INTRODUCTION

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GROWTH HORMONE (GH) is secreted in a pulsatile manner from the pituitary gland, resulting in an oscillating time course of GH concentration in the circulating blood. In the adult male rat, the regular time course of GH is characterized by biphasic secretion episodes every 3.3 h separated by intervening trough periods with undetectable basal levels (39). The secretion is governed by the two hypothalamic neuropeptides, GH-releasing hormone (GHRH) and somatostatin (SRIF), which have stimulatory and inhibitory effects, respectively, on GH release. SRIF neurons are located in the periventricular nucleus (PVN), as well as in the arcuate nucleus (ARC), of the hypothalamus, whereas GHRH cells predominantly reside in the ARC. The axons of these neurons course to the median eminence where they release the neurohormones into the portal blood. GH exerts a negative feedback on its own secretion at the level of the hypothalamus by regulating the secretion of SRIF (short loop feedback). In the liver, GH regulates the secretion of insulin-like growth factors (IGF-I and IGF-II), which exert growth-promoting effects in peripheral tissues; IGF-I and IGF-II constitute the long loop feedback of the GH neuroendocrine axis by suppressing GH release at the level of the pituitary and/or hypothalamus (for reviews, see Refs. 14 and 35).

Although many experiments were performed to elucidate the interrelationship between SRIF and GHRH in GH regulation, the mechanisms underlying normal pulsatile GH secretion remain obscure. Chen et al. (10) derived an elaborate model involving eight differential equations and five arbitrary feedback functions, which was too complex to explain the actual function of the system. We address the problem using a model that focuses on the generation of the 3.3-h rhythm of GH secretion. Due to the time scale examined, short-term alterations were assumed to be in pseudoequilibrium with the relevant variables, whereas long-term effects were treated as constants. This allows us to propose a model of the ultradian rhythm of GH secretion using only two differential equations: one for GH and one for SRIF. GHRH is assumed to be generated independently of GH and possesses an intrinsic rhythm with a mean period of ~1 h. We found that the major feedback mechanism for generation of the 3.3-h rhythm is the short feedback loop via SRIF. The release of SRIF due to GH is delayed, which reflects the kinetics of the signaling pathway in these cells. SRIF, with a resultant periodicity of 3.3 h, affects both the somatotroph cells in the pituitary and the GHRH neurons in the hypothalamus. The inclusion of two sites of SRIF action in this model resolves experimental results that have so far eluded explanation. The model also predicts a possible mechanism for the change of the male GH rhythm into the female pattern by sex steroids and vice versa, and it suggests experiments that might reveal the proposed intrinsic 1-h GHRH rhythm.

	METHODS

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Basis of the Model

Pituitary GH secretion. The interrelationship of SRIF and GHRH in GH regulation at the level of the pituitary was investigated using an adult rat model. From these experiments, Tannenbaum and Ling (38) postulated that SRIF and GHRH are released in reciprocal 3- to 4-h cycles from the hypothalamus into the hypophyseal portal blood to generate the ultradian GH rhythm. These conclusions were corroborated by measuring the concentrations of immunoreactive GHRH and SRIF in hypophyseal portal plasma (30). Our model is based on these well-established findings.

GH feedback via SRIF. GH given centrally (34) or peripherally (44) suppresses the spontaneous bursts of GH in the rat. Experimental evidence indicates that the feedback effect of GH on its own secretion is exerted by increasing hypothalamic SRIF release into the portal blood (11). In vitro studies show that the pituitary gland is not the site of GH feedback inhibition (20). The GH feedback effect also results in a high-frequency pulse train of GH (~1 h), unmasked by injecting SRIF antibody (Ab) after GH treatment (21), suggesting that the GH rhythm is generated by an intrinsic high-frequency (~1 h) GHRH release.

