Dependence of effective molarity on linker length for an intramolecular protein-ligand system

Article abstract of DOI:10.1021/ja066780e

This paper reports dissociation constants and "effective molarities" (Meff) for the intramolecular binding of a ligand covalently attached to the surface of a protein by oligo(ethylene glycol) (EG_n) linkers of different lengths (n = 0, 2, 5, 10, and 20) and compares these experimental values with theoretical estimates from polymer theory. As expected, the value of M_eff is lowest when the linker is too short (n = 0) to allow the ligand to bind noncovalently at the active site of the protein without strain, is highest when the linker is the optimal length (n = 2) to allow such binding to occur, and decreases monotonically as the length increases past this optimal value (but only by a factor of ～8 from n = 2 to n = 20). These experimental results are not compatible with a model in which the single bonds of the linker are completely restricted when the ligand has bound noncovalently to the active site of the protein, but they are quantitatively compatible with a model that treats the linker as a random-coil polymer. Calorimetry revealed that enthalpic interactions between the linker and the protein are not important in determining the thermodynamics of the system. Taken together, these results suggest that the manifestation of the linker in the thermodynamics of binding is exclusively entropic. The values of M_eff are, theoretically, intrinsic properties of the EG_n linkers and can be used to predict the avidities of multivalent ligands with these linkers for multivalent proteins. The weak dependence of M_eff on linker length suggests that multivalent ligands containing flexible linkers that are longer than the spacing between the binding sites of a multivalent protein will be effective in binding, and that the use of flexible linkers with lengths somewhat greater than the optimal distance between binding sites is a justifiable strategy for the design of multivalent ligands.

Full text of DOI:10.1021/ja066780e

Published on Web 01/10/2007
Dependence of Effective Molarity on Linker Length for an
Intramolecular Protein-Ligand System
Vijay M. Krishnamurthy, Vincent Semetey, Paul J. Bracher, Nan Shen, and
George M. Whitesides*
Contribution from the Department of Chemistry and Chemical Biology, HarVard UniVersity,
12 Oxford Street, Cambridge, Massachusetts 02138
Received September 20, 2006; E-mail: gwhitesides@gmwgroup.harvard.edu
Abstract: This paper reports dissociation constants and “effective molarities” (Meff) for the intramolecular
binding of a ligand covalently attached to the surface of a protein by oligo(ethylene glycol) (EGn) linkers of
different lengths (n ) 0, 2, 5, 10, and 20) and compares these experimental values with theoretical estimates
from polymer theory. As expected, the value of Meff is lowest when the linker is too short (n ) 0) to allow
the ligand to bind noncovalently at the active site of the protein without strain, is highest when the linker is
the optimal length (n ) 2) to allow such binding to occur, and decreases monotonically as the length
increases past this optimal value (but only by a factor of ∼8 from n ) 2 to n ) 20). These experimental
results are not compatible with a model in which the single bonds of the linker are completely restricted
when the ligand has bound noncovalently to the active site of the protein, but they are quantitatively
compatible with a model that treats the linker as a random-coil polymer. Calorimetry revealed that
enthalpic interactions between the linker and the protein are not important in determining the thermo-
dynamics of the system. Taken together, these results suggest that the manifestation of the linker in
the thermodynamics of binding is exclusively entropic. The values of Meff are, theoretically, intrinsic
properties of the EGn linkers and can be used to predict the avidities of multivalent ligands with these
linkers for multivalent proteins. The weak dependence of Meff on linker length suggests that
multivalent ligands containing flexible linkers that are longer than the spacing between the binding sites of
a multivalent protein will be effective in binding, and that the use of flexible linkers with lengths somewhat
greater than the optimal distance between binding sites is a justifiable strategy for the design of multivalent
ligands.
Introduction
estimates the probability of intramolecular binding as the
probability that the ends of the linker are separated by a
The primary motivation for this paper was to determine the
influence of the “linker”sthe structural element that connects
the binding moieties in a multivalent ligandson the binding of
a multivalent ligand to a multivalent protein (Figure 1E). As
our model system, we adopted a ligand covalently tethered to
the surface of a protein by oligo(ethylene glycol) linkers (EGn)
(Figure 1D), because this design allows us to interrogate the
system without complications from separate binding events of
the two ends of the ligand, complications that do arise when
both ends are free. We report dissociation constants (and
effective molarities, see below) for the intramolecular binding
of the tethered ligand to the active site of the protein as a
function of the linker length (n) and discuss the data in the
context of four possible models (Figure 2). We find that
only one of these models (Figure 2B) is consistent with the
following results: the linker plays an exclusively entropic
role in the thermodynamics of the system, and it has
significant conformational mobility even after the ligand is
bound at the active site of the protein. The results are
quantitatively well-explained by a model that describes the linker
as a random-coil polymer (Figure 3); this model is one originally
proposed by Lees and co-workers for a related problem and
distance (d) equal to the separation of the sites of covalent
attachment and noncovalent binding of the ligand to the protein
(Figure 1D).1
Effective molarity (Meff) is an empirical term that is com-
monly used to relate the kinetics and equilibria of intramolecular
and intermolecular reactions (both covalent and noncovalent)
in chemistry (eq 1).2,3 Kdinter, which has units of concentration
(e.g., molarity), is the dissociation constant for an intermolecular
reaction (Figure 1A), and Kdintra, which is dimensionless, is the
dissociation constant for an analogous intramolecular reaction
(Figure 1B). Meff depends on the length and flexibility of the
“linker” between the two reactive groups.2,3
intra
Meff ) Kdinter/Kd
(1)
(1) Gargano, J. M.; Ngo, T.; Kim, J. Y.; Acheson, D. W. K.; Lees, W. J. J.
Am. Chem. Soc. 2001, 123, 12909-12910.
(2) (a) Page, M. I.; Jencks, W. P. Proc. Natl. Acad. Sci. U.S.A. 1971, 68, 1678-
1683. (b) Page, M. I. Chem. Soc. ReV. 1973, 2, 295-323. (c) Kirby, A. J.
In AdVances in Physical Organic Chemistry; Gold, V., Bethell, D., Eds.;
Academic Press: London, 1980; Vol. 17, pp 183-278.
(3) Mandolini, L. In AdVances in Physical Organic Chemistry; Gold, V.,
Bethell, D., Eds.; Academic Press: London, 1986; Vol. 22, pp 1-111.
9
1312
J. AM. CHEM. SOC. 2007, 129, 1312-1320
10.1021/ja066780e CCC: $37.00 © 2007 American Chemical Society

Dependence of Effective Molarity on Linker Length
A R T I C L E S
Figure 2. Possible models to explain the binding of a ligand, covalently
attached to the surface of a protein by the “linker,” to the active site of that
protein. When the ligand is bound at the active site, the linker (A) has low
conformational mobility (i.e., free rotations of the bonds of the linker are
significantly restricted), (B) has significant conformational mobility, or (C,D)
makes stabilizing contacts with the surface of the protein. In (D), the linker
makes contacts with the surface of the protein even when the ligand is not
bound at the active site.
Figure 1. (A) A monovalent binding event between a receptor and ligand
is characterized by a dissociation constant (Kdinter) with units of concentration
Figure 3. Random-coil polymer with the number (n) of repeat units
(represented as open circles) equal to 45. (A) The polymer forms a closed
loop: the distance ( r 2 1/2) between the ends of the polymer is near zero.
