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Endocrinology Vol. 147, No. 6 2817-2828
Copyright © 2006 by The Endocrine Society

An Ensemble Model of the Male Gonadal Axis: Illustrative Application in Aging Men

Daniel M. Keenan, Paul Y. Takahashi, Peter Y. Liu, Pamela D. Roebuck, Ajay X. Nehra, Ali Iranmanesh and Johannes D. Veldhuis

Endocrine Research Unit (P.Y.L., P.D.R., J.D.V.), Primary Care Internal Medicine, Department of Internal Medicine (P.Y.T.), and Department of Urology (A.X.N.), Mayo School of Graduate Medical Education, General Clinical Research Center, Mayo Clinic, Rochester, Minnesota 55905; Endocrine Service, Medical Section, Salem Veterans Affairs Medical Center (A.I.), Salem, Virginia 24153; and Department of Statistics, University of Virginia (D.M.K.), Charlottesville, Virginia 22903

Address all correspondence and requests for reprints to: Dr. Johannes D. Veldhuis, Endocrine Research Unit, Mayo School of Graduate Medical Education, General Clinical Research Center, Mayo Clinic, Rochester, Minnesota 55905. E-mail: veldhuis.johannes{at}mayo.edu.


   Abstract
Top
 Abstract
Introduction
 Subjects and Methods
 Results
 Discussion
 References
 
Testosterone (Te) production declines in the aging male, albeit for unknown reasons. Plausible mechanisms include reduced secretion of GnRH, less feedforward by LH, and/or altered feedback by systemic Te. The present study tests all three postulates in a cohort of 10 young (20–35 yr old) and eight older (50–72 yr old) men. The experimental paradigm comprised graded blockade of the GnRH receptor to create four distinct strata of LH and Te pulsatility in each subject. A novel analytical formalism was developed to reconstruct implicit dose-response functions linking 1) virtual GnRH outflow positively to LH secretion, 2) LH pulses positively to Te secretion, and 3) Te concentrations negatively to the size and number of LH secretory bursts. Validation was by direct pituitary sampling in the horse and sheep. Statistical comparisons disclosed that age decreased the efficacy of each of 1) virtual GnRH outflow (P < 0.01), 2) LH drive of Te secretion (P < 0.01), and 3) total, bioavailable and free Te feedback on GnRH-driven LH secretion (P = 0.015). In contrast, age increased the potency of virtual GnRH feedforward (P = 0.013) and did not affect Te’s inhibition of LH pulse frequency. Unexplained variance was less than 10%. Robustness was shown by resampling techniques. Accordingly, competitive silencing of one locus of control and ensemble-based analyses identified triple regulatory deficits in the aging male gonadal axis. The generality of the present integrative model suggests utility in parsing interlinked adaptations in other physiological networks.


   Introduction
Top
 Abstract
 Introduction
Subjects and Methods
 Results
 Discussion
 References
 
AGING IS MARKED by increased physical frailty and concomitant depletion of anabolic hormones, such as testosterone (Te) (1, 2). The fundamental cause of impaired gonadal Te production in this setting remains unknown, but may be multifactorial (3). Experiments in the aged male rat provide evidence of decreased hypothalamic GnRH release, preserved GnRH action, and reduced Leydig cell Te synthesis (4, 5, 6, 7, 8, 9, 10). What remains unclear is whether aging alters negative feedback by endogenous Te and whether more than one putative deficit mediates hypogonadism in the same animal.

Indirect clinical observations have raised considerations that aging may diminish GnRH outflow and/or blunt LH-stimulated Te secretion (11). For example, elderly men exhibit enhanced gonadotrope responsitivity to exogenous GnRH pulses (12, 13, 14), but secrete less LH per burst than young individuals (12, 15, 16, 17, 18). In addition, older subjects do not achieve maximal elevations in total Te concentrations after stimulation with supraphysiological amounts of human gonadotropin chorionic gonadotropin (hCG) or LH (19, 20, 21). Assessments of negative feedback imposed by exogenous androgens have inferred both increased and decreased inhibition in aging individuals (22, 23, 24).

There are several significant experimental limitations in interpreting available data. First, no studies have assessed the release and actions of GnRH, LH, and Te concurrently in the same individual. Second, no investigations have evaluated physiological, rather than pharmacological, signal exchange within the intact male gonadal axis. Third, no simultaneous measurements exist of pulsatile GnRH release into hypothalamo-pituitary portal vessels, LH secretion into petrosal-sinus blood, and Te output into testicular veins in young and aged animals (3). Fourth, diminutive endogenous LH pulse increments in older subjects may be inadequate to maintain testicular steroidogenic gene expression, thereby secondarily impairing gonadal responses to an acute lutropic stimulus (21, 25). Fifth, high doses of hCG or LH down-regulate Leydig cell steroidogenesis both in vitro and in vivo, thus making physiological inference difficult (19, 26, 27, 28). Sixth, age-related disruption of any one control site within the GnRH-LH-Te ensemble would perforce modify the output of other connected sites (15, 16). And, seventh, no data are available to indicate whether Te’s negative feedback on GnRH and LH is exerted via total, bioavailable, or free Te concentrations. Therefore, available data are inadequate to either affirm or refute a hypothesis of multiple regulatory deficits.

