INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

PULSATILE SECRETION OF GROWTH hormone (GH) by the anterior pituitary gland is governed by several core neuromodulators, such as hypothalamic GH-releasing hormone (GHRH) and the GH release-inhibiting peptide somatostatin (SRIF) (16, 48, 56, 57, 60, 66). Both peptides are carried from hypothalamic neurons via the hypophysial portal circulation to somatotrope cells. GHRH stimulates the synthesis and release of GH, whereas SRIF antagonizes GH secretion. Circulating GH inhibits its own secretion via feed-forward (stimulation) on SRIF and feedback (repression) on GHRH (7, 13, 20, 23, 26, 48, 55, 63). The foregoing basic linkages are sufficient to engender GH pulsatility (16), but it is not known whether such simple connections will reproduce the vividly sexually dimorphic patterns of GH release (20, 22, 23, 47).

The adult male rat maintains 3.3-h-interval, multiphasic GH peaks separated by undetectable GH concentrations (58). The female rat manifests more irregular pulses of higher frequency and lower amplitude superimposed on an elevated baseline. Different patterns of GH output mediate some of the sexual dimorphism in body growth and gene expression in the rodent (23).

Sex steroid depletion and add-back studies in the rat can induce a full spectrum of male- and femalelike GH patterns (22, 42, 43). The regulatory basis for such neuroendocrine phenotypes is not known. As one approach to this issue, we have developed a simple networklike model of male GH-GHRH-SRIF interactions (16).

Earlier biomathematical constructs of the GH axis model the typical male pattern (5, 16, 65). For example, Brown et al. (3) explored the kinetics of GHRH actions at the pituitary level. Chen et al. (5) added network features but at the expense of high parameter complexity. Wagner et al. (65) assumed an autonomous GHRH pulse generator to impose repeated pulses within a GH secretory volley. More recently, Farhy et al. (16) used time-delayed feed-forward and feedback connectivity among GH, GHRH, and SRIF to drive volleys of GH secretion typical of the adult male rat. However, to our knowledge, none of the foregoing constructs explains the female-specific GH pattern of irregular, low-amplitude and high-frequency GH pulses, high baseline serum GH concentrations, and reduced autonegative feedback by GH (9, 23). The present work addresses the latter mechanistic issue.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Primary Sex Differences

Core Two-Oscillator GH Network

View larger version (59K): [in this window] [in a new window]   Fig. 1.   Schema of connections within the growth hormone (GH) feedback network (see Ref. 16 for details). Inhibitory interfaces [including elimination (elim) processes] are denoted by lines ending with solid circles, whereas stimulatory interactions are presented as "T" endings. Interactions are numbered consecutively from 1 to 5, as described in the text (see Core Two-Oscillator GH Network). Segments of the network identified by dotted lines were assumed to be sexually dimorphic (see Sex-Related Specificity of Parameter Set). Two network-specific oscillators are highlighted. P, pituitary gland; GHRH, GH-releasing hormone; SRIF, somatostatin.

We postulate that the GH-GHRH oscillator drives high-frequency (40-60 min) GH pulsatility in both sexes (see Primary Sex Differences), whereas the GH-SRIF oscillator (because of the longer delay in feedback) mediates recurrent low-frequency (3.3-h interval) malelike volleys (16). The system mimics observed patterns of GH release in the adult male rat, including GH autonegative feedback and SRIF-induced rebound GH secretion (16).

Connectivity is encapsulated in the following core equations, which describe the rate of change of each hormone with respect to feedback and feed-forward inputs

(1)

(2)

(3)

where GH, SRIF, and GHRH denote concentrations of the corresponding peptide; the derivatives (GH', SRIF', and GHRH') are taken with respect to time t; k₁, k₂, and k₃ are respective rate constants of elimination; k_r,1, k_r,2, and k_r,3 are rate constants of release; n₁, n₂, n₄, n₅ and t₁, t₂, t₄, t₅ are Hill coefficients and thresholds, respectively, for the corresponding regulatory functions numbered in Fig. 1; T and D are the time-delay constants for GH's feedback on GHRH and SRIF, respectively; and t₃ is the Michaelis-Menten constant defining feedback sensitivity.