Mediation of GH feedback by GH receptors on SRIF cells. GH receptor (GHR) transcripts have been found to colocalize with SRIF transcripts in the PVN (5). Because there is experimental evidence that GH does not affect GHRH cells in the ARC (25), we assume that the feedback of GH is mediated via GHR on SRIF neurons. The binding of GH to its receptor results in a dimerization of GHR and activates a variety of signaling molecules (7). Central injection of GH increases SRIF release into portal blood with a delay of 40-80 min (11), which is determined by the above-mentioned signaling cascade. In the simulations, we used a generally accepted model for the GHR turnover (1, 16).

Further mediation of GH feedback by SRIF receptors in brain. Evidence has been provided for the association of SRIF receptors with a subpopulation of GHRH-containing ARC neurons (3, 23, 41), implying direct regulation of the GHRH hypothalamo-hypophyseal system by SRIF. In addition, ultradian oscillation in SRIF binding within the ARC in synchrony with the pattern of GH secretion has been shown (36). These results suggest that the feedback of GH on GHRH neurons in the ARC is mediated via SRIF, at least on the timescale of a secretion episode.

Long loop feedback involving IGFs. Although there is convincing in vitro evidence that the IGFs affect GH secretion (2), the effect of the IGFs in vivo is still poorly understood. At the level of the brain, it appears that a synergistic interaction of IGF-I and IGF-II is required to reduce the amplitude of GH pulses 2-3 h after injection (15). Furthermore, no modification of plasma IGF-I levels was observed after acute or chronic GH administration (21), indicating that GH-induced negative feedback can operate independently of changes in IGF-I. We assume that the IGFs are involved in a feedback loop but that it is not essential for generation of the 3.3-h rhythm of GH.

Male-female dimorphism. In adult rats, there is a striking sex difference in the pulsatile pattern of GH secretion. In contrast to the regular 3.3-h periodicity in the male, females exhibit more frequent, irregular, low-amplitude GH pulses with an elevated baseline (see Ref. 19 for review). The level of GHR in the liver is lower in males than in females (31). It has been postulated that, in the female rat, SRIF release into portal blood is continuous, whereas GHRH release is erratic with a high frequency (12, 27). Administration of the female sex steroid estradiol to male rats converts the male GH rhythm to a female-like pattern (28), whereas, conversely, the male sex steroid testosterone masculinizes the female GH secretory profile (35). Because the high-frequency pattern of GH secretion is observed in the female rat, we used the transition between the male and female GH profiles to justify the assumed intrinsic 1-h rhythm of GHRH in the male rat.

GH secretagogues. A novel class of synthetic compounds with potent GH-releasing activity, termed GH secretagogues (GHSs), has been described (4, 33). The cellular mechanisms involved in the actions of GHSs are different from those of GHRH (33). A receptor for GHS (GHS-R) has been cloned recently (18), and there is anatomic evidence that the GHS-R is expressed by GHRH neurons (37), suggesting that an additional neuroendocrine pathway may exist to regulate pulsatile GH secretion. However, the endogenous ligand for GHS-R has not, as yet, been identified. Thus GHS is not included in the model.

Description of the Model

Mathematical implementation. The scheme of the model used for the simulation is presented in Fig. 1. The numbering convention refers to SRIF as species 1, GHRH as species 2, GH as species 3, and GH receptors as species 4. The symbol A refers to the hypothalamus, B to the portal blood or pituitary, and C to the circulation. Concentrations are denoted by c, with an appropriate subscript to indicate the species and superscript to indicate the zone. All concentrations are time dependent, unless they are doubly subscripted, in which case they are parameters of the model with assigned values (see Table 1).

View larger version (31K): [in this window] [in a new window]   Fig. 1.   Schematic drawing of the signaling pathway of the growth hormone (GH) neuroendocrine axis for generation of the ultradian GH rhythm. From the hypothalamus, somatostatin (SRIF) and GH-releasing hormone (GHRH) are released into the portal blood according to the concentration time courses indicated (~3.3-h intervals). At the pituitary, the reciprocal release patterns of GHRH and SRIF result in a GH profile in the circulation as shown. Feedback of GH on the release of SRIF is mediated via GH receptors on SRIF cells in the periventricular nucleus (PVN) of the hypothalamus, delayed by the time . SRIF is secreted both into the portal blood and within the hypothalamus at the level of the arcuate nucleus (ARC), according to a partition coefficient denoted by . In the ARC, the GHRH neurons show an ~1-h rhythm, the release being amplitude modulated (M) by SRIF. SRIF neurons are located in the ARC and the PVN, as suggested by the vertical dashed line dividing the hypothalamus. The numbers and letters in parentheses and brackets correspond to the notation used for the equations (see text).

