Ghrelin is a native ligand for the growth hormone secretagogue (GHS) receptor that stimulates pulsatile GH secretion markedly. At present, no formal construct exists to unify ensemble effects of ghrelin, GH-releasing hormone (GHRH), somatostatin (SRIF), and GH feedback. To model such interactions, we have assumed that ghrelin can stimulate pituitary GH secretion directly, antagonize inhibition of pituitary GH release by SRIF, oppose suppression of GHRH neurons in the arcuate nucleus (ArC) by SRIF, and induce GHRH secretion from ArC. The dynamics of such connectivity yield self-renewable GH pulse patterns mirroring those in the adult male and female rat and explicate the following key experimental observations. 1) Constant GHS infusion stimulates pulsatile GH secretion. 2) GHS and GHRH display synergy in vivo. 3) A systemic pulse of GHS stimulates GH secretion in the female rat at any time and in the male more during a spontaneous peak than during a trough. 4) Transgenetic silencing of the neuronal GHS receptor blunts GH pulses in the female. 5) Intracerebroventricular administration of GHS induces GH secretion. The minimal construct of GHS-GHRH-SRIF-GH interactions should aid in integrating physiological data, testing regulatory hypotheses, and forecasting innovative experiments.
- somatotropic axis
- growth hormone secretagogues
- mathematical model
- hormone pulsatility
ghrelin and synthetic growth hormone secretagogues (GHS) stimulate pulsatile growth hormone (GH) secretion via combined hypothalamohypophyseal mechanisms. The GHS receptor is expressed by somatotrope cells and arcuate nucleus (ArC) neurons containing GHRH and other peptides (40, 44). Ghrelin and GHS act directly on GH-secreting (somatotrope) cells and indirectly on the inhibitory signal somatostatin (SRIF) and the peptidyl agonist GH-releasing hormone (GHRH) (13, 27, 44, 51). In particular, GHS stimulate somatotropes in vitro but are synergistic with GHRH, induce ArC GHRH release, and antagonize certain hypothalamic actions of SRIF in vivo (3, 10, 13, 27, 37, 40, 51). GHRH potentiates feedforward drive by GHS because passive immunoneutralization or pharmacological antagonism of GHRH and truncational mutation of the GHRH receptor attenuate GHS-evoked GH secretion markedly in the rat, mouse, and human (31, 35, 63, 65, 68, 78). In contradistinction, GHS and GHRH do not synergize in vitro (70, 89). Pituitary portal vein sampling studies have indicated that GHS infusion elicits ArC GHRH release in the conscious sheep (31, 35). Other experiments have established that GHS can oppose inhibition by SRIF and octreotide in the anterior pituitary gland and the hypothalamus (25–27, 71). No formalism incorporates these multilocus actions of GHS into available constructs of self-renewable GH pulses mediated by GHRH-SRIF-GH feedback interactions (34, 53, 61, 72).
Current models of the basic properties of the GH pulse renewal process assume reciprocal interactions among GHRH, SRIF, and GH (28–30). In the present work, we have used this foundation in an effort to incorporate the known effects of GHS in a simple network-like structure, examine integrative implications of specific pathway hypotheses, and explore the relevance of specific connections in explicating the outcomes of previously published interventional experiments that have typically infused GHS systemically. We thereby formulated four primary hypotheses of physiological control. 1) Stimulation of GHRH release by GHS is required to evoke maximal GH output in both sexes, but especially in the female. 2) Time-delayed GH feedback-induced outflow of SRIF from the periventricular nucleus (SRIFPeV) to both the ArC and the pituitary gland in the male inhibits GH responses to the second of consecutive GHS pulses. 3) Sex differences in the GH autofeedback drive of SRIF release account for greater acute GHS-stimulated GH secretion in the female than in the male, on average, when GHS is administered intravenously at random times, and female-predominant blunting of pulsatile GH secretion in the transgenic central nervous system (CNS) ghrelin receptor-knockdown model.
Overview of Core Construct
The present analyses are built on an earlier basic model of the GH pulse renewal process in the adult male and female rat (30). No animal or human experiments were conducted, and the study is IRB exempt. Unforced automaticity of the pulse-generating mechanism arises from 1) intermittent time-delayed peripheral GH drive of SRIFPeV outflow, which inhibits both ArC GHRH neurons transsynaptically and pituitary GH release after release from the median eminence into hypophysial-portal blood; and 2) rapid reciprocal intrahypothalamic signaling between GHRH and SRIF neurons in the ArC (SRIFArC), wherein SRIFArC suppresses GHRH neurons and, conversely, GHRH stimulates SRIFArC neurons (34, 39, 49, 61, 72). In this formulation, the foregoing two mechanistically distinguishable (systemic CNS and intrahypothalamic) feedback loops are coupled by their convergence on GHRH neurons. The ensemble system confers infrequent (3.3 h) large volleys of GH release with intervolley troughs (nadirs) in the male rat as well as frequent, smaller GH pulses within volleys in the male and at any time in the female animal typical of physiological output patterns (19, 20).
