Adrenocortical secretory function—Communications and control aspects

Automatica, Vol. 6, pp. 193-205. Pergamon Press, 1970. Printed in Great Britain.

Adrenocortical Secretory Function Communications and Control Aspects* Fonction de srcretion de la glande surrrnale - - Aspects de communication et de c o m m a n d e Adrenocorticale secretorische Function - - Informationstibertragungsund Regelungspekte (I)yntlna BbI)Ie~e/IrI~ I-Ia/moqeqHo~ :~e.rie3bi - - AcnerTbI nepe~aqn n ynpaB~enna J. U R Q U H A R T , ? R. L. K R A L L t and C. C. L i t

Physiological regulation is achieved partly by hormones, each providing a chemical communication channel whose understanding requires knowing the underlying dynamics of hormone action. This paper describes the non-linear dynamics of the pituitary-adrenal channel Summary--Endocrinology deals with chemically mediated communication and control phenomena. Although the various hormones are believed to cooperate, on multiple time scales, in the regulation of metabolism, there is no substantive globalviewofthese cooperative hormonal actions. We contend that such a view will emerge out of the dynamic modeling of individual hormonal actions. However, there is insufficientexperimental support for dynamic modeling in the existing endocrine literature, and so new research is needed on the dynamics of hormonal action. This paper summarizes our experimental work on the dynamicsof one such hormonal action--the stimulatory effect of the pituitary hormone, ACTH, on the secretion of the steroid hormone, cortisol, by the canine adrenal cortex. We have developed a seventh order state variable model of this process in terms of current knowledge about the mechanisms of cortisol biosynthesis. The modeling plays a dual heuristic role: (1) at the very least, it provides a phenomenological description of adrenocortical secretoryfunction for use in larger models of pituitary -adrenal control mechanisms, and (2) it is an aid in evaluating postulated mechanisms by which ACTH acts on the kinetic parameters of cortisol biosynthesis.

than are neural actions, which provide electrical channels of communication and control. It is an axiom of endocrinology that, in time scales ranging from minutes to months, the known hormones, plus some yet to be discovered, cooperate in regulating metabolism and other bodily processes. Not only do different hormones act on different time scales, but a single hormone may exert multiple actions on different time scales. The foregoing generalizations notwithstanding, there is no substantive global view of these cooperative hormonal influences on metabolism. We contend that such a view will emerge from the dynamic modeling of individual hormonal actions and of the processes which regulate their secretion. Yet there have been very few attempts to model endocrine processes. One might expect that a good beginning could be made, based on information gleaned from the large endocrine literature. However, with the exception of numerous compartmental analyses of hormonal distributions in the body fluids, there is little information to support the dynamic modeling of endocrine processes. It requires experiments designed explicitly to reveal endocrine dynamics. The question naturally arises of choosing the level of organizational complexity within an endocrine system at which to begin dynamic testing. At least three such levels seem to be relevant: (1) subcellular biochemical systems involved either in hormonal action, or in hormonal synthesis and release; (2) individual glands or hormonally responsive organs; (3) systems of inter-connected glands and organs. We have chosen to begin at the

INTRODUCTION THE ENDOCRINE systems provide channels of communication by which the brain regulates many bodily processes.++ Hormonal actions are characteristically much more slowly developing and relaxing * Received 22 April 1969; revised 24 September 1969. The original version of this paper was presented at the IFAC Symposiumon Technical and Biological Problems in Control which was held in Yevevan, the capital of the Armenian Republic of the USSR during September 1968. It was recommended for publication in revised form by associate editor A. Sage. t Department of Physiology, School of Medicine and Department of Electrical Engineering, School of Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15213, U.S.A. Examples are ovulation, the onset of labor, milk let-down and the increase in metabolic rate upon exposure to cold. 193

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J. URQUHART,R. L. KRALL and C. C. Lt

