Design, synthesis, and characterization of a high-affinity trivalent system derived from vancomycin and L-Lys-D-Ala-D-Ala

Article abstract of DOI:10.1021/ja992648l

A trivalent derivative of vancomycin, tris(vancomycin carboxamide), [C₆H₃-1,3,5-(CONHC₆H₄-4-CH₂NHCOV)₃ (R(t)V₃; V = vancomycin)], binds an analogous trivalent derivative of D-Ala-D-Ala, R'(t)L'(3), (C₆H₃-1,3,5- [CON(ε)H(N(α)-Ac)-L-Lys-D-Ala-D-Ala]₃) in water with a dissociation constant that is approximately 4 x 10^-17 M, as estimated by HPLC using a competitive assay against N(α,ε)-diacetyl-L-Lys-D-Ala-D-Ala (L). This binding is one of the tightest known for low molecular weight organic species. The dissociation of R(t)V₃·R'(t)L'₃ in the presence of an excess of L could be followed by HPLC. The kinetics of dissociation are quite different from those of monovalent tight-binding systems such as avidin and biotin. In particular, the rate of dissociation of the aggregate R(t)V₃·R'(t)L'₃ is rapid in the presence of monovalent L at concentrations greater than the value of the dissociation constant for the complex of L with V; by contrast, the rate of dissociation of biotin·avidin is independent of the concentration of biotin. Two mechanisms by which the dissociation may occur are postulated and discussed. Calorimetric measurements for the trivalent system indicate that the enthalpy of association is ~-40 kcal/mol, about three times that of V + L, and thus the entropy of association is ~-18 kcal/mol, approximately 4.5 times that of V + L.

Full text of DOI:10.1021/ja992648l

2698
J. Am. Chem. Soc. 2000, 122, 2698-2710
Design, Synthesis, and Characterization of a High-Affinity Trivalent
System Derived from Vancomycin and L-Lys-D-Ala-D-Ala
Jianghong Rao, Joydeep Lahiri, Robert M. Weis,† and George M. Whitesides*
Contribution from the Department of Chemistry and Chemical Biology, HarVard UniVersity,
12 Oxford Street, Cambridge, Massachusetts 02138
ReceiVed July 26, 1999
Abstract: A trivalent derivative of vancomycin, tris(vancomycin carboxamide), [C6H3-1,3,5-(CONHC6H4-4-
CH2NHCOV)3 (RtV3; V ) vancomycin)], binds an analogous trivalent derivative of D-Ala-D-Ala, R′tL′3, (C6H3-
1,3,5-[CONꢀH(NR-Ac)-L-Lys-D-Ala-D-Ala]3) in water with a dissociation constant that is approximately 4 ×
10-17 M, as estimated by HPLC using a competitive assay against NR,ꢀ-diacetyl-L-Lys-D-Ala-D-Ala (L). This
binding is one of the tightest known for low molecular weight organic species. The dissociation of RtV3‚R′tL′3
in the presence of an excess of L could be followed by HPLC. The kinetics of dissociation are quite different
from those of monovalent tight-binding systems such as avidin and biotin. In particular, the rate of dissociation
of the aggregate RtV3‚R′tL′3 is rapid in the presence of monovalent L at concentrations greater than the value
of the dissociation constant for the complex of L with V; by contrast, the rate of dissociation of biotin‚avidin
is independent of the concentration of biotin. Two mechanisms by which the dissociation may occur are
postulated and discussed. Calorimetric measurements for the trivalent system indicate that the enthalpy of
association is ∼-40 kcal/mol, about three times that of V + L, and thus the entropy of association is ∼-18
kcal/mol, approximately 4.5 times that of V + L.
Introduction
conformational rigidity, and ease of modification of vancomycin
and DADA, combined with the wealth of relevant structural,
thermodynamic, and kinetic information obtained by Perkins,
Williams, Griffin, Pratts, and others, make this system an
attractive one with which to study the physical-organic
chemistry of polyvalent interactions.
We are developing vancomycin (V) and D-Ala-D-Ala (DADA)
as a model system with which to study the physical-organic
chemistry and physical biochemistry of polyvalency.1,2 Vanco-
mycin binds to peptides terminating in D-Ala-D-Ala with
dissociation constants ranging from about 100 µM (for N-acetyl-
D-Ala-D-Ala) to about 1 µM (for diacetyl-L-Lys-D-Ala-D-Ala
and similar compounds).3,4 Τhe geometry of these complexes
is well-defined (Scheme 1),5-7 and their thermodynamics has
been extensively described by Williams and co-workers.8-12
Vancomycin is rigid, and the values of thermodynamic param-
eters for its association with N-acetyl-D-Ala-D-Ala (at 298 K,
∆G° ) -5.2 kcal/mol; ∆H° ) -8.5 kcal/mol; ∆S° ) -11.1
e.u.; -T∆S° ) 3.3 kcal/mol) reflect this rigidity.8 The simplicity,
Polyvalent bindingsthe simultaneous interactions of multiple,
linked ligands with multiple, linked receptorssis a subject of
growing interest in biochemistry.13 A range of important
biological interactionssfrom the association of IgGs with the
surface of a bacterium to the rolling of a leukocyte along the
capillary endothelium near a site of inflammationsdepend on
oligo- or polyvalency.13 In an ideal case, the contribution of
polyvalency to the free energy of binding that would come from
linking receptors and ligands would appear primarily in the T∆S°
term.13 Thus, for example, the free energy of association of a
trivalent receptor-ligand system might be related to that of the
monomers by eqs 1-3 (Scheme 2). That is, the enthalpy of the
trivalent process would be three times that of the monomer,
while the loss in entropy (a term we assume, in the simplest
case, to be dominated by translational entropy) would be
approximately that of the monomer.
In practice, this formulation of a trivalent association neglects
obvious complexities of real molecules. In particular, association
might introduce favorable or unfavorable enthalpic terms due
to interactions among the linking groups, receptors and ligands,
and the modifications of the receptor and ligand required to
link them may also modify their association. The entropic term
will include contributions from conformational, rotational, and
vibrational terms, and from solvent release, in addition to a term
due to translational entropy. In trying to understand the interplay
of these terms, it seemed to us sensible to study a system in
* To whom correspondence should be addressed.
† Department of Chemistry, University of Massachusetts, Amherst,
Massachusetts 01003.
(1) Rao, J.; Whitesides, G. M. J. Am. Chem. Soc. 1997, 119, 10286.
(2) Rao, J.; Lahiri, J.; Lyle, I.; Weis, R. M.; Whitesides, G. M. Science
1998, 280, 708.
(3) Nieto, M.; Perkins, H. R. Biochem. J. 1971, 123, 773.
(4) Nieto, M.; Perkins, H. R. Biochem. J. 1971, 123, 789.
(5) Sheldrich, G. M.; J., P. G.; Kennard, O.; Williams, D. H.; Smith, G.
A. Nature 1978, 271, 223.
(6) Schafer, M.; Schneider, T. R.; Scheldrick, G. M. Structure 1996, 4,
1509.
(7) Loll, P. J.; Bevivino, A. E.; Korty, B. D.; Axelsen, P. H.; J. Am.
Chem. Soc. 1997, 119, 1516.
(8) Williams, D. H. Acc. Chem. Res. 1984, 17, 7, 364.
(9) Kannan, R.; Harris, C. M.; Harris, T. M.; Waltho, G. P.; Skelton, N.
J.; Williams, D. H. J. Am. Chem. Soc. 1988, 110, 0, 2946.
(10) Williams, D. H.; Williamson, M. P.; Butcher, D. W.; Hammond,
S. J. J. Am. Chem. Soc. 1983, 105, 1332.
(11) Bongini, A.; Feeney, J.; Williamson, M. P.; Williams, D. H. J. Chem.
Soc., Perkin Trans. 1981, 2, 201.
(12) Williams, D. H.; Cox, J. P. L.; Doig, A. J.; Gardner, M.; Gerhard,
U.; Kaye, P. T.; Lal, A. R.; Nicholls, I. A.; Salter, C. J.; Mitchell, R. C. J.
Am. Chem. Soc. 1991, 113, 3, 7020.
(13) Mammen, M.; Choi, S.-K.; Whitesides, G. M. Angew. Chem., Int.
Ed. 1998, 37, 2754 and references therein.
10.1021/ja992648l CCC: $19.00 © 2000 American Chemical Society
Published on Web 03/08/2000

