Eur. J. Biochem. 80, 411 -423 (1977)

Development of a Microassay for Estradiol Receptors Gtrard BARBANEL, Jean-Louis BORGNA, Jean-Claude BONNAFOUS, and Jean-Claude MAN1 Equipe de Recherche No 62 du Centre National de la Recherche Scientifique, Ecole Nationale Superieure de Chimie. M,ontpellier (Received June 1, 1977)

The calculation of equilibrium binding constants for a specific receptor-hormone interaction requires the exact determination of the unbound ligand concentration and the specifically bound concentration at equilibrium. These determinations usually require corrections for the contribution of non-specific binding. We introduce several parameters allowing equilibrium concentrations to be calculated from experimental concentration values ; these parameters can be measured for the particular receptor assay procedure used. These parameters are used in a microassay of estradiol-receptor complex by selective retention on DE-81 cellulose paper. The specific binding of a hormone to its ‘receptor’ is the earliest step in its action mechanism; the formation of this complex induces a set of events whose observed effects will constitute the hormonal activity. Studies of this specific binding are notably important in the hormone’s mechanism of action. The definition of a hormone ‘receptor’ is ambiguous, as this term overlaps in literature highly different biological structures, whose specificity and ligand affinity are quite variable. We shall consider a ‘specificreceptor’ must have three essential properties : (1) binding specificity : the property of complex formation is dependent on the ligand molecular structure and the binding site integrity (tertiary and quaternary structures of the receptor) ; (2) saturability : limited binding capacity ; (3) high affinity : high association constant of the ligand-receptor complex. These three properties are found for the uterine estradiol receptor. Besides specific receptors, many biological structures are able to bind the hormone in a ‘non-specific’ manner. This ‘non-specific’ binding is characterized by a low specificity, a very large (practically unlimited) capacity, and a small association constant. It must be stressed that the qualitative terms ‘high’ and ‘small’ association constant, ‘small’ and ‘very large’ capacity indicate a difference of several orders of magnitude between the two classes. The method used for binding measurements has to be very selective in order to distinguish specifically bound ligand from non-specifically bound and free ligand. One of the goals of this work was also to develop a method that was fast and simple for making set determinations, and very sensitive in order to allow microdeterminations. This method was developed for

checking fractions of the estradiol receptor from affinity chromatography. Many procedures have been used to determine and characterize the estradiol-receptor binding : equilibrium dialysis [l], sucrose gradient centrifugation [2], Sephadex gel chromatography [3 - 81, hydroxyapatite microcolumn adsorption [9 - 111, protamine sulfate precipitation [12,13], dextran-coated charcoal adsorption [14- 181, diethyl-aminoethyl (DEAE) cellulose filtration [19- 211. DEAE-cellulose filtration, the most recent procedure which was used to study the receptors of corticoids [19,20], sex hormones [21], and estradiol [ 191 was not thoroughly investigated. The present work deals with theoretical and experimental aspects of the determination of specific binding constants at equilibrium, for the uterine estradiol receptor, with a method derived from this ion-exchange filtration procedure. For studying the binding of estradiol by its receptor, some approximations may be used in the calculations of equilibrium concentrations because of the very high affinity constant of this complex. However we have shown here the full theoretical equations which must be used when such approximations are no longer valid as could be the case for the equilibrium between estradiol receptor and some estradiol derivatives or homologs. THEORY With the exception of equilibrium dialysis, which is the only procedure allowing equilibrium concentrations to be measured, all the methods of receptorligand complex determination induce a breakdown

Microassay of Estradiol Receptors

412

of the equilibrium between free and bound components since they separate these various components. Experimentally measured concentrations will be different from equilibrium ones and this difference must be taken into account in the calculations in order to determine the equilibrium conditions. Principle of the Method

(moljl) ; U ,U ‘ = concentrations of unbound radioactive ligand after incubations 1 and 2 respectively (molil); Bs, Bh = concentrations of specifically bound radioactive ligand after incubations 1 and 2 respectively (moljl); B N S ,BLs = concentrations of non-specifically bound radioactive ligand after incubations 1 and 2 respectively (molil); U i = concentration of unbound non-radioactive ligand after incubation 2 (molil). K, (ljmol) is the intrinsic association constant for the specific site-ligand complex; kn = C k,n, the sum of the products of the affinity constant k i times the number of binding sites n, of the non-specific binding components. Let us assume the specific binding sites are independent and equivalent. From the law of mass action :

The separation procedure is a selective retention of estradiol-receptor complexes on DEAE-cellulose filters. The procedure is as follows. Receptor-containing fractions are incubated with [6, 7-3H]estradiol producing the estradiol-receptor complex. When equilibrium is reached the different entities are separated. Aliquots of the incubation mixture are applied to DEAE-cellulose filters. The filters are washed with a buffer solution in order to remove free ligand and non-specifically bound ligand ; this washing may be more or less efficient depending on experimental conditions. The radioactivity retained on the filters after washing will represent fractions of specifically bound ligand with contaminations of non-specifically bound and free ligand. The ratio between these various ligand concentrations will depend on incubation and washing conditions. By submitting a given protein sample to different incubation types it will be possible to determine parameters concerning the method (efficiency, selectivity), incubation (receptor and ligand ratios), receptor binding site (association constant, association and exchange kinetics, binding site number) and various ligands (affinity for the binding site).

