Systems chemistry: Kinetic and computational analysis of a nearly exponential organic replicator

Article abstract of DOI:10.1002/anie.200501527

Combining kinetic, structural, and computational studies on complex dynamic feedback systems may lead to the field of "systems chemistry". The approach is exemplified by the analysis of a simple organic self-replicating system that has the potential to ex

Full text of DOI:10.1002/anie.200501527

Communications
Chirality
DOI: 10.1002/anie.200501527
Systems Chemistry: Kinetic and Computational
Analysis of a Nearly Exponential Organic
Replicator**
Maik Kindermann, Insa Stahl, Malte Reimold,
Wolf Matthias Pankau, and Günter von Kiedrowski*
In 1997, Wang and Sutherland reported a case of self-
replication in a Diels–Alder reaction.[1] This system is
remarkable for at least two reasons: it constituted the first
example of nearlyexponential growth and it had the potential
to exhibit two kinds of self-replication, homochiral autoca-
talysis and heterochiral cross-catalysis, because a chiral diene
was employed. Unfortunately, the authors could not complete
a stereochemical analysis of their system. We report herein
mechanistic and stereochemical studies of variants of the
Wang–Sutherland replicator. We show that onlyone of four
potential diastereomers is formed within our detection limits
and that this diastereomer is involved in both autocatalytic
and cross-catalytic channels. A computational study suggests
that the system can be classified as an example of a nearby
[*] Dr. M. Kindermann,[+] I. Stahl,[+] M. Reimold, Dr. W. M. Pankau,
Prof. Dr. G. von Kiedrowski
Lehrstuhl für Organische Chemie I
Ruhr-Universität Bochum
Universitätsstrasse 150, 44780 Bochum (Germany)
Fax: (+49)234-32-14355
E-mail: kiedro@rub.de
[+] These authors contributed equally to this work.
[**] This work was supported by Deutsche Forschungsgemeinschaft
(SFB 452), COST-D27, and the European integrated project PACE
(IST-FET complex systems). We thank Dr. K. Merz for performing
the X-ray analysis of 6b and Dr. A. Tamulis (University of Vilnius) for
a current recomputation of the approximated transition states.
Supporting information for this article is available on the WWW
under http://www.angewandte.org or from the author.
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strong-exponential replicator according to our minimal
[2]
replicator theory.
Self-replication of chiral information has recently
received considerable interest from its relevance to the
question of the breaking of chiral symmetry on the early
earth[3]. An impressive implementation of Frankꢀs model[4]
now exists in the reaction of Soai et al., whose kinetic analysis
[5]
has recentlyrevealed important insight. Further examples
of self-replication with prochiral precursors were successfully
designed for cycloaddition reactions.[6] Self-replication
experiments with peptides as chiral building blocks consti-
tuted the first example of homochiral autocatalysis in the
sense that templating requires the same helicity, as in the case
of template precursors.[7] The general predictabilityof homo-
chiral autocatalysis versus heterochiral cross-catalysis is,
however, far less pronounced for molecules without a
predefined secondarystructure (Figure 1).
We therefore became interested in the re-evaluation of
the Wang–Sutherland system with respect to its stereochem-
ical features.[1] Our approach is guided byour curiosityas to
whether a combination of kinetic, computational, and theo-
retical methods could lead to a better understanding of
structurally simple but dynamically complex systems. The
Figure 1. Principle of a) heterochiral cross-catalysis and b) homochiral
autocatalysis.
components and principle reactions of the Wang–Sutherland
system are shown in Figure 2a.
We thought that the replacement of the heterocyclic
recognition units by amidopyridines and carboxylic acids,
independentlyused bythe research groups of Hamilton [8] and
Philp,[6] could also expand the solubilityrange in the Wang–
Sutherland system. Our components and reaction products as
Figure 2. Reaction schemes; each arrow indicates a distinguishable reaction channel. a) Self-replicating Diels–Alder reaction as described by
[1]
Wang and Sutherland. b) Our self-replicating system taking into account both enantiomeric forms. c),d) Control reactions with compounds
without recognition properties.
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well as model components without recognition properties are
depicted in Figure 2b–d.
We synthesized diene 4 in racemic form and as separate
enantiomers from the corresponding 2,4-cyclohexadienylace-
tic acids[9] (Supporting Information). The reactions were
1
monitored by H NMR spectroscopyand evaluated byusing
our SimFit program.[10] A stack plot of the 1H NMR spectrum
of the reaction of rac-4 with 5a to give rac-6a is depicted in
Figure 3, which shows the olefinic protons of rac-6a.
Figure 4. Profiles of concentration over time for the reaction of a) rac-4
and 5a (CDCl3, 293 K, 15 mm) with template rac-6a initially added at 0
~
*
(&), 10 ( ), and 15% ( ); b) rac-4 and 5b (CDCl3, 313 K, 15 mm) with
*
template rac-6b initially added at 0 (&) and 17% ( ). Continuous lines
represent theoretical curves.
Table 1: Results of the analysis of the reactions of rac-4 and 5a/5b based
on the value of p.