Design of a High-Affinity TriValent System
J. Am. Chem. Soc., Vol. 122, No. 12, 2000 2699
Scheme 1. Model of Complexes of Vancomcyin or Trimeric Vancomycin Derivative RtV3 with NR,ꢀ-diacetyl-L-Lys-D-Ala-D-Ala
a
(L) or Trimeric Ligand of DADA R′tL′3
a The dotted lines represent intermolecular hydrogen bonds.9 Examinations of the model of the complex RtV3‚R′tL′3 reveal frozen rotors in RtV3
and R′tL′3 upon complexation, indicated by curved arrows: Three rotors are frozen in each subunit of RtV3; six more rotors are frozen in each
L-lysine subunit of R′tL′3 than in L in monovalent binding of V and L.
which the interacting components were relatively rigid, and in
which ∆S° was relatively small for the monomers. The system
comprising vancomycin and L-Lys-D-Ala-D-Ala met these
criteria.
appeared.2 Understanding the origins of this tight bindingsand
of the contribution of conformational mobility to itshelps to
clarify the nature of oligovalent interactions.
Results
Both vancomycin and DADA can be modified by synthe-
sis,14,15 and relatively straightforward procedures can be used
to generate polyvalent derivatives of both.1 Both the ꢀ-amino
group of the lysine group in L-Lys-D-Ala-D-Ala and the
carboxylate group of vancomycin can be modified relatively
easily with little influence on the binding constant.4,14 Divalency
has been inferred to be important in the biological activity of
some of vancomycin-type antibiotics.16-18 Williams et al. have
suggested that spontaneous dimerization (with head-to-tail
geometry) of these antibiotics contributes to their tight binding
to DADA groups in the bacterial cell wall.19 We have examined
the interaction of a synthetic dimer of vancomycin (V-
CONHCH2C6H4CH2NHCO-V; V) vancomycin) with a corre-
sponding dimeric derivative of DADA [CH2CONꢀH(NR-Ac)-
L-Lys-D-Ala-D-Ala]2, and demonstrated an enhancement in
binding of approximately 103, relative to unmodified monomeric
vancomycin and NR,ꢀ-diacetyl-L-Lys-D-Ala-D-Ala.1 Here we
describe a trivalent system that comprises trimeric derivatives
of vancomycin and DADA and that shows remarkably tight
binding in water. A preliminary report of this work has
Design and Synthesis of Trivalent Derivatives of Vanco-
mycin, RtV3, and of DADA, R′tL′3. The overall design for these
two derivatives was based on the positions available for
modification, and on the geometry of the complex (Scheme 1;
we use the subscript “t” to indicate trivalent derivatives). The
basic strategy was to use the ꢀ-amino group of the lysine group
of the ligand, and the single carboxylic acid of vancomycin, to
form links to central hubs. The design of the central hub for
RtV3 was critical to the success of our study. It had to be: (i)
rigid, to minimize the loss of conformational entropy on binding,
and (ii) appropriately reactive, to allow preparation of the desired
trivalent derivative of vancomycin. A rigid triamine was
designed and synthesized for this purpose (Scheme 3). Coupling
of the triamine with vancomycin mediated by 2-(1H-benzo-
triazol-1-yl)-1,1,3,3-tetramethyluronium hexafluorophosphate
(HBTU) was carried out successfully in a mixture of dimeth-
ylformamide and dimethyl sulfoxide. Purification of the reaction
residue by reverse-phase HPLC afforded the desired product
RtV3.
The RtV3 hexatrifluoroacetate was isolated as a white foam
after lyophilization. The 1H NMR spectrum showed the
resonances expected for the hub and vancomycin units. The ESI-
MS exhibited an ion at m/z 4818.8; this value is consistent with
the average calculated molecular weight of 4817.4 for the parent
ion (M + H+). Obtaining a pure sample of RtV3 was very
difficult. We made a substantial effort to purify RtV3 and were
able to obtain a small amount of RtV3 sample that was almost
pure (as judged by HPLC analysis; Figure 1A). We used this
(14) Sundram, U. N.; Griffin, J. H. J. Org. Chem. 1995, 60, 0, 1102.
(15) Shi, Z.; Griffin, J. H. J. Am. Chem. Soc. 1993, 115, 5, 6482.
(16) Gerhard, U.; Mackay, J. P.; Maplestone, R. A.; Williams, D. H. J.
Am. Chem. Soc. 1993, 115, 232.
(17) Groves, P.; Searle, M. S.; Waltho, J. P.; Williams, D. H. J. Am.
Chem. Soc. 1995, 117, 7958.
(18) Mackay, J. P.; Gerhard, U.; Beaurgard, D. A.; Westwell, M. S.;
Searle, M. S.; Williams, D. H. J. Am. Chem. Soc. 1994, 116, 4581.
(19) Beauregard, D. A.; Williams, D. H.; Gwynn, M. N.; Knowles, D.
J. C. Antimicrob. Agents Chemother. 1995, 39, 781.

2700 J. Am. Chem. Soc., Vol. 122, No. 12, 2000
Rao et al.
Scheme 2. Thermodynamics of Binding for a Monovalent System and a Trivalent System with Rigid and Flexible Linking
Groups (eqs 1-3)a
a (1) The total entropic cost of association of three monovalent receptors and three monovalent ligands is 3 T∆S°m. (2) If the three receptors and
three ligands are connected by a perfect rigid linking group (that is, one in which there is neither conformational entropy loss nor enthalpic strain
of binding), the entropy loss of binding is approximately 3 T∆S°m - 2 T∆S°trans+rot,m (eq 2; T∆S°conf ) 0). (3) Flexible trimers may associate
without enthalpic strain but with loss in conformational entropy (eq 3; T∆S°conf < 0). If -T∆S°conf is too large, monovalent binding will dominate.
∆G°m, ∆H°m and T∆S°m are the free energy, enthalpy, and entropy of monovalent binding, respectively; T∆S°trans+rot,m is the translational and
rotational entropy of monovalent binding. ∆G°t is the free energy of trivalent binding, and T∆S°conf is the loss in conformational entropy in the two
intramolecular association events.
pure sample for calorimetric measurements and for some HPLC
experiments. Most of the samples we used in the HPLC studies
contained approximately 10% impurities (estimated from the
HPLC integration; Figure 1B); these impurities are indicated
in the HPLC chromatograms.
this species with NR,ꢀ-diacetyl-L-Lys-D-Ala-D-Ala (L). In the
analysis, we assumed the binding of L to each site of RtV3 to
be an independent event with the same affinity (defined by Kmd ;
“m” indicates a monovalent association). In the absence of any
information to the contrary, the assumption that the binding
events are independent is physically reasonable: the three active
sites of RtV3 are indistinguishable, they are far apart and
separated by a rigid spacer, and there is no obvious mechanism
A similar strategy was applied to the design of R′tL′3. We
used a 1,3,5-benzene tris(carboxamide) as the core so that the
structure was compatible in symmetry with RtV3. We synthe-
sized a protected tripeptide precursor, NR-Ac-L-Lys-D-Ala-D-
Ala-O-tert-butyl ester. Coupling of this compound with 1,3,5-
benzene tris(carbonyl chloride) afforded protected R′tL′3 (Scheme
3). After deprotection, R′tL′3 was purified by reverse phase
for them to interact with one another (the head-to-tail dimer-
16-18
ization observed in monomeric vancomycin
seems to be
unlikely here, since the three vancomycin units are linked
together in a head-to-head fashion). We defined the three
stepwise dissociation constants as Kmd1, Kdm2, and Kdm3, respec-
tively (eqs 4-6). After making statistical corrections for the
number of binding sites available at each step, the relationships
between Kmd and the three stepwise dissociation constants are
1
HPLC and characterized by H NMR spectroscopy and ESI-
MS.
Association of RtV3 with a Monovalent Ligand. We began
the analysis of binding of derivatives of DADA to RtV3 by
measuring the binding constant of the vancomycin groups in

