The effect of plasma steroid hormones

protein binding on the metabolism of

J. F. Tait and S. A. S. Tait Moorlands, Main Road,

East

revised manuscript received

Boldre, Brockenhurst, Hampshire S042 7WT 22 March 1991

ABSTRACT

Earlier views indicated that globulin (corticosteroid\x=req-\ binding globulin (CBG) or sex hormone-binding globulin (SBG)) but not albumin binding in plasma, protects steroids from splanchnic metabolism in man. Also, the splanchnic extraction (HE) of a steroid seemed to be highly dependent on the rate of disassociation of the steroid\p=n-\proteincomplex. However, the faster rate of disassociation

(\g=t\ m=1/2\ 0\m=.\9s) of cortisol\p=n-\ =

CBG, as determined by later accurate fluorescence methods, intuitively meant that this complex must

disassociate completely in a single 9 s passage through the liver. The low HE of total cortisol was then a

puzzling anomaly. Using a differential equation solver (TUTSIM) and a model with unbound, albumin- and globulin-bound pools of steroid (with metabolism of unbound and also possibly albumin-bound steroid), the mechanism of splanchnic metabolism has been studied. The 'complex', probably most realistic, model includes 13 steroids, which can simultaneously bind to plasma albumin, CBG and SBG. The steroid concentration

and numbers of occupied binding sites of the globulins decrease during the time of metabolism. The experimental data used are the in-vitro binding characteristics of the steroid\p=n-\proteincomplexes, including the equilibrium constants and rates of disassociation and the in-vivo HE of nine steroids, usually measured by direct analysis of hepatic venous blood. However, the HE of cortisol had to be calculated from the metabolic clearance rate/splanchnic blood flow, giving a maximum value of 12%. The fractional metabolic rate of unbound steroid is generally represented by e. A certain value of e (RE) is required to give a remaining steroid concentration after 9 s of metabolism, which is made equal to (1 \p=n-\HE)in the model to simulate splanchnic extraction. If the fractional rate of metabolism of albumin\x=req-\ bound steroid is h (f = h/e), then RE will depend on the value of f. The maximum RE for cortisol is 0\m=.\16 for f =0 and 1 respectively. RE0 0\m=.\42and RE1 For either value of RE, there will be the appreciable reassociation of cortisol to CBG after disassociation =

=

of the cortisol\p=n-\CBGcomplex. With such reassociation, the total cortisol remaining after 9 s metabolism is fairly independent of the rate of disassociation of the cortisol\p=n-\CBGcomplex. This explains the low total HE of cortisol in spite of the high rate of disassociation of cortisol\p=n-\CBG.Generally, for all nine steroids studied, HE estimations in vivo in humans indicate that the steroid\p=n-\globulindisassociation rate will only be markedly rate-limiting for dihydrotestosterone\p=n-\ SBG and, to a lesser extent, testosterone\p=n-\SBG. These results are examples of the principle that the divergence in hormone concentration with the disassociation rate of the hormone-protein complex after metabolism depends on the value of e. The RE0 and RE1 values of the nine steroids: aldosterone, progesterone, testosterone, dihydro-

testosterone, androstenedione, androstanediol, oestraoestrone and cortisol have also been calculated from all in-vivo HE estimates. If it is assumed that the steroid in the albumin-bound pool is not metabolized (f = 0), then the RE0 values of the nine steroids considered have a large variation (s.d./mean 115%).

diol,

=

There is a correlation between the RE0 values and their albumin-binding index (BIA). However, if f 1 then the variation of RE is smaller (s.d./mean 36%) and there is no correlation between RE1 and BIA. The ratio of the RE0 and RE1 values for a particular steroid is nearly equal to (1 + BIA), which is determined solely by the dynamics of the situation. However, the appropriate value of f depends on the mechanisms involved. With the F1 hypothesis (f =1), albumin binding does not protect steroids from splanchnic extraction because of metabolism of albumin-bound steroid. With the FO hypothesis (f = 0), this seeming lack of protection of albumin binding is essentially artefactual. Albumin-bound steroid would not be metabolized directly but the fractional rate of metabolism of unbound steroid would be increased with the decreasing polarity of the steroid (i.e. with increasing BIA). With the available data, the choice between the hypotheses can only be on an intuitive basis. Journal of Endocrinology (1991) 131, 339\p=n-\357 =

