A mathematical model for the actions of activin, inhibin, and follistatin on pituitary gonadotrophs

Identification of common genetic polymorphisms associated with down-regulated gonadotropin levels in an exome-wide association study

OBJECTIVE

To investigate whether common genetic polymorphisms are associated with gonadotropin levels after down-regulation with daily gonadotropin-releasing hormone agonist and whether the polymorphisms of candidate variants influence the ovarian response to exogenous gonadotropins.

DESIGN

Genetic association study.

SETTING

University-affiliated in vitro fertilization center.

PATIENTS

Subjects enrolled in an exploratory exome-wide association study (n = 862), a replication exome-wide association study (n = 86), and a classifier validation study (n = 148) were recruited from September 2016 to October 2018, September 2019 to September 2020, and January 2021 to December 2021, respectively. The included patients were aged ≤40 years and had a basal follicle-stimulating hormone (FSH) ≤12 IU/L.

INTERVENTIONS

All participants received a luteal phase down-regulation long protocol. Genome DNA was extracted from the peripheral blood leukocytes. For the exploratory and replication cohorts, exome sequencing was conducted on a HiSeq 2500 sequencing platform. The multiplex polymerase chain reaction amplification technique and next-generation sequencing also were performed in the exploratory and replication cohorts. For the samples of the validation cohort, Sanger sequencing was performed.

MAIN OUTCOME MEASURES

The primary endpoint was the gonadotropin levels after down-regulation, and the secondary endpoints were hormone levels and follicle diameters during stimulation, the total dose of FSH, duration of FSH stimulation, number of oocytes retrieved, and clinical pregnancy rate.

RESULTS

In the exploratory cohort, we identified that FSHB rs6169 (P=2.71 × 10-24) and its single-nucleotide polymorphisms in high linkage disequilibrium were associated with the down-regulated FSH level. The same locus was confirmed in the replication cohort. Women carrying the C allele of FSHB rs6169 exhibited higher average estradiol level during stimulation (P=6.82 × 10-5), shorter duration of stimulation, and less amount of exogenous FSH (Pduration=0.0002; Pdose=0.0024). In the independent validation set, adding rs6169 genotypes into the prediction model for FSH level after down-regulation enhanced the area under the curve from 0.560 to 0.712 in a logistic regression model, and increased prediction accuracy by 41.05% when a support vector machine classifier was applied.

CONCLUSION

The C allele of FSHB rs6169 is a susceptibility site for the relatively high level of FSH after down-regulation, which may be associated with increased ovarian FSH sensitivity.

Mathematical models in GnRH research

Mathematical modelling is an indispensable tool in modern biosciences, enabling quantitative analysis and integration of biological data, transparent formulation of our understanding of complex biological systems, and efficient experimental design based on model predictions. This review article provides an overview of the impact that mathematical models had on GnRH research. Indeed, over the last 20 years mathematical modelling has been used to describe and explore the physiology of the GnRH neuron, the mechanisms underlying GnRH pulsatile secretion, and GnRH signalling to the pituitary. Importantly, these models have contributed to GnRH research via novel hypotheses and predictions regarding the bursting behaviour of the GnRH neuron, the role of kisspeptin neurons in the emergence of pulsatile GnRH dynamics, and the decoding of GnRH signals by biochemical signalling networks. We envisage that with the advent of novel experimental technologies, mathematical modelling will have an even greater role to play in our endeavour to understand the complex spatiotemporal dynamics underlying the reproductive neuroendocrine system.