intermediate level, with studies on the secretory dynamics of the intact adrenal gland.* Thereby the results can serve a dual purpose: they are one of the relatively microscopic constraints in modeling the operation of the pituitary-adrenal neuroendocrine system [1-3], and they also provide the relatively macroscopic constraints on the modeling of adrenocortical hormone synthesis and secretion and the regulation of these processes by the adrenocorticotropic hormone, abbreviated ACTH, which is secreted by the pituitary gland.* The principal biological action of this pituitary hormone, as its name implies, is its stimulation of the secretion of the adrenal hormone, cortisol. The cells of the outer layers--the cortex--of the adrenal gland synthesize and secrete cortisol. The adrenal cortex may be viewed as an endocrine transducer, converting a hormonal signal (ACTH) of one chemical form, a polypeptide, and biological action, the stimulation of cortisol secretion, into a hormonal signal of quite different chemical form, a steroid, and biological action. Cortisol has many, seemingly diverse biological actions-an antagonism to the actions of insulin, stimulation of gluconeogenesis t, dissolution of lymphocytes and other white blood cells, an ill-defined enhancement of blood vessel "tone", and others. No clearly unifying logic is apparent in these actions, most of which have been demonstrated with dosages of cortisol and related steroids which were too large to provide data relevant to their physiological role. Despite this large gap in the understanding of the physiology of adrenocortical hormones, there has been much research directed toward the neural and endocrine mechanisms involved in controlling cortisol secretion by the adrenal. The steroid hormones exert an inhibitory effect on ACTH secretion, but there are complicated time dependencies in this negative feedback action, which depends in part on the rate of increase in adrenocortical hormone concentration in blood and also on the absolute level of hormonal concentration, although there is a 2-hr time delay in the latter dependency [4]. The interpretation of such complex feedback dynamics can only come through dynamic modeling of this neuroendocrine system, and so, in that context, knowledge is required about the dynamics of A C T H action in the adrenal. Two other aspects of adrenocortical physiology which have received much attention are biochemical mechanisms of steroid hormone synthesis and of A C T H action. These mechanisms have been studied almost exclusively with in vitro methods.]" As a result, the biochemical pathway of cortisol * See Appendix for glossary of physiological terms. t See Appendix for definition.

synthesis is well worked out. However, little is known either about the ACTH-dependent kinetics of the enzymatically catalyzed reactions involved, or about the biochemical mechanisms by which A C T H acts. As will be discussed, there is good reason to believe that the dynamics of cortisol secretion, observed in the intact gland, reflect the time- and ACTH-dependent kinetics of cortisol biosynthesis. For this reason, we have modeled the dynamic relations between ACTH and cortisol secretion rate as a set of conservation equations for the compounds which are intermediates in the synthetic pathway from cholesterol--the major precursor of adrenal steroid hormones--to cortisol. In this way the modeling can incorporate hi vitro findings thought to be pertinent to the action of ACTH. One can then search for a set of physically realistic kinetic parameters in order to see if the in vitro findings can be made compatible with the macroscopic dynamics. In that way, dynamic modeling provides a means of relating functions at these two different levels of organizational complexity. Here modeling has special heuristic value, for it provides a way of making the dynamics of an intact system constrain the interpretation of experimental results which often can only be obtained after disruption of cellular integrity. METHODS The methods are described in detail in Refs. [5] and [6], but will be summarized briefly here. The logic of the experimental design was to gain experimental control over the two variables known to exert influence over the adrenocortical secretion of cortisol: (1) the rate at which blood flows through the adrenal gland and (2) the concentration of A C T H in adrenal arterial blood. To achieve control over the first of these two variables, we re-routed arterial blood destined for the left adrenal gland in a dog so that it flowed from the aorta through plastic tubing into a mechanical pump and then to the left adrenal's arteries. Thus, the pump controlled the rate at which arterial blood flowed through the left adrenal gland. To achieve the second goal, we reduced the concentration of ACTH in systematic arterial blood to negligibly low levels and then added ACTH at controlled rates to the blood being pumped to the left adrenal. We surgically removed the dog's pituitary gland at the beginning of the experiment. Since the pituitary is the source of ACTH, the concentration of that hormone in systemic arterial blood thereafter declined, and within 1"5 to 2 hr reached near-zero levels, judged not by direct measurements, which are technically impossible, but by measurements of the very low rates of cortisol secretion by the left adrenal. Having gotten the concentration of ACTH in systematic arterial blood to near-zero, we could

Adrenocortical secretory function--Communications and control aspects add A C T H at controlled rates to the blood being pumped to the left adrenal gland, and establish A C T H concentrations of our choosing in adrenal arterial blood. Standardized, commercially available preparations of A C T H were diluted to a desired concentration, and these solutions were pumped, at controlled rates, into the flow line supplying the left adrenal. The p u m p which delivered the A C T H solutions was under digital computer control [7], enabling us to vary its rate according to any desired time function. An important point about the

195

adrenal venous blood and adrenal blood flow was taken as the rate of cortisol secretion by the adrenal gland. RESULTS

Static relations between A C T H concentration and cortisol secretion rate. When adrenal blood flow is held constant at values representative of the intact animal (3-6 ml/g/min), cortisol secretion rate is a non-linear function of A C T H concentration. Figure 1 shows that this non-linear relation is of

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FIG. 1. Steady state relations between ACTH concentration in adrenal arterial blood, adrenal blood flow and cortisol secretion rate. The open symbols (circle and triangle) are data from each of two perfused adrenals when adrenal blood flow was 3.5-4.0 cc/min/g adrenal. The closed symbols are data from the same two perfused adrenals when adrenal blood flow was 7.0-8.0 cc/min/g adrenal. The four data points immediately to the right of the ordinate scale indicate the rates of cortisol secretion when ACTH concentration was zero. (Reprinted with permission, from the American Journal of Physiology 1"5].) experimental design was that the amounts of A C T H added directly to the left adrenal's arterial supply were too small to produce detectable increases in the A C T H concentration in systemic blood. The rate of cortisol secretion by the left adrenal was measured by collecting its venous blood for timed intervals of 15-60 sec and assaying the blood's cortisol concentration. The cortisol measurement is a sensitive and specific radiochemical procedure [8], our use of which is described in detail in Ref.