=

1970; Heyns & De Moor, 1971), the results of Dixon

INTRODUCTION

Empirical relationships In early studies in the field, (Samuels, Brown, Eik-Nes et al. 1957; Tait & Burstein, 1964; Baird, Horton, Longcope & Tait, 1969) certain empirical relation¬ ships were found to describe the metabolism of steroids in humans. The splanchnic circulation is the major site of the overall metabolism of steroids in humans. An important measure of such metabolism, the splanchnic extraction, can be estimated, pre¬ ferably from direct hepatic venous blood analysis (Baird et al. 1969). From these and more indirect measurements, it seemed that the binding of a steroid to certain plasma globulins, which have low plasma concentrations but relatively high equilibrium constants for their steroid complexes, protected the steroid from splanchnic metabolism (Tait & Burstein, 1964; Baird et al. 1969). The most important of these globulins are sex hormone-binding globulin (SBG) and corticosteroid-binding globulin (CBG). However, the binding of a steroid hormone to albumin, which has a high plasma concentration but a relatively low equilibrium constant for its steroid complex, did not seem

to

protect the steroid from metabolism. These

conclusions arose partly from the characteristics of the binding of steroids to the relevant proteins as measured in vitro. The % splanchnic extraction (HE%) could then be approximately related to the globulin binding (GB) by HE% (100- GB%). Later, Siiteri, Murai, Hammond et al. (1982) confirmed these findings although only the overall metabolic clearance rate (MCR) was measured. However, although these correlations between plasma binding and splanchnic extraction were reasonably quantitative, this finding was empirical and only indirectly revealed the specific mechanisms involved. =

Previously proposed mechanisms of steroid metabolism Starting with the studies of Dixon (1968), followed by similar approaches (Baird et al. 1969; Baulieu, 1970; Heyns & De Moor, 1971), it was considered that the rate of disassociation of the steroid-globulin complex determined the splanchnic metabolism of the steroid. If the disassociation half-life ( ) of the complex was greater than the 9 s transit time through the liver then it was likely that the released steroid would not be metabolized to a major extent. As the steroid-albumin complex disassociates at a very fast rate, it was thought that this would explain the experimental find¬ ing of the correlation of HE% and (100-GB%). As determined by dialysis of the released free cortisol, largely later confirmed by methods depending on the absorption of free cortisol (Baird et al. 1969; Baulieu,

(1968) for the cortisol-CBG complex at 37 °C indi¬ cated a disassociation x¡ of 10 s compared with a transit time through the human liver of 9 s, which would support this hypothesis. More recently, Stroupe, Harding, Forsthoefel & Westphal (1978) measured the disassociation of CBG-steroid complexes by a fluorescence technique which was capable of estimating shorter half-lives. This gave a value of x¡ 0-9 s for the disassociation of the cortisol-CBG complex, which intuitively indicates that this complex disassociates nearly completely in the 9 s passage through the liver. However, as will be demonstrated in the present treatment, this would not effectively occur except with very high rates of metabolism of the free cortisol. Detailed dynamic mechanisms to explain steroid metabolism have still not been elucidated by generally agreed proposals, although later theoretical treat¬ ments have been more sophisticated and usually included consideration of both the disassociation and reassociation processes (Ekins, Edwards & Newman, =

1982; Pardridge, 1988; Mendel, 1989a,Z>; Mendel, Kuhn, Weisiger et al. 1989). Also, when applicable,

disassociation rates of steroid-globulin complexes have been used, which were determined by the more accurate fluorescence method (Stroupe et al. 1978). However, previous studies have made no specific attempt to compare the theoretical quantitative predictions of the HE of different steroids with corresponding values determined in vivo in humans. The following treatment attempts to do this for nine biologically significant steroids.