(B) The polymer bears a physical pole of length d attached at one end. The
distance ( r 2 1/2) between the ends of the polymer is close to this defined
distance (d).
(M). (B) When the ligand is tethered to the receptor, the dissociation constant
inter
(Kdintra) is now dimensionless and is related to Kd
by the effective
molarity, Meff (eq 1). (C) Analogous to (A) for a binding event between a
protein and ligand. (D) Analogous to (B) for an intramolecular protein-
ligand binding event. In this case, however, the distance (d) between the
two ends of the linker in the bound state is nonzero (unlike the case in
(B)). (E) Dissociation of a bivalent ligand from a bivalent receptor. This
process can be conceptualized as occurring in two steps: the first step (with
dissociation constant 2Kdintra*) is intramolecular, and the second step (with
dissociation constant 1/4 Kdinter) is intermolecular. The equation given
provides a means of estimating Meff from the observed dissociation constant
(Kdavidity) and the intermolecular dissociation constant (Kdinter) by assuming
one another (eq 2); NA is Avogadro’s number and r 2 1/2 is the
root-mean-squared distance (in decimeters) between the ends
of the polymer.
3/2
1
3
2π
Ceff
)
(2)
(
)
NA( r 2 1/2 3
)
that the dissociation constant for the first step is equivalent to the product
intra
of a statistical factor of 2 and Kd
(defined in (D); i.e., this procedure
assumes that Kdintra* ) Kdintra). This assumption is often quite poor because
of complications arising from the influence of binding at one site on binding
at the other site (e.g., cooperativity between binding sites, enthalpy/entropy
compensation).4
The parameter r 2 1/2 can be estimated from polymer chem-
istry assuming a three-dimensional random flight (eq 3), where
n is the number of segments in the chain and C is proportional
to the distance (l) between two segments of the chain (this value
is equal to the bond length for a freely jointed polymer) and is
characteristic of a given chain structure.5,8,9 The proportionality
constant C/l gives a measure of the stiffness of the chain and
takes into account effects such as bond angles and rotational
barriers; it typically varies from 1.5 for a very flexible chain to
5.5 for a very stiff one.5,6
Effective concentration (Ceff, units of concentration) is a
theoretical parameter that allows the rate and/or equilibrium for
ring closure for intramolecular reactions (Figure 1B) to be
estimated by assuming that the linker between the two reactive
groups behaves as a random-coil polymer (Figure 3A).3-7 It is
essentially the probability that the two reactive groups (the two
ends of the polymer) will be within an infinitesimal distance of
(7) Kramer, R. H.; Karpen, J. W. Nature 1998, 395, 710-713.
(8) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press:
Ithaca, NY, 1953.
(4) Krishnamurthy, V. M.; Estroff, L. A.; Whitesides, G. M. In Fragment-
based Approaches in Drug DiscoVery; Jahnke, W., Erlanson, D. A., Eds.;
Wiley-VCH: Weinheim, 2006; Vol. 34, pp 11-53.
(5) Jacobson, H.; Stockmayer, W. H. J. Chem. Phys. 1950, 18, 1600-1606.
(6) Mulder, A.; Auletta, T.; Sartori, A.; Del Ciotto, S.; Casnati, A.; Ungaro,
R.; Huskens, J.; Reinhoudt, D. N. J. Am. Chem. Soc. 2004, 126, 6627-
6636.
(9) In order for the theory to apply, the polymer must be long enough to
eliminate the possibility of non-ideal effects (e.g., the non-Gaussian nature
of short chains, correlations between bond angles of different subunits,
transannular steric effects; see refs 5 and 10). Jacobson and Stockmayer
have argued that this minimum length is on the order of 15 atoms in the
chain, but the exact length depends on the flexibility and structure of the
polymer (see ref 10).
9
J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007 1313

A R T I C L E S
Krishnamurthy et al.
r 2 1/2 ) (C/l)l n ) C n
(3)
x
x
Winnik and Mandolini have reviewed the literature for ring-
closing (macrocyclization) reactions in small-molecule systems
and concluded that Ceff and Meff are closely correlated for many
of these reactions.3,10
In many situations (and, in particular, in protein-ligand
binding), we are not concerned with the probability that the
two ends of the linker are an infinitesimal distance apart. Rather,
we require the probability that the two ends are a distance d
apart, where d is set by the system (Figures 1D,E and 3B). Lees
and co-workers derived eq 4 for this case, where Ceff(0) is Ceff
defined in eq 2.1 The parameter p arises because of the presence
of the protein: the ligand cannot occupy the same space as the
protein, and because it is excluded from this volume, its Ceff
increases (a so-called “excluded volume” effect). Lees and co-
workers proposed a value of 2 for this term; this value assumes
that the ligand has only a hemisphere of free access when
constrained by the protein (Figure 1E), as compared to a sphere
when it is free in solution.1
Figure 4. Model for the interaction of p-H2NSO2C6H4CONH(CH2CH2O)2-
+
CH2CH2NH3 (ArEG3NH3+) with HCA based on the deposited X-ray
3
Ceff(d) ) pCeff(0) exp -
d 2
(4)
crystallographic coordinates (PDB code 1CNX).21 The arylsulfonamide
ligand is rendered as a ball-and-stick model in CPK color scheme. HCA is
depicted as a light blue ribbon diagram, with the catalytically essential Zn2+
cofactor shown as a green sphere. Lys-133 of HCA II is represented as a
red ball-and-stick model. The distance (d) between the last glycol unit of
the ligand and the γ-CH2 group of Lys-133 (corresponding to the thiol in
the LysfCys HCA** mutant) is indicated by the dashed line.
2( r 2 1/2 2
)
(
)
We have defined multivalency as multiple interactions (often
of the same kind) between two different species.4,11 Theoretical
approaches to multivalency have assumed a stepwise pathway
for dissociation, in which the first step is intramolecular (Figure
1E). The value of the dissociation constant (2Kdintra*) for this
step has been a challenge to estimate theoretically.4 Without
an estimate for this parameter, we cannot predict multivalent
avidities from the component monovalent affinities (although
the work by Lees, Reinhoudt, and others represents a significant
advance toward this capability).1,6,7 The study presented here
clarifies and simplifies this problem, because we obtain empiri-
cal estimates for the dissociation constants for intramolecular
protein-ligand binding that are applicable to the thermo-
dynamics of the intramolecular step in multivalent binding
(Figure 1D,E).