( B N s )z~ kiniC’

Calculation of Eguilihr ium Concentra tions

(Bl;s)i

kiniU’

These calculations are an extension of those developped by Blondeau and Robe1 [22]. We added two parameters: a represents the free ligand retention on filters; e represents the method efficiency. We used these authors’ symbols and abbreviations. Let us consider two different incubations of a protein sample in identical conditions of temperature, duration, protein concentration, pH, etc. The first incubation is made with a concentration T of radioactive ligand until equilibrium (incubation 1); the second incubation is made with the same concentration T of radioactive ligand, plus a concentration Tk of non-radioactive ligand. Tk is chosen so that the isotopic dilution of Twill result in a specific binding negligible in comparison to the non-specific binding (incubation 2). In practice:

(BNS) i =

C (BNs)i

Tk 2 100 N

and

Tk 2 100 T ,

N being the total concentration of specific binding sites (molil). At equilibrium the different concentrations will be: T = total concentration of radioactive ligand

NK, U 1 K,U

Bs =

+

kiniU’

-

-

1

+ ki (U‘ + U:)

With the incubation conditions we used: U < U’ + Uk < T + Tk I lop6 M. Hence ki (U’ + U i ) and a fortiori kiU are negligible compared to 1. Therefore :

U C kini

=

knU

(2)

and similarly BAS

=

knU’ .

(3)

Eqns (2) and ( 3 ) in which the non-specifically bound ligand concentrations are proportional to the free ligand concentrations are shown experimentally valid within very large area of protein and ligand concentrations. In the Experimental Procedure we measure the radioactive ligand concentrations retained on the filters after various incubation conditions : a blank incubation (without proteins) gives a Bo value, while incubations 1 and 2 give B1 and B1 values respectively. As the separation process is not completely selective, we have to introduce parameters which represent the fractions of specific complex (e),non-specific complex 0, and free ligand ( a ) retained on the filters: BO = UOU= aoT B1 = eBs

+ fBNS + a U .

(4) (5)

413

G. Barbanel, J.-L. Borgna, J.-C. Bonnafous, and J.-C. Mani

As we have chosen T&so that the isotopic dilution of T will result in a specific binding negligible in comparison to the non-specific binding, we can write for incubation 2 :

B2

=f

Bk

+ aU' .

the same calculations give the following expressions for the equilibrium concentrations of specifically bound and free ligand :

(6)

BNSand BAS can be replaced by their values according to Eqns (2) and (3). Hence :

B1

=

eBs

+ f i n + a) U

B2

=

fin

+ a) U ' .

Therefore: Bi

=

eBs

+

U B2 U' . ~

It can be written that: T = Bs BNS Hence :

+ U = Bbs + U

+

Determination of kn and Parameters a, e, f

I

T - Bs = (kn + 1) U

and T = (kn

+ 1) U' .

By combining Eqns (7), (8) and (9) we obtain:

B1

=

eBs

+ B2---T -T Bs

or

Bs = (B1 -. B2) - :

r

eT - B2

Eqns (8) and (10) lead to: U=

eT - BI T xeT-B2 1 kn

+

Eqns (12) and (13) [or (10) and (ll)] show that the equilibrium concentrations of specifically bound (Bs) and unbound (U) ligand can be calculated from the experimental values B1, B2, Ti, T2, and from two parameters e, and kn. These parameters can be easily determined by two sets of equilibrium dialyses : dialysis 1 in the conditions of incubation 1 (high specific activity of the radioactive ligand); dialysis 2 in the conditions of incubation 2 (low specific activity of the radioactive ligand). The two dialyses are made under identical conditions ot temperature, duration, pH, etc. TI and U are measured directly in dialysis 1, T2 and U ' in dialysis 2. Aliquots of each dialysis cell compartment are applied to DEAE-cellulose filters and the filters washed as in the B1 and B2 determination procedure. The concentrations of radioactive ligand retained on filters are measured (mol/l) : dialysis 1 : bl in the protein containing compartment and b3 in the reference compartment (buffer solution alone); dialysis 2: b2 in the protein containing compartment and 64 in the reference compartment. Since the protein concentrations at equilibrium, in the two dialyses, (cl and c2) are close, it can be written that:

Comments on Eqns(1- 11) a) For the determination of Bo, B1,and RZ we have to take into account the contamination of the filters during washing by the buffer solution which becomes more concentrated in radioactive ligand. However if the volume of washing solution is large enough, this contamination is negligible. b) Empirically it has been widely accepted that the difference (B1- B2) is a measure of the specifically bound ligand: BS = BI - B2. This assumption is theoretically invalid (Eqn 10). If B2 < eT, we can write : 1 Bs = -(B1 - B2). e c) When the total concentrations of radioactive ligand are not absolutely identical in incubation 1 ( T I )and in incubation 2 (T2), always with the condition : Tk 2 100 T2 and TA 2 100 N

+ BNS+ U T I = BS + (kn + 1) U .