A principal mechanism mediating the sex difference in GH pulsatility is greater GH autofeedback drive of SRIFPeV release in the male than in the female rodent (17, 28, 29). In the malelike ensemble construct, pulsatile GH feedback-induced SRIFPeV release transiently inhibits the intrahypothalamic SRIFArC-GHRH oscillatory mechanism, thereby enforcing a delimited trough (intervolley interval of secretory quiescence). Metabolic elimination of GH attenuates SRIFPeV restraint, which evokes a brief volley of more rapid GHRH and GH pulses of waning amplitude as observed in vivo (18–20, 57, 72, 75). In the male rat, experimental attenuation of periventricular nucleus inputs to the ArC blunts or abolishes high-amplitude GH pulses, consistent with an intermittently sensitizing action of cyclic SRIFPeV release and withdrawal on the presumptive GHRH-SRIFArC oscillator (48, 49, 85). On the other hand, in the femalelike model, GH feedback stimulates SRIFPeV release and damps the GHRH-SRIFArC oscillatory mechanism less effectually (30, 66). The outcome in the female includes irregular, low-amplitude GHRH and GH pulses as recorded in vivo (17, 21, 77). The foregoing core linkages thus provide a platform for integrating mechanisms of ghrelin action.
Ghrelin and GH Network: Basis of Model Structure
First, we assumed that systemic ghrelin availability is relatively stable, albeit possibly variable locally (22, 43, 44, 51, 52, 56, 78). Serum ghrelin concentrations change by <30% in relation to food intake, with no consistent correlation with GH peaks or troughs in the conscious, freely moving male rat (62, 80). One clinical study found a mean difference between women in the late follicular phase of the menstrual cycle and in men (5), and transgenic knockdown of the GHS receptor gene in catecholaminergic GHRH neurons in mice diminished GH concentrations in the adult female only (74). The model attempts to explain the latter gender contrast.
Second, GHS, like GHRH, consistently stimulate GH secretion two- to fivefold by pituitary cells in vitro (7, 12, 13, 70, 71, 89). Unlike GHRH, GHS and ghrelin induce GH gene expression only upon prolonged delivery to the infantile rat in vivo or to somatotropes in vitro (42, 54). Thus model parameters in the adult animal include GHS-dependent stimulation of GH secretion but not de novo GH synthesis.
Third, experiments have affirmed that GHS receptors are expressed in the mediobasal hypothalamus on GHRH and other neurons activated by GHS (23–25, 38, 46, 79) and that GHS stimulate total (i.e., amplitude or frequency of) GHRH release into hypothalamopituitary portal blood in vivo in the ram and ewe (31, 35). Accordingly, the model incorporates GHS-driven outflow of GHRH from the ArC.
Fourth, studies have indicated that GHS can limit hypothalamic SRIF release in vitro, but not detectably into portal blood in vivo; that it can oppose octreotide or SRIF-dependent inhibition of ArC GHRH (and NPY) neurons in the rat and guinea pig in vivo (9, 25, 27); and that it can antagonize SRIF-mediated suppression of GH secretion in the rat and human in vitro and in vivo (10, 13, 26, 71, 78). Model terms are included to represent these intrahypothalamic and hypophysial sites of SRIF-GHS antagonism.
Fifth, continuous intravenous GHS infusion amplifies GH pulse amplitude (but not frequency) 5- to 30-fold in both men and women (11, 41, 45, 73). Therefore, augmentation of GH peak height is an expectation of valid model performance.
Figure 1 is a schema showing inferred connections among ghrelin (GHS), GH, GHRH, SRIFArC, and SRIFPeV with corresponding time delays. Primary pathways include feedforward by systemic GH on SRIFPeV release after a lag D1, GHRH stimulation of SRIFArC activity after lag D2, rapid SRIFArC inhibition of GHRH secretion and GHRH stimulation of SRIFArC, and prompt SRIFPeV inhibition of pituitary GH release and hypothalamic GHRH-SRIFArC oscillations (30). Superimposed on this basic structure, ghrelin presumptively attenuates SRIFPeV- and/or SRIFArC-dependent inhibition of GHRH outflow (described below), facilitates GHRH secretion, antagonizes SRIFPeV inhibition of pituitary GH release locally, and stimulates GH secretion directly. We tested the hypothesis that these collective capabilities mediate the efficacy of ghrelin and GHS more markedly in vivo than in vitro (1, 10, 63).
General Formulation of Core Equations
The first two sections modify the earlier model to include combined (pituitary and hypothalamic) actions of GHS/ghrelin.
The rate of change of plasma GH concentrations is controlled jointly by the distribution volume, elimination kinetics, and secretion rate of GH (33, 61). In turn, the GH secretion rate is determined at least twofold by GHRH stimulation and noncompetitive SRIF inhibition (28, 29). These relationships are represented by cooperative and asymptotic dose-response Hill functions.
Two Hill functions link GHRH and SRIFPeV outflow to GH release by the pituitary gland as follows: (1) where the prime denotes the rate of change of GH concentrations; GH and GHRH define instantaneous GH and GHRH concentrations; k1 and kr,1 are rate constants of GH elimination and secretion, respectively; n1, and n2 are slope (sensitivity) terms associated with the stimulatory and inhibitory effects of GHRH and SRIF, respectively; and t1 and t2 designate potencies of GHRH and SRIF (i.e., half-maximally stimulatory or inhibitory concentrations, EC50 or IC50) respectively. The assumption is that GH release requires feedforward by GHRH and partial withdrawal of SRIF antagonism (7, 15) as defined by the large-bracketed, noncompetitive relationship shown in Eq. 1.