Design of a High-Affinity TriValent System
J. Am. Chem. Soc., Vol. 122, No. 12, 2000 2701
Scheme 3a
Figure 2. UV difference spectroscopy at 280 nm to determine Kd of
L to RtV3 at pH 7.0 in the 20 mM phosphate buffer. RtV3 (2.1 µM, 3.0
mL) in a 1-cm cell was titrated against a solution of L (8.5 mM). The
fraction function r was defined as the ratio of the change in the
absorbance at 280 nm to the maximal change (r ) ∆A280/∆Am28a0x).
Table 1. Dissociation Constants of Complexes of Vancomycin (V)
and Its Derivatives with NR,ꢀ-diacetyl-L-Lys-D-Ala-D-Ala
vancomycin and derivative
Kd (µM)
ref
a (I) Synthesis of RtV3: (a) Di-tert-butyl dicarbonate/TEA, rt; (b)
1,3,5-benzene tris(carbonyl chloride), CH2Cl2, 2 h; (c) TFA/ CH2Cl2,
1 h; (d) vancomycin hydrochloride, HBTU, DIEA, rt, overnight. (II)
Synthesis of R′tL′3: (e) 1,3,5-benzene tris(carbonyl chloride), DMF, rt
V
0.67a
1.0b
4.3c
3
15
20
20
20
1
n-C3H7NHCO-V
NH3+(CH2)2S-S(CH2)2NHCO-V
V-CONH(CH2)3S-S(CH2)3NHCO-V
V-CONH(CH2)6NHCO-V
V-CONHCH2C6H4CH2NHCO-V
RtV3
3.9c
1.5c
4.8d
5.0d,e
this work
a UV difference spectroscopy in 20 mM sodium citrate buffer (pH
5.1). b UV difference spectroscopy in 20 mM sodium citrate buffer (pH
5.1). c Fluorescence competitive titration in 10 mM HEPES, 6 mM NaCl
buffer (pH 7.0). d UV difference spectroscopy in 20 mM phosphate
buffer (pH 6.9). e Estimated error is (1.5 µM.
definition, Kmd . The value of Kmd obtained from the plot is
approximately 5.0 µM (Figure 2). For comparison, Table 1 gives
values of dissociation constants for other relevant compounds;
the value of Kmd is similar to those measured previously for
monomers and dimers. This similarity makes it unlikely that
there are large differences between the values for Kmd1, Kdm2, and
Kmd3.
Stability of the Complex of RtV3‚R′tL′3. We tested the
stability of the complex RtV3‚R′tL′3 under the conditions used
for HPLC experiments. We first injected a sample containing
RtV3 (4.5 µM) into a C18 reverse-phase analytical column and
eluted with a linear gradient starting from 85% of solvent A
[0.1% trifluoroacetic acid (TFA) in water] and 15% solvent B
(0.1% TFA in acetonitrile) to 70% A and 30% B in 45 min
(Figure 3A). We observed a peak corresponding to RtV3. We
then injected a sample containing a 1:1.1 mixture of RtV3 and
R′tL′3 ([RtV3] ≈ 4.5 µM and [R′tL′3] ≈ 5 µM in 20 mM
phosphate buffer at pH 7.0) under the same conditions. On
injecting this mixture, we observed only the aggregate RtV3‚
R′tL′3 (Figure 3C); we did not observe free RtV3 (RtV3‚R′tL′3
and RtV3 have clearly distinguishable retention times). The
symmetry of the peak did not suggest dissociation or instability.
This observation indicates, inter alia, that dissociation of this
trivalent aggregate is slow relative to the time required for the
HPLC experiment (∼45 min).
Figure 1. HPLC chromatograms of RtV3. (A) Pure RtV3 and (B) RtV3
containing about 10% impurities marked by asterisk signs (*).
defined in these equations. The overall dissociation constant of
complex RtV3‚3L can then be expressed as (Kmd )3 (eq 7).
Kmd1
RtV3‚L y z RtV3‚L Kmd1 ) Kdm1/3
(4)
(5)
Kmd2
RtV3‚2L y z RtV3‚L + L Kmd2 ) Kdm
Kmd3
RtV3‚3L y z RtV3‚2L + L Kmd3 ) 3Kdm
(6)
(7)
RtV3‚3L h RtV3 + 3L Kmd1 Kdm2 Kdm3 ) (Kdm)3
Using difference UV spectroscopy,3,4 we titrated RtV3 with
L to estimate Kmd . Scatchard analysis yielded the apparent
average dissociation constant per binding site, which is, by our
A control experiment examined a mixture of RtV3 and the
monomeric ligand L ([RtV3] ≈ 4.5 µM; [L] ≈ 19.1 mM in the

2702 J. Am. Chem. Soc., Vol. 122, No. 12, 2000
Rao et al.
added; θ is the fraction of the total RtV3 present in the sample
that is in the form of RtV3‚R′tL′3 (eq 12).
[RtV3R′tL′3]
θ )
(12)
[RtV3‚3L] + [RtV3‚R′tL′3]
The competition assay depends on being able to establish
three concentrationss[RtV3‚R′tL′3], [R′tL′3], and [RtV3‚3L]s
in a solution containing L at a fixed concentration [L] S0, and
R′tL′3 at a variable concentration. Under the conditions used in
these experiments, the complex RtV3‚3L dissociates rapidly:23
the only peak observed in HPLC on injection of this complex
is uncomplexed RtV3. The stability of the complex RtV3‚R′tL′3,
and the ability to separate these species on HPLC, allowed us
to use an HPLC assay to establish their relevant concentrations
at equilibrium in the solution. We established [RtV3‚3L]
indirectly by measuring the concentration of one of the species,
RtV3, derived from it by dissociation. On the basis of the HPLC
experiments described previously, we assume that RtV3‚3L (and
any traces of RtV3‚2L and RtV3‚L present) are converted
quantitatively to RtV3 on the HPLC column by rapid dissociation
of L.23
Figure 3. HPLC of aliquots of samples that contained (A) RtV3 (4.5
µM), (B) RtV3 (4.5 µM) + L (19.1 mM), and (C) RtV3 (4.5 µM) +
R′tL′3 (4.5 µM). Dansyl-L-leucine (10 µM) was introduced into each
sample as an internal standard. All analyses were carried out under the
same conditions: Rainin analytical reverse-phase (RP) C18 column,
linear elution gradient from 85% solvent A [0.1% trifluoroacetic acid
(TFA) in water] and 15% solvent B (0.1% TFA in acetonitrile) to 70%
A and 30% B, over 45 min. The absorbance was monitored at 280 nm.
Analysis of the Competitive Binding Assay and Estimation
m
t
of Kd . For Kd ≈ 5.0 µM, a concentration of L of ∼1.5 mM in
solution ensures that 99% of the binding sites of RtV3 are
occupied by L (eq 11). We used a value of [L] S0 ≈ 19.1 mM
(>10 times larger than 1.5 mM); because the binding of R′tL′3
to RtV3 was so tight, a high value of [L] was required to give
a quantifiable concentration of R′tL′3 in solution at equilibrium
in the system used in the competition experiments (described
by eq 9). Aliquots of a stock solution of R′tL′3 (1.06 mM) were
added to a solution of RtV3 (4.5 µM) and L (19.1 mM) in 20
mM pH 7.0 phosphate buffer. After each addition of R′tL′3,
the solution was mixed by vortexing and allowed to equilibrate
for about 40 min at room temperature (about 30 °C). A sample
was removed and examined by HPLC, eluting with a linear
gradient from 85% solvent A (0.1% TFA in water) and 15%
solvent B (0.1% TFA in acetonitrile) to 70% A and 30% B
over 45 min. Under these conditions, RtV3‚3L dissociated into
its components on injection and appeared as separate peaks for
RtV3 and L. RtV3‚R′tL′3 was stable and appeared as a well-
defined peak. Additional aliquots of R′tL′3 were added until
free RtV3 could no longer be detected by HPLC. Figure 4 shows
the HPLC chromatograms of a representative titration.
same phosphate solution (Figure 3B); that is, a concentration
that is approximately 3800 Kmd ) on HPLC using the same
elution conditions; this experiment showed only RtV3. We infer
that the 1:3 complex of RtV3‚3L that was undoubtedly present
at equilibrium dissociated completely during the passage through
the column; the fact that the peak for RtV3 was sharp indicates
that dissociation was fast under the conditions of the experiment.
We conclude that RtV3‚R′tL′3 is stable enough to survive the
HPLC experiment intact. We could therefore use HPLC to
quantitate the relative quantities of R′tL′3, RtV3, and RtV3‚R′tL′3
in a mixture of these species, and to estimate the trivalent
dissociation constant.
Design of the Competitive Binding Assay. An attempt to
determine the trivalent dissociation constant Ktd by a direct
titration of RtV3 with R′tL′3 (eq 8) was not successful; the
Kdt
RtV3‚R′tL′3 y
\
z RtV3 + R′tL′3
(8)
reaction was stoichiometric even when RtV3 was at its minimum
detectable concentration [in the µM range for the UV detector].
We thus turned to a competition assay to estimate Ktd indirectly
from the equilibrium constant K (eqs 9, 10).
Since L is present in large excess relative to RtV3, we assume
that the concentration of L, at equilibrium, is the same as its
initial concentration, [L] ≈ [L]0. Analysis of the data requires
a relationship between θ (eq 12) and [R′tL′3]. Equation 13,
K
RtV3‚3L +R′tL′3 y
\
z RtV3‚R′tL′3 + 3L
(9)
[RtV3R′tL′3] [L]3
[RtV3‚3L][R′tL′3]
(Kmd )3
Kdt
θ
K
[L]30
K
[L]30
) -
θ +
(13)
K )
)
(10)
[R′tL′3]
obtained by combination of eqs 10 and 12, was used to
characterize the binding: if the ratios of θ/[R′tL′3] are plotted
versus θ, a straight line would be expected; both the slope and
We allowed R′tL′3 to compete with the monovalent ligand L
for RtV3.22
A competition assay is most easily interpreted if the concen-
tration of L is such that all three of the binding sites of RtV3
are fully occupied in the absence of R′tL′3. The concentration
of L required to saturate 99% of the three vancomycin binding
sites, [L] S0, is given by eq 11 (see Supporting Information for
(20) Sundram, U. N.; Griffin, J. H.; Nicas, T. I. J. Am. Chem. Soc. 1996,
118, 13107.
(21) Popieniek, P. H.; Pratt, R. F. J. Am. Chem. Soc. 1991, 113, 2264.
(22) Our analyses assume that the two intermediate species, R′tL′3‚RtV3‚
2L and R′tL′3‚RtV3‚L, are present in very small amounts at equilibrium
and can thus be neglected. This assumption leads to eq 13, which predicts
a linear plot of θ/[R′tL′3] versus θ. The agreement of our experimental
results with this prediction suggests that this assumption is valid under our
experimental conditions.
[L] S0 ) 300 Kdm + 3[RtV3]0
(11)
a detailed derivation). We defined θ as a measure of the progress
of the displacement reaction as a function of the amount of R′tL′3
(23) The value of the rate constant for dissociation of the monovalent
complex of vancomycin with L is koff ) 31 s-1 (ref 21).