TI or

=

Bs

As

(kn)2 = (kn)l x T2 =

BAS

c2 c1

+ U'

Therefore

And

Let us assume that parameters a and f are linear functions of the protein concentration c in the concentration area to which c1 and c2 belong (this assump-

414

Microassay of Estradiol Receptors

tion will be verified later, for concentrations below 5 mg/ml). If we call a and 4 the slopes of a = f(c) and f = f(c) respectively, thus:

+ ac

(15 )

f=fo+4c.

(16)

a

=

a0

Eqn (21) shows that f cannot be reached directly; we can calculate only the ratio r. However at low protein concentration (c I 5 mg/ml) kn is proportional to c, A being the slope of kn = f(c): kn As a = a0 as follows :

It can be written:

+ (6+ @el)(kn)l + uo + a c ~ U} b2 = (6+ 4c2) ( k n ) l - + a. + ac2} U' c1 b~ = eBs

b3

=

uOU

b4

=

UOU'

(22)

b2 - b4 a ,-=f+n T2 - U

The variations of parameter f are represented by the variations of experimental ratio r . Comments on Eqns (20-23)

Hence : c1 u (bi - b3) - (bz - b4) c2 U' ~

= eBs

+ g5(kn)l U(cl -c2). (17)

In Eqn (17) the last term is negligible since c1 % cz and 4 has a low value (4 < 10ml/g when protein concentration c < 5 mg/ml)

eBs

k .

+ ac (Eqn 15), Eqn (21) can be rearranged r=

c2

=

=

(bl - b3) - (b2 -

By substituting BS in this equation by its expression from Eqn (14) :

For each type of assay, parameters e and r = a - a0 can be measured by equilibrium dialysis

f + ,

experiments. However it is more convenient to determineevalues without running many delicate and tedious dialyses. It is sufficient to know a particular value e0 of the parameter. In effect, if we call B? and B2"the concentration of radioactive ligand measured in the assay, the efficiency of which is eo (calculated by equilibrium dialysis) ; BI and BZ the concentrations of radioactive ligand measured in an assay of unknown efficiency e, Eqn (10) gives : T

( b~ b3) U' - (62 - b4) U

m

c1

-

Hence

Comments on Eqn (18)

a) Another expression of e can be obtained if a and f variations are neglected when c varies from c1 to c2 : c2 bl U' - bz U ci e %c2 T1U'- T2U-

If B2 6 eT and @ 6 eOT, assumptions which are valid under our experimental conditions, a relative value of the method efficiency e can be calculated:

-

b) Similarly the ratio

ci

b) If el = c2, e can be calculated without any approximation :

By running equilibrium dialyses with radioactive ligand of low specific activity (dialysis 2) and various protein concentrations it will be possible to determine :

will give an idea on the relative selectivities of two methods. EXPERIMENTAL PROCEDURE

the free ligand retention aO,

Preparation of the Cytosol.from Ewe-Lamb Uterus a - a0 the ratio r = b2 - b4 = f + = f(c) . Tz - U' kn

(21)

All operations were carried out at 4 ' C . The uteri of 5 or 6 immature ewe-lambs were excised immediately after sacrifice ; adipose tissue was immediately remov-

G. Barbanel, J.-L. Borgna, J.-C. Bonnafous, and J.-C. Mani

ed and the uterus internal wall (15 g tissue) ground with a Virtis 23 in 30 ml Tris-HC1 buffer solution (pH 7.5) containing 1 mM EDTA and 1 mM dithiothreitol (buffer A). After 30 min of 30000xg,,, centrifugation, the supernatant (supernatant 1) was removed and centrifuged again for 30 min at 220000 xgmax.25 ml of supernatant 2 (cytosol) were thus obtained with a protein content of 10 mg/ml.

415

5 nM [6,7-'H]estradiol, 8.33 pM non-radioactive estradiol and 2 % ethanol. Dialyses lasted 18 h to be sure equilibrium was reached (standard dialysis times were between 30 min and 4 h for this kind of dialysis cell). The radioactivity and protein concentration (Lowry's method [23]) were determined for each cell compartment : an aliquot of each cell compartment solution was applied to a DE-81 filter; after washing radioactivity retained on the filter was measured.

