,W.; Jiang, J.; Qin, C.; Perez, L.
M.; Parrish, A. R.; Safe, S. H.; Simanek, E. E. Supramol. Chem. 2003. In
press.
(32) Maria, G.; Rippin, D. W. T. Comput. Chem. Eng. 1997, 21, 1169-1190.
(33) Froment, G. F.; Hosten, L. H. Catalytic Kinetics: Modelling. In Cataly-
sis: Science and Technology; Anderson, L., Boudart, M., Eds.; Springer-
Verlag: Berlin, 1981.
(27) Rothwarf, D. M.; Scheraga, H. A. Proc. Natl. Acad. Sci. U.S.A. 1992, 89,
7944-7948.
(34) Matlab 2001. The Language of Technical Computing, version 6.1, release
12.1; The MathWorks Inc.: Natick, MA.
(28) Amm, M.; Platzer, N.; Bouchet, J. P.; Volland, J. P. Magn. Reson. Chem.
2001, 39, 77-84.
(35) Cerius2 Force field Based Simulations, September 1998; Accelerys, Inc.:
San Diego, 2000.
(29) Zhou, L.; Russell, D. R.; Zhao, M.; Crooks, R. M. Macromolecules 2001,
34, 3567-3573.
(36) Zhang, W.; Nowlan, D. T., III; Thomson, L. M.; Lackowski, W. M.;
Simanek, E. E. J. Am. Chem. Soc. 2001, 123, 8914-8922.
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Kinetics of Thiol−Disulfide Exchange in Dendimers
A R T I C L E S
Table 2. Exchange under Psuedo-First Order Conditions
dendrimer
[dendrimer] (µM) 70 7.0 70 7.0 35 3.5 17.5 1.75 35 3.5
1
2
3
4
5
[dansyl] (µM)
[DTT] (µM)
140 14 140 14 140 14 140 14 140 14
370 370 370 370 370 370 370 370 370 370
7.1 7.4 7.5 7.4 7.3 8.0 14 13 17 16
t
1/2 (min)
Figure 1. Half-lives for exchange under psuedo-first-order conditions at
identical concentrations of dansyl groups. Dendrimers 1-3 undergo
exchange at similar rates that are 1.8× slower than dendrimer 4 and 2.2×
slower than 5.
molecules 1, 2, and 3 is observed. For molecules 4 and 5,
dynamic light scattering is a better predictor of molecular weight
than size exclusion chromatography (SEC) which uses poly-
styrene as a standard. However, SEC reveals an excellent
agreement between weight average and number average mo-
lecular weights and, as with previous targets, low measured
polydispersities. SEC consistently underestimates the molecular
weights of the fourth-generation dendrimers by 40%, an
observation borne out in other dendrimer architectures as well.37
The smaller measured hydrodynamic volume when compared
with linear poly(styrene) is attributed to the more compact shape
of the dendritic architecture.38 This discrepancy is a “dendritic
effect” and suggests to us that if differences in release rates
result from the dendritic nature of these architectures, such
effects should be pronounced for 4 and 5, whereas similar small
molecule-like behaviors should be predicted for 1, 2, and 3.
Figure 2. Kinetics of release for 3. (a) At 1.8 mM DTT, reaction progress
was monitored at 7.5, 15, and 150 µM 3. (b) At 370 µM DTT, reaction
progress was monitored at 0.75, 1.5, 7.5, 15, and 150 µM 3.
Determination of Reaction Order
Half-Lives under Pseudo-First-Order Conditions. To
determine the order of the reaction, we performed analyses of
thiol-disulfide exchange using fluorimetry under pseudo-first-
order conditions with an excess of DTT (Figure 1). Our initial
assumptions were that no cooperative effects would be observed
and, instead, the disulfide-linked dansyl groups of a single
dendrimer could be treated as independent molecules. The
experimental reproducibility of the exchange processes can be
evaluated by comparing the half-lives of the reaction in
experiments when the concentration of the dendrimer is varied.
That is, the pseudo-first-order assumption can be checked if
the half-life is independent of dendrimer concentration as
revealed by eq 1.
of the most interesting conclusions from this work is that
comparisons of the half-lives for compounds 1-5 indicate that
structure does impact the kinetics of release. Table 2 shows the
results of the loss of dansyl groups from 1-5 when under
identical concentrations of danysl and DTT. Targets 1, 2, and
3 undergo thiol-disulfide exchange at similar rates. These rates
are 1.8× faster than the rate of exchange for 4 and 2.2× as fast
for 5. These observations are consistent with the onset of
“dendritic character” as seen by SEC.