Design of a High-Affinity TriValent System
J. Am. Chem. Soc., Vol. 122, No. 12, 2000 2703
Figure 5. A plot of the ratios of θ/[R′tL′3] versus θ for the titration of
RtV3 (4.5 µM) with R′tL′3 (0-35 µM) in the presence of L (19.1 mM).
The line is a linear fit of the data to eq 13. The slope of the line yields
a value of K/[L]3 ≈ 0.47 µM-1. The value of Ktd for RtV3‚R′tL′3 is thus
estimated as ∼4 × 10-17 M (an average value of three repetitions; the
error is within 25%).
Figure 4. HPLC chromatograms of the titrated solution of RtV3 (4.5
µM) on addition of aliquots of R′tL′3 (1.06 mM) solution in the presence
of L (19.1 mM). The sample of RtV3 used here contained small amounts
of impurities, which are indicated by the symbols (*). The HPLC
conditions were similar to those described in Figure 3, except that a
Vydac analytical RP column was used with the same linear gradient,
run over 30 min.
y-intercept of this line would afford the ratio of K/[L]3 and thus
the value of K. The values of [R′tL′3] were estimated from
integration of the peaks for R′tL′3 on the HPLC; θ was
calculated (eq 12) using the integrated intensities of RtV3‚R′tL′3
and RtV3. The Experimental Section details the procedure. The
fact that the sum of the two integrals of the peaks of RtV3‚
R′tL′3 and RtV3 during the titration was approximately constant
indicates that no species other than those in eq 9 were present
in significant amounts at equilibrium. The ratios of θ/[R′tL′3]
were then plotted versus θ. As expected, the plot gave a straight
line and yielded the value of K (Figure 5). We estimated
Ktd using Kdm and K (eq 10); our estimate of Ktd is ∼4 ( 1 ×
10-17 M.
Exchange Reaction Between RtV3‚R′tL′3 and L. At first,
the conclusion that RtV3 bound very tightly to R′tL′3 seemed at
odds with the relatively fast equilibration we observed in
solutions containing RtV3, R′tL′3, and L. We therefore turned
to an examination of the rates of equilibrium of the species
involved in this system. If we assume that kon for association
of RtV3 and R′tL′3 is 9 times that for association of V and L21
(making a statistical correction of a factor of 9 for the number
of receptor and ligand groups in the trimeric species), then kon
would be ∼2.5 × 108 M-1 s-1, and koff for RtV3‚R′tL′3 ) kon
Ktd ≈ 1 × 10-8 s-1. Even if we assume that the rate for
association of RtV3 with R′tL′3 is diffusion controlled (which
may be true for antibodies and certain other proteins but is
probably not true for association of RtV3 and R′tL′3 by extension
from the kinetic behavior of the monomeric species), and has a
Figure 6. Representative HPLC traces demonstrating the exchange
of RtV3 (3 µM) + R′tL′3 (22 µM) with L (86 mM) with formation of
RtV3‚3L. Exchange reactions were carried out by adding L to an
equilibrated mixture of RtV3 and R′tL′3, and injecting the resulting
mixture into the HPLC column after 0, 2, 45, 190, or 360 min. Symbols
(•) indicate the retention time of RtV3‚3L; this compound dissociates
to free RtV3 on the column. The sample of RtV3 used here contained
small amounts of impurities, which are indicated by the symbols (*
and 9). The conditions were similar to those in Figure 3, except that
a Vydac analytical RP column was used with the same linear gradient,
run over 30 min.
value of kon ≈ 109 M-1 s-1, the value of koff would be ∼4 ×
10-8 s-1. This value implies that dissociation of RtV3‚R′tL′3
would be too slow to be observed directly. This implication is
consistent with our observation that the aggregate is stable for
>103 s under HPLC conditions.
The exchange reaction between RtV3‚R′tL′3 and L proceeded
surprisingly rapidly, however (equilibration was complete in

2704 J. Am. Chem. Soc., Vol. 122, No. 12, 2000
Rao et al.
Figure 7. ITC titration of RtV3 by R′tL′3 (0.126 mM) in 5.0 mM phosphate buffer at 298 K. The injected volumes of the first, second, and twelfth
injections were 0.5, 35, and 35 µL, respectively, and 3.0 µL for the remaining injections. The interval between the second and third injections was
20 min; the interval between the remaining injections was 5 min.
Table 2. Thermodynamic Parameters of Binding of Derivatives of Vancomycin to Derivatives of DADA at 298 Ka
receptor/
ligand
∆G°
(kcal/mol)
∆H°
(kcal/mol)
-T∆S°
(kcal/mol)
receptor
ligand
valency
Kd (M)
RtV3
R′tL′3
1:1
tri
4 × 10-17
-22
-40
18
monob
mono
mono
mono
mono
mono
mono
-7.3
-7.9
-8.1
-7.6
-8.8
-9.5
-8.2
-13.3
-12.0
-12.4
-12.0
-17.5
-17.8
-21.0
6.0
4.1
4.3
4.4
8.7
8.3
13
Vc
RtV3
RtV3
V
RV
RV
L
R′tL′
L
R′tL′3
R′tL′3
R′tL′
1:1
1:3 d
1:3 d
3:1 d
3:1 d
1:1
1.6 × 10-6
1.1 × 10-6
2.7 × 10-6
0.34 × 10-6
0.11 × 10-6
0.96 × 10-6
a Values of ∆H° were determined by ITC titrations at pH 7.0 in 5.0 mM phosphate buffer at 298 K. Values of ∆G° were determined from Kd,
measured in the same solution, except for that of RtV3‚R′tL′3. Values of -T∆S° were calculated from ∆G° ) ∆H° - T∆S°. Each titration was at
least duplicated and differences are within 25% for Kd and 5% for ∆H°. All thermodynamic values refer to the monovalent interaction between
individual units of V and individual units of L or L′, except for those for binding of RtV3 to R′tL′3. b For convenience, the average values per V‚L
binding are also given for RtV3‚R′tL′3, and indicating by the label “mono” and brackets
.
c Measured in 20 mM phosphate buffer at 25 °C by ITC;
our values agree well with the literature values.26 d In the cases of 1:3 or 3:1 binding, the values of Kd are Kmd , the average dissociation constant
per site (defined by eqs 4-7); these values are statistically corrected for the presence of multiple binding sites. Refer to Scheme 1 for structures
of RtV3 and R′tL′3, and Scheme 4 for structures of RV and R′tL′.
<45 min), as shown by HPLC during the exchange of RtV3‚
R′tL′3 with excess L (Figure 6). We prepared the initial solution
of RtV3‚R′tL′3 by mixing 3 µM of RtV3 and 22 µM of R′tL′3 in
20 mM phosphate solution. Examination of the sample by HPLC
(using conditions similar to those used in the competition
experiments) established that RtV3‚R′tL′3 had formed (Figure
6). Then L was added to this solution of RtV3‚R′tL′3 in quantities
sufficient to make the concentration of L about 86 mM. At
intervals, samples were withdrawn and examined on HPLC.
Exchange of RtV3‚R′tL′3 with L yielded the complex of RtV3‚
3L: this complex dissociated on the HPLC column to free RtV3
(as discussed previously). The integrated areas of the peaks for
RtV3‚R′tL′3 and RtV3 (derived by dissociation of RtV3‚3L) were
used to monitor the progress of the exchange reaction; dansyl-
L-Leu was again used as an internal standard. Equilibration was
complete within 45 min, and no further significant change in
peak intensities occurred after that time. Approximately 60%
of the RtV3 remained as RtV3‚R′tL′3 at equilibrium in a system
containing L at a concentration of ∼86 mM; this value of L is
∼17 000 times greater than that of the dissociation constant for
the complex of RtV3 and L, and confirmed that RtV3‚R′tL′3 was
tightly associated.
Scheme 4. Structures of the Monovalent Derivatives of
DADA and V, R′tL′, and RV, Respectively
There is an essential difference in kinetics between this
trivalent system and biotin‚avidin. Dissociation of biotin‚avidin
necessarily proceeds to completion in one step and is slow.24
(24) Green, N. M. Biochem. J. 1963, 89, 585.

