Estradiol (E2) drives growth hormone (GH) secretion via estrogen receptors (ER) located in the hypothalamus and pituitary gland. ERα is expressed in GH releasing hormone (GHRH) neurons and GH-secreting cells (somatotropes). Moreover, estrogen regulates receptors for somatostatin, GHR peptide (GHRP, ghrelin), and GH itself, while potentiating signaling by IGF-I. Given this complex network, one cannot a priori predict the selective roles of hypothalamic compared with pituitary ER pathways. To make such a distinction, we introduce an investigative model comprising 1) specific ERα blockade with a pure antiestrogen, fulvestrant, that does not penetrate the blood-brain barrier; 2) graded transdermal E2 administration, which doubles GH concentrations in postmenopausal women; 3) stimulation of fasting GH secretion by pairs of GHRH, GHRP-2 (a ghrelin analog), and l-arginine (to putatively limit somatostatin outflow); and 4) implementation of a flexible waveform deconvolution model to estimate the shape of secretory bursts independently of their size. The combined strategy unveiled that 1) E2 prolongs GH secretory bursts via fulvestrant-antagonizable mechanisms; 2) fulvestrant extends GHRH/GHRP-2-stimulated secretory bursts; 3) l-arginine/GHRP-2 stimulation lengthens GH secretory bursts whether or not E2 is present; 4) E2 limits the capability of l-arginine/GHRP-2 to expand GH secretory bursts, and fulvestrant does not inhibit this effect; and 5) E2 and/or fulvestrant do not alter the time evolution of l-arginine/GHRH-induced GH secretory bursts. The collective data indicate that peripheral ERα-dependent mechanisms determine the shape (waveform) of in vivo GH secretory bursts and that such mechanisms operate with secretagogue selectivity.
- growth hormone releasing hormone
growth hormone (GH) secretion is at least 90% pulsatile in the healthy human and strongly controlled by sex steroid hormones (17, 19). Individual GH secretory bursts are believed to reflect the concerted effects of somatotrope stimulation by GH-releasing hormone (GHRH), inhibition by somatostatin (SS), and amplification by the potent GHR peptide (GHRP) ghrelin (14, 45). Estrogen supplementation stimulates pulsatile GH secretion in postmenopausal women and girls with ovarian dysgenesis (32, 38). Putative mechanisms include the capability of estradiol (E2) to potentiate GHRH drive (reduce the half-maximally stimulatory dose), augment GHRP stimulation (increase apparent efficacy), and antagonize SS inhibition (increase the half-maximally inhibitory dose) (2, 5, 41, 43). The topographic sites at which estrogen exerts such effects are not known (45). However, E2 can upregulate pituitary SS-type 2 and hypothalamic GHRP receptors and downregulate pituitary SS-type 5 receptors (SSTR-5), hypothalamic GHRH peptide and central nervous system GH receptors (27, 45, 49). Accordingly, discerning whether estrogen amplifies GH secretion via actions on the hypothalamus compared with the pituitary gland remains difficult. Based upon preliminary evidence that E2 may prolong GH secretory bursts (13), we hypothesized that the estrogen effect is secretagogue selective and depends upon ERα pathways outside the brain.
To begin to address the question where E2 acts in vivo, we implemented a tripartite experimental paradigm comprising 1) escalating transdermal E2 delivery on a schedule known to double GH secretion in postmenopausal women (13); 2) concomitant administration of placebo or a selective ERα antagonist [fulvestrant (FUL)] that does not cross the blood-brain barrier (33, 46, 50); 3) maximally effective stimulation with combined secretagogues that drive GH secretion via GHRP and/or GHRH receptors (12, 42, 43). The rationale was based on three considerations. First, maximally effective paired peptidyl stimuli were used, given that E2 enhances the potency (submaximal stimulation) but not the efficacy (maximal effect) of secretagogues. Under maximal stimulation, any estrogenic effects on GH secretory-burst waveform cannot then be attributed to increased GH secretion per se. Second, the drug intervention was designed to block peripheral ERα pathways selectively with a pure antiestrogen that does not gain access to hypothalamic ER (33, 46, 50). The anterior pituitary gland lies outside the blood-brain barrier and hence is construed to be peripheral (17, 45). And, third, the analytical methodology entailed reconstructing the waveform of GH secretory bursts (time course of instantaneous GH release) from serial plasma GH concentrations by way of a mathematically verified and experimentally validated variable-waveform deconvolution model (8, 23).
