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Evaluation of Three Constants Involved in the Binding of Corticosterone to Plasma Proteins in the Rat1

MICHEL JOBIN AND FRANCQIS PERRIN Enhorn toires t9'E;ndocrir~nlogk, DPp~rrrs.1 enrerat cie Pi~ysiologie, Fuculte' de ~Mhdhcirte, Universir P Lavul,

QuPbec and Itlstitut Natiosial de la SarttP et de la Recherche M(;dicale, Lubomtoire lie Bion~atizPznatiques et Sratistiques, Hdpital de 1'Hiitel-Dieu, Lyort, Frarlce

Received August 1 , 1973

Jobin, M. & Perrin, F. (1974) Evaluation of Three Constants Involved in the Binding of Corticos- terone to Plasma Proteins in the Rat. Can. J. Biochem. 52, 101-105

Equilibrium dialysis was used to evaluate three constants iilvolved in the binding of corticosterone to transcortin and albumin in rat plasma, namely ST (concentration of binding sites of transcortin), KT (association constant of transcortin), and SAKA (binding constant sf albumin). Undiluted plasma from rats adrenalectomized 24 h earlier was enriched with increasing amounts of corticosterone (0-5.0 g / m l ) and dialyzed for 4.3 h at 37 "C.

Assuming that the law of mass action applies to the interaction between corticosterone and its two binding proteins, the values of ST, KT, and SAKA were estimated by means of a new method of calculation. Derived from the maximum likelihood principle, this method allows computation of a confidence region for the parameters. The following values and statistical bounds were obtained:

ST = 6.1(3.4-9.0) X lod7 M ; KT = 1.5(0.61-2.6) X lo7 M-1; SAKA = 5.2(3.7-6.8).

Jobin, M. & Perrin, F. (1974) Evaluation of Three Constants Involved in the Binding of Corticos- terone to Plasma Proteins in the Rat. Cart J. Biochem. 52, 101-105

La mesure de trois constantes rdgissant la liaison de la corticostCrsne aux protdi~~es plasmatiques chez le rat, soit ST (le nombre de site de la transcortine), KT (la constante d'association de la trans- cortine) et SAKA (la constante de liaison de l'albumine), fut effectuCe par une mdthode de dialyse d'dquilibre. A cette fin, du plasma non diluC de rat surrdnalectomisC 24 h auparavant fut dialysC pendant 4.3 h a 37 "C avec des doses croissantes de corticostCrone (0-5.0 pg/ml).

Supposant que la loi d'action des masses s'applique, ST, KT et SAKA furent CvaluCs grace ii une nouvelle mdthode de calcul dCrivCe du principe du maximum de vraisemblance. Cette mCthode permet le calcul d'une rCgion de confiance pour les param2tres. Les valeurs suivantes furent obtenues :

Introduction Corticosterone is the principal glucocorticoid

secreted by the rat (I). In the plasma, only a fraction of this hormone is in the free or "native" form. The remaining fraction is bound to two macromolecules (proteins), one of which has been identified as transcortin (2, 3) while the other presumably is albumin (4). In the course of a study on the dynamics of corticosterone in the rat, we were led to evaluate certain charac- teristics of this binding, namely, the concentra- tion of binding sites and the association constant of transcortin (ST and KT) and the binding con- stant of albumin (SAKA). For this purpose,

'Supposted by the Medical Research Council (MT- 1SSS).

equilibrium dialysis was used to determine the concentrations of free and bound corticosterone at total plasma concentrations ranging from 0 to 275 pg/ 100 ml.

Material and Methods

Corticosterone-Free Plasr~au Sixteen male Sprague-Dawley rats (body weight,

250-358 g) were killed by decapitation 24 h after bilateral drenalectomy. Heparinized blood was centrifuged for 15 min a t 4 'C (28 800 g), and plasma was pooled. This plasma was found to be virtually free of corticosterone when assayed by a method of competitive protein binding (5). Although the plasma binding activity has been observed to increase after adrenalectomy (6, 7), such change does not seem to occur until 48 11 after the opera- tion.

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162 CAN. J. BIBCHBM. VBL. 52. 8974

Radioactive Cor'licostero/le Corticosterone-l ,2-3H (specific activity : 40 Ci /mrnol)

was obtained from New England Nuclear (Boston, Mass.). It was purified by thin-layer chromatography successively in two solvent systems: firstly, in a mixture of benzene - ethyl acetate (66:40), according to Yoshimi and Eipsett ($1, and secondly in chloroform-ethanol (90: 10) according to Lisboa (9). Methanol was used for final elution and storage a t 4".