The present experiments were designed to test the hypothesis that aging alters hypothalamic GnRH outflow, LH-driven Te secretion, and Te-enforced negative feedback in healthy men. Specific a priori predictions were that older individuals would exhibit 1) attenuation of pulsatile hypothalamic GnRH outflow, 2) a reduction in the efficacy or potency of endogenous LH pulses in stimulating Te secretion, and 3) decreased efficacy of Te feedback in suppressing GnRH/LH. We did not know which Te moieties would be aptly modeled as effective in vivo feedback signals. An ensemble model of interactions among GnRH, LH, and Te was developed, validated, and implemented to estimate multipathway adaptations in vivo.


   Subjects and Methods
Top
 Abstract
 Introduction
 Subjects and Methods
Results
 Discussion
 References
 
Study subjects
A total of 18 men, stratified into 20–35 yr (n = 10) and 50–72 yr (n = 8) age groups, were enrolled after providing voluntary written informed consent, as approved by the Mayo Clinic institutional review board. Weight averaged 80 ± 2.9 and 86 ± 4.3 kg, and height averaged 1.76 ± 0.02 and 1.80 ± 0.02 m in young and older men, respectively. Body mass index values were 26 ± 0.83 (young) and 27 ± 1.6 (older) kg/m2 [not significant (NS)]. Participants were healthy, nonsmoking, community-dwelling men, who had not undertaken transmeridian travel within 10 d or consumed alcohol, caffeine, or prescribed medications for 5 half-lives before each study session. Detailed medical inventory excluded a history of infertility, systemic disease, recent weight change (>2-kg change in the preceding 6 wk), hormonal therapy, or psychoactive drug use. Medical history (including libido and erectile function, defined by subject self-report as normal, unchanged, and not of any concern), physical examination (including testis size, defined by long axis >3.5 cm), and fasting morning (0800 h) biochemical tests of renal, hepatic, hematological, and metabolic function (plasma glucose, electrolytes, and thyroid function) were normal for age. Subjects were compensated for time spent in the study according to internal review board-defined guidelines.

Investigational protocol
Eligible volunteers were admitted to the General Clinical Research Center for four separate, randomly ordered, overnight, inpatient studies scheduled at least 10 d apart. Blood samples (1.0 ml) were withdrawn every 10 min beginning at 1800 h for 18 h through a forearm iv catheter. Samples were allowed to clot at room temperature, and sera were frozen at –20 C for later assay of LH, Te, ganirelix (GRX), SHBG, and albumin concentrations.

To establish four graded strata of LH and Te concentrations in each subject, volunteers were given injections of GRX acetate in doses of zero (saline), 0.1, 0.3, or 1.0 mg/m2 sc in double-blind, randomly assigned order at 2000 h (2 h after the beginning of blood sampling). GRX is a potent, selective antagonist of GnRH action that binds competitively to the cognate receptor. The plasma half-life of GRX is 15 ± 2 h. GRX exerts a prolonged (20–28 h) inhibitory effect on both LH and Te secretion in men after a single sc injection, with uniform suppression during the time window 10–26 h.

Assays
Serum LH concentrations were measured in each 10-min sample in duplicate by automated chemiluminescence assay (ACS 180, Bayer, Norwood, MA), using the First International Reference Preparation as the standard. Intraassay coefficients of variation (CVs) were 4.7%, 3.5%, and 3.8%, and interassay CVs were 8%, 3.7%, and 4.7% at LH concentrations of 4.4, 18, and 39 IU/liter, respectively. Procedural sensitivity was 0.2 IU/liter. All samples were measurable (3 or more SD above LH-deficient serum). Total Te concentrations were assayed by the same technique in serum collected at the beginning of blood sampling (1800 h). Intra- and interassay CVs were 6.8% and 8.3%, and assay sensitivity was 8 ng/dl (17). Equilibrium dialysis free Te, SHBG, and albumin concentrations were assayed as described previously (12).

Serum GRX concentrations were measured in duplicate by RIA using polyclonal rabbit antisera (Anaspec, Inc., San Jose, CA), as initially described by others (29). The antiserum does not cross-react detectably with native GnRH at concentrations ranging from 30–1000 ng/ml. GRX was radioiodinated via the chloramine-T reaction. Incubations were conducted with 50 µl serum, 5000 dpm radiolabeled GRX, and an antibody dilution of 1:3000 in RIA buffer [0.1 M phosphate buffer (pH 7.4), 0.8% NaCl, 0.5% BSA, 0.01% thimerosal, 0.01% Triton X-100, and 0.1 mM EDTA]. Bound and free ligands were separated by precipitation with goat antirabbit antiserum. Mean intraassay CVs were 8.9%, 5.7%, and 18.7%, and interassay CVs were 8.2%, 4.0%, and 9.2% at 0.5, 1.0, and 10 ng/ml, respectively. Assay sensitivity was 0.05 ng/ml. GRX concentrations were determined in a 2-h serum pool collected during the sampling interval 15 and 16 h after GRX injection.