[5]. A C T H is measured in International Units (U), which are units of biological activity defined in the United States Pharmacopoeia. In this paper A C T H concentrations are given in ~tU/ml blood. Cortisol secretion rate is expressed as pg cortisol/min. Measurements of the concentration of cortisol in systemic arterial blood never exceeded 0.1 pg/ml, and so the product of cortisol concentrations in

the logarithmic type, and also illustrates that adrenal blood flow is an important parameter of the A C T H concentration--cortisol secretion rate relation. As adrenal blood flow is elevated into the supranormal range, the relation becomes much steeper, although the maximum secretion rate stays the same. We considered describing cortisol secretion rate as a function of the rate of presentation, or delivery, of A C T H to the adrenal gland, that is, the product of A C T H concentration and blood flow. However, there is a residual influence of blood flow in the A C T H presentation rate, cortisol secretion rate relation, and so we have chosen instead to regard blood flow as a parameter of the relation between A C T H concentration and cortisol secretion rate. In the experiments discussed subsequently, blood flow was held constant. The static relation between A C T H concentration and cortisol secretion rate is subject to random

196

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URQUHART,R. L. KRALL and C. C. LI

fluctuations, whose magnitude clearly limits both the communication and control functions which the adrenal cortex may perform. As Fig. l shows, cortisol secretion rate varies between a minimum value always slightly in excess of 0, and a seemingly fixed maximum value, which has a mean value of approximately 8/~g/min. The statistical uncertainties of adrenocortical secretion are such that at constant A C T H concentration and adrenal blood flow, 95 per cent of the cortisol secretion rate values fall within an approximate range of +0.5 /tg/min about the mean. This range is independent of the mean cortisol secretion rate. Since cortisol secretion rate varies over a range of 8 Fg/min, the statistical uncertainties in the ACTH-cortisol relation quantize adrenal function into about eight levels. Figure 2 shows the results in one of these experiments, in which steady state cortisol secretion rate

In order to make these measurements, it is necessary to extract from the data the error of the radiochemical assay of cortisol. The small error of the assay is dependent on the mean level of cortisol being measured; its coefficient of variation is 1.8 per cent.

Summary of the static relations between A CTH concentration and cortisol secretion rate (1) Cortisol secretion rate is non-linearly related to concentration of A C T H in blood. The nonlinearity is of the logarithmic form. (2) Adrenal blood flow is an important parameter in this relation. (3) The statistical uncertainties in the adrenal secretory response to A C T H indicate that this endocrine signal conversion operates with approximately 3 bit accuracy.

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FIG. 2. Statistical uncertainties in the steady state rate of cortisol secretion. The left hand column of numbers indicates the various ACTH concentrations which were established in adrenal arterial blood. The associated rates of cortisol secretion are plotted on the vertical scale, expressed as a mean (solid horizontal line) + two standard deviations of the mean (shaded area). The measurements were made at intervals from the 40th to the 80th min of exposure to each ACTH concentration. The measurement error in the radiochemical assay of cortisol was extracted from the data, as described in the text. The residual error, represented by the shaded regions, is presumably inherent in the biological process. was measured over a 40 min period at each of four levels of ACTH. In this experiment the range of cortisol secretion rate was somewhat greater than the mean value in all experiments. The shaded areas show the 95 per cent confidence limits of cortisol secretion rate at each level of stimulation. It is apparent from the figure that approximately eight of these shaded areas could be fitted between the minimum and maximum rates of cortisol secretion.

Dynamic relations between ACTH concentration and cortisol secretion rate Choice of operating range. Because of the adrenal's static non-linearity we have performed most of our dynamic tests in the range of ACTH concentrations and adrenal blood flows which result in cortisol secretion rates below half-maximal. Much physiological interest focusses here also, because cortisol secretion rate in the intact animal

Adrenocortical secretory function--Communications and control aspects usually lies between l0 and 30 per cent of maximal [9, 10]. Step tests. The adrenal's response to stepwise changes in ACTH concentration is shown in Fig. 3. The response is dynamically asymmetrical, in that it shows a large, single overshoot in response to a step increase in ACTH concentration, but only a simple monotonic decay after the fall in

197

ACTH concentration. The second response shown in Fig. 3 repeats the time course of the first, which reassures us that the overshoot phenomenon is not the artifact of a dying experimental preparation. The same sort of dynamic asymmetry is demonstrable when stepwise changes in ACTH concentration are made from a concentration greater than zero, as shown in Fig. 4.

