Mouse brain glucocorticoid receptors


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Mouse brain glucocorticoid receptors
Glucocorticoid receptors
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vii, 320 leaves : ill. ; 29 cm.
Gray, Harry E., 1943-
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Glucocorticoids   ( mesh )
Neuroscience thesis Ph.D   ( mesh )
Dissertations, Academic -- Neuroscience -- UF   ( mesh )
bibliography   ( marcgt )
non-fiction   ( marcgt )


Thesis (Ph.D.)--University of Florida.
Bibliography: leaves 299-318.
Statement of Responsibility:
by Harry E. Gray.
General Note:
Photocopy of typescript.
General Note:

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University of Florida
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Full Text







This dissertation is dedicated to the memory of

Clarence Phillips Connell


I gratefully acknowledge the interest and support of my supervisory

committee: Drs. William G. Luttge, Robert J. Cohen, Adrian J. Dunn,

John B. Munson, and Don W. Walker.

I would also like to thank Elizabeth Webster and Dr. Neal Kramarcy

for assistance with the steroid radioimmunoassay, Dr. Richard Bonsall

for a particularly concise derivation of the solution to the rate

equation, Charles Densmore for assistance with animal surgery, and Nancy

Gildersleeve for assistance with computer programming and with a number

of biochemical techniques.



ABSTRACT . . . vi


Biosynthesis, Secretion, and Metabolic
Effects of Glucocorticoids . 1
Regulation of Glucocorticoid Secretion . 5
Overview of Corticosteroid Mechanisms . 9
Anatomical Distribution of Corticosteroid Binding 17
Characterization of Soluble Corticosteroid Receptors
in Brain . . 21
Physiological Regulation of Corticosteroid Receptors 27
Corticosterone "Membrane Effects" and Receptors 32
Summary . . . 36


Introduction . . 39
Theory . . 40
Applications and Discussion . 44


Introduction . . 55
Theory and Application . . 57
Discussion . . 84


Introduction . . .
Materials and Methods . . .
Results . . .
Discussion . . .


Introduction . . .
Materials and Methods . . .
Results .. . . .
Discussion . . .


Introduction .
Materials and Methods .
Results . .
Discussion .





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Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


Harry E. Gray

December 1982
Chairman: William G. Luttge
Major Department: Neuroscience

Glucocorticoid binding sites in cytosol prepared from whole brains
of female CD-1 mice perfused 3-5 days after ovariectomy-adrenalectomy
were studied by equilibrium, kinetic and transport methods. In the
standard buffer (containing 10 mM Na2MoO4 and 2 mM dithiothreitol, DTT)

both unoccupied and occupied binding sites for [3HJdexamethasone (DEX)
were stable at 20C. The absence of DTT resulted in rapid loss of

unoccupied sites, and the absence of molybdate resulted in loss of
unoccupied sites with a t, of 1 h at 120C and 10 h at 20C.

Equilibrium isotherms revealed one apparent class of saturable,
high-affinity binding sites (each) for [3H]DEX, [3H]triamcinolone

acetonide (TA), and [ 3H]corticosterone (B), but the concentration of
sites for [3HJDEX and [3H]TA (putative receptors) was only 63% of the
complete ensemble of [3H]B sites. The concentration of DEX-displaceable

[3H]B sites was equivalent to the receptor concentration measured with

[3H]DEX and [3H]TA. DEX failed to interact with 37% of the [3H]B sites;

these sites resembled corticosterone binding globulin (CBG). The

(decreasing) order of steroid affinity for the putative receptors

measured with the [3H]ligands was: [3H]TA > [3H]DEX > [3H]B. The

competing steroids that were tested fell into the following order of

decreasing affinity (increasing Kdi) for the [3H]dexamethasone binding

sites: DEX > B > 11-deoxycorticosterone > progesterone n cortisol >

aldosterone > cortexolone > testosterone.

Measured rate constants for the association of [3H]DEX, [3H]TA, and

[3H]B with the receptors were very similar. The very different
affinities of these agonist ligands resulted from their quite different

dissociation rate constants. Progesterone at concentrations greater

than 10-6 M (but not DEX itself) significantly accelerated dissociation

of the L 3H]DEX-receptor complexes.

Nonactivated [3H]TA-receptor complexes possessed Stokes radius
77 A, sedimentation coefficient 9.7 S, and molecular weight 315,000

daltons; heat-activated [3H]TA-receptor complexes (confirmed by

DNA-cellulose binding) possessed Stokes radius 58 A, sedimentation

coefficient 3.7 S, and molecular weight 90,000 daltons. Physical

characteristics of the cytosol CBG-like binder (Stokes radius 46 A,

sedimentation coefficient 4.1 S, molecular weight 70,000 daltons) were

indistinguishable from those of plasma CBG.



Biosynthesis, Secretion, and Metabolic
Effects of Glucocorticoids

The adrenal cortex produces over forty steroids, but only a few of

these are secreted in biologically significant quantities. The major

active secretions are classified as glucocorticoids (e.g., cortisol,

corticosterone, 11-deoxycortisol) or mineralocorticoids (e.g.,

aldosterone, deoxycorticosterone), with 21 carbon atoms, and weak

androgens (e.g., dehydroepiandrosterone), with 19 carbon atoms (see

Table 1-1). Minor amounts of progestational and estrogenic steriods are

also secreted. The predominant glucocorticoid is cortisol in some

species, e.g., hamster, sheep, and primates, but it is corticosterone in

others, e.g., rat, mouse, and rabbit (Seth, 1969). Although cortisol is

the predominant circulating glucocorticoid in primates, corticosterone

may comprise a significant or even major fraction of the glucocorticoid

bound in brain cell nuclei (Turner, Smith and Carroll, 1979).

The enzymatic pathways for the synthesis of adrenal steroids from

cholesterol, which the adrenals may take up from blood or synthesize

from acetate, are well known (e.g., Fregly and Luttge, 1982). Briefly,

cholesterol undergoes a series of hydroxylations, catalyzed by the mito-

chondrial desmolase enzyme complex, leading to pregnenolone, which is

then converted to progesterone by the actions of the microsomal enzymes

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38-hydroxy steroid dehydrogenase and 3-ketosteroid isomerase. Some

progesterone is converted to 17a-OH-progesterone by the cytoplasmic 17

a-hydroxylase. Progesterone and 170a-OH-progesterone are converted by a

cytoplasmic C-21 hydroxylase to 11-deoxycorticosterone and 11-deoxy-

cortisol, respectively. A mitochondrial 11a- hydroxylase enzyme finally

converts 11-deoxycorticosterone and 11-deoxycortisol to the finished

glucocorticoid products corticosterone and cortisol. The adrenal cortex

does not store its secretions, but it does store an abundance of the

precursor cholesterol in lipid droplets. The adrenal stimulators

adrenocorticotropic hormone (ACTH) and angiotensin II, by processes

involving cyclic AMP, accelerate the conversion of cholesterol to

pregnenolone, the rate-limiting step in adrenal steroidogenesis. This

conversion is rapidly followed by the synthesis and secretion into the

circulation of the active corticosteroids.

Glucocorticoids are so named for their role in regulating glucose

metabolism. They act directly on most tissues, and indirectly influence

all tissues. An early effect of glucocorticoids is the inhibition of

glucose uptake by adipose tissue, skin, fibroblasts, and lymphoid

tissue. There is a decrease in macromolecular (protein, lipid, and

nucleic acid) synthesis and an increase in protein degradation in these

tissues and in muscle. There is an increase in lipolysis in fat cells,

and a depletion of glycogen in muscle. These catabolic actions result

in the release of amino acids, free fatty acids, glycerol, and

nucleotides into the circulation. In contrast, the actions of

glucocorticoids in the liver are primarily anabolic, resulting in a

general increase in RNA and protein synthesis, as well as the specific

induction of a number of enzymes. The amino acids derived from

peripheral catabolism are substrates for increased glucose formation

(gluconeogenesis) in liver, and to a lesser extent in the kidney.

Glycogen accumulates in liver, and blood glucose levels tend to rise.

The latter change induces a compensatory increase in insulin, which

counteracts many of the glucocorticoid effects.

Certain tissues are spared from the catabolic actions of

glucocorticoids brain, red blood cells, heart, liver, kidney. These

tissues, perhaps more essential than others, may rather enjoy the

additional circulating glucose diverted from elsewhere or produced by

gluconeogenesis. The diverse actions of glucocorticoids may thus make

teleological sense as a coordinated mechanism for making glucose

maximally available to certain essential tissues during and immediately

following periods of environmental challenge or stress.

Glucocorticoids also have many diverse effects not related to

glucose metabolism. They act at multiple sites to suppress inflammatory

and allergic reactions, including inhibition of extravasation and

migration of leucocytes, edema, and phagocytosis, decrease in the

circulating lymphocytes and eosinophils, involution of the thymus, lymph

nodes and spleen, and decrease in antibody production. The lungs

respond to glucocorticoids with enhanced catecholamine sensitivity,

bronchodilation, and decreased vascular resistance. There may be

anabolic effects in the development of some organs, for example the

induction of surfactant secretion in the fetal lung. Glucocorticoid

actions have been reviewed comprehensively by Baxter and Rousseau

(1979). The effects of corticosteroids on the nervous system and

behavior have also been reviewed recently (Bohus, de Kloet and Veldhuis,

1982; Rees and Gray, 1983).

Regulation of Glucocorticoid Secretion

Glucocorticoids are released from the adrenals in response to ACTH,

which is in turn secreted by cells of the anterior pituitary in response

to corticotropin releasing hormone (CRH), of hypothalamic and perhaps

extrahypothalamic origin (Sayers and Portanova, 1975; Vale, Spiess,

Rivier and Rivier, 1981). Three factors are known to control

glucocorticoid secretion: stress, rhythms, and corticosteroid feedback.

The pituitary-adrenal system responds within a few minutes to a

wide variety of noxious stimuli, termed stressors. The "general

adaptation syndrome" (Selye, 1950) produced by this pituitary-adrenal

stress response is both nonspecific with respect to a variety of stimuli

and relatively slow to develop, in contrast to the autonomic responses

which can produce relatively stimulus-specific and extremely rapid

adaptive changes in many organ systems. Although a distinction is

frequently drawn between "physiological" stressors (e.g., trauma,

hemorrhage, hypoxia, infection, ether, cold, heat, fasting), and less

noxious "psychological" stressors (e.g., immobilization, handling, mild

electric shock, loud noise, and situations that produce fear, guilt,

anxiety, or frustration), this distinction is often blurred in practice.

When pain, discomfort, and emotional reactions were avoided carefully,

several "physiological stressors" (fasting, heat, exercise) no longer

elevated corticosteroid levels. This finding led Mason (1971) to

suggest that the essential property of all stressors may be the ability

to elicit a behavioral response of emotional arousal or hyperalerting,

which prepares the organism for flight, struggle, or strenuous exertion

in a threatening situation.

The circadian rhythm in glucocorticoid secretion appears to be

entrained by the organism's rest-activity cycle. The secretary peak

occurs just before the active phase, even when the relation of activity

to the lighting cycle is reversed, as in humans working on night shifts,

or in rats fed only during the day (e.g., Morimoto, Arisue and Yamamura,

1977). In addition to the circadian rhythm, higher frequency

oscillations in corticosteroid secretion have been revealed by frequent

sampling (every 20 minutes). Recent evidence (Holaday, Martinez and

Natelson, 1977) has shown that this pulsatile secretion, previously

regarded as "episodic," actually follows an ultradian rhythm (frequency

greater than one cycle in 24 hours), having a predominant periodicity of

about 90 minutes and other components harmonically related to the

circadian rhythm. These rhythmic fluctuations in plasma cortisol were

synchronized among 8 isolated, restrained, undisturbed monkeys,

indicating their entrainment by environmental factors such as the

feeding or lighting schedule. The unexpected finding that ultradian

cortisol rhythms were not disrupted by infusion of supramaximal ACTH

challenges the classic concept that periodic bursts of corticosteroid

output depend entirely on the immediately preceding release of ACTH.

The physiological function of corticosteroid rhythms is unknown.

ACTH secretion is regulated by two temporally distinct negative
feedback mechanisms, a rate-sensitive fast feedback (FFB), which occurs

5 to 30 minutes after steroid administration, and a proportional,

delayed feedback (DFB), which appears after one or more hours (Dallman

and Yates, 1969; Jones, Hillhouse and Burden, 1977). These two phases

are separated by a "silent" period, during which negative feedback is

not observed. Differences in the steroid structure-activity

relationships for FFB and DFB indicate that different receptor

mechanisms may be involved.

There is evidence that corticosteroid feedback actions may be

exerted at multiple sites. The sensitivity of ACTH-secreting pituitary

cells to inhibition by physiological doses of natural and synthetic

corticosteroids has been established clearly by studies in which the

possibility of hypothalamic involvement was circumvented and by studies

of pituitary cells in vitro (Kendall, 1971; Jones et al., 1977).

Hypothalamic tissue in vitro also showed a FFB effect of corticosterone,

due to decreased release of CRH (Jones et al., 1977). A series of

studies (e.g., Feldman and Conforti, 1980) demonstrated that posterior

hypothalamic deafferentation, dorsal fornix section, or dorsal hippo-

campectomy reduced the inhibitory DFB effect of the synthetic

fluorinated glucocorticoid, dexamethasone on both basal and ether

stress-induced corticosterone secretion in the rat. These findings

suggest that the dorsal hippocampus also participates in the feedback

regulation of pituitary-adrenal function. Furthermore, several studies

(e.g., Carsia and Malamed, 1979) have indicated a direct inhibitory

effect of corticosterone and cortisol on ACTH-induced corticoster-

oidogenesis, suggesting that the self-suppression of adrenocortical

cells by end products may provide an additional fine adjustment of

steroidogenesis. What remains to be determined is the relative

physiological importance of glucocorticoid feedback at the various

sites--anterior pituitary, hypothalamus, extrahypothalamic structures,

and the adrenal cortex itself. Although it appears that dexamethasone

may act primarily at the pituitary level (Sakakura, Yoshioka, Kobayashi

and Takebe, 1981), the pituitary may be less responsive to natural

glucocorticoids. One explanation for this difference is that anterior

pituitary cytosol contains a transcortin-like macromolecule, which like

plasma transcortin binds corticosterone but not dexamethasone and has

negligible affinity for DNA-associated acceptor sites in the nucleus

(Koch, Lutz, Briaud and Mialhe, 1976). Thus, while the transcortin-like

binders cannot interfere with the action of dexamethasone, they can, by

competing with the "true" cytoplasmic glucocorticoid receptors, reduce

the amount of corticosterone able to interact with these receptors.

Such a mechanism might insure that under non-stress conditions the

pituitary glucocorticoid receptors would not be occupied, thus allowing

them to function only in response to much higher, stress-induced levels

of corticosterone.

Glucocorticoids may also act directly upon the hypothalamus and

pituitary to modulate the production or secretion of hormones other than

CRH and ACTH, such as TRH, TSH, and GH (e.g., Burger and Patel, 1977).

The "compensatory" hypertrophy of the remaining adrenal following

unilateral adrenalectomy was long considered a result of decreased

corticosteroid feedback. However, compensatory adrenal growth was

recently shown to be neurally rather than hormonally mediated, dependent

on reciprocal neural connections between the hypothalamus and adrenal

(Dallman, Engeland and Shinsako, 1976).

While much progress has been made in elucidating individual factors

influencing pituitary-adrenal activity (neural input, feedback, stress,

rhythms), there is still a significant gap in our understanding of how

these isolated components function together in the intact organism.