We have previously argued that flexible oligomers should
not function effectively as linkers in multivalent ligands because
of the severe loss in conformational entropy of the linker (T∆S°
≈ RT ln 3 ≈ 0.7 kcal mol-1 per freely rotating single bond of
the linker) when it is bound at both ends.4,11,12 Flexible linkers
(e.g., oligo(ethylene glycol)) have, however, been used with
success in multivalent ligands.4,7,11,13 Determining how flexible
linkers could work in multivalent ligands, when this simple
theoretical model argues that they should not, was a key
motivation for this paper.
there are a number of well-characterized assays to use in
following binding, and there are a number of commercially
available, high-affinity arylsulfonamides to use for competition
experiments.14-17 Further, HCA is easy to overexpress in, and
purify from, Escherichia coli culture in high yield; this ease
allows the generation of HCA mutants with chemical “handles”
(i.e., reactive sites) to which to couple the ligands.18-20
An examination of crystal structures of HCA complexed with
p-substituted benzenesulfonamides containing oligo(ethylene
glycol) linkers (PDB codes 1CNY, 1CNX, and 1CNW)21
established that Lys-133 was spatially close to the terminus of
the ligand but outside of the conical cleft of the enzyme (Figure
4). Mutating this residue to Cys would generate a chemical
handle for thiol-selective coupling.18,20 HCA has an endogenous
Cys at position 206. In order to preclude side reaction at this
site, we mutated it to Ser to generate a double mutant (Cys-
206fSer, Lys-133fCys), which we refer to as HCA** in the
remainder of this paper. Krebs and Fierke demonstrated that
the C206S mutant of HCA is active,22 and Mårtensson et al.
determined that this mutant is as stable as wild-type HCA.20
(14) (a) Krishnamurthy, V. M.; Kaufman, G. K.; Urbach, A. R.; Gitlin, I.;
Gudiksen, K. L.; Weibel, D. B.; Whitesides, G. M., submitted. (b)
Christianson, D. W.; Fierke, C. A. Acc. Chem. Res. 1996, 29, 331-339.
(15) (a) Supuran, C. T.; Scozzafava, A.; Casini, A. Med. Res. ReV. 2003, 23,
146-189. (b) Supuran, C. T.; Scozzafava, A.; Conway, J. In Carbonic
Anhydrase: Its Inhibitors and ActiVators; Supuran, C. T., Scozzafava, A.,
Conway, J., Eds.; CRC Press: Boca Raton, FL, 2004; Vol. 1, pp 67-147.
(16) Chen, R. F.; Kernohan, J. C. J. Biol. Chem. 1967, 242, 5813-5823.
(17) Kernohan, J. C. Biochem. J. 1970, 120, 26P.
Experimental Design. We selected the combination of
human carbonic anhydrase II (HCA, EC 4.2.1.1) and p-
substituted benzenesulfonamides as our model system, because
it is the simplest one that we know for studying protein-ligand
interactions: the conserved mode of binding of sulfonamides
to HCA has been well-established by X-ray crystallography,
(18) Burton, R. E.; Hunt, J. A.; Fierke, C. A.; Oas, T. G. Protein Sci. 2000, 9,
776-785.
(10) Winnik, M. A. Chem. ReV. 1981, 81, 491-524.
(11) Mammen, M.; Choi, S.-K.; Whitesides, G. M. Angew. Chem., Int. Ed. 1998,
37, 2755-2794.
(19) Khalifah, R. G.; Strader, D. J.; Bryant, S. H.; Gibson, S. M. Biochemistry
1977, 16, 2241-2247.
(20) Mårtensson, L.-G.; Jonsson, B.-H.; Freskgård, P.-O.; Kihlgren, A.; Svensson,
M.; Carlsson, U. Biochemistry 1993, 32, 224-231.
(12) Mammen, M.; Shakhnovich, E. I.; Whitesides, G. M. J. Org. Chem. 1998,
63, 3168-3175.
(21) Boriack, P. A.; Christianson, D. W.; Kingery-Wood, J.; Whitesides, G. M.
J. Med. Chem. 1995, 38, 2286-2291.
(13) Choi, S.-K. Synthetic MultiValent Molecules: Concepts and Biomedical
Applications; John Wiley & Sons, Inc.: Hoboken, NJ, 2004.
(22) Krebs, J. F.; Fierke, C. A. J. Biol. Chem. 1993, 269, 948-954.
9
1314 J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007

Dependence of Effective Molarity on Linker Length
A R T I C L E S
Table 1. Chemical Labels and Modified HCA** Proteins Used in
This Study
dures, Supporting Information for details). We used ligands
containing disulfides activated with 2-pyridylthiol because the
aromatic thiol is an excellent leaving group; thus, incubating
the activated disulfide with HCA** should generate only the
desired products (HCA**-SSEGnSA).28 We also synthesized two
control molecules (Pyr-SSEGnCONH2 and SA-OMe) for our
studies.
We decided to use p-substituted benzenesulfonamides with
a conserved alkyl chain (p-H2NSO2C6H4CH2NHCO(CH2)4-
CO-) as our model ligands because benzenesulfonamides bind
CA in an invariant orientation, and the alkyl chain should
saturate the hydrophobic surface of the conical cleft of CA and
orient the linker into solution.14,21,23-25 We selected oligo-
(ethylene glycol) (EGn) as the linker to tether the ligand to
HCA** because it is one of the most common linkers in
multivalent ligands.4,11,13 We wanted to understand how these
flexible oligomers could be effective as linkers in multivalent
ligands. Oligo(ethylene glycol) has been shown to be resistant
to the nonspecific adsorption of proteins when displayed on
surfaces;26 this property should minimize complications from
nonspecific adsorption of the linker to the surface of the protein
(Figure 2C,D).
Design and Purification of HCA II with a Surface-
Accessible Cysteine Residue. We generated a vector encoding
HCA** by conventional site-directed mutagenesis of the plasmid
encoding the C206S mutant of HCA (pC206S) and inserted this
mutated vector into the backbone of the plasmid encoding wild-
type HCA (pACA; both pC206S and pACA were kind gifts of
Prof. Carol Fierke, University of Michigan).22,29 We overex-
pressed HCA** in E. coli (BL21(DE3)) as described by Fierke
and co-workers18 and purified it as described by Khalifah et
al.19 We confirmed the purity of the enzyme by SDS-PAGE
and its activity (∼100%) by measuring the amount of protein
that could bind ethoxzolamide (Ethox), a specific inhibitor of
CA (Figure S.1, Supporting Information).17
Synthesis of Modified HCA** Proteins and Characteriza-
tion of Conjugates. We treated HCA** with ∼5 equiv of one
of five disulfide-activated ligands (Pyr-SSEGnSA, n ) 0, 2, 5,
10, and 20) in Tris-sulfate buffer, pH 8.0, and purified the
conjugated proteins (HCA**-SSEGnSA, n ) 0, 2, 5, 10, and
20) by exhaustive dialysis. We also synthesized two control
proteins (HCA**-SSEG2CONH2 and HCA**-SCH2CO2-) by
allowing HCA** to react with ∼10 equiv of Pyr-SSEG2CONH2
or iodoacetate (see the Experimental Section for details). The
use of HCA**-SSEG2CONH2 established the influence of the
linker minus the benzenesulfonamide moiety on binding. We
We chose thiolate-disulfide interchange as a means of
coupling the ligands to HCA** because this reaction is
completely selective for thiols (vs the various other chemical
functionalities in proteins).27
Results and Discussion
Synthesis of Benzenesulfonamides Containing Activated
Disulfides for Covalent Tethering to HCA**. We synthesized
disulfide-activated p-substituted benzenesulfonamides with oli-
go(ethylene glycol) linkers of different lengths (Pyr-SSEGnSA;
n ) 0, 2, 5, 10, and 20; Table 1) using conventional amide-
bond coupling reactions (see Supporting Experimental Proce-
-
used HCA**-SCH2CO2 for control studies (see below).