Stable Corricosaersne Corticosterone (4-pregnen-11@,21-diol-3,26-dione) was

obtained from Mann Researcl~ Laboratories (New York). Concentrated solutions (10, 50, and 506pg/m1) were prepared in absolute ethanol and kept at 4'.

LabeNi~g 01 P~Q.BPBM Four microcuries of radioactive corticosterone were

evaporated to dryness in a large tube, under gentle nitrogen stream in a bath a t 40, and redissolved in 80 mi of pooled adrenalectornized plasma. The quantity of steroid added in this way was only 0.4 ng /ml plasma.

Addition qf Carrier Corticosterosze Increasing amounts of stable corticosterone in ethanol

were added to a series of 15 tubes, evaporated to dryness, and redissolved in aliquots of 5.0 an! of laklled plasma. The quantities of steroid added in this way were 0, 0.05, 0.1,8.2,0.3,0.4,0.5,0.6,0.75, 1.0, 1.25, 1.5,2.0,3.Q,and 5.0 pg /rnl plasma. The added steroids were allowed to equilibrate with plasma proteins for at least f h a t room temperature.

Dialysis Duplicate samples of 2.8 mi of plasma were placed in

bags of seamless Visking tubing, circumference 66 man, and dialyzed against 6.0 ml of 0.974 NaCh in small glass bottles closed by plastic screw caps (liquid scintillation vials, Packard Co.). Tetracycline (Weverin, Hoechst Pharmaceutical, Montreal, Quebec) ( 2 8 pg per vial) was added to prevent bacterial growth. According to Quincey and Gray (18) such concentration of tetracycline does not interfere with the binding of corticosteroids to plasma proteins. Dialysis was performed in a BubnofF shaker (rate, 70/min) a t 37' for 260 min.

The time required for reaching equilibrium had been previously determined in the following way. Plasma from intact rats (0.09 pg corticosterone /ml) was labelled with a trace of corti~osterone-l,2-~H and dialyzed under the same conditions as above. The radioactivity of the dialysate, measured in 8.02 ml samples taken at intervals ranging from 80 min to 30 h, rose rapidly and reached a plateau after 3 h. Identical results were obtained with plasma from adrenalectomized rats and with saline containing 0, 0.1, or 5.0 pg/ml of corticosterone. Using a slightly different dialysis system (cortisol and human plasma), Florini and Buyske (1 1) found that equilibrium was reached in only 2 h. Since dialysis should be as short as possible to avoid any alteration of the incubated proteins and steroid, it was decided to measure the equilibrium after 260 min (4.3h).

At the end of dialysis, aliquots of 1.6 ml of the dialysate and 0.1 ml of the dialyzed plasma were pipetted into scintillation vials containing 10 mI of Bray's solution,

and counted (itninirnum, 80000 counts) in a Packard counter (model 3375). Counting efficiency was determined in the same samples after addition of 0.5 pCi of toluene-WH.

At the end of this experiment, the volume of the di- alysate, measured in each vial by n?! ddution, had de- creased from 6.0 to about 5.5 rnl (5.52 k 0.02 ml), suggesting a corresponding dilution of the dialyzed plasma (from 2-0 to 2.5 ml). In agreement wit11 this, total re- covery of the radioactive hormone at the end of dialysis could only be accounted for by assuming volumes of 2.5 and 5.5 ml, respectively, inside and outside the dialysis bag. Appropriate correction was therefore applied in calculating the binding constants.

The concentrations of corticosterone observed at equilibrium are shown in Table 1 and in Fig. 1.

Compumtiobl of the Bbrdirtg Parameters Assuming that the observed equilibriums result from

the interaction between two separate proteins and corti- costerone, the binding parameters are defined by applica- tion of the law of mass action, and their values obtained by a maxinrmhnm likelihood method. This method, which takes into account all binding proteins, allows computa- tion of confidence regions for the binding constants. In addition, it yields two useful parameters, one cl~aracteriz- ing the goodness of fit between the experimental points and the representation, and the other k i n g an index of the agreement between the estimated binding constants and their optimal values.

Let us derive the equation relating [Cj,the concentration of free corticosterone in glasma, to C, the corresponding total concentration. At equilibrium, the law of mass action between a protein P and corticosterone C may be written as in Eq. 1

where Kp denotes the equilibrium constant, [C] the concentration of free corticosterone, [PI the concentration of unoccupied binding sites, and [CP] the concentration of occupied binding sites,

If Sp is defined as the total concentration of binding sites (Eq. 2),

then Eq. 1 can be written as (Eq. 3):

or equivalently (Eq. 4):

S,[CI [CP] = - 1 5 + [Cl In the case of transcortin T, one has therefore

151 ST[CI [CT] = 7

For the albumin A, a simplification occurs in Eq. 2 since SA is much larger than [CAI. Indeed, the concentra-