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180

J. URQUHART,R. L. KRALLand C. C. LI

198

The gland is capable of a limited number of successively overshooting responses to a staircase pattern of ACTH concentrations, as shown in Fig. 5. However, the gland does not appear to show even a transient overshoot beyond its static secretory maximum. Thus, its response to large stepwise increases in ACTH concentration is nearly monotonic.

There is a time-dependent aspect of the overshooting response which has proved to be a quite helpful guide in modeling. This time dependency is revealed by comparing Figs. 3 and 6. In Fig. 3, a period of 40 min separates the drop and subsequent increase in ACTH concentration, whereas only 5 min separates these two changes in the experiment shown m,tFlg. 6. Therefore, between 8\ °

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Adrenocortical secretory function--Communications and control aspects 5 and 40 min is required at the lower A C T H concentration to restore the conditions necessary for an overshooting response when A C T H concentration is raised. A complete report of the data from our step tests can be found in Ref. [6]. Sinusoidal tests. Since there are different apparent time constants governing decay from the peak of the overshoot, and the decay after a fall in A C T H concentration, we were interested to see which time constant dominated in the gland's frequency response. We have done two series of experiments using sinusoidal variations in A C T H concentration, at periods of 50, 20, l0 and 5 min. The first series was done at -t-20 per cent about a mean value of 2/~U/ml which meant that cortisol secretion rate fell in the nominal range of 25

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___5 per cent of maximal [9, 10]. At the time of these studies, we had not yet measured the statistical uncertainties of the gland's steady state secretory function, which later showed that only an unattenuated sinusoidal response could be detected with acceptable statistical confidence. In fact, when the results of the -t-20 per cent tests were analyzed statistically, only the data from 50 and 20 min cycle tests could be fitted with acceptable certainty by a sinusoid with the input frequency. We tentatively concluded that significant attenuation began between 0"05 and 0.1 cycles per min (0.31 and 0"63 rad./min), which would support a dominant time constant of approximately 3 min [6]. We have since performed tests at -t-40 per cent about the same mean. Some of the data are shown in Figs. 7, 8, 9 and 10. Attenuation appears to begin

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FIG. 7. Time course of cortisol secretion rate (points) during sinusoidal variations in ACTH concentration (solid line) at 0-02 cycles/min. Zero time corresponds to the 50th min of sinusoidal variation in ACTH concentration at 0.02 cycles/min. We calculated the static coupling coefficient between ACTH concentration and tort•sol secretion rate by dividingthe mean ACTH concentration (2/~U/ml) into the mean of all the measured rates of cortisol secretion less the residual rate of cortisol secretion in the absence of ACTH (6-93 pg/min). The two ordinate scales are related according to that coupling coefficient (3.47 pg/min//tU/ml), which was unusually high in this experiment. The secretory maximum of this gland was also unusually high at 16.9/~g/min. 4"00 -

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J. URQUHART, R. L. KRALL and C. C. LI

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during sinusoidal variation in ACTH concentration (solid line) at 0-2 cycles/rain. The ordinate scales are related by calculations which are described for Fig. 7. between 0.05 and 0-1 cycle/min ,and the response is virtually flat at 0"2 cycles/min (Fig. I0). A striking result, from either the control or communications point of view, is that cortisol secretion rate can be driven to run a half cycle behind A C T H concentration with little attenuation at 0.1 cycles/min, thus inverting the sign but not diminishing the amplitude of A C T H concentration changes running at this frequency. "Impulse" Tests. In our first studies, we attempted to make use of the gland's response to a single, rapid injection of A C T H into the perfusion line. This is only an approximation of an impulsive forcing, for there is an artificial time constant of about 20 sec due to mixing and dispersion in the perfusion tubing, and this distorts the input function to a short pulse. Our purpose in these studies

was to measure the gland's settling time. The results indicated that settling occurred within 15-20 min after the A C T H injection. However, this is misleadingly short, as can be seen from the step responses. The results with impulse tests misled us, and we wasted considerable time and effort in our early step tests by not sampling the gland's output for a long enough time, with the result that at first we missed altogether the overshoot [11], and later underestimated its magnitude [12]. We emphasize the very incomplete dynamic view provided by the adrenal response to a short pulse of A C T H , because when one surveys both endocrine and pharmacological literature, it is evident that the single injection of a hormone or drug is the commonest technique of demonstrating its biological action.