Analytical methodology
The goal was to address three experimental questions in older compared with young men. Does hypothalamic GnRH outflow (secretion and action) wane? Do the efficacy and potency of endogenous LH pulses decline? Does negative feedback by total, bioavailable, or free Te concentrations increase? To answer these queries, the following quantitative issues were addressed: 1) accurate a priori estimation of LH pulse times; 2) simultaneous calculation of the rates of secretion and elimination of LH using the pulse times; 3) reconstruction of the dose-response properties (efficacy, potency, and sensitivity) associated with LH’s drive of Te secretion; 4) computation of time-varying total, bioavailable, and free Te concentrations from observed total testosterone, SHBG, and albumin concentrations; 5) formulation of the virtual GnRH feedforward and Te negative feedback signals that jointly produce the LH secretion profile; and 6) reconstruction of Te’s negative feedback on GnRH secretory burst size and number. The following methods were developed to fulfill these requirements (model equations are provided as supplemental data published on The Endocrine Society’s Journals Online web site at http://endo.endojournals.org).

Model of LH feedforward drive of Te secretion.
To reconstruct how pulsatile LH concentrations drive Te secretion, the implicit in vivo LH-Te dose-response relationship was represented algebraically by a monotonic four-parameter logistic function (26). The latter structure is motivated theoretically and empirically (30, 31). The end points of the estimation procedure are target organ sensitivity (maximal absolute slope), agonist potency (ED50), and stimulus efficacy (asymptotically maximal response). The model allows for possible stochastic dose-response adaptations in pulse by pulse stimulus efficacy, potency, or sensitivity. The input signal to the unknown dose-response function is the reconvolved LH concentration time series, and the output (response) is the secretion rate of Te. All three of the LH input signal, LH-Te dose-response parameters, and Te secretion were estimated simultaneously, exactly as previously described (31, 32). To deconvolve the LH concentration profiles, the shape (time evolution) of underlying LH secretory bursts was represented by a three-parameter generalized Gamma probability density (15). The mass of LH secreted per burst was defined as the sum of basal LH accumulation in gonadotropes, a weak linear function of the preceding interpulse length and a random effect (33). LH pulse times were estimated first and applied conditionally to the statistical solution (34) (see supplemental data). In contrast to LH pulses, the shape of Te pulses was defined by the time-varying output of the estimated LH->Te dose-response function. Total, bioavailable, and free Te secretion rates were calculated from sample measurements of total Te concentrations and serum SHBG and albumin concentrations, as presented recently (31, 32).

To ensure statistically valid estimates, the four 18-h paired LH and Te time series were analyzed together in each subject (saline and three doses of GRX). Results derived from the last 8-h interval after GRX administration were segmented for statistical comparisons. The rationale was to encompass the interval of stable suppression of LH and Te concentrations by GRX (35). The analytical formalism yields a maximum likelihood statistical estimate of the set of secretion, elimination, and dose-response feedback and feedforward parameters simultaneously, conditional on predicted pulse onset times (32, 33). The supplemental data summarize mathematical relationships among the principal model-specific parameters.

Estimation of GnRH outflow.
According to classical concepts of a competitive ligand-receptor interaction, the magnitude of an observed biological response is determined 3-fold jointly by the concentration(s) of the agonist and any competing antagonist and properties of the receptor-effector response pathway (36). These minimal assumptions are satisfied because 1) GnRH is the exclusive or predominant physiological agonist of the cognate human pituitary receptor; and 2) GRX acts strictly competitively in vitro and in vivo (35, 37). Accordingly, greater inhibition of LH secretory burst mass by any given concentration of the competitive GnRH receptor antagonist would predict less opposing GnRH input. The assumed Kd values of the binding of GnRH and GRX to the GnRH receptor were 0.85 and 0.69 nM, respectively (37). Estimation assumed that gonadotropes retain responsiveness to GnRH pulses, as verified experimentally in older men (12, 13, 14).

Free Te concentration-dependent negative feedback.
Available experimental data suggest that free (unbound) and bioavailable (sum of free and albumin-bound) Te concentrations enter the brain rapidly (38, 39). However, what fraction mediates negative feedback in not known. Therefore, the present analyses assessed each of total, bioavailable, and free Te-dependent inhibitions of endogenous GnRH-driven LH secretion rates and GnRH/LH pulse frequency. LH secretion rates reflect hypothalamo-pituitary actions of Te to inhibit the release and action of GnRH on LH secretion. LH pulse frequency is assumed to reflect the frequency of the hypothalamic GnRH pulse renewal process. Independent observations indicate that negative feedback by Te represents a noncompetitive process (40, 41). Thus, the construction allows Te concentrations to suppress GnRH efficacy (supplemental data). Analyses were applied simultaneously to all four pairs of 8-h LH and Te time series in any particular individual using subject-specific estimates of LH and Te kinetics.

