Kinetic analysis of the Rebek self-replicating system: Is there a controversy?

Article abstract of DOI:10.1021/ja960324g

The Rebek self-replication reaction of 1 and 2, catalyzed by complexation of both reactants to the resulting product 3 (Tjivikua, T.; et al. J. Am. Chem. Soc. 1990, 112, 1249-1250. Nowick, J.S.; et al. J. Am. Chem. Soc. 1991, 113, 8831-8839. Wintner, E.A.; et al. Acc. Chem. Res. 1994, 27, 198-203. Conn, M.M.; et al. J. Am. Chem. Soc. 1994, 116, 8823-8824), and related work of Menger et al. (Menger, F.M.; et al. J. Am. Chem. Soc. 1994, 116, 3613-3614. Menger, F.M.; et al. J. Org. Chem. 1995, 60, 2870-2878) have been reinvestigated. On the basis of our experiments with the same systems and comparing the absolute rates of different (model) reactions, we have identified five pathways of the reaction between 1 and 2 in the presence of template 3: background (k₁ = 0.035 M^-1 min^-1), preassociative (k₂ = 0.0044 min^-1), termolecular (k₃ = 0.030 min^-1), and two bimolecular (k₄ = 0.130 M^-1 min^-1, k₅ = 0.020 M^-1 min^-1). A general kinetic model for self-replicating reactions has been used to analyze the Rebek-Menger controversy. We conclude that self-replication as defined by Rebek et al. operates in this system; other pathways obscure the simple picture of a ternary complex as the only complex that leads to the rate enhancement and one of those (bimolecular) pathways is that proposed by Menger et al. Our results show that when 1 and 2 are complexed to 3 in a termolecular complex, the rate of reaction between 1 and 2 is 6.8 times (k₃/k₂) faster than when 3 is formed from the bimolecular complex of 1 and 2, and this rate enhancement factor represents the efficiency of template 3 in the self-replication process.

Full text of DOI:10.1021/ja960324g

6
880
J. Am. Chem. Soc. 1996, 118, 6880-6889
Kinetic Analysis of the Rebek Self-Replicating System: Is
There a Controversy?
David N. Reinhoudt,* Dmitry M. Rudkevich, and Feike de Jong
Contribution from the Laboratory of Organic Chemistry, UniVersity of Twente, P.O. Box 217,
7
500 AE Enschede, The Netherlands
X
ReceiVed January 30, 1996
Abstract: The Rebek self-replication reaction of 1 and 2, catalyzed by complexation of both reactants to the resulting
product 3 (Tjivikua, T.; et al. J. Am. Chem. Soc. 1990, 112, 1249-1250. Nowick, J. S.; et al. J. Am. Chem. Soc.
1
991, 113, 8831-8839. Wintner, E. A.; et al. Acc. Chem. Res. 1994, 27, 198-203. Conn, M. M.; et al. J. Am. Chem.
Soc. 1994, 116, 8823-8824), and related work of Menger et al. (Menger, F. M.; et al. J. Am. Chem. Soc. 1994, 116,
613-3614. Menger, F. M.; et al. J. Org. Chem. 1995, 60, 2870-2878) have been reinvestigated. On the basis of
our experiments with the same systems and comparing the absolute rates of different (model) reactions, we have
3
-
1
identified five pathways of the reaction between 1 and 2 in the presence of template 3: background (k1 ) 0.035 M
-
1
-1
-1
-1
min ), preassociative (k2 ) 0.0044 min ), termolecular (k3 ) 0.030 min ), and two bimolecular (k4 ) 0.130 M
-
1
-1
-1
min , k5 ) 0.020 M min ). A general kinetic model for self-replicating reactions has been used to analyze the
Rebek-Menger controversy. We conclude that self-replication as defined by Rebek et al. operates in this system;
other pathways obscure the simple picture of a ternary complex as the only complex that leads to the rate enhancement
and one of those (bimolecular) pathways is that proposed by Menger et al. Our results show that when 1 and 2 are
complexed to 3 in a termolecular complex, the rate of reaction between 1 and 2 is 6.8 times (k3/k2) faster than when
3
is formed from the bimolecular complex of 1 and 2, and this rate enhancement factor represents the efficiency of
template 3 in the self-replication process.
Introduction
comprises the formation of a secondary amide bond by reaction
of a primary amine with an activated (pentafluorophenyl) ester.
Rebek et al. reported that, when the reactants have comple-
mentary recognition sites (ester 1 and amine 2), the resulting
product amide 3 can act as a template and catalyzes its own
formation. The proper geometry of the termolecular complex
of the product 3 and the two reactants 1 and 2 favors the amide
When von Kiedrowski showed that a protected hexadeoxy-
nucleotide catalyzes its own formation from the complementary
trideoxynucleotides, the concept of artificial “self-replicating”
systems was established.1 The initial work dealt with (deoxy)-
nucleotide chemistry, but recently also other classes of molecules
that have recognition sites have received considerable atten-
tion.1 Almost by definition such studies are complicated by
the different complexation equilibria between reactants and
products. In particular, the strong tendency of the catalyst to
dimerize because of its complementary binding sites does lead
to “inactivation” of the catalyst (product) when the concentration
increases. This means that the intuitive expectation that the
rate of product formation in time should increase is often not
3
,2
(3) (a) Tjivikua, T.; Ballester, P.; Rebek, J., Jr. J. Am. Chem. Soc. 1990,
1
12, 1249-1250. (b) Nowick, J. S.; Feng, Q.; Tjivikua, T.; Ballester, P.;
Rebek, J., Jr. J. Am. Chem. Soc. 1991, 113, 8831-8839. Evidence for self-
replicative catalysis came from a ca. 40-70% inhancement of the initial
rate when (0.2-0.5 equiv of) amide 3 was added to the reaction mixture
(
at 1.65, 8.2, and 16.5 mM concentrations). The N-methylated analog of 1
showed a ca. 6.5-fold decrease of the background rate, while 2,6-
bis(acetylamino)pyridine which is complementary to Kemp’s imide moiety
of ester 1 inhibited the reaction as well; the rate dropped from 0.01 to 0.0049
observed.1,2 Background and preassociative reaction pathways
mM min-1 at 8.2 mM initial concentration. According to Rebek, three
processes contribute to the formation of the product: the background
bimolecular reaction, the base-paired bimolecular reaction, and the ter-
molecular template-catalyzed reaction (via a termolecular complex). For a
short overview of Rebek’s work, see: Wintner, E. A.; Conn, M. M.; Rebek,
J., Jr. Acc. Chem. Res. 1994, 27, 198-203.
further obscure the actual self-replicating pathway. Even the
precise definition of self-replication is often unclear. For the
further discussion we define self-replication as autocatalysis by
a reaction product which is able to recognize at least two
indiVidual reactants with a high degree of selectiVity. There
are two ways in which the product can catalyze the reaction,
Viz., by preassociation of the reactants with the product, which
enhances their effective molarity, and/or by stabilizing an
intermediate or a transition state leading to product.
(
4) Menger, F. M.; Eliseev, A. V.; Khanjin, N. A. J. Am. Chem. Soc.
1
994, 116, 3613-3614. It was shown that primary amides (e.g., acetamide,
2-naphthamide) and secondary N-methylpropionamide also catalyze the
reaction between 1 and 2. The authors stated that, since Rebek’s template
3
is an amide itself, the reaction is not self-replicating but simply amide-
catalyzed.
(5) Menger, F. M.; Eliseev, A. V.; Khanjin, N. A.; Sherrod, M. J. J.