Adrenocortical secretory function--Communications and control aspects The foregoing dynamic tests were carried out on the assumption that both qualitatively and quantitatively the perfused adrenal functions as does the gland in the intact animal. There is only limited information with which to judge that claim. We do know that the range over which cortisol secretion rate may vary in the perfused gland corresponds with that of the adrenal in intact dogs [9, 10], but we have no information on the associated concentrations of ACTH. At present, ACTH concentration in blood cannot be measured below about 10 #U/ml. When a suitably sensitive ACTH assay is available, we shall endeavour to monitor adrenal function in the intact animal by simultaneously measuring ACTH concentration in arterial blood, adrenal blood flow, and cortisol secretion rate. These measurements will provide a stringent test of the physiological validity of the experimental work presented here. The contribution made by adrenocortical dynamics to control action within the pituitaryadrenal neuroendocrine system can only be judged as that system is modeled. The strength of such modeling depends upon the extent to which its component subsystems have been tested dynamically and modeled. Yates and Brennan have given a comprehensive view of the current status of this undertaking [2, 3]. It may be summarized by stating that there is fairly good evidence upon which to model the extra-cranial subsystems, which include the adrenal, the processes of body fluid distribution, binding and metabolism of cortisol, and, to a very limited extent, the body fluid distribution and metabolism of ACTH. However, the intracranial subsystems--the hypothalamus,* other portions of the brain, and the pituitary--are very sketchily characterized, because of formidable technical problems in experimenting with these subsystems directly. One of the goals of a wellsupported modeling of the extra-cranial subsystems is to be able to use the resulting system model together with experiments on the intact system to draw progressively sharper inferences about the function of the intracranial processes which are inaccessible to direct experimentation. We have sought to model the adrenal in terms of the underlying biochemical mechanisms of cortisol synthesis and of ACTH action. The goal of this effort is to bring the constraints of the gland's secretory dynamics to bear on the interpretation of in vitro studies of ACTH action. In particular, the overshoot in the step responses begs a biochemical interpretation. In modeling the gland, we begin with the biochemical pathway by which cortisol is synthesized from cholesterol, its major precursor. In contrast Discussion.

* See Appendixfor definition.

201

to some other endocrine glands, such as the anterior pituitary or the cells of the pancreas, which store appreciable quantities of their secretory products, the adrenal stores relatively little cortisol, but instead synthesizes it de novo in response to stimulation by ACTH. ACTH increases the adrenal content of steroid hormones; indeed, this response provides the basis for bioassay of ACTH [13]. In contrast, increased pituitary secretion of luteinizing hormone, for example, is accompanied by a drop in that gland's content of luteinizing hormone [14]. We proceed on the assumption that cortisol molecules are translocated from within adrenal cells to blood by simple diffusion. With this view, the kinetics of each enzymatic step in the biochemical pathway from cholesterol to cortisol plus the kinetics of the cortisol diffusion step become the "unit processes" of the model. The following shows the biochemical pathway (of. 15) and the suppression of some of its detail which we have imposed in the interests of simplifying the modeling. Biochemical pathway

Model

Cholesterol

c

20 e-hydroxycholesterol

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d

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|

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e

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output

As an example of the suppression of detail in the model pathway, we associate the variable 'c' with cholesterol, but regard 'd' as representing the two hydroxycholesterol compounds, giving us much the same view of their temporal behaviour that one would have from biological measurements with a nonspecific chemical method which could not distinguish between the two compounds. The modeled cascade of reactions, translates into a set of coupled, first-order differential equations of conservation, with parameters as yet unspecified, for they depend on how one chooses to represent ACTH action. This is an unresolved question, under active investigation at present, so there is no one answer. We have taken the following approach. At the outset, it was not clear to us what

J. UROUHART,R. L. KRALI. and C. C. IJ

202

sorts of kinetic mechanisms would have to operate within the reaction cascade in order to give the various non-linear dynamic features of the adrenal. We explored various possibilities, without regard to whether or not they had any supporting evidence. Several of these models are published elsewhere [6, 16]. This initial effort provided us with some intuition about possible kinetic bases for asymmetrical dynamics. On this basis, we were attracted by the findings of Koritz and Hall, who had reported a feedback inhibition by pregnenolone on the rate of cholesterol hydroxylation in an adrenal mitochondrial extract [17]. They offered a hypothesis about A C T H action, which is based upon their in vitro observation, and on the knowledge that pregnenolone is formed from cholesterol within mitochondria,* but must cross the mitochondrial membrane to undergo conversion either to progesterone or to 17 c~-hydroxypregnenolone. The hypothesis states that ACTH acts, probably indirectly through unspecified means, to increase the permeability of the mitochondrial membrane to pregnenolone, permitting its intra-mitochondrial concentration to fall, thus relieving the inhibition on cholesterol hydroxylation and allowing an increase in the rate of material flux through the pathway, ultimately to appear as cortisol. The hypothesis is supported by Hirshfield and Koritz's work [18] which showed that agents which increase mitochondrial permeability also increased the rate at which the reactions in the pathway proceeded. We have translated the verbal construct offered by Koritz and Hall into the terms of the model of the pathway. The structure of this model is as follows: s. . . . . . .

