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The binding of estrogen and estrogen antagonists to the estrogen receptor
ARCHIVES
OF BIOCHEMISTRY
AND BIOPHYSICS
Vol. 296, No. 2, August 1, pp. 583-591, 1992
The Binding of Estrogen and Estrogen Antagonists the Estrogen Receptor’ Jeffrey P. Bond, *,2 Shlomo Sasson,t and Angelo *Department tDepartment
to
C. Notides*,
of Biophysics, School of Medicine and Dentistry, University of Rochester, Rochester, New York 14642; and of Pharmacology, The Hebrew University School of Medicine, Jerusalem 91010, Israel
Received December 2, 1991, and in revised form April 8, 1992
The model of the estrogen receptor as a dimer of identical, interacting subunits and data obtained by Sasson and Notides (1988, Mol. Endocrinol. 2, 307-312) were used to find the standard free energy changes that describe the binding of estradiol and 4-hydroxytamoxifen to the estrogen receptor. For the binding of estradiol or 4-hydroxytamoxifen to the estrogen receptor the data do not deviate systematically from the best fit to the model. The standard free energy change for binding of one molecule of estradiol at one site and one molecule of 4-hydroxytamoxifen at the second site of estrogen receptor indicates that 4-hydroxytamoxifen antagonizes the o 1swA~demic binding of e&radio1 to the estrogen receptor. Press, Inc.
The estrogen receptor is a nuclear regulatory protein whose activity is controlled by estrogens. Estrogens circulate in the bloodstream and equilibrate rapidly across cell membranes. Inside target cells, estrogens bind to the estrogen receptor with high specificity, and low capacity (1). The estrogen receptor is a dimer of identical subunits that binds estradiol cooperatively and binds with high specificity to DNA sequences near genes whose transcription is regulated by estradiol (l-4). A thermodynamic linkage has been demonstrated between the binding of estradiol and DNA to the estrogen receptor (5, 6). This demonstrates that important mechanistic information can be obtained by studying the equilibrium binding of the estrogen receptor to estrogens and specific DNA sequences in uitro. Estrogen antagonists, or antiestrogens, are compounds that diminish the potency of estrogen when adi This research was supported by National Institutes of Health Grants HD06707 and ES01247. J.B. was supported by a Messersmith predoctoral fellowship and a training grant from the National Institutes of Health. ’ Present address: Department of Biochemistry, University of Wisconsin-Madison, Madison, WI 53706. ’ To whom correspondence should be addressed. 0003-9861/92 $5.00 Copyright 0 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.
ministered simultaneously. It is important to know how antiestrogens work at the molecular level, and previous studies have shown that antiestrogens alter the estrogen binding properties of the estrogen receptor. In order to understand the action of antiestrogens, it is reasonable to look for a thermodynamic property of the binding of ligands to the estrogen receptor that correlates with estrogenicity, i.e., that differentiates estrogens and antiestrogens. For example, compounds that bind to the estrogen receptor with low affinity at all concentrations are not likely to be potent estrogens. This is similar to the assumption that it makes sense to interpret models for cooperative binding of ligands to proteins (8,9) with simple structural models. It has been proposed that estrogenicity correlates with cooperative binding of a ligand (10). We investigate the observation that 4-hydroxytamoxifen, an estrogen antagonist, binds cooperatively to the estrogen receptor (11). A good correlation between in vitro binding properties and estrogenicity would be useful because it would give information about protein molecular models and because it would suggest an in vitro method for identifying estrogens and antiestrogens. Sasson and Notides (11) measured the bound [3H]estradiol as a function of the total estradiol or the total 4-hydroxytamoxifen concentration added, and found that the curves obtained had different slopes. The competition binding data contain information about the binding of estradiol and 4-hydroxytamoxifen to the same estrogen receptor multimer. Our objective is to understand the allosteric effects of 4-hydroxytamoxifen on the estrogen receptor by determining the standard free energy change for the binding of the dimer to both estradiol and 4-hydroxytamoxifen. We take a completely model dependent approach to analyze the data, but many of the conclusions do not require the validity of the model. THEORY
The ligand binding experiments that we analyze were performed by adding various concentrations of either one 583
584
BOND,
SASSON,
or two ligands to a constant concentration of a protein preparation that is not necessarily pure. Analysis of the experimental data requires an equation for the bound radiolabeled ligand as a function of the total concentrations of all the ligands and the standard free energy changes that describe binding of these ligands to the estrogen receptor. For this purpose we chose Eq. [ 131, below, a common equation from biochemical binding theory. In addition, it is desirable to understand the assumptions that are made in using Eq. [13] to obtain conclusions about molecular events. Thus we derive Eq. [ 131 from the grand partition function, so that the assumptions that enter are made clear. The binding mixtures are complex, since they consist of a protein that may form dimers, a number of ligands that compete for binding to the same binding site on the protein, and other biological molecules that may bind to the estrogen receptor. Our objective is to reduce the complexity of the problem so that useful mechanistic information can be obtained. Many of the results described here are commonly used (12-20) in thermodynamic studies. The system consists of solvent plus N elementary components that are neither created nor destroyed during the incubation. We use McMillan-Mayer theory (21-23) and consider the solution of biomolecules in solvent as a gas of biomolecules. The solvent is included exactly (implicitly) through the component activities and intermolecular potentials of mean force. These elementary components bind to form complexes that are denoted by the vector 1, where the components of l(Z(i), for i = 1 to N) are the numbers of molecules of each elementary component in the complex (1). The activity of complex 1 is cl, and its chemical potential is pl. The activity of the complex that consists only of one molecule of elementary component i is ci and its chemical potential is pi. (For example, in a simple system consisting only of protein and a single ligand, the elementary components are the protein and the ligand, and the complexes are protein-ligand complexes. A complex of i molecules of ligand bound to j molecules of protein can be labeled by (j, i), and its concentration is given by cj,i, where Z(1) is the number of protein molecules.) We derive a generating function for the amount of ligand bound as a function of the ligand chemical potential. In the grand ensemble, the amount of a component present, N, is given by N = a log = ah
’
where E is the grand partition function, and partial derivatives are assumed to be taken with all the other independent variables in the grand ensemble (i.e. volume, temperature, and the chemical potentials of all other components) held constant. Following the procedure for deriving the Gibbs adsorption equation (24) we obtain
AND
NOTIDES
the amount of ligand bound to protein, Ns , as the amount of ligand present when protein is present minus the amount of ligand present in the absence of protein.
where EP is the grand ensemble partition function in the presence of protein and & is the grand ensemble partition function in the absence of protein. Next, we use the approximate physical cluster theory (23) and assume that the components can react to form complexes but the intercomplex potentials of mean force are uniformly zero. In the absence of the protein of interest,
Mi is the number of molecules of complexes of 1 and the sum is over all numbers of all complexes such that the complexes contain no protein, component 1. In the presence of protein
It can be shown that for noninteracting F -P
=
chemical species
‘;:s -ex-0,
PI
where
El
and that log -ex = =
&dl c {llUb-0)
v.
[71
The sum on the right-hand side differs from the binding polynomial for a self-associating macromolecule by a proportionality constant and is equal to the number of complexes containing macromolecules (compare to the ideal gas law). It is usual to associate a density with an effective potential c that is related to the density by p = exp(P[p - p” + cl). The effective potential associated with Eq. [7] is the binding potential. The chemical potentials of the complexes are constrained by
BINDING
OF ESTROGEN
AND
ESTROGEN
N
N
/.LI= C I(i i=l
= C Z(i)[/.~p+ RT log ci].
PI
i=l
Assuming that the components interact only through the specific complex formation, the number of molecules of a component bound to the protein of interest is conjugate to its chemical potential in the expression for the excess free energy, and the fraction of ligand bound per unit of protein, S, is then given by the number of molecules of component 2 bound to component 1 divided by the number of molecules of component 1.
-
f3log %?&(~P2)
x2 = a log &/d&LL,)
.
