One-dimensional random walk of a synthetic small molecule toward a thermodynamic sink

Article abstract of DOI:10.1021/ja402382n

We report on the spontaneous intramolecular migration of α-methylene-4-nitrostyrene from amine group to amine group along oligoethyleneimine tracks up to eight repeat units in length (number of amine footholds, n = 3, 5, 9). Each track consists of n - 1 aliphatic secondary amine footholds plus a naphthylmethylamine group foothold situated at one end of the track. Under basic conditions the α-methylene-4-nitrostyrene unit undergoes a series of reversible intramolecular Michael-retro-Michael reactions between adjacent amine groups that move it up and down the track. For n = 3 and 5 it is possible to monitor the population of every positional isomer on the track by ¹H NMR spectroscopy. On the longest track (n = 9) the fraction of walkers on each end-foothold can be quantified with respect to those on the inner footholds. In all cases the naphthylmethylamine foothold acts as a thermodynamic sink with the steady-state distribution significantly biased in favor of the walker at that site. The dynamics of the walker migration is well described by the random walk of a Brownian particle in one dimension.

Full text of DOI:10.1021/ja402382n

Article
pubs.acs.org/JACS
One-Dimensional Random Walk of a Synthetic Small Molecule
Toward a Thermodynamic Sink
Araceli G. Campana,† David A. Leigh,*,†,‡ and Urszula Lewandowska‡
̃
†School of Chemistry, University of Edinburgh, The King’s Buildings, West Mains Road, Edinburgh EH9 3JJ, United Kingdom
‡School of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
S
* Supporting Information
ABSTRACT: We report on the spontaneous intramolecular migration of α-methylene-4-
nitrostyrene from amine group to amine group along oligoethyleneimine tracks up to eight
repeat units in length (number of amine footholds, n = 3, 5, 9). Each track consists of n − 1
aliphatic secondary amine footholds plus a naphthylmethylamine group foothold situated at one
end of the track. Under basic conditions the α-methylene-4-nitrostyrene unit undergoes a series
of reversible intramolecular Michael−retro-Michael reactions between adjacent amine groups
that move it up and down the track. For n = 3 and 5 it is possible to monitor the population of
every positional isomer on the track by 1H NMR spectroscopy. On the longest track (n = 9) the
fraction of walkers on each end-foothold can be quantified with respect to those on the inner
footholds. In all cases the naphthylmethylamine foothold acts as a thermodynamic sink with the
steady-state distribution significantly biased in favor of the walker at that site. The dynamics of the
walker migration is well described by the random walk of a Brownian particle in one dimension.
Scheme 1. Synthesis of Walker−Track Conjugate
INTRODUCTION
■
a
5-1·3[CF3CO2H]
Various motor proteins from the myosin, dynein, and kinesin
superfamilies move along filaments and microtubules in the cell,
transporting cargos such as membranous organelles, protein
complexes, and mRNA.1 These remarkable biological molecular
machines are inspiring the invention of artificial systems that
may one day be able to migrate along polymer tracks and
perform similarly useful tasks.2 In the past few years small
molecules that are able to ‘walk’ down short molecular tracks
have been described.3,4 However, many of these systems
require intervention in the form of the sequential addition of
reagents (and in some cases irradiation with light) for the
‘walker’ to take each ‘step’. Our group4a and that of Lehn4b
recently reported conceptually related model compounds in
which a molecular fragment can be transferred intramolecularly
between adjacent amine groups on a short track without the
need for the sequential addition of reagents or other forms of
intervention.4 Both systems involve dynamic covalent chem-
istry5 of nitrogen-containing functional groups: the Lehn
approach is based upon transimination reactions (the reversible
formation of CN bonds);6 ours utilizes the reversible
Michael addition of secondary amines to an α-methylene-4-
nitrostyrene unit, chemistry that is based on the equilibrium
transfer alkylating cross-linking (ETAC) reagents introduced by
Lawton in the 1970s for the cross-linking of proteins under
thermodynamic control.7
a
Reaction conditions: a) 1-naphthaldehyde, EtOH, RT, 16 h; b)
NaBH4, RT, 3 h, 34% (two steps); c) CF3CO2Et, CH2Cl2, 0 °C→RT,
16 h; d) Boc2O, Et3N, RT, 12 h; e) NaOH, MeOH/H2O, RT, 5 h,
92% (three steps); f) 3-phenylpropionaldehyde, EtOH, RT, 16 h; g)
NaBH4, RT, 3 h, 27%, (two steps); h) 4, MeOH, iPr2NEt, 50 °C, 24 h,
54%; i) CF3CO2H, CH2Cl2, RT, 3 h, quant.