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

View larger version (17K): [in this window] [in a new window]   Fig. 2.   Model for the turnover of GH receptors on SRIF cells in the hypothalamus. GH binds to the receptors with a 1:2 stoichiometry. Symbols in parentheses correspond to the notation used for the equations in text. Inset shows the concentration of internalized receptors, cA4, as a function of GH in the circulation both for the male ( = 0.05; c4,tot = 0.00094 ml/ng; solid line) and the female ( = 8; c4,tot = 0.94 ml/ng; dashed line), normalized by c4,tot.

(9)

(10)

(11)

	RESULTS

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Simulations and Comparisons with Experiments

Calculations. Simulations of time-dependent concentrations of SRIF, GHRH, and GH were performed using the Euler algorithm with a time step of 0.01 min. Figures 3-6 do not show the initial transient, and the zero point of the time window presented was shifted to match the experimental conditions. Note that the two differential equations describe a "limit cycle," which is independent of initial conditions after the initial transient.

Parameters. The differential equation system was calibrated in such a way that the simulated concentrations are comparable to measured values. Hence the release rate constants are given in nanograms per milliliter per minute for GH and picograms per milliliter per minute for SRIF. They were chosen to reproduce physiological concentrations. In contrast, the clearance rate constants were calculated according to the measured half-life. For GH, we used a half-life of 8-10 min (9), and, for SRIF, we used a value of 0.5 min (10). The amplitude variation of GHRH and the maximal amount of SRIF in the portal blood correspond to experimental findings (30).

Unperturbed GH rhythm. The simulated time courses of the unperturbed SRIF, GHRH, and GH rhythms in the male rat compared with experimental GH data are presented in Fig. 3. The simulated GH bursts exhibit a periodicity of 3.3 h, and each burst is subdivided into two GH pulses separated by 50 min. The duration of the nadir period is ~90 min with almost undetectable GH levels.

View larger version (23K): [in this window] [in a new window]   Fig. 3.   Simulation of the unperturbed SRIF (A), GHRH (B), and GH (C) profiles in the male rat compared with experimental GH data (D) taken from Tannenbaum et al. (40). In the simulations, data points are represented every 5 min for SRIF and GHRH in the portal blood and every 15 min for GH in the circulation to compare with the experiment. Dashed horizontal line in A marks the threshold of SRIF at the level of the pituitary. Vertical dotted lines on left in A-C denote the commencement of a GH secretory episode, and dotted lines on right denote the increased level of SRIF and the cut off of the hourly GHRH pulses. Distance between the two dotted lines corresponds to the time delay .

Perturbation by exogenous GHRH. The male rat shows a synchronized GH rhythm so that administration of exogenous GHRH during a GH secretory episode results in an amplified GH peak, whereas during a trough period the response is negligible (38). Injections of GHRH were modeled, and the simulations as well as the experimental result are presented in Fig. 4. The model shows two high GH peaks at 1100 and 1500 (Fig. 4C). The suppression of the GH response to GHRH at 1300, due to the high level of SRIF, fits well with the experimental data. The extended tail of GH secretion after the peak at 1100 and the increased level of GH preceding the peak at 1500 are due to endogenous pulses of GHRH.

View larger version (21K): [in this window] [in a new window]   Fig. 4.   Simulation of the effect of GHRH injections at 1100, 1300, and 1500 on SRIF (A), GHRH (B), and GH (C) profiles in the male rat compared with experimental data (D) taken from Lanzi and Tannenbaum (22). Data points are represented as described in legend to Fig. 3. Dotted lines in B denote the simulation of exogenous GHRH injections, whereas in the experiment in D the administration of GHRH is indicated by arrows.