Overview of Corticosteroid Mechanisms

Many of the effects of corticosteroids are believed to be mediated

by interactions of the steroid molecules with steroid-specific

cytoplasmic macromolecular receptors which concentrate as hormone-

receptor complexes in the target cell nuclei, where they initiate the

alterations in specific RNA and protein metabolism that then lead to the

ultimate physiological, neuroendocrine and behavioral effects. Other

less well-understood steroid effects may result from direct interactions

of the steroid molecule with components of target cell membranes. Some

established and hypothetical events in corticosteroid action are

represented in Fig. 1-1.

Although the natural adrenal steroids are soluble enough to be

transported unassisted in plasma, about 75% of the circulating

glucocorticoid (cortisol or corticosterone) is bound to an a-globulin

called transcortin or corticosteroid-binding globulin (CBG), about 15%

is bound to serum albumin, and only about 10% is free (Westphal, 1975).

Plasma transcortin does not seem to be necessary in any way for the

biological activity of the steroids; current evidence supports the dogma

that only the free steroid in the plasma can exert physiological action.

Although the brain capillary transit time is too short in relation to

the dissociation rate or half-life (t11/2) of the CBG-glucocorticoid

complex to allow the uptake of CBG-bound cortisol and corticosterone,

the albumin-bound corticosteroids dissociate rapidly enough to be

available for transport through the blood-brain barrier (Pardridge,

1981). (Liver capillary transit time and membrane permeability are








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Transcortin does reduce the amplitude of free glucocorticoid variations

in response to large rhythmic or stress-induced changes in adrenal

output. The potent synthetic fluorinated glucocorticoids (dexamethasone

and triamcinolone), as well as the natural mineralocorticoid

aldosterone, are only very weakly bound by transcortin. Since the

natural glucocorticoids can significantly occupy mineralocorticoid

receptors when present in high concentrations, and since the total

concentration of plasma glucocorticoids is much greater than the normal

concentration of aldosterone, the bufferingg" effect of glucocorticoid

binding by transcortin is apparently necessary to prevent the saturation

of mineralocorticoid receptors by glucocorticoids (Funder, Feldman and

Edelman 1973). It is not known why the glucocorticoid/mineralocorticoid

ratio is so large, requiring this rather peculiar mechanism to confer

specificity of hormone action.

It is often assumed that target cell membranes do not present a

barrier to free lipophilic steroids, and that their passage into the

target cell is governed solely by simple diffusion. Recent studies

have, however, demonstrated for at least several different cell types

(isolated rat liver and pituitary cells and ACTH-secreting mouse

pituitary tumor cells) that glucocorticoid passage through the plasma

membrane may involve carrier-mediated transport in addition to simple

diffusion (e.g., Harrison, Fairfield and Orth, 1977; Koch, Sakly and

Lutz-Bucher, 1981). It is not yet clear how general this phenomenon may

be in terms of other target cells and hormones.

It has been observed that some steroids may have several different

actions in the nervous system that are mediated independently by their

different metabolites, but there is no evidence that the metabolites of

the natural glucocorticoids corticosterone and cortisol are functionally

important and possess their own non-enzymatic high-affinity binding

sites in brain or pituitary. Following in vivo injections of

[3H]corticosterone the radioactivity extracted with methylene chloride

from the nuclear fraction of rat brain was found to consist of

approximately 90% authentic (isochromatographic) corticosterone (McEwen,

Magnus and Wallach, 1972). Further investigation of glucocorticoid

metabolism in brain tissue is required, however, since acid metabolites

of cortisol possessing different, specific biological activities (as

enzyme inducers) have recently been found in rat liver (Voigt and

Sekeris, 1980).

The cytoplasmic steroid receptors are thermolabile proteins with

stereo-specific binding sites. Before the steroid can bind to the

receptor with high affinity (Kd 10 9M), the corticosteroid receptor

protein ("aporeceptor") may be required to undergo an energy-

dependent transformation (possibly a phosphorylation) in order that the

potential binding site may be "switched on" to the appropriate

conformation for interaction with the steroid. A rapid "switching-off"

or down-regulation of the steroid-binding sites (possibly mediated by a

phosphatase) has also been observed, suggesting that cells may utilize

an internal phosphorylation-dephosphorylation feedback cycle to modulate

physiological responses by regulating the amount of receptor capable of

interacting with free steroid. Thus, under many circumstances a

substantial pool of latent or "cryptic" aporeceptors may be present in

many target cells. This dynamic regulation of the hormone binding site

itself has only recently been explored in cells derived from a few

peripheral tissues (e.g., Sando, Hammond, Stratford and Pratt, 1979),

and is an intriguing area for brain studies (e.g., Luttge, Densmore and

Gray, 1982). The number of receptors capable of interacting with free

steroid may be subject to additional regulation by certain proteolytic

enzymes that can disconnect the steroid binding site from the region of

the receptor molecule that contains the nuclear binding site, resulting

in non-functional steroid-binding fragments termed "mero-receptors"

(e.g., Niu, Neal, Pierce and Sherman, 1981).

After binding, the non-covalent cytoplasmic steroid-receptor

complex must next undergo a transformation that results in the

development of a high affinity for certain nuclear components associated

with the genome. This process of "activation" probably involves a

steroid-induced conformational change in the acidic receptor protein

which brings a positively-charged "acceptor" binding site to the surface

of the molecule (e.g., Barnett, Schmidt and Litwack, 1980). The nuclear

"acceptors" to which the activated receptor complexes now bind are

unidentified components of chromatin (possibly non-histone proteins)

that possess high-affinity and, to varying extents, tissue- and

receptor-specific binding domains. Although the acceptors are probably

not merely specific DNA nucleotide sequences, they do appear to regulate

the interactions of the steroid-receptor complexes with the DNA (e.g.,

Bugany and Beato, 1977; Cidlowski and Munck, 1980).

Following the formation of the ternary steroid-receptor-acceptor

complex the chromatin structure becomes altered in subtle ways that lead

to changes in the rates of transcription of specific mRNA species (e.g.,

Johnson, Lan and Baxter, 1979). These specific mRNA molecules are then

translated to produce the proteins that mediate the hormone-induced

physiological responses. Fig. 1-1 indicates that the proteins whose

rates of synthesis are modulated by the steroid may encompass a broad

spectrum of cellular functions: additional steroid receptors;

components or modulators of membrane transport mechanisms; enzymes of

intermediary metabolism; protein kinases, components of peptide hormone-

or neurotransmitter-sensitive receptor-adenylate cyclase complexes, and

other modulators whose altered synthesis may contribute to the so-called
"permissive" effects of steroids; and even specific proteins required

for some catabolic steroid effects (e.g., thymus involution) are all

examples of proteins that may be regulated to produce the ultimate

steroid response (e.g., Baxter and Rousseau, 1979).

After exerting their genomic effect, the receptors are either

degraded or recycled back to their unbound, nonactivated cytoplasmic

form by a process that may be linked to cell metabolism by a requirement

for ATP (e.g., Aronow, 1978). The nuclear "processing" of the

receptors, the "off-reaction," and receptor recycling are understood

very poorly; it is possible that some steroid dissociation may occur

before the receptors are released from their chromatin acceptor sites,

and there are hints that the process may be coupled to the proposed

cyclic transformations of the steroid binding sites. The released

steroid molecules may either re-enter the receptor cycle or diffuse out

of the cell into the circulation to enter another cell or to be

metabolized and excreted.

Fig. 1-1 also indicates several largely unexplored potential

mechanisms of steroid influence on cellular function that do not

directly involve events at the genome. The suggestions that

corticosteroid-receptor complexes may directly exert translational

(e.g., Kulkarni, Netrawali, Pradhan and Sreenivasan, 1976) or

post-translational (e.g., Trajkovic, Ribarac-Stepic and Kanazir, 1974)

control over specific protein synthesis or that they may directly

regulate membrane transport mechanisms are hypothetical at present. The

suggestion that some glucocorticoid effects may result from the

interaction of free steroids with intracellular membrane systems is also

hypothetical (for review, see Nelson, 1980); glucocorticoids are known

to modify some membrane properties, but no functional consequences of

such changes are yet well established. Free steroids may also exert

important effects at the cell plasma membrane; these include rapid,

steroid-specific changes in the firing rates of some neurons (for

review, see Feldman, 1981; McEwen, David, Parsons and Pfaff, 1979).

Since a steroid's affinity for the cytoplasmic receptors does not

adequately predict the magnitude of the physiological response, it is

necessary to classify all steroids into one of four categories on the

basis of their physiological effectiveness (Rousseau, Baxter and

Tomkins, 1972). Optimal inducers are steroids that all produce the same

maximal response when present in saturating amounts. For example,

aldosterone will produce as great a glucocorticoid response as

dexamethasone (in many tissues) when present in very high concen-

trations. Suboptimal inducers elicit smaller, less-than-maximal

responses even when present in saturating concentrations; 11-deoxy-

corticosterone is an example of a suboptimal glucocorticoid. Anti-

inducers or antihormones produce no typical physiological responses by

themselves, but rather behave as competitive inhibitors of the active

hormones; progesterone and cortexolone (11-deoxycortisol) are

antiglucocorticoids. Finally, inactive steroids do not bind to the

specific steroid receptors at all. It should be stressed that the

classification of a particular steroid must refer to a specific,

measurable response and may vary among species and from one tissue to


It is believed that different ligands can promote different degrees

of conformational change, leading to the formation of steroid-receptor

complexes with different states of "partial activation" (different

affinities for nuclear acceptor components). Munck and Leung (1977)

have proposed that each relevant steroid or class of steroids binds to

the receptor and promotes a subsequent conformational change that

differs in degree from that produced by other steroids. Optimal

inducers produce the highest degrees of activation, and anti-inducers

either do not promote activation or promote minimal, ineffective

increases in affinity for nuclear acceptors. Suboptimal inducers

produce intermediate states of activation. Other models of agonist and

antagonist interactions with the glucocorticoid receptor are also under

active consideration (Rousseau and Baxter, 1979; Sherman 1979).

Anatomical Distribution of Corticosteroid Binding

Neuronal nuclear concentration of [3H]corticosterone has been

demonstrated by autoradiography in structures of the limbic system,

brain stem, and spinal cord, but not in the hypothalamus (McEwen,

Gerlach and Micco, 1975; Stumpf and Sar, 1975; Warembourg, 1973). In

adrenalectomized rats, nuclear accumulation of [3H]corticosterone was

most intense in structures related to the hippocampus, including the

postcommissural hippocampus, dentate gyrus, induseum griseum

(supracallosal hippocampus), anterior (precommissural) hippocampus, and
subiculum. Strong nuclear labeling was also seen in the lateral septum,
amygdala (cortical, central, and basomedial nuclei), and the piriform,

entorhinal, suprarhinal, and cingulate cortices. Additional labeling,
although weaker and less frequent, was present in the anterior olfactory

nucleus, medial amygdaloid nucleus, habenula, red nucleus, and
subfornical organ. Motor neurons in cranial nerve nuclei and spinal

cord were strongly labeled, and some glial cells were weakly labeled

(Stumpf and Sar, 1979). The pattern of in vivo uptake of [3H]cor-
ticosterone determined by autoradiography (highest in hippocampus and

septum, followed by amygdala, cortex and hypothalamus) agrees well with
the anatomical distribution of cytoplasmic [ 3H]corticosterone binding
sites (McEwen et al., 1972; Grosser, Stevens and Reed, 1973); and with

the patterns of [3H]corticosterone binding found in purified nuclei both
following [ 3H]hormone injections in vivo (McEwen, Weiss and Schwartz,
1970) and after incubation of brain slices with [ 3H]corticosterone in

vitro (McEwen and Wallach, 1973; de Kloet, Wallach and McEwen, 1975).
Corticosterone target cells have been observed in the anterior pituitary
of the rat (Warembourg, 1973) and Pekin duck (Rhees, Abel and Haack,
1972), but not the rhesus monkey (Pfaff, Gerlach, McEwen, Ferin, Carmel
and Zimmerman, 1976).

The distribution of target cells for [3H]cortisol in the brains of
adrenalectomized rats was identical to that for [ 3H]corticosterone
(Stumpf and Sar, 1973). Nuclear binding sites for cortisol appeared to
be saturated by endogenous corticosteroids in adrenally intact mice
(Schwartz, Tator and Hoffman, 1972) and guinea pigs (Warembourg, 1973).

The synthetic glucocorticoid dexamethasone displayed a surprisingly

different pattern of uptake from that of natural glucocorticoids.

Whereas corticosterone and cortisol were concentrated strongly by

neurons, [3H]dexamethasone was accumulated weakly by all types of cells

in the brain (Rees, Stumpf and Sar, 1975; Rhees, Grosser and Stevens,

1975). The labeling was heaviest in epithelial cells of the choroid

plexus and ventricular lumen, and was also observed in vascular

endothelial cells, glia, meninges, ependyma, circumventricular organs,

and in neurons in areas near the third ventricle (preoptic area,

hypothalamus, thalamus) and lateral ventricle (septum, caudate,

amygdala). In contrast to [ 3H]corticosterone, [3H]dexamethasone was

concentrated only very weakly by hippocampal neurons. Furthermore, the

presence of endogenous adrenal hormones in intact rats did not affect

the pattern of [3H]dexamethasone localization (Rhees et al., 1975). In

the pituitary, dexamethasone was concentrated heavily by cells in the

pars distalis (particularly corticotrophs) and pars nervosa, but not

pars intermedia (Rees, Stumpf, Sar and Petrusz, 1977). The autoradio-

graphic data were consistent with the pattern of in vivo uptake of

[3H]dexamethasone revealed by direct measurements of tissue radio-

activity (de Kloet, van der Vies, and de Wied, 1974).

The strikingly different patterns of distribution of these natural

and synthetic glucocorticoids have been interpreted as evidence for the

existence of at least two classes of glucocorticoid receptors differing

in their distribution and steroid specificity. However, some of the

findings may be explained without reference to the concept of receptor

heterogeneity. There are large differences in the permeability of the

blood-brain barrier to different steroids (Pardridge and Mietus, 1979).

Dexamethasone appears to enter the brain more slowly than corti-

costerone; time course studies showed that maximal binding in hippo-

campal cell nuclei occurred one hour after injection of

[3H]corticosterone, but two hours after [ 3H]dexamethasone (de Kloet et

al., 1975). Similarly, the cellular accumulation of [3H]dexamethasone

in the hippocampus seen autoradiographically three hours after injection

was not yet evident at 30 minutes (Rees et al., 1975). The greater

blood-brain barrier to dexamethasone may also explain some discrepancies

between the patterns of nuclear binding of glucocorticoids obtained in

vivo and in slices incubated in vitro. Although the in vivo nuclear

binding of [3 H]corticosterone in hippocampus was more than ten times

that of [3H]dexamethasone, this difference was dramatically reduced

(corticosterone: dexamethasone ratio of 1.2 1.5) when slices of

hippocampus were incubated with the steroids in vitro (de Kloet et al.,

1975; McEwen, de Kloet and Wallach, 1976). It is possible that the

small but significant remaining differences in nuclear binding observed

in the in vitro slice experiments (i.e. greater binding of corti-

costerone in hippocampus and of dexamethasone in hypothalamus and

pituitary) may have resulted from factors other than glucocorticoid

receptor heterogeneity: for example, differences in the rates of

cellular penetration of the two steroids which may persist in the slice

experiments, and differences in the relative abilities of the two

steroids to promote activation and nuclear binding of the steroid-

receptor complexes (e.g., Svec and Harrison, 1979).

Characterization of Soluble Corticosteroid
Receptors in Brain
The natural glucocorticoids, corticosterone and cortisol; the

synthetic glucocorticoids triamcinolone acetonide (TA) and

dexamethasone; and the natural mineralocorticoids, aldosterone and

11-deoxycorticosterone (DOC), bind to steroid-specific, saturable brain

cytosol components believed to be the physiological transducer molecules

or "receptors." One goal of receptor research is to identify the

different classes or categories of adrenal steroid action in the brain

and to study individually the receptors mediating these actions. The

categories "glucocorticoid" and "mineralocorticoid" are defined by

distinguishable peripheral physiological effects and steroid specific-

ities; this distinction may be meaningful in the nervous system, but it

should not be assumed a priori that brain steroid effects and speci-

ficities closely correspond to those of other organ systems.

