A unified model for two modes of bursting in GnRH neurons

Estradiol elicits distinct firing patterns in arcuate nucleus kisspeptin neurons of females through altering ion channel conductances

Hypothalamic kisspeptin (Kiss1) neurons are vital for pubertal development and reproduction. Arcuate nucleus Kiss1 (Kiss1ARH) neurons are responsible for the pulsatile release of Gonadotropin-releasing Hormone (GnRH). In females, the behavior of Kiss1ARH neurons, expressing Kiss1, Neurokinin B (NKB), and Dynorphin (Dyn), varies throughout the ovarian cycle. Studies indicate that 17β-estradiol (E2) reduces peptide expression but increases Vglut2 mRNA and glutamate neurotransmission in these neurons, suggesting a shift from peptidergic to glutamatergic signaling. To investigate this shift, we combined transcriptomics, electrophysiology, and mathematical modeling. Our results demonstrate that E2 treatment upregulates the mRNA expression of voltage-activated calcium channels, elevating the whole-cell calcium current and that contribute to high-frequency burst firing. Additionally, E2 treatment decreased the mRNA levels of Canonical Transient Receptor Potential (TPRC) 5 and G protein-coupled K+ (GIRK) channels. When TRPC5 channels in Kiss1ARH neurons were deleted using CRISPR, the slow excitatory postsynaptic potential (sEPSP) was eliminated. Our data enabled us to formulate a biophysically realistic mathematical model of the Kiss1ARH neuron, suggesting that E2 modifies ionic conductances in Kiss1ARH neurons, enabling the transition from high frequency synchronous firing through NKB-driven activation of TRPC5 channels to a short bursting mode facilitating glutamate release. In a low E2 milieu, synchronous firing of Kiss1ARH neurons drives pulsatile release of GnRH, while the transition to burst firing with high, preovulatory levels of E2 would facilitate the GnRH surge through its glutamatergic synaptic connection to preoptic Kiss1 neurons.

Deconstructing sex: Strategies for undoing binary thinking in neuroendocrinology and behavior

The scientific community widely recognizes that "sex" is a complex category composed of multiple physiologies. Yet in practice, basic scientific research often treats "sex" as a single, internally consistent, and often binary variable. This practice occludes important physiological factors and processes, and thus limits the scientific value of our findings. In human-oriented biomedical research, the use of simplistic (and often binary) models of sex ignores the existence of intersex, trans, non-binary, and gender non-conforming people and contributes to a medical paradigm that neglects their needs and interests. More broadly, our collective reliance on these models legitimizes a false paradigm of human biology that undergirds harmful medical practices and anti-trans political movements. Herein, we continue the conversations begun at the SBN 2022 Symposium on Hormones and Trans Health, providing guiding questions to help scientists deconstruct and rethink the use of "sex" across the stages of the scientific method. We offer these as a step toward a scientific paradigm that more accurately recognizes and represents sexed physiologies as multiple, interacting, variable, and unbounded by gendered preconceptions. We hope this paper will serve as a useful resource for scientists who seek a new paradigm for researching and understanding sexed physiologies that improves our science, widens the applicability of our findings, and deters the misuse of our research against marginalized groups.

Characterizing spontaneous Ca2+ local transients in OPCs using computational modeling

Spontaneous Ca2+ local transients (SCaLTs) in isolated oligodendrocyte precursor cells are largely regulated by the following fluxes: store-operated Ca2+ entry (SOCE), Na+/Ca2+ exchange, Ca2+ pumping through Ca2+-ATPases, and Ca2+-induced Ca2+-release through ryanodine receptors and inositol-trisphosphate receptors. However, the relative contributions of these fluxes in mediating fast spiking and the slow baseline oscillations seen in SCaLTs remain incompletely understood. Here, we developed a stochastic spatiotemporal computational model to simulate SCaLTs in a homogeneous medium with ionic flow between the extracellular, cytoplasmic, and endoplasmic-reticulum compartments. By simulating the model and plotting both the histograms of SCaLTs obtained experimentally and from the model as well as the standard deviation of inter-SCaLT intervals against inter-SCaLT interval averages of multiple model and experimental realizations, we revealed the following: (1) SCaLTs exhibit very similar characteristics between the two data sets, (2) they are mostly random, (3) they encode information in their frequency, and (4) their slow baseline oscillations could be due to the stochastic slow clustering of inositol-trisphosphate receptors (modeled as an Ornstein-Uhlenbeck noise process). Bifurcation analysis of a deterministic temporal version of the model showed that the contribution of fluxes to SCaLTs depends on the parameter regime and that the combination of excitability, stochasticity, and mixed-mode oscillations are responsible for irregular spiking and doublets in SCaLTs. Additionally, our results demonstrated that blocking each flux reduces SCaLTs' frequency and that the reverse (forward) mode of Na+/Ca2+ exchange decreases (increases) SCaLTs. Taken together, these results provide a quantitative framework for SCaLT formation in oligodendrocyte precursor cells.