Perturbation by human GH. By administering exogenous human (h) GH, the periodicity of endogenous rat GH can be changed reproducibly. The response due to hGH perturbation is a suppression of the GH pulses and a prolongation of the GH trough period by ~1.5 h (21). The effects of the GH negative feedback loop are presented in Fig. 5. The injection of hGH at 0800 results in a shift of the spontaneous GH burst, which appears at ~1230 (Fig. 5, C and D). In addition, the GH peak amplitudes are often reduced while the system returns to the normal rhythm (21). The change in periodicity is not due to the high peak amplitude of hGH (~400 ng/ml) but to the slower decay of hGH in the circulating blood. This causes a long tail in the SRIF surge (Fig. 5A) that suppresses GH pulses for 1.5 h. The elevated SRIF level in the recovery phase of GH reduces the GHRH pulses and diminishes the amplitude of GH secretion.

View larger version (21K): [in this window] [in a new window]   Fig. 5.   Simulation of the effect of a human (h) GH injection at 0800 on SRIF (A), GHRH (B), and GH (C) profiles in the male rat compared with experimental data (D) taken from Lanzi and Tannenbaum (21). Data points are represented as described in legend to Fig. 3. Dashed lines in C and D are scaled according to the ordinate for exogenous (exo) hGH on the right-hand side.

Feminizing the male rhythm. Despite the different GH periodicities in male (3.3 h) and female (~1 h) rats, the regulatory mechanisms (Fig. 1) are probably the same since the ~1-h rhythm of the female can be detected within the GH secretory episode of the male. The transformation of a male GH profile into a female profile is presented in Fig. 6. By introducing a 1,000-fold increase in the product c_4,tot, to make the receptor function almost independent of GH (see APPENDIX), and by increasing the ratio  to eight (see Table 1), which adjusts the SRIF level (see APPENDIX), the simulations exhibit a GH profile similar to that observed in the feminized male rat (28). According to the simulations, the feminized GH rhythm is generated by an almost constant release of SRIF into the hypothalamus (Fig. 6A), where it reduces the GHRH peak amplitudes, and into the portal circulation, resulting in partly sealed somatotrophs. Consequently, the GH peak amplitude is much smaller compared with the normal male profile, and the system exhibits the intrinsic 1-h rhythm (Fig. 6C). The characteristic properties of the GH pattern in the feminized male rat, i.e., lower peak amplitude, 1-h periodicity, and an elevated baseline, are well represented by the simulations.

View larger version (28K): [in this window] [in a new window]   Fig. 6.   Simulation of the male-female transition (A-C) compared with experimental data for the male (D) and for the feminized (estradiol-treated) male (E) taken from Painson et al. (28). Data points are represented as described in legend to Fig. 3. Left-hand vertical dotted line corresponds to the time point of switching the receptor parameter set from male to female (see Fig. 2). Right-hand vertical dotted line indicates the termination of the period of adaptation to new parameter values in the model.

	DISCUSSION

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GH is essential for normal body growth and metabolism in both animals and humans. Hence, an understanding of the mode of generation of the GH secretion profile is of physiological and pathophysiological importance.

Based on experimental results, we modeled the GH neuroendocrine axis as a combination of a linear pathway that describes the sequential signaling between GHRH and GH and a cyclic pathway involving the feedback of GH on its own release via GH receptors on SRIF neurons in the hypothalamus. The GHRH-GH axis is based on an intrinsic 1-h rhythm while the SRIF-GH cycle yields the 3.3-h periodicity. The ultradian GH rhythm observed in the male rat is obtained by modulating the 1-h GHRH rhythm with an overall 3.3-h periodicity of SRIF release into both the brain and portal blood.