A total of 43 healthy postmenopausal women enrolled in and completed all four infusion sessions. Peak GH concentrations but not deconvolution data were reported earlier in abstract form (11). Participants provided voluntary written informed consent approved by the Mayo Institutional Review Board. The protocol was approved by the U.S. Food and Drug Administration under an investigator-initiated new drug number. Exclusion criteria were recent transmeridian travel or night-shift work (within 7 days), significant weight change (>2 kg in 1 mo), body mass index of <19 or >29 kg/m2, acute or chronic illness organ-system, anemia, psychiatric treatment, substance abuse, and failure to provide written informed consent. Volunteers had no known or suspected cardiac, cerebral, peripheral arterial or venous thromboembolic disease, breast cancer, or untreated gallstones. No participant was receiving neuroactive medications. Inclusion criteria were an unremarkable medical history and physical examination and normal screening laboratory tests of hepatic, renal, endocrine, metabolic, and hematologic function.
The mean ± SE age was 63 ± 2.1 yr, and body mass index was 25 ± 0.9 kg/m2. Menopausal status was confirmed by screening concentrations of FSH >50 IU/l, LH >20 IU/l and E2 <30 pg/ml. Volunteers stopped any sex hormone replacement at least 6 wk prior to study.
The study was a parallel-cohort, repeated-measures, double-blind, prospectively randomized comparison of the effects of placebo (PL), E2, FUL, and FUL/E2 on the shape of GH secretory bursts induced by saline and three secretagogue pairs. As schematized in Fig. 1, PL or 250 mg FUL was injected intramuscularly once a week for 3 wk. Conventional cancer treatment entails single monthly injection of 250 mg FUL, which has antineoplastic effects for 4 wk (33). Transdermal PL or E2 was administered daily for 18 days beginning on the day of the third FUL injection. The incremental E2 schedule was 0.5 mg, 0.10 mg, and 0.15 mg each for 4 days, followed by 0.20 mg for 7 days to mimic the normal menstrual-cycle profile of rising E2 concentrations. This regimen doubles fasting GH concentrations in postmenopausal women (13). Infusion studies were performed during any 4 of the last 5 days of this 7-day window. Beginning on the last day of the study, oral micronized progesterone (100 mg nightly) was given for 12 days according to standards of good medical practice.
Secretagogue infusions and sampling paradigm.
Each subject underwent four randomly ordered, double-blind, separate-day infusion sessions. Volunteers received a standardized outpatient meal of 8 kcal/kg distributed as 20% protein, 50% carbohydrate, and 30% fat at 1800 the night before study and then remained fasting overnight and until the end of sampling. At 0700 the next morning, catheters were placed in contralateral forearm veins to allow blood withdrawal (1.5 ml) every 10 min for 6 h from 0800 to 1400. Concomitantly, saline 20 ml/h iv was infused from 0800 to 1000 before the following secretagogues: 1) saline continuously from 1000 to 1400; 2) combined GHRH and GHRP-2 continuously from 1000 to 1400, both at the rate of 1.0 μg·kg−1·h−1; 3) l-arginine 30 g continuously from 1000 to 1030 followed by a bolus of GHRH (1 μg/kg) at 1030; and 4) l-arginine (above) followed by bolus GHRP-2 (3 μg/kg). The foregoing peptide doses reflect maximal stimulation in older women (2, 43).
Plasma GH concentrations were measured in duplicate by automated ultrasensitive double-monoclonal immunoenzymatic, magnetic particle capture chemiluminescence assay using 22-kDa recombinant human GH as assay standard (Pasteur Access; Sanofi Diagnostics, Chaska, MN). All samples (n = 148) from any given subject were analyzed together. Sensitivity was 0.010 μg/l (defined as 3 SD above the zero-dose tube). No serum GH values fell below 0.020 μg/l. Interassay coefficients of variation were 7.9 and 6.3%, respectively, at GH concentrations of 3.4 and 12.1 μg/l. Intra-assay coefficients of variation were 4.9% at 1.12 μg/l and 4.5% at 20 μg/l. Cross-reactivity with GHBP or 20-kDa GH is <5% (13). Serum E2, testosterone, LH, and FSH concentrations were quantified by chemiluminescence assays and IGF-I and sex hormone-binding globulin concentrations by immunoradiomedic assays, as previously described (12, 13).
