High fidelity kinetic self-sorting in multi-component systems based on guests with multiple binding epitopes

Article abstract of DOI:10.1021/ja063390j

The molecular recognition platforms of natural systems often possess multiple binding epitopes, each of which has programmed functional consequences. We report the dynamic behavior of a system comprising CB[6], CB[7], and guests cyclohexanediammonium (1) and adamantanealkylammonium (2) that we refer to as a two-faced guest because it contains two distinct binding epitopes. We find that the presence of the two-faced guest-just as is observed for protein targeting in vivo-dictates the kinetic pathway that the system follows toward equilibrium. The influence of two-faced guest structure, cation concentration, cation identity, and individual rate and equilibrium constants on the behavior of the system was explored by a combination of experiment and simulation. Deconstruction of this system led to the discovery of an anomalous host-guest complex (CB[6]·1) whose dissociation rate constant (k_out = 8.5 × 10^-10 s^-1) is ≈100-fold slower than the widely used avidin-biotin affinity pair. This result, in combination with the analysis of previous systems which uncovered extraordinarily tight binding events (K_a ≥ 10¹² M^-1), highlights the inherent potential of pursuing a systems approach toward supramolecular chemistry.

Full text of DOI:10.1021/ja063390j

Published on Web 10/11/2006
High Fidelity Kinetic Self-Sorting in Multi-Component Systems
Based on Guests with Multiple Binding Epitopes
Pritam Mukhopadhyay, Peter Y. Zavalij, and Lyle Isaacs*
Contribution from the Department of Chemistry and Biochemistry, UniVersity of Maryland,
College Park, Maryland 20742
Received May 15, 2006; E-mail: LIsaacs@umd.edu
Abstract: The molecular recognition platforms of natural systems often possess multiple binding epitopes,
each of which has programmed functional consequences. We report the dynamic behavior of a system
comprising CB[6], CB[7], and guests cyclohexanediammonium (1) and adamantanealkylammonium (2)
that we refer to as a two-faced guest because it contains two distinct binding epitopes. We find that the
presence of the two-faced guestsjust as is observed for protein targeting in vivosdictates the kinetic pathway
that the system follows toward equilibrium. The influence of two-faced guest structure, cation concentration,
cation identity, and individual rate and equilibrium constants on the behavior of the system was explored
by a combination of experiment and simulation. Deconstruction of this system led to the discovery of an
anomalous host-guest complex (CB[6]‚1) whose dissociation rate constant (kout ) 8.5 × 10-10 s-1) is
≈100-fold slower than the widely used avidin‚biotin affinity pair. This result, in combination with the analysis
of previous systems which uncovered extraordinarily tight binding events (Ka g 1012 M-1), highlights the
inherent potential of pursuing a systems approach toward supramolecular chemistry.
in addition to thermodynamically controlled pathways.3 As an
approach toward systems chemistry through a bottom-up
Introduction
approach we,4-6 and others,7 have begun to study complex self-
sorting systems that are under thermodynamic control. For the
preparation of chemical systems that display functional aspects
typically reserved for inherently nonequilibrium natural systems,
it is necessary to incorporate kinetic and spatial control into
our self-sorting systems. Herein we explore the hypothesis that
the use of guests containing multiple binding epitopes may allow
efficient control over both the kinetic and thermodynamic
outcomes of multicomponent self-sorting systems. We report a
four-component system whose deconstruction led to the dis-
covery of an anomalous host-guest complex (CB[6]‚1) whose
The outcomes of the majority of designed self-assembly
processes have been subject to thermodynamic rather than
kinetic control.1 Accordingly, supramolecular chemists have
better intuition in estimating ground state - ground state rather
than ground state - transition state energy differences. Notable
examples of kinetic control in assembly processes include
molecular chaperones, catenane and rotaxane threading, helicate
formation, regioselective isotopomer exchange, capsule forma-
tion, cyclodextrin complexes, and even the folding of prion
proteins.2 In contrast, systems biologistssand biological systemss
have numerous modules at their disposal for the top-down
engineering of catalytic processes, compartmentation and seg-
regation of incompatible species in time and space, and
regulatory strategies that all depend on kinetically controlled
(3) Oltvai, Z. N.; Barbasi, A.-L. Science 2002, 298, 763-764; Dueber, J. E.;
Yeh, B. J.; Bhattacharyya, R. P.; Lim, W. A. Curr. Opin. Struct. Biol.
2004, 14, 690-699; Prescher, J. A.; Bertozzi, C. R. Nat. Chem. Biol. 2005,
1, 13-21; Kitano, H. Nature 2002, 420, 206-210; Aloy, P.; Russell, R. B.
FEBS Lett. 2005, 579, 1854-1858.
(4) Wu, A.; Chakraborty, A.; Fettinger, J. C.; Flowers, R. A., II; Isaacs, L.
Angew. Chem., Int. Ed. 2002, 41, 4028-4031.
(5) Wu, A.; Isaacs, L. J. Am. Chem. Soc. 2003, 125, 4831-4835; Mukho-
padhyay, P.; Wu, A.; Isaacs, L. J. Org. Chem. 2004, 69, 6157-6164.
(6) Liu, S.; Ruspic, C.; Mukhopadhyay, P.; Chakrabarti, S.; Zavalij, P. Y.;
Isaacs, L. J. Am. Chem. Soc. 2005, 127, 15959-15967.
(7) Xu, H.; Hong, R.; Tongxiang, U.; Uzun, O.; Rotello, V. J. Am. Chem.
Soc. 2006, 128, 3162-3163; Saur, I.; Scopelliti, R.; Severin, K. Chem.
Eur. J. 2006, 12, 1058-1066; Burd, C.; Weck, M. Macromolecules 2005,
38, 7225-7230; Hwang, I.-W.; Kamada, T.; Ahn, T. K.; Ko, D. M.;
Nakamura, T.; Tsuda, A.; Osuka, A.; D., K. J. Am. Chem. Soc. 2004, 126,
16187-16198; Telfer, S. G.; Sato, T.; Kuroda, R.; Lefebvre, D. B. Inorg.
Chem. 2004, 43, 421-429; Bilgicer, B.; Xing, X.; Kumar, K. J. Am. Chem.
Soc. 2001, 123, 11815-11816; Taylor, P. N.; Anderson, H. L. J. Am. Chem.
Soc. 1999, 121, 11538-11545; Rowan, S. J.; Hamilton, D. G.; Brady, P.
A.; Sanders, J. K. M. J. Am. Chem. Soc. 1997, 119, 2578-2579; Kramer,
R.; Lehn, J.-M.; Marquis-Rigault, A. Proc. Natl. Acad. Sci. U.S.A. 1993,
90, 5394-5398; Schultz, D.; Nitschke, J. R. Angew. Chem., Int. Ed. 2006,
45, 2453-2456; Kamada, T.; Aratani, N.; Ikeda, T.; Shibata, N.; Higuchi,
Y.; Wakamiya, A.; Yamaguchi, H.; Kim, K. S.; Yoon, Z. S.; Kim, D.;
Osuka, A. J. Am. Chem. Soc. 2006, 128, 7670-7678.