The 3.3-h GH rhythm is composed of the following components. Starting at the beginning of a secretion period, the concentration of SRIF increases after a delay of 62 min and remains at a high level for 70 min, i.e., the duration of two pulses. Thereafter, SRIF follows the decay of GH in the circulation until the latter declines below the 1% threshold after 63 min (5 × 1/k_3,cl). This yields a total of 195 min, so the next pulse of GHRH (after 200 min) induces the release of GH and the cycle starts again. To obtain a 3.3-h rhythm, an integral number of GHRH pulses must occur within 200 min. Because the delay time  and the clearance rate constant k_3,cl are fixed parameters of the system, the 3.3-h rhythm can be disrupted either by changing the duration of the high level of GH in the circulation (e.g., administration of hGH) or by altering the parameters of the feedback function (resulting in a decreased sensitivity of SRIF to GH as in the case of the male-female transition).

The intriguing fact that the 3.3-h GH rhythm is conserved after an intravenous injection of SRIF-Ab with an elevated baseline (27) can be readily explained in terms of the model. SRIF-Ab is assumed to neutralize SRIF only at the level of the pituitary but not at the level of the hypothalamus (due to the blood-brain barrier). In the absence of SRIF in the pituitary, the GH profile in the circulation represents the GHRH pulses in the portal blood. Because the feedback of GH on hypothalamic SRIF release is not distorted by the perturbation, a rise in circulating GH still results in an increase of SRIF after the delay, which in turn suppresses GHRH pulses at the level of the hypothalamus. Therefore, the 3.3-h periodicity of SRIF in the brain remains conserved.

The model is designed so that release of GH can only be induced by GHRH. It follows that administration of GHRH-Ab results in an undetectable level of GH in the circulation, as observed in many experiments (27, 43).

The hypothesis of an intrinsic 1-h rhythm generated by GHRH neurons is based on the following arguments. In the male rat, a high-frequency pattern of GH is often observed in perturbation studies (13, 21), which is similar to that seen within a GH secretory episode. Because the GH profile in blood shows a periodicity of 3.3 h, it is unlikely that the high frequency of the GHRH pulses is generated by a GH feedback loop. It remains possible that the high-frequency GHRH profile is the result of mutual activation or inhibition between GHRH and SRIF neurons in the brain. Unfortunately, such a mechanism appears to require Hill coefficients greater than seven (10), which are usually not observed in biology. Thus we arrived at a 1-h rhythm intrinsic to a black box system involving GHRH neurons, which could be the result of a feedback circuit within the GHRH neuronal network (17) or via other neuropeptides such as the putative GHS (4, 33) and neuropeptide Y (8).

The model predicts a possible mechanism for the change of the male GH rhythm into the female pattern by sex steroids and vice versa. The transition was obtained by an appropriate change of the parameters (, c_4,tot) of the receptor function (see Fig. 2). The latter becomes independent of GH on sufficiently increasing c_4,tot, which can be achieved by a higher binding constant or by increasing the number of GHR; indeed, there is experimental evidence that the total amount of GHR is elevated in the female rat (31). Therefore, intravenous administration of hGH to a female rat has no effect on the rat GH profile (6) (the feedback of GH is disrupted), and the system gives a constant response to hourly injections of GHRH (12, 27) (constant SRIF release).

There is no doubt that pulsatility in GH secretion is important for growth (32). The typical GH profile shows two frequencies, namely the 3.3-h periodicity of the GH secretory episodes and the 1-h rhythm within the episodes. In the model, the origin of the multiple peaks per GH episode is the time delay . If  were <50 min, only one GH peak per period would be observed. Therefore, one might speculate that the double peak within a secretion episode is due to an intrinsic limiting parameter (), whereas the 3.3-h periodicity is the result of an evolutionary process to optimize growth.

Finally, the model suggests two experiments that might reveal the 1-h rhythm of GHRH neurons. Disrupting the feedback of GH on its own release (which entails the obliteration of internalized receptors) should cause the profile of GH in the circulation to show a 1-h periodicity according to the pulses of GHRH in the portal blood, since release of SRIF ceases. Indeed, Pellegrini et al. (29) recently demonstrated that central administration of a GHR mRNA antisense increases the pulsatility of GH and decreases hypothalamic SRIF expression. Second, antagonizing the activity of SRIF in the hypothalamus and in the pituitary, using a pure SRIF antagonist, should result in a 1-h rhythm of GH secretion in the circulating blood. This experiment is now in progress.