Org. Chem. 1995, 60, 2870-2878. Although both Rebek et al. and Menger
et al. have used strong arguments defending their mechanisms, some
One self-replicating system, depicted in Scheme 1, has
recently received considerable attention, and it has become a
subject of controversy over the last two years.3 The reaction
(
essential) differences in their experimental approaches should be pointed
-7
out. Firstly, Rebek and Menger used (in most of the cases) different initial
concentration regimes. While Rebek’s experiments were performed at 16.5
mM as a highest concentration, Menger et al. published their amide catalysis
at 30 mM concentration. At the same time, N-methylpropionamide when
tested at 8 mM failed to accelerate the reaction. This point is important
since whole the process involves hydrogen-bonding aggregation and
therefore is (highly) concentration dependent. In addition, at higher
concentrations, general base catalysis by (simple) amides cannot be
X
Abstract published in AdVance ACS Abstracts, June 15, 1996.
(1) (a) von Kiedrowski, G. Angew. Chem., Int. Ed. Engl. 1986, 25, 932-
9
35. (b) von Kiedrowski, G.; Wlotzka, B.; Helbing, J.; Matzen, M.; Jordan,
S. Angew. Chem., Int. Ed. Engl. 1991, 30, 423-426. (c) Terfort, A.; von
Kiedrowski, G. Angew. Chem., Int. Ed. Engl. 1992, 31, 654-656. (d)
Sievers, D.; von Kiedrowski, G. Nature 1994, 369, 221-224.
8
(2) For timely reviews on the problem, see: (a) Hoffmann, S. Angew.
excluded. Secondly, Rebek et al. used the HPLC technique and Menger et
Chem., Int. Ed. Engl. 1992, 31, 1013-1016. (b) Orgel, L. E. Acc. Chem.
Res. 1995, 28, 109-118.
al. employed NMR spectroscopy. Thirdly, Menger et al. never tested Rebek’s
model compounds (e.g., 6-8).
S0002-7863(96)00324-1 CCC: $12.00 © 1996 American Chemical Society

Kinetic Analysis of the Rebek Self-Replicating System
J. Am. Chem. Soc., Vol. 118, No. 29, 1996 6881
Scheme 1
Chart 1
reactions are incorporated. Despite all discussions we feel that
the kinetics of the reactions involved has not received the
attention it deserves. Although kinetics cannot prove a mech-
anism, proper kinetic data can help to unravel the different
pathways that lead to product at different concentrations of
reagents, products, and additives.
Results and Discussion
First, we have synthesized the amines, esters, and “templates”
which may have one or two binding sites (including a novel
adenosine derivative) and which are needed for the evaluation
of the basic reaction between the pentafluorophenyl ester 1 and
the 5′-aminoadenosine derivative 2 in the presence of their
reaction product (the template) 3.
1
Second, we have measured by H NMR spectroscopy the rates
of product formation for different reactants in the absence and
in the presence of 3 and of other additives.
bond formation. In two recent papers Menger et al.4,5 have
Third, we have developed a kinetic scheme in which all
relevant reactions are included together with the complexation
equilibria in which up to four components participate. From
this model and the experimental data on product formation we
have calculated the rate constants of five different pathways
that may lead to product. With these rate constants and initial
compositions of the different reaction mixtures we have
calculated the individual contributions of these five pathways
to the product formation. The same parameters have also been
used to calculate the overall product formation as a function of
time.
reported, on the basis of a series of their own independent
experiments with the same system, that another mechanism
might also explain the observed rate enhancement. They
postulated either “simple” amide catalysis or a pathway that
involves a bimolecular reaction between the ester (1 or 4) and
the bimolecular complex (2‚3) of the product 3 with the amine
2
(Scheme 1). In this case one recognition site in the product
would be sufficient to explain the observed rate acceleration of
the amide formation. Menger et al. hypothesized that the
secondary trans-amide fragment in the product might play a
role in stabilizing the tetrahedral intermediate or assist in the
rate-determining step of pentafluorophenol release. Amides are
known to (auto)accelerate aminolysis by stabilizing a tetrahedral
zwitterionic intermediate by hydrogen bonding between the
Finally, we have compared our results with some relevant
experiments described by the groups of Rebek and Menger.
Synthesis. Studying the self-replicating scheme, we first
prepared reactants which possess hydrogen-bonding sites. Thus,
3
8
pentafluorophenyl ester 1 with Kemp’s triacid imide moiety
zwitterionic NH and CdO of the amide group.
9
and 5′-aminoadenosine 2 were synthesized according to known
In this paper, we report our results with this self-replicating
system based on our independent experiments and a kinetic
analysis of the process in which all relevant equilibria and
procedures. Template 3 was prepared from the corresponding
3
acid chloride and 5′-aminoadenosine 2, and also isolated in
9
2% yield after the reaction between 1 and 2. The nonbinding
5
(6) In a later communication, Rebek et al. demonstrated that not all
ester 4 (also called the “crippled” ester or reactant) was
amides do accelerate the reaction of 1 and 2. Thus, model compounds 6-8
which have the structural fragments of template 3, namely, trans-secondary
amide, Kemp’s imide, and adenosine, respectively, show no catalysis in
the reaction between 1 and 2 when the reactions are performed at 2.2 mM
initial concentration. Since there is no primary amide function present in
the reaction mixture, acetamide and 2-naphthamide were rejected as incorrect
models. See: Conn, M. M.; Wintner, E. A.; Rebek, J., Jr. J. Am. Chem.
Soc. 1994, 116, 8823-8824.
synthesized and used as a substrate for the model reaction with
7
5′-aminoadenosine 2. Crippled templates 6-8 (Chart 1) which
only partly have the structural fragments of template 3, namely,
the trans-secondary amide in 6, Kemp’s imide in 7, and the
adenosine residue in 8, respectively, were synthesized in order
to study their influence on the reaction between esters 1 and/or
4 and amine 2. Finally, in addition to crippled ester 4, we have
(
7) Wintner, E. A.; Tsao, B.; Rebek, J., Jr. J. Org. Chem. 1995, 60, 7997-
001.
8) See, for example: (a) Titskii, G. D.; Litvinenko, L. M. Zh. Gen.
8
(
(9) Kolb, M.; Danzin, C.; Barth, J.; Claverie, N. J. Med. Chem. 1982,
25, 550-556. For the review on Mitsunobu reaction see: Mitsunobu, O.
Synthesis 1981, 1-28.
Chem. USSR (Russ. Ed.) 1970, 40, 2680-2688. (b) Su, C.-W.; Watson, J.
J. Am. Chem. Soc. 1974, 96, 1854-1857.

6
882 J. Am. Chem. Soc., Vol. 118, No. 29, 1996
Reinhoudt et al.
Scheme 2a
Table 1. Initial Rates of the Reaction between the Ester 1 (4) and
the Amine 2 (9) in the Absence and Presence of Additives in CDCl
3
at Different Initial Concentrationsa
reactants
concn, mM)
additive
(concn, mM)
obsd
relative rate
(% of blank)
(
initial rateb
1, 2 (8.25)
1, 2 (8.25)
1, 2 (8.25)
1, 2 (16.5)
1, 2 (16.5)
1, 2 (16.5)
1, 2 (16.5)
1, 2 (16.5)
1, 2 (16.5)
1, 2 (16.5)
1, 2 (30.0)
1, 2 (30.0)
1, 2 (50.0)
4, 2 (16.5)
4, 2 (16.5)
4, 2 (16.5)
4, 2 (16.5)
4, 2 (30.0)
4, 2 (30.0)
1, 9 (16.5)
1, 9 (16.5)
none
1.4
2.0
1.2
4.1
5.7
5.9
6.2
4.2
4.3
3.7
12.9
16.3
47.0
0.6
1.6
1.8
1.0
3.3
7.4
0.9
1.0
100
143
86
100
139
144
151
102
105
90
3 (4.12)
6 (4.12)
none
3 (8.25)
3 (11.55)
3 (16.5)
6 (8.25)
7 (8.25)
8 (8.25)
none
3 (30.0)
none
none
3 (8.25)
3 (16.5)
7 (8.25)
none
3 (30.0)
none
100
126
100
267
300
167
100
224
100
111
3 (8.25)
a
a
1
b
Conditions: (a) acetone, p-TsOH, rt; (b) HNEt
2
, EtOH, reflux; (c)
Determined by H NMR at 25 °C. Data collected during the first
-
1
5
phthalimide, DAC, PPh
3
, THF, rt; (d) H NNH OH, EtOH, reflux.