PI
We consider only components 1 and 2 explicitly. Equation [7] can be used to define a set of effective standard chemical potentials, cl:, by summing over the components
3, . . . 7N
ANTAGONISTS
TO ESTROGEN
impurities are not expected to change in concentration under the experimental variations, or it is necessary to study the energetics of proteins bound to multiple ligands simultaneously. 2. Free energies of interaction can be obtained in an experimentally convenient range using competing ligands. It is often the free energy of interaction that is important for understanding mechanism and not the absolute standard free energy changes. By making use of competing ligands, these measurements can be performed in regions where the free energy of interaction can be accurately determined. We are interested in the case where the protein is a dimer with and there are two ligands that bind to the same two binding sites on the dimer. In the analysis presented here, the data (i.e., the bound ligand, Xs, as a function of the total ligand concentration) were fitted to the general model for a nondissociating dimer. The fraction bound is given by
X, = Tif= where m is a vector of two components and the sum is over all 1 such that 1(l) and l(2) are given by m(1) and m(2). If it is the case experimentally that changing the total amount of a component or components does not change the chemical potential of all the other components, then it is useful to reduce the number of unknowns by renormalizing the reacting species in this manner. It is useful to define standard free energy changes for binding reactions
585
RECEPTOR
T(e&x + eL%l+&)X2) 1 +
2&3x
+
ePkl+g2)~2
’
iI31
where T is the total concentration of receptor subunits and g, and g2 are effective standard free energy differences as in Eq. [ll]. The free ligand concentration appearing in Eq. [ 131 is implicitly a function of the total ligand concentration and the concentration of ligand bound, since experimentally the total ligand concentration is the independent variable. There are two justifications for using Eq. [13]:
1. Experimental evidence shows that the estrogen receptor is a dimer that does not dissociate in the concentration range used in these experiments (25). The cooperativity of ligand binding is an inherent property of the so that the observed microscopic equilibrium constant kti complex and does not require association-dissociation is given by kij = -RT log gij. For example, consider a reactions of the estrogen receptor (6, 22). protein that exists as monomers and dimers, and each 2. The dimer model (Eq. [13]) can be used to describe subunit binds to one molecule of ligand 2. The generating any ligand binding problem (whether or not the protein function, Eq. [7], for this system is is a dimer) as long as significant protein concentration dependent behavior is not observed in the concentration log -f%X = = Vp + Vpxe@” + Vp2eagzo range used, since the dimer model, Eq. [9], serves as a It is much more ef+ V2p2xesgz1 + Vp2x2eBgz2,rational functional approximation. fective to approximate a binding curve by a function that looks like a binding curve (e.g., certain types of rational where p is the concentration of species containing one protein molecule and no component 2 (m( 1) = 1, m(2) = functions) than by other arbitrary functions (e.g. polynomials, trigonometric functions). This permits model 0) and x is the concentration of component 2. independent results to be derived accurately from the data Two conclusions from this derivation are used to an(e.g., the median ligand activity, interpolations, the Hill alyze the data of Sasson and Notides (11): coefficient, and minimum of the free energy of interac1. A multiple ligand binding problem can be studied tion). In other words, although the validity of the dimer as a single ligand binding problem if the concentrations model is essential for certain conclusions, many concluof all but one of the ligands are approximately constant. sions can be made independent of its validity, since they This is useful when either the preparation is impure, but depend only on the fit of the function to the data.
586
BOND, SASSON, AND NOTIDES TABLE
Weighted
Nonlinear
Least-Squares
Analysis
Ligands 1. [3H]Estradiol 2. 4-[3H]Hydroxytamoxifen 3. Estradiol-[3H]estradiol 4. 4-Hydroxytamoxifen-[3H]estradiol
of the Binding
I
of Estradiol
and 4-Hydroxytamoxifen
to the Estrogen Receptor
-a
-g2
-2
-49
11.70 (11.58, 11.91) 11.71 (11.58, 11.86) 11.57 (11.18, 11.95) 10.63 (10.31, 10.93)
13.44 (13.16, 13.73) 13.33 (13.05, 13.60) 11.28 (11.14, 11.42) 10.80 (10.62, 10.99)
12.57 (12.49, 12.66) 12.52 (12.44, 12.61) 11.43 (11.27, 11.60) 10.72 (10.62, 10.82)
1.75 (1.35, 2.14) 1.62 (1.25, 2.00) -0.303 (-0.771, 0.152) 0.167 (-0.262, 0.688)
Note. The physical interpretation of the free energies, g,, g,, g, and Ag, are given under Theory. The four experiments analyzed are: 1. The binding of [3H]estradiol to the estrogen receptor ([3H]estradiol). 2. The binding of 4-[3H]hydroxytamoxifen to the estrogen receptor (4-[‘H]hydroxytamoxifen). 3. The binding of a constant total amount of [3H]estradiol to the estrogen receptor in the presence of varying amounts of estradiol (estradiol[3H]estradiol). 4. The binding of a constant total amount of [3H]estradiol to the estrogen receptor in the presence of varying amounts of 4-hydroxytamoxifen (4-hydroxytamoxifen-[3H]estradiol). The numbers in parentheses give the 67% confidence intervals for the determination. Source. The data are from (11).
The result obtained using Eq. [ 131 is an estimate of the total binding site concentration and estimates of the standard free energy changes (gl, g2). It is also useful to calculate the average standard free energy change for binding and the free energy of interaction (g; Ag) using the formulas:
g=
g1
+
g2
2 & =
g2
- g1.
The average standard free energy change can be determined from the median ligand activity (12). For the case of a nondissociating dimer, this is the value of the free ligand concentration at which the dimer is half saturated. g= -Flnx,.
The free energy of interaction can be estimated from the Hill coefficient determined at half saturation, nli2, using the formula Ag=2RTln
c-1 (
)
or from the difference between the binding energy of the ligand to the protein at very low and at very high ligand concentrations (e.g., from the asymptotes of the Hill plot). These free energies correspond to locating the binding curve on a titration plot @) and then changing its sigmoidicity (Ag).
Using the results derived above (Eq. [13]), data obtained from the binding of one ligand to a nondissociating dimer in the presence of high concentrations of another ligand were also analyzed using the nondissociating dimer model, described by Eq. [13]. To determine the standard free energy change of the hybrid dimer, the free energies of the dimer doubly liganded with both estradiol and 4-hydroxytamoxifen were determined, the free energy of interaction was determined in the presence of saturating quantities of one ligand, and the free energy level of the hybrid dimer is determined using the equation z-EST
GT,E =
+ Z-TAM
_
&
g
2 It is possible, then, to describe the binding of a ligand to a dimer by g”, Ag” and GxsE,where x is the ligand and E represents estradiol bound to the dimer (see Results and Discussion). RESULTS AND DISCUSSION Binding of Ligands to a Dimer of Identical, Interacting Subunits Experimental studies of the estrogen receptor have shown that it is a dimer with identical, interacting subunits (25). We used this model to analyze data obtained by Sasson and Notides (11) from studies of the binding of estradiol and 4-hydroxytamoxifen to the estrogen receptor. For validation of the model, it is necessary but not sufficient that the model describe binding data. We determined the standard free energy changes for binding of estradiol to the estrogen receptor by weighted leastsquares fitting of data for the bound [3H]estradiol con-
BINDING
OF ESTROGEN
AND
ESTROGEN
Log Total Estradiol, nM FIG. 1. Binding of [3H]estradiol to the estrogen receptor. The data (open squares) were taken from Sasson and Notides (11) for the bound [3H]estradiol as a function of the total [3H]estradiol concentration. The solid line is the best fit of the data to Eq. 1131, obtained using nonlinear least-squares parameter estimation (Johnson and Frasier (27)). The parameters that best described the data are 7’ = 2.08 nM, g, = 11.7 kcal/ mol, g, = 13.44 kcal/mol (Table I).
centration as a function of the total [3H]estradiol concentration (11) to Eq. [13] (Table I, [3H]estradiol). The best-fit parameters were found using a program (NONLIN) provided by Johnson and Frasier (26). The resulting fit did not deviate systematically from the data (Fig. 1). This provides additional support for the model of the estrogen receptor as a dimer with interacting estradiol binding sites. The free energy of interaction corresponds to a Hill coefficient of 1.6. We also determined standard free energy changes for the binding of 4-[3H]hydroxytamoxifen to the estrogen receptor by weighted least-squares fitting of data obtained for the bound 4- [3H] hydroxytamoxifen concentration as a function of the total 4-[3H]hydroxytamoxifen concentration (11) to Eq. [ 131 (Table I, 4-[3H]hydroxytamoxifen). The free energy levels are approximately the same as those for estradiol binding to the estrogen receptor, as originally concluded from visual assessment of the data (11); that is, the free energies for binding of the two ligands to the receptor are well within the 67% confidence intervals. No significant systematic error was observed (Fig. 2). The observation that the standard free energy changes are the same for binding of estradiol and 4-hydroxytamoxifen to the estrogen receptor does not imply that 4-hydroxytamoxifen is an estrogen in vivo, since it does not require that the binding of 4-hydroxytamoxifen to the receptor induces the same conformational changes that the binding of estradiol induces. In order to rigorously measure the antiestrogenic activity of 4-hydroxytamoxifen in vitro, it is necessary to include the function that
ANTAGONISTS
TO ESTROGEN
587
RECEPTOR
is antagonized in the assay, since this would add additional freedom thermodynamically. For example, it is possible that if a DNA fragment were included in the assay, different free energy levels would be observed for the different ligands. Although the receptor preparation is impure, it is possible to make use of standard free energy changes to study binding phenomena, as long as the addition of the ligands does not significantly change the activities of the impurities. For example, if a protein (e.g., heat shock protein) or polyanion (e.g., heparin) were present that bound to the receptor, and this binding was linked to ligand binding at the estrogen binding site, the interpretation of the standard free energy levels does not change. It is possible, then, that different preparations or concentrations would exhibit different apparent affinities. Throughout we have interpreted all energy levels in terms of specific molecular models. However, the derivation admitted the possibility that the free energies obtained do not correspond to homogeneous chemical species. Therefore, the free energy levels contain energy derived from subpopulations which react by pseudo-first-order reactions. For example, the reference free energy may represent unliganded dimer partially bound to contaminating polyanions. In addition, the free energies may also contain pseudolinkages. For example, 4-hydroxytamoxifen may bind with different affinity than estradiol to the estrogen receptor with polyanions bound. It is therefore possible that estradiol and 4-hydroxytamoxifen binding are not directly antagonistic, but that the antagonism occurs through some contami-
Log Total Hydroxytamoxifen,
nM
FIG. 2. Binding of 4-[3H]hydroxytamoxifen to the estrogen receptor. The data (open squares) were taken from Sasson and Notides (11) for the bound 4-[3H]hydroxytamoxifen as a function of the total 4[3H]hydroxytamoxifen concentration. The solid line is the best fit of the data to Eq. [13], obtained using nonlinear least-squares analysis (Johnson and Frasier (27)). The parameters that best described the data are T = 2.11 nM, g, = 11.71 kcal/mol, g, = 13.33 kcal/mol (Table I).