Assay of the Estradiol Receptor (Standard Conditions) In 1.5 ml polypropylene conic test-tubes 100 pl cytosol were incubated with 20 pl 30 nM [6,7-3H]estradiol (60 Ci/mmol) in buffer A/ethanol (88jl2), mixture (incubation 1) or 20 p1 30 nM [6,7-3H]estradiol (60 Ci/mmol) plus 50 pM non-radioactive estradiol, in the same mixture (incubation 2). The final concentrations were 5 nM [6,7-3H]estradiol and 8.33 pM non-radioactive estradiol ; the incubation medium contained 2 % ethanol. The incubation was performed with shaking and lasted either 1 h at 25 "C, or 3 h at 4 "C. When the incubation was completed, the testtubes were cooled at 4 " C , if necessary, and 50 pl of each sample were applied to 6x2-cm strips of DE-81 (Whatman) paper. After a 4-min drying period at 4 "C, the paper strips were hung up in a washing bath 16 1 of 20 mM Tris-HC1 buffer (pH 7.9), 1.5 mM EDTA (buffer B) with gentle stirring]. The same washing bath could be used for 60 samples, without any appreciable contamination. After 1 h washing, the paper strips were drained and then oven-dried at 120 "C. The 2.3 x 2-cm areas where the samples were applied were cut out and their radioactivity measured with a Packard Tri-Carb 3320 liquid scintillation spectrometer in 10ml Unisolve 1 (Koch-Light Laboratories Ltd).

Equilibrium Dialysis Equilibrium dialyses were run in triplicate, at 4 " C , with a Dianorm apparatus, allowing 20 samples to be handled simultaneously under standard conditions. Union Carbide membranes were extensively washed in distilled water and equilibrated in buffer A before use. Dialysis 1. Compartment A was filled with 1 ml cytosol sample containing 5 nM [6,7-3H]estradioland 2% ethanol; compartment B was filled with 1 ml buffer A containing 5 nM [6,7-3H]estradiol and 2 % ethanol. Dialysis 2. Compartment A was filled with 1 ml cytosol sample containing 5 nM [6,7-3H]estradiol, 8.33 pM non-radioactive estradiol and 2 % ethanol; compartment B was filled with 1 ml buffer A containing

RESULTS AND DISCUSSION CHOICE OF THE EXPERIMENTAL CONDITIONS OF MEASUREMENTS

Washing Time Variations of Bo, B I , and BZ as a function of washing time at 4 "C are presented in Fig. 1. For the blank (without proteins), there is a rapid decrease of the concentration of filter-retained ligand (Bo): after 1 h, less than 1 % radioactivity remains on DE-81. The decrease of B2 (non-specifically bound and free ligand) is fast but less notable than the decrease of Bo. B2 will be smaller as cytosol will be less concentrated: after 1 h washing, 10% radioactivity remains on the filters with a 7.1 mg/ml protein concentration (Fig. 1). It should be noted that a and f , and therefore B, and B2, for a fixed washing duration, may vary depending on stirring conditions. The decrease of BI (specifically and non-specifically bound ligand, plus free ligand) is quite similar to that of B2 for short washing times (10 rnin); for longer washing times it becomes weaker and almost disappear. Fig. 2 presents the variations of (B1- B2)and (B2Bo) (apparent values of specific and non-specific bindings, respectively) as a function of the washing duration. (Bz-Bo) increases rapidly to a maximum (1012 min) and then decreases steadily up to 2 h, while (Bt - B2) value grows uniformly until 1 h and remains constant after that. These results show that the selectivity is good . only after 1 h washing in the experimental conditions of Fig. 1 and 2 (high protein concentration): Bt

-

B2 2 3 B2

B2 < 0.1 T . 1 The approximation Bs = (Bt - B2) (26) e of the BS value given by Eqn (10) (cf. Comments on Eqns (1 - 1l), comment b) does not introduce a considerable error. This error will be negligible at a low protein concentration ( c < 5 mgjml).

and

~

Microassay of Estradiol Receptors

416

0

100

200

300

400

I (mM)

0

30

60

120

-

Fig. 3. [3H]Estradiol retention on DE-81 as a function of washing buffer ionic strength (1). With the exception of the washing buffer ionic strength, the cytosol samples (1 .5 mg protein/ml) are assayed as described in Experimental Procedure: (A-A) Bz;(A---A) (Bi - Bz)

Washing time (min)

Fig. 1. [3H]Estradiol retention on DE-81 as u function of washing time. With the exception of washing time, the cytosol samples are assayed as described in Experimental Procedure: (A-A) Bo (blank: buffer alone); (-0) BI (cytosol 7.1 mg protein/ml, incubation 1); (m----m) BZ (same cytosol as for B I , incubation 2)

10

30

60

120

Washing time (min)

Fig.2. Variations of apparent .rpecifc (Bl - B z ) and non-specific (B2 - Bo) bindings with respect to washing time. The data Bo, B1, BZ are from Fig. 1 : m ( ).(Bz- Bo);(D--o) (B1- B z )