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JOBIN AND PERKIN: PLASMA PROTEIN BINDING OF CORTICOSTEKOWE 103

TABLE I . Equilibrium obtained after dialysis of various concentrations of corticosterone in rat plasma

- - - - -

Corticosterone concentration (pg /ml)

Final Initial

(plasma) Total (plasm) Free (dialysate)

1 0 - W ) and, a .fi~rriori, much larger than [CAI. Thus, replacing (SA - [CAI) by SA, Eq. 3 becomes Eq. 6

By assumption, the total plasma conce~ltrationl Ct is the sum of the concentration of unbound corticosterone C, plus the concentration of the occupied binding sites of transcsrtin and of albumin, i.e. (Eq. 7)

or by using Eqs. 5 and 6 and setting [C] = C,

From this equation and from our 38 measures of the pairs (C, C,), estimates of STY KT. and SAMA can be obtained.

To have i1at only estimates, but also some kind of evaluation of their precision, the following statistical hypotheses were made: firstly, each measure C (or C,) belongs to a gaussian distribution with mean m (or m,) and standard deviation B (or at) and secondly, B (or a,) is proportional to m (i.e. a = Em or at - Emb, for some constant E), a hypothesis which implies a constant coefficient of variation. The parameter E characterizes globally the adequacy sf Eq. 8 to represent the measures.

The second hypothesis is supported by the existence of a significant positive correlation ( r > 0.8) between the duplicates' absolute differences and their means, and, conversely, by the lack of significant correlation (r . < 0.1) between the duplicates' relative differences and their means. The average relative difference is 0.026.

This being assumed, the estimates of ST, KT, and SAMA are obtained by the maximum likelihood method, which is best described using the following notation.

Firstly, individual measures are given an indice i, varying from 1 to 30, verbia graria, C,,, C,, m,, and m,,. Secondly, the total quantity of steroid present in the ith bag at the beginning of dialysis is called q,. Finally, lee a be the set of our four unknown parameters.

PI a = ST^ KT, SAKA, E ) By definition (14), the likelihood function L(a) is the

density of the probability of obtaining the 30 pairs of tion of albumin in rat plasma is 4 g/100 ml(12), or 0.61 X measures (Ci, Ct,), knowing ST, KT, SAKA, and E. It is

M (M.W., 65 080). Assuming two binding sites per calculated as the product of 30 individual densities of the molecule of albumin (1 3), the value of SA is 1.2 X M , probability p(Ci, Cttla) of obtaining one pair of measures much larger than the maximal total corticosterone (C,, C,,), knowing ST, KT, SAKA, and E. concentration at the end of dialysis (3 pg/ml or 8.6 X From our previous statistical hypotheses

where ml and mti are given by

6111 mt% = mi(1 + (SAKA 9 ST I( 1 /KT + mi)) X 2 / V) el21 4a = V X mtt + W X ma

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CAN. J . BIOCHEM. V8L. 52, 1944

FIG. 1 . Relationship between total and free corticosterone in rat plasma at various csncentrations, as determined by equilibrium dialysis.

in which V and W are the respective volumes of the dialyzed plasma and of the dialysate at the end of dialysis.

Thus, for assumed values of ST, KT, SAKAl and E, the likelihood function can be computed. The maximum likelihood method consists of taking as estimates far ST, KT, SAKA, and E, those values for which the likelihood function is maximum. This is equivalent to finding the values that give the minimum of

The estimates obtained by this method are the following

The confidence limits of the estimates are then evaluated in the following way. Let a, be the exact but unknown value for the set of parameters. The statistical hypotheses previously made imply that the distribution of T(a,) is a x2(6Q) distribution. Considering that four parameters were estimated from the data by the maximum likelihood method and that the number of measures is large enough, then the distribution of T(a l ) is approximately a x"56); distribution. Therefore, a 99"; confidence region for the parameters can be defined, which corresponds to the set of all points, such that

[21 1 T ( ~ ) 5 56 $. 2 . 6 4 ~ ~ or such that

Pa T(a) 2 ?-(al) - 4 + 2 . 6 % I m or, almost equivalently, such that

- -

and the curve calculated from these estimates is shown [231 ' ' ' stcl) )- 2'642 as a solid line in Fig. 1. The intersections of the surface Bimitinag this region by

If a , denotes the set of these estimates, then the parallels to the axis through cul are the bounds given

[181 S(al) = -2'70 Let

JO

below :

ST = 6.8(3.4-9.0) X lW7 h4;

KT = 1.5(0.61-2.6) X 10: h4-I;

A simple derivation shows that, for the optimal esti- Biscussisn mates, T(cr,) nsust be equal to the number of measures. providing a simple criterion for evaluating the quality of Reported values for the binding constants the minimum. relating transcortin, albumin, sand crarticosterone