To incorporate ghrelin action on the pituitary gland, we modified the stimulatory and inhibitory terms in Eq. 1. First, the feedforward term is replaced by where GHRELIN denotes the concentration of ghrelin, the coefficient ng,0 defines sensitivity to ghrelin, tg,0 designates stimulatory potency (EC50) of GHRELIN, and g0 corresponds to maximal efficacy of ghrelin action. Second, the feedback term in Eq. 1 is replaced by where n2 and ng,1 define the respective sensitivities of SRIFPeV inhibition and ghrelin stimulation, t2 designates inhibitory potency (IC50) of SRIFPeV when GHRELIN = 0, tg,1 represents potency (EC50), and g1 denotes efficacy of ghrelin action. The function F1 limits opposition by ghrelin of SRIF action on the pituitary as evident in vitro (10).
The rate of change of SRIFArC is determined by local SRIF elimination and GHRH feedforward within ArC as follows: (2) where SRIFArC denotes the SRIF concentration in ArC, k2 and kr,2 are respective rate constants of elimination and release of SRIFArC, D2 reflects the time delay for GHRH to stimulate SRIFArC release, n3 is the slope (sensitivity) of GHRH drive of SRIFArC outflow, and t3 is the EC50 of GHRH feedforward on SRIFArC secretion. In Eqs. 2 and 3, we use sharp (i.e., direct) delays to simplify the model (28–30, 66), thus obviating the need for additional parameters to define a delay distribution.
The rate of change of SRIFPeV is governed by the elimination process and GH feedback drive superimposed on low basal SRIFPeV outflow as defined by the following equation: (3) where SRIFPeV is the SRIF concentration in PeV, SRIFbasal is the constitutive (time-invariant basal) SRIFPeV release, k4 and kr,4 are the respective rate constants of elimination and release of SRIFPeV, D1 is the time delay for systemic GH concentrations to stimulate SRIFPeV release, n5 is the slope (i.e., sensitivity) of GH drive of SRIFPeV outflow, and t5 is the EC50 of GH feedforward on SRIFPeV secretion. A gender distinction arises from unequal efficacy (kr,4) of GH feedback in stimulating SRIFPeV secretion (17, 21, 58), which here is assumed nominally to be 4.5-fold less in the female than in the male.
The rate of change of GHRH concentrations was described previously (30) using the following equation: (4) To represent noncompetitive antagonism between total SRIF in ArC and ghrelin on GHRH output and concentration-dependent stimulation of GHRH release from ArC by ghrelin, we replaced the rightmost inhibitory term in Eq. 4 by the following: where SRIF = SRIFPeV + SRIFArC; t4 and tg,2 are the IC50 and EC50 of total SRIF and ghrelin, respectively; n4 and ng,2 are inhibitory and stimulatory slopes associated with the actions of SRIF and ghrelin, respectively; and g2 is maximal ghrelin action on GHRH secretion (viz., GHS efficacy). We assume that supramaximal SRIF suppresses GHRH action and release noncompetitively with respect to GHS stimulation (7, 15, 27, 88, 89). Small biological variation in stochastic input to the GHRH-SRIFArC oscillator is achieved by allowing random variability in the sensitivity of GHRH neurons to total SRIFArC and SRIFPeV inhibition (30). Specifically, the half-maximally inhibitory concentration of SRIF (t4 in the control function above) is varied by imposing random, zero-mean, unit-normalized Gaussian noise at a nominal 5% coefficient of variation (standard deviation/mean × 100%) at 30-min intervals. Recent analyses indicate that endogenous stochastic inputs may modulate in vivo dose responsiveness in other neuroendocrine axes (50).
We use two different models in the simulations. Model A (discussed in Construct for preliminary single-component analyses) includes a minor modification of the basic earlier construct (30) to represent the capability of high concentrations of ghrelin to stimulate GH secretion directly ∼2.5-fold (see the introduction). Model A is applied to test the impact of four putatively separate GHS actions before examining their aggregate effects. The simulations demonstrated that no single action of ghrelin is sufficient to reproduce in vivo observations fully. Accordingly, we developed model B (described in Integrative construct) to combine all four presumptive actions of GHS.
Construct for preliminary single-component analyses (model A).
By extension of an earlier construct (Eqs. 1–4), we tested the impact of direct pituitary stimulation by ghrelin; i.e., a 2.5-fold effect at zero GHRH and zero SRIF. The reference model (model A) thus comprises the following (note change from Eq. 1): (A1) (A2) (A3) (A4) with the coefficients as summarized in a previous publication (30) (Sbasal = 0) and ng,0, tg,0, and g0 as shown in Table 1. The gender contrast is incorporated by an approximately fourfold lower value for kr,4 in the female to reflect reduced GH-on-SRIF feedforward (30).
Noncompetitive features include the fact (see Eq. A1) that ghrelin cannot overcome inhibition by pharmacological SRIF concentrations as previously reported experimentally (9, 12, 13). Given a nominal blood concentration of GHRELIN = 250 pg·ml−1, values of ng,0, tg,0, and g0 permit greater effects of injected than endogenous ghrelin in model A (80).