Earlier deconvolution methods in some cases yield nonunique estimates of basal and pulsatile hormone secretion and elimination rates (44). To address this technical impasse, basal and pulsatile GH secretion were estimated simultaneously by using a new maximum likelihood deconvolution methodology (discussed fully in Refs. 23 and 25). The methodology has been validated directly by analyses in the sheep and horse (22, 24). The basic assumptions are that 1) peaks in concentrations reflect the mass of hormone released in delimited secretory bursts; 2) the burst waveform (time course of instantaneous release rates) may be defined by a three-parameter generalized gamma probability density; 3) combined diffusion, advection, and irreversible elimination may be represented via biexponential kinetics; and 4) parameter estimation is statistically conditioned on a priori estimates of pulse onset times obtained by an incremental smoothing algorithm and then selected recursively on probabilistic grounds (see Ref. 8 and appendix).
A modification of the general model was implemented wherein the principal analytical outcomes are cohort-defined estimates of basal and pulsatile GH secretion during saline infusion (μg·l−1·h−1); the summed mass of GH secreted in bursts after stimulation with secretagogues (μg·l−1·h−1); and the reconstructed shape of GH secretory bursts, defined by the modal time in minutes to attain maximal secretion. Interpulse-interval times were modeled as a two-parameter Weibull probability density. Unlike the one-parameter Poisson distribution that defines interpulse variability with a coefficient of variation of 100% (SD/mean × 100%), the Weibull renewal process includes an additional term (gamma) that allows for less variability than 100% for gamma >1.0 independently of the probabilistic mean frequency (lambda).
Generalized likelihood ratio tests were utilized to compare the Weibull distributions for the interpulse interval times under saline (baseline). One-way ANOVA for untransformed and log-transformed GH responses, as well as two-way ANCOVA of log-transformed GH responses were performed, followed by the post hoc Tukey honestly significant difference test to contrast multiple means. Non-Gaussian data (GH responses) were logarithmically transformed. Waveform parameters were compared at 99% confidence intervals to obviate type I errors. Data are presented as the mode, means ± SE, or 99% statistical confidence intervals.
Randomization resulted in the assignment of 10 women to PL/PL, 10 to PL/E2, 12 to FUL/PL, and 11 to FUL/E2 regimens. There were no dropouts after randomization.
The four interventional groups did not differ with respect to baseline fasting serum hormone concentrations. Thus, aggregate baseline data (n = 43) are given in Table 1. Following the interventions, serum E2 concentrations were comparably elevated in the PL/E2 and FUL/E2 cohorts (respectively, 152 ± 15 and 136 ± 16 pg/ml, P > 0.10), and remained low in the PL/PL and FUL/PL cohorts (10.6 ± 1.6 and 10.4 ± 1.1 pg/ml), indicating that the anti-E2 did not alter transdermal E2 delivery. Two-way ANCOVA of integrated GH concentrations identified significant effects of drug intervention (P = 0.025), secretagogue type (P < 0.001), and the saline covariate (P < 0.001) with a nonsignificant interaction (P = 0.12). Considering all four cohorts together, the paired l-arginine/GHRP-2 stimulus was the most effective (P < 0.01 vs. the other 2 active stimuli), and each secretagogue pair augmented GH levels compared with saline (P < 0.001). Based upon ANOVA of unstimulated fasting GH concentrations (averaged over all four 90-min intervals prior to secretagogue infusions in each of the 43 subjects), the effect of FUL/E2 was 2.6-fold greater than that of PL/PL (P < 0.01), whereas the effect of PL/E2 was intermediate (1.8-fold PL/PL). In contrast, the FUL/PL (0.28 ± 0.073 μg/l) and PL/PL (0.29 ± 0.073 μg/l) cohorts had comparable GH concentrations.
Deconvolution-based estimation of pulsatile GH secretion employed all 6 h of sampling in each subject (6,192 samples). The response to secretagogues was then segmented over the first 90 min of each stimulatory infusion during which time >95% of the secretory response occurs (17, 45). Figure 2 summarizes baseline unstimulated (saline) and dual secretagogue-stimulated pulsatile GH secretion in the four cohorts. E2/FUL in the saline state elevated GH secretion over PL/FUL and PL/PL (both P < 0.025), whereas E2/PL had a nonsignificant intermediate effect. In addition, PL/FUL elevated pulsatile GH secretion over E2/PL when GHRH/GHRP-2 was infused (after Bonferroni correction, P < 0.05). E2 alone did not augment GH responses to any of the three secretagogue pairs, as reported earlier and implicit in the experimental design (introduction).