Other statistics
The statistical significance of postulated age-related contrasts in individual dose-response and kinetic parameters was assessed by maximum likelihood ratio estimation or by regression of subject-specific estimates on age. ANOVA was applied to contrast the effects of age stratum on GRX, LH, and Te concentrations. P < 0.05 was construed as significant. Data are given as the mean (±SEM) or median (range).


   Results
Top
 Abstract
 Introduction
 Subjects and Methods
 Results
Discussion
 References
 
On the saline day, serum concentrations (mean over 8 h) of total and bioavailable (non-SHBG-bound) Te and LH were age invariant (Table 1Go). Free Te concentrations were lower (P < 0.05), whereas SHBG concentrations were higher (P < 0.025) in older than young men. The fractions of Te bound to SHBG were 35% (young) and 56% (older; P < 0.025). Because the age difference was evident for free Te, we first present estimates of free Te’s negative feedback actions.


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  		TABLE 1. Baseline hormone concentrations in young and older men

 
Figure 1Go illustrates LH concentration and secretion profiles in one young (23 yr old) and one older (68 yr old) man and highlights the paradigm used. Compared with saline, the highest dose of the GnRH receptor antagonist reduced pulsatile LH secretion and total Te concentrations by more than 80% in the cohort as a whole (P < 0.001). A two-way repeated measures ANOVA model demonstrated that 1) drug dose (P < 0.001), but not age stratum (P = 0.44), determined serum GRX concentrations; 2) GRX suppressed LH and Te concentrations in a dose-dependent fashion in both cohorts (P < 0.001); and 3) age potentiated inhibition of LH and Te by GRX (interaction effect, P < 0.01). Thus, the next step was to assess LH secretion rates under the four interventions.


Figure 1
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  		FIG. 1. Schema of study paradigm (left) and examples of time series of LH and total Te concentrations [measured (continuous lines) and calculated (interrupted lines)] in two men, one 23 yr old and the other 68 yr old (right, top and bottom). Data were obtained on separate days by sampling blood every 10 min for 2 h before and 16 h after the injection of each of four randomly ordered doses of the potent and selective GnRH receptor antagonist, GRX [GRX, 0 (saline), 0.1, 0.3, and 1.0 mg/m2; left to right in columns].

 
Figure 2AGo presents the results of analytical reconstruction of LH secretion from LH concentrations (top two rows), virtual GnRH concentrations (middle) from LH secretion rates and free Te concentrations (next to bottom row), and GnRH->LH feedforward functions (bottom) in relation to each of four GRX doses in a 23- and a 64-yr-old individual. Increasing doses of GRX shifted the GnRH->LH dose-response function to the right (reduced potency), whereas higher concentrations of free Te lowered the maximum (reduced efficacy). Two GnRH->LH functions are shown at each GRX dose, reflecting feedback effects of the maximal and minimal free Te concentrations observed in that session. The three-dimensional GnRH/LH/Te response surfaces and algebraic formulation are highlighted below the stepwise reconstructions. The same procedures were applied for all 18 subjects. To illustrate the distribution of the data contributing to the response surface, Fig. 2BGo gives the 432 data points in one young and one older male (chosen as the group medians).


Figure 2
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  		FIG. 2. A, Illustrative reconstruction of GnRH->LH feedforward dose-response functions using (top to bottom) the reconvolved LH concentration, calculated LH secretion rate, virtual GnRH signal (combined release and action), and free Te concentrations (maximum and minimum) at each of four GRX doses in a 23- and a 64-yr-old male. The two dose-response curves at each GRX stratum reflect the extrema of free Te negative feedback in that study session. GRX shifts the GnRH->LH dose response to the right (competitive inhibition), and Te lowers the maximum (noncompetitive suppression). Corresponding surface plots for the two subjects and feedback/feedforward equation are shown (bottom). B, Data distribution in one young and one older male (selected as group medians) plotted analogously. The virtual GnRH values were reconstructed, as described in the supplemental data (equation 9).

 
The primary model-based outcome was estimation of three-dimensional response surfaces for bivariate control of pulsatile LH secretion (8-h summed mass of LH secreted in bursts; dependent variable) jointly by 1) a positive logistic function of the virtual GnRH signal (independent variable) and 2) a negative exponential function of free Te concentrations (independent variable; Fig. 3AGo). Group estimates entailed analyses of all 3456 and 4320 LH/Te sample pairs in older (n = 8) and young (n = 10) men, respectively. The analytical imprecisions of the model (percent unexplained variance of the parameter estimate) were 3.3% (young) and 7.2% (older) for GnRH efficacy [in absolute terms the SD/efficacy estimates were 0.02/1.21 (young] and 0.02/0.55 (older)]. Statistical comparisons of the efficacy of virtual GnRH outflow (asymptotically maximal LH output under extrapolated zero free Te concentrations) predicted a 58% reduction in older compared with young men (P < 0.01). The reduction in GnRH outflow in older subjects was demonstrated for total Te, bioavailable Te, and free Te (Fig. 3BGo). Diminished efficacy of virtual GnRH outflow was selective, because calculated sensitivity to GnRH did not differ, and estimated GnRH potency was 41% higher in older than young men (29% lower median ED50, 3.4 vs. 4.8; P = 0.013).