(1) The concept of kinetic versus thermodynamic control is well developed in
covalent bond-forming reactions. Curtin, D. Y. Rec. Chem. Prog. 1954,
15, 111-128; Winstein, S.; Holness, N. J. J. Am. Chem. Soc. 1955, 77,
5562-5578; Seeman, J. I. Chem. ReV. 1983, 83, 83-134.
(2) Paraschiv, V.; Crego-Calama, M.; Ishi-i, T.; Padberg, C. J.; Timmerman,
P.; Reinhoudt, D. N. J. Am. Chem. Soc. 2002, 124, 7638-7639; Tashiro,
S.; Tominaga, M.; Yamaguchi, Y.; Kato, K.; Fujita, M. Chem. Eur. J. 2006,
12, 3211-3217; Oshikiri, T.; Takashima, Y.; Yamaguchi, H.; Harada, A.
J. Am. Chem. Soc. 2005, 127, 12186-12187; Hori, A.; Yamashita, K.-I.;
Fujita, M. Angew. Chem., Int. Ed. 2004, 43, 5016-5019; Badjic, J. D.;
Cantrill, S. J.; Stoddart, J. F. J. Am. Chem. Soc. 2004, 126, 2288-2289;
Hasenknopf, B.; Lehn, J.-M.; Boumediene, N.; Leize, E.; Dorsselaer, A.
V. Angew. Chem., Int. Ed. 1998, 37, 3265-3268; Davis, J. T.; Kaucher,
M. S.; Kotch, F. W.; Iezzi, M. A.; Clover, B. C.; Mullaugh, K. M. Org.
Lett. 2004, 6, 4265-4268; Dyck, A. S. M.; Kisiel, U.; Bohne, C. J. Phys.
Chem. B 2003, 107, 11652-11659; Yamanaka, M.; Yamada, Y.; Sei, Y.;
Yamaguchi, K.; Kobayashi, K. J. Am. Chem. Soc. 2006, 128, 1531-1539;
Lin, C.-F.; Liu, Y.-H.; Lai, C.-C.; Peng, S.-M.; Chiu, S.-H. Angew. Chem.,
Int. Ed. 2006, 45, 3176-3181; Baskakov, I. V.; Legname, G.; Prusiner, S.
B.; Cohen, F. E. J. Biol. Chem. 2001, 276, 19687-19690.
9
10.1021/ja063390j CCC: $33.50 © 2006 American Chemical Society
J. AM. CHEM. SOC. 2006, 128, 14093-14102
14093

A R T I C L E S
Mukhopadhyay et al.
Scheme 1. Kinetic versus Thermodynamic Self-Sorting
dissociation rate constant (koff ) 8.5 × 10-10 s-1) is ap-
proximately 2 orders of magnitude slower than that of avidin‚
biotin.
Origin of the Hypothesis that Multiple Binding Epitopes
Would Deliver Kinetic Control in Multicomponent Systems.
Biological systems are inherently nonequilibrium in both time
and space. A natural starting point for our investigations of
kinetic control in self-sorting systems, therefore, was a literature
review of the strategies that Nature uses to maintain its control
over temporal (kinetic) and spatial distribution of important
biological species such as proteins, nucleic acids, and ions.
Although issues of kinetic control pervade nearly all aspects of
biochemistry (e.g. control of transmembrane ionic gradients,
spatial segregation of incompatible metabolic pathways, and
chaperone-mediated protein folding), we concentrate in this
section on three examples of protein targeting8 that greatly
influenced our design of the system described in this paper.
Protein targetingsalso referred to as a sorting processsis
initiated during ribosomal peptide synthesis in the cytosol by
the covalent attachment of a signal peptide sequence. The signal
sequence directs the ribosome to the membrane of the endo-
plasmic reticulum (ER) where protein synthesis continues, the
peptide is then translocated across the membrane where a signal
peptidase removes the tagging peptide, and then the folded
protein is released into the lumen of the ER. Subsequent
modifications (e.g., glycosylation) are used to determine the
ultimate destination of the protein (e.g., lysosomes, sectretory
vesicles, or the plasma membrane). A second example is the
co-translational modification of cytosolic proteins with myris-
toyl, palmitoyl, farnesyl, or geranylgeranyl groups that send
them to the cytosolic side of plasma or compartment membranes.
All four of these groups amount to long hydrocarbon tails that
anchor the protein to a membrane. A final example involves
the trafficking and adhesion of blood-borne cells to specific
tissues which are critical components of immune response. As
a specific example, the transition of leukocytes from unbound
to rolling to adherent has been shown to depend on a number
of factors including the presence of a specific binding epitope
on the walls of the microvasculature and its valency (e.g., ligand
density).9 In all of these cases, spatio/temporal control is
achieved by the appendage of a signaling group in the form of
an additional binding epitope. These specific examples lead us
to hypothesize that the study of guests containing multiple
binding epitopes in complex multicomponent systems might
result in interesting dynamic behavior.
family11,12 (CB[n]; n ) 6, 7) as hosts because their complexes
exhibit tight binding, high selectivity, and slow kinetics of
1
exchange which allow the use of H NMR as our primary
analytical tool.5,13-16 The two guests used in this paper were
settled upon by an iterative process17 that involved the prepara-
tion and screening of four-component mixtures with no prior
knowledge of the precise equilibrium or rate constants of
formation of their CB[6] or CB[7] complexes. This iterative
process resulted in the selection of cyclohexanediamine (1) as
one of the guests for detailed study. Two considerations that
guided the iterative process toward 1 were (1) guests containing
cyclohexane rings were given priority since Nau and co-workers
have shown they display slow kinetics of association15 that
1
enables H NMR monitoring of the kinetics, and (2) guests
should form tight 1:1 complexes with both CB[6] and CB[7].
For our guests containing two-binding epitopes, we iteratively
settled upon guests 2a-2c which we refer to as two-faced guests
because they contain two distinct (e.g., adamantylammonium
and alkylammonium) binding epitopes (Scheme 1). Guests 2a-
2c can be used to study the influence of the length of the
alkylammonium tail on the behavior of the system. For a control
compound we selected adamantaneamine (3) which lacks a
second binding epitope. Although we exclusively used the
CB[n] hosts in this study because their dynamic processes are
(11) Lagona, J.; Mukhopadhyay, P.; Chakrabarti, S.; Isaacs, L. Angew. Chem.,
Int. Ed. 2005, 44, 4844-4870.
Results
(12) Lee, J. W.; Samal, S.; Selvapalam, N.; Kim, H.-J.; Kim, K. Acc. Chem.
Res. 2003, 36, 621-630.
Design Aspects of the Chemical Components Used in this
Study. On the basis of the observations described above for
natural systems, we decided to explore the behavior of guests
bearing multiple binding epitopes10 in multicomponent systems.
We hypothesized that the presence of multiple binding epitopes
on a single guest might control the kinetic partitioning of species
within a complex system (e.g. fast and weak versus slow and
tight) resulting in a well-defined, kinetic, self-sorting state. For
this study, we selected two members of the cucurbit[n]uril
(13) Mock, W. L.; Shih, N. Y. J. Org. Chem. 1986, 51, 4440-4446.