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model was obtained by simulations on an analog computer, with a cut-and-trial procedure, to gixe a satisfactory overall lit to three sets of average experimental responses to increasing and decreasing step inputs of 0 to 2,2 to 0 and 0 to 30 IdJ/ml. The resulting set of equations (20) is: Initial conditions d = 0 " 5 I - 0"59a

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f=0.451 g =0.558

h =0"558

I = [ACTH] in pU/ml output = h = cortisol secretion rate in pg/min. This system of equations does not include the adrenal blood flow effect, nor does it account for the statistical uncertainties in adrenal function;l" however, the equations simulate almost all of the known dynamic properties of the adrenocortical secretory response to ACTH. References [20] and [21] document the quality of the simulation. Several comments are necessary about the details of the model. The state variables, 'a' and 'b', which do not appear in the model pathway, have no explicit biological counterpart, except to represent the fact that both the input (ACTH) and 'e' (pregnenolone) must act with characteristic dynamic lags. There is no conservation equation for 'c' (cholesterol), which is presumed to be present in sufficient quantities that its hydroxylation can be regarded as a zero-order reaction. The function qS(b) is derived from Koritz and Hall's data. It has the same negative exponent as does the relation shown in Fig. 2 of their paper [17], although the asymptote of ~b(b) is zero, whereas their data show it to be about half the maximal rate [17]. Hall has informed us that his more recent experiments with a more highly purified mitochondrial preparation show more nearly complete inhibition [19]. If the inhibitory action of pregnenolone is to account for the 10-100-fold range over which steroidogenesis may vary, then it should be possible to demonstrate a comparable range in the inhibitory action of pregnenolone. Finally, the non-linear t The reader should consult ref. [22] for a derived quasilinearized model of adrenal cortex as an information channel which gives a reasonable estimate of the information transmission capacity of the adrenal at 'the normal operating level.

A d r e n o c o r t i c a l secretory f u n c t i o n - - C o m m u m c a t i o n s a n d c o n t r o l aspects function in the e q u a t i o n s for f a n d g represent M i c h a e l i s - M e n t e n enzymatic kinetics, p r o v i d i n g a saturable step, which we h a d to p o s t u l a t e in o r d e r to prevent the m o d e l f r o m o v e r s h o o t i n g excessively with large step increases in input. The resulting m o d e l provides a mechanistic basis for a d r e n o c o r t i c a l secretory d y n a m i c s which has the strongest s u p p o r t in experimental evidence. In an absolute sense, o f course, t h a t s u p p o r t is quite w e a k , indicating that the synthesis we offer is tentative. Nevertheless, it serves n o t only to stimulate a closer experimental scrutiny o f the details o f a d r e n o c o r t i c a l p h y s i o l o g y b u t also to i n t r o d u c e into e n d o c r i n o l o g y the e x p e r i m e n t a l strategy o f d y n a m i c testing a n d m o d e l i n g at i n t e r m e d i a t e levels o f o r g a n i z a t i o n a l complexity. CONCLUSIONS T h e chemical c o m m u n i c a t i o n channel u n d e r scrutiny here, the p i t u i t a r y h o r m o n e A C T H a n d its s t i m u l a t o r y a c t i o n on the secretory f u n c t i o n o f the a d r e n a l gland, has c o m p l e x a n d n o n - l i n e a r d y n a m i c s which have been revealed experimentally b y large a n d small m a g n i t u d e step function tests a n d b y small a m p l i t u d e sinusoidal tests. A l s o , s o m e o f the noise characteristics in the channel have been revealed experimentally. A deterministic m o d e l was suggested by one t h e o r y a b o u t the biochemical m e c h a n i s m s b y which A C T H acts on the a d r e n a l gland. T h e result is a set o f n o n - l i n e a r conservation equations, whose state variables can be related to the b i o c h e m i c a l theory, a n d whose p a r a m e t e r s were selected by c u t - a n d -try fitting with an a n a l o g c o m p u t e r a g a i n s t the few constraints n o w known. The non-linearities are o f three f o r m s : p a r a m e t r i c forcing implicit in the b i o c h e m i s t r y o f h o r m o n e action, n o n - l i n e a r feedback, a n d the kinetics o f enzymatically catalyzed reactions. W e suggest that this w o r k illustrates a new research strategy in e n d o c r i n o l o g y , the e x p e r i m e n t a l p o r t i o n o f which is the testing o f the d y n a m i c s o f h o r m o n e action, a n d the c o n c e p t u a l p a r t o f which is to a t t e m p t to m o d e l the observed d y n a m i c s f r o m available i n f o r m a t i o n on the b i o c h e m i c a l level. Acknowledgements--This work was supported by grant # GM-14637 of the National Institute of General Medical Science. Dr. Urquhart is the recipient of a Research Career Development Award from the National Heart Institute. The authors are indebted to Charles Pearson for surgical assistance and to Amy Maxwell for radiochemical assistance.

REFERENCES [1] F. E. YATES and J. URQUHART: Control of plasma concentrations of adrenocortical hormones. Physiol. Rev. 42, 359 (1962). [2] F. E. YATESand R. D. BRENNAN: Study of the Mammalian Adrenal Glucot'corticoid System by Computer Simulation. Conference on Hormonal Control Systems in Health and Disease, Rancho Santa Fe, Calif., October, (1967). (IBM Technical Report #320-3228, 1967.)