If baseline "tonic" SRIF availability to somatotrope cells is viewed as S_min [replacing the positive constants k_r,2S_min and k_r,2(1  S_min) by S_min and k_r,2, respectively], then the rate of change of SRIF availability to somatotrope cells (SRIF'), is

(4)

where the first term denotes SRIF's decay from the system, S_min corresponds to baseline (GH-independent) SRIF secretion, and the third term defines additional GH feedback-dependent SRIF release. The following minimal system of first-order nonlinear differential equations then reflects the GH network

(5)

(6)

(7)

Sex-Related Specificity of Parameter Set

Diminished feedback of GH on SRIF could be modeled by decreasing the rate of SRIF release (k_r,2) and/or elevating t₃ of feedback sensitivity. No direct experimental data are available to distinguish between these choices in the female [unlike measurements of SRIF responses to a GH bolus in the male rat (6)]. Thus we tested the impact of both a decrease in the constant k_r,2 (e.g., 15-fold less SRIF release than in the male) and an increase in t₃ (e.g., 5-fold lesser sensitivity). These changes would reduce the efficacy (maximum) and blunt the potency (sensitivity) of GH's upregulation of SRIF release. Smaller changes preserve some delayed-feedback action of GH on SRIF at very high (e.g., pharmacological) GH levels.

The other SRIF-related parameters, viz., the thresholds t₂ and t₄, govern the onset of SRIF's inhibition of pituitary GH and hypothalamic GHRH secretion, respectively (Fig. 1). A physiological expectation is that GH-induced SRIF release does not block GHRH-driven GH peaks in the female. Altering (increasing) t₂ and t₄ would meet this expectation but would eliminate the known inhibitory effect of SRIF on pituitary GH release in the female (9). Thus we have not presently explored the effects of altering t₂ or t₄. Data regarding possible gender differences in t₅ (GH autofeedback on GHRH) are incomplete (8, 37, 52). Accordingly, we have tested the impact of "escape" of GHRH from GH auto repression further (see RESULTS).

In summary, the foregoing reference female model (see Table 1) corresponds to known experimental data in the rat. This construct generates uniform low-amplitude (<70 ng/ml) and high-frequency (~45 min) oscillations on an elevated baseline GH concentration (~30 ng/ml) (see Basic Female Model Output in METHODS).

GH Irregularity

Although variability in the system feedback parameters (modeling options 1 and 2 above) cannot be excluded, preliminary efforts to achieve physiologically realistic GH variability by modeling options 1 and 2 above were unsuccessful (see RESULTS). Moreover, direct hypophysial portal venous blood-sampling protocols establish considerable variability [~30% coefficient of variation (CV)] in baseline SRIF release over time in individual ovariectomized ewes (J. D. Veldhuis, T. P. Fletcher, K. L. Gatford, A. R. Egan, and I. J. Clarke, unpublished observations). The latter variability is essentially random, based on approximate entropy (ApEn) estimates. Hence, we here allow S_min to vary stochastically with a CV of 30%. For comparison, we explored the impact of the same stochastic input on S_min in the male reference model.

ApEn and Sample Entropy Approach

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Basic Female Model Output and GH Irregularities

View larger version (23K): [in this window] [in a new window]   Fig. 2.   A: output for the reference female GH model. B: impact of gradually increasing the threshold of GH's inhibition of GHRH. C: effects of prolonging the latency of GH's feedback on GHRH by 4-fold.

Figure 2, B and C, illustrates the impact of altered variability in the feedback actions of GH on GHRH and in the delay constant D (see GH Irregularity in METHODS). Only a large (7-fold) increase in the GH-on-GHRH action threshold (t₅) elevated GH levels, and blunted GH oscillations (Fig. 2B). Changing the delay constant D also resulted in physiologically irrelevant model output (Fig. 2C): GH peak amplitudes of 200 ng/ml required a fourfold increase in D (D = 0.5 h), resulting in lower baseline GH concentrations and prolonged interpeak intervals (2 h). Therefore, we infer that variability in the feedback actions of GH on GHRH or in the feedback-delay constants (see modeling options 1 and 2 in GH Irregularity in METHODS) does not readily account for the female rat GH pattern (10).

Figure 3 shows the influence of baseline SRIF variability (0.1, 0.3, and 0.5 SD) on GH profiles simulated in the female reference model. No other sources of stochastic variation are included in these plots. Variability in SRIF release about an unchanging mean induced visually evident and stochastically quantifiable irregularity in the female but not the male model (below). Further analyses used a baseline variability of 0.3 SD to emulate data reported in the ewe (J. D. Veldhuis, T. P. Fletcher, K. L. Gatford, A. R. Egan, and I. J. Clarke, unpublished observations).