(14) Mock, W. L.; Shih, N. Y. J. Am. Chem. Soc. 1989, 111, 2697-2699.
(15) Marquez, C.; Nau, W. M. Angew. Chem., Int. Ed. 2001, 40, 3155-3160;
Marquez, C.; Hudgins, R. R.; Nau, W. M. J. Am. Chem. Soc. 2004, 126,
5808-5816.
(16) Jeon, W. S.; Moon, K.; Park, S. H.; Chun, H.; Ko, Y. H.; Lee, J. Y.; Lee,
E. S.; Samal, S.; Selvapalam, N.; Rekharsky, M. V.; Sindelar, V.;
Sobrasingh, D.; Inoue, Y.; Kaifer, A. E.; Kim, K. J. Am. Chem. Soc. 2005,
127, 12984-12989.
(17) The iterative process involved three steps: (1) preparation of four-
component mixtures and observation of the outcome by 1H NMR (e.g.
fidelity of kinetic and thermodynamic sorting), (2) use of GEPASI to
rationalize the outcome with guessed (estimated) kinetic and thermodynamic
values as inputs and thereby inform chemical intuition, and (3) the use of
these insights to guide the next round of iteration. We investigated
approximately 20 pairs of guestssmainly derivatives of adamantylamines
and cyclohexylaminessbefore discovering the system described in this
paper. The discovery process took approximately 3 months including time
for synthesis of the requisite two-faced guests.
(8) Stryer, L. Biochemistry, 4th ed.; W. H. Freeman and Co.: New York, 1995.
(9) Chang, K.-C.; Tees, D. F. J.; Hammer, D. A. Proc. Natl. Acad. Sci. U.S.A.
2000, 97, 11262-11267.
(10) Mammen, M.; Choi, S.-K.; Whitesides, G. M. Angew. Chem., Int. Ed. 1998,
37, 2755-2794.
9
14094 J. AM. CHEM. SOC. VOL. 128, NO. 43, 2006

Kinetic Self-Sorting
A R T I C L E S
Scheme 2. Synthesis of 2a-2c
followed easily by 1H NMR, we expect that the lessons learned
with the CB[n] hosts will be transferable to other host systems
(e.g., cyclodextrins and calixarenes), provided an analytical tool
with sufficient time and structural resolution is available (e.g.
stopped flow coupled with fluorescence or UV/vis).
Synthesis of Guests 2a-2c. The synthesis of two-faced
guests 2a-2c is shown in Scheme 2. For example, the reaction
of 1-bromoadamantane with butylamine yielded the correspond-
ing amine that was isolated and characterized as its hydrochlo-
ride salt 2a in 64% yield. Separate treatment of 1-bromoada-
mantane with hexanenitrile and octanenitrile under strongly
acidic conditions yielded amides 4b (74%) and 4c (70%) in
good yield via a Ritter-type reaction. Reduction of amides 4b
and 4c with LiAlH4 in dimethoxyethane proceeded smoothly
to give the corresponding amines which were isolated as the
corresponding hydrochloride salts 2b and 2c in 84% and 87%
yields, respectively.
A Single System Displays Both High-Fidelity Kinetic and
Thermodynamic Self-Sorting. Our first observation that two-
faced guests lead to well-defined dynamic behavior occurred
when we mixed equimolar solutions of hosts CB[6] and CB[7]
with guests 1 and 2a (Scheme 1). Under kinetic control (6 min
after mixing), two-faced guest 2a used its slim and weakly
binding butylammonium epitope to associate with CB[6] (e.g.,
CB[6]‚2a), whereas 1 formed the CB[7]‚1 complex. Comparison
1
Figure 1. 1H NMR spectra (400 MHz, 298 K, 5mM Na2SO4 in D2O, pH
7.0) for: (a) CB[6]‚2a, (b) CB[7]‚1, (c) CB[6]‚1, (d) CB[7]‚2a, (e) mixture
of CB[6]‚2a and CB[7]‚1 recorded 6 min after mixing the components, (f)
mixture of CB[6]‚1 and CB[7]‚2a recorded 56 days after mixing the
components. Color code: CB[6]‚2a, orange; CB[7]‚1, green; CB[6]‚1, aqua;
CB[7]‚2a, pink.
of the H NMR spectra recorded shortly after mixing (Figure
1e) with those of the individual complexes (Figure 1a,b)
demonstrates the high-fidelity (95:5) of this kinetic self-sorting
process. After 56 days we observed a dramatically different
spectrum (Figure 1f) which is nearly the superposition of those
recorded for CB[6]‚1 and CB[7]‚2a (Figure 1c,d). Chemical shift
analysis shows that two-faced guest 2a has now used its bulkier,
but much tighter binding, adamantylammonium face in the
formation of the thermodynamically self-sorted state comprising
CB[6]‚1 and CB[7]‚2a.
Influence of Key Experimental Variables on the Fidelity
of Kinetic and Thermodynamic Self-Sorting. Although the
observation that two-faced guests such as 2a control both the
kinetic and thermodynamic outcomes of this system was
intuitively appealing based on the precedent from natural
systems, we wanted to explore the fundamental factors govern-
ing the efficiency of the process. For this purpose, we
investigated the influence of two-faced guest structure (2a-2c
and 3), salt concentration, salt identity, and values of binding
and rate constants by a combination of experiment and simula-
tion.
binding epitope, we observed the rapid formation of CB[7]‚3
along with free CB[6] and 1. CB[6] and 1 then associate
remarkably slowly (kin ) 0.0012 M-1 s-1, Supporting Informa-
tion) at room temperature to yield the thermodynamic self-sorted
state. When guests 2b and 2c with their longer alkyl tails were
used, we observed a decrease in the fidelity of the kinetic self-
sorting (CB[6]‚2:CB[7]‚2; 2b ) 81:19; 2c ) 36:64; Supporting
Information). The fidelity of the thermodynamic self-sorting
state remains high when guests 2b, 2c, and 3 are used.
Influence of Cation Concentration on the Fidelity of
Kinetic Self-Sorting. It is well-known that cations (e.g., alkali
metal ions and protons) bind to the ureidyl-carbonyl lined
portals of CB[6] and CB[7] and thereby compete with guest
binding which lowers the observed value of Ka for the host-
guest complex.11,12 We thought it would be interesting, therefore,
to increase the complexity of the system even further by the
addition of alkali metal cation and observe the influence on the
fidelity of the kinetic and thermodynamic self-sorting states of
the system. We found that as the concentration of Na2SO4 is
increased (0-500 mM), the fidelity of the kinetic self-sorting
state is compromised. Figure 2a shows a plot of the distribution
Influence of the Length of the Alkylammonium Binding
Epitope on the Fidelity of Kinetic Self-Sorting. We studied
the influence of the presence and length of the alkylammonium
chain of the two-faced guests (2b, 2c, and 3) on the fidelity of
kinetic self-sorting for four-component mixtures with CB[6],
CB[7], and 1. When compound 3 was used, which lacks a CB[6]
9
J. AM. CHEM. SOC. VOL. 128, NO. 43, 2006 14095

A R T I C L E S
Mukhopadhyay et al.