Figure 3
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  		FIG. 3. A, Three-dimensional surface plots of pulsatile LH secretion rates (dependent variable; vertical axis) driven by virtual GnRH outflow (independent variable) and inhibited by free Te concentrations (independent variable) estimated analytically in young (20–35 yr old; top) and older (50–72 yr old; bottom) cohorts of men. Note the different z-axis scales. B, Analogous plots for total Te, bioavailable (non-SHBG bound) Te, and free Te (unbound) in the two cohorts. C, Estimates of virtual GnRH efficacy (left) and GnRH ED50 (right; reciprocal of potency) given as the mean ± 1 SD obtained statistically by repeating the entire analyses in all subsets of N-1 subjects (thus, nine young and seven older men).

 
The robustness of the model solution to group size was shown by refitting each response surface after leaving out one subject repeatedly in each age group (jackknife procedure). This resampling procedure yields data in the form of mean GnRH efficacy and potency determined for N-1 subjects in each cohort (viz., nine young and seven older men; Fig. 3CGo). The SD associated with resampling and model fit were thereby calculated (supplemental Table 1Go). Statistical comparisons of the resampled data verified the age effects, viz. lower GnRH efficacy and greater GnRH potency in older men.

The robustness of statistical estimates for this model at the original group sizes was verified by bootstrap resampling (random reassignments of residuals, 1000 times) of the response surface. The SD values of the key parameters were thereby calculated, as shown in Table 2Go. The primary conclusions were confirmed (P < 0.01) with good parameter precision.


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  		TABLE 2. Bootstrap estimates of standard errors of cohort parameters

 
Interindividual variability in parameter estimates was assessed by fitting the response surface separately for each subject, thereby allowing calculation of cohort SD values (Table 3Go). The SD values for intersubject variability were larger than those for analytical error, as expected.


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  		TABLE 3. Cohort SEs of parameter estimates

 
Figure 4Go illustrates LH->Te feedforward analyses based upon observed (measured) 18-h LH and Te concentration time series in all four interventions in one subject (27 yr old). Full 18-h profiles were analyzed to ensure statistical validity in calculating the dose-response function during the last 8 h (supplemental data). Increasing doses of GRX reduced LH concentrations, calculated Te secretion rates, and total Te concentrations. Inspection indicated that the GnRH receptor antagonist decreases the size of both LH and Te pulses. Analytical estimates of four-parameter LH concentration-Te secretion (dose-response) relationships are given for each 8-h sampling interval (Fig. 4Go, bottom row). A set of LH->Te dose-response functions is shown for each GRX dose in an individual subject. The set reflects statistical allowance for possible (but not required) random pulse to pulse variability in LH efficacy. The modal LH->Te dose-response function is identified by the bold interrupted curve. The degree of pulse by pulse stochastic variability was quantified by the CV (SD/mean x 100%). Median CVs were not affected by GRX dose (P > 0.60), but were lower in older (24%) than young men (37%; P < 0.05). This outcome signifies that LH->Te feedforward coupling is more consistent from pulse to pulse in older individuals.


Figure 4
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  		FIG. 4. Illustrative time plots of reconvolved LH concentrations (LH signal; topmost row), measured (continuous lines) and estimated (interrupted curves) Te concentrations (Te Con; second row), calculated Te secretion rates (Te Sec; third row), and analytically reconstructed LH-Te feedforward dose-response relationships (logistic functions; bottom row) in a 27-yr-old man. Columns (left to right) present data obtained after randomly ordered separate-day injections of 0, 0.1, 0.3, and 1.0 mg/m2 GRX at 120 min (x-axis). The set of LH->Te dose-response curves (bottom) constructed at each dose of GRX reflects predictions for the set of LH->Te pulse pairs under statistical allowance for possible pulse by pulse random effects on LH efficacy. The bold line denotes the modal dose-response estimate across all four sessions in this subject.

 
To assess the strength of LH->Te coupling, cohort-defined LH->Te feedforward functions were reconstructed separately for the 18- and 8-h paired LH/Te time series under each of the three stochastic models (viz. random effects on LH efficacy, LH potency, and testis sensitivity; Fig. 5Go). Independently of the length of the time series and type of stochastic model examined, the mean efficacy of LH drive was lower in older than young subjects (0.005 < P < 0.01). LH ED50 (potency) values were comparable across GRX doses, among stochastic models, and in relation to age [viz. median, 1.7 (young) and 2.0 IU/liter (older)]. Estimated testis sensitivity to LH concentrations (exponential coefficient) was also age invariant [median, 3.3 (young) and 3.0 (older) slope units].