2
3
100 min. Rates in M‚min × 10 ((10%). Average rate over the
first 100 min.
synthesized the novel crippled 5′-aminoadenosine 9 in which
the adenyl amino group bears two ethyl moieties and therefore
is unable to form hydrogen bonds (Scheme 2). Isopropylidene
riboside 11 was synthesized from the corresponding 6-chloro-
purine riboside 10 by reaction with acetone in the presence of
p-toluenesulfonic acid monohydrate followed by aminolysis
with diethylamine in refluxing ethanol. Subsequent Mitsunobu
reaction with triphenylphosphine, phthalimide, and diethyl
azodicarboxylate (DAC) in THF afforded the corresponding
phthalimide derivative 12 which after subsequent refluxing with
hydrazine hydrate in ethanol gave pure 9.
time plot of the data collected during the first 100 min and were
obtained by linear least squares analysis. Our results are
presented in Table 1.
1
2
The initial rate for the reaction between 1 and 2 at 8.25 mM
-
1
is 0.014 mM min . In the presence of 0.5 equiv of template
10
-1
3
the initial rate increased by 43% to 0.020 mM min . trans-
Amide 6 when added to the reaction mixture slightly inhibited
-
1 13
the process (initial rate 0.012 mM min ). At 16.5 mM the
reaction of 1 and 2 produced 3 with an initial rate of 0.041
-
1
mM min . In the presence of 0.5, 0.7, and 1.0 equiv of
template 3 the initial rate increased by 39, 44, and 51%,
Kinetics Studies. All kinetic experiments were performed
-1
respectively ([3] ) 0.057, 0.059, and 0.062 mM min ,
1
using H NMR spectroscopy in CDCl3 containing 4 equiv of
respectively). trans-Amide 6 as well as both individual ends
of the template (7 and 8), when added to the reaction mixture,
Et3N as a base, at 25 °C.11 Reactions of amine 2 and
pentafluorophenyl esters 1 and 4 were studied at 8.25, 16.5,
exhibited no catalytic activity; initial rates of 0.042, 0.043, and
3
0, and (in one case) 50 mM concentrations. In experiments
-1
0
.037 mM min , respectively, were found.
where templates, crippled templates, or other additives were
used, either 0.5 or 1.0 mol equiv was employed. Generally,
ribose signals were monitored, but in some cases naphthyl
signals were additionally employed. Evaporative loss was
excluded. All reactions were followed until g95% conversion.
The reaction product amide 3 was also isolated in 92% yield
on a preparative scale after reaction of 1 and 2. We have neVer
observed byproducts, and pentafluorophenyl ester hydrolysis was
not detected. In addition, we used toluene as an internal
standard for the determination of conversion. In order to
compare our results with those published in the literature, the
The reaction between 2 and 4 at 16.5 mM gave a surprisingly
-1
low initial rate of 0.006 mM min , which is 6.8 times lower
14
than for the reaction of 1 and 2. In the presence of 0.5 and
1
2
.0 equiv of template 3 the initial rates of the reaction between
-1
and 4 significantly increased to 0.016 and 0.018 mM min
which means 167 and 200%(!) rate enhancement, respectively.
However, the absolute rate Values are still, respectively, 3.6
and 3.4 times lower than for the reaction of 1 and 2 catalyzed
(
12) The initial rates from our experiments were calculated from
3
4
conversion during the first 100 min. Rebek and Menger published the
initial rates obtained from data collected after 60 and 40 min, respectively.
Strictly speaking, however, product formation is not linear in time, the
deviation being dependent on concentration, the composition of the reaction
mixture, and conversion. Therefore, the initial rates obtained from conversion
Vs time plots are generally somewhat lower than the “true” initial rates,
i.e., (dP/dt)t)0. We calculated the latter on the basis of corresponding kinetic
equations from the composition of the mixtures at time t ) 0 and the
determined reaction rate constants. Therefore, the initial rates can only be
used to compare relatiVe catalytic trends.
“
initial rates” were defined as the slope of the conversion Vs
(
10) Hampton, A. J. Am. Chem. Soc. 1961, 83, 3640-3645.
(11) Both Rebek et al. and Menger et al. reported no specific purification
of CDCl3, and therefore we have used for all our experiments spectroscopic
quality CDCl3 (Merck) which was passed through Al2O3 and stored over
molecular sieves before use. It should be realized that small amounts of
protic solvents (H2O, EtOH, phenols, etc.) might influence the absolute
values of association constants. However, we needed values of association
constants under reaction conditions, and therefore those values were
determined in the same CDCl3 which was used in all kinetic experiments.
(13) Essentially higher than observed by Rebek et al. initial rates at 8.25
mM can be reasonably explained by hydrolysis which (for some reason)
took place under their conditions (yielding only ca. 65% of 3 after >1500
min). See ref 3b.
3
Rebek et al. observed, in addition to broad NH resonances, overlapping
1
multiplets which did not allow him to follow kinetics by H NMR
(14) Menger et al. did not run the reaction 2 + 4 at 16.5 mM
4
,5
1
19
-1
spectroscopy. In contrast, Menger et al. used both H and F NMR
techniques with reasonable accuracy. We also observed sharp and well-
concentration but observed a 0.0018 mM min rate at 8.2 mM which is
5.6 times lower than the rate Rebek et al. reported at 8.2 mM for the reaction
between 1 and 2. See ref 5.
1
resolved H NMR spectra at 8.25, 16.5, and 30 mM concentrations.

Kinetic Analysis of the Rebek Self-Replicating System
J. Am. Chem. Soc., Vol. 118, No. 29, 1996 6883
Scheme 3
amine 2 (A) in the presence of template 3 (T). When either E
or A has no hydrogen-bonding sites as in a number of model
reactions described in this paper, we can simply incorporate
these situations by taking the corresponding association con-
stants as zero. Firstly, we consider a mixture containing an
amine component A (equipped with a hydrogen-bonding site)
and an ester component E (equipped with a complementary
hydrogen-bonding site) in the presence of a template T, being
nonreactive, and bearing both the hydrogen-bonding sites.
When we restrict the system to complexes composed of at most
1
6
four species, the following equilibria become established:
A + E a A‚E
A + T a A‚T
E + T a E‚T
K
K
K
K
K
K
K
K
1
E + T‚T a E‚T‚T
T + T‚T a T‚T‚T
K
K
K
K
K
K
K
K
11
12
13
14
15
16
17
18
2
3
T‚T‚T a T
3
A + E‚T a A‚T‚E
E + A‚T a A‚T‚E
T + T a T‚T
4
E + A‚T‚T a A‚T‚T‚E
A + E‚T‚T a A‚T‚T‚E
T + A‚T‚T a A‚T‚T‚T
T + E‚T‚T a E‚T‚T‚T
T + T‚T‚T a T‚T‚T‚T
5
8
T‚T a T
2
9
A + T‚T a A‚T‚T
10
3
Rebek et al. used a dimerization constant for the template, and
an association constant for the ternary complex; they are related
to the above through
T + T a T2 K ) K K
8 9
6
A + E + T a A·T·E
K ) K K ) K K
7 3 4 2 5
In general amine A reacts with ester E to give the product
amide P (A, E, and P may have hydrogen-bonding group(s) or
not; when A is 2 and E is 1, product P is template 3). When
the equilibrated mixture is allowed to react, the following
reactions have to be taken into account. Firstly, we define the
background reaction as the bimolecular reaction between A and
E in the case that these components would lack (or do not use)
the hydrogen-bonding properties:
by 3. The crippled template Kemp’s imide 7, which can only
form a complex with amine 2, also accelerated the reaction with
-
1
a rate of 0.010 mM min ; this corresponds to a 67% increase.