R
p
ka [mÀ(p+1) sÀ1
]
kb [mÀ1 sÀ1
]
RMS [%] T [K]
H
0.89 (4.48Æ0.01)”10À1 (2.10Æ0.02)”10À4 2.21[a]
293
313
CH3 0.9
(6.32Æ0.13)”10À2 (4.43Æ0.23)”10À4 1.09[b]
[a] Based on experiments with added template initially at 0, 10, and 15%.
[b] Based on experiments with added template initially at 0 and 17%.
1
Figure 3. Stack plot of H NMR spectra of the reaction of rac-4 with 5a
to give rac-6a (CDCl3, 600 MHz, 293 K).
Three phenomena are directlyobservable: an induction
period, an autocatalytic increase of integrals, and a concom-
itant change of chemical shifts for the development of the
product signal. The latter caused bythe transition of free
templates at low concentrations to template complexes and
duplexes at higher product concentrations. Minimal modeling
according to A + B + pC!(1 + p)C for the autocatalytic
channel and A + B!C for the non-autocatalytic channel,
both for the building blocks 5a and 5b as B, leads to the
profiles of theoretical concentration over time shown in
Figure 4 and yields the kinetic parameters given in Table 1.
From this data it is evident that our variants are reasonable
approximations of the Wang–Sutherland system, of which the
autocatalytic reaction order p over similar conversion was
0.8.[1]
Wang and Sutherland assumed an endo product but were
not sure whether one or two diastereomers that differ in the
configuration of the stereocenter carrying the recognition site
at the [2.2.2]bicyclo-octene scaffold are formed. We were able
to crystallize a single racemic diastereomer of the reaction
product, rac-6b, the X-raycrystallographic structure is shown
in Figure 5.[11]
Figure 5. X-ray crystallographic structure of rac-6b.
There is no indication for another diastereomer above the
detection limits of NMR spectroscopy. Transition-state mod-
eling of simplified model reactions at the B3LYP/6-31G* level
of calculation confirmed that the diastereomer with NN or-
ientation is expected (Supporting Information).[12] An inter-
esting detail from these studies is the presence of weak
bifurcating hydrogen bonds, which stabilize the transition
state of the model reaction between 5’-methyl-1,3-cyclohex-
adiene and N-carboxymethylmaleimide, but these are absent
in the product. Weak bifurcating hydrogen bonds were also
found to stabilize the transition state of the noncatalyzed
template-formation reaction in the NNN conformation.[12] As
expected, model reactions with the building blocks 7a and 9
that are without recognition properties revealed no autoca-
talysis, but allowed us to determine the second-order rate
constants:
(rac-4 + 7a!rac-8a,
T= 293 K,
k = 4.49 ”
10À5 mÀ1 sÀ1; 9 + 5a!10, T= 293 K, k = 5.83 ” 10À5 mÀ1 sÀ1).
We studied the individual reactions involving diene (R)-4
and (S)-4 in the presence of the template (R)-6a at 10%.
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From Figure 6 it is clear that the effect of the template is
similar in both cases, which indicates the presence of
autocatalytic and cross-catalytic reaction channels. This find-
ing could be confirmed bykinetic modeling and fitting both
Figure 6. Profiles of concentration over time for the reaction of male-
imide 5a with: a) diene (R)-4 to give (R)-6a (the gray line demon-
strates product formation without any template added initially);
b) diene (S)-4 to give (S)-6a, both with 10% of template (R)-6a added
initially (CDCl3, 293 K, 15 mm). The first four hours of the reaction
time were analyzed.
data sets simultaneouslyto the model shown in Figure 7. The
ratio of the association constants of the template duplexes
(K2 hetero/K2 homo ꢀ 2) suggests that homochiral and heterochi-
ral duplexes are nearlyequallypopulated.
The limited structural and dynamic complexity of our
replication system led us to the question of whether computa-
tional chemistrycould help to explain the kinetic data on the
base of an energyprofile. We took the following approach: a
conformational search of the noncomplexed template at the
MMFF94 level followed byfurther refinement at the B3LYP/
6-31G* level led to two conformational families, NNN and
NNX,[12] which differed in the orientation of the carboxy
À
group relative to the C C double bond.
Formation of template duplexes requires the units of
recognition to be in a specific orientation, coaligned in the
same direction. Considering that each of these template
conformations can exist in both enantiomeric forms, we
systematically constructed the six possible duplexes by
manual docking and energyrefinement at MMFF94, PM3,
Figure 7. Full model that considers the complexes participating in the
reaction (CDCl3, 293 K, 15 mm), which results from a distinction
between the diene enantiomers (A=diene 4, B=maleimide 5a,
C=template 6a). RMS=1.44%.
and B3LYP/6-31G* levels, successively. As expected, the approximated counterparts in Figure 8. We observed that
duplexes arising from inner-familycombinations were found
to be centrosymmetric in the heterochiral case and to have
rotational symmetry in the homochiral case. The lowest-
energyduplex has the conformation that was found in the
crystal structure of 6b. Transition states were derived from a
transition-state search of the model reaction between N-
methylmaleimide and 5-methyl-1,3-cyclohexadiene; all
atoms, except those of the methyl groups, were frozen and
the skeleton of frozen atoms were inserted into the respective
position of the corresponding duplex. Geometryoptimization
of the nonfrozen atoms was carried out at the B3LYP/6-61G*
level. The termolecular complexes were derived from the
transition states byrelaxation after unfreezing. Figure 8 shows
the energydifference between the respective conformations is
similar to their counterparts in the approximated transition
states with frozen atoms. Therefore, we trust the approxi-
mated transition states.