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[3] F. E. YATES, R. D. BRENNAN and J. URQUHART: Adrenal glucocorticoid control system. Fedn Proc. 28, 71 (1969). [4] M. f . DALLMANand F. E. YATES: Dynamic asymmetries in the corticosteroid feedback path and distribution-metabolism-binding elements of the adrenocortical system. Ann. N. Y. Acad. Sci. 156, 696 (1969). [5] J. URQUHART: Adrenal blood flow and the adrenocortical response to corticotropin. Am. J. PhysioL 209, 1162 (1965). [6] J. URQLII-IARTand C. C. LI: The dynamics of adrenocortical secretion. Am. d. PhysioL 214, 73 (1968). [7] P. REHKOI'F,J. URQL1HARTand C. L. CROSS: A computer controlled infusion pump. Proc. Ann. Conf. on Eng'g. in Med. and Biol., 20th, 1967. [8] B. KLIMAN and R. E. PETERSON: Double isotope derivative assay of aldosterone in biological extracts. J. biol. Chem. 235, 1639 (1960). [9] J. O. DAVIS,C. C. J. CARPENTER,C. R. AYERSand R. C. BAHN: Relation of anterior pituitary function to aldosterone and corticosterone secretion in conscious dogs. Am. J. Physiol. 199, 212 (1960). [10] Personal observations. [11] J. URQUHART, C. C. LI and W. L. MONTGOMERY: Studies of the dynamic response of the adrenal cortex to corticotropin. Proc. Ann. Conf. on Eng'g. in Med. and Biol., 17th, 8 (1964). [12] W. L. MONTGOMERY,J. URQUHARTand C. C. LI" Studies of adrenocortical dynamics. Proe. Ann. Con~. on Eng'g. in Med. and Biol., 18th, 192 (1965). [13] F. MONCLOA,F. G. PERON and R. I. DORFMAN: The fluorometric determination of corticosterone in rat adrenal tissue and plasma: effect of administering ACTH subcutaneously. Endocrinology 65, 717 (1959). [14] N. B. ScnwARz: Acute effects of ovariectomy on pituitary LH, uterine weight, and vaginal cornification. Am. J. Physiol. 207, 1251 (1964). [15] O. HECHTERand I. D. K. HALKERSTON" On the action of mammalian hormones. In: The Hormones, (Ed. G. P1NCUS, K. V. THIMANN and E. B. ASTWOOD) Vol V, p. 697. Academic Press, New York (1964). [16] J. URQL1HARTand C. C. LI: Dynamic testing and modeling of adrenocortical secretory function. Ann. N.Y. Acad. Sci. 156, 756 (1969). [17] S. B. KORITZ and P. F. HALL: End-product inhibition of the conversion of cholesterol to pregnenolone in an adrenal extract. Biochemistry 3, 1298 (1964). [18] I. N. HIRSHFIELDand S. B. KORITZ: The stimulation of pregnenolone synthesis in the large particles from rat adrenals by some agents which cause mitochondrial swelling. Biochemistry 3, 1994-1998 (1964). [19] P. F. HALL: Personal communication. [20] J. URQUHART,R. L. KRALLand C. C. LI: Analysis of the Koritz-Hall hypothesis for the regulation of steroidogenesis by ACTH. Endocrinology 83, 390 (1968). [21] C. C. LI and J. URQUHART: Modeling of adrenocortical secretory dynamics. In: Concepts and Models of Biomathematics: Simulation Techniques and Methods. (Ed. F. HEINMETZ and L. D. CADY), Marcel-Dekker, New York (In press). [22] C. C. LI and J. URQUHART" Information Transfer Implicit in the Adrenocortical Secretory Response to Corticotropin. Proc. Ann. Conf. on Eng'g. in Med. and Biol., 21st, 295 (1968). APPENDIX Glossary o f physiological terms Adrenal gland. A n e n d o c r i n e gland o f verteb r a t e s also k n o w n as the s u p r a r e n a l gland. In m a m m a l s there is one a d j a c e n t to each kidney. T h e g l a n d is c o m p o s e d o f two p a r t s : an o u t e r cortex, w h i c h secretes steroid h o r m o n e s , such as cortisol a n d a l d o s t e r o n e ; a n d a n inner medulla, which secretes c a t e c h o l a m i n e h o r m o n e s such as

J. URQUHART,R. L. KRALL and C. C. LI

204

epinephrine (adrenaline) and norepinephrine (noradrenaline).