Analytical reconstruction of the underlying shape of GH secretory bursts yields the mode of the waveform, defined by the time delay from the mathematically demarcated onset to the maximum of the secretory burst. From a statistical vantage, the waveform is estimated independently of the amount of hormone released (23). Figure 3 presents the set of 16 waveforms estimated from a total of 132 h of 10-min blood sampling in 43 women. The rate of GH release increases rapidly over the first 12 to 20 min, reaches a maximum (the mode), and then declines gradually over the next 50–90 min. The precise waveform (shape) of secretory bursts varied among the different sex-steroid milieus and in response to the distinct secretagogues. Significant differences were quantified from the mode and its SE.
As depicted in Fig. 4A, in the unstimulated (saline infusion) state, exposure to PL/E2 extended the modal time delay to peak GH secretion by 1.49-fold (21.9 vs. 14.7 min P < 0.005). FUL/PL increased the mode by 1.36-fold compared with PL/PL (20.0 vs. 14.7 min P < 0.01), resulting in a value not different from that in E2/PL cohort (21.9 min). Administration of FUL/E2 yielded a GH secretory-burst mode comparable to that of PL/PL and PL/FUL, but P = 0.018 shorter than that of E2/PL. Thus, in the saline condition, PL/E2 and FUL/PL each prolong, whereas combined FUL/E2 does not affect, the waveform of GH release compared with PL/PL.
GHRH/GHRP-2 stimulation in the PL/PL setting had no effect on GH secretory-burst shape compared with saline infusion (Fig. 4B). In relation to GHRH/GHRP-2 stimulation, PL/FUL exposure increased the mode compared with that estimated for PL/PL (P = 0.01) and E2/PL (P < 0.01). Modes in the groups receiving PL/FUL and E2/FUL did not differ, but the mode associated with E2/FUL exceeded that of E2/PL (P < 0.01). Within the cohort of women treated with E2/FUL, stimulation with GHRH/GHRP-2 (Fig. 4B) compared with saline (Fig. 4A) increased the mode to 21.6 min from 17.6 min (P < 0.01).
Infusion of l-arginine/GHRH did not alter the GH waveform compared with saline in the PL/PL context. In addition, the effect of l-arginine/GHRH did not differ among the four drug interventions (PL/PL, E2/PL, PL/FUL, or E2/FUL) (Fig. 4C).
Administration of l-arginine/GHRP-2 in the PL/PL group, but not in any of the other three treatment groups, prolonged the latency to maximal GH secretion (20 min) compared with that after saline infusion (14.7 min, P < 0.01) (Fig. 4D). In the case of l-arginine/GHRP-2 stimulation, E2/PL and E2/FUL both significantly reduced the mode compared with PL/PL (P < 0.01 and P < 0.001, respectively), whereas PL/FUL had no effect. In addition, the mode in women receiving E2/PL was shorter after the infusion of l-arginine/GHRP-2 (15.1 min) than saline (21.9 min). These data establish strong interactions among secretagogue types and estrogenic milieus.
Figure 5 shows that GH pulse frequency (lambda of the Weibull renewal process) was weakly influenced by the E2 and anti-E2 milieu, such that pulse number was highest (interpulse-interval was lowest) in the PL/PL cohort (extrapolated value 38 pulses/24 h) compared with the mean of the other three cohorts considered together (30 ± 1.9 pulses/24 h, P < 0.005). In contrast, gamma (a measure of interpulse-interval variability) was not significantly affected by drug intervention (median, gamma = 2.4; range, 2.2–2.5). Values of gamma >1.0 signify greater regularity of the pulsing mechanism than that due to a one-parameter Poisson process (26).