588
BOND,
SASSON,
AND
NOTIDES
nating species. This does not detract significantly from the conclusions, however, since such linkages are very likely to reflect physiologically important events. This is a usual consideration, since proteins interact in this way with protons and salts, except that the contaminants may be polyanions that behave like DNA, or contaminating proteins that play a role in estrogen action. Competition Binding with One Ligand Present at a Saturating Concentration Sasson and Notides (11) equilibrated the estrogen receptor with a saturating concentration of [3H]estradiol, and measured the bound [3H]estradiol concentration as a function of the added 4-hydroxytamoxifen or estradiol concentration. They observed that the slopes of these two competition curves are different. If the binding of 4-hydroxytamoxifen to the estrogen receptor was identical to that of estradiol these two curves would have the same slopes. Therefore, the binding of 4-hydroxytamoxifen to the [3H]estradiol saturated estrogen receptor is cooperative. We fit this data to Eq. [13] (Table I, Figs. 3 and 4). In this case there was significant systematic error since (a) the estradiol binding should have fit to the binding of a ligand to identical and independent binding sites, as predicted by the theory, and (b) the data deviate systematically from the best fit. However, it is apparent that the 4-hydroxytamoxifen binds to the estrogen receptor cooperatively relative to the estradiol. Since we expected
-2.0
-1 a
0.0
1.0
3.0
3.0
Log Total Estradiol FIG. 3. Binding of [3H]estradiol to the estrogen receptor in the presence of various concentrations of estradiol. The data (open circles) were taken from Sasson and Notides (11) for the bound [3H]estradiol as a function of the total estradiol concentration in the presence of a constant concentration of total [3H]estradiol. The solid line is the best fit of the data to Eq. [ 131, obtained using nonlinear least-squares analysis (Johnson and Frasier (27)). The parameters that best described the data are T = 1.19 nM, g, = 11.57 kcal/mol, g, = 11.28 kcal/mol (Table I).
0
Log Total Hydroxytamoxifen FIG. 4. Binding of [3H]estradiol to the estrogen receptor in the presence of various concentrations of 4-hydroxytamoxifen. The data (open circles) were taken from Sasson and Notides (11) for the bound [3H]estradiol as a function of the total I-hydroxytamoxifen concentration in the presence of [3H]estradiol. The solid line is the best fit of the data to Eq. [13], obtained using nonlinear least-squares analysis (Johnson and Frasier (27)). The parameters that best described the data are T = 1.21 nM, g, = 10.63 kcal/mol, g, = 10.80 kcal/mol (Table I).
Ag = 0 for the [3H]estradiol-estradiol competition, we determined the free energy of interaction between the ligands by summing the Ag values to get Ag = 0.47, or a Hill coefficient of 1.2. These free energies are well outside the 67% confidence intervals, so that this difference is not due to random variations in the data. However, we repeat that this may be due to systematic error. Since estradiol and 4-hydroxytamoxifen bind with almost identical energy levels, but are relatively cooperative, this result implies that 4-hydroxytamoxifen is at least a partial estradiol antagonist. An additional feature of the competition binding experiments described here is that they permit measurement of the free energy of interaction at high concentrations of ligands. When a protein binds a ligand with a very high affinity, it may be difficult to measure the free energy of interaction for binding of this ligand, since affinity measurements require knowledge of the difference between the concentration of ligand that is bound and the total ligand concentration. The high affinity of the protein for the ligand makes binding measurements prone to systematic error, for example, the data may result in a nonlinear Scatchard plot. Since the nonlinearity of a Scatchard plot is directly related to the free energy of interaction, the result is an inaccurate determination of the free energy of interaction. Using competition binding experiments, it may be possible to demonstrate interaction between binding sites if a ligand can be found that binds noncooperatively or antagonizes the binding of the agonist.
BINDING
OF ESTROGEN
AND
ESTROGEN
The free energy of interaction between [3H]estradiol and 4-hydroxytamoxifen determined by the parameter estimation procedure (Table I) was small (-0.17 kcal/ mol), and the case of noninteracting sites is within the 67% confidence intervals. However, the actual case of noninteracting (i.e., the free energy of interaction between [3H]estradiol and estradiol binding to the estrogen receptor) sites shows apparent negative cooperativity (0.3 kcal/ mol). (The competition of estradiol with [3H]estradiol must have a free energy of interaction equal to zero, since [3H]estradiol does not bind differently than estradiol, so there cannot be differences in binding to the first and second sites.) Since this case corresponds to noninteracting sites, we used this as the control instead of the case where aFi = 0. This systematic error is not necessarily related to the systematic error we claim to obviate by using competition studies. That error is specifically due to requiring knowledge of the free ligand concentrations when these concentrations are less than can be detected accurately by the assay. There are two sources of systematic error in the experiments as they were performed: 1. The experiment was not performed at constant chemical potential of the [3H]estradiol; instead, the concentration of total [3H]estradiol was maintained at 5 nM. As the concentration of competitor (i.e., estradiol or 4hydroxytamoxifen) is increased, the concentration of free [3H]estradiol increases from 4 to 5 nM. The result is a small amount of apparent negative cooperativity, since as the competitor concentration increases, the competition becomes increasingly difficult. This apparent interaction (about 0.12 kcal/mol) appears in the results for both estradiol and 4-hydroxytamoxifen, so it does not affect the difference between them. 2. The total unlabeled estradiol concentration was not directly measured, but was estimated from knowledge of the amount of unlabeled estradiol that was added. Since estradiol binds to the test tube walls, the total unlabeled estradiol concentration is overestimated. While this leads to an underestimate of the actual affinity constants, it should not affect the measurement of the interaction between binding sites. Since 4-hydroxytamoxifen binds more to the test tube than estradiol, it is predicted to have an apparently lower affinity in competition experiments (as observed). Thus, although the data deviate systematically from Eq. [ 131, it is unlikely that this systematic deviation detracts from the reliability of the conclusion that the binding of 4-hydroxytamoxifen to the estrogen receptor antagonizes the binding of estradiol to the estrogen receptor. The dimer model, Eq. [ 131, can still be used as a rational function approximation to get the apparent free energy of interaction that we used to compare estradiol binding with 4hydroxytamoxifen binding.
