Modelling the luteinizing hormone-releasing hormone pulse generator

Mathematical modeling approaches of cellular endocrinology within the hypothalamo-pituitary-gonadal axis

The reproductive neuroendocrine axis, or hypothalamo-pituitary-gonadal (HPG) axis, is a paragon of complex biological system involving numerous cell types, spread over several anatomical levels communicating through entangled endocrine feedback loops. The HPG axis exhibits remarkable dynamic behaviors on multiple time and space scales, which are an inexhaustible source of studies for mathematical and computational biology. In this review, we will describe a variety of modeling approaches of the HPG axis from a cellular endocrinology viewpoint. We will in particular investigate the questions raised by some of the most striking features of the HPG axis: (i) the pulsatile secretion of hypothalamic and pituitary hormones, and its counterpart, the cell signaling induced by frequency-encoded hormonal signals, and (ii) the dual, gametogenic and glandular function of the gonads, which relies on the tight control of the somatic cell populations ensuring the proper maturation and timely release of the germ cells.

Corticotrophin-releasing factor and stress-induced inhibition of the gonadotrophin-releasing hormone pulse generator in the female

It is well established that stress activates the hypothalamo-pituitary-adrenal (HPA) axis and suppresses the hypothalamo-pituitary-gonadal (HPG) axis. A large literature dealing with various stressors that regulate gonadotrophin-releasing hormone (GnRH) secretion in a variety of species (including nonhuman primates, sheep, and rats) provides evidence that stress modulates GnRH secretion by activating the corticotrophin-releasing factor (CRF) system and sympathoadrenal pathways, as well as the limbic brain. Different stressors may suppress the HPG axis by activating or inhibiting various pathways in the CNS. In addition to CRF being the principal hypophysiotropic factor driving the HPA axis, it is a potent inhibitor of the GnRH pulse generator. The suppression of the GnRH pulse generator by a variety of stressful stimuli can be blocked by CRF antagonists, suggesting a pivotal role for endogenous CRF. The differential roles for CRF receptor type 1 (CRF-R1) and CRF-R2 in stress-induced suppression of the GnRH pulse generator add to the complexity of CRF regulation of the HPG axis. Although the precise sites and mechanisms of action remain to be elucidated, noradrenergic and gamma-amino-butyric acid (GABA) neurones are implicated in the system's regulation, and opioids and kisspeptin in the medial preoptic area (mPOA) and hypothalamic arcuate nucleus (ARC) may operate downstream of the CRF neuronal system.

Motivations and methods for analyzing pulsatile hormone secretion

Endocrine glands communicate with remote target cells via a mixture of continuous and intermittent signal exchange. Continuous signaling allows slowly varying control, whereas intermittency permits large rapid adjustments. The control systems that mediate such homeostatic corrections operate in a species-, gender-, age-, and context-selective fashion. Significant progress has been made in understanding mechanisms of adaptive interglandular signaling in vivo. Principal goals are to understand the physiological origins, significance, and mechanisms of pulsatile hormone secretion. Key analytical issues are: 1) to quantify the number, size, shape, and uniformity of pulses, nonpulsatile (basal) secretion, and elimination kinetics; 2) to evaluate regulation of the axis as a whole; and 3) to reconstruct dose-response interactions without disrupting hormone connections. This review will focus on the motivations driving and the methodologies used for such analyses.

Mathematical modelling in neuroendocrinology

In neuroendocrinology, mathematical modelling is about formalising our understanding of the behaviour of the complex biological systems with which we deal. Formulating our explanations mathematically ensures their logical consistency, and makes them open to structured analysis; it is a stringent test of their intellectual coherence. In addition, however, modellers are seeking to extend our understanding in new ways, by seeking novel, simple explanations for complex behaviour. Here we discuss some styles of modelling as they have been applied to neuroendocrine systems, and discuss some of their strengths and limitations.

Modelling the hypothalamic control of growth hormone secretion

Here, we construct a mathematical model of the hypothalamic systems that control the secretion of growth hormone (GH). The work extends a recent model of the pituitary GH system, adding representations of the hypothalamic GH-releasing hormone (GHRH) and somatostatin neurones, each modelled as a single synchronised unit. An unpatterned stochastic input drives the GHRH neurones generating pulses of GHRH release that trigger GH pulses. Delayed feedback from GH results in increased somatostatin release, which inhibits both GH secretion and GHRH release, producing an overall pattern of 3-h pulses of GH secretion that is very similar to the secretory profile observed in male rats. Rather than directly stimulating somatostatin release, GH feedback triggers a priming effect, increasing releasable stores of somatostatin. Varying this priming effect to reduce the effect of GH can reproduce the less pulsatile form of GH release observed in the female rat. The model behaviour is tested by comparison with experimental observations with a range of different experimental protocols involving GHRH injections and somatostatin and GH infusion.