We characterized all of the modified proteins by ESI-MS and,
in all cases, observed peaks corresponding to the combined
masses of the protein and the reacted ligand (Table S.1,
Supporting Information). We examined the HCA**-SSEGnSA
proteins by size-exclusion high-performance liquid chromatog-
raphy (SE-HPLC) in order to determine whether a noncovalent
dimer was present in any of the samples (Figure S.2, Supporting
Information). For HCA**-SSEGnSA with n ) 2, 5, 10, and 20,
we saw no evidence for a dimer at a concentration of protein
of 20 µM. For HCA**-SSEG0SA (i.e., n ) 0), we observed a
peak (∼14% of total protein) corresponding in size to a dimer;
this peak quantitatively dissociated in the presence of a large
excess of Ethox (a high-affinity arylsulfonamide; see next
(23) (a) Gao, J.; Qiao, S.; Whitesides, G. M. J. Med. Chem. 1995, 38, 2292-
2301. (b) King, R. W.; Burgen, A. S. V. Proc. R. Soc. London B 1976,
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(25) Jain, A.; Whitesides, G. M.; Alexander, R. S.; Christianson, D. W. J. Med.
Chem. 1994, 37, 2100-2105.
(26) (a) Prime, K. L.; Whitesides, G. M. Science 1991, 252, 1164-1167. (b)
Prime, K. L.; Whitesides, G. M. J. Am. Chem. Soc. 1993, 115, 10714-
10721. (c) Mrksich, M.; Whitesides, G. M. In Poly(ethylene Glycol):
Chemistry and Biological Applications; 1st ed.; Harris, J. M., Zalipsky, S.,
Eds.; American Chemical Society: Washington, DC, 1997; Vol. 680, pp
361-373.
(27) (a) Gilbert, H. F. In AdVances in Enzymology and Related Areas of
Molecular Biology; Meister, A., Ed.; Wiley: New York, 1990; Vol. 63,
pp 69-172. (b) Lees, W. J.; Whitesides, G. M. J. Org. Chem. 1993, 58,
642-647. (c) Erlanson, D. A.; Wells, J. A.; Braisted, A. C. Annu. ReV.
Biophys. Biomol. Struct. 2004, 33, 199-223. (d) Erlanson, D. A.; Braisted,
A. C.; Raphael, D. R.; Randal, M.; Stroud, R. M.; Gordon, E. M.; Wells,
J. A. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 9367-9372. (e) Erlanson, D.
A.; Hansen, S. K. Curr. Opin. Chem. Biol. 2004, 8, 399-406.
(28) Carlsson, J.; Drevin, H.; Axe´n, R. Biochem. J. 1978, 173, 723-737.
(29) Nair, S. K.; Calderone, T. L.; Christianson, D. W.; Fierke, C. A. J. Biol.
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(30) Krishnamurthy, V. M.; Bohall, B. R.; Semetey, V.; Whitesides, G. M. J.
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A R T I C L E S
Krishnamurthy et al.
Table 2. Measured and Calculated Enthalpy and Entropy Values for Intermolecular and Intramolecular Binding of Sulfonamides to Modified
and Unmodified HCA** Proteins
∆
G
°
,
∆
H
°
,
−T∆S°,
kcal mol-
1
1
1
protein
ligand
Kd
×
106
kcal mol-
kcal mol-
HCA**
HCA**-SSEG2CONH2
HCA**-SCH2CO2
DNSA
DNSA
DNSA
Ethox
0.30 ( 0.014a,b,c
0.26 ( 0.008a,b,c
0.23 ( 0.007a,b,c
0.0002 ( 0.00004a,b,d
0.51 ( 0.018a,b
0.55 ( 0.03a,e
-8.90 ( 0.15
-8.98 ( 0.10
-9.05 ( 0.10
-13.2 ( 0.6
-8.58 ( 0.11
-8.54 ( 0.16
-7.12 ( 0.08
-6.1 ( 0.6
-
-17.7 ( 0.4e,f
+4.5 ( 0.7
SA-OMe
SA-OMe
Ethox
-6.10 ( 0.12e,f
-11.0 ( 0.6e,f
-6.7 ( 0.7e,f
-2.4 ( 0.2
+3.9 ( 0.6
+0.6 ( 0.9
HCA**-SSEG10SA
6.1 ( 0.01a,e,g
intrah
33 ( 7i
a Units of M. b Measured by fluorescence either directly or through competition with DNSA.16,17,24,25 Uncertainties are 95% confidence intervals from
curve-fitting. c Compare to literature value of 0.3 µM for the binding of DNSA to a Cys-206fSer mutant of HCA.22 d Compare to literature value of 0.2
nM for the binding of Ethox to bovine carbonic anhydrase II.17 e Measured by calorimetry. f Uncertainties were assumed to be due primarily to errors in the
quantitation of titrant.30 An uncertainty of 2% of ∆H° was taken for the binding to HCA**-SCH2CO2- and 5% of ∆H° for the binding to HCA**-SSEG10SA.
h
g Compare to value from fluorescence of 2.4 µM (Table 3). Thermodynamic parameters are those for the intramolecular equilibrium shown in Figure 1D.
i Dimensionless.
section) and thus represents a noncovalent dimer that is stable
on the time scale of the analysis (∼25 min). As a stable,
noncovalent dimer represents a minor contaminant for HCA**-
SSEG0SA and is not present for any of the other HCA**-SSEGn-
SA proteins, it should not complicate our analysis of dissociation
constants (see next section).
We measured the affinity of a well-characterized fluorescent
arylsulfonamide, dansylamide (DNSA), for HCA**, HCA**-
SCH2CO2-, and HCA**-SSEG2CONH2 (Figure S.3, Supporting
Information).16 The values of Kd for the three proteins were the
Figure 5. Schematic diagram depicting the strategy for the measurement
intra
of Kd
for HCA**-SSEGnSA using the observed dissociation constant
same (Table 2); this observation suggests that the EGn linker
itself has no effect on the binding of arylsulfonamides to the
modified HCA** proteins and that we can use HCA**-SCH2-
(Kdcomp,Ethox) for a competing ligand, Ethox (shown as black triangle). For
intra
comp,Ethox
this thermodynamic cycle, Kd
) KdEthox/Kd
(eq 5).
Measurement of Dissociation Constants of Ethoxzolamide
(Ethox). Ethox is a high-affinity ligand for CA that quenches
∼70% of the fluorescence of the Trp residues of the enzyme
(so-called “intrinsic” protein fluorescence) and thus offers a
spectrophotometric method of following binding and determin-
ing values of Kd (Figure S.1B, Supporting Information).17 We
treated HCA**-SSEGnSA (n ) 0, 2, 5, 10, and 20) and HCA**
(incubated with 2 equiv of SA-OMe) with different concentra-
tions of Ethox and followed the fluorescence of the free,
unbound protein (excitation wavelength ) 290 nm, emission
wavelength ) 340 nm) to determine dissociation constants
(Figure 5). Figure 6 shows the normalized data and fits to the
-
CO2 as a surrogate for HCA** for control studies because it
is easier to handle (e.g., there is no need for added reductant
and no possibility of dimer formation without the reductant).