View larger version (33K): [in this window] [in a new window]   Fig. 3.   Reference female GH model responses to 3 levels of stochastic variability of the SRIF baseline (top: 0.1 SD; middle: 0.3 SD; bottom: 0.5 SD) imposed between 1100 and 3200.

In the present model, oscillations in GH and GHRH release in the female evolve as follows. GHRH released into portal blood drives secretion of GH as the GHRH level approaches its action threshold (t₁). The rise in GH concentrations suppresses GHRH release ~7 min (the time delay T) after GH reaches its feedback threshold t₅. The GHRH concentration then begins to decline because of elimination. Increased GH output continues until GHRH concentrations fall below the stimulatory threshold. Withdrawal of GHRH input allows GH concentrations to decay because of waning secretion and continuing elimination. Diminished GH levels permit a time-delayed resumption of GHRH release. This reciprocal interaction between GHRH and GH produces recurrent peaks in the femalelike secretory profile, as long as excessive somatostatin inhibition is not present (male pattern). Unequal GH pulse amplitudes and interpulse intervals reflect modulation of GHRH action by the variable SRIF baseline (above). Notably, the same perturbation in SRIF baseline applied to the male fails to induce irregularity (Fig. 4).

View larger version (34K): [in this window] [in a new window]   Fig. 4.   Contrasting effect of a variable SRIF baseline (time line: 1100-3200; 0.3 SD) on male (top) and female (bottom) GH model profiles. Procedural uncertainty (20% Gaussian noise) was imposed on the model output.

The latter plots illustrate the further effects of additive Gaussian noise (0.2 SD) on the GH concentrations, whereby we simulate experimental uncertainties.

Model Reactivity to Defined Interventions

Simulated responses to continuous human GH infusions. To mimic the laboratory experiments of Clark et al. (11), we simulated continuous 6-h infusion of human GH in both the male- and femalelike constructs. To this end, we added constant "secretion" of GH in Eqs. 6 and 7. The analysis was repeated by imposing a second infusion threefold greater than the first. Variable SRIF baseline release (0.3 SD) was initiated at 1100, 3 h after the simulated GH infusion was begun (8000) (Fig. 5).

View larger version (30K): [in this window] [in a new window]   Fig. 5.   Comparison between female (left) and male (right) GH model responses to dose-varying continuous infusions of human GH (time line: 8000-1400). SRIF baseline variability (0.3 SD) was initiated at 1100 (see METHODS).

Predicted GH secretory-pattern responses to multiple GHRH injections. We tested the response of both the male- and femalelike model to series of 12 simulated injections of GHRH every 45 min to mimic the experimental protocol of Carlsson et al. (4). Simulated infusion of human GH for 6 h was added after the third GHRH pulse (Fig. 6).

View larger version (28K): [in this window] [in a new window]   Fig. 6.   Left: male and female GH model responses to a simulated series of 12 consecutive GHRH injections (arrows) at 45-min intervals starting at 1000 (x-axis). Right: added infusion of exogenous GH for 6 h (solid bars) beginning at 1130. Data are presented otherwise as described in the legend of Fig. 5.

Infusion of GHRH antibodies. The model-predicted effect of antiserum to GHRH is illustrated in Fig. 7, wherein we increased the elimination rate of GHRH by 100-fold starting at 1600. Simulated GH profiles agree well with experimental data showing suppression of GH release after the administration of GHRH antibodies in both sexes (39, 66).

View larger version (12K): [in this window] [in a new window]   Fig. 7.   Model predictions of malelike (left) and femalelike (right) responses to GHRH antiserum (solid bars) introduced at 1600. Data are presented otherwise as described in the legend of Fig. 5.

Intermittent SRIF infusion. Intermittent SRIF delivery comprised a 9-h simulated SRIF infusion, which was interrupted for 0.5 h every 3 h (Fig. 8). This analysis assumed that peripheral infusion of SRIF does not directly alter hypothalamic GHRH or SRIF release (16). Analyses were performed without (Fig. 8, left) or with (Fig. 8, right) simulated continuous infusions of human GH during the third SRIF infusion period (see Simulated responses to continuous human GH infusions). Baseline SRIF variability was not imposed here. Corollary experiments (not shown) demonstrated that stochastic variability in S_min did not affect output of the malelike model (because GH-driven SRIF secretion dominates the SRIF baseline variability), whereas the female model displayed large deviations in rebound amplitudes. Simulated GH responses in both sexes agree well with the data reported by Clark et al. (9), wherein concurrent GH infusion abolishes post-SRIF GH rebound in the male but not in the female. The ability of exogenous GH to suppress rebound GH release depends on GH's inhibition of GHRH and stimulation of SRIF release, but the latter action is diminutive in the female (see METHODS).