Figure 2. Fidelity of kinetic self-sorting. (a) Percentage of CB[6]‚2a (O)
and CB[7]‚2a (9) formed after 6 min as a function of [Na2SO4]. (b)
Percentage of CB[6]‚2a (O) and CB[7]‚2a (9) formed after 6 min as a
function of ionic radius.
of 2a into its CB[6]‚2a and CB[7]‚2a complexes as determined
by 1H NMR integration 6 min after mixing (Supporting
Information) as a function of concentration of Na2SO4. Low
concentrations of Na2SO4 (e.g., 0 or 5 mM) result in a high-
fidelity kinetic self-sorting step, whereas at higher concentrations
increasing amounts of the thermodynamically preferred CB[7]‚
2a complex is formed after only 300 s. The fidelity of the
thermodynamic self-sorting state is high (g95:5) over the full
range of Na2SO4 concentrations.
Figure 3. 1H NMR spectra (400 MHz, D2O, pD 7.4, 298 K, 2.5 mM
components, 6 min after mixing) recorded for a mixture of CB[6], CB[7],
1, and 2a as a function of metal sulfate identity (25 mM): (A) Li2SO4, (B)
Na2SO4, (C) K2SO4, (D) Cs2SO4, (E) MgSO4, and (F) CaSO4. Color code:
CB[6]‚2a, orange; CB[7]‚1, green; CB[6]‚1, aqua; CB[7]‚2a, pink. The
marked resonances (*) correspond to unbound 1. The sphere sizes are scaled
according to their ionic radii.
Influence of Cation Identity on the Fidelity of Kinetic Self-
Sorting. Given that the concentration of Na+ controls the
partitioning of the two-faced guest into CB[6]‚2a and CB[7]‚
2a we wondered whether the identity of the cation would exhibit
a similarly pronounced effect on the fidelity of kinetic self-
sorting. For these experiments we used a common fixed
concentration (25 mM) of metal sulfate salts. Figure 3 shows
1
the H NMR spectra recorded for the kinetically controlled
partitioning in the presence of six different cations (Li+, Na+,
K+, Cs+, Mg2+, and Ca2+). Integration of the resonances in
Figure 3 allowed us to determine the ratio of CB[6]‚2a to CB-
[7]‚2a; these data were used to construct Figure 2b. Interestingly,
the ionic radius of the cation shows a good correlation with the
degree of fidelity of the kinetic self-sorting step.
X-ray Crystal Structure of CB[6]‚1. Figure 4 shows the
X-ray structure of one of the three molecules of complex CB-
[6]‚1 which appear in the unit cell of the crystal. The structure
clearly demonstrates that the CB[6] cavity expands to accom-
modate the large cyclohexane ring (volume ) 125 Å3).
Furthermore, the normally circular cavity of CB[6] undergoes
a large ellipsoidal deformation (0.95-1.22 Å)18 upon formation
of CB[6]‚1 to accommodate the cyclohexane ring of guest 1.
Guest 1 fills the cavity of CB[6] so efficiently that the ground
state of the complex CB[6]‚1 exhibits substantial distortions.
The transition state to ingression of 1 through the eVen smaller
Figure 4. X-ray crystal structure of one of the three independent complexes
of CB[6]‚1 in the unit cell. Solvating H2O has been removed for clarity.
Color coding: C, gray; H, white; N, blue, O, red.
ureidyl-carbonyl-lined portal of CB[6] should exhibit large
structural distortions which provides a rationale for observed
extremely slow association rate constant.15
Experimental Determination of Kinetic and Thermody-
namic Parameters for Use in GEPASI Simulations. To assess
the influence of the key thermodynamic and kinetic parameters
in this system we first needed to determine or estimate values
of kin, kout, and Ka for all four CB[n]‚guest pairs to be used in
simulations using GEPASI (vide infra).19 GEPASI is a user-
friendly program with a graphical user interface designed for
biochemical simulations that uses symbolic reactions, component
concentrations, and individual rate constants as input. GEPASI
(19) GEPASI can be downloaded free-of-charge at http://www.gepasi.org;
Mendes, P. Comput. Appl. Biosci. 1993, 9, 563-571; Mendes, P. Trends
Biochem. Sci. 1997, 22, 361-363; Mendes, P.; Kell, D. B. Bioinformatics
1998, 14, 51-67.
(18) Samsonenko, D. G.; Virovets, A. V.; Lipkowski, J.; Geras’ko, O. A.; Fedin,
V. P. J. Struct. Chem. 2002, 43, 664-668.
9
14096 J. AM. CHEM. SOC. VOL. 128, NO. 43, 2006

Kinetic Self-Sorting
A R T I C L E S
sets up the differential equations that govern the system and
solves them to yield the concentrations of the components of
the system as a function of time and at steady state as output.
Determination or Estimation of the Values of Ka, kin, and
kout. We estimated the values of Ka for CB[6]‚2a, CB[7]‚2a,
and CB[7]‚1 using literature values recently determined by us
for a similar solvent composition.6,13 To determine the value of
kin for CB[6]‚1 (kin ≈ 0.0012 M-1 s-1) we monitored its
1
formation by H NMR from a solution containing equimolar
amounts of CB[6] and 1 (2.5 mM) and fitted the data to a simple
bimolecular association model (Supporting Information). To
determine the values of kout for the CB[6]‚1, CB[6]‚2, CB[7]‚
1, and CB[7]‚2 complexes we performed competitive displace-
ment assays13,14 or used EXSY spectroscopy.20 For example,
we followed the dissociation of 2a-2c from the CB[7]‚2
complex by NMR in the presence of 13 equiv of tighter binding
guest 5. Values of kout for CB[7]‚2 (2a: 2.4 × 10-5 s-1; 2b:
2.3 × 10-5 s-1; 2c: 2.5 × 10-5 s-1) at room temperature were
determined (assuming a unimolecular irreversible dissociation
model) and analyzed over greater than two half-lives using eq
1 in the standard way (Supporting Information). The comparable
values of kout for CB[7]‚2a-CB[7]‚2c is not surprising since
the same binding epitope (e.g., adamantylammonium) is used
for all three complexes. A similar experiment yielded a value
of kout for CB[6]‚2a (kout ) 2.2 × 10-3 s-1) by competition
with 2 equiv of hexanediamine. We had to resort to EXSY
spectroscopy to determine the value of kout for the more quickly
dissociating CB[7]‚1 (kout ) 2.7 s-1) and CB[6]‚2c (kout ) 0.5
s-1) complexes.
Figure 5. (a) Plot of the dissociation of CB[6]‚1 (2.5 mM, 298 K, 5 mM
Na2SO4 in D2O, pH 7.0) as a function of time at different temperatures. (b)
Arrhenius plot of the data from part a.
Discussion
This discussion section has two goals. The first is to clarify
the advantages of pursuing a systems chemistry approach toward
the discovery of a multicomponent system with anomalous
properties and collective function followed by its deconstruction
relative to an approach based on an a priori study of all pairwise
components of the system followed by its construction. Second,
we use GEPASI simulations to rationalize the experimental
results for the system comprising CB[6], CB[7], 1, 2 (3), and
metal ions which elucidate the key factors controlling the fidelity
of the kinetic and the thermodynamic self-sorted states.