In order to determine the purity of the sulfonamide-conjugated
proteins (HCA**-SSEGnSA), we examined the fluorescence of
the protein (excitation wavelength ) 290 nm, emission wave-
length ) 460 nm) when treated with 5 µM DNSA; this
concentration is ∼16-fold greater than the Kd of DNSA for
HCA** (Table 2). The only fluorescent species under these
conditions is the HCA**-DNSA complex. We assumed that any
fluorescence observed was due to residual, unmodified HCA**,
because all of the modified proteins have dissociation constants
for DNSA too high to bind it at the concentration of DNSA
used in the experiment (see below). We constructed a standard
curve for the fluorescence of 5 µM DNSA as a function of the
concentration of HCA** and used it to interpolate the concen-
tration of unmodified HCA** remaining in the coupling
reactions (Figure S.4, Supporting Information). Using these
values and the concentrations of total HCA** protein from UV
spectroscopy,31 we obtained purities of 90-95% for HCA**-
SSEGnSA where n ) 0, 2, 10, and 20 and ∼80% for n ) 5
(see Supporting Experimental Procedures for details). This
amount of contamination will not affect values of dissociation
constants for these proteins (see next section).
data assuming a single-site binding model (see Experimental
comp,Ethox
Section). As linker length (n) increased, Kd
(Figure 5)
for HCA**-SSEGnSA reached a peak when n ) 2, and then
comp,Ethox
decreased. The magnitude of the decrease in Kd
was
only weakly dependent on n (only a ∼8-fold decrease from
n ) 2 to n ) 20; Table 3).
To account for the presence of unmodified HCA** in the
HCA**-SSEG5SA sample (see previous section), we normalized
the fluorescence data (Figure 6) to the intensity observed when
[Ethox] ) 40 nM (this concentration is sufficient to saturate
the binding sites of all of the residual unmodified HCA**).
Given the high value of Kdcomp,Ethox (5.6 µM) observed for this
protein, <1% of the HCA**-SSEG5SA in the sample will bind
Ethox at this concentration.
The fluorescence of HCA** that had been incubated with
∼2 equiv of SA-OMe (the ligand that was covalently tethered
to HCA** in the modified proteins HCA**-SSEGnSA) de-
creased linearly with increasing concentrations of Ethox until
a stoichiometric amount of Ethox was present (Figure 6). This
result demonstrates that the presence of free, unbound SA-OMe
For calorimetric studies where completely homogeneous
protein was required, we purified the sulfonamide-conjugated
protein (HCA**-SSEG10SA) over a column of benzenesulfona-
mide-conjugated agarose (see Supporting Experimental Proce-
dures for details). Purities were g99% (assessed using the
standard curve) after this procedure.
(31) Nyman, P. O.; Lindskog, S. Biochim. Biophys. Acta 1964, 85, 141-151.
9
1316 J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007

Dependence of Effective Molarity on Linker Length
A R T I C L E S
the same competition experiment with DNSA to determine the
inter
value of the dissociation constant of SA-OMe (Kd
) 0.51
-
µM; Figure 1C and eq 1) for HCA**-SCH2CO2 (Figure S.5,
Supporting Information; Table 2).
intra
Measurement of Kd
and Calculation of Meff. Equation
5 gives the dissociation constant (Kdintra) for the intramolecular
binding of the tethered ligand to the active site of HCA for
HCA**-SSEGnSA from a thermodynamic cycle for the binding
of Ethox to HCA**-SSEGnSA (Figure 5). Values of Kd
(for HCA**-SSEGnSA) and Kd
comp,Ethox
Ethox
-
(for HCA**-SCH2CO2 )
were measured as described in the previous section. Table 3
intra
lists the calculated values of Kd
Kdintra ) KdEthox/Kd
Table 3 also lists values of Meff calculated using eq 1 with
.
comp,Ethox
(5)
intra
inter
Figure 6. Decrease in fluorescence of modified HCA** proteins (HCA**-
SSEGnSA, n ) 0, 2, 5, 10, or 20) and HCA** (incubated with 2 equiv of
SA-OMe) with increasing concentration of ethoxzolamide (Ethox). The
intrinsic fluorescence of 200 nM protein in 20 mM sodium phosphate, pH
7.5, at 298 K with different concentrations of the fluorescence quencher
Ethox was measured (excitation wavelength ) 290 nm, emission wavelength
) 340 nm). The data are shown after background subtraction, correction
for the inner filter effect, and normalization to a maximum signal of unity
(see Experimental Section). The solid curves are fits to the data using the
full quadratic equation for binding (eq 7; this equation does not make the
assumption that [Ethox]free ≈ [Ethox]total), and using a value for the minimum
in fluorescence intensity of all samples of 0.3 (Figure S.1B, Supporting
Information). Error bars represent the maximum variation of an independent
measurement from the mean of four experiments (duplicates from two
independent experiments). Inset: The data on a logarithmic scale for the
x-axis. The solid curves are fits to the data using a single-site Langmuir
values of Kd
and Kd
(the dissociation constant for the
binding of SA-OMe to HCA**-SCH2CO2-; see previous section
and Figure 1C,D). Meff was only weakly dependent on linker
length (n) when n g 2: it decreased by approximately a factor
of 8 between n ) 2 and n ) 20. The model shown in Figure
2A anticipates a much greater dependence of Meff on n than
that observed: the simplest model, which assumes that each
single bond in an EG unit of the linker has three possible
conformations before binding and only one after binding,
anticipates a >10-fold decrease in Meff per EG unit (see
Introduction).4,11,12 This model is inconsistent with the weak
dependence of Meff on n observed experimentally and can be
eliminated.
binding model (eq 8), which makes the assumption that [Ethox]free
[Ethox]total; this assumption is poor when n ) 0 or 20 (see Experimental
Section).
≈
Theoretical Values of Ceff for Intramolecular Binding of
Sulfonamide-Conjugated HCA** (HCA**-SSEGnSA). As
mentioned in the section on Experimental Design, the “ligand”
in HCA**-SSEGnSA consists of the benzenesulfonamide moiety
and the alkyl chain that is directly attached to it (p-H2NSO2C6H4-
CH2NHCO(CH2)4CO-); thus, the linker consists of the EGn
chain and the remainder of the alkyl chain (-NH(CH2CH2O)n-
CH2CH2NHCOCH2CH2S-). Treating the linker as a copolymer
allowed us to estimate a value for r 2 1/2 from the sum of the
contributions from the EGn and the non-EGn portions of the
linker (eq 6).8 For the EGn portion of the linker, we used a
literature value of 0.58 nm for the parameter C in eq 3.32 We
assumed that the non-EGn portion of the linker was “alkyl-like”
and contributed a constant value of 0.40 nm to the linker
length.33
Table 3. Experimental and Theoretical Values for the
Intermolecular and Intramolecular Binding of Sulfonamides to
Sulfonamide-Conjugated HCA** Proteins (HCA**-SSEGnSA)
comp,Ethox
intra
b
n
Kd
(µ
M)a
Kd
×
105
Meff (mM)c
0
2
5
10
20
0.31 ( 0.015
10 ( 0.7
66 ( 14
2.0 ( 0.4
3.6 ( 0.8
8.3 ( 1.8
17 ( 4
0.8 ( 0.16
26 ( 5
5.6 ( 0.5
14 ( 3
2.4 ( 0.17
1.2 ( 0.08
6.1 ( 1.3
3.1 ( 0.7
a Observed dissociation constants for the binding of Ethox to HCA**-
SSEGnSA (Figure 5). Uncertainties are 95% confidence intervals from curve-
fitting. b Calculated dissociation constants for the binding of the tethered
ligand to the active site of HCA (Figure 5). Uncertainties were propagated
from uncertainties in Kdcomp,Ethox and KdEthox (see Table 2). c Calculated using
inter
eq 1. Uncertainties were propagated from uncertainties in Kdintra and Kd
(see Table 2).