Salient outcomes of the present investigations were that, first, E2 administration in ovariprival women prolongs (saline infusion), does not alter (GHRH/GHRP-2 and l-arginine/GHRH stimulation), or abbreviates (l-arginine/GHRP-2) the time delay to achieve maximal GH release. These actions occur without any change in the amount (mass) of GH released per burst, thus demonstrating estrogenic control of the pituitary secretory process per se. Second, in the absence of E2 supplementation or antiestrogen exposure, only l-arginine/GHRP-2 extended GH secretory-burst duration, consistent with secretagogue specificity. Third, administration of the peripheral [non-central nervous system (non-CNS) permeant] antiestrogen FUL increased the secretory-burst response latency by 1.36-fold during saline infusion and by 1.38-fold during paired GHRH/GHRP-2 infusion. These results suggest that low endogenous estrogen concentrations in postmenopausal women exert significant pituitary effects, which can be opposed by a peripherally acting pure antiestrogen. Finally, combined E2/FUL exposure 1) overcame the burst-prolonging effect of E2/PL after saline injection (P = 0.012), implying that pituitary ERα mediates this action of E2; 2) did not reverse the burst-prolonging effect of PL/FUL in women stimulated with GHRH/GHRP-2, suggesting no major role for peripheral ERα in this effect; and 3) potentiated the burst-abbreviating effect of PL/FUL when the secretagogue pair was l-arginine/GHRP-2. The aggregate outcomes indicate that selective secretagogue pairs and specific estrogenic milieus together govern the GH secretory process, and suggest further that such interactions are mediated via peripheral ERα-dependent as well as -independent mechanisms.
The principal FUL-antagonizable effect of E2 was the latter's prolongation of unstimulated GH secretory bursts. E2 was shown earlier to profoundly slow the exocytosis of catecholamines from bovine chromaffin cells (31). Given the peripheral ERα selectivity of FUL (see introduction), a straightforward interpretation would be that peripheral ERα-dependent mechanisms mediate the burst-prolonging effect of E2. A plausible mechanism is known estrogenic repression of pituitary SSTR-5 gene expression, since SSTR-5 transduces inhibition of GH release (27, 49). Figure 6 illustrates this proposition. An unexplored theoretical possibility would be that ERα activation antagonizes an unrecognized inhibitory (burst-abbreviating) effect of ERβ. This consideration arises because ERβ is upregulated by depletion of ERα in some systems, and exerts countervailing transcriptional effects on certain gene promotors (21, 34, 35). The notion is consistent with the fact that both ERα and ERβ are expressed in the human pituitary gland (6, 39).
The primary effect of FUL administered alone was to prolong GH secretory bursts in women infused with saline or GHRH/GHRP-2. Since FUL has no known intrinsic estrogenicity (16, 33), we postulate that low concentrations of endogenous estrogens in postmenopausal women normally abbreviate GH secretory bursts. Given that FUL does not enter the CNS (46, 50), the ERα antagonist could not directly reduce hypothalamic SS secretion, which otherwise restrains GH secretion. However, exogenous E2 can upregulate IGF-I signaling and induce pituitary SSTR-2, both of which serve to quench GH release (7, 27, 45) (Fig. 6). If endogenous E2 concentrations acted analogously to maintain IGF-I receptor signaling and SSTR-2 expression, then FUL/PL by antagonizing these effects would predictively prolong GH secretory bursts compared with the PL/PL state. The first postulate fits with the capability of FUL to reduce the expression of IGF-I receptors and block IGF-I actions in other tissues (7, 20, 37). The second postulate conforms with the fact that the FUL effect was exerted on GH secretion stimulated by GHRH/GHRP-2, but not l-arginine/GHRH or l-arginine/GHRP-2. The reason is that l-arginine inhibits GH-induced SS outflow (1, 36), which would inferentially mask any upregulation of SSTR-2.
The rapid initial phase of burst-like GH secretion is mediated via secretagogue-activated exocytosis of membrane-associated secretory granules (10). GHRH and GHRP induce, whereas SS selectively inhibits, GH exocytosis (40). Thus, prolongation of the time delay to maximal GH release by E2 in the saline condition could signify more extended endogenous secretagogue secretion or action, diminished SSergic restraint, or altered mechanics of exocytosis. When maximal secretagogue drive is imposed exogenously via GHRH/GHRP-2 infusion, the explanation for FUL/PL-induced prolongation of GH release would be limited to disinhibition of SSergic restraint or extension of the exocytosis process. Decreased SSergic restraint during FUL administration would be in accord with the fact that E2 induces the SSTR-2 promoter in the pituitary gland, as well as in the breast (27, 48). The observation that E2 supplementation did not significantly reverse the FUL effect during combined GHRH/GHRP-2 stimulation may mean that peripheral ERα is markedly depleted by FUL, since this antiestrogen blocks ERα gene transcription and forces ERα protein degradation (30). However, given that E2 was able to reverse (saline) and to potentiate (l-arginine/GHRP-2) other effects of FUL, a more likely postulate is that maximal stimulation by GHRH/GHRP-2 can activate pathways distinct from those governed by either peptide alone or by lower concentrations of endogenous GHRH and ghrelin. In addition, E2 stimulates SSTR-2 but represses SSTR-5 expression in the rat (27), which could allow for opposing effects on GH release depending upon the in vivo dose-response characteristics E2. By way of precedence, low concentrations of E2 stimulate, whereas 100-fold higher concentrations suppress or do not affect GH synthesis in vitro (9).