Method of Initial Rates. We focused further attention on
dendrimers 3 and 5, architectures representative for the series.
Analysis of the initial rates of the reactions performed under
different concentrations of either dansyl or DTT establishes that
the reaction is first-order in both [dansyl] and [DTT]. Repre-
sentative data of 3 are given in Figure 2 in which the
concentration of DTT is held constant in two separate experi-
ments (2a and 2b) and the [dansyl] is varied. The insets show
the linear relationship of the logarithms of the initial rates versus
the logarithm of initial concentrations. For both lines the slope
) 1. Starting with the assumed first-order rate eq 2, we can
define an initial rate (rateo, eq 3) and take the logarithm (eq 4)
to reveal that the resulting plot should produce a straight line
C
t1/2 ) ln o ) ln 2
(1)
1
k
1
k
C
We find excellent internal agreement for half-lives of release
for each of the targets 1-5 over a range of concentrations (Table
2), suggesting that the reaction is first-order in [dansyl]. One
(37) Hawker, C. J.; Frechet, J. M. J. J. Am. Chem. Soc. 1990, 112, 7638-7647.
(38) Aharoni, S. M.; Crosby, C. R.; Walsh, E. K. Macromolecules 1982, 15,
1093-1048.
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Zhang et al.
Figure 3. Kinetic analysis of exchange in 3 by MALDI-TOF mass spectrometry. Exchange in both 3 and 5 (Supporting Information) were monitored by
mass spectrometry by integrating the signal from starting material A and the appearance of lines corresponding to loss of 1-4 disulfide-linked dansyl
groups. The experimental data can be modeled to afford rate constants for the process. See text for details.
with a slope of â ) 1, corresponding to a first-order reaction
with respect to the concentration of dansyl groups. Additional
data verifying the first-order dependences of [dansyl] and [DTT]
on rate for 3 and 5 appear in the Supporting Information.
used to monitor the course of thiol-disulfide exchange for 3
(and 5, Supporting Information) as indicated in Figure 3 where
A through E correspond to intermediates displaying different
numbers of dansyl groups. The spectra are remarkably clean.
A detailed picture of the kinetics of the process can be obtained
by integrating and normalizing the lines corresponding to loss
of one through all four dansyl groups. The results with three
representative spectra are shown in Figure 3.
rate ) kobs[dansyl]â
(2)
rateo ) kobs[dansyl]oâ
(3)
(4)
At the beginning of the experiment only A displaying all four
dansyl-linked chromophores is present, showing a line at MW
4334 Da. Loss of one dansyl group through thiol-disulfide
log(rateo) ) log(kobs) + â log[dansyl]o
Mass Spectrometry. MALDI-TOF mass spectrometry was
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Kinetics of Thiol−Disulfide Exchange in Dendimers
A R T I C L E S
Figure 4. Simple model linking A-E by equilibrium processes that involve oxidized and reduced DTT (DTTo and DTTr). The processes and intermediate
F in the dashed boxed are omitted in the simple equilibrium model but are addressed later in the text in a cooperative model.
exchange produces B with a peak at MW 4026 Da which
increases rapidly before dendrimers displaying two, C (MW
3717 Da), and one, D (MW 3409 Da), appear after subsequent
exchange reactions. The appearance of E that has undergone
complete exchange to lose all four dansyl groups is indicated
by the line at MW 3100 Da. The populations measured reflect
contribution of five lines for each species: the major ion, M +
H+, its alkali metal adducts M + Na+ and M + K+, and its
two major fragmentation products (M - NH3)+ and (M -
2NH3)+. Mass resolution supports the existence of dendrimers
as poly(thiols) instead of mixtures of thiols and intramolecular
(macrocyclic) disulfides. A very similar trend is observed for
5.
Kinetic Modeling. Modeling a process including potential
cooperative (macrocylization) pathways is intractable because
of the large number of unknown parameters, including both
intermediates and rate constants. Indeed, our attempt to fit rate
constants simultaneously to the data using such a scheme yielded
estimated parameters of very low statistical significance. As a
result, we constructed a minimalist description of the system,
four linked species A-E, and expanded it until the data were
adequately described.39
assumed to contribute insignificantly to the rate of release of
dansyl groups. The observed first-order dependence of rate on
both dansyl group and DTTr supports this assumption. The
simplest model relating 3 to the species observed by mass
spectrometry is shown in Figure 4. While populations A and E
comprise single species, there are four discrete species repre-
sented by B and D, and six discrete species represented by C.