Similarly, we found that the reaction between ester 1 and the
crippled 5′-aminoadenosine 9 is slow with an initial rate of 0.009
-1
mM min at 16.5 mM concentration. Surprisingly, the addition
of 0.5 equiv of template 3 did not (significantly) accelerate the
-
1
reaction between 1 and 9; the rate was 0.010 mM min .
As expected, the reaction of 1 and 2 was considerably faster
at higher concentrations with initial rate values of 0.129 mM
A + E f P
k1
-
1
-1
In addition to the background reaction, the bimolecular A‚E
complex may internally form product P:
min at 30 mM and 0.47 mM min at 50 mM, respectively.
The addition of 1.0 equiv of 3 gave, at 30 mM 1 and 2, a rate
-
1
of 0.163 mM min (increase of 26%).
A·E f P k2
A mixture of 30 mM 2 and 4 reacted with an initial rate of
-
1
0
.033 mM min to yield 5. The addition of 1.0 equiv of 3
The termolecular complex A‚T‚E may also directly form product
P through
-
1
resulted in an initial rate of formation of 5 of 0.074 mM min
(increase of 124%). We have eliminated the possibility that
the reactivities of the pentafluorophenyl esters 1 and 4 might
be different. A competition experiment utilizing equimolecular
quantities of n-butylamine and of both esters 1 and 4 in CDCl3
with 1% Et3N as a base showed no preference for one of the
esters; the corresponding amides 13 and 14 were formed in a
ratio of ca. 1:1 (Scheme 3). The analogous competition
experiment with equimolecular quantities of the aminoadenosine
A·T·E f P·T
k3
Furthermore, the possibility exists that the template activates
the bonded substrate A in components such as A‚T for the
bimolecular reaction with free E:
E + A·T f PT
k4
2
and of the esters 1 and 4 in CDCl3 with 1% Et3N as a base
exhibited a preference for the ester which has Kemp’s imide
moiety (1). The corresponding amides 3 and 15 were formed
in a ratio of ca. 4.5:1 (Scheme 3).
We conclude that esters 1 and 4 behave differently because
ester 1 binds amine 2 and ester 4 does not. The base-paired
bimolecular reaction is essentially faster and takes place when
both reactants have recognition sites.15
The same reasoning as given above for the activated A‚T
fragment could in principle be given for E‚T as well:
A + E·T f P·T
k5
In order to calculate the concentrations of all species present
before and during the reaction, association constant K was
1
1
determined by H NMR spectroscopy in CDCl3 using Kemp’s
Kinetic Modeling (see also the supporting information).
Basically our model describes the reaction of ester 1 (E) and
ester 1 and a nonreactive acetyladenosine, 16 (Figure 1). Since
in our hands the imide NH proton, which was used as a probe
(15) This is in agreement with Rebek’s observation that the nonbinding
N-methylated analog of 1 showed a ca. 6.5-fold decrease of the background
rate. In fact, Rebek used the latter reaction as the background reaction in
his kinetic modeling.
(16) The results show that, with the current set of parameters, the
concentrations of species composed of four components are very low up to
50 mM concentration.

6
884 J. Am. Chem. Soc., Vol. 118, No. 29, 1996
Reinhoudt et al.
3
Figure 2. Dilution curve of template 3 in CDCl : experimental points
and the theoretical curve.
The value of 100 M- (corrected for statistical factors where
appropriate) was subsequently used for all interactions between
the same unrestricted hydrogen-bonding sites.
1
Dimerization of template 3 was studied in detail (see Figure
1
).1 The general equilibrium scheme presented above was used
8
to calculate the concentrations of the species T, TT, TTT, TTTT,
T2, and T3 as a function of total template concentration. The
observed chemical shift of the mixture is
δobsd ) ffreeδfree + f δ + fcyclicδcyclic
lin lin
with
ffree ) ([T] + [TT] + [TTT] + [TTTT])/[T0]
flin ) ([TT] + 2[TTT] + 3[TTTT] + 3[T ])/[T ]
3
0
fcyclic ) 2[T ]/[T ]
2
0
The chemical shifts correspond to the free template T (δfree), to
the linear oligomers TT, TTT, and TTTT (δlin), and to the cyclic
dimer T2 (δcyclic) ([T0] is the total template concentration). We
assumed that the chemical shift of the cyclic trimer T3 is the
same as in the linear oligomers. For the regression analysis,
-
1
-1
we assumed that K8 ) 200 M , K12 ) K18 ) 100 M , and
K13 ) 0.1K9. Subsequent multilinear regression analysis
according to the equation for δobsd with K9 and the three
-
1
chemical shifts as variables gave a value of 0.3 M for K9 and
yielded reasonable values for the unknown chemical shifts: δfree
2
0
)
5.65, δlin ) 7.13, and δcyclic ) 7.02. Agreement between
theory and experiment is very good (see Figure 2). This result
implies that the formation of the cyclic dimer is an unfavorable
process. Our calculations show that, at a 5-10 mM concentra-
tion of 3 (which is normally the case), ca. 41-30% of 3 exists
Figure 1. Base-paired complex of Kemp’s ester 1 and acetyladenosine
6, and cyclic and linear dimers of template 3.
1
(18) Initially, we employed the Horman-Dreux algorithm and calculated
2
-1
a KD value of 1.45 × 10 M from dilution experiments. This is somewhat
lower than that found by Rebek et al.3 (6.3 × 10
2
M
-1
). At this stage,
by Rebek et al.,3,17 undergoes broadening upon titration, binding
studies were performed using as a probe the relatively sharp
adenine NH2 signal. In order to verify our results, the aromatic
signals of the naphthalene moiety were employed in addition.
The concentration of acetyladenosine 16 was kept constant at
-1
assuming that KD ) K6 ) K8K9 (see above) and K8 ) 200 M (value of
-
1
100 M multiplied by a statistical factor of 2), one can conclude that the
-
1
-1
cyclization value itself is rather low; K9 ) 0.73 M (or 3.15 M when
Rebek’s value is used). However, the Horman-Dreux algorithm gives only
an approximate dimerization KD value which characterizes the oVerall
aggregation process including the formation of a cyclic dimer. When there
are aggregates of more than two species, the Horman-Dreux algorithm
cannot correctly describe the dimerization process. See: Horman, I.; Dreux,
1
mM while up to 20 equiv of 1 was added in our titration
experiments. Self-association of 16 will be low at this
19
B. HelV. Chim. Acta 1984, 67, 754-764. Molecular mechanics calculations
suggest that two molecules of 3, being quite flexible, fit much better in the
concentration. The results indeed show hydrogen bonding for
-
1
Kemp’s imide-adenine pair; a K value of 100 ( 10 M was
obtained for 1 + 16 which is in good agreement with the values
linear than in the cyclic dimer structure.
(19) Brooks, B. R.; Bruccoleri, R. E.; Olafsen, B. D.; States, D. J.;
Swaminathan, S.; Karplus, M. J. Comput. Chem. 1983, 4, 187. Quanta was
bought from Molecular Simulations Inc., Burlington, MA.
3
-1
found by Rebek et al. for similar compounds (60-105 M ).