Modeling and high-throughput experimental data uncover the mechanisms underlying Fshb gene sensitivity to gonadotropin-releasing hormone pulse frequency

Neuroendocrine control of reproduction by brain-secreted pulses of gonadotropin-releasing hormone (GnRH) represents a longstanding puzzle about extracellular signal decoding mechanisms. GnRH regulates the pituitary gonadotropin's follicle-stimulating hormone (FSH) and luteinizing hormone (LH), both of which are heterodimers specified by unique β subunits (FSHβ/LHβ). Contrary to Lhb, Fshb gene induction has a preference for low-frequency GnRH pulses. To clarify the underlying regulatory mechanisms, we developed three biologically anchored mathematical models: 1) parallel activation of Fshb inhibitory factors (e.g. inhibin α and VGF nerve growth factor-inducible), 2) activation of a signaling component with a refractory period (e.g. G protein), and 3) inactivation of a factor needed for Fshb induction (e.g. growth differentiation factor 9). Simulations with all three models recapitulated the Fshb expression levels obtained in pituitary gonadotrope cells perifused with varying GnRH pulse frequencies. Notably, simulations altering average concentration, pulse duration, and pulse frequency revealed that the apparent frequency-dependent pattern of Fshb expression in model 1 actually resulted from variations in average GnRH concentration. In contrast, models 2 and 3 showed "true" pulse frequency sensing. To resolve which components of this GnRH signal induce Fshb, we developed a high-throughput parallel experimental system. We analyzed over 4,000 samples in experiments with varying near-physiological GnRH concentrations and pulse patterns. Whereas Egr1 and Fos genes responded only to variations in average GnRH concentration, Fshb levels were sensitive to both average concentration and true pulse frequency. These results provide a foundation for understanding the role of multiple regulatory factors in modulating Fshb gene activity.

Mathematical modeling of perifusion cell culture experiments on GnRH signaling

The effects of pulsatile GnRH stimulation on anterior pituitary cells are studied using perifusion cell cultures, where constantly moving culture medium over the immobilized cells allows intermittent GnRH delivery. The LH content of the outgoing medium serves as a readout of the GnRH signaling pathway activation in the cells. The challenge lies in relating the LH content of the medium leaving the chamber to the cellular processes producing LH secretion. To investigate this relation we developed and analyzed a mathematical model consisting of coupled partial differential equations describing LH secretion in a perifusion cell culture. We match the mathematical model to three different data sets and give cellular mechanisms that explain the data. Our model illustrates the importance of the negative feedback in the signaling pathway and receptor desensitization. We demonstrate that different LH outcomes in oxytocin and GnRH stimulations might originate from different receptor dynamics and concentration. We analyze the model to understand the influence of parameters, like the velocity of the medium flow or the fraction collection time, on the LH outcomes. We show that slow velocities lead to high LH outcomes. Also, we show that fraction collection times, which do not divide the GnRH pulse period evenly, lead to irregularities in the data. We examine the influence of the rate of binding and dissociation of GnRH on the GnRH movement down the chamber. Our model serves as an important tool that can help in the design of perifusion experiments and the interpretation of results.

Cooperative Effects of FOXL2 with the Members of TGF-β Superfamily on FSH Receptor mRNA Expression and Granulosa Cell Proliferation from Hen Prehierarchical Follicles

Forkhead box L2 (FOXL2) is a member of the forkhead nuclear factor 3 gene family and plays an essential role in ovarian growth and maturation in mammals. However, its potential effects and regulative mechanism in development of chicken ovarian prehierarchical follicles remain unexplored. In this study, the cooperative effects of FOXL2 with activin A, growth differentiation factor-9 (GDF9) and follistatin, three members of the transforming growth factor beta (TGF-β) superfamily that were previously suggested to exert a critical role in follicle development was investigated. We demonstrated herein, using in-situ hybridization, Northern blot and immunohistochemical analyses of oocytes and granulosa cells in various sizes of prehierarchical follicles that both FOXL2 transcripts and FOXL2 proteins are predominantly expressed in a highly similar expression pattern to that of GDF9 gene. In addition, the FOXL2 transcript was found at lower levels in theca cells in the absence of GDF9. Furthermore, culture of granulosa cells (GCs) from the prehierarchical follicles (6–8 mm) in conditioned medium revealed that in the pcDNA3.0-FOXL2 transfected GCs, there was a more dramatic increase in FSHR mRNA expression after treatment with activin A (10 ng/ml) or GDF9 (100 ng/ml) for 24 h which caused a stimulatory effect on the GC proliferation. In contrast, a significant decrease of FSHR mRNA was detected after treatment with follistatin (50 ng/ml) and resulted in an inhibitory effect on the cell proliferation. The results of this suggested that FOXL2 plays a bidirectional modulating role involved in the intracellular FSHR transcription and GC proliferation via an autocrine regulatory mechanism in a positive or negative manner through cooperation with activin A and/or GDF9, and follistatin in the hen follicle development. This cooperative action may be mediated by the examined Smad signals and simultaneously implicated in modulation of the StAR, CCND2, and CYP11A1 expression.