The preliminary publications from both groups focused on
establishing the reversibility and intramolecular nature of the
‘stepping’ dynamics on model systems, demonstrating that the
small-molecule fragment is randomly exchanged between
adjacent amines on short (up to three or four repeat units)
oligoethyleneimine tracks. Here we describe the extension of
the Michael−retro-Michael walker concept to long (up to nine
footholds) tracks and investigate the effect of acid and base on
Received: March 7, 2013
© XXXX American Chemical Society
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migration. Moreover, we show that under basic conditions a
naphthylmethylamine foothold introduced at one end of the
oligoethyleneimine track acts as a thermodynamic sink for the
walker. Although the steps taken on the internal regions of the
track proceed at the same rate in either direction, the rate that
the walker departs from the naphthylmethylamine site is
significantly slower than from the other footholds, meaning that
the walker distribution is biased toward this site generating net
directional transport from one end of the track to the other
even on long (up to nine footholds) tracks. The α-methylene-4-
nitrostyrene walker migrates from one end of a nine-foothold
track to the other under dynamics that correspond well to the
theoretical description of a one-dimensional random walk of a
Brownian particle.8
RESULTS AND DISCUSSION
■
Influence of Acid and Base on Michael and retro-
Michael Reactions of α-Methylene-4-nitrostyrene on a
Diethylenetriamine Track. We previously investigated the
migration of α-methylene-4-nitrostyrene walker unit between
adjacent amine groups of short oligoethyleneimine tracks under
neutral conditions. To probe the effect of acid and base on
these reactions a three-foothold walker−track conjugate 5-1
was synthesized as the tris-trifluoroacetic acid salt (Scheme 1).
Boc-protected diethylenetriamine 1 was desymmetrized
through reductive amination with 1-naphthaldehyde (Scheme 1 a,b),
followed by a sequence of Boc-protection−deprotection reactions
(Scheme 1 c−e) to yield free primary amine 2, which after reduc-
tive amination with 3-phenylpropionaldehyde (Scheme 1 f,g)
afforded track 3 featuring a single site for walker attachment. The
α-methylene-4-nitrostyrene walker unit 4 was subsequently
introduced exclusively at foothold 1 (Scheme 1 h). Removal of
the Boc group gave compound 5-1 as the tris-trifluoroacetic acid
salt. With all of the amine groups of the track protonated, the α-
methylene-4-nitrostyrene group does not migrate away from its
original position.
Figure 1. (a) Intramolecular migration of the α-methylene-4-
nitrostyrene unit of 5-1·3[CF3CO2H] in the presence of 4 equiv of
iPr2NEt. (b) Population of isomers (1H NMR integration; see Figure 2).
After 48 h, 67 3% of walkers are positioned on foothold 3 of the
track (isomer 5-3). Lines show the best fit of the experimental data to
the kinetics of exchange between 5-1, 5-2, and 5-3 using SimFit9 (see
Supporting Information for details). Error bars are indicative of the
error associated with 1H NMR integration using equivalent protons in
each positional isomer.
Walker Migration on a Diethylenetriamine Track in
the Presence of One Equivalent of Excess Base.
Treatment of 5-1·3[CF3CO2H] in DMSO-d6 (20 mM, 298 K)
with 4 equiv of diisopropylethylamine (iPr2NEt), i.e. one equiv
Figure 2. Partial 1H NMR spectra (400 MHz, 20 mM, DMSO-d6, 298 K) of 5-1·3[CF3CO2H] + 4 equiv of iPr2NEt, showing the interconversion of
5-1 (black resonances), 5-2 (blue resonances), and 5-3 (green resonances) over 48 h.
B
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excess of base, led to spontaneous migration of the α-methylene-4-
2 and 3 are populated to a comparable extent (43 3% and
47 3%, respectively).
nitrostyrene unit along the track (Figures 1 and 2). The
1
reaction was monitored by H NMR spectroscopy (Figure 2).
Walker Migration on a Diethylenetriamine Track in
the Presence of One Equivalent of Excess Acid. When
5-1·3[CF3CO2H] was treated with 2 equiv of iPr2NEt (i.e. only
sufficient to deprotonate two of the three ammonium groups
of the track), the dynamic behavior of the walker was very
different from that under neutral or basic conditions (Figure 4).
Under these conditions the initial migration from foothold 1 to
foothold 2 is fast, with more than half of the walkers having left
foothold 1 after 4 h (Figures 1 and 2). The steady-state is
reached after 24−48 h, with 67
3% of walkers ultimately
located at the naphthylmethylamine foothold (foothold 3). The
dynamics of the exchange of the positional isomers was simulated
using the SimFit program9 (Figure 1b; see Supporting
Information for details).