2
2
r 2 1/2
)
0.58 n + 0.40
(6)
x
could not explain the observation that the affinity of Ethox is
much lower for HCA**-SSEGnSA than for HCA**, and that
the value of Kd
determined directly by this method (i.e., the value of Kd
for HCA** is much lower than the concentration of protein,
∼200 nM, required for a detectable signal from intrinsic
fluorescence).
In order to estimate Ceff (eq 4), we need a value for the
distance (d) between the sites of covalent attachment of the
ligand to the protein and of the ligand bound at the active site
(Figure 1D). There are no reported X-ray crystal structures of
complexes of HCA with p-substituted benzenesulfonamides with
alkyl tails, so we examined the crystal structure of a complex
Ethox
(Figure 5) for HCA** is too low to be
Ethox
To determine the value of KdEthox, we allowed Ethox and
DNSA (5 µM) to compete for the active site of HCA**-SCH2-
CO2- and measured the decrease in fluorescence of the HCA**-
SCH2CO2--DNSA complex (excitation wavelength ) 290 nm,
emission wavelength ) 460 nm) with increasing concentration
of HCA with a p-substituted benzenesulfonamide having a tri-
(ethylene glycol) tail (ArEG3NH3
+
;
Figure 4). We
(32) Knoll, D.; Hermans, J. J. Biol. Chem. 1983, 258, 5710-5715.
(33) There are a seven single bonds in the non-EGn portion of the linker (between
the thiol of the linker and the -NH- of the carboxamide closest to the
alkyl chain of the ligand). Using eq 3 with an estimate for l of 0.153 nm
(the C-C bond length) and assuming an ideal, random-flight polymer
(C/l ) 1) gives an estimate of ∼0.4 nm for the value of the non-EGn portion
of the linker.
of Ethox (Figure S.5, Supporting Information; Table 2).16,24,25
Ethox
The value we obtained (Kd
agreement with one from the literature (Table 2).17 We used
) 0.2 nM) was in good
9
J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007 1317

A R T I C L E S
Krishnamurthy et al.
than unitysthe unbound ligand has a full sphere of volume to
explore and is in an environment similar to that of a polymer
that is free in solution. At present, we do not have a clear
understanding of what effect could contribute the additional
8-fold decrease in p. We speculate that the geometry of the
catalytic cleft of CA (∼1.5 nm deep and conical; Figure 4) could
result in the polymer being excluded from the cleft because of
steric interaction; this excluded volume effect would lower p
(and Ceff).
Calorimetric Investigation To Determine Enthalpy and
Entropy of Binding for Kdintra. Our previous work suggested
that EGn tails interacted with a hydrophobic patch in the conical
cleft of CA, albeit with no effect on the observed dissociation
constants.21,24 We have recently shown that increasing the length
of these tails makes the enthalpy of association of these ligands
with CA more favorable and the entropy less favorable in a
way that perfectly balances to give no change in values of Kd.30
As mentioned in the section on Experimental Design, we
designed HCA**-SSEGnSA to include a conserved alkyl
chain to saturate this hydrophobic surface in the conical cleft
of the enzyme. Thus, we would not anticipate that contacts
between the EGn linker and the surface of HCA could occur
(Figure 2C,D).
Figure 7. Variation of effective concentration (Ceff) and effective molarity
(Meff) with linker length (n; related to the root-mean-squared distance
between the ends of the linker r 2 1/2, see eq 6) for HCA**-SSEGnSA. The
points are empirical values of Meff (eq 1) from this study (Table 3). The
solid curve is a fit to the data using the definition of Ceff (eq 4) with estimates
of r 2 1/2 from eq 6. The best fit to the data was obtained with a value for
d (the distance between the site of covalent attachment of the ligand to the
protein and the active site of the protein; Figure 4) of 0.82 ( 0.03 nm and
a value for p of 0.12 ( 0.009.
To test this idea, we used isothermal titration calorimetry
intra
(ITC) to dissect the intramolecular dissociation constant (Kd
;
assumed that the alkyl chain of the ligand in HCA**-SSEGn-
SA interacts with the same hydrophobic patch of CA and has
the same orientation in the active site as the EG3 tail in ArEG3-
NH3+. From the crystal structure, we estimated a distance of
∼0.9 nm between the first methylene group of the third glycol
Figures 1D, 2, and 5) for HCA**-SSEG10SA into its enthalpic
(∆H°intra) and entropic (∆S°intra) components. We examined the
binding of Ethox to HCA**-SSEG10SA (Figure S.6, Supporting
-
Information) and to the control protein HCA**-SCH2CO2
(Figure S.7A, Supporting Information). We calculated ∆H°intra
and ∆S°intra for HCA**-SSEG10SA by making use of the
thermodynamic cycle shown in Figure 5 (Table 2). The value
of Kdcomp,Ethox that we measured by ITC for the binding of Ethox
to HCA**-SSEG10SA was in good agreement (a difference of
a factor of 2-3) with the one that we measured by fluorescence
quenching (Tables 2 and 3).
+
unit of ArEG3NH3 (a position that should correspond to the
-NH- group of the linker in HCA**-SSEGnSA) and the
γ-carbon of Lys-133 of HCA (a position that should correspond
to the thiol of HCA**) (Figure 4).
Figure 7 shows our experimental values of Meff (see previous
section) and a fit to the data calculated using eq 4 for Ceff and
eq 6 for r 2 1/2. We allowed the values of d and p to vary in
order to optimize the fit. The value of d (0.82 ( 0.03 nm) that
gave the best least-squares fit to the data is very close to the
value (0.9 nm) that we determined from analyzing the X-ray
crystal structure of the HCA-ArEG3NH3+ complex (Figure 4).
This observation, together with the excellent fit to the experi-
mental data, suggests that the theoretical model based on
polymer theory successfully (if unexpectedly) rationalizes the
dependence of the intramolecular binding of the tethered ligand
to the active site of the protein, as a function of the length of
the variable part of the linker. Further, because the theory from
which Ceff is derived explicitly ignores enthalpic contributions
to ring closure, these observations suggest that entropy is
dominant in intramolecular binding (see the next section for
further discussion).