MODEL FOR THE SPLANCHNIC METABOLISM OF STEROIDS

A model for splanchnic steroid metabolism is shown in Fig. 1, where Sv, SA and SG represent the concen¬ trations of unbound albumin (A)- and globulin steroid (G)-bound respectively. The globulin can be CBG (C) or SBG. It is assumed that the association and disassociation rates for the steroid-protein complex are equivalent for the in-vitro and in-vivo situations. Where represents the protein-bound steroid pools, the ratio of the dis-

(Ü),

association

and association (aP) rate constants, the equilibrium constant. The fractional disassociation rate constant (kpu) is the fraction of the steroid-protein complex disassociating in unit time, and is equivalent to . The fractional association rate constant (kUP) is the fraction of the unbound steroid pool reassociating to the complex in unit time and is given by kup ap, where is the concentration of

ap/^p [K]p,

( )

=

=

sa

sS

kuG

A

fh

=

->

f

s9

0

V

s9

1. Simplest and simple model for the splanchnic metabolism of steroids. Plasma concentrations of steroids and corresponding fractional rates of metabolism are Su and e (unbound), SA and h (albumin-bound) and SG and 0 (globulin-bound). The fractional rate of metabolism of globulin-bound steroid is assumed to be zero. The superscripts indicate the time in s. Also shown are the transport rate constants kUA and kUG (association rates) and kAU and kGU (disassociation rates). In the simplest model, the association and disassociation rates are constant. In the simple model, the association rates depend on the steroid concentration. figure

unoccupied receptor molecules of the binding protein (Fig. 1). The ratio, kup/kpu [K]p, is the equilib¬ rium binding index (BIP), which is the equilibrium ratio of the bound to unbound steroid in biological fluids (Tait & Burstein, 1964; Westphal, 1971). These include peripheral and arterial blood entering the splanchnic circulation, which are often assumed to have equal steroid concentrations (Tait & Burstein, =

1964).

The actual binding proteins considered were albumin (A) and globulin (G). Therefore, A or G was substituted for in the appropriate constants, e.g. kUA, kAU, kUG, kGU, [K]A, [K]G, BIA and BIG. The fractional metabolic rate constant for the unbound steroid pool is rep¬ resented by e and the fractional metabolic rate con¬ stant for albumin bound steroid by h, where h fxe (Fig. 1). Therefore, f is the ratio of the fractional metabolic rate constant of albumin bound to unbound steroid. The fractional metabolic rate constant for globulin-bound steroid is not considered here as it is not established that this process is significant. =

splanchnic circulation. This blood contains steroid at equilibrium specific activity after the continuous

an

constant infusion of tracer amounts of radioactive

steroid into the peripheral circulation. Then, the processes in the model (Fig. 1), with metabolism of unbound steroid and, possibly, of steroid in the albumin pool (but no metabolism in the globulin

pool), are described by:

dSu/dt= e.S,j kUG.S,j kUA.S,j-(kGU-SG + kAu-SA-(equation 1) —

dSA/dt

pool

no

metabolism of steroid in the

globulin

The theoretical treatment examines the fate of a sample of blood of very small volume entering the

-

—

kAU. SA + kUA. Sö

-

h. SA-(equation

2)

dSG/dt -kGU.SG + kUG.Su-(equation 3) =

S$,

The initial values of SA, S¿ are usually taken as the equilibrium values, representing the concen¬ trations entering the splanchnic circulation. Then, S Sv + SA + SG and S° S°+S°+S¿. When all concen¬ trations are expressed as a % of the initial total steroid concentration, S°= 100%. Superscripts 0 or 9 indicate the time in seconds after the start of the operation. The steroids investigated were: testosterone, androstenediol (androst-5-ene-3ß,17ß-diol), androstenedione, =

Processes with

=

—

=

androstanediol (5a-androstane-3a,17ß-diol),

dihydro(DHT; 17ß-hydroxy-5a-androstan-3one), dehydroepiandrosterone (DHA), oestradiol (OE2), oestrone (OE,), progesterone, aldosterone, corticosterone, cortisone and cortisol. For the sake of brevity, cortisol analysed using the data of Stroupe et al. (1978) or Dixon (1968) is termed either Stroupe or testosterone