ANTAGONISTS
TO ESTROGEN
589
RECEPTOR
In addition to measuring the free energy of interaction between estrogen binding sites, the free energy of interaction suggests that 4-hydroxytamoxifen binding antagonizes estradiol binding. Although the binding of these ligands to the estrogen receptor independently is very similar, the conformational changes induced are not necessarily the same. If the conformational changes were the same, then the free energy of interaction would have been very small. The free energy of interaction is too small, however, for conclusive evidence that 4-hydroxytamoxifen antagonizes estradiol binding because another competition experiment (Fig. 5) suggests that the affinity of 4hydroxytamoxifen for the estrogen receptor is actually slightly higher than the affinity of estradiol for the estrogen receptor, contrary to the results shown in Table I. This would diminish the free energy of interaction between 4-hydroxytamoxifen and estradioi binding to the estrogen receptor. We have found the standard free energy change, GXY, for binding of two different ligands, x and y, to the same binding sites on a dimer. We interpret the interaction between the two ligands by dividing all possible values of this standard free energy change into three regions:
3 3 TI e v W z a *+
9 0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
s.0
10.0 11.0 12.0 13.0 14.0
.O
Total Estradiol FIG. 5. Binding to [3H]estradiol to the estrogen receptor in the presence of a constant ratio of total [3H]estradiol to total I-hydroxytamoxifen concentration. The data (open squares) were taken from Sasson and Notides (1) for the bound [3H]estradiol as a function of the total [3H]estradiol concentration in the presence of a constant ratio of total 4-hydroxytamoxifen concentration to total [3H]estradiol concentration: 0 (0); 0.5 (A); 1.0 (X); 1.5 (V). The solid line is the best fit of the data to the model for binding of two ligands to identical and independent binding sites with only the total site concentration and two standard free energy changes for binding used as parameters, obtained using nonlinear least-squares analysis (Johnson and Frasier, (27)). The parameters that best described the data are T = 2.87 nM, g, = -12.8 kcal/mol, g, = -13.4 kcal/mol.
590 I
BOND, SASSON, AND NOTIDES
G”.Y> gf + gs;
II
gi” + gf > G&Y> gJ + g;
III
g+’+ g; 2 Gxpy.
A
kq = kf -
This division is not symmetric with respect to interchange of the two ligands. We interpret the result in terms of the effect of ligand y on the binding of ligand X. If QJ is in region I, then ligand y antagonizes the binding of ligand X, since the binding of ligand x to the dimer bound to one molecule of ligand y occurs with a lower affinity than to the unliganded dimer. If G’” is in region II, then ligand y is a partial antagonist of the binding of ligand X, since x binds to the dimer bound to ligand y with a higher affinity than to the unliganded dimer, but with a lower affinity than if the dimer were bound to another x molecule. If Gxy is in region III, then ligand y is an agonist of the binding of ligand X, since binding of ligand r to the dimer bound to a molecule of ligand y occurs with greater affinity binding to the dimer bound to another molecule of ligand X. These regions were chosen based on a macroscopic understanding of agonist and antagonist action. The Monod-Wyman-Changeux model of allosteric regulation of proteins permits a precise definition of competitive antagonism, so it is possible to calculate the values of G”” for agonists and antagonists for this model. According to the Monod-Wyman-Changeux model, a dimer can exist in two states, T (taut) and R (relaxed), that are in equilibrium according to an equilibrium constant, L(L = (T)/ (R)). Two ligands, x and y, bind to the dimer with apparent microscopic affinity constants k$ kf, kj’, and kg as determined using Eq. [13]. These constants are apparent affinity constants resulting from the binding of each ligand to the T state with affinities 6 and k%, and to the R state with affinities FR and k&. We define these ligands to be agonists if they bind preferentially to the same state of the dimer (i.e., k& > k+ and k$ > kyT) and antagonists if they bind preferentially to different states of the dimer (i.e., k& > k+ and kq > kg). The R and T states are chosen so that k& 2 &. The apparent affinity constants, &, kfj, kf, and k$, can be determined from the binding curves but L, k&, k$, kg, and k$ cannot. However, having measured the apparent affinity constants, there are only two possibilities:
and either
kW
k$ = kj’ + L
kW
- k9 L - kl) L
or B
kl(kS - k3’) L
k& = kr - L
KG = kf f
kj’(k$ - k:) L
Case A corresponds to agonists, and case B corresponds to antagonists. It is possible to determine whether case A or B holds by performing the competition experiment described under Theory. It is not possible, however, to find k+, kg, kyT, and k$. The result of the experiment is a value for m, the equilibrium constant for binding of the two ligands to the dimer: RXY
m=2RXxXy.
If the ligands are antagonists (case B) it is possible to show that
This falls in region I above. If ligand y is an agonist of ligand X, then m is between k$kj’ and k$kf. This falls in region II if kfkf > k$kf and in region III if k$kf > k$k$. Recently several papers have appeared addressing the estimation of affinity constants from competition binding studies (27-30). These authors point out that the affinity constants may be inaccurately calculated if the excess ligand is depleted during the variation of the competing ligand. Using the simulations of Goldstein and Barrett (27), we have estimated that our constants are in error by less than 5%. Competition Binding Concentrations
at a Constant Ratio of Total Ligand
Previous studies have shown that information about the binding of weak agonists to the estrogen receptor can be gained by measuring the bound radiolabeled ligand concentration as a function of ligand and competitor concentrations while maintaining a constant ratio of the total radiolabelled ligand concentration to the total competitor concentration (10, 11). We analyzed data for the bound [3H]estradiol concentration as a function of the total [3H]estradiol concentration while maintaining a con-
BINDING
OF ESTROGEN
AND
ESTROGEN
stant ratio of total [3H]estradiol concentration to total 4-hydroxytamoxifen concentration (11). The bound [3H]estradiol concentration reached a maximum and then decreased at high [3H]estradiol concentrations. The data were fit to the model for the binding of a ligand to identical, independent binding sites (e.g., binding to a monomer) in the presence of a competing ligand. The identical and independent binding sites model is capable of predicting qualitatively similar results (Fig. 5). We used this simpler model because our purpose is to show the simplest model that is capable of predicting negative slopes. The systematic error is due to the fact that we did not include the ratios of ligands as parameters (hence the data and the fit to the data plateau at different levels), and because the simple model cannot describe cooperativity. The decrease in the bound [3H]estradiol concentration can be accounted for if two ligands bind to the same binding sites with very high, but different, affinities. At total ligand concentrations less than the total receptor concentrations, the ligands are mostly bound to the receptor, regardless of their relative concentrations. At high concentrations, however, the amount of radiolabeled ligand bound depends on both the relative affinities and the relative concentrations. The falling curves may also be observed if Haldane’s laws (12) are not obeyed; that is, the two ligands have different cooperativities, and the less cooperative ligand binds initially with a higher affinity. Therefore, the ligands will have different relative fractional saturations at different concentrations. However, a decrease in the bound [3H]estradiol has been observed under conditions where the estrogen receptor is primarily monomeric (data not shown), so this is not a possible explanation. SUMMARY We described how it is possible to interpret competition binding data obtained from preparations when the binding protein is not pure and contains multiple binding sites. We used the equations that describe binding of a ligand to a dimer of identical and interacting subunits (Eq. [ 131) to analyze data from the binding of estradiol to the estrogen receptor and the binding of 4-hydroxytamoxifen to the estrogen receptor. The results show that the data fit the model with no systematic error and that the binding of both estradiol and 4-hydroxytamoxifen to the estrogen receptor is highly cooperative. In addition, we used the same equation to analyze data obtained from the binding of 4-hydroxytamoxifen to the estrogen receptor in the presence of saturating concentrations of [3H]estradiol. The analysis suggested that the binding of estradiol and 4-hydroxytamoxifen to the estrogen receptor is relatively
ANTAGONISTS
TO ESTROGEN
RECEPTOR
591
cooperative. This is consistent with the fact that 4-hydroxytamoxifen is an estradiol antagonist. However, there was systematic error in the binding data. Finally, we analyzed our competition binding data using the MonodWyman-Changeux model. REFERENCES 1. Jensen, E. V., and DeSombre,
E. V. (1973) Science 182, 126-134.
2. Skafar, D. F., and Notides, A. C. (1987) Biochem. Actions Horm. 14,317-348. 3. Evans, R. M. (1988) Science 240,889-894. 4. Yamamoto, K. R. (1985) Annu. Reu. Genet. 19, 209-252. 5. Skafar, D. F., and Notides, A. C. (1985) J. Biol. Chem. 260,12,20812,213. 6. Bond, J. P. (1989) Ph.D. thesis, University of Rochester, Rochester, NY.
7. Wood, J. R., Wren, R. J., and Bitmen, J. (1968) Endocrinology
82, 69-71. 8. Monod, J., Wyman, J., and Changeux, J.-P. (1965) J. Mol. Biol. 12, 88-118. 9. Koshland, D., Nemethy, G., and Filmer, D. (1966) Biochemistry 5,
365-385. 10. Sasson, S., and Notides, A. C. (1982) J. Viol. Chem. 257, 11,54011. 12. 13. 14. 15. 16.
17. 18. 19. 20. 21.