Although the displacement of 1 from the CB[6]‚1 complex
was impractically slow at room temperature, we were able to
monitor its displacement by competition with 2 equiv of
Reasons To Pursue a Systems Chemistry Approach
toward Complexity. One of the common features of scientific
studiessthat has worked remarkably well for centuriessis the
application of a reductionist approach. Reductionism holds that
complex phenomena can be understood by analyzing the
fundamental chemical, physical, or biological components
operating in the system. The application of a reductionist
approach in certain areas of 21st century science, however,
seems less appropriate. Biologists, for example, appreciate the
fact that the level of connectivity and complexity present in
biological systems precludes a complete understanding of life
processes by a reductionist approach and have responded by
creating the field of systems biology22 to tackle the issues that
emerge from complex, highly interconnected systems. Computer
scientists recognize that the form and connectivity of the
worldwide webswhich resembles biological systems in many
wayssdictate that they must approach certain problems by an
application of systems-wide approaches.23 Despite the fact that
all biological and life processes may be simply considered as
1
hexanediamine over the 80-96 °C temperature range by H
NMR. Figure 5a shows a plot of ln([CB[6]‚1]/[CB[6]‚1]0])
versus time used to determine the values of kout for CB[6]‚1 at
five temperatures; Figure 5b shows an Arrhenius plot of the
data. From the Arrhenius plot we were able to extrapolate
kout,(CB[6]‚1) ) 8.5 × 10-10 s-1 at room temperature along with
an estimate of the activation energy for this dissociation process
(Ea ) 30.0 kcal mol-1). The CB[6]‚1 pair has a half-life of 26
years at room temperature! Both values are remarkably anoma-
lous for the dissociation of a monovalent host-guest pair. For
example, avidin‚biotin with its dissociation rate constant of a
mere 10-7 s-1 is widely used in biological applications.21
Despite its relatively low affinity (Ka ) 0.0012 M-1 s-1/8.5 ×
10-10 s-1 ) 1.4 × 106 M-1), the readily available CB[6]‚1 pair
dissociates ∼100-fold slower than the natural pair which
suggests its great potential in applications typically reserved for
avidin‚biotin (e.g., immobilization and affinity column purifica-
tion applications).
(22) Aloy, P.; Russell, R. B. Nat. ReV. Mol. Cell. Biol. 2006, 7, 188-197.
(23) Milo, R.; Itzkovitz, S.; Kashtan, N.; Levitt, R.; Shen-Orr, S.; Ayzenshtat,
I.; Sheffer, M.; Alon, U. Science 2004, 303, 1538-1542.
(20) Perrin, C. L.; Dwyer, T. J. Chem. ReV. 1990, 90, 935-967.
(21) Green, N. M. Methods Enzymol. 1990, 184, 51-67.
9
J. AM. CHEM. SOC. VOL. 128, NO. 43, 2006 14097

A R T I C L E S
Mukhopadhyay et al.
Figure 6. Simulation of the system comprising CB[6], CB[7], 1, and 2a: (a) equilibria considered, (b) values of Ka, kin, and kout (known values: green;
literature estimates: orange; calculated from known or estimated values: black), and (c) concentrations used as input for the simulation, (d) plot of concentration
versus time. Color code: CB[7]‚1, blue; CB[7]‚2a, pink; CB[6]‚2a, green; CB[6]‚1, red.
complex chemical systems, chemists have been slower to
embrace the concept of a systems approach to chemistry.24
Within the molecular recognition communityswhose general
aim is to understand noncovalent interactions and use them to
build up functional systems of our own design or to augment
biological systems to respond to external stimulisthere are
several significant reasons to pursue a systems chemistry
approach toward the discovery of new function and fundamental
insights. Some scientists assert that systems chemistry and self-
sorting systems produce behaviors that are simply the sum of
their parts and therefore could have been predicted beforehand
with a detailed knowledge of all the values of Ka, kon, and koff
for each of the possible pairwise interactions. Such assertions
are, of course, correct in theory, but that approach would be
inefficient and impractical to implement experimentally. For
example, in a 10-component system there are 55 (102/2 + 10/
2) pairwise interactions. Rarely, if ever, are such large collec-
tions of values of Ka, kon, and koff measured in common media
(e.g., solvent, buffer, pH, ionic strength, temperature) for a series
of homologous hosts and guests with sufficient accuracy to allow
the a priori prediction of the behavior of a system of even
modest complexity. Given that the measurement of 155 kinetic
and thermodynamic constants would likely take more than 1
year and would allow the prediction of the behavior of one 10-
component system which may have no interesting function, our
view is that the systems chemistry approach which relies on
the preparation and NMR observation of mixtures of modest
complexity (e.g. a 10-component mixture requires at most 1
day) is far superior.
n components) are studied as a single entity whose overall
behavior depends on the matrix of all pairwise interactions.
Simple behavior in the form of self-sorting at modest concentra-
tions signals the presence of a number of high affinity (Ka) and
highly selective (∆∆G) binding events as components of the
interaction matrix. As a specific example of this route to
discovery, I note that our observation of 12-component self-
sorting systems containing CB[n] hosts11,12 leads us to measure
values of Ka in excess of 1012 M-1 in water for complexes of
CB[7] with cationic adamantane derivatives by competition
experiments.6 As such values exceed the upper limits of
measurement by direct techniques, it is unlikely they would ever
have been measured without the clues provided from the self-
sorting experiments. Similarly, a systems chemistry approach
that monitors concentrations as a function of time until
equilibrium is achieved reflects the matrix of values of kon and
koff and provides a route to discover systems and complexes
with unusual dynamics. The discovery of the CB[6]‚1 pair which
has a dissociation rate constant approximately 100-fold slower
than avidin‚biotin illustrates the great potential of this ap-
proach.21
Third, the systems chemistry approach is versatile in that it
may be tailored to test specific hypotheses and goals (e.g. the
influence of guests’ multiple binding epitopes, vide infra) and
also offers the opportunity for serendipitous discoveries that
often result in significant scientific advancement. For example,
given a large matrix of known values of Ka, kon, and koff it would
be possiblesusing currently known principlessto predict the
behavior of the complex self-sorting systems reported to date.
Such an approach, however, would be unable to predict the
behavior of a system whose underlying reductionist principles
are not already known. As one of the goals of all science is to
discover functional systems that do not obey current rules and
to make them predictable on the basis of newly formulated
principles, we believe that the systems chemistry approachs
with its focus on collective output and functionsoffers signifi-
cant advantages.
Second, as a community we need to devise strategies that
allow us to uncover anomaliessextremely tight or weak (i.e.,
Ka) binding events, extremely fast or slow (i.e., kon and koff)
binding events, or extremely high selectivity binding eventss
since those cases are most likely to require the development of
new fundamental principles and lead to practical applications.
