Mathematical modelling elucidates core mechanisms underpinning GnRH pulse generation

Abstract

Reproduction critically depends on the pulsatile secretion of gonadotrophin-releasing hormone (GnRH) from the hypothalamus. This ultradian rhythm drives the secretion of gonadotrophic hormones (LH and FSH) from the pituitary gland, which are critical for gametogenesis and ovulation, and its frequency is regulated throughout the life course to maintain normal reproductive health. However, the precise mechanisms controlling the pulsatile GnRH dynamics are unknown. Here, we propose and study a novel mathematical model of a population of neurones in the arcuate nucleus (ARC) of the hypothalamus that co-expresses three key modulators of GnRH secretion: kisspeptin; neurokinin B (NKB); and dynorphin (Dyn). The model highlights that positive feedback in the population exerted by NKB and negative feedback mediated by Dyn are the two key components of the pulse generator, which operates as a relaxation oscillator.Furthermore, we use the model to study how external inputs modulate the frequency of 1 peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission.The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/245548 doi: bioRxiv preprint first posted online Jan. 12, 2018; the pulse generator, a prediction that can be readily tested in-vivo using optogeneticallydriven stimulation. Finally, our model predicts the response of the system to various neuropharmacological perturbations and reconciles inconsistent experimental observations following such interventions in-vivo. We anticipate that our model in combination with cutting-edge, in-vivo techniques, allowing for neuronal stimulation and recording, will set the stage for a quantitative, system-level understanding of the GnRH pulse generator.

Mathematical Modelling of Endocrine Systems

“…Furthermore, the model predicts that pulsatile dynamics depend on basal activity levels in the kisspeptin population and highlights the tipping-point behaviour of the system as basal activity increases. Using optogenetics, these model predictions were confirmed in vivo , showing that pulses can be directly controlled in oestrous mice by selectively exciting kisspeptin neurons in the arcuate nucleus with continuous low-frequency (1 Hz and 5 Hz) light stimulation [64] . Thus, this is yet another example of how even simple phenomenological models can lead to useful and experimentally testable insights.…”

“…Gonadotropins act on the gonads, initiating processes involved in gametogenesis and ovulation and triggering the release of sex steroids (oestradiol, testosterone, progesterone) that feedback on the brain and pituitary gland to modulate GnRH and LH/FSH secretion dynamics. Mathematical models [64] have offered insight into how hypothalamic neurons coexpressing kisspeptin, neurokinin-B, and dynorphin control the pulsatile dynamics of GnRH secretion and how these pulsatile signals are decoded by single cells at the pituitary gland. …”

“…At the level of the hypothalamus, a coarse-grained neuronal population model has advanced our understanding of how GnRH pulsatility is sustained and regulated [64] . The model draws on recent experimental work, which demonstrates the pivotal role of neuropeptide signalling within the arcuate nucleus kisspeptin population for GnRH pulse generation 65 , 66 .…”

Cell Networks in Endocrine/Neuroendocrine Gland Function

“…Moreover, a huge effort in mathematical analysis and modelling has been devoted to these hormonal profiles giving a classification of gender differences and hormone diseases with regard to GH profile parameters (e.g. pulse and nadir characteristics, approximate entropy inversely correlated to regularity, etc) (430), and providing theoretical regulatory loops of the hypothalamic-pituitary-adrenal axis (439) and hypothalamic-pituitarygonadal axis (436). Second, recent developments of high-sensitive ELISA assays for murine pituitary hormones (GH, PRL and LH) combined with frequent tail-tip blood micro-sampling (a couple of µl every few minutes) now make pituitary hormone profiles in mice possible, including with the use of the wide variety of genetically-modified mouse models available worldwide (162).…”