The role of the locus coeruleus in corticotropin-releasing hormone and stress-induced suppression of pulsatile luteinizing hormone secretion in the female rat

Despite a wealth of evidence for CRH mediating stress-induced suppression of the hypothalamic GnRH pulse generator, and hence reproductive dysfunction, the site and mechanism of action remains elusive. The locus coeruleus (LC), a prominent noradrenergic brain stem nucleus, is innervated by CRH neurons, mediates several behavioral stress responses, and is implicated in the control of pulsatile LH secretion. The aim of this study was to test the hypothesis that LC CRH has a critical role in mediating stress-induced suppression of pulsatile LH secretion in the rat. Ovariectomized rats with 17beta-estradiol or oil-filled s.c. capsules were implanted with bilateral LC and i.v. cannulae. Central administration of CRH (10 ng to 1 microg) resulted in a dose-dependent suppression of LH pulses, which was reversed by a CRH receptor antagonist (alpha-helical CRF(9-41), 1 microg). The induction of c-fos expression in glutamic acid decarboxylase67 immunostained neurons in the preoptic area suggests activation of the secretion of gamma-aminobutyric acid in response to intracoerulear administration of CRH; 17beta-estradiol further increased the percentage of glutamic acid decarboxylase67-positive neurons that expressed fos and augmented suppression of LH pulses. Furthermore, intracoerulear administration of alpha-helical CRF(9-41) completely blocked restraint stress-induced suppression of LH pulses, without affecting the inhibitory response to hypoglycemia. These results suggest that CRH innervation of the LC may play a pivotal, but differential, role in the normal physiological response of stress-induced suppression of the GnRH pulse generator and hence the reproductive system.

Estrogen biphasically modifies hypothalamic GABAergic function concomitantly with negative and positive control of luteinizing hormone release

The principal role of estrogen is its control of the female ovulatory cycle via negative and positive feedback on gonadotropin secretion. However, a detailed, cohesive picture of how the steroid specifically regulates the excitability of hypothalamic neurons involved in the central control of gonadotropin secretion is still emerging. Here, we used an ovariectomized female guinea pig model to test the hypothesis that estrogen acts on GABAergic neurons in the preoptic area (POA) to elicit a biphasic profile of luteinizing hormone (LH) secretion. Intracellular electrophysiological recordings revealed that estradiol benzoate (EB; 25 microgram, s.c.) decreased the hyperpolarizing response of GABAergic neurons to the GABA(B) receptor agonist baclofen 24 hr after treatment. This effect of GABA(B) receptor stimulation in unidentified POA neurons was still depressed 42 hr after EB administration. By the use of a ribonuclease protection assay, however, EB reduced glutamic acid decarboxylase mRNA expression 42 hr but not 24 hr after its administration. Thus, estrogen attenuated the autoinhibition of GABAergic POA neurons during the initial LH suppressive (i.e., negative feedback) phase and subsequently reduced GABAergic function during the LH surge (i.e., positive feedback). These studies demonstrate that the effects of estrogen on hypothalamic GABAergic neurons coincide with the inhibitory and stimulatory actions, respectively, of the steroid on LH secretion. Furthermore, the data provide novel insights into the mechanism by which estrogen regulates hypothalamic GABAergic neurons, which are critical for the biphasic modulation of LH release observed over the course of the female ovulatory cycle.