View larger version (28K): [in this window] [in a new window]   Fig. 8.   Left: simulation of rebound GH secretion in male (top) and female (bottom) rats induced by intermittent SRIF infusion (solid bars). Right: modeled effect of human GH infusion (hatched bars) on the rebound GH secretion induced by the third SRIF infusion (solid bars) in males (top right) and females (bottom right) (See METHODS for details).

ApEn and SampEn Analysis

Approximate entropy was quantitated for data pairs (I₁) and triples (I₂) (i.e., parametric choices m = 1 and m = 2) at a normalized tolerance of r = 0.2SD, where SD is the standard deviation of the particular data set (for details see Refs. 45, 46, and 49). Higher ApEn or SampEn denotes greater disorderliness of time series, as evident in the female compared with the male (Table 2). As summarized in the APPENDIX, an analogous procedure was used to calculate the normalized ApEn and SampEn ratios for a transitional sequence of noise-free malelike to femalelike models.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

The present work illustrates that a simple mechanism of sex-specific regulation of SRIF release could account for female- vs. malelike GH secretory patterns in the adult rat (14, 16, 20, 23, 26, 33, 34, 38, 50, 56-59, 65). This inference arises from a core network of GHRH's feed-forward drive of pituitary GH release, SRIF's competitive inhibition of GH release, GH's stimulation of SRIF after a time delay, SRIF-dependent inhibition of GHRH secretion, and GH's autonegative feedback on GHRH (16). The foregoing minimal connections generate two coupled oscillators, whose output emulates GH patterns in the adult male rat (see the introduction). We extend this formulation first by demonstrating that relaxation of GH autofeedback drive of SRIF outflow induces a femalelike pattern of GH release. The notion of limited GH feedback on SRIF is well documented in this species (11, 12, 23, 26, 36, 38). Reduced autofeedback drive of SRIF outflow induced high-frequency GH oscillations. Mechanistically, recurrent GH pulses are mediated by putative GH-GHRH interactions, whereas loss of 3.3-h-interval volleylike GH release is mediated by the decrease in GH-SRIF connectivity inferred in the female (see METHODS and Fig. 1) (16). Second, we could show that elevating mean baseline SRIF activity in the femalelike model diminishes GH pulse amplitude. Heightened tonic (noncyclic) activity of SRIF is consistent with the results of SRIF-neutralization experiments in the adult female rat and with the ability of estrogen to upregulate pituitary SRIF receptors (31, 64, 68). And, third, we observed that adding variability about mean SRIF release evokes pulse-amplitude irregularity. Variability in central SRIF release is readily apparent in ewes sampled at 5-min intervals for several hours (J. D. Veldhuis, T. P. Fletcher, K. L. Gatford, A. R. Egan, and I. J. Clarke, unpublished observations). Thus all three of reduced GH drive of SRIF outflow, increased SRIF activity and accumulated variability in mean (baseline) SRIF release in the present femalelike model of GH neuroregulation are concordant with physiological data.

Several pivotal experiments have examined mechanistic differences in the neuroregulation of GH patterns in the adult male and female rat in vivo. For example, exogenous GH infusions of sufficiently high dose suppress endogenous GH secretion in both genders (11, 33) but more readily in the adult male than female animal (Fig. 5). In addition, repeated GHRH injections evoke continued GH responses in the female but not in the male rat. Similarly, low-dose infusions of human GH extend GH suppression despite exogenous GHRH stimulation in the male but not the female rat (4). Because GHRH-stimulated GH secretion is abolished in the female by SRIF infusion (4), Clark et al. (11, 12) and Robinson (50) inferred that the female rat is relatively insensitive to GH-induced hypothalamic SRIF release (albeit responsive to SRIF when available) compared with the male. The ability of a high dose of exogenous GH to inhibit endogenous GH output in the female of this species is explained by GH-induced repression of GHRH release (8, 20, 36, 37, 39, 50, 53, 62, 66). The present biomathematical model illustrates the foregoing concept, wherein a reduction of GH's stimulation of SRIF, but not of GH's inhibition of GHRH release, reproduces the femalelike GH secretory pattern and preserves sensitivity to somatostatin.