(20) This δfree value is in good agreement with δ values in CDCl3 for
(17) For typical examples from the Rebek group see: (a) Askew, B.;
adenine NH2 protons published in the literature which range from 5.4 to
6.4 ppm. See, for example: Pieters, R. J.; Huc, I.; Rebek, J., Jr. Tetrahedron
1995, 51, 485-498. In the N-methylimide analog of 3, which is not able to
dimerize, the NH2 signal of the adenine fragment is found at 5.69 ppm; see
ref 3b.
Ballester, P.; Buhr, C.; Jeong, K. S.; Jones, S.; Parris, K.; Williams, K.;
Rebek, J., Jr. J. Am. Chem. Soc. 1989, 111, 1082-1090. (b) Williams, K.;
Askew, B.; Ballester, P.; Buhr, C.; Jeong, K. S.; Jones, S.; Rebek, J., Jr. J.
Am. Chem. Soc.1989, 111, 1090-1094.

Kinetic Analysis of the Rebek Self-Replicating System
J. Am. Chem. Soc., Vol. 118, No. 29, 1996 6885
Figure 5. Generation of product for the reaction 1 + 9 in the presence
of 0.5 equiv of 3 as a function of time.
Figure 3. Generation of product for the reactions 2 + 4 and 1 + 9 as
a function of time.
Figure 6. Generation of product for the reaction 1 + 2 in the absence
of template 3 as a function of time.
Figure 4. Generation of product for the reaction 2 + 4 in the presence
of 0.5 equiv of 3 as a function of time.
as the monomeric open form (T) along with 34-36% of 3‚3
(TT), and 10-11% of cyclic dimer (T2), linear trimer (TTT),
etc.
The overall initial rate of reaction between A and E in the
presence of template T can be given by
dP/dt ) k [A ·E ] + k [A·E] + k [A·T·E] +
1
o
o
2
3
k [E ]([A ] - [A] - [A·E]) + k [A ]([E ] - [E] - [A·E])
4
o
o
5
o
o
A. Background Reaction. The rate constant k1 ) 0.035
M- min for the background reaction could be obtained from
normal second-order plots of 2 + 4 and 1 + 9 reactions (when
measured at 16.5 mM concentration) (Figure 3). This value is
1
-1
Figure 7. Generation of product for the reaction 1 + 2 in the presence
of 0.5 equiv of 3 as a function of time.
in fair agreement with Rebek’s value of k1 ) 0.023 M- min
1
-1
3
obtained for compound 2 and the N-methylated analog of 1.
B. Activated Bimolecular Reaction between A‚T and E.
Reacting genuine A (possessing a hydrogen-bonding site) with
a nonbinding analog of E in the presence of 0.5 equiv of
template requires that K1 ) K3 ) K4 ) K5 ) K7 ) K11 ) K14
sion curves (Figure 5) over a time interval of 200 min gave an
-
1
-1
optimum value of k5 ) 0.020 M min .
D. Preassociative Mechanism. Under conditions where
components A and E react in the absence of template, the
relevant equilibrium constants are K1 ) K2 ) K3 ) K4 ) K5 )
-
1
)
K15 ) K17 ) 0 M with K2 ) K10 ) K12 ) K16 ) K18 )
-
1
-
1
-1
-1
-1
K10 ) K11 ) K12 ) K14 ) K15 ) K16 ) K17 ) K18 ) 100 M ,
1
00 M , K8 ) 200 M , K9 ) 0.3 M (K6 ) 60 M ), K13 )
.03 M , and k1 ) 0.035 M min . The formation of the
-
1
-1
-1
-
1
-1
-1
K8 ) 200 M , K9 ) 0.3 M (K6 ) 60 M ), K7 ) 10 000
0
-
2
-1
M , and K13 ) 0.03 M with the already determined rate
product was calculated as a function of time, assuming that all
equilibria are fast compared to the chemical reactions, for
different values of k4. From curve-fitting of the theoretical and
experimental curves (Figure 4) over a time interval of 200 min,
-
1
-1
-1
-1
constants k1 ) 0.035 M min , k4 ) 0.130 M min , and
-
1
-1
k5 ) 0.020 M min . Curve-fitting of the theoretical and
experimental conversion (200 min) curves (Figure 6) led to an
-
1
-
1
-1
21
optimum value of k2 ) 0.0044 min .
the optimum value of k4 ) 0.130 M min was obtained.
E. Reaction of the Termolecular Complex. With the same
C. Bimolecular Reaction between E‚T and A. In the same
way as described above, the reaction of a crippled A and the
genuine ester E in the presence of template can be restricted by
parameter values as given above, and the newly determined
-
1
reaction rate constant k2 ) 0.0044 min , the theoretical
conversion curves were calculated for the reaction between A
and E in the presence of 0.5 equiv of template for various values
-
1
K1 ) K2 ) K4 ) K5 ) K7 ) K10 ) K14 ) K15 ) K16 ) 0 M
-
1
-1
with K3 ) K11 ) K12 ) K17 ) K18 ) 100 M , K8 ) 200 M ,
-
1
-1
-1
of k . Least squares analysis gave an optimum value of k )
K9 ) 0.3 M (K6 ) 60 M ), K13 ) 0.03 M , and k1 ) 0.035
3
3
-
1
-1
-1
0.030 min (see Figure 7).
M
min . The fitting of theoretical and experimental conver-
Predictions of Initial Rates Based on the Model. The
model has been used to calculate the composition of the mixture
of 1 and 2 with additives as a function of starting conditions
(
21) Theoretical curves were calculated on the basis of the model derived
in the supporting information, on a normal PC using Lotus 123 software.
Conversion as a function of time was calculated taking 4 min intervals.

6
886 J. Am. Chem. Soc., Vol. 118, No. 29, 1996
Reinhoudt et al.
Chart 2
Table 2. Calculated Initial Rates for Equimolar Amounts of
and 2a
and time. In all cases, the above derived rate constants were
used for the pathways depicted in Chart 2: background via I
1
-
1
-1
contribution to
initial rate (%)
(
0
k1 ) 0.035 M min ), preassociatiVe via complex II (k2 )
-
1
.0044 min ), termolecular via complex III (k3 ) 0.030
min ), actiVated bimolecular via complex IV (k4 ) 0.130 M
min ), and bimolecular via complex V (k5 ) 0.020 M min ).
[2]o
[1]o
[3]o (dP/dt)calcd (dP/dt)obsdb
I
II III IV
V
-1
-1
-1
-1
-1
1.67 1.67
0.10
9.5 90.5 0.0 0.0 0.0
7.0 56.4 33.7 2.5 0.4
10.1 89.9 0.0 0.0 0.0
7.2 52.5 36.8 3.0 0.5
15.8 84.2 0.0 0.0 0.0
10.7 46.6 36.9 5.0 0.8
9.6 35.8 45.9 7.5 1.2
21.9 78.1 0.0 0.0 0.0
27.7 72.3 0.0 0.0 0.0
27.7 72.3 0.0 0.0 0.0
13.7 38.3 38.5 8.3 1.3
12.9 33.2 42.4 10.0 1.5
12.2 28.1 45.7 12.2 1.9
29.7 70.3 0.0 0.0 0.0
17.4 31.1 37.2 12.5 1.9
15.2 22.0 42.2 17.9 2.8
38.3 61.7 0.0 0.0 0.0
21.2 25.3 33.8 17.2 2.6
18.2 17.0 37.1 24.0 3.7
1
2
2.2
8
8
8
.67 1.67 1.67
0.14
0.17
0.24
1.5
2.2
2.5
4.4
6.9
6.9
6.9
7.4
7.8
10.6
18.2
20.7
22.9
41.3
48.1
In the case where both starting compounds A and E have a
hydrogen-bonding site, which is the case for 2 and 1, the relevant
equilibrium constants are (Vide supra): K1 ) K2 ) K3 ) K4 )
K5 ) K10 ) K11 ) K12 ) K14 ) K15 ) K16 ) K17 ) K18 ) 100
.2
2.2
2.2
8.2
8.2
8.2
2.2
.2
.2
.2
1.4
2.0
4.1
8.2
-
1
-1
-1
-1
M , K8 ) 200 M , K9 ) 0.3 M , K6 ) 60 M , K7 ) 10 000
4.1c
1
6.5 16.5
16.5 33.0
-
2
-1
M , and K13 ) 0.03 M . The calculated initial rates (dP/
dt)t)0 and also the contribution (%) of the different pathways
8.2
7.9
5.7
3
1
1
1
3.0 16.5
6.5 16.5
6.5 16.5 11.5
6.5 16.5 16.5
c
8.2
2
2
via I-V to the product formation are compiled in Table 2.