Integrative construct (model B).
Model B embodies the direct pituitary effect of GHS and four other putative actions (see Ghrelin and GH network: basis of model structure). The ensemble interactions are encapsulated algebraically as follows: (B1) (B2) (B3) (B4) Nominal values of interactive constants are summarized in Table 1 and discussed further in the text. Analogously to model A, we assumed that GH feedback efficacy (kr,4) was nominally fourfold less in the female than in the male.
The choice of model parameters was discussed previously (28–30) on the basis of direct measurements in the case of GHRH, SRIF, and GHS/ghrelin (76, 88, 89). The resultant parameter set under the basic model assumptions yields established pulsatile properties of GH secretion (34, 61).
In addition to a direct pituitary action of GHS in model A (mathematically modeled by the addition of a ghrelin-dependent feedforward term in Eq. B1), model B assumes that GHS opposes SRIF competitively at sites of SRIF action. There are various ways to incorporate this feature. Herein we have chosen an expression that preserves SRIF competition at the pituitary by the function F1 and at the ArC by F2. Because both functions are bounded from above and the action of SRIF is not restricted, GHS has a limited capability to overcome the suppressive effect of high pharmacological SRIF concentrations. The parameter choices that define F1 and F2 assume the following: 1) at low concentrations (including the postulated typical endogenous levels GHRELIN = 250 pg·ml−1; Table 1), GHS is more potent at the ArC than the pituitary (tg1 > tg2), and 2) at high concentrations, GHS is more effective at the pituitary than at the ArC (mathematically, g1 > g2). Thereby, in model B, uninfused ghrelin primarily opposes the negative action of SRIF at the ArC rather than at the pituitary. The distinction is crucial in explaining the results of the experiment of Shuto et al. (74) involving transgenic silencing of the ArC (but not the pituitary) GHS receptor in the male and female mouse.
Under model B assumptions, ghrelin is active on the hypothalamus at endogenous concentrations (mathematically by means of the control function F2). In addition, the GHRH secretion function (Eq. B4) differs from that in model A (30) by way of higher values of n1 and n3 to drive the GHRH-SRIFArC oscillator under the added GHS linkages.
Partial sensitivity analysis of model B (see appendix; see also Table 6) shows that individual parameters can be varied within certain limits without disruption of model output. In addition, random Gaussian variability between 5% and 25% superimposed on GHS-driven GHRH release does not disrupt model oscillations (see appendix).
Simulation of Peptide Injection
Intravenous or intracerebroventricular (ICV) bolus injection of ghrelin (and in one analysis GHRH) was incorporated by adding ghr(t) to GHRELIN (or to GHRH) in core equations to reflect the hypothesized site of ghrelin action, wherein (5) and (6) where C defines the relative magnitude and “onset” designates the time of apparent GHS (or GHRH) delivery, k is the rate constant of elimination of bioactive peptide, and 0.1 h represents a nominal delay for peptide distribution and access to all sites of action.
The function ghr(t) simulates a change in the concentration of any given signal in the system without altering linkages. For example, in the initial analysis of model A, we imitated a 30-fold decrease in SRIF concentration at certain sites by dividing the corresponding local SRIF concentration by 1 + ghr(t), where ghr(t) is determined by setting C = 50 and k = 1.7 h−1 in Eqs. 5 and 6.
Numerical Procedures and Initial Conditions
To integrate model equations, we used a Runge-Kutta 4 algorithm (Berkeley Madonna software, version 8.0.1). To solve delayed equations, we assumed a constant value for the unknown delayed functions on the required time interval to generate appropriate initial conditions.
Infusion simulations were performed after generating 50-h profiles, thereby marginalizing any impact of initial conditions. Random changes in the initial conditions were used to verify that simulation results are robust.
Numerical results are divided into three groups. First (see Feedforward by Systemic Ghrelin: Single-Component Analyses of Pathway Relevance) model A is used to establish the need to combine putative sites of ghrelin action into a single construct. Second (see Impact of Systemic GHS Delivery on Predicted Outflow of SRIFPeV, SRIFArC, GHRH, and GH; Gender Contrasts in GHS Stimulation; Female-Predominant Reduction in GH Concentrations After Partial Molecular Silencing of the GHS Receptor Expressed by Catecholaminergic Neurons in ArC; Simulation of Continuous Peripheral Ghrelin Stimulation; and Impact of Simulated Central Neural Administration of Ghrelin), model B is evaluated to explain key published observations. Third (see Analyses of Complementary and Alternative Model Connections), we extend the analysis of model B system-parameter changes.
Feedforward by Systemic Ghrelin: Single-Component Analyses of Pathway Relevance
Initial analyses (model A) were performed to test the individual assumptions that iv ghrelin stimulates GHRH secretion, opposes SRIFPeV-mediated inhibition of GHRH release, antagonizes SRIFArC-enforced repression of GHRH secretion, or restrains SRIFPeV-dependent inhibition of pituitary GH secretion. By implementation of Eq. A1 only, we show that four simulated iv ghrelin doses defined by C values (in thousands) of 20, 60, 200, and 600 yield unopposed peak GH concentrations (secretory-burst area shown in parentheses) of 115 (106), 305 (354), 385 (660), and 408 (940). These values are the same in the male- and femalelike formulations of this particular question (59, 68, 81, 89).