11,545. Sasson, S., and Notides, A. C. (1988) Mol. Endocrinol. 2, 307-312. Wyman, J. (1964) Adu. Protein Chem. 19, 223-286. Weber, G. (1975) Adu. Protein Chem. 29, l-83. Wyman, J. (1975) Proc. Natl, Acad. Sci. USA 72, 1404-1408. Schellman, J. A. (1975) Biopolymers 14, 999-1018. Alberty, R. A., and I. Oppenheim (1988) J. Chem. Phys. 89,36893693. Smith, W. R., and Missen, R. W. (1982) Chemical Reaction Equilibria: Theory and Algorithms, Wiley, New York. Wyman, J. (1984) Q. Reu. Biophys. 17, 453-488. Heck, H. d’A. (1971) J. Am. Chem. Sot. 93, 23-29. Record, M. T., Anderson, C. F., and Lohman, T. F. (1978) Q. Reu. Biophys. 11,103-178. McMillan, W. G., Jr., and Mayer, J. E. (1945) J. Chem. Phys. 13,
276-304. 22. Hill, T. L. (1956) Statistical
Mechanics, McGraw-Hill, New York. 23. Hill, T. L. (1955) J. Chem. Phys. 23,623-636. 24. Rowlinson, J. S., and Widom, B. (1982) Molecular Theory of Capillarity, Clarendon Press, Oxford. 25. Notides, A. C., Lerner, N., and Hamilton, D. E. (1981) Proc. Natl. Acad. Sci. USA 78,4926-4930. 26. Johnson, M. L., and Frasier, S. G. (1985) in Methods in Enzymology (Hirs, C. H. W., and Timasheff, S. N., Eds.), Vol. 117, pp. 301-342, Academic Press, San Diego. 27. Goldstein, A., and Barrett, R. W. (1987) Mol. Pharmacol. 31, 603-
609. 28. Chatelier, 29. Horovitz,
R. C. (1987) J. Recept. Res. 7.871884. A., and Levitski, A. (1987) Proc. Natl. Acad. Sci. USA
84,6654-6658. 30. Munson, P. J., and Rodbard, D. (1988) J. Recept. Res. 8, 533-546.
OF BIOCHEMISTRY
AND BIOPHYSICS
Vol. 296, No. 2, August 1, pp. 583-591, 1992
The Binding of Estrogen and Estrogen Antagonists the Estrogen Receptor’ Jeffrey P. Bond, *,2 Shlomo Sasson,t and Angelo *Department tDepartment
to
C. Notides*,
of Biophysics, School of Medicine and Dentistry, University of Rochester, Rochester, New York 14642; and of Pharmacology, The Hebrew University School of Medicine, Jerusalem 91010, Israel
Received December 2, 1991, and in revised form April 8, 1992
The model of the estrogen receptor as a dimer of identical, interacting subunits and data obtained by Sasson and Notides (1988, Mol. Endocrinol. 2, 307-312) were used to find the standard free energy changes that describe the binding of estradiol and 4-hydroxytamoxifen to the estrogen receptor. For the binding of estradiol or 4-hydroxytamoxifen to the estrogen receptor the data do not deviate systematically from the best fit to the model. The standard free energy change for binding of one molecule of estradiol at one site and one molecule of 4-hydroxytamoxifen at the second site of estrogen receptor indicates that 4-hydroxytamoxifen antagonizes the o 1swA~demic binding of e&radio1 to the estrogen receptor. Press, Inc.
The estrogen receptor is a nuclear regulatory protein whose activity is controlled by estrogens. Estrogens circulate in the bloodstream and equilibrate rapidly across cell membranes. Inside target cells, estrogens bind to the estrogen receptor with high specificity, and low capacity (1). The estrogen receptor is a dimer of identical subunits that binds estradiol cooperatively and binds with high specificity to DNA sequences near genes whose transcription is regulated by estradiol (l-4). A thermodynamic linkage has been demonstrated between the binding of estradiol and DNA to the estrogen receptor (5, 6). This demonstrates that important mechanistic information can be obtained by studying the equilibrium binding of the estrogen receptor to estrogens and specific DNA sequences in uitro. Estrogen antagonists, or antiestrogens, are compounds that diminish the potency of estrogen when adi This research was supported by National Institutes of Health Grants HD06707 and ES01247. J.B. was supported by a Messersmith predoctoral fellowship and a training grant from the National Institutes of Health. ’ Present address: Department of Biochemistry, University of Wisconsin-Madison, Madison, WI 53706. ’ To whom correspondence should be addressed. 0003-9861/92 $5.00 Copyright 0 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.
ministered simultaneously. It is important to know how antiestrogens work at the molecular level, and previous studies have shown that antiestrogens alter the estrogen binding properties of the estrogen receptor. In order to understand the action of antiestrogens, it is reasonable to look for a thermodynamic property of the binding of ligands to the estrogen receptor that correlates with estrogenicity, i.e., that differentiates estrogens and antiestrogens. For example, compounds that bind to the estrogen receptor with low affinity at all concentrations are not likely to be potent estrogens. This is similar to the assumption that it makes sense to interpret models for cooperative binding of ligands to proteins (8,9) with simple structural models. It has been proposed that estrogenicity correlates with cooperative binding of a ligand (10). We investigate the observation that 4-hydroxytamoxifen, an estrogen antagonist, binds cooperatively to the estrogen receptor (11). A good correlation between in vitro binding properties and estrogenicity would be useful because it would give information about protein molecular models and because it would suggest an in vitro method for identifying estrogens and antiestrogens. Sasson and Notides (11) measured the bound [3H]estradiol as a function of the total estradiol or the total 4-hydroxytamoxifen concentration added, and found that the curves obtained had different slopes. The competition binding data contain information about the binding of estradiol and 4-hydroxytamoxifen to the same estrogen receptor multimer. Our objective is to understand the allosteric effects of 4-hydroxytamoxifen on the estrogen receptor by determining the standard free energy change for the binding of the dimer to both estradiol and 4-hydroxytamoxifen. We take a completely model dependent approach to analyze the data, but many of the conclusions do not require the validity of the model. THEORY
The ligand binding experiments that we analyze were performed by adding various concentrations of either one 583
584
BOND,
SASSON,
or two ligands to a constant concentration of a protein preparation that is not necessarily pure. Analysis of the experimental data requires an equation for the bound radiolabeled ligand as a function of the total concentrations of all the ligands and the standard free energy changes that describe binding of these ligands to the estrogen receptor. For this purpose we chose Eq. [ 131, below, a common equation from biochemical binding theory. In addition, it is desirable to understand the assumptions that are made in using Eq. [13] to obtain conclusions about molecular events. Thus we derive Eq. [ 131 from the grand partition function, so that the assumptions that enter are made clear. The binding mixtures are complex, since they consist of a protein that may form dimers, a number of ligands that compete for binding to the same binding site on the protein, and other biological molecules that may bind to the estrogen receptor. Our objective is to reduce the complexity of the problem so that useful mechanistic information can be obtained. Many of the results described here are commonly used (12-20) in thermodynamic studies. The system consists of solvent plus N elementary components that are neither created nor destroyed during the incubation. We use McMillan-Mayer theory (21-23) and consider the solution of biomolecules in solvent as a gas of biomolecules. The solvent is included exactly (implicitly) through the component activities and intermolecular potentials of mean force. These elementary components bind to form complexes that are denoted by the vector 1, where the components of l(Z(i), for i = 1 to N) are the numbers of molecules of each elementary component in the complex (1). The activity of complex 1 is cl, and its chemical potential is pl. The activity of the complex that consists only of one molecule of elementary component i is ci and its chemical potential is pi. (For example, in a simple system consisting only of protein and a single ligand, the elementary components are the protein and the ligand, and the complexes are protein-ligand complexes. A complex of i molecules of ligand bound to j molecules of protein can be labeled by (j, i), and its concentration is given by cj,i, where Z(1) is the number of protein molecules.) We derive a generating function for the amount of ligand bound as a function of the ligand chemical potential. In the grand ensemble, the amount of a component present, N, is given by N = a log = ah
’
where E is the grand partition function, and partial derivatives are assumed to be taken with all the other independent variables in the grand ensemble (i.e. volume, temperature, and the chemical potentials of all other components) held constant. Following the procedure for deriving the Gibbs adsorption equation (24) we obtain
AND
NOTIDES
the amount of ligand bound to protein, Ns , as the amount of ligand present when protein is present minus the amount of ligand present in the absence of protein.
where EP is the grand ensemble partition function in the presence of protein and & is the grand ensemble partition function in the absence of protein. Next, we use the approximate physical cluster theory (23) and assume that the components can react to form complexes but the intercomplex potentials of mean force are uniformly zero. In the absence of the protein of interest,
Mi is the number of molecules of complexes of 1 and the sum is over all numbers of all complexes such that the complexes contain no protein, component 1. In the presence of protein
It can be shown that for noninteracting F -P
=
chemical species
‘;:s -ex-0,
PI
where
El
and that log -ex = =
&dl c {llUb-0)
v.