In comparison with the corticosteroid receptors found in other

tissues, the few reported physicochemical properties of brain receptors

are generally unremarkable. They have been distinguished from those of

transcortin by a number of criteria; unlike transcortin, the brain

cytoplasmic glucocorticoid binding protein was found to bind the

synthetic steroids dexamethasone and TA with high affinity and to

possess sulfhydryl groups whose modification led to the loss of

functional steroid binding sites (e.g., Chytil and Toft, 1972; McEwen

and Wallach, 1973).

The resolution of the different classes of brain corticosteroid

receptors is confusing because it involves two distinct but related

issues: the possible existence of separate binding sites for natural

and synthetic glucocorticoids; and the distinction between

glucocorticoid and mineralocorticoid binding sites. The principal

technique for defining distinct binding sites is the in vitro

measurement of steroid specificity in competition experiments. Oddly,

the actual affinities of different competing steroids for brain cytosol

[3H]steroid binding sites have seldom been reported. Specificity data

have typically been reported only as a rank ordering of the abilities of

different steroids to compete for the binding of a given [ 3H]steroid.

Although both natural and synthetic agonists were bound with

similar high affinities by brain cytosol (Chytil and Toft, 1972),

dexamethasone did not reduce the binding of [ 3H]corticosterone in whole

brain cytosol to the extent that was predicted from its physiological

potency as a peripheral glucocorticoid (Grosser et al., 1973; McEwen and

Wallach, 1973). In most studies, corticosterone and dexamethasone were

equally effective in competition for [3 H]dexamethasone and [3H]TA

binding (e.g., Chytil and Toft, 1972; Stevens, Reed and Grosser, 1975;

de Kloet and McEwen, 1976).

Comparative measurements of the total cytosol binding capacity for

corticosterone and dexamethasone have been reported. Because a number

of poorly understood variables (such as the composition of the

incubation buffer, the presence or absence of phosphatase inhibitors,

the time elapsed between tissue homogenization and cytosol labeling with

[3H]steroid, etc.) have not yet been fully explored or controlled,
published estimates of apparent binding capacity (Bmax ) are often in
conflict. The discovery by de Kloet et al. (1975) that the spontaneous

loss of [3H]dexamethasone binding capacity from unlabeled cytosol was

more rapid than the loss of [ 3H]corticosterone binding sites, stimulated
experiments in which tissues were homogenized in the presence of the

[3 H]steroids. With this alteration in methodology, binding capacities

for [ 3H]dexamethasone and [3 H]corticosterone in hippocampal cytosol were

found to be equal, and hypothalamic cytosol had an even slightly higher

capacity for [ 3H]dexamethasone than for [ 3H]corticosterone (e.g., de
Kloet et al., 1975; Turner and McEwen, 1980).

High affinity mineralocorticoid (type I) binding sites, which occur

in significant concentrations principally in the hippocampus and

associated structures, have been studied in rat brain cytosol (Anderson

and Fanestil, 1976; Moguilewsky and Raynaud, 1980). The mineralo-

corticoid receptors have high affinity for aldosterone and DOC and,

surprisingly, an almost equally high affinity for progesterone. Since

[3H]aldosterone, [3H]corticosterone and [3H]dexamethasone all bind (with
different affinities) to both glucocorticoid and mineralocorticoid brain

receptor sites, it has been most productive to study the binding of

[3H]aldosterone in the presence of an excess of the "pure" gluco-
corticoid R26988 (Moguilewsky and Raynaud, 1980). Although concen-

trations of glucocorticoid and mineralocorticoid receptor sites were
comparable in hippocampal cytosol, the concentration of high-affinity

mineralocorticoid binding sites was much lower than the concentration of

glucocorticoid binding sites in whole brain.

Although the discrepancies between in vivo and in vitro (brain
slice) nuclear binding of [3H]corticosterone and [3H]dexamethasone can
be explained largely without reference to the possible heterogeneity of
unbound glucocorticoid receptors, several observations (such as the
relatively poor ability of dexamethasone to compete for [3H]corti-
costerone binding sites) have suggested that natural and synthetic
glucocorticoids may bind to somewhat different receptor populations.

When cytosol samples were chromatographed on DEAE-cellulose ion-exchange

columns, complexes formed with [3H]corticosterone and [3H]dexamethasone
were eluted as multiple peaks, and the proportion of bound [3H]steroid
in each of the two major peaks differed for the two glucocorticoids (de
Kloet and McEwen, 1976). Although it is unlikely that the two major

peaks of both hippocampal [3 H]dexamethasone and [3H]corticosterone
binding merely represent different pools of activated and nonactivated
receptors, it is quite possible that they are distinct proteolytic
fragments (created in vitro) of a single larger intact glucocorticoid
receptor. Affinity chromatography of rat brain cytosol on columns of
immobilized deoxycorticosterone (DOC) hemisuccinate (subsequently eluted
with [3H]corticosterone) selectively purified one of the two major
[3H]corticosterone binding peaks resolved by ion exchange chromatography
(de Kloet and Burbach, 1978).

Apparent receptor heterogeneity was also observed in rat brain (and
pituitary) cytosol following isoelectric focussing of labeled samples on
polyacrylamide gels (MacLusky, Turner and McEwen, 1977). In brain
cytosol three major specific [3 Hcorticosterone binding peaks were
resolved; these had isoelectric points (pIs) of approximately 6.8, 5.9
and 4.3. When [3H]dexamethasone was the ligand only two peaks were
found (the peak at pI 4.3 was absent). Furthermore, the relative sizes
of the two remaining peaks were different for the two ligands. Wrange
(1979) has suggested that the apparent receptor heterogeneity observed
by MacLusky et al. (1977) may have resulted from proteolytic artifacts
and that the brain cytosol [3H]cortiscosterone binding peak at pI 4.3
(reported by the same workers) can probably be attributed to residual
transcortin (CBG) remaining in the tissue following incomplete

perfusion. Wrange found only a single peak of radioactivity (at pI 6.1)

when rats were extensively perfused and hippocampal cytosol samples

labeled with either [ 3H]corticosterone or [ 3H]dexamethasone were

analyzed. However, it was not possible to conclude that CBG or a class

of CBG-like binding sites was definitely not present, since free steroid

was removed from the samples prior to the relatively long focussing

procedure, which would have both allowed extensive dissociation of

steroid from the CBG and eventually denatured the steroid binding sites

as they entered the region of low pH. Wrange also found that limited

tryptic digestion of hippocampal cytosol labelled with either

[3 H]corticosterone or [3H]dexamethasone produced two peaks of bound

radioactivity having pI values of 6.0 and 6.4. These pI values are

close enough to those reported by MacLusky et al. (1977) to suggest that

proteolytic fragments of a single molecule may have been responsible for

the observed heterogeneity. The relative sizes of the two trypsin-

induced peaks were different when [3H]dexamethasone was substituted for

[3H]corticosterone; this situation may have resulted either from the

possession of slightly different trypsin substrate characteristics by

the receptor complexes formed with the different steroids or from

different rates of dissociation of [ 3H]corticosterone from the two

trypsin-induced receptor fragments.

The autoradiographic data reviewed above have led to the suggestion
that neurons contain glucocorticoid receptors that preferentially bind

corticosterone and cortisol, whereas glial cells contain glucocorticoid

receptors having higher affinity for dexamethasone and TA (e.g., McEwen

et al., 1979). There is, however, very little evidence to support this

dichotomy. Although dexamethasone is a potent inducer of glycerol-

phosphate dehydrogenase (GPDH) in cultured glial tumor cells, and

cytosol prepared from these tumor cells and from optic nerve

oligodendrocytes contains high-affinity [3H]dexamethasone binding sites,

glial cells also respond to natural glucocorticoids (e.g., Breen,

McGinnis and de Vellis, 1978; Cotman, Scheff and Benardo, 1978).

Furthermore, there is no evidence (e.g., Clayton, Grosser and Stevens,

1977) that brain [ 3H]dexamethasone binding capacity increases faster

than [3H]corticosterone binding capacity during the period of rapid

glial growth associated with myelination. Glial tumor cells were found

to contain only one glucocorticoid receptor with a pI of 5.9,

corresponding to the molecular species that bound [3H]dexamethasone

preferentially in the rat brain (MacLusky, unpublished, cited by McEwen

et al., 1979). This observation cannot, however, be considered strong

evidence for a neuronal-glial receptor dichotomy, since Wrange (1979)

reported a similar isoelectric binding profile containing only a single

radioactive peak in hippocampal cytosol from perfused animals. It is

possible that different concentrations of proteolytic enzymes in the

cytosol samples prepared from brain tissue and from cultured glial cells

could explain the differences between the [3H]glucocorticoid binding

profiles observed by MacLusky and colleagues in these different

preparations. The demonstration that [3H]dexamethasone binding sites

disappear from hippocampal cytosol (in the absence of steroid) more

rapidly than [ 3H]corticosterone binding sites (de Kloet et al., 1975)

may result from the gradual alteration of a single initial population of

steroid binding sites by enzymatic processes that are triggered upon

cell disruption and that proceed rapidly in the absence of protective

steroid ligands. This apparent differential loss of free binding sites

for [ 3H]dexamethasone and [3 H]corticosterone may also result, at least

in part, from the presence of a population of relatively more stable CBG

or CBG-like binding sites in the hippocampal cytosol. Clarification of

this complex issue must await the purification and comparison of both

intact unbound receptors and steroid-receptor complexes.

Physiological Regulation of Corticosteroid Receptors

The ontogeny of the capacity of rat brain cytosol to bind both

natural and synthetic glucocorticoids has been studied. Binding of

[3H]dexamethasone was very low immediately after birth, but it reached

the adult level sooner than [3H]corticosterone binding, which was higher

than that of [ 3H]dexamethasone immediately after birth. Adult levels of

[3H]corticosterone binding were similar to those of [ 3H]dexamethasone in

both hippocampal and hypothalamic cytosols (Olpe and McEwen, 1976).

Turner (1978) found that the amount of [ 3H]corticosterone bound by

hippocampal nuclei in adrenalectomized rat pups injected with steroid in

vivo was very small in comparison with adult levels. Furthermore, the

nuclear binding of [3H]corticosterone by hippocampal pyramidal and

dentate granule cells as determined by autoradiography was correlated

directly with neuronal age; in the neonatal hippocampus the oldest cells

revealed the heaviest labeling, whereas newly arrived cells showed

little nuclear retention of steroid. Thus, although the aporeceptor
proteins may appear much earlier in development, the production of

receptors with functional binding sites and the potential for activation

to the nucleophilic state may occur relatively late in the differ-

entiation of these neurons.

An age-related decline in corticosterone receptors has been

reported in mouse hippocampus (Finch and Latham, 1974) and in rat

cerebral cortex (Roth, 1974). Evidence suggests that senescent

intracellular biochemical changes rather than cellular losses are

responsible for the decline in cortical receptors (Roth, 1976).

The concentration of intracellular corticosteroid binding sites

rises in response to steroid deprivation. Adrenalectomy caused a

two-stage increase in the nuclear binding of [ 3H]corticosterone by

hippocampus in vivo and in vitro (McEwen, Wallach and Magnus, 1974) and

increased glucocorticoid cytosol receptor concentrations (Stevens et

al., 1975; Olpe and McEwen, 1976). The apparent receptor content

increased rapidly for the first 2 hours after adrenalectomy and then

remained at a plateau for about 12 hrs; the second, slower increase

began between 12 and 18 hours after adrenalectomy and approached a new

plateau after about 3 days. The first, rapid change, which parallels

the decline in plasma corticosterone, certainly represents the

disappearance of endogenous corticosterone from brain binding sites and

may also reflect the "switching-on" of the steroid binding sites of

receptors. The interesting long-term increase results from either the

synthesis of new receptors on the "switching-on" of previously

unobservable "cryptic" aporeceptors.

Both the concentration of endogenous corticosteroids and the

occupancy of corticosteroid receptors in the brain vary with changes in

plasma steroid levels. Brain glucocorticoid concentrations, which were

intermediate between free and total plasma concentrations and therefore

possibly equal to the plasma glucocorticoid concentration available for

brain uptake (the free + albumin-bound or "BBB-transportable"

concentration) (Carroll, Heath, and Jarrett, 1975), were found to

fluctuate in parallel with both basal circadian and stress-induced

changes in the plasma steroid concentrations (Butte, Kakihana and Noble,

1976; Carroll et al., 1975). Furthermore, the diurnal and stress-

induced increases in plasma corticosterone decreased the in vitro

cytosol binding of [3H]corticosterone in all brain regions examined

(Stevens, Reed, Erickson and Grosser, 1973). In most brain regions of

unstressed animals, glucocorticoid receptor occupancy varies between

about 50% at the diurnal trough and approximately 80% at the peak

(Stevens et al., 1973; McEwen et al., 1974; Turner, Smith and Carroll,

1978a,b). In contrast to other brain regions, the preoptic and septal

areas exhibited a high level of receptor occupancy even during the

morning corticosterone minimum, and no increase at the evening peak

(Turner et al., 1978a,b). However, all brain regions showed a circadian

variation in the total concentration of cytosol [3H]corticosterone

binding sites. Furthermore, the same dose of [ 3H]corticosterone

injected into adrenalectomized mice produced higher hippocampal steroid

concentrations at different times of the day (Angelucci, Valeri,

Palmery, Patacchioli and Catalani, 1980). The peak brain concentra-

tions varied as the normal circadian rhythm, suggesting that a

steroid-independent rhythm of receptor concentration may persist in the

adrenalectomized animals.

An investigation of the temporal relationship between

glucocorticoid nuclear binding and the availability of cytosol binding

sites led to the unexpected finding that there was no net depletion of

total hippocampal cytosol binding capacity as a result of nuclear

translocation 15-60 min after the injection of fully saturating doses of

either [3H]corticosterone or [3H]dexamethasone (Turner and McEwen,

1980). The predicted cytosol receptor depletion was based on

hippocampal nuclear uptake measured following the in vivo [3H]steroid
injections. Cytosol samples from rats injected with [3H]steroids were

incubated in vitro with additional [3H]steroids to determine the maximal

cytosol steroid binding capacity, but no depletion of this total

capacity as a result of nuclear translocation was ever observed. This
investigation also revealed that [3H]corticosterone injected in vivo

could occupy no more than 40% of the total cytosol binding sites

measured in vitro. These results suggest the existence of a reserve

pool of aporeceptors or "cryptic" receptors which can be rapidly

converted to the form capable of binding steroids. However, it must not

be assumed that these findings are characteristic only of brain tissue;

the same glucocorticoid injection produced large differences in

cytoplasmic receptor depletion among 6 different rat glucocorticoid

target tissues (Ichii, 1981). For example, an injection of

dexamethasone that depleted 75% of heart and muscle cytoplasmic

receptors depleted only 40% of liver and lung receptors and only 10% of

thymic and spleen receptors (brain samples were not included). Much

larger injections were able to fully deplete receptors in all 6 tissues.

Neuropeptide effects on functional steroid receptor concentra-

tions have been observed. The increase in [3H]corticosterone binding

capacity of rat hippocampal cytosol observed after hypophysectomy

combined with adrenalectomy was greater than that after adrenalectomy

alone. Both ACTH1-24 (steroidogenic) and ACTH4-10 (devoid of

corticotrophic activity) eliminated the additional increase attributed

to hypophysectomy. Furthermore, vasopressin-deficient (Brattleboro

strain) rats were found to have abnormally low hippocampal cytosol

[3 H]corticosterone receptor levels that could be restored by

physiological doses of vasopressin or des-glycinamide -arg 8-vasopressin

(a behaviorally potent analog having low antidiuretic activity) (de

Kloet and Veldhuis, 1980; de Kloet, Veldhuis and Bohus, 1980).