None of the estrogenic milieus modified the shape of GH secretory bursts induced by l-arginine/GHRH. A consideration is that l-arginine, by repressing GH feedback-induced SS outflow to the pituitary gland (1, 36), limits detection of any effects of E2 and/or FUL on pituitary SS receptors. However, E2 abbreviated GH secretory bursts induced by l-arginine/GHRP-2. GHRPs are unique in their multifaceted capabilities to stimulate somatotropes directly in vitro, synergize with GHRH in vivo, release GHRH from the arcuate nucleus, and oppose certain hypothalamic actions of SS (4, 14, 18, 28, 45, 47). Estrogens can enhance GHRP action and upregulate transcription of the GHRP/ghrelin receptor (2, 3, 29). Whether such actions of E2 account for acceleration of l-arginine/GHRP-2-stimulated GH release is not known.
Qualifications include, first, the relatively imprecise determination of the GH secretory-burst mode in one of the 16 interventions. E2/PL associated with GHRH/GHRP-2 infusion. The CV (expressed as the percentage ratio of the mean ± SE to the mode) was 18% in this case compared with a median value of 4.6% (absolute range, 2.8 to 8.9%) in the other 15 interventions. Second, although the present study entailed 172 study sessions of 6 h in 43 women (and 6,364 measurements of GH concentrations), larger cohorts would be required to establish generality of inference. Third, in the absence of secretagogue infusions, FUL may potentiate the effect of E2 on the amount of GH secreted by antagonizing direct pituitary inhibition by higher concentrations of E2, as inferred in vitro in the rat (9). And, third, the present data introduce the need to assess the effects of chronic sex-steroid exposure and other secretagogues on the GH secretion process.
In conclusion, selective antagonism of peripheral (non-CNS) ERα pathways identifies three categories of E2-dependent regulation of GH secretion: 1) FUL-antagonizable effects of E2 inferably transduced via peripheral ERα pathways; 2) FUL-independent actions of E2 putatively mediated via ERβ or CNS sites; and 3) FUL-potentiated effects of E2, which may involve disinhibition of peripheral ERα-mediated pathways. Implications of this work are that both the topographic location of ER expression (pituitary or brain) and the subtype of ER expressed (α or β) determine the actions of E2 on GH secretion. Accordingly, the development of ER subtype-selective agonists and antagonists that penetrate or do not penetrate the blood-brain barrier could provide a novel means to selectively augment GH secretion in hyposomatotropic individuals and repress GH secretion in patients with excessive GH secretion.
APPENDIX: VARIABLE WAVEFORM DECONVOLUTION ANALYSIS
From a technical perspective, there are four interventional assignments involving four cohorts of postmenopausal women. The following model applies to each of the four cohorts. Each subject, j = 1, 2, …, was sampled every 10 min for 6 h under each of the four conditions. The four secretagogue types are here denoted as k = 1, 2, 3, 4. At a given time (t) the GH secretion rate (unobserved) and GH concentration (measured) in subject j for condition k are designated by Zj(k) (t) and Xj(k) (t), respectively. The group basal (nonpulsatile) GH secretion rate is given by γ, with a random effect (Rj(k)) allowing for variation for each subject and intervention day: γ + Rj(k). Burst-like hormone secretion, before and following secretagogue injection at time T*, is described by two terms: 1) the waveform or instantaneous (unit-area normalized) rate of secretion over time, ψ(·) and 2) the mass (M) of GH released per unit distribution volume in the burst (μg/l) (25). The secretagogue was administered at time T* = 2 h. A preinjection (baseline) waveform is defined [ψ(0)], as well as waveforms for the postinjection k= 1, 2, 3, 4 responses. These waveform functions (burst shapes) are defined by the generalized gamma probability density (1)
The three beta parameters of the gamma distribution permit variable asymmetry or Gaussian-like symmetry of the secretory-burst shape.