Design of a High-Affinity TriValent System
Scheme 5. Mechanism 1
J. Am. Chem. Soc., Vol. 122, No. 12, 2000 2705
The presence of a large excess of biotin does not accelerate the
dissociation of biotin‚avidin. As we have demonstrated here,
dissociation of RtV3‚R′tL′3 is slow in isolation, but rapid when
carried out in the presence of excess monoValent ligand L.
Dissociation of RtV3‚R′tL′3 therefore proceeds by a mechanism
different from that of the single-step dissociation of biotin‚
avidin. We discuss the kinetics of this dissociation in the
Discussion section.
vancomycin and DADA, and the value of T∆S° for the trivalent
system is approximately 4.5 times that for the monovalent
system.
We were also concerned about the effect of the interaction
between the two linking groups in RtV3 and R′tL′3 on the binding
in the trivalent system. We therefore synthesized two monova-
lent derivatives of DADA and V, R′tL′ (NR-acetyl-Nꢀ-benzoyl-
L-Lys-D-Ala-D-Ala) and RV (C6H5CONHC6H4-4-CH2NHCOV),
respectively (Scheme 4), to simulate the influence of the R′t
group in R′tL′3 and the Rt group in RtV3. The ITC titrations
characterized the interactions between these ligand/receptor pairs
thermodynamically, and Table 2 summarizes the results.
All of the bindings examined in Table 2 are monovalent
except that for the binding of RtV3 to R′tL′3. The parameters
listed in this table thus referred to monovalent binding between
V (or V unit in RtV3) and its ligand except in the binding of
RtV3 to R′tL′3. In particular, in the cases of 1:3 or 3:1 complexes,
the dissociation constant (Kd) refers to a monovalent dissocia-
tion constant (Kmd with units of molar), not a collective
constant (a product of three monovalent binding constants, which
is equal to (Kmd )3 and which has units of M3; eqs 4-7). The
results indicate that the value of Kd is essentially indifferent to
substitution on either vancomycin or L-Lys-D-Ala-D-Ala groups,
so long as the interaction is monovalent; only the trivalent
interaction is exceptionally strong. In broad terms, the data
suggest that the high free energy of association of RtV3‚R′tL′3
originate primarily in the enthalpy of association of three V
and L groups. The values of ∆H° of binding of V, or of its
monomeric derivative RV to R′tL′3 are, however, about 5 kcal/
mol more negative than that of V to L. A discussion of these
thermodynamic data follows in the next section.
Estimation of ∆H° of the Binding of RtV3 to R′tL′3. A
direct estimation of ∆H° for the association of RtV3 with R′tL′3
would separate ∆G° into enthalpic and entropic terms, and
clarify the thermodynamic basis for the very high binding
constant of this receptor/ligand pair. We have characterized the
association of RtV3 to R′tL′3 using isothermal titration calorim-
etry (ITC).25 ITC can be used to estimate dissociation constants
(Kd) in the millimolar to nanomolar range. It allowed us to
estimate both the enthalpy of binding, ∆H°, and the dissociation
constant Kmd for the monovalent interactions, but only ∆H° for
the interaction of RtV3 with R′tL′3. Experiments were carried
out by adding aliquots of a solution of R′tL′3 (∼0.126 mM) in
5.0 mM phosphate buffer to a solution of RtV3 (∼3 µM) in 5.0
mM phosphate buffer in the cell of the calorimeter (Figure 7).
By integration of the peaks, we estimated ∆H° to be -40 kcal/
mol (Table 2). Titrations were repeated three times and the
maximum difference among these values of ∆H° was less than
2 kcal/mol. The value of T∆S° for binding of RtV3 to R′tL′3 is
thus approximately -18 kcal/mol (T∆S° ) ∆H° - ∆G°). The
value of ∆H° for the binding of vancomycin to L has been
reported as -12.8 kcal/mol.26 The value of ∆H° of the trivalent
system is thus approximately three times that for monovalent
Discussion
(25) Wiseman, T.; Williston, S.; Brandt, J. F.; Lin, L.-N. Anal. Biochem.
1989, 179, 131.
The dissociation constant describing the dissociation of RtV3‚
R′tL′3 into RtV3 + R′tL′3 (Ktd ≈ 4 × 10-17 M) is 10-10 that of
(26) Cooper, A.; McAuley-Hecht, K. E. Philos. Trans. R. Soc. London
A 1993, 345, 23.

2706 J. Am. Chem. Soc., Vol. 122, No. 12, 2000
Scheme 6. Mechanism 2
Rao et al.
V‚L into V + L (Kdm ≈ 1.6 × 10-6 M).2 The relationship
between thermodynamic and kinetic characteristics of this
dissociation is strikingly different from that of avidin‚biotin:
although the rate of dissociation of RtV3‚R′tL′3 is slow (as is
that of avidin‚biotin), equilibration of RtV3‚R′tL′3 with mono-
meric L to give RtV3‚3L is relatively fast, and monomeric L
competes relatively effectively with trimeric R′tL′3 for the
receptor sites on RtV3. We consider the issues of kinetics and
thermodynamics separately.
Kinetics. The essential difference between RtV3‚R′tL′3 and
biotin‚avidin is that dissociation of the former, when carried
out in the presence of excess L, proceeds in three steps, while
the latter necessarily proceeds to completion in one step. We
considered two plausible mechanisms for the exchange reaction
between RtV3‚R′tL′3 and excess L.
A. Mechanism I. The first mechanism (Scheme 5) involves
complete dissociation of RtV3‚R′tL′3 into RtV3 and R′tL′3,
followed by association of free RtV3 with three equivalents of
L. This mechanism is similar to that for dissociation of biotin‚
avidin, which proceeds to completion in one step. We presume
that the rate-determining step in this mechanism would be the
last one: that is, the step leading to complete dissociation of
RtV3‚R′tL′3 into RtV3 + R′tL′3. The rate of this process would
be independent of [L], and would, as we have indicated, be
very slow (koff ≈ 10-8 s-1, even if kon were diffusion limited).
This expectation is contrary to the experimental observation that,
in the presence of excess L, exchange of RtV3‚R′tL′3 with L is
complete within 45 min. We therefore discard this mechanism.
B. Mechanism II. The second mechanism (Scheme 6)
involves a sequence of successive dissociation and association
events occurring at the vancomycin binding sites of RtV3‚R′tL′3.
After initial dissociation of DADA groups (A f B; C f D),
the empty binding sites could associate with L (B f C; D f
E) before the next step of dissociation. Association of L with
each empty active site would inhibit rebinding of dissociated
DADA groups on R′tL′3. This mechanism predicts a fast
exchange between RtV3‚R′tL′3 and L and is consistent with our
experimental observations. We therefore infer that excess
monovalent ligand L competes for the binding sites of RtV3 on
a site-by-site basis and thus accelerates the dissociation of the
trivalent complex of RtV3‚R′tL′3.
C. Kinetics of Association of RtV3 with R′tL′3. Scheme 7
outlines the stepwise association of RtV3 with R′tL′3. So far,
we have not been able to measure the rate constants for each
kinetic step in this model experimentally. We thus applied rate
constants obtained for the monovalent interaction between V
and L to an estimate of theoretical values of the kinetic
parameters in the binding of RtV3 to R′tL′3. This estimate should
also provide insight into the kinetic origin of the high stability
of RtV3‚R′tL′3. We make three assumptions in our estimation.
(i) The value of the rate constant for the first step in association
of RtV3 with R′tL′3, k1, is 9 times that of kon for monomeric V
and L: k1 ) 9kon. (ii) The rate constant for dissociation of each
V/DADA pair in RtV3‚R′tL′3 is, after corrections for statistical
factors, approximately the same as koff for V‚L, k-1 ) k-2/2 )
k-3/3 ) koff. (iii) The rate constants of the two intramolecular
associations, after corrections for statistical factors, are ap-
proximately the same: k2/4 ) k3. Combining these assumptions
and the literature values of kon and koff for V and L, (kon ≈ 2.8
21
× 107 M-1 s-1; koff ≈ 30 s-1), we estimated k2 and k3 as
follows
Ktd ) (k-1k-2k-3 )/(k1k2k3 )
) (30 × 2 × 30 × 3 × 30)/[(9 × 2.8 × 107)k2k3]
≈ 4 × 10-17 M
(14)
With the assumption that k2/4 ) k3, we estimated the rate