[71
The sum on the right-hand side differs from the binding polynomial for a self-associating macromolecule by a proportionality constant and is equal to the number of complexes containing macromolecules (compare to the ideal gas law). It is usual to associate a density with an effective potential c that is related to the density by p = exp(P[p - p” + cl). The effective potential associated with Eq. [7] is the binding potential. The chemical potentials of the complexes are constrained by
BINDING
OF ESTROGEN
AND
ESTROGEN
N
N
/.LI= C I(i i=l
= C Z(i)[/.~p+ RT log ci].
PI
i=l
Assuming that the components interact only through the specific complex formation, the number of molecules of a component bound to the protein of interest is conjugate to its chemical potential in the expression for the excess free energy, and the fraction of ligand bound per unit of protein, S, is then given by the number of molecules of component 2 bound to component 1 divided by the number of molecules of component 1.
-
f3log %?&(~P2)
x2 = a log &/d&LL,)
.
PI
We consider only components 1 and 2 explicitly. Equation [7] can be used to define a set of effective standard chemical potentials, cl:, by summing over the components
3, . . . 7N
ANTAGONISTS
TO ESTROGEN
impurities are not expected to change in concentration under the experimental variations, or it is necessary to study the energetics of proteins bound to multiple ligands simultaneously. 2. Free energies of interaction can be obtained in an experimentally convenient range using competing ligands. It is often the free energy of interaction that is important for understanding mechanism and not the absolute standard free energy changes. By making use of competing ligands, these measurements can be performed in regions where the free energy of interaction can be accurately determined. We are interested in the case where the protein is a dimer with and there are two ligands that bind to the same two binding sites on the dimer. In the analysis presented here, the data (i.e., the bound ligand, Xs, as a function of the total ligand concentration) were fitted to the general model for a nondissociating dimer. The fraction bound is given by
X, = Tif= where m is a vector of two components and the sum is over all 1 such that 1(l) and l(2) are given by m(1) and m(2). If it is the case experimentally that changing the total amount of a component or components does not change the chemical potential of all the other components, then it is useful to reduce the number of unknowns by renormalizing the reacting species in this manner. It is useful to define standard free energy changes for binding reactions
585
RECEPTOR
T(e&x + eL%l+&)X2) 1 +
2&3x
+
ePkl+g2)~2
’
iI31
where T is the total concentration of receptor subunits and g, and g2 are effective standard free energy differences as in Eq. [ll]. The free ligand concentration appearing in Eq. [ 131 is implicitly a function of the total ligand concentration and the concentration of ligand bound, since experimentally the total ligand concentration is the independent variable. There are two justifications for using Eq. [13]:
1. Experimental evidence shows that the estrogen receptor is a dimer that does not dissociate in the concentration range used in these experiments (25). The cooperativity of ligand binding is an inherent property of the so that the observed microscopic equilibrium constant kti complex and does not require association-dissociation is given by kij = -RT log gij. For example, consider a reactions of the estrogen receptor (6, 22). protein that exists as monomers and dimers, and each 2. The dimer model (Eq. [13]) can be used to describe subunit binds to one molecule of ligand 2. The generating any ligand binding problem (whether or not the protein function, Eq. [7], for this system is is a dimer) as long as significant protein concentration dependent behavior is not observed in the concentration log -f%X = = Vp + Vpxe@” + Vp2eagzo range used, since the dimer model, Eq. [9], serves as a It is much more ef+ V2p2xesgz1 + Vp2x2eBgz2,rational functional approximation. fective to approximate a binding curve by a function that looks like a binding curve (e.g., certain types of rational where p is the concentration of species containing one protein molecule and no component 2 (m( 1) = 1, m(2) = functions) than by other arbitrary functions (e.g. polynomials, trigonometric functions). This permits model 0) and x is the concentration of component 2. independent results to be derived accurately from the data Two conclusions from this derivation are used to an(e.g., the median ligand activity, interpolations, the Hill alyze the data of Sasson and Notides (11): coefficient, and minimum of the free energy of interac1. A multiple ligand binding problem can be studied tion). In other words, although the validity of the dimer as a single ligand binding problem if the concentrations model is essential for certain conclusions, many concluof all but one of the ligands are approximately constant. sions can be made independent of its validity, since they This is useful when either the preparation is impure, but depend only on the fit of the function to the data.
586
BOND, SASSON, AND NOTIDES TABLE
Weighted
Nonlinear
Least-Squares
Analysis
Ligands 1. [3H]Estradiol 2. 4-[3H]Hydroxytamoxifen 3. Estradiol-[3H]estradiol 4. 4-Hydroxytamoxifen-[3H]estradiol
of the Binding
I
of Estradiol
and 4-Hydroxytamoxifen
to the Estrogen Receptor
-a
-g2
-2
-49
11.70 (11.58, 11.91) 11.71 (11.58, 11.86) 11.57 (11.18, 11.95) 10.63 (10.31, 10.93)
13.44 (13.16, 13.73) 13.33 (13.05, 13.60) 11.28 (11.14, 11.42) 10.80 (10.62, 10.99)
12.57 (12.49, 12.66) 12.52 (12.44, 12.61) 11.43 (11.27, 11.60) 10.72 (10.62, 10.82)
1.75 (1.35, 2.14) 1.62 (1.25, 2.00) -0.303 (-0.771, 0.152) 0.167 (-0.262, 0.688)
Note. The physical interpretation of the free energies, g,, g,, g, and Ag, are given under Theory. The four experiments analyzed are: 1. The binding of [3H]estradiol to the estrogen receptor ([3H]estradiol). 2. The binding of 4-[3H]hydroxytamoxifen to the estrogen receptor (4-[‘H]hydroxytamoxifen). 3. The binding of a constant total amount of [3H]estradiol to the estrogen receptor in the presence of varying amounts of estradiol (estradiol[3H]estradiol). 4. The binding of a constant total amount of [3H]estradiol to the estrogen receptor in the presence of varying amounts of 4-hydroxytamoxifen (4-hydroxytamoxifen-[3H]estradiol). The numbers in parentheses give the 67% confidence intervals for the determination. Source. The data are from (11).
The result obtained using Eq. [ 131 is an estimate of the total binding site concentration and estimates of the standard free energy changes (gl, g2). It is also useful to calculate the average standard free energy change for binding and the free energy of interaction (g; Ag) using the formulas:
g=
g1
+
g2
2 & =
g2
- g1.
The average standard free energy change can be determined from the median ligand activity (12). For the case of a nondissociating dimer, this is the value of the free ligand concentration at which the dimer is half saturated. g= -Flnx,.
The free energy of interaction can be estimated from the Hill coefficient determined at half saturation, nli2, using the formula Ag=2RTln
c-1 (
)
or from the difference between the binding energy of the ligand to the protein at very low and at very high ligand concentrations (e.g., from the asymptotes of the Hill plot). These free energies correspond to locating the binding curve on a titration plot @) and then changing its sigmoidicity (Ag).
Using the results derived above (Eq. [13]), data obtained from the binding of one ligand to a nondissociating dimer in the presence of high concentrations of another ligand were also analyzed using the nondissociating dimer model, described by Eq. [13]. To determine the standard free energy change of the hybrid dimer, the free energies of the dimer doubly liganded with both estradiol and 4-hydroxytamoxifen were determined, the free energy of interaction was determined in the presence of saturating quantities of one ligand, and the free energy level of the hybrid dimer is determined using the equation z-EST
GT,E =
+ Z-TAM
_
&
g
2 It is possible, then, to describe the binding of a ligand to a dimer by g”, Ag” and GxsE,where x is the ligand and E represents estradiol bound to the dimer (see Results and Discussion). RESULTS AND DISCUSSION Binding of Ligands to a Dimer of Identical, Interacting Subunits Experimental studies of the estrogen receptor have shown that it is a dimer with identical, interacting subunits (25). We used this model to analyze data obtained by Sasson and Notides (11) from studies of the binding of estradiol and 4-hydroxytamoxifen to the estrogen receptor. For validation of the model, it is necessary but not sufficient that the model describe binding data. We determined the standard free energy changes for binding of estradiol to the estrogen receptor by weighted leastsquares fitting of data for the bound [3H]estradiol con-
BINDING
OF ESTROGEN
AND
ESTROGEN
Log Total Estradiol, nM FIG. 1. Binding of [3H]estradiol to the estrogen receptor. The data (open squares) were taken from Sasson and Notides (11) for the bound [3H]estradiol as a function of the total [3H]estradiol concentration. The solid line is the best fit of the data to Eq. 1131, obtained using nonlinear least-squares parameter estimation (Johnson and Frasier (27)). The parameters that best described the data are 7’ = 2.08 nM, g, = 11.7 kcal/ mol, g, = 13.44 kcal/mol (Table I).