Several observations indicate the possibility of a rapid, dynamic

regulation of the availability of brain steroid binding sites.

Hippocampal electrical stimulation resulted in increased in vivo uptake

of [3H]cortisol into hypothalamic cells and an increase in the

proportion of intracellular hormone bound in the nucleus (Stith, Person

and Dana, 1976a). A single injection of reserpine into cats resulted

(at 16 hrs post injection) in a decreased concentration of cytosol
binding sites for [ 3H]dexamethasone (Weingarten and Stith, 1978). A

rapid influence of metyrapone (an inhibitor of adrenal 11B-hydroxylase)

on the binding of [3H] cortisol in pig hypothalamic slices incubated in

vitro at 370C has also been reported (Stith, Person and Dana, 1976b).

The quantity of [3H]cortisol bound to cytosol components after 30 min

was reduced by 50%, and nuclear-bound [3 Hcortisol was inhibited by 70%;

the mechanism of this inhibition is unknown.

Lesions have been used to explore possible influences of

hippocampal afferents and efferents on the concentration of hippocampal

glucocorticoid receptors. Transection of the fimbria bilaterally for a

duration of 6 or 80 days did not affect either the concentration of

hippocampal [ 3H]corticosterone and [3H]dexamethasone receptors or the

increase in this concentration observed following adrenalectomy (Olpe

and McEwen, 1976). Furthermore, fimbria transaction in 3-day-old rats

did not affect the normal ontogenetic increase in hippocampal binding

sites for [ 3H]dexamethasone and [3Hjcorticosterone. In contrast, the

concentration of hippocampal [3H]corticosterone receptors was elevated

30 days (but not 10 days) following lesions which included the lateral

septal nuclei and the precommissural fornix; lesions which included the

medial septal and diagonal band nuclei and the main septal projection to

the hippocampus did not alter hippocampal receptor concentrations at

either 10 or 30 days after the lesions (Bohus, Nyakas and de Kloet,

1978; Nyakas, de Kloet and Bohus, 1979). Following unilateral dorsal

hippocampectomy the concentration of [3 Hcorticosterone binding sites in

the contralateral hippocampus was increased by 74% and 41%, respec-

tively, 10 and 20 days after lesioning (Nyakas, de Kloet, Veldhuis and

Bohus, 1981). Thus, some hippocampal afferents and efferents may

modulate steroid receptor concentrations.

Corticosterone "Membrane Effects" and Receptors

Some corticosteroid effects on the nervous system are not mediated

by the mobile cytoplasmic receptors that affect gene expression; these

effects may derive from the alteration of membrane properties by the

free steroids themselves or may be mediated by specific membrane-

associated receptors. Proposed mechanisms for such effects have

included the stabilization of lysosomal membranes, which could delay the

release of hydrolytic enzymes; alteration of ribosomal attachment to

the endoplasmic reticulum, which could modify protein synthesis; and

alteration of the binding of calcium to intracellular membranes, which

could influence synaptic function (reviewed in Baxter and Rousseau,

1979; Nelson, 1980).

Dexamethasone appeared to elevate tyrosine hydroxylase activity in

the superior cervical ganglion of adrenally intact rats by exerting an

excitatory pharmacological influence directly on preganglionic

cholinergic nerve terminals; very large doses of corticosterone were

completely ineffective, and the slowly-developing effect of

dexamethasone was abolished by a cholinergic receptor antagonist (Sze

and Hedrick, 1979). The effects of synthetic glucocorticoids on

cholinergic neurotransmission have been both excitatory and inhibitory.

The excitability of cat somatic motoneurons was increased (Riker, Baker

and Okamoto, 1975), and the contraction of guinea pig ileum in response

to nerve stimulation was decreased (Cheng and Araki, 1978) by the

steroids; in both cases the evidence suggested a direct steroid action

on cholinergic terminals.

Systemic or local injection of glucocorticoids has been observed to

affect the spontaneous activity of neurons in many brain loci (for

review, see Feldman, 1981). Injection of cortisol in intact,

freely-moving rats rapidly increased spontaneous activity of units in

the anterior hypothalamus and mesencephalic reticular formation, and

decreased unit activity in the ventromedial and basal hypothalamus

(Phillips and Dafny, 1971a,b). Spontaneous activity of basal

hypothalamic neurons in completely deafferented hypothalamic islands was

also rapidly decreased following systemic injection of either cortisol

(Feldman and Sarne, 1970) or dexamethasone in intact rats (Ondo and

Kitay, 1972). Similarly, iontophoretic application of dexamethasone

onto medial basal hypothalamic neurons in intact rats produced an

immediate depression of cell firing (Steiner, Ruf and Akert, 1969).

Mesencephalic neurons also responded to direct application of

dexamethasone with a decrease in firing rate (Steiner et al., 1969), in

contrast to the increase in firing rate after systemic injection of

cortisol reported by Phillips and Dafny (1971a,b). The injection of

dexamethasone into the vicinity of the recording electrode rapidly

produced a dramatic decrease in hippocampal multiple unit activity

(Michal, 1974), but none of 500 hippocampal neurons tested were

responsive to iontophoretic application of either cortisol or corti-

costerone (Barak, Gutnick and Feldman, 1977). It is not known if some

of these reported electrophysiological effects of corticosteroids are

mediated by specific receptors, but their short latencies suggest that

they are direct membrane effects not mediated by changes in gene


The membrane effects of glucocorticoids probably also include the

physiologically important fast feedback (FFB) suppression of the release

of CRH by hypothalamic neurons. The addition of corticosterone to the

in vitro incubation medium blocked the release of CRH produced by the

electrical stimulation of sheep hypothalamic synaptosomes (Edwardson and

Bennett, 1974), and there is evidence that the FFB action of corti-

costerone, which is unaffected by a number of pharmacologic agents, may

be mediated by a direct stabilizing interaction of the steroid with the

membrane of the CRH-secreting cell, which decreases the flux of calcium

into its terminals (Jones et al., 1977).

Glucocorticoids regulate the uptake of [3H]tryptophan by isolated

brain synaptosomes incubated in vitro with the steroids; corticosterone

and dexamethasone at concentrations above 10-7M elevated the maximal

rate (Vmax) of tryptophan transport by a high affinity synaptosomal

uptake system from mouse brain (e.g., Sze, 1976). This effect contrasts

sharply with the reversal by glucocorticoids of the increase in the V
of high affinity GABA uptake into rat hippocampal synaptosomes observed

after adrenalectomy (Miller, Chaptal, McEwen and Peck, 1978). The

latter effect required hormone pretreatment in vivo and was not observed

when the synaptosomes were incubated in vitro with glucocorticoids,

suggesting that in this case the steroid action was probably mediated by

the "classical" mobile receptor pathway.

Synaptic plasma membranes prepared from osmotically-shocked rat

brain synaptosomes have been reported to contain specific binding sites

for glucocorticoids (Towle and Sze, 1978). Specific, saturable binding

of [3Hjcorticosterone by synaptic membranes was greatest in the

hypothalamus, and lower (but approximately equal) levels were found in

hippocampus and cerebral cortex. The affinity of corticosterone for the

binding sites (Kd 10-7M) was similar in the three brain regions, and

both corticosterone and synthetic glucocorticoids had similar affinities

for the membrane sites. Soluble cytoplasmic receptors and synaptic

membrane binding sites in brain are characterized by somewhat different

properties of thermal stability and resistance to hydrolytic enzyme

attack, making unlikely the possibility of artifactual contamination of

the membranes by cytoplasmic receptors. Since the affinity of

corticosterone for the membrane binding sites (Towle and Sze, 1978)

agrees well with the concentration-response relation for the in vitro

stimulation of synaptosomal tryptophan uptake by corticosterone (e.g.,

Sze, 1976), it is possible that the membrane binding sites are involved

in the regulation of tryptophan uptake in the brain.

Glucocorticoids have profound metabolic, neuroendocrine, and

behavioral effects in the mammalian brain (e.g., Rees and Gray, 1982).

Although some of the less-well-understood effects may result from direct

interactions of the steroid with components of target cell membranes,

many of the effects are thought to be mediated by interactions of the

hormone molecules with steroid-specific cytoplasmic and nuclear

macromolecular receptors that concentrate as activated hormone-receptor

complexes in the target cell nuclei, where they initiate the changes in

gene expression that produce the ultimate physiological effects. The

objectives of brain corticosteroid receptor research are to improve our

extremely limited understanding of the basic mechanisms of receptor

capacitation, activation, nuclear concentration and recycling; to

examine whether the receptor systems for corticosteroid hormones in

brain (and pituitary) resemble closely those operative in other target

tissues; and to determine how the components of the receptor system are

altered in the clinically relevant conditions (such as experimentally-

induced diabetes, genetically-determined obesity and hypertension, and

normal age-related brain senescence) that are correlated with changes in

receptor function.

The experiments presented in this dissertation have been designed

to examine a number of the specific physicochemical properties of

soluble mouse brain glucocorticoid binding sites. The mouse has been

chosen for this research for several reasons. Although a few published

studies have indicated the existence of receptors in the mouse brain

(e.g., Finch and Latham, 1974; Nelson, Holinka, Latham, Allen and Finch,

1976; Angelucci et al., 1980), no basic characterization of the kinetic

and equilibrium binding parameters or the steroid specificity of these

receptors has been reported. Although a modest body of literature

(reviewed above) concerned with the properties of rat brain gluco-

corticoid receptors already exists, recent improvements in receptor

methodology have led us to believe that many of the published rat brain

results are probably questionable, and thus that complete reexamination

of the rat brain receptor system must eventually be undertaken.

Therefore, we have chosen the mouse primarily for obvious economic

reasons, and because it is relatively easy to rapidly perfuse and remove

a large number of mouse brains. The decision to use the mouse instead

of the rat has had little impact on the choice or design of specific


Since it is necessary to eliminate both endogenous gonadal and

adrenal steroids before killing the animals, females have been used

because they can be simultaneously ovariectomized and adrenalectomized

through the same incisions. We have used whole mouse brain cytosol

because most of the experiments required large amounts of receptor

material and since there is no evidence that there are brain regional

differences in the physicochemical properties of corticosteroid

receptors. Since the use of smaller brain regions would not have

enabled us to distinguish between cell types, it was felt that the

additional expense and effort required to work with a smaller brain

region such as dorsal hippocampus would not be rewarded adequately.

We have used the labeled glucocorticoids [ 3H]corticosterone,

[3H]dexamethasone and [ 3H]triamcinolone acetonide (cyclic acetal).
[3H] Dexamethasone was used to perform both equilibrium and kinetic
studies; [ 3H]corticosterone was employed to examine the possible

contribution of transport proteins to the total pool of [3H]corti-

costerone binding sites, whereas the nearly-irreversible ligand

[3H]triamcinolone acetonide was used for the lengthy procedures

examining the size and shape of the receptors. In contrast to many of

the older receptor studies with rat brain reviewed above, our

experiments have used a buffer containing ingredients that prevent loss

of unoccupied binding sites at 0-4C; used a rapid assay that can both

measure association kinetics conveniently and assay rapidly-

dissociating binding complexes; considered the possible consequences of

the failure to allow adequate time for "equilibrium" incubations at low

ligand concentrations; determined steroid specificity by applying

mathematically correct procedures to the analysis of competition data;

explored the contribution of CBG-like binding sites to the total pool of

corticosterone binding sites, and examined binding site sizes and shapes

to assess the homogeneity of the in vitro receptor population. Before

presenting experimental data we discuss (in chapters II and III) some

simple applications of the binding rate equation and propose some

improvements to the methods of graphical analysis of equilibrium

competition data currently in use.


The rate equation for noncooperative, single site ligand binding

systems may be written

dBL/dt = ka (SL-BL)(BO-BL)-kdBL, (2-1)

where BL is the concentration of specifically-bound ligand, SL is the

total ligand concentration, B0 is the total concentration of binding

sites, ka and kd are the second-order and first-order association and

dissociation rate constants, and t is the time of incubation. The exact

solution to this equation gives the value of BL as a function of time

for the given incubation conditions if the rate constants (or the

equilibrium dissociation constant, KdL, and one of the rate constants)

and the concentration of ligand and binding sites are known (e.g.,-De

Lean and Rodbard, 1979; Vassent, 1974). Thus, if nonspecific binding

and loss due to the inactivation of binding sites may be neglected as an

approximation, the solution to the rate equation provides an estimate of

the time required for any arbitrary degree of approach to the

equilibrium value of specific binding. As an example of its utility,

the solution to the rate equation has been used to examine the effect of

inadequate incubation time (during which equilibrium was not attained

under conditions of low ligand concentration) on measured "equilibrium"

dissociation constants (Aranyi, 1979; Yeakley, Balasubramanian and

Harrison, 1980). The solution to the rate equation can also provide

insight into several superficially paradoxical phenomena, such as the

observation that the degree of approach to equilibrium within a given

time is not always a monotonically increasing function of ligand

concentration (Vassent, 1974). We present a concise derivation of a

computationally convenient form of the solution and discuss several of

its applications. Methods for the determination of association and

dissociation rate constants (not requiring the complete solution to the

rate equation) are also discussed.

Equation (2-1) may be rewritten in the classical Ricatti form as

dBL/dt = k -ka(KdL+SL+BO)BL+kaSLB (2-2)

where kd has been replaced by kaKdL. At equilibrium dBL/dt=O and thus

(at equilibrium)

B2 (KdL+SL+BO)BL+SLB = 0. (2-3)

This may be rewritten as

(BL-P)(BL-Q) = 0,




P = (KdL +SL+B-[(KdL+SL+)2-4 SL B01/2)/2

Q = (KdL+SL+Bo+[(KdL+SL+Bo)2-4 SLB0 1/2)/2.



The smaller root, P, gives the value of BL at equilibrium. Now equation
(2-2) may be rewritten as

dBL/(BL-P)(B L-Q) = kadtS

which, on integrating, gives

kat + c = (ln[(BL-P)/(BL-Q)])/(P-Q),



where c is the integration constant determined by the initial condi-
tions. If (BL)o0 denotes the value of BL at t = 0 then

c = (ln[[(BL)o-P]/[(BL)o-Q]])/(P-Q).

Upon substituting (2-9) into (2-8) we get

t = (ln[[BL-P][(BL )O-Q]/[(BL )O-P][BL-Q]])/ka(P-Q),



and thus

exp [kat(P-Q)] = [BL-P][(BL)o-Q]/[(BL)o-P][BL-Q]. (2-11)

Solving for BL, we eventually find that

BL = [P(d/e) Q exp (-ft)]/[(d/e) exp (-ft)], (2-12)

where d = Q (BL 0, e = P (BL ), and f = ka(Q-P). If the initial
binding is zero (a common application), then equation (2-12) simplifies

BL = [1-exp(-ft)]SLBo/[Q-P exp(-ft)], (2-13)

since QP = SLBO. (This form of the solution is computationally
convenient because it avoids the generation of large exponentials as t
becomes large.)
The relative error or fractional deviation from equilibrium is
defined as

E = absolute value of [(BL-P)/P], (2-14)

and is easily calculated. If equation (2-12) and (2-14) are solved for
t (e.g., Vassent, 1974), then an expression giving the time required for
an arbitrary degree of approach to equilibrium is obtained:

t (e) = [1/ka (Q-P)] In ([Q-P(1-c)]/ P[1+(Q-P)/e]).