Design of a High-Affinity TriValent System
J. Am. Chem. Soc., Vol. 122, No. 12, 2000 2707
Scheme 7
Table 3. Effective Molarities for Some Oligovalent Association
Reactions
constants for the intramolecular association to be k2 ) 8 × 106
s-1 and k3 ) 2 × 106 s-1. These large values of the rate constant
for intramolecular association inside the complex suggest the
kinetic origin of the high stability of RtV3‚R′tL′3: fast intramo-
lecular rebinding of partially dissociated V/DADA pairs in the
complex. (This estimation is obviously highly approximate; it
does not consider possible variations in the off-rate in each step
of dissociation).
For a value of k2 ) 8 × 106 s-1, the value of effective molarity
of the DADA group is approximately 290 mM (k2/k1 ) 8 ×
106 s-1/2.8 × 107 M-1 s-1), and a value of k3 ) 2 × 106 s-1
corresponds to an effective molarity of about 70 mM. For
comparison, Table 3 lists values of effective molarity for several
intramolecular processes.27-33 The values of effective molarity
in our system, in general, are comparable to (slightly larger than)
those for most biochemical systems, but they are smaller than
those observed in systems involving smaller components (for
example, the chelate effect in the coordination of small ligands
with metal ions). This fact indicates that intramolecular binding
in our system does not convey as much advantage as it does in
chelation of metal ions. Our analysis of the entropic loss in this
trivalent system suggests that the relatively small value of
effective molarity that we observe here is due to loss in
conformational entropy.
One interesting inference from this analysis is that exception-
ally high values of effective molarity are not necessarily required
to achieve very tight binding in the system RtV3 + R′tL′3. We
would, thus, anticipate that a number of systems of receptors
and ligands might give very tight binding in tri- or higher-valent
form.
Thermodynamics. The free energy of trivalent binding of
RtV3 + R′tL′3 is approximately three times that of monvalent
binding of V to L (Table 2): that is, ∆G°t ≈ 3∆G°m ≈ 3∆H°m
a Calculated from the reported values of Kd. b Presented at a self-
assembly monolayer on gold. c In the presence of sodium dodecylsul-
phate. d Assuming that the values of effective molarity for the two
intramolecular associations are the same in this trivalent binding. e DNP:
2,4-dinitrophenyl group. f â-CD: â-cyclodextrin. g EDTA: ethylene-
diaminetetraacetate.
- 3T∆S°m. Calorimetric measurements indicated that ∆H° for
association of RtV3 and R′tL′3 (∼-40 kcal/mol) is approximately
three times that for V and L (∆H° ) -12.8 kcal/mol). The
value of -T∆S° for association of the two trivalent species is
thus 18 kcal/mol; this value is approximately 4.5 times that of
V and L (T∆S° ) -4.1 kcal/mol) (Table 2). In the simplest
analysis, we envision two limiting cases for association of RtV3
+ R′tL′3 (Scheme 2). In one, after the first V and L′ group
interact, the other two pairs of V and L′ groups are correctly
(27) Rao, J.; Yan, L.; Xu, B.; Whitesides, G. M. J. Am. Chem. Soc. 1999,
121, 2629.
(28) Westwell, M. S.; Bardsley, B.; Dancer, R. J.; Try, A. C.; Williams,
D. H. J. Chem. Soc., Chem. Commun. 1996, 589.
(29) Lee, Y. C.; Townsend, R. R.; Hardy, M. R.; Lo¨nngren, J.; Arnarp,
J.; Haraldsson, M.; Lo¨nn, H. J. Biol. Chem. 1983, 258, 199.
(30) Hornick, C. L.; Karush, F. Isr. J. Med. Sci. 1969, 5, 163.
(31) Breslow, R.; Zhang, B. J. Am. Chem. Soc. 1996, 118, 8495.
(32) Zhang, B.; Breslow, R. J. Am. Chem. Soc. 1993, 115, 9353.
(33) Irving, H.; Williams, R. J. P.; Ferrett, D. J.; Williams, A. E. J. Chem.
Soc. 1954, 3494.

2708 J. Am. Chem. Soc., Vol. 122, No. 12, 2000
Rao et al.
positioned to interact with negligible further loss in entropy; in
this case, ∆G°t ≈ 3 ∆H°m - T∆S°m + 2T∆S°trans+rot,m
(T∆S°trans+rot,m is the translational and rotational entropy for the
association of V and L). In the second, the linkers are so long
and flexible that after interaction of the first V and L′ pair, there
is large entropic penalty (conformational entropy loss) that
prevents any further intramolecular association. In practice,
interactions involving the linkers and hubs can make ∆H°t
different from 3 ∆H°m, and can also disguise any simple
relationship between T∆S°t and T∆S°m.
We wish to understand the thermodynamic origins of these
values. This task would require separating the enthalpic and
entropic contributions of each binding event to the free energy
of the association of the two trivalent species. Unfortunately,
we do not have the information required to carry out this
separation, and given the fact that we do not observe intermedi-
ates in association or dissociation in HPLC analyses, we are
unlikely to be able to obtain this information. Instead, we have
inferred the enthalpic and entropic contributions of certain
binding events to the ∆G° of trivalent binding from semiquan-
titative analyses of ∆H° and T∆S°.
∆H°. To analyze the value of ∆H°t, we need first to decide
on the appropriate reference value to which ∆H°t should be
compared: that is, should the reference value for the “compa-
rable” monomeric interaction, ∆H°m, be considered the value
for V and L or for these species with linkers attached? And if
the latter, what types of linkers? Our instinct is that the most
appropriate structural comparisons for processes involving RtV3
and R′tL′3 will be derivatives of V and L that have linking
groups attached, but it is difficult to justify this instinct
analytically: unfortunately, we cannot draw a clear conclusion
concerning the influence of structures that are, or mimic, the
linking groups on the values of ∆H°m. Table 2 contains values
of enthalpy that range from that for V + L (∆H°m ≈ -12 kcal/
mol; two examples) to substantially larger (∆H°m ≈ -17.5 to
-21 kcal/mol; three examples). Thus, we can conclude only
that the average value of ∆H° for association of one V and one
L′ group in RtV3 and R′tL′3 is approximately equal to or larger
than (i.e., energetically less favorable than) ∆H° for reference
monomers.
Having said that we are confident that the data are largely
free of artifact, we point out that they are not simple: we do
not see an obvious, qualitative explanation for the trends. For
example, for most of the data, increasing the molecular surface
of the molecule containing the DADA group increases ∆H°,
but the value for RtV3 + R′tL′3 is an exception. We therefore
believe, but cannot prove, that increases in contacting surface
and changes in entropy, probably due to restrictions on
conformational mobility, compensate.
Linker-Vancomycin Interactions. We examined possible
contributions of the linker groups to the enthalpy of binding.
The values of ∆H° for binding of RtV3 to monovalent ligands
(L or R′tL′) are similar to that for the binding of V to L. This
result, by itself, seems to imply that the contribution of the linker
groups to ∆H° is small. The value of ∆H° for binding of R′tL′3
to RV (a monovalent vancomycin containing an R group that
was designed to simulate the structure of Rt) is, however, about
5 kcal/mol more negative than that for V to L (Table 2). This
result seems to conflict with the previous implication that the
influence of the linker groups on the value of ∆H° is small.
Moreover, the value of ∆H° for binding of R′tL′3 to V was,
surprisingly, still approximately 5 kcal/mol more negative than
that for binding of V to L, although only R′tL′3 bears a linker
group in this binding pair. We do not to see a simple, consistent
relationship between linker groups and their contributions to
binding enthalpies that makes it clear what the appropriate
reference compound is against which to compare the thermo-
dynamic values for binding of RtV3 to R′tL′3.
Dimerization of Vancomycin. Vancomycin has a strong
16-18
tendency to form a noncovalent dimer.
This tendency to
dimerize is enhanced by ligand binding.34 The pattern of
dimerization identified by Williams is head-to-tail, and this
geometry is not possible for the vancomycin groups of RtV3. It
is more plausible that it might play a role for the combination
of V (or RV) interacting with R′tL′3, but we have, at present,
no direct evidence for or against dimerization of vancomycin
as a process that influences the thermodynamics of this system.
T∆S°. There is an approximately 18 kcal/mol loss of entropy
on association of RtV3 with R′tL′3. As we discussed previously
(Scheme 7), the trivalent binding process takes place in three
steps: a bimolecular association as the first binding event, then
two intramolecular binding steps. The problem in any analysis
of T∆S° for the trimeric interaction is, however, the same as
that mentioned for ∆H°m: that is, deciding on an appropriate
reference value of T∆S°m.
We have considered three explanations for the differences in
∆H° for the compounds in Table 2: (i) experimental error, (ii)
linker-vancomycin interactions, and (iii) dimerization of van-
comycin. We discuss each in turn.
We have analyzed the value of T∆S° for association of RtV3
+ R′tL′3 assuming, for explicitness, that the association of V
to L provides an appropriate reference value. For the first
binding event, we assume that the loss in entropy is mainly
associated with translational and rotational terms. The effect of
molecular size on the loss of translational and rotational entropy
is relatively small (e15% for an increase in molecular weight
of a factor of 3 12). For binding of V to L, T∆S° is ∼-4.1
kcal/mol. We thus assume the value of T∆S° for the first binding
step of association of RtV3 + R′tL′3 to be ∼-4.7 kcal/mol
(based on this 15% correction). We expected the next two steps
to be less entropically unfavorable than the first, since they take
place intramolecularly. The total value of T∆S° for these two
steps is, however, a surprisingly negative number: ∼-13.3 kcal/
mol (estimated by subtracting T∆S° for the first binding from
the total T∆S° for the trivalent binding). If this value is correct,
where does it come from? A review of the contributors to the
entropic loss of binding of V to L suggests clues to its origin.
Experimental Error. A troublesome aspect of the data in
Table 2 is the observation that, with the exception of RtV3 +
R′tL′3, ∆G° varies by less than 1.5 kcal/mol, while ∆H° (and
of course T∆S°) varies by 9 kcal/mol. The appearance of
apparent example of enthalpy/entropy compensation is always
a warning, although Williams and others have made a convinc-
ing case for the existence of compensating relationships in
circumstances in which tighter binding (and a more negative
enthalpy of binding) is accompanied with loss in conformational
mobility (and a greater loss in entropy). In the data in Table 2,
the historically most common and plausible origin of an
artifactual enthalpy/entropy compensationsan inaccurate de-
composition of ∆G° into ∆H° and T∆S° based on the temper-
ature dependence of ∆G°sis eliminated since ∆G° and ∆H°
were obtained using independent experimental techniques (UV
or HPLC for ∆G°; ITC for ∆H°). The values were also
consistent over three replications. We therefore believe that they
are accurate within the stated uncertainties, and that, as usual,
the trends are even more reliable than the numerical data.
(34) Williams, D. H.; Maguire, A. J.; Tsuzuki, W.; Westwell, M. S.
Science 1998, 280, 711.