Modelling KNDy neurons and gonadotropin-releasing hormone pulse generation

The pulsatile release of gonadotropin-releasing hormone (GnRH) and its frequency are crucial for healthy reproductive function. To understand what drives GnRH pulses, a combination of experimental and mathematical modelling approaches has been used. Early work focussed on the possibility that GnRH pulse generation is an intrinsic feature of GnRH neurons, with autocrine feedback generating pulsatility. However, there is now ample evidence suggesting that a network of upstream neurons secreting kisspeptin, neurokinin-B and dynorphin are the source of this GnRH pulse generator. The interplay of slow positive and negative feedback via neurokinin-B and dynorphin, respectively, allows the network to act as a relaxation oscillator, driving pulsatile secretion of kisspeptin, and consequently, of GnRH and LH. Here, we review the mathematical modelling approaches exploring both scenarios and suggest that with pulsatile GnRH secretion driven by the KNDy pulse generator, autocrine feedback still has the potential to modulate GnRH output.

How does apelin affect LH levels? An investigation at the level of GnRH and KNDy neurons

Hypothalamic control of reproduction relies on GnRH and kisspeptin (KP) secretions. KP neurons are sensitive to sex steroids and metabolic status and their distribution overlaps with neurons producing apelin, a metabolic hormone known to decrease LH secretion in rats. Here, we observed neuroanatomical contacts between apelin fibers and both KP and GnRH neurons in the hypothalamus of male rodents. Intracerebroventricular apelin infusion for 2 weeks in male mice did not decrease LH levels nor did it affect gene expression for KP, neurokinin B and dynorphin. Finally, increasing apelin concentrations did not modulate Ca²⁺ levels of cultured GnRH neurons, while 10 μM apelin infusion on forskolin pretreated GnRH neurons revoked a rhythmic activity in 18% of GnRH neurons. These results suggest that acute apelin effect on LH secretion does not involve modulation of gene expression in KP neurons but may affect the secretory activity of GnRH neurons.

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.

Gonadotrophin-releasing hormone and kisspeptin: It takes two to tango

Kisspeptin (Kp), a family of peptides comprising products of the Kiss1 gene, was discovered 20 years ago; it is recognised as the major factor controlling the activity of the gonadotrophin-releasing hormone (GnRH) neurones and thus the activation of the reproductive axis in mammals. It has been widely documented that the effects of Kp on reproduction through its action on GnRH neurones are mediated by the GPR54 receptor. Kp controls the activation of the reproductive axis at puberty, maintains reproductive axis activity in adults and is involved in triggering ovulation in some species. Although there is ample evidence coming from both conditional knockout models and conditional-induced Kp neurone death implicating the Kp/GPR54 pathway in the control of reproduction, the mechanism(s) underlying this process may be more complex than a sole direct control of GnRH neuronal activity by Kp. In this review, we provide an overview of the recent advances made in elucidating the interplay between Kp- and GnRH- neuronal networks with respect to regulating the reproductive axis. We highlight the existence of a possible mutual regulation between GnRH and Kp neurones, as well as the implication of Kp-dependent volume transmission in this process. We also discuss the capacity of heterodimerisation between GPR54 and GnRH receptor (GnRH-R) and its consequences on signalling. Finally, we illustrate the role of mathematical modelling that accounts for the synergy between GnRH-R and GPR54 in explaining the role of these two receptors when defining GnRH neuronal activity and GnRH pulsatile release.