Growth differentiation factor 9 (GDF9) forms an incoherent feed-forward loop modulating follicle-stimulating hormone β-subunit (FSHβ) gene expression

Gonadotropin-releasing hormone (GnRH) is secreted in brief pulses from the hypothalamus and regulates follicle-stimulating hormone β-subunit (FSHβ) gene expression in pituitary gonadotropes in a frequency-sensitive manner. The mechanisms underlying its preferential and paradoxical induction of FSHβ by low frequency GnRH pulses are incompletely understood. Here, we identify growth differentiation factor 9 (GDF9) as a GnRH-suppressed autocrine inducer of FSHβ gene expression. GDF9 gene transcription and expression were preferentially decreased by high frequency GnRH pulses. GnRH regulation of GDF9 was concentration-dependent and involved ERK and PKA. GDF9 knockdown or immunoneutralization reduced FSHβ mRNA expression. Conversely, exogenous GDF9 induced FSHβ expression in immortalized gonadotropes and in mouse primary pituitary cells. GDF9 exposure increased FSH secretion in rat primary pituitary cells. GDF9 induced Smad2/3 phosphorylation, which was impeded by ALK5 knockdown and by activin receptor-like kinase (ALK) receptor inhibitor SB-505124, which also suppressed FSHβ expression. Smad2/3 knockdown indicated that FSHβ induction by GDF9 involved Smad2 and Smad3. FSHβ mRNA induction by GDF9 and GnRH was synergistic. We hypothesized that GDF9 contributes to a regulatory loop that tunes the GnRH frequency-response characteristics of the FSHβ gene. To test this, we determined the effects of GDF9 knockdown on FSHβ induction at different GnRH pulse frequencies using a parallel perifusion system. Reduction of GDF9 shifted the characteristic pattern of GnRH pulse frequency sensitivity. These results identify GDF9 as contributing to an incoherent feed-forward loop, comprising both intracellular and secreted components, that regulates FSHβ expression in response to activation of cell surface GnRH receptors.

A computational model to predict rat ovarian steroid secretion from in vitro experiments with endocrine disruptors

A finely tuned balance between estrogens and androgens controls reproductive functions, and the last step of steroidogenesis plays a key role in maintaining that balance. Environmental toxicants are a serious health concern, and numerous studies have been devoted to studying the effects of endocrine disrupting chemicals (EDCs). The effects of EDCs on steroidogenic enzymes may influence steroid secretion and thus lead to reproductive toxicity. To predict hormonal balance disruption on the basis of data on aromatase activity and mRNA level modulation obtained in vitro on granulosa cells, we developed a mathematical model for the last gonadal steps of the sex steroid synthesis pathway. The model can simulate the ovarian synthesis and secretion of estrone, estradiol, androstenedione, and testosterone, and their response to endocrine disruption. The model is able to predict ovarian sex steroid concentrations under normal estrous cycle in female rat, and ovarian estradiol concentrations in adult female rats exposed to atrazine, bisphenol A, metabolites of methoxychlor or vinclozolin, and letrozole.