Populations A-E can be connected by eight rate expressions
(eqs 5-12).40
r1 ) k1[A][DTTr]
r-1 ) k-1[B][DTTo][LSH]
r2 ) k2[B][DTTr]
(5)
(6)
(7)
r-2 ) k-2[C][DTTo][LSH]
r3 ) k3[C][DTTr]
(8)
(9)
r-3 ) k-3[D][DTTo][LSH]
r4 ) k4[D][DTTr]
(10)
(11)
(12)
Our starting point for the model was the assumption that the
intermolecular reactions between dendrimer and DTTr (forming
a more reduced dendrimer, free dansyl group, and oxidized
DTTo) dominated the reaction kinetics. That is, cooperative
intramolecular processes carried out within the dendrimer were
r-4 ) k-4[E][DTTo][LSH]
We initially evaluated the system as a series of unidirectional
reactions (k-1 ) k-2 ) k-3 ) k-4 ) 0). The resulting four
differential kinetic equations were solved, and the best-fit for
the rate constants k1-k4 were obtained by using a weighted least-
(39) Maria, G.; Rippin, D. W. T. Chem. Eng. Sci. 1993, 48, 3855-3864.
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A R T I C L E S
Zhang et al.
Figure 5. Computational models of 1-5. Representations of 1-5 as (top to bottom) wire, wire showing only the dansyl chromophores, and space-filling
before and after a 180° rotation.
squares criterion. The model was statistically adequate,41,42 but
deficient because it predicted that [E] increases exponentially
to ultimately become the only species in solution. This observa-
tion neither is realized in the experimental data nor is it
consistent with chemical intuition which would suggest that an
equilibrium of all species A-E should be reached. Data from
mass spectrometry suggest that the concentration of E flattens
in time and that an equilibrium likely exists between A-E.
Consequently, our second model assumed that each step was
reversible. We made the simplifying assumption that the reverse
reactions were third-order (dendritic thiol, dansyl thiol, and
oxidized DTT) although they are actually the sum of at least
two reactions. The equations were resolved by using the same
weighted least-squares criterion.43 The best-fit rate constants are
shown in Figure 4. The predicted kinetic curves in Figure 3
(solid lines) as well as residual plots and adequacy tests show
good agreement between the data and model.44
The equilibrium constants for each step of this model, as
estimated from the kinetic rate constants, are tabulated in Figure
4. An apparent Keq can be calculated by taking the quotient of
the forward and reverse rate constants for a step. However, this
constant represents the sum of the species denoted with A-E
(A:B:C:D:E ) 1:4:6:4:1).45 To convert the apparent Keq to the
corrected Keq (denoted Kij) which has clearer physical meaning
(Vis-a`-Vis a single disulfide exchange event linking a single A
(40) Throughout all these models, we also assumed that the rate constants
associated with these reactions were identical for each dansyl group in
dendrimers of the same oxidation state (Supporting Information).
(41) The four reactions model is roughly adequate (i.e., øc2 ) 32.6 < ø2(36 ×
5 - 4; 95%), see Appendix B).
(43) The residuals for the sum of the squares difference (obsd - exp) of A-E
were assigned weights to more precisely describe C, D, and E such that
A:B:C:D:E ) 1:2:10:10:2. Appendix B of the Supporting Information
elaborates on this strategy. These adopted weights ensured that fits were
equally sensitive to all species residuals (i.e. the difference between the
observed and predicted concentrations).
(42) The ø2 test is a comparison of the predicted model error and the experimental
one. The ratio of these errors is validated if it is less than the tabulated ø2
distribution quantila for a certain assumed confidence level, in this case,
95%. Zwillinger, D. Standard Mathematical Tables and Formulae; CRC
Press: Boca Raton, 1996.
(44) øc2 ) 32.6 < ø2(36 × 5 - 4; 95%), see Table S2 in Appendix B of the
Supporting Information for a description of all the statistical tests.
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5092 J. AM. CHEM. SOC. VOL. 125, NO. 17, 2003

Kinetics of Thiol−Disulfide Exchange in Dendimers
A R T I C L E S
Conclusions
and B, KAB), correction factors of 4, 3/2, 2/3, and 1/4 were
applied respectively to Keq’s to yield KAB, KBC, KCD, and KDE
based the complete reaction scheme which accounts for
individual species of each population (elaborated in the Sup-
porting Information). These constants increase, suggesting that
dansyl groups exchange more favorably as the architecture
becomes less sterically hindered. Intuitively, we expect the rates
of disulfide exchange to be similar for A, B, C, and D as these
groups of species can adopt a variety of conformations.
However, as disulfide groups are lost, the molecular architecture
should have more volume accessible to reduced DTT and
subsequent reactions, interestingly, for both 3 and 5.