centration as a function of the total [3H]estradiol concentration (11) to Eq. [13] (Table I, [3H]estradiol). The best-fit parameters were found using a program (NONLIN) provided by Johnson and Frasier (26). The resulting fit did not deviate systematically from the data (Fig. 1). This provides additional support for the model of the estrogen receptor as a dimer with interacting estradiol binding sites. The free energy of interaction corresponds to a Hill coefficient of 1.6. We also determined standard free energy changes for the binding of 4-[3H]hydroxytamoxifen to the estrogen receptor by weighted least-squares fitting of data obtained for the bound 4- [3H] hydroxytamoxifen concentration as a function of the total 4-[3H]hydroxytamoxifen concentration (11) to Eq. [ 131 (Table I, 4-[3H]hydroxytamoxifen). The free energy levels are approximately the same as those for estradiol binding to the estrogen receptor, as originally concluded from visual assessment of the data (11); that is, the free energies for binding of the two ligands to the receptor are well within the 67% confidence intervals. No significant systematic error was observed (Fig. 2). The observation that the standard free energy changes are the same for binding of estradiol and 4-hydroxytamoxifen to the estrogen receptor does not imply that 4-hydroxytamoxifen is an estrogen in vivo, since it does not require that the binding of 4-hydroxytamoxifen to the receptor induces the same conformational changes that the binding of estradiol induces. In order to rigorously measure the antiestrogenic activity of 4-hydroxytamoxifen in vitro, it is necessary to include the function that
ANTAGONISTS
TO ESTROGEN
587
RECEPTOR
is antagonized in the assay, since this would add additional freedom thermodynamically. For example, it is possible that if a DNA fragment were included in the assay, different free energy levels would be observed for the different ligands. Although the receptor preparation is impure, it is possible to make use of standard free energy changes to study binding phenomena, as long as the addition of the ligands does not significantly change the activities of the impurities. For example, if a protein (e.g., heat shock protein) or polyanion (e.g., heparin) were present that bound to the receptor, and this binding was linked to ligand binding at the estrogen binding site, the interpretation of the standard free energy levels does not change. It is possible, then, that different preparations or concentrations would exhibit different apparent affinities. Throughout we have interpreted all energy levels in terms of specific molecular models. However, the derivation admitted the possibility that the free energies obtained do not correspond to homogeneous chemical species. Therefore, the free energy levels contain energy derived from subpopulations which react by pseudo-first-order reactions. For example, the reference free energy may represent unliganded dimer partially bound to contaminating polyanions. In addition, the free energies may also contain pseudolinkages. For example, 4-hydroxytamoxifen may bind with different affinity than estradiol to the estrogen receptor with polyanions bound. It is therefore possible that estradiol and 4-hydroxytamoxifen binding are not directly antagonistic, but that the antagonism occurs through some contami-
Log Total Hydroxytamoxifen,
nM
FIG. 2. Binding of 4-[3H]hydroxytamoxifen to the estrogen receptor. The data (open squares) were taken from Sasson and Notides (11) for the bound 4-[3H]hydroxytamoxifen as a function of the total 4[3H]hydroxytamoxifen concentration. The solid line is the best fit of the data to Eq. [13], obtained using nonlinear least-squares analysis (Johnson and Frasier (27)). The parameters that best described the data are T = 2.11 nM, g, = 11.71 kcal/mol, g, = 13.33 kcal/mol (Table I).
588
BOND,
SASSON,
AND
NOTIDES
nating species. This does not detract significantly from the conclusions, however, since such linkages are very likely to reflect physiologically important events. This is a usual consideration, since proteins interact in this way with protons and salts, except that the contaminants may be polyanions that behave like DNA, or contaminating proteins that play a role in estrogen action. Competition Binding with One Ligand Present at a Saturating Concentration Sasson and Notides (11) equilibrated the estrogen receptor with a saturating concentration of [3H]estradiol, and measured the bound [3H]estradiol concentration as a function of the added 4-hydroxytamoxifen or estradiol concentration. They observed that the slopes of these two competition curves are different. If the binding of 4-hydroxytamoxifen to the estrogen receptor was identical to that of estradiol these two curves would have the same slopes. Therefore, the binding of 4-hydroxytamoxifen to the [3H]estradiol saturated estrogen receptor is cooperative. We fit this data to Eq. [13] (Table I, Figs. 3 and 4). In this case there was significant systematic error since (a) the estradiol binding should have fit to the binding of a ligand to identical and independent binding sites, as predicted by the theory, and (b) the data deviate systematically from the best fit. However, it is apparent that the 4-hydroxytamoxifen binds to the estrogen receptor cooperatively relative to the estradiol. Since we expected
-2.0
-1 a
0.0
1.0
3.0
3.0
Log Total Estradiol FIG. 3. Binding of [3H]estradiol to the estrogen receptor in the presence of various concentrations of estradiol. The data (open circles) were taken from Sasson and Notides (11) for the bound [3H]estradiol as a function of the total estradiol concentration in the presence of a constant concentration of total [3H]estradiol. The solid line is the best fit of the data to Eq. [ 131, obtained using nonlinear least-squares analysis (Johnson and Frasier (27)). The parameters that best described the data are T = 1.19 nM, g, = 11.57 kcal/mol, g, = 11.28 kcal/mol (Table I).
0
Log Total Hydroxytamoxifen FIG. 4. Binding of [3H]estradiol to the estrogen receptor in the presence of various concentrations of 4-hydroxytamoxifen. The data (open circles) were taken from Sasson and Notides (11) for the bound [3H]estradiol as a function of the total I-hydroxytamoxifen concentration in the presence of [3H]estradiol. The solid line is the best fit of the data to Eq. [13], obtained using nonlinear least-squares analysis (Johnson and Frasier (27)). The parameters that best described the data are T = 1.21 nM, g, = 10.63 kcal/mol, g, = 10.80 kcal/mol (Table I).
Ag = 0 for the [3H]estradiol-estradiol competition, we determined the free energy of interaction between the ligands by summing the Ag values to get Ag = 0.47, or a Hill coefficient of 1.2. These free energies are well outside the 67% confidence intervals, so that this difference is not due to random variations in the data. However, we repeat that this may be due to systematic error. Since estradiol and 4-hydroxytamoxifen bind with almost identical energy levels, but are relatively cooperative, this result implies that 4-hydroxytamoxifen is at least a partial estradiol antagonist. An additional feature of the competition binding experiments described here is that they permit measurement of the free energy of interaction at high concentrations of ligands. When a protein binds a ligand with a very high affinity, it may be difficult to measure the free energy of interaction for binding of this ligand, since affinity measurements require knowledge of the difference between the concentration of ligand that is bound and the total ligand concentration. The high affinity of the protein for the ligand makes binding measurements prone to systematic error, for example, the data may result in a nonlinear Scatchard plot. Since the nonlinearity of a Scatchard plot is directly related to the free energy of interaction, the result is an inaccurate determination of the free energy of interaction. Using competition binding experiments, it may be possible to demonstrate interaction between binding sites if a ligand can be found that binds noncooperatively or antagonizes the binding of the agonist.
BINDING
OF ESTROGEN
AND
ESTROGEN
The free energy of interaction between [3H]estradiol and 4-hydroxytamoxifen determined by the parameter estimation procedure (Table I) was small (-0.17 kcal/ mol), and the case of noninteracting sites is within the 67% confidence intervals. However, the actual case of noninteracting (i.e., the free energy of interaction between [3H]estradiol and estradiol binding to the estrogen receptor) sites shows apparent negative cooperativity (0.3 kcal/ mol). (The competition of estradiol with [3H]estradiol must have a free energy of interaction equal to zero, since [3H]estradiol does not bind differently than estradiol, so there cannot be differences in binding to the first and second sites.) Since this case corresponds to noninteracting sites, we used this as the control instead of the case where aFi = 0. This systematic error is not necessarily related to the systematic error we claim to obviate by using competition studies. That error is specifically due to requiring knowledge of the free ligand concentrations when these concentrations are less than can be detected accurately by the assay. There are two sources of systematic error in the experiments as they were performed: 1. The experiment was not performed at constant chemical potential of the [3H]estradiol; instead, the concentration of total [3H]estradiol was maintained at 5 nM. As the concentration of competitor (i.e., estradiol or 4hydroxytamoxifen) is increased, the concentration of free [3H]estradiol increases from 4 to 5 nM. The result is a small amount of apparent negative cooperativity, since as the competitor concentration increases, the competition becomes increasingly difficult. This apparent interaction (about 0.12 kcal/mol) appears in the results for both estradiol and 4-hydroxytamoxifen, so it does not affect the difference between them. 2. The total unlabeled estradiol concentration was not directly measured, but was estimated from knowledge of the amount of unlabeled estradiol that was added. Since estradiol binds to the test tube walls, the total unlabeled estradiol concentration is overestimated. While this leads to an underestimate of the actual affinity constants, it should not affect the measurement of the interaction between binding sites. Since 4-hydroxytamoxifen binds more to the test tube than estradiol, it is predicted to have an apparently lower affinity in competition experiments (as observed). Thus, although the data deviate systematically from Eq. [ 131, it is unlikely that this systematic deviation detracts from the reliability of the conclusion that the binding of 4-hydroxytamoxifen to the estrogen receptor antagonizes the binding of estradiol to the estrogen receptor. The dimer model, Eq. [ 131, can still be used as a rational function approximation to get the apparent free energy of interaction that we used to compare estradiol binding with 4hydroxytamoxifen binding.