Design of a High-Affinity TriValent System
J. Am. Chem. Soc., Vol. 122, No. 12, 2000 2709
Williams et al. have carefully examined the entropic loss of
binding of N-Ac-D-Ala-D-Ala to vancomycin and ristocetin A
(a vancomycin group antibiotic).12 In this semiquantitative
analysis, they dissected T∆S° for binding of V to N-Ac-D-Ala-
D-Ala into three major terms (eq 15): loss of translation and
rotation due to a bimolecular association (T∆S°trans+rot ≈ -17
kcal/mol), the freezing out of four rotors of the peptide
(T∆S°rotors ≈ -5 kcal/mol), and the release of water (T∆S°solv
≈ 19 kcal/mol). The predicted value of T∆S° is close to the
experimental value in this system (∼T∆S° ≈ -4.1 kcal/mol).
enthalpy of association of three V and L groups, and the gains
in T∆S°tran+rot that come from trivalency are coincidentally
largely offset by the loss in conformational entropy of the linking
groups on binding.
Aside from its demonstration of a large binding constant, the
work carries a prescription for systems in which trivalency might
give even larger binding constants. The features in these systems
would include (i) rigid receptors and ligands, (ii) conformational
stiff linkers, correctly designed to allow receptors and ligands
to interact without enthalpic strain and with minimal loss in
entropy due to freezing of conformational and rotational terms,
and (iii) a large hydrophobic component to binding to give a
large positive contribution from T∆S from release of water.
T∆S°m ) T∆S°trans+rot + T∆S°rotors + T∆S°solv (15)
≈ -17-5 + 19 ≈ -3 kcal/mol
Experimental Section
Using analogous reasoning, we estimated the entropic loss
in the two intramolecular binding steps for RtV3 + R′tL′3. We
estimate the total entropic loss for the two intramolecular binding
steps by eq 16, where T∆S°conf defines the additional confor-
mational entropy loss in the two intramolecular binding steps.
As estimated above, the value of T∆S°second+third for the second
and third binding steps is approximately -13.3 kcal/mol. We
therefore estimate T∆S° conf ∼-41 kcal/mol (eq 17).
General Methods. The 1H NMR spectra were recorded at 400 MHz.
Chemical shifts are reported in parts per million downfield from
tetramethylsilane. Vancomycin hydrochloride was purchased from
Sigma and used without further purification. Amino acids were
purchased from Sigma (St. Louis, Missouri), except for D-Ala-O-tBu
from BACHEM Bioscience (King of Prussia, Pennsylvania). The
peptide coupling reagent HBTU was purchased from Applied Biosys-
tems (Atlanta, Georgia). Dimethylformamide (DMF) and dimethyl
sulfoxide (DMSO) were dried overnight over silica gel and 4 Å
molecular sieves, respectively, followed by distillation under reduced
pressure. Diisopropylethylamine (DIEA) was distilled from ninhydrin.
The monomeric peptide ligand diacetyl-L-lysyl-D-alanyl-D-alanine (L)
was available from a previous study.1
tert-Butyl 4-Aminobenzylamine Carboxylate. To a solution of
4-aminobenzylamine (3.66 g, 30 mmol) in 60 mL of acetone solution
was slowly added di-tert-butyl dicarbonate (2.84 g, 15 mmol) in 10
mL of acetone and 6 mL of triethylamine. The reaction was stirred at
room temperature for 30 min, and the solvent was removed by rotary
evaporation. The residue was purified by flash chromatography (eluting
with 2:3 hexane/ethyl acetate) to give 2.67 g (12 mmol, 80%) of the
product as a white solid: Rf ) 0.43 (1:1 hexane/ethyl acetate); 1H NMR
(300 MHz, CDCl3) δ 1.45 (s, 9 H, CCH3), 3.65 (s, 2 H, NH2), 4.18 (d,
J ) 5.4 Hz, 2 H, CH2NH), 4.73 (b, 1 H, NHCO), 6.64 (d, J ) 6.4 Hz,
2 H, C6H4), 7.07 (d, J ) 8.1 Hz, 2 H, C6H4); HRMS-FAB (M +
Na+) calcd for C12H18N2O2Na 245.1266, found 245.1253.
T∆S°second+third ) 2 T∆S°rotors + 2 T∆S°solv + T∆S°conf (16)
≈ 2 × (-5) + 2 × 19 + T∆S°conf
≈ -13.3 kcal/mol
(17)
This large loss of conformational entropy can partly be
rationalized in terms of structures of RtV3 and R′tL′3. Although
RtV3 is fairly rigid, it still contains nine rotors that are frozen
upon complexation to R′tL′3 (Scheme 1). R′tL′3 is a more
flexible molecule, and its complexation to RtV3 freezes, or partly
freezes, additional 18 rotors (Scheme 1). Page and Jencks
estimated a value of ∼1.2-1.5 kcal/mol per rotor frozen upon
complexation.35 The entropic penalty from freezing out these
rotors, (assuming that all are free in the unassociated state, and
frozen in the complex), thus would range between 32 and 40
kcal/mol. This range is reasonably close to the value of our
estimate of T∆S°conf in the two intramolecular binding steps,
given the high degree of approximation in this estimation (the
entropic loss per rotor frozen obviously is not the same for the
cases considered by Page and Jencks and those considered here,
nor are all the rotors in RtV3 and R′tL′3 the same).
In summary, our analysis of T∆S° for the trivalent binding
of RtV3 and R′tL′3 is compatible with (but does not demand) a
scheme in which the loss in conformational entropy in two
intramolecular bindings offsets the gain in T∆S°tran+rot from
linking three monomers as trimers. The observation that overall
T∆S° for the trivalent binding appears to be slightly more than
three times of that for binding of V to L is thus, in this analysis,
a coincidence.
1,3,5-Benzene Tris(N-(tert-butyloxycarbonyl)-4′-aminomethyl-
phenyl-carboxamide). To a solution of tert-butyl 4-aminobenzylamine
carboxylate (1.01 g, 4.5 mmol) in 50 mL of dry CH2Cl2 was added 1.0
mL of DIEA and 1,3,5-benzene tris(carbonyl chloride) (0.40 g, 1.5
mmol) at 0 °C under stirring. After 2 h, the reaction mixture was poured
into 5 mL of saturated aqueous NaCl solution and extracted with CH2-
Cl2. The solvent was removed by rotary evaporation, and the residue
was purified by flash chromatography (eluting with 100:3 CH2Cl2/
methanol) to give 1.01 g (1.2 mmol, 82%) of the product as a white
1
powder: Rf ) 0.50 (20:1 CH2Cl2/methanol); H NMR (DMSO-d6) δ
1.39 (s, 27 H, CCH3), 4.10 (d, J ) 5.96 Hz 6 H, CH2), 7.24 (d, J ) 8.3
Hz, 3 H, C6H4), 7.36 (t, J ) 6.1 Hz, 6 H, CH2NH), 7.72 (d, J ) 8.2
Hz, 6 H, C6H4), 8.67 (s, 3 H, C6H3), 10.55 (s, 3 H, CONH); HRMS-
FAB (M + Na+) calcd for C45H54N6O9Na 845.3850, found 845.3834.
1,3,5-Benzene Tris(N-4′-aminomethylphenyl-carboxamide). A
solution of 1,3,5-Benzene Tris(N-(tert-butyloxycarbonyl)-4′-amino-
methyl-phenyl-carboxamide) (170 mg, 0.21 mmol) in 5 mL of 1:1 CH2-
Cl2/TFA was stirred at room temperature for 1 h. After the solvent had
been removed by rotary evaporation, we recovered 170 mg of a white
powder (95%) as tris(trifluoroacetate) salt: 1H NMR (DMSO-d6) δ 4.02
(q, 6 H, CH2), 7.46 (d, J ) 8.6 Hz, 6 H, C6H4), 7.83 (d, J ) 8.6 Hz,
6 H, C6H4), 8.21 (bs, 9 H, NH3+), 8.70 (s, 3 H, C6H3), 10.71 (s, 3 H,
CONH); HRMS-FAB (M + H+) calcd for C30H31N6O3 523.2458,
found 523.2464.
Conclusions
Polyvalency aims to enhance binding through entropic
advantage. The trivalent system we have designed, based on
vancomycin and DADA, demonstrates the successful application
of this approach, and clarifies some of its principles: this system
is the tightest binding one (among relatively low molecular
weight organic species) of which we know. Our current
understanding of thermodynamics of this trivalent system shows
that, as expected, ∆H° for the trimer originates primarily in the
RtV3. To a solution of 100 mg of vancomycin hydrochloride (67
µmol), in 0.5 mL of dry DMSO, were added 0.5 mL of dry DMF and
1,3,5-benzene tris(N-4′-aminomethylphenyl-carboxamide) (19 mg, 22
µmol). The mixture was cooled to 0 °C, and 38 mg (100 µmol) of
HBTU was added, followed by 26 mg (206 µmol) of DIEA. The
(35) Page, M. I.; Jencks, W. P. Proc. Natl. Acad. Sci. U.S.A. 1971, 68,
1678.