To simulate ghrelin injection during a spontaneous GH peak or trough in the male, we defined GHS times of onset as 53.5 h (volley) and 55.5 h (trough). These times occur randomly in the female GH pulse renewal process. Stimulus strength was designed to elicit a near-maximal GH response to the first GHS injection. The network structure included direct GHS drive of GH secretion plus any one of the following. 1) GHRH stimulation: in Eq. 6, C = 115,000, with the term ghr added to the right-hand side of Eq. A4. 2) Opposition to SRIFPeV-mediated inhibition of GHRH release: in Eq. 6, C = 50, with the term SRIFPeV in Eq. A4 divided by (1 + ghr). 3) Antagonism of SRIFArC-enforced repression of GHRH secretion: in Eq. 6, C = 50, with the term SRIFArC in Eq. A4 divided by (1 + ghr); or 4) Restraint of SRIFPeV-dependent inhibition of pituitary GH secretion: in Eq. 6, C = 50, with the term SRIFPeV in Eq. A1 divided by (1 + ghr). Significant GH secretory responses are predicted by each separate connection (Fig. 2). However, no single action with direct pituitary GHS drive is sufficient to reproduce the combined experimental observations reported previously (78).
The analyses presented in Fig. 3 combine direct pituitary GHS actions and all four of the connections (items 1-4 in the preceding paragraph) in the presence or absence of the same two consecutive GHS stimuli. The composite model predicts that the first pulse of ghrelin will elicit comparable GH secretion if administered during a volley in the male and anytime in the female. In the male (but not in the female), the second pulse stimulates GH to a lesser degree.
On the basis of the above preliminary analysis, model B is expected to explain both key experimental outcomes and self-renewable GH pulsatility (30). The mathematical formulation comprises Eqs. B1, B2, B3, and B4 as well as Table 1, which was implemented to probe specific mechanistic hypotheses (described below).
Impact of Systemic GHS Delivery on Predicted Outflow of SRIFPeV, SRIFArC, GHRH, and GH
In the adult female rat, the amplitude of GH secretory responses to consecutive identical GHS injections is consistent, but in the male animal it depends on whether stimuli are administered in rapid succession (within 3 h or less) and during a spontaneous GH peak or trough (78). To examine the possible mechanisms underlying this sex distinction, we reconstructed the predicted patterns of hypothalamic peptide outflow after sequential iv GHS pulses. Figure 4 depicts inferred time courses of the release of SRIFPeV to the pituitary gland, the sum of SRIFArC plus SRIFPeV within ArC, GHRH from ArC, and GH from the pituitary. Injections were simulated during spontaneous GH pulses (Fig. 4, top) and a putative peak vs. trough (in the male) and at any time (in the female) by way of two putative GHS doses (C = 6,000 and C = 30,000; Fig, 4, middle and bottom). Under these conditions, SRIFPeV released by the first GHS-stimulated GH pulse in the male acted to repress intrahypothalamic SRIFArC-GHRH oscillations, which otherwise maintained pulsatile GHRH secretion; attenuate the amplitude of the second GHS-induced GH peak; and introduce a time delay before the onset of GH secretion in the second peak as inferred in vivo (78).
The ensemble model B thus reproduces the results shown in Fig. 3 (generated with model A, wherein ghrelin action is superimposed). This explains the necessary similarity between the curves in Figs. 3 and 4.
Gender Contrasts in GHS Stimulation
The impact of iv GHS and GHRH pulses was simulated using C = 3,000 for GHS and C = 10,500 for GHRH imposed singly or together at different times in a 3.3-h GH cycle. Peripheral GHS, but not GHRH, was assumed to gain access to ArC. When the GHS stimulus was introduced during a spontaneous volley, GH release in the male construct exceeded that in the female (Table 2). Conversely, when the GHS pulse was delivered during an interpeak trough, responses were reduced in the male only. Given that the duration of a GH volley is shorter than that of a trough, randomly timed GHS pulses over 3.3 h evoked 38% more GH secretion in the female model. This distinction is due to higher time-integrated SRIFPeV outflow in the male (Fig. 1). Combined GHS and GHRH stimulation yielded a mean gender contrast of 24% (female > male). The outcomes are consistent with previous studies in which untimed GHS injections evoked greater GH secretion in either the male or the female (6), average responses to GHS were greater in the female than in the male rodent and human (1, 2, 10, 11, 55, 71), and GHS and GHRH were found to act in synergy (3, 10, 14, 37, 78).
There may be other explanations for the gender difference in GHS efficacy. For example, estradiol induces transcription of the GHS receptor gene in vitro (64), and pituitary expression of the GHS receptor is higher in the female rat than in the male rat (47). To examine the first issue, we simulated GHS efficacy at both hypothalamic and pituitary sites (parameters g1 and g2) in the female that were 1.77-, 3.16-, and 5.62-fold those in the male. The result was a higher mean amplitude of spontaneous GH pulses and a greater sex difference in GHS action (Table 3).