With 2 h washing the selectivity is better and the approximation of Eqn (26) is completely valid, even at a high protein concentration : BI - B2 z 20 B2 B2 z 0.017 T . However we shall see later that efficiency decreases with increasing washing time; so we chose a 1 h duration for the standard experimental conditions. Ionic Strength of the Washing Bufler

We determined B1 and B2 after 1 h washing at 4 "C in buffer B supplemented with increasing KC1 concentrations in order to obtain ionic strength ( I ) between 0 and 400 mM. Variations of B2 and ( B I - B2)

as a function of I are presented in Fig. 3. In the experimental conditions of Fig. 3 : B2 I 0.005 T . (BI - Bz) represents a relative measurement of efficiency e (cf: Eqn 25). The retention of radioactive ligand on filters decreases notably when the buffer ionic strength increases. Moreover the determinations of Bo and B2 are much more dependent on the stirring speed when I has a high value. Drying Time Drying time is the period between application of the incubation medium to filters and the washing of the filters. No significative variation of (BI - B2) can be detected when drying times change from 2 to 8 min; after 8 min (BI - B2) decreases. For the standard conditions we chose a 4 min drying time. Temperature Effects

The temperature for applying cytosol to filters has no effect on the results; for practical purpose we chose to work in a cold room at 4 "C. On the contrary, the washing bath temperature must be 4 "C. If washing is carried out at 20 "C for 1 h, the (B1- B2) value decreases markedly (25 % with respect to a 4 "C washing). Composition of the Washing Bath

Because of the low solubility of estradiol in water, the incubation medium contains 2 % ethanol. It was determined that (Bi- B2) was not affected by

41 7

G. Barbanel, J.-L. Borgna, J.-C. Bonnafous, and J.-C. Mani

the ethanol content (between 0.5 and 2.5%) of incubation medium and washing bath. The addition of glycerol or sucrose to the incubation medium is necessary for certain cytosol studies [24]. It was determined that (BI - B2) remained unchanged in the presence of 5 - 10 % glycerol or 125250 mM sucrose. Fig.4 presents the effect of the pH of buffer B on the amount of radioactive ligand retained on filters. Between pH 6.9 and 8.5 the retention of both specifically bound (B1- B2) and non-specifically bound (B2) ligands is almost pH independent. At more alka-

line pH, a decrease of the specific complex retention can be shown. Preequilibration of DE-81 Paper Filters

In standard conditions DE-81 ion exchange paper is used directly without any treatment. The preequilibration of filters with washing buffer does not bring about any change in the results.

CHARACTERIZATION AND PROPERTIES O F [6,7-3H]ESTRAD10L-RECEPTOR COMPLEXES

In this paper we do not describe the characterization of [6,7-3H]estradiol-receptorcomplexes. We show that the receptor is saturable, and thermolabile (fast and irreversible denaturation at 65 "C). The ligand binding is reversible (rapid exchange with non-radioactive estradiol at 25 "C). The complex formation shows little pH dependence between 6.5 and 9.0, but decreases drastically out of this pH area. These data agree with earlier results [25]. The kinetics of complex formation at 4 "C and 25 "C are presented in Fig.5. For specific binding the plateau is reached after 1 h at 25 "C or 2 h at 4 "C. 6 9 7.5 8.0859.0

PH Fig.4. EfSect of washing huj'er p H on [3H]estradiol retention on DE-81. Cytosol (1.8 mg proteiniml) is incubated under standard conditions (incubations 1 and 2) and applied on DE-81 filters which are washed with a buffer at a different pH: ( m 4 ) BZ (apparent non-specific binding) ; (0-0) (B1- B2) (apparent specific binding)

Determination of Intrinsic Association Constant

Eqns (12) and (13) enable us to calculate the concentrations of specifically bound (Bs)and unbound (U) ligands from experimental measurements, and

,

1

2 Time ( h )

3

4

Fig. 5. Kinetics qf estradiol-receptor complexation. Cytosol (2.5 rng protein/ml) is incubated with [3H]estradiol (incubalions 1 and 2) during different periods. Samples are assayed using standard conditions (see Experimental Procedure): incubation at 4 "C [M (B1 , -Bz); -, B z ] ;incubation at 25 "C [O -0,( E l - & ) ; H, B2]

Microassay of Estradiol Receptors

418

DETERMINATION OF THE METHOD CHARACTERISTICS

Proportionality between (6,7-3HjEstradiol Amounts Retained on Filters and Those Used during Incubation 7

The hypothesis about the expressions of Bo and B2 necessitate that BOand B2 are proportional to T o r U : when T varies, we have already shown that:

6

BO = aoU

5

and

3

Bz

1

=

(fkn

=

aoT

+ a)U' .