Walker Migration on a Diethylenetriamine Track
under Neutral Conditions. Treatment of 5-1·3[CF3CO2H]
in DMSO-d6 (20 mM, 298 K) with 3 equiv of iPr2NEt (i.e. just
sufficient to deprotonate all of the ammonium groups of the
track) also led to spontaneous migration of the α-methylene-4-
nitrostyrene unit along the track (Figure 3). Initial migration
away from foothold 1 occurs at a rate similar to that in the
presence of excess base, but at the steady-state, footholds
Figure 4. (a) Intramolecular migration of the α-methylene-4-
nitrostyrene unit of 5-1·3[CF3CO2H] in the presence of 2 equiv of
iPr2NEt. (b) Population of isomers (1H NMR integration). After 48 h,
90 3% of walkers are positioned on foothold 2 of the track (isomer
5-2). Lines show the best fit of the experimental data to the kinetics of
the exchange between 5-1, 5-2, and 5-3 using SimFit9 (see Supporting
Information for details). Error bars are indicative of the error
associated with 1H NMR integration using equivalent protons in each
positional isomer.
The kinetics of the initial migration from foothold 1 to foothold
2 is significantly slower: after 4 h only ∼30% of walkers had left
foothold 1. Furthermore, even after 48 h only a trace of walker
units (<3%) could be detected on foothold 3 with the majority
(88 3%) situated on foothold 2. This is presumably a result
of the relative basicity of the three amine groups of the track, with
the most basic naphthylmethylene secondary amine10 remaining
protonated and thus unavailable to take part in Michael reactions.
Walker Migration on a Tetraethylenepentamine
Track. Given the ability of the naphthylmethylamine foothold
to act as a thermodynamic sink for the α-methylene-4-
nitrostyrene walker on a three-foothold track in the presence
of excess base (Figure 1), we investigated the walker’s behavior
Figure 3. (a) Intramolecular migration of the α-methylene-4-
nitrostyrene unit of 5-1·3[CF3CO2H] in the presence of 3 equiv of
iPr2NEt. (b) Population of isomers (1H NMR integration). After 48 h,
47 3% of walkers are positioned on foothold 3 of the track (isomer
5-3) and 43 3% on position 2 (isomer 5-2). Lines show the best fit
of the experimental data to the kinetics of the exchange between 5-1,
5-2, and 5-3 using SimFit9 (see Supporting Information for details).
Error bars are indicative of the error associated with 1H NMR
integration using equivalent protons in each positional isomer.
C
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on longer, five- and nine-foothold tracks (Figures 6−9). A
walker−five-foothold-track conjugate was prepared as the
penta-trifluoroacetic acid salt, 6-1[5 × CF3CO2H], according
to Scheme 2 (see Supporting Information). Upon treatment
with 6 equiv iPr2NEt in DMSO-d6 (20 mM, 298 K) the walker
processively11 migrated along the track. 1H NMR signals
diagnostic for each positional isomer could be identified
(Figure 5b) and thus the population of each positional isomer
monitored over time (Figure 6). After 48 h the steady-state had
been reached with 46 3% of the walkers having taken a net
four steps directionally along the track to be positioned on the
naphthylmethylamine foothold.
Figure 6. Intramolecular migration of the α-methylene-4-nitrostyrene
i
unit of 6-1·5[CF3CO2H] in the presence of 6 equiv of Pr2NEt.
Population of isomers (1H NMR integration). After 48 h, 46 3% of
walkers are positioned on foothold 5 of the track (isomer 6-5). Lines
show the best fit of the experimental data to the kinetics of the
exchange between 6-1, 6-2, 6-3, 6-4 and 6-5 using SimFit9 (see
Supporting Information for details). Error bars are indicative of the
error associated with 1H NMR integration using equivalent protons in
each positional isomer.
a
Scheme 2. Synthesis of a Walker−Track Conjugate 6-1
a
Reaction conditions: a) 1-naphtaldehyde, EtOH, RT, 16 h; b)
NaBH4, RT, 3 h, 34% (two steps) c) CF3CO2Et, CH2Cl2, 0 °C→RT,
16 h; d) Boc2O, Et3N, RT, 12 h; e) NaOH, MeOH/H2O, RT, 5 h,
74% (three steps); f) 3- phenylpropionaldehyde, EtOH, RT, 16 h; g)
NaBH4, RT, 3 h, 35%, (two steps); h) 4, MeOH, iPr2NEt, 50 °C, 24 h,
49%; i) CF3CO2H, CH2Cl2, RT, 3 h, quant.