We now examine some applications of the rate equation and its

solution. In the following discussions we shall assume that B0 remains

constant with time (unless a deliberate dilution or concentration is
performed). Many in vitro steroid receptor preparations do not,

however, possess this stability. For example, a frequent observation
has been the gradual inactivation or loss, with time, of unoccupied

(free) receptor binding sites (e.g., Luttge et al., 1982). If this is

the case, then the rate equation (2-1) must be supplemented with the
simultaneous inactivation equation

d(Bo-BL)/dt = -kin (BO-BL) dBL/dt, (2-16)

where kin is an empirical inactivation constant describing a process of
simple unimolecular decay of the normal binding site conformation.

(This assumption has, of course, no theoretical basis; it is merely a
statement of the observation that the relative early regions of slow

receptor inactivation curves may be approximately fit to simple
exponentials.) Equation (2-16) simplifies to

dB0/dt = kin(BO-BL), (2-17)

which may be solved simultaneously with the rate equation (2-1) by
standard computerized numerical integration methods (e.g., Yeakley et
al., 1980).

Applications and Discussion
If the chosen binding assay can be performed rapidly then the
association rate constant may be determined conveniently by measuring BL

as a function of t for a relatively short period of time (during which
dissociation may be neglected) following the mixing of ligand with the
receptor preparation. If t is small then dissociation may be neglected
and equation (2-1) becomes simply

dBL/dt = ka(SL-BL)(BO-BL), (2-18)

which, upon integration with the initial condition that BL=O at t=0,

kat = [1/(SL-BO)] In ([Bo(BL-SL)]/[SL(BL-Bo)]). (2-19)

It follows immediately that

kat (SL-Bo) = In (BO/SL) + In [(SL-BL)/(BO-BL)]. (2-20)

It is apparent that at short times a plot of In [(SL-BL)/(BO-BL)] as a
function of time will be a line with slope ka (SL-BO). The ordinate of
this plot is more easily remembered as In [(free ligand)/(free
receptor)]. This method for the determination of ka obviously requires
both knowledge of SL and an estimate of B0 derived from an equilibrium
experiment performed with the same receptor preparation.

It is also possible to determine the association constant ka by
measuring BL following brief incubations of constant (short) duration

conducted at different ligand concentrations. These values of BL, when

divided by the incubation time, are taken as estimates of the initial

rate of increase of binding (dBL/dt), which is plotted on the ordinate

as a function of the total ligand SL. To analyze this experimental

strategy we note that since BL = 0 at t = 0, equation (2-1) reveals that
the initial rate of appearance of bound complex is given simply by

dBL/dt (at t=0O) = BOkaSL. (2-21)

Thus, the plot of dBL/dt (initial) as a function of SL is a line

possessing slope B0ka. In fact, the observed curvature of such a plot

(a decrease in slope at high values of SL) has even been offered as

possible evidence that the glucocorticoid receptor binding process may

involve multiple steps and unobserved transient intermediate states

(Pratt, Kaine and Pratt, 1975). (The most probable explanation of this

anomaly is that the constant incubation time was too long to provide a

reliable estimate of the initial dBLdt at the high ligand

concentrations.) The two aforementioned experimental designs may be

combined, of course, by accumulating the early regions of temporal

binding curves generated at different ligand concentrations. The

individual binding curves will generate independent measurement of ka

that should not be correlated with the ligand concentration SL.
Information (in the form of the derived values of ka) from the
individual binding curves may also be merged by plotting (1/BO)dBL/dt

(initial) = ka SL as the ordinate vs. SL as the abscissa for each
binding curve. The plot should pass through the origin, and the
resulting slope provides the merged estimate of k a .

The dissociation rate constant kd is determined by simply measuring

the bound ligand BL as a function of time following some manipulation
that prevents any further association (or reassociation) of labeled

ligand with the receptors. Ordinarily this is accomplished by adsorbing
the free labeled steroid onto activated charcoal, followed by either

dilution of the preparation to further reduce the concentration of free
steroid to a negligible level or by the addition of a high concentration
of unlabeled steroid to dilute the specific activity of any remaining
labeled free steriod (and to dilute the labeled steroid that is released

into the free pool during the course of dissociation). Thus, since the

association of labeled ligand is blocked, equation (2-1) becomes

dBL/dt = kdBL, (2-22)

where BL now represents only labeled bound ligand. Upon integration we

obtain the familiar first order dissociation relations

In[BL/(BL)o] = kdt (2-23)

and finally

BL = (BL)o exp (-kdt), (2-24)

where (BL)0 is the initial bound concentration at the beginning of the
dissociation period. The rate constant kd is simply the slope of the
plot of In[BL/(B L)O] as a function of t. The dissociation rate is also
frequently reported as the half-life (t11/2) of the bound complex:

tl/2 = (in 2)/kd* (2-25)

Depending on the experimental design, a measurement of the

dissociation rate constant may be performed under conditions of

decreasing, constant, or increasing receptor occupancy (BL/BO). If no

unlabeled steroid is added, the occupancy obviously will decline.

(However, if unoccupied receptors are inactivated or degraded at a rate

comparable to the dissociation rate, then occupancy will not decline as

rapidly as BL itself.) If the receptors are saturated at t=O, then

addition of a large amount of unlabeled ligand will maintain the high

level of binding. If the receptors are not initially near saturation,

then the addition of unlabeled steroid will lead to a condition of

rapidly increasing occupancy. If necessary, the concentration of

unlabeled ligand may be chosen to maintain a desired intermediate level

of occupancy. If the dissociation kinetics are biphasic or complex

under conditions of constant occupancy or saturation, then the

possibility of several classes of binding sites must be considered

(e.g., Weichman and Notides, 1979). If the kinetics are complex under

conditions of declining occupancy, then the possibility of cooperativity

must be considered; the experiment should then be repeated at high or

constant occupancy to see if the apparent cooperativity is really a

reflection of heterogeneity (e.g., DeMeyts, Roth, Neville, Gavin and

Lesniak, 1973).

If excess unlabeled steroid is not added to the preparation at the
beginning of the dissociation period, the possible reassociation of

newly-dissociated labeled ligand or the association of the small amount

of residual labeled steroid not removed initially may reduce the

measured apparent dissociation constant. The magnitude of this

reduction may be estimated approximately by using the solution to the

rate equation to monitor the relaxation of BL to the new, low-but-
nonzero value of P (equilibrium value of BL) in the following way.
First, assume for kd the (underestimated) value that has been measured

experimentally; call this value kd(apparent). A previously estimated
value of ka or KdL must also be assumed; if a value of ka is assumed,

then KdL is taken to be kd(apparent)/ka. Measured values of SL, BO, and

(B L)0 are also available. Now equation (2-12) is used with these values
of the independent variables to calculate BL for the same values of t at

which actual measurements of BL have been made. These calculated values
of BL(t) are then used to derive, from the slope of a plot of t vs. ln
[calculated BL(t)/(BL)o], another underestimated dissociation rate
constant, called kd. Next assume simply that the amount by which kd

underestimates kd(apparent) is equal to the amount by which kd(apparent)
underestimates the "true" value of kd that is sought. Thus

"true" kd kd(apparent) kd(apparent) kd, (2-26)
and finally

"true" kd 2 kd(apparent) kd. (2-27)

This rough estimate of the correction is reasonable when SL is small.

The solution to the rate equation may also be used to predict the
error in a determination of KdL derived from a "nonequilibrium" isotherm

generated by measurements performed before equilibrium has been attained
in the incubation vessels containing the lower concentrations of SL.

(Estimates of the rate constants and B0 are required, of course, in

order to perform this simulation.) A predicted value of BL is calcu-

lated for each experimental value of SL (at the constant value of t used

for the incubation) using equation (2-13), and the resulting values are

used to construct the predicted (curved) Scatchard plot resulting from

the inadequate incubation time. A line is fitted to the points by the

same technique that is used to fit the experimental points (e.g., linear

regression), and a value of KdL is derived from the resulting "slope"

(e.g., right inset to fig. 4-10). The entire procedure may be iterated
for different values of t in order to simulate the approach of the

apparent, measured KdL to its "true" equilibrium value as the incubation

time is prolonged. It is instructive to examine the dependence of the

relative error function upon SL; when combined with equation (2-13),

equation (2-14) becomes

E = (Q-P) exp(-ft)/[Q-P exp(-ft)], (2-28)

which is plotted as a function of SL in fig. 4-10 (left inset) for

several different incubation times using one specific set of the other

independent variables. It is apparent that E rises rapidly to a maximum

and then declines slightly as SL is decreased from a high concentration.

Thus, as SL is decreased below the transition zone, e becomes essen-

tially constant at a value given by equation (2-29) below, which is

simply the limiting value of e as SL declines:

lim c (as SL is decreased) = exp(-ft) = exp [-kat(KdL+Bo)].


Thus, if a time and receptor concentration B0 are chosen such that

equation (2-29) is reduced to an acceptable level, then very low values

of SL may be used to generate an isotherm. (More rigorously, one may

find by setting equal to 0 the partial derivative of equation (2-28)

with respect to SL, the exact nonzero value of SL that maximizes e; then

a time may be chosen that reduces this maximum relative error to an

acceptable level.)

Predicting the effect of the addition of a competing, cold ligand

(C) on the rate of approach to equilibrium of BL is a more complex

problem; this calculation requires the numerical integration of the two

simultaneous rate equations

dBL/dt = ka (BOL-B-Bc)(SL-BL) kdBL (2-30)


dBc/dt = kaC (B-BL-BC)(Sc-BC) kdCBC, (2-31)

where the subscript C refers to the competing ligand. Several

qualitative inferences can be drawn, however, from the fact that the

only effect of the competitor C is to decrease the free receptor

concentration in equation (2-30). Consider now the relative error E as

a function of B0 rather than of SL; since SL and B0 appear symmetrically

in equation (2-28), the left inset to fig. 4-10 also portrays the shape

of the plot of e considered as a function of B0 (with SL now held

fixed). If SL is sufficiently large, then the position of B0 will be to

the left of the maximum value of c on the plot; if SL is small enough,

however, the position of the same value of B0 will now be to the right

of the e maximum value. Thus, depending on the relations among SL, B0

and KdL, the effect of the reduction of free receptor concentration by

the competing ligand can be either to increase, decrease, or leave

essentially unchanged the value of e at a given time. Under the right

conditions a competitor may easily increase e from near 0 to the maximum

value consistent with the given values of SL and t. (The rate constants

for ligand C and its concentration will, of course, affect e by

determining how fast the competitor depletes the free receptor

concentration.) A very rough estimate of the effect of a high-affinity

competing ligand on the time required for BL to approach equilibrium may

be obtained simply by assuming that the competitor is identical to the

labeled ligand. In this simple case SL becomes the sum of the labeled

and competing ligands, and equation (2-28) predicts E for the total

bound ligand (BL + BC) for different times. Clearly this value of the

relative error also applies to BL, since for this special case

BL = SL (BL +Bc)/(SL+Sc). (2-32)

In order to facilitate estimation of the times required for the

approach to equilibrium under a variety of conditions, we present in

table 2-1 a short summary of solutions to the rate equation (2-1) for

several useful combinations of the variables BO, SL, and KdL (i.e.,

kd/ka) for the case of a single ligand and binding site. The initial

condition is simply (BL)o = 0, and the solution is presented as a table

of pairs of numbers representing the number of hours required for BL to

attain 80% and 95%, respectively, of the equilibrium value. These


0 C0
*) r -

0 -> *0-

*j 0 0 .0

-J0 0 .0

00 C

S0 0
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.0o o W

*i- ,-'- 0


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4 4- C
0 "--- 0
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Vo g


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a 0 w"-
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W C 4U 40

E a i U) 0

= *- 1-0
-0 0 4 0 C-

0 r .- to .-

N 0

C4 in
0 0

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44 in

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C4 en

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4.) .- r _
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.4 .4 .4


durations were calculated for ka = 10 M1 min-1. For other values of

ka simply multiply the tabulated values by 105 and divide the resulting

product by ka. Table 2-2 presents estimates of the fractional occupancy

of the binding sites (BL/BO) and the fraction of the ligand bound at

equilibrium (P/SL) under the same hypothetical conditions as in

table 2-1. (These percentages apply to all values of k a.)


The affinity of a ligand for a particular class of binding sites is

measured frequently by constructing an isotherm describing the binding

of an available labeled ligand having specificity for the same set of

binding sites, first in the absence and then in the presence of a fixed

total concentration of the unlabeled competitive inhibitor whose

affinity constant is to be estimated (e.g., Ginsburg, MacLusky, Morris

and Thomas, 1977; Katzenellenbogen, Katzenellenbogen, Ferguson and

Krauthammer, 1978; Kono, 1975; for review of competition experimental

designs see Rodbard, 1973). The data resulting from such an experiment

are often analyzed by making the approximation that the concentration of

free competitive inhibitor is equal to the total concentration present

and therefore constant over the entire range of labeled ligand

concentration, since the effect of a constant concentration of free

competitive inhibitor on a Scatchard plot (Scatchard, 1949) describing

the binding of a labeled ligand to a single class of noncooperative

binding sites is solely to decrease the slope of the plot by a factor

which, in combination with the concentration of free competitive

inhibitor, yields immediately the equilibrium constant of the inhibitor

(Cantor and Schimmel, 1980). Thus, if the above approximation is valid,

then the affinity of the competitor results directly from the slopes of

the two straight lines and the total concentration of the inhibitor.

However, if the competitive inhibitor is not present in great excess

over the total concentration of binding sites, then the above

approximation will not be valid, the resulting Scatchard plot will be

curved (Feldman, 1972), and the error in the derived equilibrium

constant caused by making the approximation may be substantial. In the

present communication we suggest a simple procedure for eliminating this

error by linearizing the curved Scatchard plot resulting from this

experimental design.

The very popular competition displacement experimental design

(known as the "ED50" method) also generates data that are somewhat

difficult to analyze in the laboratory without the aid of computerized

nonlinear regression techniques. Within this design one measures the

fraction of initially bound labeled ligand remaining bound at

equilibrium in the presence of increasing concentrations of the

unlabeled competitive inhibitor whose affinity is to be measured (e.g.,

Abrass & Scarpace, 1981; Lindenbaum & Chatterton, 1981; for review, see

Rodbard, 1973). The total concentration of inhibitor that displaces

half the initially bound labeled ligand ("ED50") is determined, and one

then attempts to relate this inhibitor concentration to its actual

affinity for the binding sites. This design presents two major

problems: the curvature of the displacement plot makes the precise

determination of ED50 difficult, and the ED50 itself is often quite

different from, and difficult to relate to, the actual equilibrium

dissociation constant of the competing ligand. In many situations the

curvature of the competition displacement plot cannot be eliminated

simply by performing a "logit-log" transformation (e.g., De Lean, Munson

and Rodbard, 1978) of the data. Furthermore, the use of approximations

(e.g., the Cheng-Prusoff (1973) formula) to relate the estimated ED50 to

the equilibrium dissociation constant of the competitor is often

inappropriate and can lead to substantial additional error.

We now suggest that if the initial receptor occupancy is not too

high this experimental design can also be analyzed without approximation

by the simple procedure (to be described) that we recommend for

linearization of the curved, two-ligand Scatchard plot obtained in the

presence of a fixed concentration of competitive inhibitor. With this

method the equilibrium dissociation constant is obtained directly,

obviating calculation of the ED50 value itself. Furthermore, a more

nearly exact approximation that can be used to relate ED50 estimated

from an approximately linear logit-log plot of the competition

displacement data to the actual affinity of the competitive inhibitor

for the binding sites is presented. This method is particularly useful

when the initial receptor occupancy is rather high.