In the present case, in rat plasma are listed in Table 2. Although these [20] Ttcr,) = 59.95 constants may vary in &Rerent strains sf rats, it which is very close to its theoretical value of 60. is likely that methodological and computational

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JOBIN AND PERRIN: PLMMA PROTEIN BINDING OF CORFICOSTERONE

TABLE 2. Values reported in the literature for some parameters of interaction between plasma proteins and corticosterone in the rat

Transcor tin 1 Albumin Transcortin association binding binding sites constant constant

Method ST M ) KT (lo9 M-I) SA KA Reference - - -

Ultracentrifugation 13.9 1.46 2.8 (14) Equilibrium dialysis

and gel filtration 14.4 1.95 6.4 (15) Ey uilibrium dialysis

and gel filtration 10.7 2.02 - (7) Equilibrium dialysis

and gel filtration 14.4 1.75 3.7 (16) Equilibrium dialysis 9.8 3 .O (17) Equilibrium dialysis 6.1 I .5 5.2 This paper

differences are mainly responsible for the ob- served discrepancies. For instance, when'adrenal- ectomy is used to abtain corticasterone-free plasma, the time interval after adrenalectomy may be critical: recent observations (Forest, M., and Perrin, F.: unpublished observations), based on dialysis experiments with rat plasma, have shown an initial decrease of the number of transcortin sites until 24 h after adrenalectamy, followed by a progressive increase. This may explain the rather low value of ST that we ob- tained (plasma obtained 24 h after adrenalec- tomy) compared with the values of the literature.

With respect to other methodological factors, it appears that the ideal procedure should involve no appreciable dilution or concentration of the plasma, since it was reported that the binding parameters may be a function of protein con- centration rather than of constants (13). Simi- larly, the procedure should be as short as pos- sible, because of possible alterations of proteins and hormone during very long incubations.

On the other hand, it is obvious that the precision of the estimates depends not only on the number of corticosterone concentrations used, but also on their range and distribution. In this sense, one should try to cover equally well the ranges below and above the expected concentration corresponding to the saturation of the binding sites of transcortin.

Finally, the method of computation of the estimates may also be of some importance. For instance, the method of simple least-squares minimization, which does not take into account the heteroscedasticity of the measures, gives estimates that differ from those obtained by the method of maximum likelihood or by a method

of weighted least squares, which takes into ac- caunt such variation in the precision of the measures.

The authors are grateful t s Mrs. M. A. Ho-Kim, from the Endocrine Laboratory of the Centre Hospitalier de I'Universitk Laval, for cl~romatographic purification of the radioactive csrticosterone.

1. Bush, J. E. (1953) J. Erzdosrirtol. 9,95-100 2. Chader, G. 3. & Westphal, U. (1968) Biochemistry

7,4272-4282 3. Seal, U. S. & Doe, R. P. (1963) Endocrir~ology 73,

37 1-376 4. Westphal, U. & Be Venuto, F. (1966) Biochim.

Biophys. Asta 115, 187-196 5. Murphy, B. E. P. (1967) 1. Clin. Endocritzol.

Mctab. 27, 973-990 6. Westphal, U., Williams, W. C., Ashley, B. D. &

De Venuto, F. (1963) Hoppe Seylers Z . Physiol. Chrnt. 332,54-69

7. Labrie, F., Pelletier, G., Raynaud, J. P., Ducom- mun, P., Delgado, A., Macintosh, B. & Fortier, C. ( 1970) Me'd. Hyg. 28,266-28 1

8. Yoshimi, T. & Lipsett, M. B. (1968) Steroids 11, 527-540

9. Lisboa, B. P. (1963) Astn Endocrirtol. 43,47-66 10. Quincey, R. V. & Gray, C. H. (1963) 1. Endocri-

izol. 26, 509-5 16 11. Florini, J. R. & Buyske, D. A. (1961) J. Biol.

Chem. 236,247-25 1 12. Spector. W. S. (1953) in Handbook of Biological

Duta, p. 53, W. B. Saunders, London 13. Westphal, U. ( 197 1 ) in Steroid-Protein Irtter-

actions, pp. 119-120, Springer-Verlag, New York, N.Y.

14. Mather, K. (1964) in Statistical Analysis in Bi- ology, Methuen, London

15. Keller, N., Sendelbeck, L. R., Richardson, U. I., Moore, C. & Yates, F. E. (1966) Endocrinology 79,884-906

16. Koch, B., Lutz, B., Mialhe-Voloss, C. & Stutinsky, F. (1969) Hornz. Metub. Res. 1, 183-186

17. Westphal, U. (1967) Arch. Biochem. Biophys. 118, 556-567

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