Figure 5
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  		FIG. 5. Four-parameter logistic functions relating calculated pulsatile Te secretion rates (y-axis) to reconvolved LH concentrations (x-axis) in young (20–35 yr old) and older (50–72 yr old) men. The upper and lower panels give respective estimates based upon all 18 h and the last 8 h of blood sampling. The three columns (left to right) depict the results of stochastic models, in which allowable random effects are apportioned to feedforward efficacy, potency, or sensitivity. In all six analytical constructs, older subjects exhibit lower endogenous LH efficacy (asymptotically maximal Te secretion rate) than young individuals (0.005 < P < 0.01).

 
Virtual GnRH waveform (shape of secretory bursts) estimates in young and older volunteers were reconstructed as shown in Fig. 6AGo. The modal times to achieve maximal GnRH secretion within each burst were 9.6 min (young) and 9.3 min (older; P = NS). Comparison of exponential coefficients defining the relative magnitude of free Te’s feedback on GnRH efficacy disclosed 44% less suppression in older than young men (P = 0.015; Fig. 6BGo). In contrast, age did not affect inhibition of GnRH/LH pulse frequency by free Te concentrations; i.e. exponential inhibition constants averaged –0.076 ± 0.017 (young) and –0.094 ± 0.028 (older; P = NS; Fig. 6CGo). Such estimates signify that a mean increment of 8.3 (7.4–9.1) ng/dl in the free Te concentration across the low to midphysiological range reduces LH secretory burst frequency ({lambda} of Weibull process) by 50%. In absolute terms, after placebo injection, {lambda} values were 16.1 ± 0.67 (young) and 20.4 ± 1.4 (older) pulses/24 h (P = 0.02); after GRX (1.0 mg/m2) administration, values were 27.8 ± 1.4 (young) and 29.2 ± 0.89 (older; P = NS by age; both P < 0.01 vs. placebo). Interpulse interval regularity ({gamma} of Weibull process) over the time window of 8 h was independent of GRX dose and age (global median, 1.8; range, 1.7–2.1).


Figure 6
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  		FIG. 6. A, Individual (thin lines) and modal (dark line) estimates of the waveform (time evolution of secretion rates) of virtual GnRH secretory bursts in 10 younger (upper) and eight older (lower) men. B, Scatterplots and median exponential values of free Te’s feedback on the efficacy of endogenous GnRH-driven pulsatile LH secretion in young and older men. C, Individual exponential regressions of LH secretory burst frequency (normalized to 24 h) on free Te concentrations (nanograms per deciliter) in young (dark lines) and older men (light lines).

 
Calculated half-lives (rapid and slow phases) of secreted LH and Te did not differ with respect to GRX dose or age stratum. Global medians (range) for the rapid and slow components of LH elimination were 13 (7–40) and 97 (63–142) min, respectively; for the rapid (diffusion and advection) and slow (elimination) phases of free Te, values were 0.86 (0.42–1.7) and 4.9 (2.0–9.1) min; and for the disappearance of total Te, the value was 47 (24–86) min.

Central hypothalamo-pituitary sampling data from the horse and sheep are presented in Fig. 7Go. All four of the virtual GnRH signals, LH secretion rates, non-SHBG-bound Te concentrations, and the GnRH feedforward/Te feedback/LH secretion surfaces were estimated using only measured LH and Te concentrations and the identical analytical formalism. Bioavailable and total Te values were equivalent in these two species, which lack SHBG. The reconstructed LH secretion profiles accounted for observed data within 3% (r2 > 0.97). Predicted GnRH signals coincided with prominent LH secretory bursts. Unexplained variations were evident in experimentally measured GnRH values, which did not coincide with LH pulses. These variations, when unassociated with LH pulses, were definitionally not identified as significant GnRH pulses in the model.


Figure 7
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  		FIG. 7. GnRH-LH-Te feedforward/feedback reconstruction based upon data obtained in a conscious, unmedicated, unrestrained stallion or ram sampled every 5 min centrally for 6 h (A) or 12 h (B), respectively. In each pictograph, left, measured (thin line) and estimated (dark line) LH secretion rates using serial LH concentrations (top two rows); observed (thin line) and predicted (virtual; dark line) GnRH signals based on simultaneously estimated LH secretion and Te feedback (middle row); reconvolved non-SHBG-bound Te concentrations (penultimate row); and reconstructed GnRH->LH dose-response functions (bottom row) for the highest and lowest Te concentrations; right, Three-dimensional response surface linking LH secretion rates to both the virtual GnRH signal and the non-SHBG-bound Te concentration in the same animal.