The value of p (0.12 ( 0.009; eq 4) that gave the best fit to
the data is significantly lower than the value of 2 proposed by
Lees and co-workers for the bivalent protein-ligand complex
(Figure 1E).1 Because the point of attachment of the benzene-
sulfonamide ligands to HCA for HCA**SSEGnSA is at the
periphery of the conical cleft (Figures 1D and 4), the ligand
will encounter less steric repulsion with the protein (when it is
not bound at the active site of CA) than the unbound ligand in
the intermediate state in a bivalent protein-ligand complex
(Figure 1E). This effect can decrease the value of p to no less
The value of ∆H°intra for HCA**-SSEG10SA (-6.7 ( 0.7
kcal mol-1, Table 2) was the same, within error, as ∆H°obs for
the binding of SA-OMe (a ligand containing the benzene-
sulfonamide moiety and alkyl chain of HCA**-SSEG10SA) to
-
HCA**-SCH2CO2 (-6.1 ( 0.12 kcal mol-1, Table 2 and
Figure S.7B, Supporting Information). This result suggests that
there is little, if any, interaction of the EGn linker with the
protein: our previous results suggested that any interaction of
the EGn chain with CA should occur with a measurable change
in enthalpy.30 Thus, this result serves to rule out the model
shown in Figure 2C.
There remains the possibility that the linker makes stabilizing
contacts with the protein whether the ligand is bound or not
bound at the active site (Figure 2D), and thus there would be
no change in enthalpy for these contacts between the two states.
We cannot rigorously rule out this possibility. The fact that a
theory from polymer chemistry that is based entirely on entropic
terms fits the experimental data very well (Figure 7), however,
persuades us to prefer the simpler model shown in Figure 2B.
Conclusions
This paper reports values of effective molarity (Meff) as a
function of the length (n) of linkers of oligo(ethylene glycol)
for a ligand covalently tethered to a protein (Figure 2). Values
9
1318 J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007

Dependence of Effective Molarity on Linker Length
A R T I C L E S
of Meff reach a maximum when the linker is the optimal length
to allow the ligand to bind to the active site of the protein, and
then decrease weakly with increasing linker length (decrease
in Meff by only a factor of ∼8 over the range n ) 2 to n ) 20)
beyond this value (Figure 7). The experimental data are well-
explained by a theoretical, entropic model from polymer
chemistry based on the probability that the ends of the linker
are separated by the same distance as the sites of covalent
attachment and of noncovalent binding of the tethered ligand.
Calorimetry revealed that enthalpic contacts of the linker with
the protein are not important in this system and that entropy is
dominant (Table 2; Figure 2C,D).
make Meff even less sensitive to the length of the linker than in
the results presented here (Figure 2C,D).
Finally, ligands with flexible linkers can adopt a number of
conformations without steric strain (unlike ligands with rigid
linkers); this flexibility should allow the multivalent ligand to
sample conformational space to optimize its binding to the
multiple binding sites. This sampling of conformational space
reduces the possibility of a sterically obstructed fit, a circum-
stance that can occur readily with rigid linkers that are not
perfectly designed.4
Experimental Section
General Methods. All chemicals were obtained from Sigma (St.
Louis, MO), Aldrich (Milwaukee, WI), or Alfa Aesar (Ward Hill, MA)
and used without further purification, unless otherwise noted. DNSA
was recrystallized from ethanol prior to use. DNA sequencing was
performed by the DNA sequencing facility at the Harvard University
Department of Molecular and Cellular Biology. Fluorescence measure-
ments were performed on a Molecular Devices SpectraMax M5
instrument for detection at 340 nm (intrinsic protein fluorescence for
Ethox binding assays) and on a Molecular Devices SpectraMax Gemini
XS instrument for detection at 460 nm (for DNSA binding assays).
Isothermal titration calorimetry was performed using a VP-ITC
microcalorimeter from MicroCal (Northampton, MA). Varian Inova
spectrometers operating at 400 and 500 MHz (1H) were used for NMR
experiments. UV-vis spectroscopy was conducted on a Hewlett-
Packard 8453 spectrophotometer (Palo Alto, CA). UV spectroscopy
Our results suggest that, at least in the case of oligo(ethylene
glycol) linkers, contacts of the linker with the surface of the
protein (outside of the active site) can be safely ignored. These
results are consistent with previous studies that demonstrated
that surfaces displaying oligo(ethylene glycol) groups did not
adsorb proteins nonspecifically.26 These results can be reconciled
with our previous findings that suggested an interaction of oligo-
(ethylene glycol) tails with CA: in these previous studies, the
tails interacted with a surface of the protein inside the conical
cleft of CA.21,30 This possibility is precluded for the ligands
studied here (HCA**-SSEGnSA) because they have alkyl chains
of sufficient length to saturate this hydrophobic surface.
Most importantly, our results are not consistent with a model
in which the linker is completely restricted upon association of
the ligand with the active site of the protein (when the linker is
bound at both ends; Figure 2A). This model requires that Meff
decrease sharply with the length of the linker (>10-fold decrease
with each ethylene glycol unit), an expectation that is not met
by the experimental results. Our results support a model in which
the linker has significant conformational mobility when bound
at both ends (Figure 2B).
was used to quantify HCA** proteins (ꢀ280 ) 54 000 M-1 cm-1 31 and
)
DNSA (ꢀ326 ) 4640 M-1 cm-1).25 Ethox and SA-OMe were quantified
1
by H NMR spectroscopy.24,25,30,34
Preparation of Plasmid Encoding HCA**. The plasmids encoding
wild-type HCA II (pACA) and a Cys-206fSer mutant of HCA II
(pC206S) were gifts from Professor Carol Fierke)22,29 The Lys-
133fCys mutation was introduced into the pC206S plasmid using
oligonucleotide site-directed mutagenesis with a Quickchange Mu-
tagenesis Kit (Strategene) and following the manufacturer’s directions.
This plasmid was digested with the restriction enzymes BamHI and
KasI (New England BioLabs), purified by agarose gel electrophoresis
using a Quick Gel extraction kit (Qiagen), and ligated into the pACA
backbone, which had been digested with BamHI and KasI, treated with
calf intestinal alkaline phosphatase (CIP, from New England BioLabs;
to prevent recircularization of the vector without the insert), and
purified by gel electrophoresis. The presence of the desired mutation
was verified by sequencing the entire HCA II gene using the method
of Sanger et al.35
Expression and Purification of HCA**. BL21(DE3) cells were
transformed with the HCA** plasmid and grown as described by Fierke
and co-workers (see, for example, ref 18). Cell lysates were prepared
as described by Krebs and Fierke,22 and the HCA** protein was purified
using sulfonamide-conjugated agarose (Sigma-Aldrich) as described
by Khalifah et al.19 The purified HCA** protein was stored at -80 °C
in 50 mM Tris-sulfate buffer, pH 8.0, with 0.2 mM ZnSO4 and 1 mM
DTT (to prevent oxidation of the thiol).
The values of Meff reported here should be intrinsic properties
of the oligo(ethylene glycol) linkers themselves. These values
can, thus, be used to predict the avidities of multivalent ligands
containing oligo(ethylene glycol) linkers for a multivalent
protein, if the monovalent affinity is known (Figure 1E). Our
results suggest, however, that the quantitative accuracy of
these predictions is limited by difficulties in estimating the
influence of such effects as the “excluded volume” term and
the geometric and steric demands of the active site of the protein
target on ligand binding (both of which appear in the parameter
p in eq 4).
We did not anticipate the weak dependence of Meff on the
length of the linker (when it is longer than the optimal length).