$ 4

By substituting U' by its value from Eqn (9): 3

2

1

*

0

0

0.1

0.2

0.3

04

0.5

BS

Fig. 6 . Scatchard plot of the equilibrium between ewe-lamb uterus cytosol and [3H]estradiol. Cytosol (2.5 mg protein/ml) is incubated 18 h at 4 "C with [3H]estradiol (0.3-22 nM) (incubation I), or with [3H]estradiol (0.3 - 22 nM) plus non-radioactive estradiol (8.33 pM) (incubation 2). Samples are assayed in duplicates by the DE-81 method (standard conditions) which gives BI and Bz. The specifically bound ligand concentration (Bs) and the free ligand concentration (qare determined using Eqns (12) and (13). The straight line is fitted using a least square method

from parameters e and k n which we will determine in the next paragraph. Several determinations of BS and U were made at 4 "C with various protein and ligand concentrations. Fig. 6 presents the variations of Bs/U as a function of Bs, according to Scatchard's method [26]:

We incubated three sets of samples : a blank (buffer alone) and two different concentrations of denaturated cytosol (cytosol heated 10 min at 65 'C lost its specific bindings) with increasing amounts of [6,7-3H]estradiol. The amounts of [6,7-3H]estradiol retained on DE-81 were plotted against the [6,7-3H]estradiol concentrations in incubation medium (Fig. 7), showing a good proportionality between 0.5 nM and 10 nM [6,73H]estradiol concentrations. From the slopes of the straight lines we determined : a0 =

p p

2x

= 3.3 x

(c = 1.5 mg/ml)

=9 . 2 ~

(c = 5 mg/ml) .

Determination of kn, f, and e by Equilibrium Diulysis

In dialysis 2 (equilibrium dialysis with [6,7-3H]estradiol of low specific activity), T2 and U' (total and free ligand concentrations at equilibrium) can be measured directly. Plotting kn

T2- U' U'

=

(20)

as a function of c, gives roughly a straight line with the origin (Fig. 8), for protein concentrations between 0.5 and 5 mg/ml: kn

By the least square method the experimental points give a straight line the slope of which can be used to determine the intrinsic association constant : K,

=

2.2

0.5 x 10" l/mol .

The intercept with the abscissae is a measure of the binding site concentration :

=

0.27 c .

At higher protein concentrations : k n < 0.27 c .

We have already shown (cJ Theory) that at low protein concentrations (c < 5 mg/ml) the variations of parameter f are represented by those of the ratio 6 2 - b4 T2 - U '

y =--

N

=

0.35 k 0.04 pmol/mg protein .

The experimental values of K, and N are in agreement with results published elsewhere 181.

which can be determined experimentally by equilibrium dialysis [Eqn (23)].Fig. 9 presents the variations

419

G. Barbanel, J.-L. Borgna, J.-C. Bonnafous, and J.-C. Mani

5

1

.-..

[3H]Estradiol used (pM)

.-.,

Fig. 7. Proportionality between [3H]estradiol retention and [3H]estrrrdiol amounts in incubation medium. The different samples are incubated 4 h at 4 "C with [3H]estradiol in various concentrations (5.2 nM, 67 nM, 335 nM, 1.67 pM; 8.33 FM) and then assayed under standard conditions on DE-81: Bo (blank: buffer A alone); B2 (cytoxol, 1.5 mg proteinlml, denaturated by preincubation 10 min at 65 "C); A--- -A,Bz (cytosol, 5 mg protein/ml, denaturated as above)

between 0.02 and 0.05 [2- 5 % non-specifically bound ligand taken into account in the specifically bound ligand concentration, Eqn (5)]. Blondeau and Robe1 [22] determined f for the androgen receptor in rat ventral prostate :f = 0.05 for the separation technique using protamine sulfate precipitation or hydroxyapatite adsorption and f = 0.3 for the dextrancoated charcoal procedure. Parameter e was calculated for various washing times (Fig. 10). After equilibrium dialysis Eqn (18) gives the following e values : e = 0.73 e = 0.66 c (mglml)

Fig. 8. Proportionality between the non-specific binding parameter kn and the cytosol concentration c. Cytosol samples are equilibrium dialysed in the presence of 4.2 pM [3H]estradiol (100 Ci/mol) as described in Experimental Procedure; after isolation, the radioactivities of the cell compartments are determined. The parameter kn (sum of the products of the affinity constants times the number of binding sites, for the non-specific associations) is calculated from Tz - U ' Eqn (20) : k n = U-,-

of r as a function of c. When the protein concentration increases, r and therefore f increase and the method selectivity decreases. However it appears in Fig. 9 that the ratio Y (and j) is practically constant for protein concentrations between 0.5 and 4 mg/ml. Within this concentration area,fvalue can be estimated c

+ 0.05 (1 h washing) k 0.05 (2 h washing) .