Walker Migration on an Octaethylenenonamine
Track. A nine-foothold walker−track conjugate 10 was
synthesized starting from commercially available 2-(2-
aminoethylamino)ethanol (11), which was subjected to a
sequence of protection−deprotection reactions (Scheme 3 a−c)
to give 12. Reductive amination of 12 with 3-phenyl-
propionaldehyde afforded 13 (Scheme 3 d,e). Subsequent Cbz
protection and oxidation using Dess−Martin periodinane
(DMP) yielded the aldehyde building block 14 (Scheme 3 f,g).
The second half of the track was synthesized, starting from the
reductive amination of 11 with 1-naphthaldehyde (Scheme 3 h,i)
followed by selective Boc protection to give 15 (Scheme 3 j).
The primary alcohol was oxidized to aldehyde 16 (Scheme 3 k)
and then subjected to reductive amination with commercially
Figure 5. (a) Walking of 6-1·5[CF3CO2H] in the presence of 6 equiv
i
1
of Pr2NEt. (b) Partial H NMR spectra of of 6-1·5[CF3CO2H] + 6
i
equiv of Pr2NEt (400 MHz, 20 mM, DMSO-d6, 298 K) showing the
successive formation of the five positional isomers (the colors of the
signals corresponds to the structures shown in part (a)).
D
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a
available tetraethylenepentaamine (Scheme 3 l,m). The pri-
mary amine was protected as the trifluoroacetate, followed by
quadruple Boc protection of the remaining secondary amines
to give 17 (Scheme 3 n,o). Deprotection of the primary amine
(Scheme 3 p) afforded 18 and reductive amination with 14
furnished the nine-foothold track with one ‘free’ secondary
amine (Scheme 3 q,r), which was subsequently Boc-protected
to give 19 (Scheme 3 s). The Cbz group was reductively
cleaved (Scheme 3 t) and the walker was attached and the
protecting groups were removed (Scheme 3 u,v) to give 10-
1·9[CF3CO2H] (see Supporting Information for experimental
procedures and characterization data).
Scheme 3. Synthesis of a Walker−Track Conjugate 7-1
In order to investigate the processive11 walking process on
the nine-foothold track, 10-1·9[CF3CO2H] was treated with
i
10 equiv of Pr2NEt in DMSO-d6 (10 mM, 298 K), and the
reaction monitored by 1H NMR spectroscopy (Figures 7 and 8).
Although the assignment of each of the nine positional isomers
is not possible, we were able to quantify the number of walkers
on each of the terminal footholds (i.e., 10-1 and 10-9) and
compare each of those to the number sited on the internal
footholds (i.e., 10-2−10-8). After 15 h, signals corresponding
to 10-9 (the walker molecule reaching the last foothold of the
track) were apparent (green resonances, Figures 7 and 8b) and
gradually increased in intensity until after 90 h (Figure 8b) 19
3% of the walker units were present on the last foothold.
Intramolecular Migration As a One-Dimensional
Random Walk toward a Thermodynamic Sink. Figure 10
shows the rate of diffusion of the walker along the various
length tracks (compounds 5, 6, and 10) and confirms that the
net distance varies as the square root of the elapsed time.12 The
rate constants for the interconversion of adjacent positional
isomers (e.g., between 10-3 and 10-2 and 10-4) suggested by
SimFit are similar for almost all exchanges between amine
groups on the internal positions of the track (Figure 8a).
Although the influence of the naphthylmethylamine group is
diminished in the presence of eight alternative amine footholds,
there is still a significant bias for the site, resulting in net
directional walking of the α-methylene-4-nitrostyrene unit
a
Reaction conditions: a) CF3CO2Et, CH2Cl2, 0 °C→RT, 3 h; b)
Boc2O, Et3N, RT, 12 h, 60% (two steps); c) NaOH, MeOH/H2O, RT,
5 h, 73%; d) 3-phenylpropionaldehyde, EtOH, RT, 16 h; e) NaBH4,
RT, 3 h, 36% (two steps); f) CbzCl, Et3N, CH2Cl2, RT, 4 h, 68%; g)
DMP, CH2Cl2, RT, 12 h, 81%; h) 1-naphthaldehyde, EtOH, RT, 16 h; i)
NaBH4, RT, 3 h; j) Boc2O, MeCN, RT, 12 h, 64% (three steps); k)
DMP, CH2Cl2, RT, 12 h, 68%; l) tetraethylenepentaamine, EtOH, RT,
16 h; m) NaBH4, RT, 3 h; n) CF3CO2Et, CH2Cl2, 0 °C→RT, 16 h; o)
Boc2O, Et3N, RT, 12 h, p) NaOH, MeOH/H2O, RT, 5 h, 20% (five
steps); q) 14, EtOH, RT, 16 h; r) NaBH4, RT, 3 h; s) Boc2O, Et3N, RT,
12 h, 30% (three steps); t) Pd/C, H2, THF, RT, 20 h, 50%; u) 4, MeOH,
iPr2NEt, 50 °C, 48 h, 50%; v) CF3CO2H, CH2Cl2, RT, 7 h, quant.