The systems chemistry approach is quite efficient in discovering
such anomalies. Most commonly, a single host-guest complex
is studied in detail which yieldsswith large input of efforts
information regarding Ka, kon, and koff for a single host-guest
complex. In a systems chemistry approach multiple species (e.g.,
GEPASI Simulations of the System Comprising CB[6],
CB[7], 1, and 2a. We used GEPASI to simulate the kinetic
and thermodynamic outcomes of the four-component system
comprising CB[6], CB[7], 1, and 2a. Figure 6a-c shows the
equilibria considered, the kinetic and thermodynamic values,
and the concentrations employed to generate the simulation
shown in Figure 6d. The simulations reproduce the essential
(24) Corbett, P. T.; Leclaire, J.; Vial, L.; West, K. R.; Wietor, J.-L.; Sanders, J.
K. M.; Otto, S. Chem. ReV. 2006, 106, 3652-3711; Gerdts, C. J.; Sharoyan,
D. E.; Ismagilov, R. F. J. Am. Chem. Soc. 2004, 126, 6327-6331;
Stankiewicz, J.; Eckardt, L. H. Angew. Chem., Int. Ed. 2006, 45, 342-
344.
9
14098 J. AM. CHEM. SOC. VOL. 128, NO. 43, 2006

Kinetic Self-Sorting
A R T I C L E S
aspects of the experiments and validate the importance of the
two-faced guests despite small differences in the degree of
fidelity of the kinetic and thermodynamic self-sorting processes
and the precise time course of the process.
chaperonessit should be possible to tune the behavior of the
system by straightforward environmental changes.
The Fidelity of the Thermodynamic Self-Sorting State Is
not Influenced by Guest Structure, Metal Ion Concentration,
or Metal Ion Identity. Factors which decrease the difference
in free energy between the various complexes (e.g. CB[7]‚2a
versus CB[6]‚2a; CB[7]‚1 versus CB[6]‚1) have the potential
to decrease the fidelity of thermodynamic self-sorting. Increasing
the length of the alkyl tail of the two-faced guest (2b or 2c) or
removing it completely (3) does not influence its affinity for
CB[7] because a common adamantylammonium binding epitope
is used to form this complex, whereas its affinity toward CB-
[6]swhere the effect of chain length is well-known13sis
decreased by the structural change. Therefore, the difference in
free energy (e.g. CB[7]‚2a versus CB[6]‚2a) that drives the
thermodynamic self-sorting process increases with the structural
change. Accordingly, the fidelity of the thermodynamic self-
sorting state remains high for all four guests (2a-2c, 3).
Cations are well-known to bind to the carbonyl-lined portals
of the CB[n] family.11,12 For example, Buschmann has studied
the interaction of CB[6] with a variety of metal cations
(including Li+, Na+, K+, Cs+, and Ca2+) and found that Ka does
not vary significantly (Ka g 103 M-1).25 Kaifer demonstrated
that increased concentrations of NaCl and CaCl2 in the aqueous
buffer decrease the observed binding constant of CB[7] toward
methyl viologen.26 Therefore, one might expect that the presence
of high concentrations of Na+ would also reduce the fidelity of
the thermodynamic self-sorting state by competitive binding
although that is not observed experimentally. We rationalize
that the increase in [Na+] concentration in this system reduces
all four Ka (∆G) values similarly and therefore does not
significantly effect the overall values of ∆∆G (e.g. CB[7]‚2a
versus CB[6]‚2a; CB[7]‚1 versus CB[6]‚1) needed to drive
thermodynamic self-sorting.
The System Comprising CB[6], CB[7], 1, and 2a Under-
goes High-Fidelity Thermodynamic Self-Sorting. The fidelity
of this thermodynamic state depends on the initial concentrations
of CB[6], CB[7], 1, and 2a and the values of Ka for CB[6]‚1,
CB[7]‚1, CB[6]‚2a, and CB[7]‚2a but not on any of the
individual rate constants. Interestingly, our estimates of Ka
(Figure 6b) based on the literature suggest that guests 1 and 2
both prefer to bind to CB[7] (e.g. Ka (CB[7]‚1) > Ka (CB[6]‚1) and
Ka (CB[7]‚2a) . Ka (CB[6]‚2a)). Why then is high-fidelity thermo-
dynamic self-sorting achieved? When there is a stoichiometric
balance of hosts and guests (e.g. [CB[6]] ) [CB[7]] ) [1] )
[2a]), the much larger free energy difference between the
complexes of 2a (∆∆G ) 6.4 kcal mol-1) can be used to drive
1 into its less thermodynamically stable CB[6]‚1 (∆∆G ) 3.0
kcal mol-1) complex. The behavior of the more complex four-
component system is significantly different from those of the
individual host-guest pairs because the overall free energy of
the entire system is minimized.
The System Comprising CB[6], CB[7], 1, and 2a also
Undergoes High-Fidelity Kinetic Self-Sorting. Which factors
govern the fidelity of the kinetic self-sorting step? Initially, both
CB[6] and CB[7] are in their free uncomplexed states. CB[7]
with its wider carbonyl-lined portals exhibits faster association
rate contants and is therefore filled first; the competition between
1 and 2a greatly favors the formation of CB[7]‚1 kinetically
because of the g20-fold difference in the values of kin. The
second critical variable governing the kinetic self-sorting step
is the presence of the alkylammonium binding epitope on 2a
which allows it to be sequestered (kin ) 4.4 × 104 M-1 s-1
)
rapidly (e.g. complete in ∼0.1 s) as the CB[6]‚2a complex. The
final critical variable is that the dissociation rate constant for
the CB[7]‚1 complex (kout ) 2.7 s-1) is significantly slower
than the amount of time needed to form the CB[6]‚2a complex.
If the CB[7]‚1 complex dissociates during the sequestration of
2a as its CB[6]‚2a complex then additional competitive op-
portunities occur between 1 and 2a for the formation of
CB[7]‚2a and CB[7]‚1 which inevitably leads to increased
amounts of the thermodynamically more stable CB[7]‚2a. In
summary, the fast sequestration of both 1 and 2a into their
respective kinetic complexes (CB[6]‚2a and CB[7]‚1) is critical
because that keeps the concentrations of uncomplexed CB[6],
CB[7], 1, and 2a low which reduces the rate of transition to
the thermodynamic state by simple mass action considerations.