Luteinizing hormone-releasing hormone (LHRH) neurons: mechanism of pulsatile LHRH release

Many types of neurons and glia exhibit oscillatory changes in membrane potentials and cytoplasmic Ca2+ concentrations. In neurons and neuroendocrine cells an elevation of intracellular Ca2+ concentration is associated with neurosecretion. Since both oscillatory membrane potentials and intracellular Ca2+ oscillations have been described in primary LHRH neurons and in GT1 cells, it is evident that an endogenous pulse-generator/oscillator is present in the LHRH neuron in vitro. The hourly rhythms of LHRH neurosecretion appear to be the synchronization of a population of LHRH neurons. How a network of LHRH neurons synchronizes their activity, i.e., whether by the result of synaptic mechanisms or electrical coupling through gap junctions or through a diffusible substance(s), remains to be clarified. Even though LHRH neurons themselves possess an endogenous pulse-generating mechanism, they may be controlled by other neuronal and nonneuronal elements in vivo. NE, NPY, glutamate, and GABA are neurotransmitters possibly controlling pulsatile LHRH release, and NO, cAMP, and ATP may be diffusible substances involved in pulsatile LHRH release without synaptic input. Although synaptic inputs to the perikarya of LHRH neurons could control the activity of LHRH neurons, a line of evidence suggests that direct neuronal and nonneuronal inputs, especially those from astrocytes to LHRH neuroterminals, appear to be more important for pusatile LHRH release.

Suppression of tonic luteinizing hormone secretion and norepinephrine release near the GnRH neurons by estradiol in ovariectomized rats

One of the major neurotransmitters that controls pulsatile luteinizing hormone (LH) secretion is norepinephrine (NE). NE pulses detected in the median eminence of ovariectomized rhesus monkeys are highly correlated with both GnRH and LH pulses. In contrast, previous reports suggest that this is not the case in rats, thus it remains to be determined whether NE stimulates LH release on a pulse-by-pulse basis in that species. Further, a variety of indirect evidence supports the hypothesis that in rats, estradiol exerts its negative feedback action on LH secretion in part by inhibiting noradrenergic neurotransmission that is stimulatory to LH release, but there is no direct evidence to support this hypothesis. Therefore the following study was designed to test the hypothesis that estradiol suppresses NE release in the vicinity of the GnRH neurons after ovariectomy. In addition, we examined whether episodes of NE release are correlated with LH pulses in ovariectomized rats. Blood samples and microdialysates of the diagonal band of Broca/medial preoptic area (DBB/MPOA) were collected every 5 min from 09:00 to 14:00 h from untreated or estradiol-treated (4-5 days), long-term ovariectomized (1-4 months) rats for determination of plasma LH by RIA and NE release by HPLC. The results indicate that in both untreated and estradiol-treated ovariectomized rats, LH pulses are not correlated with episodes of NE. Thus, NE may play a permissive role in the control of pulsatile LH secretion in rats. Further, estradiol treatment leads to a suppression of both plasma LH levels and NE release in the DBB/MPOA, supporting the hypothesis that a decrease in NE neurotransmission that is stimulatory to LH release mediates the negative feedback action of estradiol on tonic LH secretion.

Noradrenergic neurotoxin suppresses gonadotropin-releasing hormone (GnRH) and GnRH receptor gene expression in ovariectomized and steroid-treated rats

The present study was designed to investigate whether noradrenergic neurotransmission regulates the gene expression of gonadotropin-releasing hormone (GnRH) in the preoptic area and GnRH receptor in the pituitary. To this end, N-(2-chloroethyl)-N-ethyl-2-bromobenzylamine (DSP4, 50 mg/kg), an intraperitoneal (i.p.) injection of selective noradrenergic neurotoxin, was administered 1 h before progesterone (1 mg) treatment in ovariectomized and estradiol-treated prepubertal rats. Treatment with DSP4 effectively blocked the progesterone-induced increase in hypothalamic noradrenaline content, but not dopamine content, indicating that DSP4 selectively inhibits noradrenergic neurotransmission. DSP4 significantly blocked progesterone-induced increase in serum luteinizing hormone (LH) concentrations as well as GnRH release from hypothalamic fragments incubated in vitro. DSP4 concomitantly down-regulated GnRH mRNA levels in the preoptic area, as determined by competitive reverse transcription-polymerase chain reaction. DSP4 also clearly down-regulated progesterone-induced GnRH receptor mRNA levels in the pituitary, whereas it failed to alter LHbeta mRNA levels. In summary, blockade of noradrenergic neurotransmission with DSP4 resulted in profound reductions of hypothalamic GnRH and pituitary GnRH receptor gene expression.