This weak dependence suggests that the most effective strategy
for the design of multivalent ligands will connect the ligand
moieties by a flexible linker that is significantly longer than
the spacing between the multivalent sites of the target protein
(Figure 1E). Our results suggest that the penalty in conforma-
tional entropy for such a linker in the association of these
multivalent ligands with their multivalent proteins will be low
(much lower than we previously hypothesized4,11,12). Indeed,
the results presented here using oligo(ethylene glycol) linkers,
which do not interact with the surfaces of proteins, can be seen
as a worst-case scenario. Other types of linkers (e.g., alkyl
chains) are likely to interact with the surfaces of proteins, and
these interactions should effectively “shorten” the linker and
Preparation of Modified HCA** Proteins. HCA** was desalted
over a NAP-10 column (Amersham) into 50 mM Tris-sulfate buffer,
pH 8.0, from which oxygen had been removed by bubbling Ar through
it for >1 h. HCA** (50-100 µM) was treated with 5-10 equiv of the
appropriate modifying agent (Pyr-SSEGnSA, Pyr-SSEG2CONH2, or
iodoacetate) to generate the desired modified HCA** (HCA**-SSEGn-
SA, HCA** -SSEG2CONH2, or HCA**-SCH2CO2-, respectively). The
reaction was allowed to proceed for 1 h at 25 °C and then for ∼18 h
(34) Krishnamurthy, V. M.; Bohall, B. R.; Kim, C.-Y.; Moustakas, D. T.;
Christianson, D. W.; Whitesides, G. M. Chem. Asian J. 2007, 2, 94-105.
(35) Sanger, F.; Nicklen, S.; Coulson, A. R. Proc. Natl. Acad. Sci. U.S.A. 1977,
74, 5463-5467.
9
J. AM. CHEM. SOC. VOL. 129, NO. 5, 2007 1319

A R T I C L E S
Krishnamurthy et al.
comp,Ethox
at 4 °C. The reaction products were purified by exhaustive dialysis
and then characterized by electrospray ionization mass spectrometry
(ESI-MS) to verify the appearance of a peak corresponding to the
combined masses of HCA** and the chemical reactant (see Table S.1,
Supporting Information). For the HCA**-SSEGnSA proteins, contami-
nation by unmodified HCA** was assessed by examining the binding
of DNSA (see Supporting Experimental Procedures and Figure S.4,
Supporting Information).
Determination of Dissociation Constants (Kdcomp,Ethox) for the
Binding of Ethox to HCA**-SSEGnSA. To the wells of a black
microwell plate were added dilutions of Ethox and then the appropriate
HCA** protein (200 nM) in a final volume of 200 µL of 20 mM sodium
phosphate, pH 7.5. The plate was allowed to incubate at 25 °C for 2 h,
and then its fluorescence was measured with an excitation wavelength
of 290 nm and an emission wavelength of 340 nm (with a 325 nm
cutoff filter). Wells were read ∼50 times. Fluorescence intensities were
normalized to the fluorescence intensity of the protein with no added
Ethox and then corrected for the inner filter effect36 by using a control
experiment where soybean trypsin inhibitor (a protein with no affinity
for sulfonamides)37 was treated with Ethox. The corrected data were
fit to eq 7, where [CA]total is the total concentration of modified HCA**
in the assay (200 nM) and [Ethox]total is the total concentration of Ethox
(the independent variable). Only the parameter Kdcomp,Ethox was allowed
Kd
Kdcomp,Ethox + [Ethox]total
F ) 0.3 + 0.7
(8)
agarose (see Supporting Experimental Procedures), in 20 mM sodium
phosphate buffer, pH 7.5 (with 0.6% DMSO-d6), was titrated with 120
or 440 µM Ethox, respectively, in the same buffer at 25 °C. HCA**-
-
SCH2CO2 (∼6 µM) was also titrated with 120 µM SA-OMe. (See
Figures S.6 and S.7, Supporting Information, for details.) After
subtraction of background heats, the data were analyzed by a single-
site binding model using the Origin software (provided by Microcal)
and allowing the values of binding stoichiometry, ∆H°, and Kd to vary
to optimize the fit.
Acknowledgment. This work was supported by the National
Institutes of Health (GM30367). V.M.K. and P.J.B. acknowledge
support from NDSEG and NSF pre-doctoral fellowships,
respectively. V.S. acknowledges support from La Ligue Contre
Le Cancer (France). We thank Prof. Carol Fierke (University
of Michigan) for the kind gift of the HCA-encoding plasmids,
and Andrea Stoddard (Fierke group, Michigan) for helpful
discussions about protein purification. We thank Dr. Julian P.
Whitelegge (The Pasarow Mass Spectrometry Laboratory,
University of California, Los Angeles) for ESI-MS analysis.
We thank Prof. Greg Verdine (Harvard University) for use of
the Spectramax M5, and Marie Spong (Verdine group, Harvard)
for helpful discussions about molecular biology. We acknowl-
edge the Bauer Center for Genomics Research (Harvard
University) for the use of the Spectramax Gemini XS and
Perspective Biosystems Voyager-DE PRO for MALDI.
F ) 0.3 + 0.7(1 - 0.5/[CA]total(Kdcomp,Ethox + [CA]total + [Ethox]total
-
(K comp,Ethox + [CA]total + [Ethox]total)2 - 4[CA]total[Ethox]total))
x
d
(7)
to vary to optimize the fit by nonlinear least-squares fitting (Origin),
with the other parameters held constant at their known values. Equation
7 assumes that Ethox quenches 70% of the fluorescence of HCA**;
this value was determined by examining the fluorescence of HCA**
in the presence of Ethox (Figure S.1B, Supporting Information).
The data were also fit to eq 8, which assumes that the concentration
of Ethox not bound by CA is equal to the total concentration of Ethox
([Ethox]total) and gives a sigmoid fit to the data when the concentration
of Ethox is plotted on a logarithmic scale. This equality is not true for
Supporting Information Available: Synthetic procedures and
characterization, assay protocols, SDS-PAGE and assessment
of activity of HCA**, mass spectra and SE-HPLC chromato-
grams of modified HCA** proteins, fluorescence titration curves
for the binding of DNSA to control HCA** proteins, fluores-
cence calibration plot for determining purity of HCA**-SSEGn-
SA proteins, fluorescence titration curves for determination of
Kd of SA-OMe and Ethox to HCA**-SCH2CO2-, and ITC
thermograms for the binding of Ethox and SA-OMe to HCA**-
SCH2CO2- and to HCA**-SSEG10SA. This material is available
free of charge via the Internet at http://pubs.acs.org.
HCA**SSEG0SA and HCA**SSEG20SA, because in those cases
comp,Ethox
Kd
∼ [CA]total (200 nM).
Isothermal Titration Calorimetry. In order to determine values
-
of ∆H° and Kd, ∼6 µM HCA**-SCH2CO2 or ∼60 µM HCA**-
SSEG10CA, which had been purified over sulfonamide-conjugated
(36) Lakowicz, J. R. Principles of Fluorescence Spectroscopy, 2nd ed.; Kluwer
Academic/Plenum: New York, 1999.
(37) Colton, I. J.; Carbeck, J. D.; Rao, J.; Whitesides, G. M. Electrophoresis
1998, 19, 367-382.
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