The Fidelity of Kinetic Self-Sorting Is Influenced by Guest
Structure. Why is the fidelity of kinetic self-sorting decreased
when the length of the alkylammonium binding epitope is
increased (e.g., 2b and 2c) or when it is removed completely
(3)? As described above for 2a, the degree of kinetic self-sorting
depends critically on the rate of sequestration of the two-faced
guest as its CB[6]‚2a complex. It is well-known in cucurbit-
[n]uril chemistry that butylammonium cation binds more tightly
to CB[6] than longer alkylammonium ions (e.g., octyl- or
hexylammonium) by approximately 10-fold per methylene
group.13 Using this information, we are able to extrapolate values
of Ka for CB[6]‚2b and CB[6]‚2c (Ka ) 2.0 × 105 M-1 and 2.0
× 103 M-1, respectively) in our solvent system. When combined
with the experimentally determined value of kout for CB[6]‚2c
(0.5 s-1)swhich shows a decrease of 2.6-fold per methylene
group relative to that for 2asand an interpolated value of kout
for CB[6]‚2b (0.033 s-1), it is apparent that the association rate
constant for the formation of CB[6]‚2c decreases as the length
of the alkyl chain increases. In the extreme case of 3 which
lacks an alkylammonium binding epitope we set Ka (CB[6]‚3)
) 0. Figure 7 shows kinetic simulations of these three systems
based on the kinetic and thermodynamic parameters detailed
above. In accord with the experimental findings (vide supra)
Interestingly, the simulations establish that the rate of
approach to thermodynamic equilibrium after the kinetic self-
sorting step is not governed by the individual rate constants,
but rather by the value of Ka for CB[6]‚2a. This value of Ka
controls the amount of free CB[6] and 2a after the initial kinetic
self-sorting step. When Ka increases, the amount of free 2a
decreases, which in turn slows down the competition between
2a and the even smaller amount of free 1 for CB[7]. Conversely,
smaller values of Ka increase the rate of approach to equilibrium
by increasing the concentration of uncomplexed 1. Because the
amount of uncomplexed 2a is influenced by a number of
variablesshost:guest stoichiometry, total concentration, ionic
strength, temperature, and the presence of competitors or
(25) Buschmann, H.-J.; Jansen, K.; Meschke, C.; Schollmeyer, E. J. Solution
Chem. 1998, 27, 135-140.
(26) Ong, W.; Kaifer, A. E. J. Org. Chem. 2004, 69, 1383-1385.
9
J. AM. CHEM. SOC. VOL. 128, NO. 43, 2006 14099

A R T I C L E S
Mukhopadhyay et al.
Figure 7. Simulation of the system comprising CB[6], CB[7], 1, and (a)
2b, (b) 2c, and (c) 3. The equilibria considered, the kinetic and thermody-
namic values, and the intial concentrations of CB[6], CB[7], and 1 are the
same as in Figure 6. Color code: CB[7]‚1, blue; CB[7]‚2 (3), pink; CB-
[6]‚2 (3), green; CB[6]‚1, red.
Figure 8. Simulation of the system comprising CB[6], CB[7], 1, 2a (all
2.5 mM), and Na2SO4. (a) Equilibria considered, (b) [Na+] ) 5 mM, (c)
[Na+] ) 25 mM, (d) [Na+] ) 100 mM. The kinetic and thermodynamic
constants for complexes of CB[6], CB[7], 1, and 2a are the same as in
Figure 6. Color code: CB[7]‚1, blue; CB[7]‚2a, pink; CB[6]‚2a, green;
CB[6]‚1, red; CB[6]‚Na+, aqua; CB[7]‚Na+, orange.
the simulations show greatly reduced levels of kinetic self-
sorting after 6 min as the length of the alkylammonium binding
epitope is lengthened or removed. The reduced levels of kinetic
self-sorting for 2b, 2c, and 3 relative to that for 2a can be
attributed to two factors: (1) the less efficient kinetic sequestra-
tion (e.g. reduced association rate constant kin) as their CB[6]
complexes, and (2) the increased amounts of free two-faced
guest as the valued of Ka for the alkylammonium binding epitope
decreases which enhances competition with 1 for binding to
CB[7].
The Fidelity of Kinetic Self-Sorting Is Influenced by
Sodium Concentration. Alkali metal cations are well-known
to bind to the members of the CB[n] family with a relatively
constant value of Ka (≈103 M-1).11,25 As such, one might expect
that increasing the concentration of sodium cation would simply
reduce the concentration of free CB[6] and CB[7] by formation
of CB[6]‚Na+ and CB[7]‚Na+ and thereby slow the kinetics of
the system, but that the degree of kinetic and thermodynamic
self-sorting would not change. Why then does the fidelity of
kinetic self-sorting decrease as the concentration of sodium
cation increases? Figure 8 shows a simulation of the system as
a function of Na+ concentration that serves as a basis for
discussion. First, note that at the beginning of the simulation
(Figure 8, point 1), the higher the Na+ concentration, the higher
the concentration of CB[6]‚Na+ and CB[7]‚Na+ and the lower
the concentration of free CB[6] and CB[7] available to form
9
14100 J. AM. CHEM. SOC. VOL. 128, NO. 43, 2006

Kinetic Self-Sorting
A R T I C L E S
host-guest complexes with 1 and 2a. The competition of Na+
with 1 for binding to CB[7] results in a delay in the formation
of the CB[7]‚1 complex (Figure 8, point 2) from ∼10-8 to 10-6
s as Na+ increases (5, 25, 100 mM). The plateau region for
detailed assessment of the importance of this direct conversion
process is not possible with our current experimental data.28
Conclusions
CB[7]‚1 concentration under kinetic control occurs at ∼10-3
s
This paper advocates the use of systems chemistrysas
opposed to a more traditional approach based on single host-
guest complexessas a route to discover aggregates with
anomalous properties and systems with collective function. This
paper explored the hypothesis that compounds that contain
multiple binding epitopes might result in systems with unusual
dynamic behavior. We employed an iterative approach involving
the preparation of four-component mixtures and observation of
their dynamic properties by 1H NMR spectroscopy which
ultimately lead to the system comprising CB[6], CB[7], 1, and
2 (3) which was deconstructed in detail in this paper. Just like
their natural counterparts, complex systems containing two-faced
guests such as 2 are found to display unusual dynamic
phenomena including kinetic self-sorting. For example, under
kinetic control two-faced guest 2a uses its slim alkylammonium
binding epitope to form CB[6]‚2a, whereas 1 engages in the
CB[7]‚1 complex; at thermodynamic equilibrium the roles are
completely reversed. We have explored several of the factors
governing the fidelity of the kinetic self-sorting step including
the concentration and identity of metal cations present in
solution, the length of the alkylammonium binding face of 2,
and the influence of individual rate and equilibrium constants.
We find that factors which retard the rate of sequestration of
the two-faced guest within CB[6] reduce the fidelity of the
kinetic self-sorting step.
More fundamentally, we believe that systems chemistrys
with its focus on collective output and functionshas great
potential to enhance the rate of discovery of compounds with
anomalous recognition properties and functional supramolecular
systems. For example, the study of a thermodynamic self-sorting
system previously led us to the discovery of compounds with
affinities exceeding 1012 M-1 in water.6 In this paper, we
discovered a four-component system whose deconstruction lead
to the measurement of a host-guest system with truly anoma-
lous propertiessnamely CB[6]‚1 with a dissociation rate
constant of 8.5 × 10-10 s-1 which is approximately 2 orders of
magnitude slower than avidin‚biotin. The CB[6]‚1 complex has
a half-life of 26 years at room temperature! The remarkably
slow dissociation rate constant for CB[6]‚1 suggests that this
binding pair may find use in immobilization and affinity column
applications typically reserved for avidin‚biotin. These results
highlight how the kinetic and thermodynamic behavior of
complex n-component systemsswhich depend on the matrix
of possible pairwise interactionssefficiently directs the re-
searcher toward recognition anomalies that stimulate a deeper
understanding of recognition phenomena.
at a relatively constant value of 2.25 mM (Figure 8, point 3).