Pituitary. An endocrine gland of vertebrates, also known as the hypophysis. There is one gland, located in the midline, in a depression of the sphenoid bone, which is part of the skull. The gland is composed of two parts: an anterior lobe, which secrets polypeptide hormones such as ACTH, which stimulates the secretions of the adrenal cortex, TSH, which stimulates the secretions of the thyroid, and several others, including luteinizing hormone, which regulate testicular or ovarian functions; and a posterior lobe which secretes polypeptide hormones such as vasopressin, which regulates the osmolarity of body fluids and oxytocin, which stimulates milk let-down by the mammary glands. Hypothalamus. A portion of the brain lying immediately above the pituitary. The regulation of many functions is localized in the hypothalamus, including body temperature, thirst and appetite. In the context of this paper, an important hypothalamic function is the control of ACTH secretion from the pituitary. This control is mediated by the hypothalamic secretion of an incompletely characterized hormone which passes directly, via small veins, from hypothalamus to pituitary and stimulates the pituitary to secrete ACTH. Mitochondria (singular, mitochondrion). One to two # particles within cells which are surrounded by a specialized membrane and in which are localized the enzymes which catalyze reactions of oxidative phosphorylation. In the context of this paper, an important aspect of mitochondria is that those in adrenocortical cells also contain the enzymes which catalyze several of the reactions by which cholesterol is converted to cortisol. Gluconeogenesis. The synthesis of glucose, a 6carbon sugar, from three carbon metabolites such as lactate, pyruvate or various amino acids. This process occurs mainly in the liver, though to a small extent in the kidney as well. Cortisol is one of several hormones that are capable of enhancing the rate of gluconeogenesis. In vitro. From Latin "in a glass", referring to biochemical reactions observed in a test tube.

Michaelis-Menten enzyme kinetics. An enzymatically catalyzed reaction whose velocity may be described by Vmax S

Km+S

where o is reaction velocity, S is the concentration of reactant, V,nax is a constant, the observed maximal velocity when S is very large, and K m is a constant characteristic of the enzyme.

R6sum6--L'6ndocrinologie traite des ph6nom~nes de communication et de commande ~ l'aide de moyens chimiques. Malgr6 le fait que l'on suppose que les divers hormones collaborent, ~t des 6chelles de temps multiples, ~t la r6gulation du m6tabolisme, il n'existe aucune vue globale substantielle de ces actions hormonales associ6es. Nous estimons qu'une telle vue r6sultera de la simulation dynamique des actions hormonales individuelles. On ne trouve pas c6pendant de base exp6rimentale suffisante pour la simulation dynamique dans la lit6rature existante de l'endocrinologie, de sorte qu'une nouvelle recherche est n6cessaire dans la dynamique de l'action hormonale, le pr6sent article r6sume notre travail exp6rimental sur l'une de ses actions hormonales--l'effet stimulant de l'hormone pituitaire ACTH sur la s6cretion de l'hormone st6roide, le cortisol, par la glande surr6nale canine. Nous avons r6alis6 un module du septi~me ordre de la variable d'6tat de ce proc6d6 en tant que r6sultat de la connaissance courante du m6canisme de biosynth~se du cortisol. La simulation joue un double rfle heuristique: (1) elle furnit, tout au moins, une d6scription ph6nom6nologique de la fonction de s6cretion de la glande surr6nale pour son utilisation dans les modules plus importants de m6canismes de commande pituitaire surr6nale et (2) elle constitue une facilit6 pour l'6valuation des m6canismes suppos6s selon lesquels I'ACTH agit sur les parametr~s cin6tiques de la biosynth~se du cortisol.

Zusammeafassung--Die Endokrinologie befal3t sich mit chemisch vermittelten Ph~inomenen der Informationstibertragung und Regelung. Obgleich die verschiedenen Hormone zusammenwirken dtirften, etwa in mannigfachen zeitlichen MafSst/iben, in der Regulation von Stoffwechselgiften, gibt es noch keine wirklich globale Gbersicht tiber diese zusammenwirkenden hormonalen Aktionen. Wir behaupten, dab sich eine solche Obersicht aus der dynamischen Modellierung yon individuellen Hormonaktionen ergeben wird. Die vorhandene endokrinologische Literatur liefert jedoch nur eine ungentigende Unterstiitzung ftir eine dynamische Modellierung, so dal~ tiber die Dynamik der hormonalen Aktion neue Forschung erforderlich ist. Die Arbeit fal3t unsere experimentelle Arbeit tiber die Dynamik einer solchen hormonallen Aktion, den stimulierenden Effekt des PituitaHormons A C T H auf die Sekretion des Steroidhormons Cortisol durch den Hundecortex zusammen. Wir entwickelten von diesem Proze$ ein Modell siebenter Ordnung mit Zustandsvariablen im Rahmen unseres gegenw~irtigen Wissens tiber den Mechanismus der Cortisol-Biosynthese. Die Modellierung spielt eine duale heuristische Rolle" (1) Zumindest erlaubt sic eine ph/inomenologische Beschreibung der adrenokortikalen sekretorischen Funktion im Hinblick auf gr6$ere Modelle des Pituita-Adrenal-Regelungsmechanismus und (2) ist sic eine Hilfe bei der Bestimmung der postulierten Mechanismen, dutch die das A C T H auf die kinetischen Parameter der Cortisol-Biosynthese wirkt.

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