Dixon cortisol. The 'simplest' model, shown in Fig. 1, can represent the metabolism of cortisol with binding only to CBG and albumin and of testosterone with binding only to SBG and albumin. A proportion of the initial steroid concentration would be bound to the appropriate globulin and the number of unoccupied binding sites would determine the rate of association of the steroid. For male plasma, other steroids occupy a lower number of binding sites and the binding of testoster¬ one to SBG and cortisol to CBG can be considered to be dominant. In predicting the metabolism of the weaker binding steroids, the number of globulinbinding sites can then be considered to be determined solely by the dominant steroid. In the 'simplest' model, it is assumed that the number of unoccupied binding sites remains constant. However, as the steroid is metabolized and its concentration decreases, the number of binding sites and the rate of association actually increase. This is allowed for in the 'simple' model. Only the metabolism of cortisol, aldosterone and progesterone (predominantly CBG bound) and tes¬ tosterone and androstenedione (predominantly SBG bound) are considered in the simplest and simple models. Nevertheless, even in male plasma, there

is appreciable competition with testosterone for SBG binding by the combined effect of several steroids (Dunn, Nisula & Rodbard, 1981). Therefore, although the approximations for steroid concentra¬ tions are usually reasonable for mainly SBG-bound steroids, more accurate estimates are sometimes desirable. In female plasma, because of the much lower plasma concentrations of testosterone, it is not

the dominant binding steroid and a more complex model is essential. Therefore, a 'complex' model has been devised with: (1) varying numbers of unoccupied binding sites, (2) simultaneous binding of steroids to plasma albumin and to CBG and/or SBG and (3) the involve¬ ment of all steroids with significant binding to CBG and/or SBG (Dunn et al. 1981) with no steroid being regarded as dominant. The simplest, simple or complex models have been used when appropriate. The complex model is the most realistic representation but results from the simplest model can give algebraic solutions without numerical analysis and insight into the mechanisms involved (see APPENDIX).

APPLICATION OF THE MODEL USING A DIFFERENTIAL EQUATION SOLVER, TUTSIM

The

equations cannot be completely solved algebrai¬ cally, i.e. without the use of numerical methods, particularly with the simple model (varying number of binding sites during metabolism) and the complex model which has, in addition, several simultaneously participating steroids and binding proteins. Even the simplest model does not provide complete solutions, except in certain situations with high transport rates for the steroid-protein complexes (see APPENDIX). Attempts at arriving at complete solutions by simpli¬ fying assumptions have lead to controversy over their selection (Ekins et al. 1982). Another approach is to preserve the complexity of the equations and to use numerical solutions. For this purpose TUTSIM, a differential equation solver devised initially for the Apple He by Twente University of Technology, The Netherlands, has been used. The general TUTSIM programme is now also available for IBM PCs from Meerman Automatisering, Postbus 154, 7160, AC Neede, The Netherlands. Using the TUTSIM procedure, the simple, simplest or the more realistic complex model, including all 13 steroids with significant binding to the plasma CBG and/or SBG can be applied (Dunn et al. 1981). These steroids were testosterone, androstenediol, DHT,

DHA, androstenedione, androstanediol, OE2, OE,,

progesterone, aldosterone, corticosterone, cortisone and cortisol. As indicated by Dunn et al. (1981) and our present calculations, it can be assumed that the

binding of androstenediol, DHT, DHA, androstane¬ diol, OE, and OE2 to CBG is negligible. However, of the 13 steroids, only the binding of aldosterone to SBG could be neglected (Fig. 2). Therefore, six

steroids are assumed to be bound significantly to both CBG and SBG. The most important quantity to be predicted by the model and TUTSIM programme is the total steroid concentration after 9 s of metabolism (S9). This represents the final total steroid concen¬ tration after the passage of the blood through the human liver (S9% 100 HE%). The total mean liver transit time is taken as 9 s. The detailed TUTSIM programmes for steroid metabolism can be obtained from the authors. =

-

Validity of the TUTSIM approach Time-intervals of computation With increasing complexity of the model and/or the higher the transport rates, the time-interval taken for the computation has to be smaller otherwise insta¬ bility occurs. Therefore, the total time of computation becomes longer, i.e. with the complex model shown in

CBG 0-087

.

SBG 0-14

-9-0

5-1

5 -f-

—

3-9

.

1-5

-DHT-^2-7 3-6 -DHA-^0-011 0009 0-39 0-99 -4-JL- AN ->019 0051 -5aA -^.

.

.

v

—

0056

0-29

0020.

010

OE2--^-

OEi--^0-017 0015 0-11 0-005 -—

.

0-008

.

0-79

v

0-011

-

.