Encoding and decoding mechanisms of pulsatile hormone secretion

Ultradian pulsatile hormone secretion underlies the activity of most neuroendocrine systems, including the hypothalamic-pituitary adrenal (HPA) and gonadal (HPG) axes, and this pulsatile mode of signalling permits the encoding of information through both amplitude and frequency modulation. In the HPA axis, glucocorticoid pulse amplitude increases in anticipation of waking, and, in the HPG axis, changing gonadotrophin-releasing hormone pulse frequency is the primary means by which the body alters its reproductive status during development (i.e. puberty). The prevalence of hormone pulsatility raises two crucial questions: how are ultradian pulses encoded (or generated) by these systems, and how are these pulses decoded (or interpreted) at their target sites? We have looked at mechanisms within the HPA axis responsible for encoding the pulsatile mode of glucocorticoid signalling that we observe in vivo. We review evidence regarding the 'hypothalamic pulse generator' hypothesis, and describe an alternative model for pulse generation, which involves steroid feedback-dependent endogenous rhythmic activity throughout the HPA axis. We consider the decoding of hormone pulsatility by taking the HPG axis as a model system and focussing on molecular mechanisms of frequency decoding by pituitary gonadotrophs.

Pituitary network connectivity as a mechanism for the luteinising hormone surge

Ovulation in vertebrates is caused by a surge of luteinising hormone (LH) from the pituitary. The LH surge is initiated by rising oestradiol concentration, although the precise mechanism of oestradiol action in humans and primates is not yet understood. Recent advances in labelling and three-dimensional imaging have revealed a rich pituitary structure of interwoven networks of different cell types. In the present study, we develop a mathematical model to test the hypothesis that oestradiol modulation of connectivity between pituitary cells can underlie the LH surge. In the model, gonadotrophin-releasing hormone (GnRH) pulses stimulate LH secretion by two independent mechanisms. The first mechanism corresponds to the well known direct action of GnRH on gonadotrophs, which is inhibited by the rising oestradiol concentration. The second mechanism of GnRH action is to stimulate a recurrent network of pituitary cells; in this case, the folliculostellate cells, which in turn stimulate LH secretion from the gonadotrophs. The network activity is modelled by a one-dimensional ordinary differential equation. The key to the LH surge in the model lies in the assumption that oestradiol modulates network connectivity. When the circulating oestradiol concentration is low, the network is barely connected, and cannot maintain a recurrent signal. When the oestradiol concentration is high, the network is highly connected, and maintains a high level of activity even after GnRH stimulation, thereby leading to a surge of LH secretion.

A dynamical model for the control of the gonadotrophin-releasing hormone neurosecretory system

The gonadotrophin-releasing hormone (GnRH) neurosecretory system involves both endocrine neurones and associated brain cells responsible for the control of GnRH release into the pituitary portal blood. Alternation between a pulsatile regime and the pre-ovulatory surge is the hallmark of GnRH secretion in ovarian cycles of female mammals. In previous studies, we have introduced a mathematical model of the pulse and surge GnRH generator and derived appropriate dynamics-based constraints on the model parameters, both to reproduce the right sequence of secretion events and to fulfil quantitative specifications on GnRH release. In the present study, we explain how these constraints amount to embedding time- and dose-dependent steroid control within the model. We further examine under which conditions the oestradiol-driven surge may be withdrawn by pre-surge progesterone administration and simulate both oestradiol and progesterone challenges in the pulsatile regime.

Bursting and calcium oscillations in pancreatic beta-cells: specific pacemakers for specific mechanisms

Oscillatory phenomenon in electrical activity and cytoplasmic calcium concentration in response to glucose are intimately connected to multiple key aspects of pancreatic β-cell physiology. However, there is no single model for oscillatory mechanisms in these cells. We set out to identify possible pacemaker candidates for burst activity and cytoplasmic Ca(2+) oscillations in these cells by analyzing published hypotheses, their corresponding mathematical models, and relevant experimental data. We found that although no single pacemaker can account for the variety of oscillatory phenomena in β-cells, at least several separate mechanisms can underlie specific kinds of oscillations. According to our analysis, slowly activating Ca(2+)-sensitive K(+) channels can be responsible for very fast Ca(2+) oscillations; changes in the ATP/ADP ratio and in the endoplasmic reticulum calcium concentration can be pacemakers for both fast bursts and cytoplasmic calcium oscillations, and cyclical cytoplasmic Na(+) changes may underlie patterning of slow calcium oscillations. However, these mechanisms still lack direct confirmation, and their potential interactions raises new issues. Further studies supported by improved mathematical models are necessary to understand oscillatory phenomena in β-cell physiology.