One of our long-term goals for these molecules is their use
as models for drug delivery.46-48 To this end, disulfides could
play two roles. First, disulfides might be employed for linking
pharmacophores until exposure to cellular concentrations of
reductant.4-6 Second, disulfides could be used to append
targeting groups such as peptides49,50 to direct in a “magic-
bullet” sense the dendrimer to specific sites within the body
that could complement size-based targeting resulting from the
enhanced permeability and retention of tumors for large
molecules (the EPR effect).51-53 The current study shows that
both roles remain feasible. Most importantly, dendrimers bearing
multiple disulfide-linked hydrophobic groups are tractable and
highly water soluble. The opportunity to tailor rates of release
as a function of dendrimer structure is very interesting to us
(and others, as Takaguchi and co-workers reported thiol-
disulfide exchange in a dendrimer with a disulfide core)54 and
may be relevant for delivery regimes that require the dendrimer
be internalized by the target cell.
By providing relative populations of the products of thiol-
disulfide exchange over time, mass spectrometry provides a
description of the kinetics of the process upon which kinetic
models can be formulated. The models for both 3 and 5 are
tantalizing in that they suggest that the rate of exchange increases
as the dendrimer becomes less crowded. The quality of the data
and the errors associated with the experiment make such
conclusions noteworthy, but preliminary. An additional limita-
tion to these studies merits some comment. While we success-
fully approached the equilibrium position of A-E with pure
A, we have been unsuccessful in purifying E by HPLC and
reconstituting the reaction mixture. The size and common
polarities associated with these dendrimers have made what
would be an ordinarily difficult exercise intractable. In conclu-
sion, we add thiol-disulfide-exchange reactions to the list of
“dendritic effects” that dendrimers have been shown to impart
including catalysis,55 molecular recognition,56 cellular uptake,57
and redox58 and optical processes.59
To determine whether a more extended kinetic scheme
incorporating cooperative pathways for release could be statisti-
cally supported by the available experimental data, the reversible
model was expanded to include macrocyle F linked by two
additional reactions (eqs 13 and 14, Figure 4, including the
dashed box). However, when this expanded system was analyzed
as above for 3, the improvement obtained in adequacy was
insignificant, while the parameter statistical tests were negatively
affected. Accordingly, we have rejected reactions 13 and 14
and conclude that the eight-reaction model adequately describes
the kinetics of the system.
r5 ) k5[B]
(13)
(14)
r6 ) k6[F][DTTr]
Computational Rationalization. Recognizing that the struc-
ture of the dendrimer does affect the rate of thiol-disulfide
exchange, we turned to computation in an attempt to rationalize
these differences. Gas-phase simulations presumably mimic the
hydrophobic collapse of these structures. Targets 1-5 are shown
in Figure 5 as stick models of the full architecture, of only the
disulfide-linked chromophores, as space-filling models from the
front and back (after a 180° rotation). The radii of gyration
calculated for these models (in Å) (1-5: 7.9, 9.2, 9.8, 16.8,
12.4) are consistent with the hydrodynamic trend observed using
GPC of the protected precursors.
Acknowledgment. Robert A. Welch Foundation (E.E.S.:
A-1439), and the National Institutes of Health (P.A.L.: GM63958;
E.E.S.: GM64650) supported these investigations. The Labora-
Unfortunately, no simple metric for predicting the kinetics
of release emerges on the basis of these structures. Instead, and
perhaps surprisingly, the best predictor of rate turns out to be
the location of the labile bond in the two-dimensional repre-
sentations shown in Chart 1. The shortcomings of these
simulations can be attributed to a number of factors including
the large size of these architectures, very few conformational
restrictions, a limited pool of target structures to survey, the
absence of solvent, and the relative abundance of local minima
and relatively large conformational space available for search.
Regardless, these computations continue to provide interesting
pictures of candidate architectures which serve as excellent
mechanisms for challenging our intuition.
(46) Liu, M.; Frechet, J. M. J. Pharm. Sci. Technol. Today 1999, 2, 393-401.
(47) Stiriba, S.-E.; Frey, H.; Haag, R. Angew. Chem., Int. Ed. 2002, 41, 1329-
1334.
(48) Schultz, L. G.; Zimmerman, S. C. Pharm. News 1999, 6, 25-29.
(49) Pasqualini, R.; Rouslahti, E. Nature 1996, 380, 364-366.
(50) Arap, W.; Pasqualini, R.; Ruoslhati, E. Science 1998, 279, 377-380.
(51) Duncan, R.; Pratten, M. K.; Cable, H. C.; Ringsdorf, H.; Llyod, J. B.;
Biochem. J. 1981, 196, 49-55.