Theory and Application
The nomenclature for the two ligand-one binding site problem will

be as follows: BL and BC are, respectively, the concentrations of

specifically bound labeled ligand L and competitive inhibitor C. The

total concentration of binding sites is BO. The equilibrium

dissociation constants for the binding of the labeled ligand and

competitor are, respectively, KdL and KdC; and SL and SC are the total

concentrations of these ligands. The free (unbound) concentrations of



C 4
*r- U

U) 0
c 4 -
O 0) r-
*r- C 4.)
.- -.0

3 .U

r- 4-1 (r,
0J U) .cu
) 4.)
0 *- 0)
4- U) C

4O 0)4u

-to +j .-J

C-4-) r-
tO 0-
c; Q. in"
c *C- *-

C.a.-- -9-
*r- o AQ

- 0) .r_ 0-
*r- 0

0D4-) S- U.
S- 4a
*r- Q. S- C

or 0 <0 0
0 0
.- 0l0
4O- *d. -
4- 0

a- U) *- U
0. 0 + +.
*- U *i-

5- U)

XC C 4L. C

CO 4- C .0

U) 4) SO U


C) U) C (U
** .C *- C0 -

C LJC C o t)
O *- /l C *- r0 U)
*r- *- 0 .0 CJ cI
C E 4 9- r0 I 0
r0 0 0 0 /) U ) -J
S- *- *- 0) t *4 -
--.4- U S- C *r- C .- V n
CM 0 4.)'-- *r- *r- 01. 0
W C E ) U) C O U **- -
-- () U () 0 CL. U LA. I *
.M *r- QJ **- Q. ***-* -
0 C 4+ 4. U C M
0 +4 C 0 0 -U) Li
*(- E U) E 3-
(a) 3 .-C 4 0 0 to
So W. Sr- 4- C ( -c c r _O
4- 2 .3 0 *r- (U G1 10
U) *- 3 U 4.) 4. .C O)
U r 0- U C C .C 40 -U 4- = -
C U or- 0 U (U A -
4- m 3 C .0 ) *r- C t
0 0T U *r- 0*- C0
S-. a n 9- r- C *- -
0 0 a) 0 *r- U )0 r-
C 4-> S-. O C = E 0)
*r- u 0. C 3 r- 0 4+ Gu .0m
" U) C 0 4J CM 4) S- to
C U o U -a- 1-4 C a-
*- u r- C 4J u -)- *r- +4-
.0 o -) (o > o O u
s- *- C r- C a- -
u) C CJ C +4 +4- 0o 3 CL 0)
.c ) LU r- c r E 0 C
4J 0) U 4) + () .C -O -r-
0 CMJU U) a- .C- a ) VU )
& s- .. L* j C E O. U) +-)
.0 4-) 0 E LL-.. t Q
*r- ) C U 0 C E 0 .C
SUJ *- ** 0 WU) 4- +4
U -- 4. U) 4. U)
) U) 0 CE > U) 0 U) C >4
I- r- .Q U) > r0 .
0 *u- .C 0. QU )- U U S..
0) u 0 0 U U- r >u
4- 4-) r0 U) 0. U) Q. 4J +W 4
0 3 S. > Z wU t0 .C t0
-4- + S-. U) -0 a) C +- S-
Q. 4- w = _r S- -r- o)
UI 4 > C U -0 4- C
CU 0 0 U) 3 S- O O)
=c U U w S-4 U ) o 0I
+-> Cl. )J o .0 0 a)
-0 3 X 4- C U Q. 40
U) U) = 0 U)o 00
4.-) 4 tD > r- r-
t0 0 O 0- )U Q. *
5. > **. -- .- t N
J *L- U L- S 5- o
C +jC> oo 11 W *r- 5- .C a a
) u Co-I M ) 4- <0 i- a) *-
0m to 01 I c) S- r- U) a) C
C q -4 r0 4- .C= C *r- U
0 0 .- .- C k .. 4- -
4-+ C U W O r- +4) X
t X +4- +4) Q. Q. X e- 0
SU u C" o O >1 U U o I
SC -o I. 0 U S-. .C .C 4-) C X
V) 4-) 4- ) / Q) CL *4) -
4J r-I U) > W U d CD
00 C O V U r- O .C *9- E
U) 4-) z II o U) W U) 4- +4J S.- 4J
5- U > o S- C 0
a ) -0 -1 S- .C 3 T- C C
+4) m= C E 3 0. *- U) 0
U Lii 0 3 U 0. .C
E -- *- M o U 4-) 4
0o C 4.J 5 U )- -- E D CL
5-- o C .0.C f0 m n ( ()
0 0 E to *- I- .0 V U) 0 U
Q. .C 4) r- 5-U wU = 5S-
L. U w U U > = U 4) 0U
(U 4) *r- C 4 Q. S- r- tW 0 4J
.C U U) U o 0o >- = 0 *r- .C- C
I- U 3c U U C .Cr U > '0 4> -r-

0 n

* I!



the ligands are FL and FC. In order to discuss the "ED50" experimental

design we let (BL)0 and (FL)0 represent the initial values of BL and FL

when SC=0. ED50 is the value of SC when BL has been reduced by half

(i.e., when B = (BL)o/2), and we let FC50 and FL50 represent the

corresponding values of FC and FL (i.e., when SC = ED50).

As the first illustrative example we have used the equilibrium
dissociation constants that describe the binding of estradiol (E2) and

estriol (E3) to the nonactivated calf uterine cytosol estrogen receptor

(Weichman and Notides, 1980) in order to generate the purely

hypothetical Scatchard plots (Fig. 3-1) of theoretical data that would

be observed for the binding of labeled E2, first in the absence and then

in the presence of SC = 1 nM "cold" E3. (The experimental design under

discussion here was not employed by Weichman and Notides (1980); we have

merely used the affinity constants, which were measured and reported

appropriately by these authors.) The concentration of binding sites

B0 = 2.3 nM is also taken from Weichman and Notides (1980); the

equilibrium constants are KdL = 1.7 x 10-10M (for E2) and

KdC = 2.6 x 10-10M (for E3). The linear Scatchard plot (for the case

SC = 0) is, of course, described by the standard equation (e.g.,

Rodbard, 1973; Scatchard, 1949):

BL/FL = (BL-Bo)/KdL (3-1)

and thus has slope (-1/KdL) and intercept B0 on the x-axis (Fig. 3-1).

The lower, curvilinear Scatchard plot (Fig. 3-1) for the purely

competitive two ligand situation is a hyperbola whose geometric

properties have been described by Feldman (1972) and whose equation is
(Feldman, 1972; Rodbard and Feldman, 1975)

BL/FL = KdC[-1-(BL+SC-Bo)/Kdc+[(I-[BL+SC-Bo]/Kdc)2

+ 4Sc/Kdc]/2]/2KdL. (3-2)

This hyperbolic Scatchard plot has one asymptote with slope (-1/KdL)
parallel to the linear Scarchard plot and an x-intercept (Bo-SC), and
another horizontal asymptote below the x-axis at BL/FL = (-Kdc/KdL).
The actual points on the curve are completely hypothetical and have been
calculated and placed on the plot at equally spaced intervals of BL
(0.275 nM) in order to indicate how specific binding values map into the
modified coordinate systems to be discussed.
We now calculate the error in the derived value of KdC resulting
from the assumption that the concentration of free inhibitor FC is
constant in this experiment and therefore that the expression (derived
from simple Michaelis-Menten kinetics for the case of pure competitive
inhibition) sometimes called the Edsall-Wyman equation (Cantor and
Schimmel, 1980) is valid when applied to some estimate of the "slope" of
this (actually curved) plot. The Edsall-Wyman equation can be
rearranged to the convenient "Scatchard" form given by
(cf. equation 3-1)

BL/FL = (BL-Bo)/KdL(1+FC/Kdc).


Thus, it predicts simply that the slope of the Scatchard plot will be
reduced by a factor of 1/(l+Fc/Kdc) in the presence of a constant
concentration of free inhibitor FC. We now substitute the total
concentration SC for the (actually variable) free concentration FC.
Thus, the estimated value of KdC derived from the use of this
approximation (which we call KdC(app) will be given by

KdC(app) = [reduced slope/(original slope-reduced slope)]SC.


Thus, the percentage error (E) will be given by

E/100 = [KdC(app)/KdC]-l (3-5)

and hence, from above,

E/100 = (-KdLSC)(reduced slope)/KdC[l1+KdL(reduced slope)]-1.


For the "reduced slope" we substitute the derivative of the equation of
the curvilinear Scatchard plot, d(BL/FL)/dBL, obtained directly from
equation (3-2) above. Thus, if the error is estimated by using as the
"reduced slope" the slope of the tangent to the curve at the abscissa

BL = B0/2, then the error in the derived equilibrium constant is given
explicitly by

E/100 = (Kdc[Sc-Kdc]Y-X[SC+Kdc])/(Kdc2Y+KdCX), (3-7)

where X = Sc-Kdc-(B0/2) and

Y = ([l-(2Sc-Bo)/2Kdc]2+4S/Kd)12.

Thus, the error is independent of KdL and vanishes under the ideal
conditions approached when KdC B0 and SC KdC. In the hypothetical
example involving estradiol (E2) and estriol (E3) the error resulting
from the use of this approximate method is large: the derived KdC
(calculated from the slope obtained from a linear regression on the
eight hypothetical points shown on the curvilinear Scatchard plot in
Fig. 3-1) for E3 is 1.6 x 10 M, whereas the actual value used to
generate the curve is 2.6 x 10- 10M, a 5-fold discrepancy. In fact, a
significant and variable fraction of the competitor E3 is obviously
bound to the receptors in this hypothetical experiment.
The error discussed above may be avoided by analyzing the data from
the same experimental design in a slightly different manner. At
equilibrium the simple mass action rate equations for the binding of the
two ligands may be written as

(BO-BL-Bc)FL = KdLBL and (3-8)

(Bo-BL-BC)FC = KdCBC, (3-9)

which suggest immediately the linearizedd Scatchard" forms given by

BL/FL = [(BL+BC)-Bo]/KdL and


B/F = [(B L+Bc)-B0]/KdC. (3-11)

Thus, if BL/FL or Bc/FC on the ordinate are plotted against (BL + BC) on
the abscissa, then a linear "Scatchard-like plot with slope (-1/KdL) or
(-I/Kdc) and x-intercept B0 results (insets to Figs. 3-1 and 3-2).

Furthermore, since BO (as well as KdL) is derived from an initial

Scatchard plot constructed in the absence of the competitor, KdC may be
measured simply by plotting [BO-BL-Bc, (free binding sites)] on the

abscissa against Bc/FC on the ordinate, as suggested by equation (3-9).

The resulting plot (Fig. 3-2) must pass through the origin and possess

slope (1/Kdc). This is the analysis we recommend for the determination
of KdC by this experimental method.

The implementation of this analysis is scarcely more difficult than
the method that we have criticized: the only additional requirement is

the calculation of BC and FC for each data point. We note that B0 and
KdL have been determined already from an initial Scatchard plot.
Equation (3-8) is now rearranged to give

Bo-BL-BC = KdLBL/FL. (3-12)

Thus, the abscissa of the recommended plot is determined directly from
equation (3-12), as is the value of BC = [Bo-BL-(KdLBL/FL)]. Since SC
is known, FC Sc-BC. (Note that nonspecific binding of the "cold"
competitive ligand must still be neglected, unless it can be estimated
from other experiments, e.g. Katzenellenbogen et al., 1978). The
best-fitting straight line passing through the origin is then fit to the
points as shown (Fig. 3-2), and the reciprocal of its slope is then


In I m
3 (U
0 4-) C C; I
C 0 0 *- X
<- I *i l- O
) C 4-) C 4- 00
.- -r- 4O) -o -t U
0 E 0 4-) C C
C CO CU #A CU 0 *r-
-- o ) In to
,. *. "- C '- 01
S0) C (0 *O 0
) 4.- C (o) CU
S 4- CU LU w w ) + )
I 4- --- *r- .C C *
0- U 4) 4-) CM
-0 S- n 4
S S- 0 .0 4- 0 0
00 4-) CU 0 4-)' (A a)
C +) U0
0 < + (U A- t -)
C MC I- M 4-J U 4.J Wn 4->
E*- O 0 U( Cr
0 C S- l *
C 0U U O 0 X C I
3 .0 *- ) 3 X
o C U a) 0
I S- -4-) S =
4-, 0 "0 0 a0 0
0 0
C C 4. 4- : C C
L 0) 0 (C CU 0 C0
*r 3 *r- U) U C *'
3 LI- .)- C- 4.O ",-
0- U 0 C 0U0 4-)
CU C --:- In -+
= 50 0 0 C- '
( c cU < 4U -j1I.. a) U I
U 4-) 4-) 0 CM --4 IW C -
C/I C ) 0 r_ 0 *-U 0
In CC a *o-
5O 1 -C CQ 0(U CU 0
(a 0) 0 0
u In L- S-. 4-) 4-.),
4-) 0 4-) C) (
0) C 4-C In.C 0)
1 (U = (U
4-) 0 v u cn LJ 4-'.
4-- 0 C
o CU C U CU .- =
4.- 4) 0 C4-
C CU EC *. *4J 3 'C
0 E -c 0 E
- 0 4-J 4 "0 S-
4- u o) 0) ( 0 0
QU CU (O U n- 0- 0 4-) 4-
N U 4- 4) S- S- E-= 4-)
- -0 0 0 -0
S- *4-) U -
E (0 0)- a- =.
C 4-' *n +- C U U
0 >, U C 4-J S- 4-)
0. V 0 a CU
*r- M 4- u
0i .1-i 3 0 0 V)
*1 X 0 0 0- z
C c CU 9-- r- -4 C
I E C C4 C C( I
C4 *- C 4. C CL
In0 Qo 0) 4.' w. 4-c
5-&0 U In U) 4->
wO c0 O 4-C 0 C C
L I- U S- U X0. U 4. 0-4


0 0 0 0
v 0





determined. For statistical reasons it may be advisable simply to apply

the least squares criterion (i.e., to use the method of simple linear

regression) and not force the line to pass through the origin. Since

the plot of Bc/FC vs. [free binding sites] is used to estimate only one

binding parameter (Kdc), data sets arising from experimental

preparations differing in total binding site concentration may be merged

prior to the final analysis.

We have extended the analysis presented above to cover a very

limited case of the two ligand-two binding site problem: the method has

been used to linearizee" data resulting from investigation of the

specific mouse brain glucocorticoid receptor in crude cytosol containing

significant amounts of CBG (transcortin). We have measured the affinity

of "cold" dexamethasone (which has negligible affinity for CBG) for the

specific [ 3H]corticosterone, non-CBG, binding sites (putative receptors)

in CBG-containing brain cytosol in order to compare the resulting

equilibrium constant with that obtained by using [ 3H]dexamethasone

itself to construct a one-ligand Scatchard plot. The experiment is

performed by first constructing separate single-ligand binding isotherms

using [3H]dexamethasone and [3H]corticosterone; then an isotherm

describing the binding of [3H]corticosterone in the presence of a fixed

concentration of dexamethasone is constructed and analyzed. (The same

cytosol preparation is used throughout, of course.) This analysis is

simplified dramatically both by the absence of a significant interaction

of dexamethasone with CBG and by the observation that the one-ligand

[3H]corticosterone Scatchard plot is not biphasic, which suggests that

the affinity of corticosterone for CBG is very similar to its affinity

for the putative receptors.