A higher frequency, and also higher mean amplitude, of GH peaks in the female model was achieved solely by attenuating GH's drive of SRIF release. Elevating average basal SRIF release was required to limit GH pulse height. Effectual SRIF action in the female has been inferred experimentally by SRIF-immunoneutralization experiments (41), the evident suppressibility of GH secretion by exogenous SRIF (4), and estradiol's upregulation of SRIF receptor expression in somatotrope cells and immortalized tumoral cell lines (31, 64, 68). Direct measurements of hypothalamo-pituitary portal venous SRIF release under identical sampling and assay conditions in the female and male will be required to document and distinguish between heightened release and/or action of SRIF in the female rodent.

Exogenous GHRH injection evokes GH release in both sexes (4, 39). In addition, abrupt cessation of SRIF inhibition elicits rebound GH release in both genders (9). The ability of adult female rats to engender occasional high-amplitude GH peaks spontaneously (10) further documents pituitary responsiveness to GHRH. However, other studies allow for reduced GHRH production and/or action in the estrogen-enriched milieu of the rat (20, 23, 26, 37, 38). Although strictly comparable data are not available in humans, recent analyses of the dose-dependent actions of randomly ordered single injections of recombinant human GHRH-(1-44)-amide in postmenopausal women show enhanced GHRH potency (but not efficacy) in response to short-term estrogen repletion (2). In addition, altered actions of GHRH in the female could be mediated by reciprocal changes in basal SRIF outflow. The latter mechanism might also contribute to species differences. For example, where GH and GHRH peak amplitudes are smaller in the female than male rat (Fig. 9, panels 1 and 6), GH pulse heights are larger in premenopausal women than comparably aged men (62). Further studies will be required to asses whether reduced GHRH drive or heightened basal SRIF release maintains low-amplitude GH pulsatility in the female.

View larger version (45K): [in this window] [in a new window]   Fig. 9.   Sensitivity analysis illustrated for 1 of the 200 realizations each of malelike (panel 1, top left) to femalelike (panel 6, bottom right) parameter transitions (see Table 3). Parameter evolution consisted of gradually relaxing the feedback of GH on SRIF and elevating baseline SRIF release with constant variability. The arrows (before 1100) track the emergence of a single GHRH (light line)-GH (dark line) spike within the initially malelike intervolley region with femalelike parameter evolution. Data are presented otherwise as described in the legend of Fig. 5. Objective quantitation of regularity changes was performed via approximate entropy and sample entropy analyses on each of 200 simulations carried out for each parameter set shown (see Table 4).

Random variability in (constant mean) baseline SRIF release triggered marked pulse-to-pulse amplitude variability in the femalelike (but not malelike) feedback model (Fig. 4). Irregular SRIF signaling could reflect nonuniform secretion and/or delivery of SRIF to somatotropes as well as inconsistent pituitary responsiveness (28, 29). The degree of stochastic variation in basal SRIF outflow postulated here (i.e., a 30% CV) is observed in hypophysial portal blood in the ewe (Ref. 21; J. D. Veldhuis, T. P. Fletcher, K. L. Gatford, A. R. Egan, and I. J. Clarke, unpublished observations). However, further studies will be required to monitor SRIF oscillations in the female of various species and in potential pathophysiology (23).

Extensive experimental data (23) document that the GH-GHRH-SRIF network is subject to multiple internal and external influences [e.g., insulin-like growth factor (IGF)-I, IGF-II, metabolic factors (e.g., glucose, free fatty acids, acidosis), glucocorticoids, gonadal sex hormones, thyroid hormones, catecholamines, and gastrointestinal and neuropeptides]. We did not include these factors in the present minimal model, because none (with the exception of ghrelin, IGF-I, and IGF-II) has been proven to participate in the GH network in a reciprocal feedback fashion. Further model extension may allow more complex input by such extrinsic regulators. For example, it will be important to obtain detailed data on feedback time dependencies of the actions of IGF-I and IGF-II (23). One could speculate that a prolonged delay in IGF-I feedback on GH release might contribute to the daily rhythmicity of GH release in the female rat, as observed in some studies (10). Thus additional experimental interventions will be important to distinguish both rapid and delayed regulation by other negative and positive inputs to the core GH-GHRH-SRIF system.

Perspectives