The largest energydifferences between autocatalytic and
cross-catalytic pathways were found at the level of transition
states and template duplexes. Interestingly, transition-state
stabilization byweak bifurcating hydrogen bonds (approx-
imately À1.5 kcalmolÀ1) leads to the lowest-energyconfor-
mations only in the autocatalytic cases. For the cross-catalytic
cases the effect is counterbalanced byrepulsive and/or
dihedral distortion, which leads to a less optimal geometry
at the recognition sites. The cross-catalytic pathway shows the
the result of our computational study. For the case of the lowest enthalpyof activation. There is alwasy a clear
nontemplated reactions, we were able to find the true
enthalpic preference of termolecular complexes over the
respective template duplexes. Further work on the temper-
transition states. These are greater than 6 kcalmolÀ1 below
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optimal docking of the reactants with the template, template
duplexes are conformationallyrestricted in their finding of an
optimal orientation of the recognition units. A similar ration-
ale was reported to explain the nearlyexponential growth of a
peptide replicator.[14] Our replicator theorypredicts that for
systems with a negligible background channel, the question of
parabolic versus exponential growth is solelyanswerable by
the stabilities of the ground-state and not the transition-state
complexes involved.[2] Further cases are needed to prove that
exponential growth can be literallydesigned bytaking into
account the conformational control of ground states. If this
recipe can be generalized, it could open a door to a field that
may be termed “systems chemistry”, namely, the design of
prespecified dynamic behavior.
Received: May4, 2005
Revised: July5, 2005
Published online: September 27, 2005
Keywords: chirality · computer chemistry · molecular modeling ·
.
supramolecular chemistry · template synthesis
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Figure 8. Energy profiles correlated to the corresponding structures
(B3LYP/6-31G*) of the reaction of 4 and 5a through the a) autocata-
lytic and b) nontemplate-directed pathways.
[11] Crystallographic data for rac-6b: crystal size = 0.2 ” 0.2 ”
0.3 mm3; crystal system = monoclinic; space group = P21/n;
unit cell dimensions: a = 5.8973(17), b = 26.318(8), c =
V= 2929.1(15) Š3;
1calcd =
ature dependence of rates and equilibria in a slightlymodified
self-replicating system has revealed evidence that the above
enthalpic preference is not overcompensated bythe respec-
18.881(5) Š,
b = 91.693(6)8;
2qmax = 458; lMoKa = 0.71073 Š; T= 213(2) K;
0.931 gcmÀ3
;
reflections collected = 10714, unique reflections = 3803, for
2983 reflections observed (I > 2s(I)); The structure was solved
bydirect methods and refined byfull-matrix least squares by
using SHELXTL-97; 271 parameters; the non-H atoms were
refined anisotropically, H atoms were included but not refined;
final R indices: R1 = 0.0670, wR2 = 0.1893; R indices (all data):
R1 = 0.0785, wR2 = 0.1998; goodness-of-fit on j F2 j = 1.079; max-
[13]
tive entropydifferences.
In summary, our re-evaluation of the Wang–Sutherland
replicator with simplified variants reveals that the exponen-
tial dynamics arise from conformational constraints. Whereas
the termolecular complexes offer enough freedom for an
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imum positive and negative peaks in DF map were 1max
=
0.348 eŠ and 1min = À0.292 eŠÀ3. CCDC 269658 contains the
supplementarycrystallographic data for this paper. These data
can be obtained free of charge from the Cambridge Crystallo-
graphic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.
[12] We use a four-letter notation to describe the configuration and
conformation of template molecules. The first letter is either N
or X to indicate an endo or exo Diels–Alder product, respec-
tively. The latter distinction is based on the relative orientation
À3
=
of the C C double bond to the maleimide ring. We employed the
=
C C double bond also as a reference to describe the relative
orientation of the 5-pyridinylaminocarbonylmethyl substituent
(second letter) and of the carboxymethyl substituent (third
letter). R/S (fourth letter) is determined bythe absolute
configuration of the precursor diene.
[13] I. Stahl, Analysis and classification of minimal self-replicating
systems based on Diels–Alder ligation chemistry, PhD thesis,
Ruhr-Universitꢁt Bochum, 2005: http://www-brs.ub.ruhr-uni-
bochum.de/netahtml/HSS/Diss/StahlInsa/.
[14] R. Issac, J. Chmielewski, J. Am. Chem. Soc. 2002, 124, 6808 –
6809.
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