5.9
6.2
12.9
The results show the following. First of all, the model predicts
the formation of product 3 as a function of time with a
surprisingly good fit with the experimental data in the concen-
tration range up to 30 mM (see Table 2 and Figures 3-7). At
30
30
30
30
50
50
50
3
3
5
5
0
0
0
0
15
30
16.3
47.0
5
0 mM the actual rates are higher than predicted (probably due
25
50
7,8
to general base amide catalysis ). The relative contribution
of the background reaction increases when the concentration
increases at the expense of the preassociative mechanism. The
template effect is highest at 8.25 and 16.5 mM concentrations
50
a
-1
5 b
Concentrations in mM; rates in M‚min × 10 . Average rate over
the first 100 min. Used for parametrization.
23
c
+
(up to 46%). In the presence of an equimolar amount of
involved in hydrogen bonding via a CdO‚‚‚HsN interaction
2
4
template, the contribution of the termolecular complex III to
the initial rate is in the range of 34% (1.67 mM) to 46% (16.5
mM). The contribution of the “amide catalysis” through the
activated complex IV increases with increasing concentration.
The template probably holds a complementary tetrahedral
zwitterion in close proximity to the NHsC(O) group which is
(Figure 8). At 30 mM, it contributes almost 7 times as much
to the overall initial rate than at 1.67 mM. In reactions where
only the amine has a recognition site (e.g., 2 + 4) three of the
five pathways are excluded: the preassociative pathway via II,
the termolecular pathway via III, and the route via bimolecular
complex V. Table 3 shows that the relative contribution of the
pathway via the only possible bimolecular complex IV increases
with concentration (28% at 1.67 mM to 59% at 30 mM).
When only the ester has a recognition site (e.g., 1 + 9), the
preassociative pathway via II, the termolecular pathway via III,
(22) We have tested the sensitivity of the results of our model as a
function of the values for K1, K9, and K6. When we take, e.g., values as
-
1
-1
-1
published by Rebek (K1 ) 60 M , K9 ) 3 M , and K6 ) 360 M ), only
small variations in k2-k5 are found. The relative contributions of I-V to
(
dP/dt)calcd are e4%. Estimated accuracies in the rate constants are as
-
1
-1
-1
follows: k1 ) 0.035 ( 0.005 M min , k2 ) 0.0044 ( 0.0006 min , k3
(24) MM calculations show that in the termolecular complex the distance
-
1
-1
-1
+
)
M
0.03 ( 0.015 min , k4 ) 0.13 ( 0.03 M min , k5 ) 0.02 ( 0.02
between the zwitterionic N sH and the template carbonyl CdO group
-
1
-1
min . These accuracies of k1-k5 lead to upper and lower limits for
might be too large to form a hydrogen bond (>4.5 Å). Therefore, amide
catalysis may be excluded in this case. Rebek et al. have recently published
the similar conclusion; see ref 7. On the other hand, our MM calculation
confirms hydrogen bonding within complex IV (e.g., amide catalysis); the
the ratio k3/k2 of 3.0 and 10.7, respectively.
23) In the so-called “self-replicating molecules of second generation”
(
Rebek et al. forced the reaction to the template-catalyzed mechanism by
restraining the preassociative bimolecular pathway. See: Wintner, E. A.;
Conn, M. M.; Rebek, J., Jr. J. Am. Chem. Soc. 1994, 116, 8877-8884.
+
distance between the zwitterionic N sH and the template carbonyl CdO
group is 1.65 Å in this case.

Kinetic Analysis of the Rebek Self-Replicating System
J. Am. Chem. Soc., Vol. 118, No. 29, 1996 6887
structure of their template (3) for self-replication. On the other
4
,5
hand, Menger et al. concentrated their work on reactions of
crippled esters that lack a recognition site and that form amide
products which are structurally different from 3. They suggested
that simple secondary amides act as catalysts, even at low
4
concentration. It remains possible that at (very) high concen-
trations (g30 mM) nonspecific amide catalysis would play a
7
,8
role. However, such high concentrations are not the case in
our work and in Rebek’s experiments.
Crucial in the subsequent discussion is that both groups try
to disprove the validity of the other experiments. However,
experiments were never done under the same conditions with
the same reactants and additives. As a consequence they
generally interpret their own results correctly without disproving
the conclusions of the other side.
The fact that concentrations of reactants and template(s) are
often low in Rebek’s original work and much higher in Menger’s
experiments is understandable because of the different analytical
techniques used, but is very dangerous in a system that is
governed by a multitude of equilibria among reactants, products,
and additives.
Our approach was to describe this very complex problem in
a (large) matrix of equilibria and reaction pathways. We have
first determined all relevant association processes (and their
constants) either by model experiments or by nonlinear regres-
sion analysis. Subsequently we have reduced all the reactions
in the system to their most simple form and have experimentally
determined the background (k1) and preassociative (k2) rate
constants. In all those cases we had to assume one value for
the equilibrium constants of all species with the same recognition
site, and the same reactivity for free reactants and reactants
complexed into linear associates. From two model reactions
with crippled reactants we have obtained the rate constants k4
and k5 for the formation of the corresponding amides that
proceed via the A‚T + E′ and E‚T + A′ pathways. Therefore,
we have determined all rate constants except that of the self-
replicating termolecular pathway. This crucial rate constant (k3)
is now simply obtained from the reaction between 1 and 2 in
the presence of template 3 by subtracting the contributions of
the other four pathways to the amount of product 3 which is
formed.
Figure 8. Possible tetrahedral zwitterionic intermediates 2 + 4 + 3
1
9
and 1 + 9 + 3 based on MM calculations. The distances between
the amide carbonyl of 3 and the nitrogen proton of the tetrahedral
intermediate are 1.65 and 2.12 Å, respectively.
Table 3. Calculated Initial Rates for Equimolar Amounts of 4 (1)
a
and 2 (9)
contribution to
initial rate (%)
[3]o (dP/dt)calcd (dP/dt)obsdb
[
2]o
.67 1.67
.67 1.67 1.67
[4]o
I
II III IV
V
1
0.0095
100 0.0 0.0 0.0 0.0
72.4 0.0 0.0 27.6 0.0
100 0.0 0.0 0.0 0.0
68.7 0.0 0.0 31.3 0.0
100 0.0 0.0 0.0 0.0
63.9 0.0 0.0 36.1 0.0
52.2 0.0 0.0 47.9 0.0
100 0.0 0.0 0.0 0.0
100 0.0 0.0 0.0 0.0
100 0.0 0.0 0.0 0.0
57.4 0.0 0.0 42.6 0.0
51.5 0.0 0.0 48.5 0.0
45.6 0.0 0.0 54.4 0.0
100 0.0 0.0 0.0 0.0
53.0 0.0 0.0 47.0 0.0
41.5 0.0 0.0 58.5 0.0
100 0.0 0.0 0.0 0.0
50.4 0.0 0.0 49.6 0.0
38.8 0.0 0.0 61.2 0.0
1
2
2
8
8
8
0.0132
0.0169
0.0247
0.24
.2
.2
.2
.2
.2
2.2
2.2
8.2
8.2
8.2
2.2
4.1
8.2
0.37
0.45
0.95
0.6c
1
1
3
1
1
1
3
3
3
5
5
5
6.5 16.5
6.5 33.0
3.0 16.5
6.5 16.5
1.91
1.91
1.66
The final test of our model is the correct prediction of product
formation Vs time for different sets of experiments with Rebek’s
original system and Menger’s model experiments (see Tables
2 and 3 and Figures 3-7).