Bursting in cerebellar stellate cells induced by pharmacological agents: Non-sequential spike adding

Cerebellar stellate cells (CSCs) are spontaneously active, tonically firing (5-30 Hz), inhibitory interneurons that synapse onto Purkinje cells. We previously analyzed the excitability properties of CSCs, focusing on four key features: type I excitability, non-monotonic first-spike latency, switching in responsiveness and runup (i.e., temporal increase in excitability during whole-cell configuration). In this study, we extend this analysis by using whole-cell configuration to show that these neurons can also burst when treated with certain pharmacological agents separately or jointly. Indeed, treatment with 4-Aminopyridine (4-AP), a partial blocker of delayed rectifier and A-type K⁺ channels, at low doses induces a bursting profile in CSCs significantly different than that produced at high doses or when it is applied at low doses but with cadmium (Cd²⁺), a blocker of high voltage-activated (HVA) Ca²⁺ channels. By expanding a previously revised Hodgkin–Huxley type model, through the inclusion of Ca²⁺-activated K⁺ (K(Ca)) and HVA currents, we explain how these bursts are generated and what their underlying dynamics are. Specifically, we demonstrate that the expanded model preserves the four excitability features of CSCs, as well as captures their bursting patterns induced by 4-AP and Cd²⁺. Model investigation reveals that 4-AP is potentiating HVA, inducing square-wave bursting at low doses and pseudo-plateau bursting at high doses, whereas Cd²⁺ is potentiating K(Ca), inducing pseudo-plateau bursting when applied in combination with low doses of 4-AP. Using bifurcation analysis, we show that spike adding in square-wave bursts is non-sequential when gradually changing HVA and K(Ca) maximum conductances, delayed Hopf is responsible for generating the plateau segment within the active phase of pseudo-plateau bursts, and bursting can become “chaotic” when HVA and K(Ca) maximum conductances are made low and high, respectively. These results highlight the secondary effects of the drugs applied and suggest that CSCs have all the ingredients needed for bursting.

Excitable cells, including neurons, fire action potentials (APs) in their membrane voltage that allow them to communicate with each other and to serve certain physiological purposes. They do so either tonically by firing APs periodically, or episodically by repeatedly firing clusters of APs (called bursts) separated by quiescent periods. Each one of those firing patterns can be neuron-specific and dependent on synaptic inputs and/or their physiological environment. Cerebellar stellate cells (CSCs) that synapse onto Purkinje cells, the sole output of the cerebellum responsible for motor control, are spontaneously active inhibitory interneurons that fire APs tonically. We previously studied the excitability properties of these neurons and showed that they possess several important key features, including type I excitability, runup, non-monotonic first spike latency and switching in responsiveness. In this study, we show that CSCs can also exhibit two modes of burst firing, called square-wave and pseudo-plateau, when treated with certain pharmacological agents. Using bifurcation theory, we demonstrate that spike adding in the square-wave burst is non-sequential, changing by several spikes when certain conductances are altered gradually. This study thus sheds lights onto the overall effects of the pharmacological agents and highlights the ability of CSCs to burst in certain biological conditions.

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.

How Pulsatile Kisspeptin Stimulation and GnRH Autocrine Feedback Can Drive GnRH Secretion: A Modeling Investigation

Pulsatile secretion of GnRH from hypothalamic GnRH neurons tightly regulates the release of mammalian reproductive hormones. Although key factors such as electrical activity and stimulation by kisspeptin have been extensively studied, the underlying mechanisms that regulate GnRH release are still not fully understood. Previously developed mathematical models studied hormonal release and electrical properties of GnRH neurons separately, but they never integrated both components. Herein, we present a more complete biophysical model to investigate how electrical activity and hormonal release interact. The model consists of two components: an electrical submodel comprised of a modified Izhikevich formalism incorporating several key ionic currents to reproduce GnRH neuronal bursting behavior, and a hormonal submodel that incorporates pulsatile kisspeptin stimulation and a GnRH autocrine feedback mechanism. Using the model, we examine the electrical activity of GnRH neurons and how kisspeptin affects GnRH pulsatility. The model reproduces the noise-driven bursting behavior of GnRH neurons as well as the experimentally observed electrophysiological effects induced by GnRH and kisspeptin. Specifically, the model reveals that external application of GnRH causes a transient hyperpolarization followed by an increase in firing frequency, whereas administration of kisspeptin leads to long-lasting depolarization of the neuron. The model also shows that GnRH release follows a pulsatile profile similar to that observed experimentally and that kisspeptin and GnRH exhibit ∼7-1 locking in their pulsatility. These results suggest that external kisspeptin stimulation with a period of ∼8 minutes drives the autocrine mechanism beyond a threshold to generate pronounced GnRH pulses every hour.