(52) Searle, F.; Gac-Breton, S.; Keane, R.; Dimitrijevic, S.; Brocchini, S.;
Sausville, E. A.; Duncan, R. Bioconjugate Chem. 2001, 12, 711-718.
(53) Maeda, H.; Wu, J.; Sawa, T.; Matsumura, Y.; Hori, K. J. Controlled Release
2000, 65, 271-284.
(54) Takaguchi, Y.; Saito, K.; Suzuki, S.; Hamada, K.; Ohta, K.; Motoyoshiya,
J.; Aoyama, H. Bull. Chem. Soc. Jpn. 2002, 75, 1347-1351.
(55) See, for example: (a) Kleij, A. W.; Gossage, R. A.; Jastrzebski, J. T. B.
H.; Boersma, J.; Van Koten, Ge. Angew. Chem., Int. Ed. 2000, 39, 176-
178. (b) Kleij, A. W.; Gossage, R. A.; Klein Gebbink, R. J. M.; Brinkmann,
N.; Reijerse, E. J.; Kragl, U.; Lutz, M.; Spek, A. L.; van Koten, G. J. Am.
Chem. Soc. 2000, 122, 12112-12124.
(56) See, for example: (a) Richter-Egger, D. L.; Tesfai, A.; Tucker, S. A. Anal.
Chem. 2001, 73 (23), 5743-5751. (b) Koenig, S.; Muller, L.; Smith, D.
K. Chem. Eur. J. 2001, 7, 979-986. (c) Valerio, C.; Ruiz, J.; Fillaut, J.-
L.; Astruc, D. C. R. Acad. Sci. 1999, 2, 79-83. (d) Cardona, C. M.; Alvarez,
J.; Kaifer, A. E.; McCarley, T. D.; Pandey, S.; Baker, G. A.; Bonzagni, N.
J.; Bright, F. V. J. Am. Chem. Soc. 2000, 122, 6139-6144.
(57) Wiwattanapatapee, R.; Carreno-Gomez, B.; Malik, N.; Duncan, R. Pharm.
Res. 2000, 17, 991-998.
(45) The relationship between the full and reduced models is shown in the
Supporting Information. The results are that k1 ) 4kAB, k-1 ) kBA, k2
)
3kBC, k-2 ) 2kCB, k3 ) 2kCD, k-3 ) 3kDC, k4 ) 4kED, k-4 ) kDE. Equilibrium
constants describing individual reactions in the full reaction scheme (KAB
BC, KCD, and KDE) can be related to those obtained by fitting the reduced
,
K
model to the data (Keqs) with specific corrections described in the text. As
required, the product of the Keqs in the reduced system equals that of the
full system.
9
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A R T I C L E S
Zhang et al.
tory for Biological Mass Spectrometry is a university research
facility supported by the Office of the Vice President for
Research (TAMU). We thank the Laboratory for Molecular
Simulation (TAMU) for providing software and computer time.
Supporting Information Available: Synthesis, modeling, and
kinetic data (PDF). This material is available free of charge via
the Internet at http://pubs.acs.org.
JA0210906
(58) See, for example: (a) Chow, H.-F.; Chan, I. Y.-K.; Fung, P.-S.; Mong, T.
K.-K.; Nongrum, M. F. Tetrahedron 2001, 57, 1565-1572. (b) Stone D.
L.; Smith D. K.; McGrail P. T. J. Am. Chem. Soc. 2002, 124, 856-864.
(c) Astruc, D.; Blais, J.-C.; Cloutet, E.; Djakovitch, L.; Rigaut, S.; Ruiz,
J.; Sartor, V.; Valerio, C. Top. Curr. Chem. 2000, 210, 229-259. (d) Turrin,
C.-O.; Chiffre, J.; de Montauzon, D.; Daran, J.-C.; Caminade, A.-M.;
Manoury, E.; Balavoine, G.; Majoral, J.-P. Macromolecules 2000, 33,
7328-7336.
(59) See, for example: (a) Voegtle, F.; Gorka, M.; Hesse, R.; Ceroni, P.; Maestri,
M.; Balzani, V. Photochem. Photobiol. Sci. 2002, 1, 45-51. (b) Jen, A.
K.-Y.; Ma, H.; Sassa, T.; Liu, S.; Suresh, S.; Dalton, L. R.; Haller, M.
Proc. SPIE-Int. Soc. Opt. Eng. 2001, 4461, 172-179. (c) Zhu, A.; Bharathi,
P.; Drickamer, H. G.; Moore, J. S. J. Polym. Sci., Part A 2001, 39, 2859-
2865.
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