Modulating mechanisms of neuroendocrine cell activity: the LHRH pulse generator

1. Luteinizing hormone-releasing hormone (LHRH), synthesized in specialized neurons in the hypothalamus, is the prime regulator of reproduction. In its absence, reproductive development is arrested and disorders of LHRH secretion result in several reproductive dysfunctions. 2. The LHRH neuronal network plays a paramount role in the regulatory loop controlling gonadal homeostasis. LHRH input to the pituitary gland maintains gonadotropin secretion, which, in turn, is responsible for gonadal trophism. Steroidal and peptidergic hormones from the gonad close the regulatory system by establishing negative (male and females) and positive (females) feedback loops. 3. Interestingly, LHRH input to the pituitary is intermittent rather than continuous. In fact, continuous exposure to LHRH results in paradoxical hypogonadism. Several studies in animals have provided direct evidence for episodic secretion of LHRH into the hypophyseal portal system. However, the nature of the system(s) responsible for the generation of the LHRH pulsatile profile is not currently known. The recent observation that immortalized LHRH neurons secrete LHRH in a pulsatile manner suggests that the pulse generating mechanism resides within the LHRH neuronal network. 4. In this overview, we compile several lines of evidence supporting this notion and put this characteristic of LHRH neurons in perspective with gonadal influences both internal and external to the LHRH neuronal network. Some recent data regarding the site of action of gonadal steroids on the LHRH neuronal system, the functional significance of galanin colocalization with LHRH, and the role of nitric oxide in the pulse generating mechanism are also discussed.

Mathematical exploration of pulsatility in cultured gonadotropin-releasing hormone neurons

Pulsatile gonadotropin-releasing hormone (GnRH) release has been demonstrated in cultures of an immortalized line of GnRH expressing neurons (GT1 cells) in experiments by four different research groups. Pulsatile release is known to play a crucial role in GnRH-mediated signaling in vivo, and thus deserves theoretical and quantitative consideration, especially as GT1 cells are presumably genetically homogeneous. Here we have modeled idealized GT1 cells with a differential equation/logic based modeling program, Stella II. We have created a network of 'neurons', with randomized (within the same preset limits for each neuron) thresholds, number and weight of connections to other neurons, and build-up of signal; as well as continuous decay of stored signal. Surprisingly, we found that with this minimal set of assumptions, without any sort of predefined pacemaking cells, it is possible to create pulsatility similar to that observed in the laboratory. A variety of different parameter sets was found to produce these pulses. Network behaviors similar to those of GT1 cells depended on the degree of interconnection between neurons and their functioning within a critical range of network excitability. These findings allow for a clearer consideration of the critical elements of such networks as well as experimental predictions regarding the production of pulsatile behavior.

Hormonal and neurotransmitter regulation of GnRH gene expression and related reproductive behaviors

Gonadotropin-releasing hormone (GnRH), having a highly conserved structure across mammalian species, plays a pivotal role in the control of the neuroendocrine events and the inherent sexual behaviors essential for reproductive function. Recent advances in molecular genetic technology have contributed greatly to the investigation of several aspects of GnRH physiology, particularly steroid hormone and neurotransmitter regulation of GnRH gene expression. Behavioral studies have focused on the actions of GnRH in steroid-sensitive brain regions to understand better its role in the facilitation of mating behavior. To date, however, there are no published reports which directly correlate GnRH gene expression and reproductive behavior. The intent of this article is to review the current understanding of the way in which changes in GnRH gene expression, and modifications of GnRH neuronal activity, may ultimately influence reproductive behavior.

Discrete-time stimulation of the oscillatory and excitable forms of a FitzHugh-Nagumo model applied to the pulsatile release of luteinizing hormone releasing hormone

A model for the pulsatile release of luteinizing hormone releasing hormone (LHRH) can be reduced to a FitzHugh-Nagumo model subject to regular and quasiregular (i.e., with slight random variation in the interstimulus interval), discrete-time stimulation. The relationship of output pulse frequency (OPF) to stimulus frequency is compared between the excitable and oscillatory forms of the model and discussed in the context of results from other pulse-driven model systems. Some examples of the changes in OPF caused by quasiregular and purely Poissonian stimuli are given for the excitable case. The unstimulated system frequently interacts with the stimulation in such a complex manner that the OPF bears little resemblance to the frequency of stimulation or of the unstimulated system. Furthermore, the inability of the oscillatory form of the model to allow complete suppression of output pulses for moderate stimulation frequencies suggests that the LHRH system can be more appropriately described by the excitable form of the model. (c) 1995 American Institute of Physics.