Changes in Both Neuron Intrinsic Properties and Neurotransmission Are Needed to Drive the Increase in GnRH Neuron Firing Rate during Estradiol-Positive Feedback

Central output of gonadotropin-releasing hormone (GnRH) neurons controls fertility and is sculpted by sex-steroid feedback. A switch of estradiol action from negative to positive feedback initiates a surge of GnRH release, culminating in ovulation. In ovariectomized mice bearing constant-release estradiol implants (OVX+E), GnRH neuron firing is suppressed in the morning (AM) by negative feedback and activated in the afternoon (PM) by positive feedback; no time-of-day-dependent changes occur in OVX mice. In this daily surge model, GnRH neuron intrinsic properties are shifted to favor increased firing during positive feedback. It is unclear whether this shift and the observed concomitant increase in GABAergic transmission, which typically excites GnRH neurons, are independently sufficient for increasing GnRH neuron firing rate during positive feedback or whether both are needed. To test this, we used dynamic clamp to inject selected previously recorded trains of GABAergic postsynaptic conductances (PSgs) collected during the different feedback states of the daily surge model into GnRH neurons from OVX, OVX+E AM, and OVX+E PM mice. PSg trains mimicking positive feedback initiated more action potentials in cells from OVX+E PM mice than negative feedback or OVX (open feedback loop) trains in all three animal models, but the positive-feedback train was most effective when applied to cells during positive feedback. In silico studies of model GnRH neurons in which >1000 PSg trains were tested exhibited the same results. These observations support the hypothesis that GnRH neurons integrate fast-synaptic and intrinsic changes to increase firing rates during positive feedback.SIGNIFICANCE STATEMENT Infertility affects 15%-20% of couples; failure to ovulate is a common cause. Understanding how the brain controls ovulation is critical for new developments in both infertility treatment and contraception. Ovarian estradiol alters both the intrinsic properties of gonadotropin-releasing hormone (GnRH) neurons and synaptic inputs to these cells coincident with production of sustained GnRH release that ultimately triggers ovulation. We demonstrate here using dynamic clamp and mathematical modeling that estradiol-induced shifts in synaptic transmission alone can increase firing output, but that the intrinsic properties of GnRH neurons during positive feedback further poise these cells for increased response to higher frequency synaptic transmission. These data suggest that GnRH neurons integrate fast-synaptic and intrinsic changes to increase firing rates during the preovulatory GnRH surge.

Gonadotropin-Releasing Hormone (GnRH) Neuron Excitability Is Regulated by Estradiol Feedback and Kisspeptin

Gonadotropin-releasing hormone (GnRH) neurons produce the central output controlling fertility and are regulated by steroid feedback. A switch from estradiol negative to positive feedback initiates the GnRH surge, ultimately triggering ovulation. This occurs on a daily basis in ovariectomized, estradiol-treated (OVX+E) mice; GnRH neurons are suppressed in the morning and activated in the afternoon. To test the hypotheses that estradiol and time of day signals alter GnRH neuron responsiveness to stimuli, GFP-identified GnRH neurons in brain slices from OVX+E or OVX female mice were recorded during the morning or afternoon. No differences were observed in baseline membrane potential. Current-clamp revealed GnRH neurons fired more action potentials in response to current injection during positive feedback relative to all other groups, which were not different from each other despite reports of differing ionic conductances. Kisspeptin increased GnRH neuron response in cells from OVX and OVX+E mice in the morning but not afternoon. Paradoxically, excitability in kisspeptin knock-out mice was similar to the maximum observed in control mice but was unchanged by time of day or estradiol. A mathematical model applying a Markov Chain Monte Carlo method to estimate probability distributions for estradiol- and time of day-dependent parameters was used to predict intrinsic properties underlying excitability changes. A single identifiable distribution of solutions accounted for similar GnRH neuron excitability in all groups other than positive feedback despite different underlying conductance properties; this was attributable to interdependence of voltage-gated potassium channel properties. In contrast, redundant solutions may explain positive feedback, perhaps indicative of the importance of this state for species survival.SIGNIFICANCE STATEMENT Infertility affects 15%-20% of couples; failure to ovulate is a common cause. Understanding how the brain controls ovulation is critical for new developments in both infertility treatment and contraception. Gonadotropin-releasing hormone (GnRH) neurons are the final common pathway for central neural control of ovulation. We studied how estradiol feedback regulates GnRH excitability, a key determinant of neural firing rate using laboratory and computational approaches. GnRH excitability is upregulated during positive feedback, perhaps driving increased neural firing rate at this time. Kisspeptin increased GnRH excitability and was essential for estradiol regulation of excitability. Modeling predicts that multiple combinations of changes to GnRH intrinsic conductances can produce the firing response in positive feedback, suggesting the brain has many ways to induce ovulation.