In order to describe the analysis we extend slightly the
nomenclature used above; this nomenclature will apply only to the
specific two-ligand, two-site isotherm to be linearizedd." BL and BC
are the total concentrations of specifically bound [3 H]corticosterone
and "cold" dexamethasone, respectively. BLR and BLT are the
concentrations of [ 3H]corticosterone bound to the putative receptors and
to CBG (transcortin), respectively. (Thus, BL = BLR + BLT). BMAX is
the total concentration of all binding sites, composed of B0 putative
glucocorticoid receptors and TO transcortin binding site
(BMAX = B0 + TO). KdL describes (approximately) the common affinity of
[3 H]corticosterone for both the receptor and CBG binding sites, and KdC
is the equilibrium constant for the binding of dexamethasone to the
glucocorticoid receptor sites. FL and FC are the concentrations of
unbound (free) [ 3H]corticosterone and "cold" dexamethasone,
From the mass-action equations (cf. equations 3-8 and 3-9 above) we
have the following:

(Bo-BLR-Bc)FC = KdCBC, (3-13)

(B -BLRB C)FL = KdLBLR, (3-14)

(TO-BLT)FL = KdLBLT (3-15)

and, adding equations (3-14) and (3-15) we get



Since dexamethasone does not bind to CBG, recall that the plot of Bc/FC
as ordinate vs. abscissa [(Bo-BLR-Bc), free receptor sites] is a line
passing through the origin with slope (1/Kdc). This is the plot used to
find KdC for dexamethasone by competition with [ 3H]corticosterone.
The calculation deriving KdC from the competition data is
straightforward. B0 is determined from the one-ligand isotherm of
[3H]dexamethasone binding, and B MAX and KdL are derived from the
one-ligand [3H]corticosterone plot; TO is then estimated from the
relation TO = BMAX-BO. The abscissa, [free glucocorticoid receptor
sites], is now rewritten as

BO-BLRB C = (BMAX-BL-BC) (TO-BLT); (3-17)

i.e. [free receptor sites] = [total free sites]-[free CBG sites].
Substituting from equation (3-16) above we obtain for the abscissa

Bo-BLR-BC = (KdLBL/FL) (TO-BLT). (3-18)

Solving equation (3-15) for BLT and substituting the resulting
expression into equation (3-18) yields finally the computational form
for the abscissa:

Bo-BLR-Bc = KdL[(BL/FL) TO/(FL+KdL)]. (3-19)

Now only BC must be found, since FC and Bc/FC follow immediately. The
calculated value of the abscissa, [free receptor sites], is used to find
BC from the identity

Bc = BO-BLR- [free receptor sites]. (3-20)

By substituting the expression for BLR obtained from equation (3-14)

into equation (3-20) above, the convenient computational form for BC is

found to be

BC = B0 [free receptor sites] (1+FL/KdL). (3-21)

The estimate of KdC then follows directly from the slope of the

recommended plot described above.

We now turn to an analysis of the "ED50" experimental design.

Figure 3-3 depicts theoretical competition displacement curves generated

by the same binding parameters (taken from Weichman and Notides, 1980)

that were employed in the construction of figs 3-1 and 3-2 and used in

the above analysis of the design in which the inhibitor is present at a

single concentration (the "Edsall-Wyman" design). Furthermore, it is

presumed that KdL and B0 have previously been measured in the absence of

competitor by constructing the one-ligand isotherm. If the initial

receptor occupancy [(BL)o/BO] is not too high, it is obvious that

linearization of the displacement curves may be achieved by plotting the

data in the same BL/FC vs. [BO-BL-BC, free binding sites] coordinate

system discussed above in connection with the Edsall-Wyman experimental

design, using the same data manipulations to determine the abscissa and

ordinate of the plot (shown as inset to fig. 3-3). If the initial

receptor occupancy is too high, then the range of the plot will be

compressed severely and this method will not be useful.

*f > S-
*-A 0 CO
-o -> oL) mu LO
C -. S- 0 w =
0- U to W. I
S ,' *" 4.) ) -
0 C7 (' S- (a
n ,0) 2 C ) 0.) 3 U
-4-> -- 0 x "4- ""
0 t0 *r- 0 .- *4- U*
r- C- =
= E U0 4 u

.-* o C4 4 M
0() 0) 4. C O

- r- 0 0 0
0 (L CD oi 4x a) 0
S-.- U S M = C r

W > 4 C- 4- '- C,-

0).. 4- 4-) C.) -0
- rC- 0 O (r0 0

0) *a C r- C U C -
'a m -- 0* 0 C
E>-- > C 4- C S- O
4U 1 a *r- 4- *S- *
U 44- S 4. ( C
-3 U0 =. 4>) C 0
a) (a -4 Co) t u -
*.-.- > C C)- a) C
p *C 0. U 0. ) U0 'U S
+- ( V W aC 1 a. o
>0 0 4 4 U t o
*C 4 4 U
>0L 4-) C 0 (0 )
00 0 r_ ) C)u 'a u
4-.). C 0 > L r- CU
*i 3 r L 0 a.
4) to j0 () U ) 0 0.
> 0 CC = 4 ) )
SC 4> C) 0 a
0 4 U) C) C 4- ) C)
O 4. 0r- S C C
Cc *- *- a w 4 i-
CO C + 4- U 0 =U -
4 C *'- 'U 'U O. C) O
4- .- 0r- 4m 4-
-)4- 4) 4-) 4 0.0 4-)-
00 O C U S- C 4.)
4- )0 E- C )- C4
) 0OU C U r-, C 0.
(U .0.O 0) C) C) 0).C 0
> U 4.) *- U

U U C =
U > r.JC 1. ^- 0
s C) 0 0 0 C U)
C4 C U-C C m U CU
U-- O 0 3 3 O0
* U *- 4- *- -0 *rC

- 'U 1 -N C) 4-

C;- C) ('U Et' C (-
CU( 4-C C C
> C *r *- 0
D-C V_ .0. U
I U ) 3 I 01E 1-0o *. iJC 'U .c
C) C) 1 o
0)1 0.C) C) U) OC C)0
II- =3 +^ + C l- -Q --> (

N -


M L\
*J I

J -.o
W* Qm

Other methods must be used to determine KdC from the displacement
plot when the initial receptor occupancy is too high. The direct
estimation of an ED50 value from the curved displacement plot (fig. 3-3)
is statistically naive, but a "pseudo-Hill" or logit-log transformation
of the data (fig. 3-4) may be used to approximate a straight line for
the estimation of ED50 by simple linear regression. The subsequent
calculation of KdC from the ED50 estimate presents further difficulties.
We shall consider sequentially the problems of estimating ED50 and then
using this estimate to calculate KdC.
The "logistic" equations (see De Lean et al., 1978, for review;
these are only approximations, as we shall demonstrate) that are used to
transform the competition displacement data of fig. 3-3 into the
approximately linear logit-log plots shown in fig. 3-4 are the

BL = (BL)o/(1+Sc/ED50) 1.0 (3-22)


BL = (BL)o/(+Fc/FC50 (3-23)

(The above Hill coefficient or "slope-factor" of 1.0 in the logistic
equations is appropriate for non-interacting binding sites such as those
under consideration here.) These logistic equations may be immediately
transformed into the "pseudo-Hill" or logit-log expressions

logit [BL/(BL)0] = log (BL/[(BL)O-BL]) = log ED50 log SC (3-24)


4-) a) -

(0 4- W
U) C I
C ,- 00 C)
4S 4- (-

. -, 4) o .- .J W W
S S- C. r LO )

0 U) E L *r-

U) .0 *- 0 *
E 4 o 0.3 )
U) > U C >4-
0 V C O -e 0
4-0 = 4 U) .0 a)

U 4)u 41 *' 4.I- U0
0 *r -0 0 C

e S.- 3:. ( 0-

-o0 0 "- U) 0 -- D
4J *U 0 0
U-) U CO t U) C -

n:3 4-.) 4-) 4-) w U0
S- ( U X U -

4. ..J 4. .C IB
0 m 4*r- C C 0 CD0

U- 0 S- U ) r- 0 I
0 >E CL ) M

0. *r- 4.) .C )I E4
E -. -U 4- U) 0 L 0
o cu (. .e u 0
SuO E -.4 ()
L-j 0 "0a C 0)
cU u(- s C 4-
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logit [BL/(BL)o] = log (BL/[(BL)o-BL]) = log FC50 log FC,


which may be fit (approximately) to the binding data by simple linear
regression. If equations (3-22) and (3-24) were exact, then the ED50
plot (upper curve, fig. 3-4) would be linear; if equations (3-23) and
(3-25) were exact, then the FC50 plot (lower curve, fig. 3-4) would be
linear. Equations (3-23) and (3-25) are (as we will show) always better
approximations than equations (3-22) and (3-24). In the example under
consideration equations (3-23) and (3-25) provide an excellent
near-linear transformation of the binding data, as one can see upon
examination of fig. 3-4; the nonlinearity of the ED50 plot, however, is
quite apparent in this example.
We shall now derive the exact (but not computationally useful)
expression for logit [BL/(BL)o] and then note the condition under which
it may be approximated by equations (3-24) and (3-25). If the
Edsall-Wyman equation (3-3, above) is combined with the obvious initial

(BL 0 = B(FL)o/[KdL+(FL)o 0], (3-26)

then we obtain, upon eliminating B0 from equations (3-3) and (3-26),

BL = C1(BL)OFL/[KdL(1+FC/KdC)+FL],


where the constant C, = [(FL)0 + KdL]/(FL) 0 = 1 + KdL/(FL)0. From
equation (3-27) we immediately obtain

BL/[(BL)o-BL] = C1FL/[KdL(I+Fc/Kdc)+FL(1-Cl)], (3-28)

which, upon elimination of C1 from the denominator and division by
FLKdL, yields

BL/[(BL)o-BL] = (Cl/KdL)/[(1/FL) (1+Fc/Kdc)-(/(FL)o).'


Thus, the exact logit-log equation is given by

logit [BL /(BL)o = log (C1/KdL)
log [(1/FL)(1+Fc/Kdc)-(I/(FL)o)], (3-30)

which is not computationally useful (since the term for the logit-log
abscissa itself contains the unknown KdC). If, however, we may assume
that FL is approximately constant over the entire range of SC (i.e.,
that FL 2 (FL)o), then equation (3-30) reduces to the simplified form

logit [BL /(BL)] ) log [C1KdC(FL)o/KdL] log FC, (3-31)

which is the linear logit-log plot equivalent to equation (3-25) above.
A comparison of equations (3-25) and (3-31) shows that the assumption FL
1 (FL 0 leads to the expression

FC50 C1Kdc(FL)o/KdL = KdC[1+(FL)o/KdL], (3-32)

thus indicating clearly that FC50 (and, of course, ED50) is quite
different from the desired parameter KdC, which must be determined by an

additional calculation. Although the above approximation that leads to
linearization of the logit-log FC plot (i.e., FL (FL)o) is derived
from the initial occupancy condition (BL)0 < SL, the approximate
linearity of the plot is fairly robust over a broad spectrum of
experimental conditions and depends only on the initial conditions

relating to the labeled ligand L. Specifically, the approximate
linearity of the logit-log FC plot does not depend on the relative

affinity of the two ligands, (Kdc/KdL). The logit-log plot containing
log SC as abscissa (the "ED50" logit-log SC plot), however, departs
significantly from linearity because the approximation FC SC is a poor

one at low values of SC. If KdC >> KdL then the large values of SC

required to achieve ligand displacement will also make this formula
approximately valid and thus lead to linearization of the simpler ED50

plot. The calculation of FC for the construction of the logit-log FC
plot from the measured data has been described above (equation 3-12
combined with the relation FC = SC BC), and the initial binding (BL)0

may either be measured directly or calculated from the values of KdL and

B0 (in combination with the known SL) measured previously. In the
specific example under consideration simple linear regressions of the
theoretical logit-log data of fig. 3-4 yield the following results:
[ED50 (lin. regress.)/"true" ED50] = 1.12 (13% error), and [FC50 (lin.
regress.)/"true" FC50] = 0.999 (0.1% error). (The "true" values of
ED50 and FC50 are, respectively, 4.80 and 3.20 nM.)

Further analysis is, of course, required to calculate KdC from the
estimates of either ED50 or FC50 obtained from the logit-log plots
discussed above. If, in equation (3-32) above, FC50 is replaced by ED50
and (FL)o by SL, one obtains the Cheng-Prusoff (Cheng and Prusoff, 1973;
Munson and Rodbard, 1980) correction

KdC L EDO5/(1+SL/KdL). (3-33)

This formula is derived from equations (3-2) and (3-3) above by using
the definition of ED50 (i.e., that (BL)0 = 2BL when SC = ED50) and
applying the drastic approximation that both FC SC and FL SL. As
the illustrative example will demonstrate, this does not provide a good
estimate of KdC when the affinity of the competing ligand is too high.
We now show that this Cheng-Prusoff correction can be improved
substantially by including in the calculation the value of (BL )o, which
easily can be measured experimentally or calculated from the values of
KdL and B0 measured previously. Combining the above equations (3-3),
(3-23) and (3-26) yields, upon elimination of BO, the expression

(FL)OFC50/[KdL + (FL)o][FC50+FC] j FL/[KdL(1+Fc/Kdc)+FL],


which, when evaluated at the 50% displacement point, becomes

(FL )0/2[KdL+(FL )0] FL50/[KdL( 1+F50/Kdc)+FL50].


(Expressions (3-34) and (3-35) above are not exact, since they are
derived from the logistic equation (3-23), which is itself only an
approximation.) Since FL50 = SL (BL)o/2 and (FL)0 = SL (BL 0 we
finally obtain, after elimination of FL50 and (FL)0 and some
rearrangement and simplification,

KdC FC50 x 2KdL[SL-(BL)o 0]/[(BL)o02 + 2SL2
+ 2SLKdL-3SL (BL)o]. (3-36)

This is a much better approximation than the Cheng-Prusoff
equation (3-33), to which it reduces when (BL 0 is neglected and FC50 is
replaced by ED50. Equation (3-36) remains approximately valid, and is
still superior to equation (3-33), when ED50 is substituted for FC50:

KdC ED50 x 2KdL[SL-(BL)]/[(BLo + 2SL2
+ 2SLKdL-3SL(BL)0]. (3-37)

Equation (3-36) will, however, always be superior to equation (3-37);
similarly, the Cheng-Prusoff expression itself will always be more
nearly exact if a good estimate of FC50 is substituted for the estimate
of ED50. Table 3-1 lists, for the example that we have been
considering, the KdC estimates derived from the two different
approximations; each method has been used in combination with both the
estimated and the exact values of FC50 and ED50 listed above. It will
be seen that the retention of (BL)0 in the approximation is required for


04 c)0

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the accurate derivation of KdC from the competition displacement data

under consideration here. The ease of implementation of equation (3-36)

suggests that it (or at least equation 3-37) should always be used

instead of the Cheng-Prusoff approximation.

Although the graphical linearization of competition data is

achieved most conveniently in the recommended coordinate systems

discussed above, it can be displayed in simple modifications of any of

the popular binding plots. For example, a modified "Lineweaver-Burke"

plot (Lineweaver and Burke, 1934) that is linear with slope KdC (and

y-intercept 1.0) can be constructed by plotting (BO-BL)/BC on the

ordinate with 1/FC on the abscissa. A modified "direct linear" plot

(Eisenthal and Cornish-Bowden, 1974) may even be used to estimate KdC by

finding the median of the abscissae of the intersections where lines

plotted for each of the individual observations in the usual "direct

linear" parameter space (Fc, BC) intersect the horizontal lines having

ordinates BO-BL.