8.2
1.6c
6.5 16.5 11.5
6.5 16.5 16.5
1.85
2.09
3.15
1.8
3.3
0
0
0
0
0
0
30
30
30
50
50
50
15
30
5.94
7.60
Our results can be briefly summarized as follows:
7.4
(
i) The experiments of Rebek et al. and Menger et al. are
basically correct (but are in different concentration regimes).
ii) We have identified five different pathways that lead to
8.75
25
50
17.40
22.60
(
contribution to
initial rate (%)
product (three are bimolecular and two are unimolecular). Their
individual contributions to product formation are strongly
concentration dependent.
[
9]o [1]o [3]o (dP/dt)calcd (dP/dt)obsdb
I
II III IV
V
1
1
6.5 16.5
6.5 16.5 8.25
0.95
1.06
0.9
1.0
100.0 0.0 0.0 0.0 0.0
89.8 0.0 0.0 0.0 10.2
(iii) In agreement with Menger et al., the bimolecular pathway
A‚T + E (k4) has been identified as a major contributor in
reactions between 2 and 4. However, for reactions between 1
and 2 its contribution is small at concentrations e16.5 mM and
can be virtually neglected at the concentrations that were used
by Rebek et al. Only at 50 mM the contribution increases to
24%.
a
-1
5 b
Concentrations in mM; rates in M‚min × 10 . Average rate over
c
the first 100 min. Used for parametrization.
and the route via bimolecular complex IV are excluded. Since
k5 is low, there is hardly any contribution to the pathway via V
(
10%).
(iv) The other bimolecular pathway E‚T + A (k5), ignored
by both Menger and Rebek, hardly contributes (e4%) over the
entire concentration range (1.67-50 mM). Both bimolecular
pathways must have similar transition states or tetrahedral
intermediates. Still there is a large difference in rate (k4 ) 0.130
Comparison with the Work of the Rebek and Menger
Groups. Although the experiments described in this paper are
very similar, our approach is essentially different from those of
Rebek and Menger. Rebek et al.3
,6,7
focused on different
-
1
-1
-1
-1
template structures in order to prove the importance of the
M
min , k4/k1 ) 3.7, and k5 ) 0.020 M min , k5/k1 )

6
0
888 J. Am. Chem. Soc., Vol. 118, No. 29, 1996
Reinhoudt et al.
.6). We can only conclude that in the reaction A‚T + E the
obscure the simple picture of a ternary complex as the only
complex that leads to the enhancement. It would be interesting
to analyze other self-replicating systems reported in the litera-
ture in the same way because reactions via the bimolecular
complexes, e.g., pathways via IV and V, may also play a role
amide moiety (or another structural element of T) is precisely
positioned for catalysis but that structural requirements are very
+
1,2
critical for the N sH‚‚‚OdC distance. Apparently, in the
“
mirror” reaction E‚T + A this specific stereochemistry cannot
be met (see Figure 8). This means that an amide bond in the
template cannot be the only source of catalysis.
there.
(v) In agreement with Rebek et al., there is a kinetically
Experimental Section
favorable pathway via the termolecular complex A‚T‚E that
contributes 34-46% to product formation (depending on
concentration). When we compare the rates of both unimo-
lecular reactions, e.g., the preassociative pathway (k2 ) 0.0044
1H, 13C, and COSY NMR spectra were recorded in CDCl
as the internal standard at 25 °C unless stated otherwise. CDCl
passed through Al and stored over molecular sieves (4 Å) before
use. Ion fast atom bombardment (FAB) mass spectra were obtained
with m-nitrobenzyl alcohol as a matrix. CH Cl and CHCl were
with TMS
was
3
3
2
O
3
-
1
-1
min ) and the termolecular pathway (k3 ) 0.030 min ), the
ratio k3/k2 is 6.8! With the accuracies in the values of k1-k5
2
2
3
distilled from CaCl and stored over molecular sieves (4 Å). Hexanes
2
(see ref 22) the lower and upper limits of the value of k3/k2 are
refer to the fraction with bp 40-60 °C. Other chemicals were of reagent
grade and were used without purification. Column chromatography
was performed with silica gel (Merck; 0.040-0.063 mm). All reactions
3
.0 and 10.7, respectively. In our opinion this factor reflects
the rate enhancement of the reaction between 1 and 2 when 3
is present (self-replication). Both reactants always have comple-
mentary binding sites, and when they associate this leads to
reaction when the geometry of the associate allows the reactive
groups a close proximity. When both reactants associate with
the product 3 and subsequently react faster, this can be defined
as genuine autocatalysis Via self-replication. On the basis of
our results, we can conclude that this is the case in the Rebek
system. To what extent this pathway contributes to the total
product formation depends on the concentrations of 1, 2, and 3
and on the rate constants k1-k5 for the five different pathways
3
,5,9
were carried out in an argon atmosphere. Compounds 1-4
and
7
6
-8 were synthesized according to literature procedures and stored
under an argon atmosphere. Compound 3 was also obtained in 92%
yield by reaction of equimolecular amounts of pentafluorophenyl ester
1
and the 5′-aminoadenosine 2 and 4 equiv of Et
CHCl (24 h, 25 °C). The organic layer was washed with 1 N HClaq
and H , and evaporated to afford pure 3.
O (2×), dried over MgSO
Binding studies were performed in CDCl at 25 °C. An association
3
N as a base in dry
3
2
4
3
constant value between acetyladenosine 16 and Kemp’s ester 1 was
determined at a constant concentration of 16 of 1 mM and a varying
concentration of 1 of 0.5-20 mM. The chemical shifts of the adenine
2
NH signal and naphthalene protons were used as a probe. The Kass
(see Table 2).
value was obtained with a nonlinear two-parameter fit of the chemical
shift and the association constant.25 The results gave good fits for a
typical 1:1 stoichiometry as could be concluded from the function
values.25 Self-association experiments with template 3 were performed
(vi) Crucial in the Rebek-Menger debate is the comparison
of rate enhancement factors between reactions with and without
template. Whereas Rebek et al. reported a 40-70% rate
increase upon the addition of template 3 to a mixture of 1 and
by following the chemical shift of the adenine NH
concentration of 1-60 mM.
2
signal of 3 at a
2
(reactions that have both recognition sites), Menger et al.
18
reported rate enhancements of 55% when 3 was added to a
mixture of nonbinding ester 4 and amine 2. Our results show
clearly how dangerous it is to use rate enhancement factors for
comparison. When in model reactions at 16.5 mM one of the
reactants has no binding site (e.g. Menger’s 2 + 4), the absolute
rate is a factor of ca. 7 lower than for the reaction 1 + 2. When
template 3 is added, only one of the bimolecular pathways (k4)
can operate in addition to the background reaction (k1), but this
still results in a rate enhancement of 167-200% (see Table 1).
However, this cannot be compared with the rate enhancement
when template 3 is added to the mixture of 1 and 2 that both
have a recognition (binding) site. In that case the blank reaction
is the result of two pathways, Viz., background (k1) and
preassociative (k2) mechanisms. In the presence of template 3
all fiVe pathways (k1-k5) participate. For Menger’s reaction
the rate enhancement factor is given by
Aminolysis reactions were carried out by dissolving appropriate
amounts of pentafluorophenyl ester and amine (and an additive if used)
in CDCl containing 4 equiv of Et N. Et N was freshly distilled over
3 3 3
NaOH before use. Spectra were recorded after equal time intervals.