Female-Predominant Reduction in GH Concentrations After Partial Molecular Silencing of the GHS Receptor Expressed by Catecholaminergic Neurons in ArC
Shuto et al. (74) reported significant reduction in GH pulse amplitude in the adult female, but not in the male, transgenic mouse after partial molecular silencing of the ArC GHS receptor. To simulate attenuation of CNS GHS action, we imposed a graded (1.77-, 3.16-, and 5.62-fold) decrease in the system parameter g2 (efficacy of GHS feedforward on GHRH and antagonism of total SRIF in the ArC) and disallowed stochastic variability in ArC responsiveness for clarity (Fig. 5). According to these simulations, GHS drive is more important to maintaining GH secretion in the female feedback construct.
Parameter sensitivity analyses showed that graded 1.33-, 1.77-, 3.16-, and 5.62-fold increases in tg,2 (the ED50 or potency of GHS-induced drive of GHRH release) diminished GH peak height in the female, but not in the male, feedback construct (Table 4). Thus, in principle, either unequal GHS efficacy or unequal potency (ED50) could heighten the basic sex difference in GHS action in vivo.
Simulation of Continuous Peripheral Ghrelin Stimulation
Figure 6 depicts model-predicted GH secretory responses to 1.3-, 1.7-, 2.4-, and 3.1-fold elevation of continuous peripheral ghrelin drive in the male and female constructs [imposed by increasing the term GHRELIN (250 pg·ml−1) by these graded amounts in Eqs. B1 and B4]. Constant GHS infusion augmented the amplitude of GH pulses without disrupting their frequency or altering the sex difference in GH secretion. The effects of continuous peripheral infusion of synthetic GHS on pulsatile GH release in the human mirror the foregoing outcomes (11, 41, 45, 73).
Impact of Simulated Central Neural Administration of Ghrelin
One report inferred inhibition of GH secretion by ICV delivery of GHS in the male rat when injections were administered during a trough (87). In other studies, dose-dependent stimulation of GH secretion was quantitated over a large range of ICV GHS stimulus intensities (27, 87). To evaluate the implications of ICV ghrelin delivery, we assumed that central GHS acts on GHRH and SRIF neurons in ArC, but not on the pituitary gland. Therefore, the term ghr was added to Eq. B4, but not Eq. B1; the ICV stimulus parameter C in Eq. 6 was arbitrarily defined as 6,000 or 30,000; and GHS stimuli were applied during a peak or a trough in the male and at any time in the female. As shown in Fig. 7, the predicted effects of the first of consecutive ICV GHS injections on SRIFPeV, SRIFArC, GHRH, and GH were similar to those inferred for the first of two peripheral GHS injections. On the other hand, the second ICV GHS pulse was less effective, especially in the male construct. The reason for this finding is that ICV delivery of ghrelin cannot antagonize inhibition of GH release by SRIFPeV secreted in the male after the first GH pulse. Impaired responsiveness to the second of consecutive ICV GHS stimuli is observed experimentally in the adult male rat (78). Data are lacking in the female rat.
Analyses of Complementary and Alternative Model Connections
First, we tested the implications of stepwise muting of ghrelin's bipartite capabilities to stimulate GHRH secretion and antagonize total SRIF inhibition in the ArC. Simulations comprised two iv GHS stimuli of identical strength C = 30,000 (a maximally effective input) administered 2 h apart. The two central actions of GHS in the ArC were blunted by reducing the system parameter g2 3.1-, 10-, and 31.6-fold, which progressively decreased GHS-stimulated GH secretion, especially in the female (Fig. 8).
Second, we examined the notion that centrally injected ghrelin stimulates SRIFPeV neurons via internuncial connections between ArC to PeV as suggested recently by other investigators (8). The hypothesis was modeled by adding a term to represent GHS feedforward on SRIFPeV outflow as follows: to the right-hand side of Eq. B3 and the term ghr to Eqs. B3 and B4, but not to Eq. B1. Different efficacies of GHS are imposed by adjusting values of the factor f. The coefficient kr,g = 12 pg·ml−1·h−1 was chosen a priori to yield a minimal change in the GH response to ICV ghrelin if f = 1 (<1% difference between f = 0 and f = 1). Because the kinetics of ICV ghrelin are not known, we explored fixed, near-maximal GHS efficacy (f = 300) and each of nine nominal ICV ghrelin half-lives (1-, 1.33-, 1.77-, 2.37-, …, and 10-fold less than the reference plasma value) (Table 5). We postulated that reboundlike GH secretion would occur with rapid decay of ICV ghrelin, allowing withdrawal of putative GHS-stimulated SRIFPeV outflow. Rebound GH release was generated in the female at any time and in the male during a trough. These analyses suggest that GHS-induced rebound GH release would require a shorter half-life of ghrelin in the brain than it would in the circulation.
To appraise the impact of rapid feedforward by ICV GHS on SRIFPeV release, we fixed the half-life of ICV GHS at 10-fold less than that in plasma and simulated four strata of GHS drive [viz., 1-, 30-, 100-, and 300-fold increases in kr,g]. A GHS stimulus of strength C = 30,000 was imposed in the male GH peak (top), in the female (bottom), or in the male trough (middle) (Fig. 9). The outcomes were that greater ICV GHS efficacy in inducing prompt SRIFPeV secretion abbreviated the GHS-driven GH secretory burst (during the male volley and in the female at any time, top and bottom) and augmented rebound GH release (male trough and female, middle and bottom). When the GHS stimulus was applied in the male, 1) during a spontaneous GH peak, GH autofeedback-driven SRIFPeV release blocked the rebound phase (top); and 2) during a trough high intervolley, SRIFPeV outflow to the pituitary suppressed GHRH-stimulated GH secretion. Time-delayed relief of elevated SRIFPeV restraint enhanced GH rebound (middle).