The present analytical formulation is distinctive by way of reconstructing 1) a common baseline (unstimulated) gamma function for each cohort of volunteers, as well as for each of the four stimuli, k; and 2) a cohort-specific mean amount of GH secreted at baseline, M(0), as well as after each secretagogue infusion, M(k). For subject j, the m[= m(j,k)] pulse times for intervention k are denoted as Tj,l(k), l = 1,…, m(j,k). The mass secreted by subject j at pulse time Tj,l(k) is then M(0) plus a random variation, Aj,l(0), if the pulse is prestimulus, or M(k) plus a random variation, Aj,l(k), k = 1, 2, 3, 4, if it is poststimulus. The pulse times for each profile were determined by a recently published pulse detection method. First, trends are removed and the data series is normalized to [0,1], so that the algorithmic parameters do not depend upon scale (23). Second, the method utilizes a nonlinear diffusion equation, in which the diffusion coefficient is inversely related to the rate of increase. Thus, putative pulse times are identified as points of rapid increase that are not easily smoothed away. The algorithm is run to obtain sets of decreasing numbers of candidate pulse times.
All parameters are estimated simultaneously for each candidate set of pulse times. The total (basal and pulsatile) GH secretion rate (μg·l−1·min−1) in subject j under condition k (k = 1, 2, 3, 4) is (2) and the GH concentration is (3) [“basal” + “prestimulus pulsatile” + “poststimulus pulsatile” components], where a is the proportion of rapid-to-total elimination, α1 and α2 are rate constants of rapid and slow elimination, and X(0) is the starting hormone concentration (25). Here, α1 is fixed at 3.5 min and α2 at 20.8 min as reported for endogenous GH (15).
The model is represented fully by the set of parameters defined by θ = [θ(k), k = 0, 1, 2, 3, 4], where θ(0) = (γ, β1(0), β2(0), β3(0), M(0), σR(0), σA(0)), and (4) Measured GH concentrations, Yj,l(k) are considered a discrete time sampling of the foregoing continuous processes, as distorted by observational error, εi We assume that the random effects for basal (Rj(k)), pulse masses (Aj,l(k)), and the observational errors εj,i(k) are independent, identically distributed, Gaussian random variables with mean zero and SDs, σR(0), σA(0), σA(k), σε(k), k = 1, 2, 3, 4.
Because the preinjection parameters, θ(0), describe the preinjection secretion for each subject under each of the four interventions, all of the parameters must be estimated simultaneously using all of the data. Utilizing the above models and assumptions, a Gaussian likelihood can be written (23). Let l denote the log likelihood.
The discretized secretion rate, Zj,i(k) = Zj(k) (ti), i = 1,…, n, is estimated by the conditional expectation evaluated at the maximum likelihood estimate, θ̂ (5)
The reconstruction of the unobserved secretion rates involves statistical estimation of each subject's random effects contributing to GH secretory-burst mass (e.g., subject j, intervention k) as well as the random effect for basal
Variances and covariances estimates of maximum likelihood estimation parameter estimates, θ̂, are obtained explicitly from the inverse of the estimated information matrix evaluated at the maximum likelihood estimate, θ̂. Thereby, statistical confidence intervals are calculated directly for basal secretion γ and waveform parameters, β̂1(k), β̂2(k), and β̂3(k), k = 0, 1, 2, 3, 4. The statistical mode (most commonly represented value) of the time delay to attain the maximal GH secretion rate within a burst is given as: (for k = 0, 1, 2, 3, 4) h(β̂1(k), β̂2(k), β̂3(k))=β̂2(k)(β̂1(k)−(1/β̂3(k)))(1/β̂3(k)). Variance of this value is computed by the multivariate delta method as: σ̂ij evaluated at (β̂1(k), β̂2(k), β̂3(k)), where σ̂ij is the (i,j)element of ∑̂.
This study was supported, in part, via the General Clinical Research Center Grant MO1-RR-00585 (to the Mayo Clinic), Foundation from the National Center for Research Resources (Rockville, MD), and National Institutes of Health Grants R01-AG-019695, AG-29362-01, and R21-DK-072095.
We thank Kay Nevinger for supporting manuscript preparation; Ashley Bryant for data analysis and graphics; Dr. Mihaela Cosma and Joy Bailey for assisting in patient screening; the Mayo Immunochemical Laboratory for assay assistance; and the Mayo research nursing staff for implementing the protocol.
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.
- Copyright © 2007 the American Physiological Society