1-3

--

digits. Therefore,

it can be concluded from these results that the usual time-interval of 0 005 s for the com¬ plex model gives valid results for computed steroid concentrations under the conditions described in the subsequent treatments; see, however, Steroid-albumin disassociation and association rates.

.

E

49-4

-4—N F 53-5

AL

Increases in the time-interval do not result in significant alterations to the computed values until instability occurs, and this is readily detected. For the nine steroids considered in the complex model with in-vivo HE values, the computed steroid concen¬ tration (S9) was determined with time-intervals of 00005 and 0 0005 s, which correspond to 60 and 600 min of real computing time. For the 0-0005 s timeinterval, S9% was made equal to (100 —HE%), which is in the usual working range. The ratios of corres¬ ponding S9% values for the two time-intervals were 1 0000609±0000183 (s.e.m., d.f. 8). The ratio was only greater than 10005 for DHT (1-0012). This indi¬ cates that the effect of this tenfold lowering in the time-interval has usually an insignificant effect on the calculated values of S9. Repeated computation with the same input indicated 'perfect' reproducability, i.e. no detectable repetitive variation to five significant

F

< Total >

0-96

>

/

1-8

.

-

F

58-5

M 17-8

% SBG occupied binding sites

2. Complex model for the splanchnic metabolism of 13 steroids bound to plasma albumin, corticosteroidfigure

binding globulin (CBG) and sex hormone-binding globulin (SBG). Numbers indicate any significant % total globulin

binding sites occupied by steroid. Total protein concen¬ trations are albumin (0-56 mmol/1) and CBG (0-7 µ / ) for both males (M) and females (F) and SBG (males, 28 nmol/1 and females, 37 nmol/1). TE, testosterone; 5 , androstenediol; DHT, dihydrotestosterone; DHA, dehydroepiandrosterone; AN, androstenedione; 5aA, androstanediol; OE2, oestradiol, OE,, oestrone; PR, pro¬

gesterone; AL, aldosterone; B, corticosterone; E, cortisone;

F, cortisol.

2 and the Apple He computer (plus accelerator) a total time of about 60 min of computation (with 0 005 s time-intervals) represents 9 s of real

Fig.

used,

time metabolism. This is a feasible period of com¬ putation time and further complexity seems to be unnecessary with the present knowledge of the plasma binding of steroids in normal humans.

Different methods of integration Results of the TUTSIM analysis are equivalent using integration according to either Adams-Bashforth or Euler integration, which are the methods available. In order to reduce the possibility of cancelling errors using the complex model, the 'simple' models were used. Initially, (Adams-Bashforth), e was adjusted to give S9% (100-HE%). Using these e values the ratio in the S9 values (Euler/Adams-Bashforth), was 0-9999 (TE) and 10000 (cortisol). The corresponding ratios for the other steroids, using either Adams=

Bashforth or Euler integration for both the dominant and subordinate steroids, were 0-9992 (androstene¬ dione), 0-9998 (progesterone) and 0-9945 aldosterone. The mean ratio was 0-9988 + 0-0011 (s.e.m., d.f. 4). Therefore, either method gives accurate results which are not significantly (P>01) different for these five steroids. Surprisingly, the Adams-Bashforth method results in instability at slightly longer time-intervals than with the Euler procedure. However, as the Adams-Bashforth procedure reputedly gives more accurate results generally for smooth functions, such as the examples of steroid dynamics considered here, this method of integration was used subsequently.

Applications of the TUTSIM model Binding sites

In the TUTSIM programme, the concentration of unoccupied globulin-binding sites at any time is

as the total concentration of the particular minus the sum of the sites occupied by the different participating steroids. The initial concen¬ tration of steroid bound to globulin is calculated as the initial % of the total bound steroid multiplied by the initial total steroid concentration. This concen¬ tration of bound steroid allows the calculation of occupied and unoccupied binding sites, expressed in nmol/1 or as a % of the total concentration of pro¬ tein (Fig. 2). These values are estimated from the equilibrium values assuming no metabolism (e and h 0). With assumption of significant metabolism, for any but the simplest model, the concentration of unoccupied binding sites will depend on the varying concentration of steroid after different times of metabolism. In the actual examples studied, the effect on total concentration of steroid (s9) of this variation in the number of binding sites is not large (see APPENDIX). This is because the change in total steroid concentration (and numbers of binding sites) is maximal when the effect of binding globulin is mini¬ mal. However, it was considered that this effect should be included in the TUTSIM programme for the simple or complex model. The concentration of albumin is much higher than the total of all interacting steroids in the situations considered. Therefore, the concentration of the unoccupied receptor sites of albumin was regarded as constant and equal to the total albumin concentration.