Integrations were performed in the absolute intensity mode and using
toluene as an internal standard. All measurements were performed at
least twice, showing a good reproducibility. The results are collected
in Table 1.
Molecular mechanics (MM) calculations of structures 1-16, their
complexes, and the zwitterionic intermediates were performed with
1
9
Quanta 3.3. The MM calculations were run with CHARMm 22.0,
as implemented in the Quanta/CHARMm package. Energy minimiza-
tions (conjugate gradient) were carried out (steepest descents followed
by adopted based Newton-Raphson) until the root mean square of the
-
1
gradient was less than 0.01 kcal M Å.
6
2′,3′-(1-Methylethylidene)-N ,N-diethyladenosine (11). p-Tolu-
enesulfonic acid monohydrate (6.60 g, 35.0 mmol) was added to a
magnetically-stirred suspension of 6-chloropurine riboside 10 (Aldrich)
(
1.00 g, 3.5 mmol) in anhydrous acetone10 (150 mL). The resulting
[
k [A ·E ] + k [E ]([A ] - [A] - [A·E])]/k [A ·E ]
1 o o 4 o o 1 o o
solution was stirred for 1 h at rt and subsequently added to a vigorously
stirred solution of NaHCO (6.7 g, 80 mmol) in ice and water (80 mL).
3
In Rebek’s reaction this rate enhancement factor is given by
The mixture was evaporated to dryness under reduced pressure, and
the residual solid was extracted with acetone (2 × 100 mL). The
solvent was evaporated, and the residual oil was refluxed with
diethylamine (50 mL) in EtOH (150 mL) overnight. Solvent was
evaporated, and the residue was redissolved in hot water (50 mL). After
1 h the oil was separated and recrystallized from hexanes to afford
[k [A ·E ] + k [A·E] + k [A·T·E] +
1 o o 2 3
k [E ]([A ] - [A] - [A·E]) +
4
o
o
k [A ]([E ] - [E] - [A·E])]/[k [A ·E ] + k [A·E]]
5
o
o
1
o
o
2
1
colorless needles (0.5 g, 39%): mp 114 °C (hexanes); H NMR δ 8.23,
(
see also the supporting information). From these two ratios it
7.71 (2 s, 2 H), 7.0 (br s, 1 H), 5.79 (d, J ) 5.0 Hz, 1 H), 5.24 (t, J )
5.0 Hz, 1 H), 5.10 (dd, J ) 5.0 Hz, J ) 1.0 Hz, 1 H), 4.51 (d, J ) 1.0
Hz, 1 H), 4.0-3.7 (m, 6 H), 1.63, 1.35 (2 s, 6 H), 1.26 (t, J ) 7.0 Hz,
is easy to see that in the two cases the reference reactions are
different and rate enhancement factors cannot be compared. This
is particularly true for these reactions where the contribution
of k2[A‚E] is much larger than of k1[Ao‚Eo] (see Table 2).
Our general conclusion is that self-replication as defined by
6
H); 13C NMR (DMSO-d
6
) δ 153.1 (s), 152.0 (d), 149.5 (s), 138.6
(d), 119.1, 113.0 (s), 89.7, 86.3, 83.3, 81.3 (d), 61.6, 42.4 (t), 27.0,
(25) de Boer, J. A. A.; Reinhoudt, D. N.; Harkema, S.; van Hummel, G.
3
Rebek et al. operates in this system but that other pathways
J.; de Jong, F. J. Am. Chem. Soc. 1982, 104, 4073-4076.

Kinetic Analysis of the Rebek Self-Replicating System
J. Am. Chem. Soc., Vol. 118, No. 29, 1996 6889
+
6
2
5.0, 13.3 (q); MS-FAB m/z 364.3 [(M+H) , calcd 364.2]; HRMS-EI
5′-Amino-2′,3′-(1-methylethylidene)-5′-deoxy-N ,N-diethyladeno-
+
m/z 363.1873 (M , calcd for C17
H
25
N
5
O
4
363.1907). Anal. Calcd for
C H N O : C, 56.19; H, 6.93; N, 19.27. Found: C, 55.90; H, 6.78;
17 25 5 4
N, 18.96.
′-(1,3-Dihydro-1,3-dioxo-2H-isoindol-2-yl)-2′,3′-(1-methyleth-
ylidene)-5′-deoxy-N ,N-diethyladenosine (12). Freshly distilled di-
ethyl azodicarboxylate (0.025 g, 0.14 mmol) was added to a magnetically-
stirred suspension of 2′,3′-(1-methylethylidene)-N ,N-diethyladenosine
11) (0.05 g, 0.14 mmol), phthalimide (0.02 g, 0.14 mmol), and
triphenylphosphine (0.04 g, 0.14 mmol) in dry THF (5 mL). After 1
sine (9). A mixture of 12 (0.49 g, 1 mmol) and hydrazine hydrate
(1.5 mL) in EtOH (10 mL) was refluxed for 1 h. The solution was
evaporated to dryness in Vacuo, and the residue was redissolved in
5
CH
2
Cl
2
(15 mL), washed with H
2
O (3 × 20 mL), and dried over
6
MgSO
4
. Solvent was evaporated, and the residue was dried in Vacuo
1
(1 mmHg, 75 °C) for 3 h to give 9 as a colorless oil (0.30 g, 83%): H
6
NMR δ 8.23, 7.76 (2 s, 2 H), 5.96 (d, J ) 3.0 Hz, 1 H), 5.4-5.3 (m,
1 H), 5.0-4.9 (m, 1 H), 4.15-4.05 (m, 1 H), 4.0-3.7 (m, 4 H), 3.0-
2.8 (m, 2 H), 1.55, 1.31 (2 s, 6 H), 1.21 (t, J ) 7.0 Hz, 6 H); C NMR
δ 153.8 (s), 152.7 (d), 150.0 (s), 137.5 (d), 120.3, 114.4 (s), 90.4, 87.5,
83.7, 81.8 (d), 43.9, 43.1 (t), 27.3, 25.4, 13.5 (q); MS-FAB m/z 363.1
[(M + H) , calcd 363.2]. HRMS-EI m/z 362.2030 (M , calcd for
362.2066).
(
9
13
h the solution was evaporated in Vacuo. The mixture was purified by
2 2
flash chromatography (silica gel, EtOAc-CH Cl , 1:1) to give 12 as a
+
+
colorless glass (0.05 g, 74%) which was slightly contaminated with
9
1
diethyl hydrazinedicarboxylate; H NMR δ 8.00, 7.71 (2 s, 2 H), 8.8-
.6 (2 m, 4 H), 5.95 (d, J ) 1.8 Hz, 1 H), 5.43 (dd, J ) 5.0 Hz, J )
.8 Hz, 1 H), 5.15-5.05 (m, 1 H), 4.4-4.3 (m, 1 H), 4.0-3.8 (m, 6
H), 1.50, 1.29 (2 s, 6 H), 1.21 (t, J ) 7.0 Hz, 6 H); C NMR δ 168.2,
53.7 (s), 152.5 (d), 150.0 (s), 137.8, 134.0 (d), 132.0 (s), 123.3 (d),
20.0, 114.4 (s), 90.5, 84.9, 84.2, 82.6 (d), 43.1, 39.5 (t), 27.2, 25.5,
17 26 6 3
C H N O
8
1
Supporting Information Available: A detailed kinetic
1
3
scheme describing all equilibria and rate equations (6 pages).
See any current masthead page for ordering and Internet access
instructions.
1
1
1
4
+
3.5 (q); MS-FAB m/z 493.9 [(M + H) , calcd 493.2]; HRMS-EI m/z
+
92.2129 (M , calcd for C25
H N O
28 6 5
492.2121).
JA960324G