Third, we assessed a hybrid hypothesis that systemic GHS suppresses SRIFPeV release to both the ArC and the pituitary gland without stimulating GHRH secretion. GHS-dependent suppression of SRIFPeV was increased 3.1-, 10-, and 31.6-fold by dividing SRIFPeV by (1 + ghr · f) and scaling f appropriately. GHS-stimulated GHRH release was eliminated by decreasing the system parameter g2 1,000-fold. Also, a maximally stimulatory GHS pulse of C = 30,000 was imposed by adding ghr to GHRELIN in Eqs. B1 and B4. This reconstruction forecast paradoxically greater efficacy of a GHS pulse imposed during a trough than during a volley in the male feedback model and small spontaneous GH peaks due to diminished outflow of SRIFPeV to the GHRH-SRIFArC oscillator in the male but not in the female (Fig. 10). These model-based data argue against a hypothesis of GHS-induced inhibition of SRIFPeV release to both the ArC and the pituitary.
Fourth, to test the postulate that iv ghrelin stimulates GH and GHRH release directly and antagonizes SRIFArC (but not SRIFPeV) inhibition in either the ArC or the pituitary gland, we simulated two identical, maximal (C = 30,000) systemic GHS stimuli 2 h apart. The term ghr was added only to GHRELIN in Eq. B1. Opposition to SRIFArC was mimicked by dividing SRIFArC in Eq. B4 by (1 + ghr · f), where adjusted f yields increasing values for (1 + ghr · f) of magnitude 3.1-, 10-, or 31.6-fold. The outcome of simulating the foregoing dual (rather than triple) CNS actions of GHS were marked GH secretion after the first GHS injection (during a volley in the male and at any time in the female) and blunted GH release after the second GHS stimulus during a trough (Fig. 11). In this postulated model structure, initial GHS-driven GH secretion stimulated SRIFPeV outflow, which suppressed GHS-induced GHRH and GH secretion, thus violating expected outcomes in the female.
In the present analyses, we have explored the dynamic implications of the putative linkages among GHS, GHRH, SRIF, and GH feedback using an ensemble-based model. We first formalized intuitive hypotheses of how ghrelin might regulate specific loci within a basic framework of time-delayed reciprocal signaling (30, 66). We thereby extended the construct (model B) to incorporate GHS-dependent stimulation of GH secretion by the pituitary gland directly (13, 51), GHS-dependent evocation of GHRH release from ArC as observed in the ram and ewe (31, 35), and GHS-dependent antagonism of pituitary and ArC actions of SRIF as reported in the rat and guinea pig and inferred indirectly in the dog and human (13, 25–27, 67, 71, 82). The resultant network of interactions reproduces expected patterns of spontaneous GH pulse renewal and explicates how a systemic or ICV GHS stimulus may augment the amplitude (without altering the frequency) of pulsatile GH secretion in a sex-related, GH feedback-sensitive, SRIF-modulated, and GHRH-dependent fashion (11, 13, 25–27, 31, 35, 41, 45, 67, 71, 73, 82, 83). In contrast, no single proposed action of GHS mimics the foregoing physiological features of regulated GH secretion (model A simulations).
Simulation studies supported the thesis that important loci of GHS action comprise the following: 1) antagonism of the combined actions of SRIFPeV and SRIFArC within ArC, thereby sustaining high-amplitude GH pulsatility under continuous GHS drive; 2) inhibition of SRIFPeV-imposed repression of the GHRH-SRIFArC oscillator, thus maintaining sex-related distinctions in GH secretory burst frequency; 3) enhancement of GHRH release acutely from ArC; and 4) direct stimulation of GH secretion from the pituitary gland. In this light, experimental data indicate that anatomic hypothalamopituitary disconnection attenuates GHS efficacy markedly in the rat, pig, and human (65, 78); GHRH antiserum or a GHRH receptor antagonist inhibits GHS-stimulated GH secretion by >80% (27, 63); truncational deletion of the GHRH-receptor gene reduces GHS efficacy profoundly in the human and mouse (32, 63, 68, 69); transgenic knockdown of GHS receptors on GHRH neurons reduces GH secretion in the adult female mouse but not the male (74); and GHS and GHRH stimulate GH secretion synergistically in vivo but only additively in vitro (3, 10, 14, 37, 78).
On the basis of these assumptions, the current model predicts that stimulation of GHRH release by GHS is required to evoke maximal GH output in both sexes, but especially in the female, and time-delayed, GH feedback-induced SRIFPeV outflow to both the ArC and the pituitary gland in the male could inhibit GH responses to the second of consecutive GHS pulses. A corollary prediction is that a single GHS stimulus will evoke less GHRH-GH outflow in the male during a spontaneous trough than during a pulse but comparable GHRH-GH release at any time in the female animal. These inferences coincide with in vivo observations (17, 36, 58, 78).