ANTAGONISTS
TO ESTROGEN
589
RECEPTOR
In addition to measuring the free energy of interaction between estrogen binding sites, the free energy of interaction suggests that 4-hydroxytamoxifen binding antagonizes estradiol binding. Although the binding of these ligands to the estrogen receptor independently is very similar, the conformational changes induced are not necessarily the same. If the conformational changes were the same, then the free energy of interaction would have been very small. The free energy of interaction is too small, however, for conclusive evidence that 4-hydroxytamoxifen antagonizes estradiol binding because another competition experiment (Fig. 5) suggests that the affinity of 4hydroxytamoxifen for the estrogen receptor is actually slightly higher than the affinity of estradiol for the estrogen receptor, contrary to the results shown in Table I. This would diminish the free energy of interaction between 4-hydroxytamoxifen and estradioi binding to the estrogen receptor. We have found the standard free energy change, GXY, for binding of two different ligands, x and y, to the same binding sites on a dimer. We interpret the interaction between the two ligands by dividing all possible values of this standard free energy change into three regions:
3 3 TI e v W z a *+
9 0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
s.0
10.0 11.0 12.0 13.0 14.0
.O
Total Estradiol FIG. 5. Binding to [3H]estradiol to the estrogen receptor in the presence of a constant ratio of total [3H]estradiol to total I-hydroxytamoxifen concentration. The data (open squares) were taken from Sasson and Notides (1) for the bound [3H]estradiol as a function of the total [3H]estradiol concentration in the presence of a constant ratio of total 4-hydroxytamoxifen concentration to total [3H]estradiol concentration: 0 (0); 0.5 (A); 1.0 (X); 1.5 (V). The solid line is the best fit of the data to the model for binding of two ligands to identical and independent binding sites with only the total site concentration and two standard free energy changes for binding used as parameters, obtained using nonlinear least-squares analysis (Johnson and Frasier, (27)). The parameters that best described the data are T = 2.87 nM, g, = -12.8 kcal/mol, g, = -13.4 kcal/mol.
590 I
BOND, SASSON, AND NOTIDES
G”.Y> gf + gs;
II
gi” + gf > G&Y> gJ + g;
III
g+’+ g; 2 Gxpy.
A
kq = kf -
This division is not symmetric with respect to interchange of the two ligands. We interpret the result in terms of the effect of ligand y on the binding of ligand X. If QJ is in region I, then ligand y antagonizes the binding of ligand X, since the binding of ligand x to the dimer bound to one molecule of ligand y occurs with a lower affinity than to the unliganded dimer. If G’” is in region II, then ligand y is a partial antagonist of the binding of ligand X, since x binds to the dimer bound to ligand y with a higher affinity than to the unliganded dimer, but with a lower affinity than if the dimer were bound to another x molecule. If Gxy is in region III, then ligand y is an agonist of the binding of ligand X, since binding of ligand r to the dimer bound to a molecule of ligand y occurs with greater affinity binding to the dimer bound to another molecule of ligand X. These regions were chosen based on a macroscopic understanding of agonist and antagonist action. The Monod-Wyman-Changeux model of allosteric regulation of proteins permits a precise definition of competitive antagonism, so it is possible to calculate the values of G”” for agonists and antagonists for this model. According to the Monod-Wyman-Changeux model, a dimer can exist in two states, T (taut) and R (relaxed), that are in equilibrium according to an equilibrium constant, L(L = (T)/ (R)). Two ligands, x and y, bind to the dimer with apparent microscopic affinity constants k$ kf, kj’, and kg as determined using Eq. [13]. These constants are apparent affinity constants resulting from the binding of each ligand to the T state with affinities 6 and k%, and to the R state with affinities FR and k&. We define these ligands to be agonists if they bind preferentially to the same state of the dimer (i.e., k& > k+ and k$ > kyT) and antagonists if they bind preferentially to different states of the dimer (i.e., k& > k+ and kq > kg). The R and T states are chosen so that k& 2 &. The apparent affinity constants, &, kfj, kf, and k$, can be determined from the binding curves but L, k&, k$, kg, and k$ cannot. However, having measured the apparent affinity constants, there are only two possibilities:
and either
kW
k$ = kj’ + L
kW
- k9 L - kl) L
or B
kl(kS - k3’) L
k& = kr - L
KG = kf f
kj’(k$ - k:) L
Case A corresponds to agonists, and case B corresponds to antagonists. It is possible to determine whether case A or B holds by performing the competition experiment described under Theory. It is not possible, however, to find k+, kg, kyT, and k$. The result of the experiment is a value for m, the equilibrium constant for binding of the two ligands to the dimer: RXY
m=2RXxXy.
If the ligands are antagonists (case B) it is possible to show that
This falls in region I above. If ligand y is an agonist of ligand X, then m is between k$kj’ and k$kf. This falls in region II if kfkf > k$kf and in region III if k$kf > k$k$. Recently several papers have appeared addressing the estimation of affinity constants from competition binding studies (27-30). These authors point out that the affinity constants may be inaccurately calculated if the excess ligand is depleted during the variation of the competing ligand. Using the simulations of Goldstein and Barrett (27), we have estimated that our constants are in error by less than 5%. Competition Binding Concentrations
at a Constant Ratio of Total Ligand
Previous studies have shown that information about the binding of weak agonists to the estrogen receptor can be gained by measuring the bound radiolabeled ligand concentration as a function of ligand and competitor concentrations while maintaining a constant ratio of the total radiolabelled ligand concentration to the total competitor concentration (10, 11). We analyzed data for the bound [3H]estradiol concentration as a function of the total [3H]estradiol concentration while maintaining a con-
BINDING
OF ESTROGEN
AND
ESTROGEN
stant ratio of total [3H]estradiol concentration to total 4-hydroxytamoxifen concentration (11). The bound [3H]estradiol concentration reached a maximum and then decreased at high [3H]estradiol concentrations. The data were fit to the model for the binding of a ligand to identical, independent binding sites (e.g., binding to a monomer) in the presence of a competing ligand. The identical and independent binding sites model is capable of predicting qualitatively similar results (Fig. 5). We used this simpler model because our purpose is to show the simplest model that is capable of predicting negative slopes. The systematic error is due to the fact that we did not include the ratios of ligands as parameters (hence the data and the fit to the data plateau at different levels), and because the simple model cannot describe cooperativity. The decrease in the bound [3H]estradiol concentration can be accounted for if two ligands bind to the same binding sites with very high, but different, affinities. At total ligand concentrations less than the total receptor concentrations, the ligands are mostly bound to the receptor, regardless of their relative concentrations. At high concentrations, however, the amount of radiolabeled ligand bound depends on both the relative affinities and the relative concentrations. The falling curves may also be observed if Haldane’s laws (12) are not obeyed; that is, the two ligands have different cooperativities, and the less cooperative ligand binds initially with a higher affinity. Therefore, the ligands will have different relative fractional saturations at different concentrations. However, a decrease in the bound [3H]estradiol has been observed under conditions where the estrogen receptor is primarily monomeric (data not shown), so this is not a possible explanation. SUMMARY We described how it is possible to interpret competition binding data obtained from preparations when the binding protein is not pure and contains multiple binding sites. We used the equations that describe binding of a ligand to a dimer of identical and interacting subunits (Eq. [ 131) to analyze data from the binding of estradiol to the estrogen receptor and the binding of 4-hydroxytamoxifen to the estrogen receptor. The results show that the data fit the model with no systematic error and that the binding of both estradiol and 4-hydroxytamoxifen to the estrogen receptor is highly cooperative. In addition, we used the same equation to analyze data obtained from the binding of 4-hydroxytamoxifen to the estrogen receptor in the presence of saturating concentrations of [3H]estradiol. The analysis suggested that the binding of estradiol and 4-hydroxytamoxifen to the estrogen receptor is relatively
ANTAGONISTS
TO ESTROGEN
RECEPTOR
591
cooperative. This is consistent with the fact that 4-hydroxytamoxifen is an estradiol antagonist. However, there was systematic error in the binding data. Finally, we analyzed our competition binding data using the MonodWyman-Changeux model. REFERENCES 1. Jensen, E. V., and DeSombre,
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