e values for shorter washing times were determined using Eqn (24) in comparison with the l-h washing value obtained by equilibrium dialysis. Variations of e are linear with respect to washing time (Fig.lO), at least until 2 h washing. The very low kinetics constant for the dissociation of the estradiol-receptor complex may account for the observed linearity ; we have shown a hyperbolic decrease of e with respect to washing time for some estradiol derivatives with higher kinetics constant of dissociation. The method efficiency decreases slowly with increasing washing times; several phenomena may account for this slow decrease, especially : elution of complexes from DEAEcellulose filters ; denaturation of receptor with release of ligand ; equilibrium breakdown. Upon extrapolating the straight line to the point of zero washing time an e value was determined that

Microassay of Estradiol Receptors

420

0.5

-

*

04 0

30

60

120

Washing time (min)

Fig. 10. Variations of the DE-81 method elficiency (e) ith t’t’spect to washing time. e values are calculated as described in the text, with data from Fig. 1

Reproductibility of DE-81 Method . )

5

0

10

c (rngirnl)

Fig.9. Selectivity of DE-81 method as a ,function of the cytosol concentration c. Cytosol samples with different protein concentrations are submitted to equilibrium dialyses in the presence of 4.2 pM [3H]estradiol (100 Ci/mol) as described in Experimental Procedure; the radioactivities of the different cell compartments are measured (Tzand U ’ ) while aliquots are applied to DE-81 filters and the radioactivities retained after washing are determined bz - hq (h2 and bl). The ratio r = [Eqn (23)] is calculated for each Tz- U ‘ protein concentration. Each r value represents the mean of four determinations

In the standard procedure determinations are made in triplicate. In order to have a better estimate of the method reproductibility, we made 12 independent measurements of each value Bo, B I , B2. Results in the Table 1 show that relative errors are low, especially for B1 value: the relative error on its radioactivity determination is almost negligible because of its large amount of radioactivity.

~

was not equal to unity (100% efficiency); this means that phenomena other than those considered above affect the method efficiency.

Table 1. Reproductihility of the DE-81 method Mean values of 12 independent determinations of BO (incubation without cytosol), BI (incubation with radioactive estrddiol of high specific activity) and BZ (incubation with radioactive estradiol of low specific activity) Determination

Mean value

Standard deviation

Relative error

55 110 264

7.8 1.2 3.3

x

dis./min

Comparison wilh Other Assay Procedures We compared the assay on DE-81 with two classical separation techniques used for estradiol-receptor complexes, namely Sephadex G-25 chromatography [3 - 81 and dextran-coated charcoal adsorption [14- 181. We determined B1 and Bz for a similar cytosol sample, using these three different procedures. In the three cases B2 values are low (B2 < 0.04 T), so we used Eqn (26) which gives an approximation of e value:

e = - Bi

-

B2

Bs Using the value e = 0.73 we determined for the DE-81 method, we found e = 0.85 for G-25 chromatography and e = 0.72 for dextran-coated charcoal adsorption.

BO

BZ Bi

561 1235 6374

DE-8 1 Retention o j Estvadiol-Receptor Complexes as a Function of Applied Amounts We have already shown (Fig. 7) that for the blank (without proteins) there is good proportionality between the applied amounts of estradiol and the retentions on DE-81 filters. In the presence of cytosol, two kinds of experiments were made : we applied different amounts of complexes in a buffer volume either variable (Fig. 11) or constant (Fig. 12). The results of these two sets of experiments are concordant : B1 and B2 are proportional to the applied amount for low concentrated cytosol (1 mgiml),

42 1

G. Barbanel, J.-L. Borgna, J.-C. Bonnafous, and J.-C. Mani

while linearity is no longer observed for high concentrated cytosol (10 mgiml). However even at high protein concentration, the variation of ( B I - Bz) remains proportional to the amount of applied cytosol.

Sensitivity Threshold of the Method One of major advantages of the DE-81 method is its extreme sensitivity, allowing determinations of very small biological samples. In the case of immature ewe-lamb uterus 60 pg of proteins from 3 mg fresh tissue are enough for triplicate measurements of B1 and Bz. In the case of 16-20-day-old rats two uteri weighing 20 mg each homogenized in 1 ml buffer allowed the Scatchard’s determination of both the intrinsic association constant K, ( & 50 %) and the receptor concentration ( f 20 %) by measuring BI and Bz in triplicate for three different values of T (total [6,7-3H]estradiol concentration). One uterus is generally sufficient for determining the receptor concentration with a good precision.

Selectivity of DE-81 Method with Respect to Estradiol Receptors The DE-81 method is specific for estradiol receptor complexes. We compared the saturation curves of ewe-lamb uterus cytosol with those of plasma preparation from the same animals. The two sample concentrations were matched so as to allow the comparison in the very unfavorable case where the cytosol preparation is contaminated with 50% plasma proteins. The two sample determinations were made under the same experimental conditions. Fig. 13 presents the variations of B1 and B2 for the two samples as a function of T. For plasma proteins, B1 and BZ variations superimposed in one straight line very close to that of nonspecific cytosol complex.