Third, the multipeptide model allowed indirect assessment of plausible mechanisms conferring sex differences in GHS action. For example, the sex difference in GH autofeedback could account fully for greater acute GHS stimulation in the female than in the male, on average, when GHS is administered intravenously at random times and female-predominant blunting of pulsatile GH secretion in the transgenic CNS ghrelin receptor-knockdown model. The first outcome is recognized in the rat and human and the second in the mouse (1, 11, 55, 74, 78). Nonetheless, available experimental data do not exclude additional feedback-independent mechanisms of heightened GHS action in the female compared with the male. For example, estrogen induces transcription of the human GHS receptor gene in vitro and stimulates synthesis of GH in the autotransplanted pituitary gland in vivo (16, 64).
A simplifying assumption was made that blood ghrelin provides a stable stimulus in both the CNS and the pituitary gland (80). Acylated ghrelin is transported from the blood into the CNS, where it exerts pleiotropic effects (4, 23, 84, 86). Ghrelin is synthesized not only in gastric oxyntic cells (44) but also in the anterior pituitary gland, hypothalamus, placenta, kidneys, and elsewhere (22, 51, 52). The sources of ghrelin that primarily drive pulsatile GH secretion are not known.
Previous laboratory and clinical investigations have suggested that GHS may attenuate SRIF-dependent inhibition of GHRH secretion from the ArC and GH release from the pituitary gland (13, 25–27, 60, 67, 71). The relative importance of these two neuroanatomic sites of action is not known (74). From a modeling perspective, definitive estimation will require precise knowledge of the dose-response properties and kinetics of ghrelin at these locations.
By way of qualification, the GHS-GHRH-SRIF-GH feedback model does not embody all possible loci of ghrelin action, but rather focuses on fundamental connections. The objective is to extend intuitive insights by incorporating time delays and nonlinear interface functions objectively in an interlinked system and thereby explore potential pathway adaptations with regard to sex, pubertal development, and aging (54, 55, 89). For example, CNS actions of GHS to promote GHRH release and oppose intra-ArC inhibition by SRIF were crucial to explicate two published paradoxes: the female-predominant response to neuronal GHS-receptor silencing in the mouse (74) and unequal reboundlike GH release in the male and female rat after ICV injection of ghrelin (8). In contrast, simulated inhibition of PeV SRIF outflow by GHS did not reproduce these contrasts.
A second limitation of the current effort is that the model is not completely validated, given that not all parameter values are definable on the basis of earlier experimental data. However, partial parameter sensitivity assessment (see appendix) indicated that particular numerical choices are not highly constraining to general model performance, thus indicating the pivotal importance of relevant connectivity per se. Peptide elimination rates may be viewed as relatively stable within species. Amplifying and damping parameters, such as Hill coefficients, remain to be determined at local interface sites, such as GHS-driven GHRH release or antagonism of SRIF in the ArC. Although precise delay times within the hypothalamus are not known, simulation of a range of kinetics suggested general boundaries for CNS vs. systemic GHS elimination. Last, although stochastic biological inputs operate in some complex physiological systems (50), we did not systematically explore such properties.
The burgeoning repertoire of CNS, pituitary, and systemic signals that are reported to direct pulsatile GH secretion underscores the need to extend integrative concepts that account for variable biological time delays and the nonlinearity of concentration-dependent effects (34, 61). The collective properties of neuroendocrine regulation make intuitive estimates of such dynamic control difficult. For objective estimates, minimal requirements include valid representation of structural connectivity among primary regulatory signals and more precise experimental estimates of in vivo effector kinetics and dose-response properties. The expectation is to thereby reexamine earlier experimental inferences, test the implications of proposed connections, and facilitate alternative interpretations of complex data. Ultimate objectives are to stimulate new mechanistic hypotheses and achieve accurate analytical reconstruction of unobserved interactions.
Partial Parameter Sensitivity Analysis
By testing a nominal range of individual parameter choices, one may estimate boundaries of stable operating properties. The outcomes of this approach are shown in Table 6 for the male rat output model. A valid male system has the minimal requirement of generating recurrent multiphasic volleys as verified over a finite parametric grid.
Although it is not computationally practicable to fully map a 31-dimensional hyperspace, individual parametric sensitivity analysis showed that the reference parameter set (Table 1) has some flexibility. This is consistent with expected physiological variability among individuals. The analysis has limitations when based on exploring each parameter range individually and on the use of a simple sensitivity criterion. Consequently, some parameters allow variation from zero to infinity and, therefore, do not affect the typical features of the male profile as long as all other parameters are fixed. In particular, parameters related to the control function F1(g1, tg,1, and ng,1) that governs the model response to pharmacological GHS are not relevant within the physiological operating range.
Impact of Increased Variability in the Sensitivity of GHRH Neurons to GHS (t4)
We tested the impact of elevated random variability in t4 by increasing the coefficient of variation of superimposed gaussian noise from 5% to 25% (methods). The increase does not disrupt the general characteristics of male or female GH profiles (Fig. 12).
This work was supported by National Institutes of Health Grants K25 HD-01474, R01 AG-14799, and R01 AG-19695 and National Center for Research Resources General Clinical Research Center Grant RR M01 00585.
We acknowledge excellent assistance provided by Kris Nunez and Kandace Bradford in preparing the manuscript.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
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