The problem of determining the best-fitting line for the

recommended Bc/FC vs. [BO-BL-BC, (free binding sites)] plot is similar

to the problem of regression for the original one-ligand Scatchard plot

and has, in this context, been adequately discussed (e.g. Cressie and

Keightley, 1979; Rodbard, 1973; Rodbard and Feldman, 1975). In

addition, by the very nature of the definition of logit [BL/(B L)o], the

logit-log plots of competition displacement data are quite sensitive to

error in the measurements of BL performed at the low concentrations of

the competing ligand. Although the assumptions underlying the use of

the method of least squares (e.g., uniformity of variance,

noncorrelation of error in the independent and dependent variables) are

clearly violated in both the Scatchard and logit-log transformations of

the data (e.g., Rodbard, 1973), the method of least square is still used

frequently as a convenient first approximation and is probably not too
seriously biased if "outliers" are few and if confidence intervals are
strengthened by repetition of the experiment. Thus, the method of

simple linear regression or of linear regression through a fixed point

(the origin) may be applied to the recommended Bc/FC vs [free binding
sites] plot; the calculation for the latter (Pollard, 1977) is routine

and directly yields

KdC = 1/slope = KdL(BL/FL)i/(BL/FL)i (BC/FC)i. (3-38)

The approximate analysis of variance and confidence intervals are given

in standard tests (e.g., Pollard, 1977). It is also convenient to use
the simple and more "robust" median parameter estimates discussed by
Cressie and Keightley (1979). This procedure (Cressie and Keightley,

1979) may be used to determine KdL and B0 from the initial Scatchard
plot; and then if the line is to be forced to pass through the origin,

the "free receptor" plot for the direct determination of KdC may be
analyzed by calculating the median estimate

KdC = 1/slope = median of (BLKdLFC/BCFL)i. (3-39)

In any case, the statistical complexity of the experiment demands that
confidence in the parameter estimates obtained by any of the methods
discussed above must come from replication of the complete design.


A simple procedure for linearizing the curved Scatchard plot of the

binding of a labeled ligand to a single class of noninteracting binding

sites in the presence of a fixed total concentration of competitive

inhibitor has been presented. Since the nonlinearity of the Scatchard

plot constructed in the presence of the inhibitor may not be apparent

upon visual inspection because of variance in the data, the method of

calculating the equilibrium constant of the competitive inhibitor

recommended above should be used unless it is known that the equilibrium

dissociation constant of the inhibitor (KdC) is much larger than the

total concentration of binding sites. The same procedure may also be

applied to the analysis of data derived from the "ED50" competition

displacement experimental design (if the initial receptor occupancy is

not too high). In addition, a useful approximation (a generalization of

the Cheng-Prusoff formula) that may be used to relate the ED50 or FC50

estimates obtained from approximately linear logit-log plots of

competition displacement data to the actual affinity of the competitive

inhibitor for the binding sites has been presented.

Significant sources of error remain inherent in both experimental

designs and cannot be eliminated easily; these include nonspecific

binding of the competitive inhibitor and also the potential presence of

additional receptor sites having significant affinity for the

competitive inhibitor but negligible affinity for the labeled ligand.

Furthermore, the statistical characteristics of the simple graphical

methods suggested above currently remain untested and must eventually be

examined in detail by the Monte-Carlo simulation procedure (e.g. Thakur,

Jaffe and Rodbard, 1980); for example, the competition "free receptor"

plot is probably less sensitive to error in B0 and KdL when it is
"relaxed" (i.e., not forced to pass through the origin). Whenever

practical, a computer program (e.g., Munson and Rodbard, 1980) should be

used to fit binding isotherms by a weighted, nonlinear regression

technique performed with a relatively error-free independent variable.

The plot of Bc/FC vs [free binding sites] or the competitive

displacement logit-log plot may still be used to display the actual data

points and the fit of the resulting computer-generated parameters.




Glucocorticoids have profound metabolic, neuroendocrine, and

behavioral effects in the mammalian brain (for reviews, see: Bohus et

al., 1982; Rees and Gray, 1982). Although some of the less-

well-understood effects may result from direct interactions of the

steroid with components of target cell membranes, many of the effects

are thought to be mediated by interactions of the hormone molecules with

steroid-specific cytoplasmic and nuclear macromolecular receptors that

concentrate as activated hormone-receptor complexes in the target cell

nuclei, where they initiate changes in gene expression that produce the

ultimate physiological effects.

The experiments reported here examine a number of physiochemical

characteristics of soluble mouse brain glucocorticoid binding sites, in

order to determine whether the glucocorticoid receptor system in mouse

brain resembles closely that operative in other target tissues and.

species. Although a few published studies have reported the existence

of glucocorticoid receptors in the mouse brain (e.g., Finch and Latham,

1974; Nelson et al., 1976; Angelucci et al., 1980), no basic

characterization of the kinetic and equilibrium binding parameters or

the steroid specificity of these receptors has yet been reported.

Although a body of literature concerned with the properties of rat brain

glucocorticoid receptors already exists (for review, see: Bohus et al.,
1982), recent improvements in receptor methodology have made it possible
to study the brain glucocorticoid receptor system under conditions that

prevent receptor activation (nucleophilic transformation) and maximize

in vitro receptor stability, permitting the relatively lengthy
incubations and procedures required to generate equilibrium isotherms
and to investigate the size and shape of the receptors.

We have used the labeled glucocorticoids [3H]corticosterone,

[3H]dexamethasone and [3 H]triamcinolone acetonide (cyclic acetal).
[3H]Dexamethasone and [3 H]corticosterone were used to measure
equilibrium and kinetic binding parameters, whereas the

nearly-irreversible ligand [3H]triamcinolone acetonide ([3H]TA) was used
for the lengthy sedimentation and chromatography procedures required to

examine receptor size and shape. The experiments reported here have
explored buffer components and employed a buffer that prevents the loss
of unoccupied binding sites at 20C; used a rapid and convenient binding

assay; considered the possible consequences of failure to allow adequate
incubation time when ligand concentrations are low; compared equilibrium
binding parameters derived from the same pool of experimental data by

several different methods of analysis; determined ligand specificity by
applying mathematically correct procedures to the analysis of steroid
competition data; observed that CBG-like molecules contribute
significantly to the total pool of corticosterone binding sites, and
examined binding site sizes and shapes to assess the stability and
homogeneity of the in vitro receptor population.

Materials and Methods

Chemicals, Steroids and Isotopes

The [1,2,6,7-3H]corticosterone (SA = 80 Ci/mmole),
[6,7-3H]dexamethasone (SA = 36 Ci/mmole) and [6,7-3H]triamcinolone
acetonide (SA = 37 Ci/mmole) were purchased from New England Nuclear

(Boston, MA) and checked for purity by chromatography on 60 cm LH-20
columns (Sippell, Lehmann and Hollmann, 1975) or by thin layer
chromatography (TLC) on Silica Gel G (plates were developed in

cyclohexane : methyl ethyl ketone, 1:1, or in dichloromethane :
methanol, 24:1). All nonradioactive steroids were purchased from
Steraloids, Inc. (Wilton, NH). Additional radiochemicals

([14C]antipyrene, [2-3H]deoxy-D-glucose, [14C]formaldehyde,
[carboxyl-14C]inulin and [3H]water) and a [1251]cortisol Solid Phase
Radioimmunoassay kit were purchased from New England Nuclear.

Chromatography and filtration supplies were purchased from Pharmacia

Fine Chemicals (Piscataway, NJ), Bio-Rad Laboratories (Richmond, CA),
Whatman, Inc. (Clifton, NJ), Brinkmann Instruments, Inc. (Westbury, NY),

and the Amicon Corp. (Danvers, MA). Rabbit antiserum to corticosterone
was a gift from R.H. Underwood and G.H. Williams (Peter Bent Brigham

Hospital, Boston, MA). Other chemicals and solvents were of the highest

purity available commercially.


All studies used adult female CD-1 mice (outbred, 20-25g Charles
River Laboratories, Wilmington, MA) that were subjected to combined
ovariectomy and adrenalectomy 3-5 days prior to the experiment in order

to remove known sources of endogenous steriods. Ovariectomy and

adrenalectomy were performed bilaterally via a lateral, subcostal

approach under Nembutal anesthesia, and mice were given 0.9% NaCl in

place of drinking water. On the day of the experiment mice were

anesthetized with ether (in some cases a .5-1 ml blood sample was then

withdrawn directly from the heart) and slowly perfused (over a period of

5 min) through the heart with cold HEPES-buffered saline (3 ml,

isotonic, pH 7.6) to reduce blood-borne CBG contamination of the brain

tissue. The efficacy of this procedure was assessed by a [ 14C]inulin

washout study (see Chapter V).

The effectiveness of the surgery was verified by measurement of

corticosterone levels in plasma samples obtained from some of the

adrenalectomized mice at the time of killing. This was accomplished by

radioimmunoassay (RIA) both with rabbit antiserum to corticosterone (by

a modification of the method of Underwood and Williams, 1972) and with

the New England Nuclear [125I]Cortisol solid phase RIA kit using corti-

costerone to construct the standard curve. Plasma samples (101l) were

extracted with 1 ml dichloromethane and then dried down prior to RIA.


For most of the experiments cytosol was prepared in buffer A: 20 mM

HEPES, 1 mM EDTA, 2 mM DTT, 10 mM Na2Mo04, 10% (w:v) glycerol, pH 7.6.

The effects of pH and of the dithiothreitol (DTT) and molybdate

(Na2MoO4) concentrations on binding site stability were explored in

several initial experiments, and gel filtration and sedimentation were

performed at elevated ionic strength (with the addition of KC1). In the

descriptions of these experiments buffer compositions are reported as

modifications of the basic buffer A formulation (e.g., buffer A DTT,

buffer A + .15M KC1, etc.).

Cytosol Preparation and Aging

Brains were removed from the perfused animals and homogenized (20

strokes at 1000 rev/min) in 1-6 volumes of cold buffer A in a glass

homogenizer with a Teflon pestle milled to a clearance between the

pestle and homogenization tube of 0.125 mm on the radius (to minimize

rupture of the brain cell nuclei, as suggested by McEwen and Zigmond,

1972). The crude homogenate was centrifuged at 20C for 10 min at 15,000

rpm (27,000 x g) in a 15 ml Corex centrifuge tube. The supernatant was

transferred to a 10 ml "Oak Ridge" polycarbonate tube, and the pellet

was washed by resuspension in half the initial volume of buffer A (used

for the homogenization) and recentrifugation at 2 C for 10 min x 27,000

g. The resulting supernatant wash was added to the original supernatant

in the "Oak Ridge" tube, which was then centrifuged at 2 C for 1 h at

106,000 x g (average) to produce the cytosol used in the incubations.

Approximately 2 h elapsed between the time of killing and termination of

the high-speed centrifugation. Cytosol protein concentrations for the

equilibrium experiments ranged from approximately 2 mg/ml (with

homogenization in 6 volumes buffer A, initial pellet then washed with 3

volumes buffer A) to 12 mg/ml (homogenization in 1 volume buffer A,

pellet washed with 0.5 volume additional buffer A). The cytosol protein

content was determined by a modification of the Lowry method (Bailey,

1967) using bovine serum albumin as the standard.

In several experiments cytosol samples were incubated without

steroid for variable lengths of time before labeling with the

[ 3H]steroid ligand (i.e., the cytosol was deliberately "aged" beyond the
approximately 2 h required for cytosol preparation). In such

experiments the duration of aging was measured from the time when

cytosol preparation was completed (t = 0).

In order to examine the subcellular distribution of glucocorticoid

binding sites in mouse brain the standard subcellular fractionation

scheme (Cotman, 1974) was employed to generated crude nuclear (Pl),

crude mitochondrial (P2), and microsomal (P3) fractions in addition to

the cytosol; the fractionation scheme was modified, in that buffer A

(which is hypertonic because it contains 10% glycerol) was used instead

of isotonic .32 M sucrose. The concentrations of high-affinity

glucocorticoid binding sites measured in the subcellular fractions

(other than cytosol) generated in this way were negligible, and thus

these hypertonically-produced particulate fractions were not further


Binding Assays

The principal assay used to measure bound [ 3H]steroid was the DEAE
(Whatman DE-81) filter assay, modified from similar assays developed to

measure glucocorticoid and mineralocorticoid binding to cytosolic

proteins in liver and kidney (e.g., Warnock and Edelman, 1978; Santi,

Sibley, Perriard, Tomkins and Baxter, 1973). The 25 mm filters were

equilibrated at 0-40C in buffer A and then washed 2 times with 2 ml
buffer A in a Millipore suction manifold. For each of the triplicate
assays that commonly were performed a 50 'l aliquot of the sample was

pipeted directly onto the moist filter and allowed to penetrate it for
at least 1 min. Filters were then washed with 5 x 1 ml buffer A,

suctioned to near dryness, and then transferred to scintillation vials.

Filtration was performed at 0-4C in a cold room. Radioactivity was

determined by liquid scintillation counting at 38% efficiency following

the addition of 1 ml H20 and 10 ml Triton-toluene scintillation cocktail

(toluene-Triton X-100, 2:1; 2, 5-diphenyloxazole, 4.375 g/l; dimethyl

POPOP, 43.75 mg/1) and disruption of the filters by vortexing of the

vials. Alternatively, the filters were dried overnight in a warm oven

and then counted at higher efficiency in a toluene based scintillation

cocktail not containing Triton X-100. The efficiency of the DEAE filter

assay was determined (as described below) by two different methods and

found to be 76%.

In order to calculate the efficiency of the DEAE filter assay some

of the binding data obtained with it were compared with those obtained

from the same samples with a Sephadex G-25 minicolumn gel filtration

assay and with a dextran-charcoal adsorption assay. In the former

procedure 50 pl aliquots of the sample were loaded onto Pasteur pipet

minicolumns filled with 1.5 ml Sephadex G-25 equilibrated in buffer A;

following collection of a 0.51 ml fraction that was discarded, a 0.8 ml

void volume containing bound radioactivity was collected and assayed by

liquid scintillation in a Triton-toluene cocktail. The dextran-charcoal

adsorption assay was performed by adding the 50 pl sample aliquot to a

1 ml suspension of dextran-coated charcoal (0.5% Norit A activated

charcoal, Fisher; 0.05% Dextran T-70, Pharmacia); following incubation

at 0-40C for 5 min with occasional vortexing the charcoal was pelleted

by centrifugation at 10,000 x g for 5 min. The supernatant was then

taken for the determination of bound radioactivity by liquid

scintillation counting.

Gel Chromatography and Gradient Sedimentation

The in vitro stability and molecular size of the receptors were
examined by Sephacryl S-300 chromatography and glycerol gradient

sedimentation. Concentrated cytosol prepared in buffer A + 150 mM KCI

was incubated at 20C for 12-16 h with 10 nM [3H]TA or 10 nM [3H]TA and
200-fold excess of unlabeled TA. Following incubation, free [3H]TA was
removed by gel filtration in the same buffer on a large (1.5 x 98 cm)
Sephadex G-25 (fine) column. Samples from the void volume of the G-25

column (2 ml, approximately 5 mg/ml) were then chromatographed on a

column of Sephacryl S-300 (superfine, 1.5 x 98 cm) at 12 ml/h in the
same buffer (A + .15 M KCI). Fractions (2 ml) were collected, and 1 ml
aliquots of these were assayed for radioactivity by liquid

scintillation. (The remaining 1 ml from the relevant fractions was
saved for gradient sedimentation.) Distribution coefficients (Kd) were

calculated from elution volumes (V e), the void volume (V ) indicated by
blue dextran, and the total liquid volume (Vi) marked by [3H]water,

[14C]antipyrene and [2-3H]deoxy(D)glucose: Kd = (Ve Vo)/(Vi Vo).
The column was calibrated (figure 4-29) with 7 standard proteins

(chromatographed in separate runs as two different mixtures and detected
by absorbance at 280 nm), and the Stokes radius of the receptor complex

(Rs) was calculated from regressions of Rs vs. several different
functions of the calibration Kd values as shown in figure 4-30.
Standard curves were generated by the linear methods of Porath (1963)
and Ackers (1967), and by the nonlinear regression of Laurent and
Killander (1964). The methods of regression were in close agreement.

After locating the peak of the gel chromatographic profile, the
remaining 1 ml aliquots from each of the 5 fractions bracketing the

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