2710 J. Am. Chem. Soc., Vol. 122, No. 12, 2000
Rao et al.
solution was allowed to warm to room temperature and stirred
overnight. Analytical reverse-phase HPLC showed nearly complete loss
of vancomycin and appearance of a much less polar major product.
Removal of the solvent afforded 130 mg of crude product. Preparative
reverse-phase HPLC purification and lyophilization afforded a white
foam as the RtV3 hexa(trifluoroacetate). The 1H NMR spectrum showed
the resonances expected for vancomycin and the hub units [dry DMSO-
d6, δ 4.45 (d, CH2NH), 7.28 (d, ArH), 7.74 (d, ArH), 8.70 (s, ArH),
10.60 (s, CONH)]. The ESIMS exhibited an ion at m/z 4818.8 consistent
with the calculated average molecular weight of 4817.4 for the parent
ion (M+H+), C228H250N33O72Cl6.
7.81 (d, 2 H, ArH), 8.02 (d, 1 H, NH), 8.06 (d, 1 H, NH), 8.15 (d, 1
H, NH), 8.43 (t, 1 H, NH); HR-FABMS (M + H+) calcd for
C21H31N4O6 435.2244, found 435.2221.
UV Spectrophotometry. The binding constant for association of
RtV3 with L was determined by UV difference spectrophotometry, using
the method described previously.3 The data were fit to a simple 1:1
binding model, assuming that the association of L with each site of
RtV3 is an independent event with the same affinity. A nonlinear least-
squares curve fitting routine was used in extracting the binding constant.
High-Pressure Liquid Chromatography. HPLC was performed
using a Waters 600E or a Rainin Dynamax Model SD-300 HPLC
chromatography system with a UV detector using C18 columns from
Rainin or Vydac. A 4.6 mm i.d. column was used for analysis and a
21.4 mm i.d. column was used for preparative separations. Linear
gradients of 0.1% TFA in acetonitrile and 0.1% TFA in water were
used in HPLC elution. The flow rate for the analytical study was 1.0
mL/min, and 7.5 mL/min for the preparative separation. The injection
volume for analytical separation was 20 µL. The parameters in eq 12
were determined as follows. Values of [L] were assumed to be constant
since L was in excess in the experiments. Values of [R′tL′3] and [RtV3‚
R′tL′3] were estimated from the integrals of their peaks on HPLC.
Values of [RtV3‚3L] were estimated from integrals of RtV3 because
RtV3‚3L dissociated to RtV3 on the column. Values of θ were thus
calculated using eq 12. Integrations were performed using Baseline
810, a program provided by Waters, by plotting chromatograms,
estimating baselines, and integrating areas of peaks.
Isothermal Titration Calorimetry. Calorimetry experiments were
carried out using a MicroCal MCS titration calorimeter as described
in detail elsewhere.25 Briefly, titrations were performed in 5.0 mM
phosphate buffer at pH 7.0, and typically consisted of 3- or 5-µL of
ligand solution in a schedule of 20 to 30 injections spaced at intervals
of 4-5 min with a syringe stirring speed of 500 rpm. The calibrated
feedback current (µcal/s) was recorded as a function of time and was
used to determine the heat released following an injection by integration.
Heats were nomarlized to give the enthalpy of binding (∆H°, kcal/
mol). For experiments in which binding constants were determined,
the data were analyzed by a single-set-of-sites binding model with
MicroCal Origin software. Concentrations of R′tL′3 were determined
by amino acid analysis.
R′tL′3. A suspension of 86 mg of NR-Ac-L-Lys-D-Ala-D-Ala-O-tBu
(0.22 mmol) in CH2Cl2 was cooled to 0 °C. To this suspension was
added 20 mg of 1,3,5-benzene tris(carbonyl chloride) (0.075 mmol) in
2 mL of CH2Cl2 in portions. The ice bath was removed, and the solution
was stirred under argon for 2 h, and a fine white precipitate formed.
Filtration afforded 25 mg of product as white flaky solid (0.019 mmol).
The crude tert-butyl ester-protected peptide was then stirred in a 1:1
mixture of TFA/CH2Cl2 for 1 h to cleave tert-butyl groups. After
removal of the solvent and TFA by rotary evaporation, the final residue
was purified by reverse phase HPLC and afforded the desired R′tL′3.
1H NMR (DMSO-d6) δ 1.16 (d, 9 H, CHCH3), 1.26 (d, 9 H, CHCH3),
1.22-1.36 (m, 6 H, CH2), 1.43-1.64 (m, 12 H, CH2), 1.81 (s, 9 H,
COCH3), 3.24 (d, 6 H, CH2NH), 4.13-4.19 (m, 6 H, COCHNH), 4.28
(m, 3 H, CHCH3), 8.03 (d, 3 H, NH), 8.08 (d, 3 H, NH), 8.15 (d, 3 H,
NH), 8.34 (s, 3 H, ArH), 8.65 (t, 3 H, NH); ESIMS exhibited an ion
at m/z 1148.7 consistent with the calculated m/z of 1147 for C51H79N12O18
(M + H+).
RV. To a solution of 100 mg of vancomycin hydrochloride (67
µmol), in 0.5 mL of dry DMSO, were added 0.5 mL of dry DMF and
4-aminomethylphenyl-carboxamide trifloroacetate salt (51 mg, 135
µmol). The mixture was cooled to 0 °C, and 31 mg (82 µmol) of HBTU
was added, followed by 26 mg (206 µmol) of DIEA. The solution was
allowed to warm to room temperature and stirred overnight. Analytical
reverse-phase HPLC showed nearly complete loss of vancomycin and
appearance of a much less polar major product. The residue after
removal of the solvent was subject to preparative reverse-phase HPLC.
Lyophilization of collected fractions afforded a white foam as RV di-
(trifluoroacetate). The 1H NMR spectrum showed the resonances
expected for vancomycin and the R unit [dry DMSO-d6, δ 4.47 (d,
CH2NH), 7.25 (d, ArH), 7.50-7.58 (m, ArH), 7.70 (d, ArH), 7.94 (d,
ArH), 8.42 (t, CONH), 10.23 (s, CONH)]. The ESIMS exhibited an
ion at m/z 1658.9 consistent with the calculated average molecular
weight of 1658.5 for the parent ion (M + H+), C80H88N11O24Cl2.
R′tL′. A suspension of 98 mg of NR-Ac-L-Lys-D-Ala-D-Ala-O-
Benzyl ester (0.19 mmol) in CH2Cl2 was cooled to 0 °C. To this
suspension was added 30 µL of benzoyl chloride (0.26 mmol) and 100
µL of triethylamine (1.1 mmol). The ice bath was removed, and the
solution was stirred under argon for 2 h. The solvent was removed by
rotary evaporation, and the residue was purified by flash chromatog-
raphy (eluting with 10:1 CH2Cl2/methanol) to give a white powder:
Rf ) 0.45 (10:1 CH2Cl2/ methanol). Deprotection of the benzyl ester
by hydrogenation afforded the desired free peptide R′tL′ (70 mg; 85%
Acknowledgment. This work was supported in part by the
National Science Foundation NSF CHE-9801358, the National
Institutes of Health (NIH) Grants GM30367, and GM53210 (to
R.M.W.). J.R. thanks Eli Lilly (1996), Hoffman-La Roche
(1997), and Glaxo Wellcome (1998) for Predoctoral Fellow-
ships. NMR instrumentation was supported by National Insti-
tutes of Health Grant 1 S10 RR4870 and National Science
Foundation Grant CHE-88-14019. FAB-Mass spectra were
obtained by Dr. Andrew Tyler at Harvard University. ESI-Mass
spectra of RtV3 and R′tL′3 and concentrations of R′tL′3 solution
were obtained by the Harvard MicroChem Facilities.
Supporting Information Available: Complete derivation
of eq 11 (PDF). This material is available free of charge via
the Internet at http://pubs.acs.org.
1
yield). H NMR (DMSO-d6) δ 1.15 (d, 3 H, CHCH3), 1.26 (d, 3 H,
CHCH3), 1.12-1.36 (m, 3 H, CH2), 1.43-1.60 (m, 3 H, CH2), 1.81 (s,
3 H, COCH3), 3.19-3.24 (m, 2 H, CH2NH), 4.12-4.20 (m, 2 H,
COCHNH), 4.26-4.29 (m, 1 H, COCHNH), 7.41-7.48 (m, 3 H, ArH),
JA992648L