 

   Discussion
Top
 Abstract
 Introduction
 Subjects and Methods
 Results
 Discussion
References
 
The present investigation in 18 healthy men, 20–25 and 50–72 yr of age, disclosed that older individuals exhibit triple regulatory deficits defined by 1) diminished maximal hypothalamic outflow of GnRH to gonadotropes, 2) decreased efficacy of pituitary LH pulses in stimulating pulsatile Te secretion, and 3) reduced negative feedback by total, bioavailable, and free Te concentrations on endogenous GnRH-driven LH secretion. Concomitantly, older subjects manifest greater potency (lower ED50) of the reconstructed GnRH signal and lesser pulse by pulse variability in LH->Te feedforward efficacy. The model was robust to cohort size (as assessed by jackknife resampling), well determined statistically (small SE values of cohort parameters by bootstrap analysis), and applicable to data from single subjects. The foregoing mechanistic inferences are selective, because age did not affect the dose dependence of serum concentrations of the GnRH receptor antagonist, the elimination kinetics of secreted LH and Te, the putative waveform of GnRH secretory bursts, or the efficacy of free Te’s concentration-dependent feedback on GnRH/LH pulse frequency. Thus, assuming that high-amplitude LH pulses reflect intermittent GnRH drive (42, 43, 44), the accompanying data imply that aging significantly reduces the amount of GnRH released per burst. This inference would account for smaller LH pulses in older male volunteers (15) despite less negative feedback by systemic Te as well as greater potency of submaximally effective GnRH pulses. Likewise, assuming that LH pulses stimulate Te secretory bursts (45), decreased efficacy of endogenous LH in the elderly male would signify impaired maximal Leydig cell steroidogenesis, and diminished suppression of endogenous GnRH-driven LH secretion, but not pulse number, by physiological Te concentrations would denote impaired feedback on the amplitude, but not the frequency, of GnRH/LH pulse renewal. Accordingly, the accompanying analyses unveil triple concomitant deficits in GnRH outflow, LH action, and Te action in the aging male. The relatively small number of healthy older men studied may not be representative of a larger and wide-ranging sample of unselected older men with illness, morbidity, or medication exposure.

Impairment of multipathway control of the gonadal axis provides a potentially unifying explanation for some disparate previous reports (3). For example, discrepant inferences of augmented negative feedback by exogenous Te in older men might be accounted for by failure to relate physiological Te concentrations to the degree of inhibition in the same volunteer. If the present outcomes are verified independently, longitudinal investigations will be required to establish the precise age dependency of the inferred regulatory deficiencies. In addition, future studies will be necessary to determine the generality among species of putative ensemble pathway failure in aging individuals.

A salient analytical prediction was that the efficacy of hypothalamic GnRH outflow is significantly lower in older than young men. This inference is based upon mathematical reconstruction of endogenous GnRH-driven pulsatile LH secretion after creating four graded echelons of LH and Te pulses in each subject. The age contrast in GnRH outflow was verified for total Te, bioavailable Te, and free Te concentration signals. This important outcome is the first, to our knowledge, to establish comparability of age-related differences in the actions of total, bioavailable, and free Te. Whether other target tissue responses behave similarly in not known (3). The same analysis forecast that age does not greatly alter the virtual GnRH waveform, but enhances the potency of the endogenous GnRH drive. In the latter regard, LH secretory responses to submaximally stimulatory doses of exogenous GnRH are accentuated in aging men (12, 13, 14).

From a modeling perspective, estimates of the apparent efficacy and potency of GnRH derive from kinetic principles of single-ligand, single-receptor coupling in the presence of a competitive inhibitor (GRX) and a noncompetitive inhibitor (Te concentrations) (36). In particular, serum concentrations of the GnRH-receptor antagonist (GRX) were measured in each subject and related via the Kd values of GRX and LH secretion rates (positively) and Te concentrations (negatively). The analytical forecast of decreased maximal GnRH outflow (release and action) in aging men agrees with experimental findings in the aged male rat of altered GnRH synaptology (46), impaired secretion of GnRH by cultured hypothalamic fragments (7), preserved GnRH stimulation of LH release by perifused pituitary tissue (8), and decreased castration-induced LH secretion (9). Nonetheless, proof of an age-related decline in central-neuronal GnRH secretion would require intensive sampling of hypothalamo-pituitary portal blood. Direct measurements could also test the present inferences that GnRH secretory burst waveform does not differ with age, whereas baseline LH burst frequency is increased in the older male. These issues are relevant, because GnRH secretory burst mass, number, and shape appear to govern LH secretion (47, 48).

In experimental models, LH pulses detected in the systemic circulation are preceded by bursts of GnRH release into hypothalamo-pituitary portal-venous blood with high consistency (42, 43, 44). Accordingly, we validated analytical estimation of GnRH and LH pulse locations by direct pituitary-venous sampling every 5 min for 6 and 12 h in the awake, unrestrained, and unmedicated horse and sheep. In addition, assuming that objectively demarcated LH pulses provide a surrogate measure of intermittent GnRH outflow, we regressed GnRH/LH pulse frequency exponentially on Te concentrations in young and older men. Quantifiable negative feedback by endogenous Te on LH burst number is distinct conceptually from, but agrees with, clinical and laboratory studies using exogenous Te, 5{alpha}-dihydrotestosterone, or a selective androgen receptor antagonist to modify feedback (40, 49, 50). Statistical comparisons revealed that age stratum does not significantly alter free Te’s concentration-dependent repression GnRH/LH pulse number. Verification of this outcome will require direct monitoring of GnRH neuronal output in a suitable animal model of aging.