CONCLUSION The study of the equilibrium between a receptor and its ligand necessitates knowledge of the specifically bound and unbound ligand concentrations at equi-

* 0

10

20

40

80

Applled volume (PI)

Fig. 11, Retention of estradiol-receptor complexes as a function of cytosol volumes applied to DE-Xlfilters. Standard conditions are used for cytosol incubation and assay. Different volumes of each cytosol sample are applied to filters: 10 mg protein/ml (0 0,BI ; -0, Bz);1 mg protein/ml(O-O, BI ; b - m , 82); blank Bo (bufler alone) A-A,

5

1

c (mgirnl)

Fig. 12. Retention of estradiol-receptor complexes as a function of protein concentration c. Standard conditions are used for cytosol incubation and assay. Constant volumes of cytosol with different protein concentrations (0.11 -6.9 mg/ml) are applied to DE-81 filters: 0- -0,( B t -Bz);I BZ= ,

Microassay of Estradiol Receptors

422

0

1

2

4

6

J (nM)

Fig. 13. DE-81 method selectivity with respect to estradiol receptors. C'ytosol (3.7 mg protein/ml) is incubated 18 h at 4 "C either with [3H]estradiol (0.15-7.5 nM), or with [3H]estradiol (0.15-7.5 nM) plus 8.33 pM non-radioactive estradiol. These samples are assayed by the B I ; t H. Bz).Plasma is prepared by collecting on heparin the blood from DE-81 method under standard conditions (D---Q, 6 ewe-lambs which were also used for uterus cytosol preparation. After 15 min of centrifugation at 1500 x K , supernatant is diluted to a protein concentration of 2 mg/ml. Incubation and assay of this plasma are made exactly as for the cytosol above (A-A, BI : v-v , Bz)

librium. In the simple case where only one biological entity binds the ligand, equilibrium dialysis is the only method giving these concentrations. All methods involving separation of the equilibrium components induce an equilibrium breakdown with complex dissociation. The experimentally measured concentrations of bound ligand will be smaller than the equilibrium concentrations. On the other hand the presence of non-specific contaminants complicates the determination of the specifically bound ligand concentration as it is impossible to eliminate entirely these non-specific bindings. We studied the case of only one specific receptor with all binding sites independent and equivalent in the presence of other components which bind the ligand in a non-specific way. We introduced several parameters (efficiency e, selectivity f , and kn, factor related to non-specific complexes) allowing equilibrium concentrations to be calculated from experimental concentration values. These parameters can be measured for the chosen assay procedure. We then used this theoretical development to set up a procedure of selective retention of estradiolreceptor complexes on ion-exchange paper (DEAEcellulose). This method for determining estradiol receptors had several advantages. (a) Simplicity and speed: 60 samples can be assayed in two hours. (b) Great versatility of use : experimental conditions can change rather widely around their optimum values, without notably influencing the results (drying time, washing bath stirring, pH and ionic strength of washing buffer, washing time). (c) Good specificity: even at high protein concentration, when the percentage of

non-specific binding retention is significant, a good selectivity can be reached simply by increasing washing time. (d) Reproductibility : experimental deviations are less than 10%. (e) Efficiency: identical to other methods. (0Extreme sensitivity: is a major advantage. This procedure allows determinations of very small samples: 10 pl of solution containing 5 pg proteins, from impurified uterus cytosol. This method seems well suited to determine estradiol receptor in fractions from affinity chromatography.

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G. Barbanel, J.-L. Borgna, J.-C. Bonnafous, and J.-C. Mani 12. Steggles, A. W. & King, R. J. B. (1970) Biochem. J . 118, 695701. 13. Korach, K. S . & Muldon, T. (1974) Endocrinology, 94, 785793. 14. Korenman, S. G. & Rao, B. R. (1968) Proc. Natl Acad. Sci. U.S.A.61, 1028-1033. 15. Korenman, S . G., Perrin, L. E. & Mc Callum, T. P. (1969) J . Clin. Endocrinol. 29, 879- 883. 16. Mester, J., Robertson, D. M., Feherenty, P. & Kellie, A. E. (1970) Biochem. J . 120,831-836. 17. Alberga, A,, Jung, I., Massol, N., Raynaud, J. P., RaynaudJammet, C., Rochefort, H., Truong, H. & Beaulieu, E. E. (1970) Adv. Biosci. 7, 45 - 74.

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G. Barbanel, J.-L. Borgna, J.-C. Bonnafous, and J.-C. Mani *, Ecole National Superiere de Chimie, 8 Rue de I’Ecole Normale, F-34075 Montpellier-Cedex, France

*

To whom correspondence should be addressed.