calculated

globulin

=

The TUTSIM

concentrations

procedure to calculate steroid

Equilibrium values with no metabolism For the simplest or simple model, the equilibrium values can be calculated algebraically (Tait & Burstein, 1964; Mendel, I9%9a,b). However, for the complex model, TUTSIM analysis must first be carried out with

metabolism assumed for all 13 steroids until the calculated concentrations of the unbound, albuminbound and SBG- and CBG-bound fractions of all the steroids become constant. This usually takes a maximum of about 120 min of actual computing time. This time can be shortened by inserting estimated approximate initial values but this is not essential. The final equilibrium values are then entered into the programme together with the assumed fractional metabolic rate constants for unbound and, if necess¬ ary, albumin-bound steroid. These equilibrium values are not dependent on the values of the determined and assumed disassociation and association rates but only on the ratio of their values, the equilibrium constant. Another approach is the iterative method of Dunn et al. 1981. zero

Values with metabolism These equilibrium steroid concentrations are then inserted as initial values into the next programme, which involves significant metabolism. The subsequent computation then gives the concentration of the 13 steroids unbound and bound to SBG and/or CBG after various times of metabolism. These results are depen¬ dent on the values for the individual disassociation and association rates in addition to their ratio. The required value for the calculated fractional metabolic rate constant of unbound steroid (e), to give S9, can also be calculated (Tables 1 and 2). In repeated simulations of 9 s of real time metabolism (60 min of computation), the value of e is altered in discrete steps until S9 is equal to a particular value to five significant digits. With any of the models of splanchnic metab¬ olism, this defined value of S9% would correspond to (100 —HE%), where HE% is the in-vivo splanchnic extraction determined as described later (see INPUT DATA). Then, RE represents this required value

ofe.

Iterative procedure

Computation with the complex model and assumed significant rates of metabolism requires the initial insertion of approximate e values for all the steroids considered. The values calculated from application of the simplest or simple model are sufficiently accurate

for this purpose (see Comparison of RE values using the simplest, simple and complex models). Using these approximate initial RE values for all the steroids in males, the accurate RE value for every steroid, whose HE has been determined in vivo, is calculated in turn by TUTSIM analysis using the complex model. The process is then repeated for all steroids using these more accurate RE values. In this repeated procedure, the RE of the steroids, whose HEs have not been determined, is calculated as the mean of the other five non-phenolic steroids, whose HEs are known. In this iterative method, the interactions are small so that the values rapidly converge and usually only one overall repeat pro¬ cedure (and maximally two repeats) is necessary to attain RE values, which are effectively constant. This is ascertained to five significant digits for any RE for the nine steroids with in-vivo estimates of HE. For the females (follicular phase), the HE of only two steroids, testosterone and androstenedione, have been determined. The RE values for males are there¬ fore used for all but these two steroids. The calcu¬ lations for their RE values and the S9 concentrations for all steroids then assume that the fractional rates of metabolism for unbound steroid in males and females are

equivalent.

table

1.

Transport constants for 13 steroids and three binding proteins SBG

Albumin

Equib.

constant1

(x 10" litres/ mol per s) Steroid Testosterone Androstenediol

(pers)

4 2 6 4 2 18 6 4 6 0-2 1

Dihydrotestosterone Dehydroepiandrosterone

Androstenedione Androstanediol Oestradiol Oestrone

Progesterone

Aldosterone Corticosterone Cortisone Cortisol

Equib.

Dis. rate2

0-5 0-3

constant'

Dis.

(xl0"litres/ mol per s)

rate

1600 1500 5500 66 29 1300 680 150

(10) (10) (10) (10) (10) (10) (10) (10) (10) (10) (10) (10) (10)

CBG

8-8 0-21 2-2 2-7 1-6

Equib.

constant1 (x 10" litres/

(per s) 0-05253-4-5

(01)

00164

(10) (30) (01)

0-0834

(10) (10) (10)

rate

mol per s)

(pers)

5-3