Analytical estimation of the virtual GnRH signal required accounting for putatively noncompetitive inhibition of pulsatile GnRH release (amount), action (feedforward), and burst number (frequency) by Te concentrations (41). Initial analyses used free Te concentrations as a plausible negative feedback signal, given strong correlations of this moiety with spermatogenesis in mice and the metabolic clearance rate of Te, symptoms of eugonadism, and bioavailable Te concentrations in humans (51, 52, 53). However, additional analyses established that age reduces the efficacy of negative feedback by total, bioavailable, and free Te concentrations. A possible mechanism for such feedback failure in older individuals would be decreased expression of hypothalamo-pituitary androgen and/or estrogen receptors, which putatively mediate Te-induced negative feedback (54, 55). In this regard, long-term castration in the ram, albeit more severe than the gradual gonadal steroid-depleting effect of aging, decreases pituitary androgen, but not estrogen, receptor number (56).

Analytical reconstruction of LH’s concentration-dependent stimulation of pulsatile Te secretion revealed a marked age-associated decrement in efficacy (0.005 < P < 0.01) without any detectable differences in LH potency or testicular sensitivity to LH. The latter results corroborate previous estimates (31), but disagree with one report of decreased LH bioactivity in older men (57). Diminished efficacy of endogenous LH pulses is consistent with, but physiologically distinct from, previous findings that aging impairs pharmacological stimulation by hCG, because the latter agonist measurably down-regulates gonadal steroidogenesis (3). Whether prolonged normalization of LH pulse number, size, and regularity would also normalize Te secretion in older animals and humans is not known. The issue is relevant, because both the pattern and the duration of LH exposure determine gonadal steroidogenesis in some species (28).

Analytical estimates of LH->Te feedforward efficacy were reproducible across the four experimentally imposed strata of LH and Te pulsatility in any given subject. Nonetheless, in vivo verification of calculated LH potency, sensitivity, and efficacy will ultimately be required in young and older individuals. To our knowledge, such data are not currently available in any species. Allowance for both stochastic and deterministic elements in the model structure permitted (but did not require) identification of intrinsic biological variability in the efficacy of LH->Te feedforward coupling within individual trains of paired LH and Te pulses. The concept of burst to burst nonuniformity of stimulus-response parameters was inferred initially in the horse, sheep, and human by direct sampling of pituitary and testicular blood (32). In the cohorts we studied, age diminished stochastic variability in the efficacy of LH->Te drive. A theoretically proposed basis for attenuated signal variability is a reduction in the number or strength of modulatory inputs (58). In the case of LH->Te feedforward, modulatory factors include autocrine, paracrine, neuronal, and systemic inputs to the testis (59). Another analysis quantified reduced physiological variability of the GnRH/LH pulse renewal process in older men (15). Thus, collective outcomes strongly suggest that aging diminishes multipathway interactions in the human male gonadal axis.

In summary, graded competitive GnRH receptor blockade and analytical reconstruction of resultant dose-response adaptations among GnRH, LH, and Te disclose tripartite attenuation of GnRH outflow, LH feedforward, and feedback by total, bioavailable, and free Te in healthy older men. Accordingly, analogous combined interventional and analytical paradigms may have utility in dissecting mechanisms of physiological control in other self-adaptive systems, such as the corticotropic, thyrotropic, somatotropic, and insulin-glucagon axes.


   Acknowledgments
 
We thank Kris Nunez for manuscript support, Ashley Bryant for graphical presentations, and Jason Kerkvliet for performing the GRX assays.


   Footnotes
 
This work was supported in part by National Center for Research Resources (Rockville, MD) Grant M01-RR-00585 (to the General Clinical Research Center, Mayo Clinic and Foundation), National Institutes of Health (Bethesda, MD) Grants RO1-AG-023133, R21-AG-023777, and K01-AG-019164; and National Science Foundation (Washington, DC) Interdisciplinary Grant in the Mathematical Sciences, DMS-0107680. P.Y.L. was supported by a Neil Hamilton Fairley Research Fellowship from the National Health and Medical Research Council of Australia (Grant ID-262025), and P.Y.T. was supported by a Medicine Innovation Development and Advancement System award (Department of Medicine, Mayo Clinic, Rochester, MN).

Current address of P.Y.L.: Endocrinology Division, Department of Internal Medicine, Harbor-University of California-Los Angeles Medical Center, Torrance, California 90509-2910.

All authors have nothing to declare.

First Published Online March 2, 2006

Abbreviations: CV, Coefficient of variation; GRX, ganirelix; hCG, human gonadotropin chorionic gonadotropin; NS, not significant; Te, testosterone.

Received October 25, 2005.

Accepted for publication February 17, 2006.


   References
Top
 Abstract
 Introduction
 Subjects and Methods
 Results
 Discussion
 References
 

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