1
Figure 7. Partial H NMR spectra (400 MHz, 10 mM, DMSO-d6, 298 K) monitoring the intramolecular exchange of 10-1·9[CF3CO2H] (black
i
resonances at t = 0 h) in the presence of 10 equiv of Pr2NEt, showing the disappearance of 10-1 and formation of positional isomers 10-2−10-8.
Resonances corresponding to 10-9 are shown in green.
E
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Figure 10. Calculated net displacement (distance along the vector of the
track, Å, left-hand axis; average number of footholds traveled, <n>, right-
hand axis) of α-methylene-4-nitrostyrene walker as a function of time.
naphthylamine foothold itself. Due to the track’s architecture, the
walker unit can only take forward and backward steps of equal
distance, and therefore the migration is well described as a one-
dimensional random walk toward a modest thermodynamic sink.8,12
CONCLUSIONS
■
We have shown that the migration of α-methylene-4-nitrostyrene
along oligoethyleneimine tracks by Michael−retro-Michael reactions
is hindered in the presence of acid but occurs readily under neutral
and basic conditions. The intramolecular transfer from amine group
to adjacent amine group is not limited to short model systems but
also occurs on extended tracks up to nine footholds long. Moreover,
under basic conditions a naphthylmethylamine foothold can act as a
thermodynamic sink, leading to net directional migration of the
walker even in the presence of eight other amine footholds.
Directional movement along tracks over significant distances may
enable synthetic small-molecule systems to transport cargoes and
perform other useful tasks13 at the molecular level.
Figure 8. (a) Walking of 10-1·9[CF3CO2H] in the presence of 10
i
1
equiv of Pr2NEt. (b) Partial H NMR spectra (400 MHz, 10 mM,
DMSO-d6, 298 K) of the reaction mixture over time. After 90 h of
exchange, 19 3% of walkers are positioned on the 9th foothold of
the track (10-9). Green resonances correspond to 10-9. Rate constants
obtained from the fitting of the experimental values to a kinetic model
using SimFit9 (see Figure 9 and Supporting Information for details).
ASSOCIATED CONTENT
* Supporting Information
■
S
Experimental procedures, synthesis and characterization data,
processivity experiments, kinetic measurements, and rate
constant determinations. This material is available free of
charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
Corresponding Author
David.Leigh@manchester.ac.uk
■
Funding
Notes
The authors declare no competing financial interest.
Figure 9. Intramolecular migration of the α-methylene-4-nitrostyrene
ACKNOWLEDGMENTS
■
i
unit of 10-1·9[CF3CO2H] in the presence of 10 equiv of Pr2NEt.
We thank the EPSRC National Mass Spectrometry Service
Centre (Swansea, UK) for high-resolution mass spectrometry.
This research was funded by the ERC. A.G.C. thanks the
Population of isomers (1H NMR integration). After 90 h, 19 3% of
walkers are positioned on foothold 9 of the track (isomer 10-9). Lines
show the best fit of the experimental data to the kinetics of the
exchange between 10-1, 10-2, 10-3, 10-4, 10-5, 10-6, 10-7, 10-8, and
10-9 using SimFit9 (see Supporting Information for details). Error bars
́ ́
Fundacion Ramon Areces (Spain) for a postdoctoral fellowship.
We thank Prof. Dr. G. von Kiedrowski for the use of the
program SimFit, Dr. C. C. Robertson for useful discussions, and
Dr. B. Lewandowski and M. R. Wilson for their assistance in
1
are indicative of the error associated with H NMR integration using
equivalent protons in each positional isomer. Error of fit 10%.
1
acquiring H NMR data for the kinetic experiments.
along the track. Interestingly, however, the preference for the
walker to spend more time toward one end of the track
appears to be a result of kinetics associated with foothold 8, the
amine adjacent to the naphthylamine group, as well as the
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(11) Processivity is the tendency of the molecular fragment (i.e., the
walker) to remain attached to the track during operation, i.e. to
migrate along a molecular scaffold without detaching or exchanging
with other molecules in the bulk (ref 2a). We previously reported3a
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adjacent amines on model (up to four repeat units) oligoethylenei-
G
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