Similarly, competition of Na+ with 2a for CB[6] delays the
formation of CB[6]‚2a from ∼10-4 to 10-2 s as sodium ion
concentration increases (Figure 8, point 4). Sodium ion competi-
tion does, in fact, slow the formation of both CB[7]‚1 and
CB[6]‚2a similarly, although it does so at different times. The
measured fidelity of kinetic self-sorting (Figure 8, point 5)
decreases as [Na+] increases because the sequestration of 2a
as CB[6]‚2a and dissociation of the initially formed CB[7]‚1
complex (kout ) 2.7 s-1, half-life ) 0.26 s) begin to occur on
the same time scale, allowing for increased competition between
1 and 2a for CB[7]. The Na+ ion and chain length effects are
completely analogous since both variables act by slowing down
the sequestration of the two-faced guest and thereby decrease
the degree of kinetic self-sorting. The simulations reveal a small
change in the fidelity of thermodynamic self-sorting (Figure 8,
point 6) due to competition between Na+ and 1 for CB[6] at
the higher Na+ concentrations. We do not observe this decrease
experimentally; small changes in one or more Ka values could
account for this discrepancy. As mentioned above, the simula-
tions reproduce the overall behavior of the system although the
precise fidelity of kinetic and thermodynamic self-sorting
depends quite sensitively on the input kinetic and thermody-
namic constants.
The Fidelity of Kinetic Self-Sorting Is Influenced by the
Identity of the Cation. Figure 2b shows that the fidelity of
kinetic self-sorting decreases as the ionic radius of the cation
increases. As mentioned above, the affinities of most cations
for CB[6] are similar (≈103 M-1) although the ionic radius of
the larger cations should match better to the van der Waals
radius of the CB[6] portal (1.95 Å).27 Our first hypothesis,
therefore, was that the rate constants for CB[n]‚M+ might be
the source of the observed cation identity dependence. Simula-
tions (not shown) establish that, while rate constants for
CB[n]‚M+ can influence the observed fidelity of kinetic self-
sorting, they only do so when kon/koff are unreasonably small
(e.g. ,103 M-1 s-1/1 s-1) given the structure of CB[6]. A second
hypothesis is based on the potential direct conversion of CB[n]‚
M+ and guest into CB[n]‚guest and M+. In none of the
simulations reported above (Figures 6-8) did we allow such a
process. One can imagine, however, that the smaller cations
(e.g. Li+, ionic radius ) 0.68 Å) which block the portal of CB[6]
less completely than the larger cations (e.g. Cs+, ionic radius
) 1.67 Å) might participate more readily in such a direct
conversion process. When such direct conversion is allowed,
the larger cations would be predicted to result in lower-fidelity
kinetic self-sorting processes as is observed experimentally. A
Finally, the systems chemistry approach is quite versatile and
allows the testing of hypotheses derived from observations of
more complex natural systems that have always served as
stimulation for chemists. In this paper we explored the
hypothesis that the presence of multiple binding epitopes plays
(28) One approach to address this question would involve measurement of the
association rate constant for CB[6] and 2a as a function of metal ion
concentration. Unfortunately, the analytical tools at our disposal do not
allow the measurement of such rapid processes (e.g., 104 M-1 s-1);
Tarmyshov, K. B.; Muller-Plathe, F. J. Phys. Chem. B 2006, 110, 14463-
14468.
(27) The observed correlation with the ionic radius of the desolvated cations
may seem strange given that these cations are hydrated in water. Upon
complexation to CB[n], some of the hydrating H2O molecules are displaced
by coordination with O-atoms of the carbonyl-lined portals of CB[n].
9
J. AM. CHEM. SOC. VOL. 128, NO. 43, 2006 14101

A R T I C L E S
Mukhopadhyay et al.
experiments samples were prepared by adjusting the pH from 2.8 to
12.8 in step 3. The same procedure was followed for all the other steps.
Determination of Values of kout. The values of kout at 298 K for
CB[7]‚2a, CB[7]‚2b, CB[7]‚2c were determined using 13 equiv of 5
as displacing ligand as described in the text and detailed in the
Supporting Information. The value of kout for the CB[6]‚2a complex
was determined in a similar manner at 298 K using 1,6-hexanediamine
as the displacing ligand. The value of kex for CB[7]‚1 was determined
by standard 2D-EXSY experiments using a solution containing CB[7]‚
1 and free 1. The spectra were recorded at 298 K with mixing time of
200 ms. EXSY measurements were also used to determine kout CB[6]‚
2c ) 0.50 s-1. Compound 2b in the complex CB[6]‚2b did not show
cross-peaks in the 2D-EXSY spectrum over a broad range of mixing
times (50-900 ms); accordingly we could not measure a value of kex
for this pair by this method.
a key role in controlling the dynamic behavior within complex
systems. By using an iterative approach based on these broad
design principlessin concert with simulation to inform chemical
intuition along the waysit is possible to program both the
thermodynamic outcome of self-sorting systems and the kinetic
pathways by which they evolve toward equilibrium. When the
strategy for temporal control introduced in this paper is
combined with future modules that enable catalytic processes,
feedback loops, compartmentation, and metastable states, we
anticipate that the toolbox available to systems chemists will
be sufficiently diverse to allow the engineering of functional
systems currently only accessible to systems biologists.
Experimental Section.
Simulations. Simulations were performed using Gepasi 3.30 running
on a Windows XP workstation. The Gepasi model files used in these
simulations are deposited in the Supporting Information.
Sample Preparation. The four-component kinetically self-sorted
mixture comprising CB[6], CB[7], 1, and 2 was prepared as follows:
(1) the calculated amounts of each component were weighed out
separately. The hosts CB[6] and CB[7] and the guests 1 and 2 were
transferred, respectively, into two separate 5-mL screw-capped vials;
(2) CB[6] and CB[7] were dissolved in 1 mL of D2O containing the
desired amounts of Na2SO4; (3) 1 and 2 were dissolved in 1 mL of
D2O containing the desired amounts of Na2SO4. The solutions contain-
ing the components were maintained at 5 mM; (4) the pD of each
solution was adjusted to 7.4 with concentrated NaOD or DCl solution;
(5) 0.3 mL of solution from each of the vials was transferred using a
Hamilton syringe to an NMR tube for analysis; (6) the NMR spectra
were recorded at 298 K within 10 min after mixing. Similar procedures
were followed for preparing the other four-component mixtures.
Samples for the variable Na ion concentration experiments were
prepared using 0-500 mM of Na2SO4 in step 2. Samples for the variable
metal ions experiments were prepared using 25 mM solutions of the
corresponding salt (Li+/K+/Cs+/Mg2+/Ca2+) in step 2. For variable pD
Acknowledgment. We thank the National Institutes of Health
(GM61854), the National Science Foundation (CHE-0615049),
and the University of Maryland for financial support of this
work. We thank the reviewers for comments that helped improve
the manuscript.
Supporting Information Available: Synthetic procedures and
characterization data, selected 1H NMR spectra for CB[n]‚guest
complexes, determination of kout and kin values, 1H and 13C NMR
spectra for all new compounds; Gepasi model files; and details
of the X-ray structure of CB[6]‚1 in CIF format. This material
is available free of charge via the Internet at http://pubs.acs.org.
JA063390J
9
14102 J. AM. CHEM. SOC. VOL. 128, NO. 43, 2006