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Voliotis M, Plain Z, Li XF, McArdle CA, O’Byrne KT, Tsaneva‐Atanasova K. Mathematical models in GnRH research. J Neuroendocrinol 2022; 34:e13085. [PMID: 35080068 PMCID: PMC9285519 DOI: 10.1111/jne.13085] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/25/2021] [Revised: 11/18/2021] [Accepted: 12/16/2021] [Indexed: 12/05/2022]
Abstract
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.
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Affiliation(s)
- Margaritis Voliotis
- Department of Mathematics and Living Systems InstituteCollege of Engineering, Mathematics and Physical SciencesUniversity of ExeterExeterUK
| | - Zoe Plain
- Department of Mathematics and Living Systems InstituteCollege of Engineering, Mathematics and Physical SciencesUniversity of ExeterExeterUK
| | - Xiao Feng Li
- Department of Women and Children’s HealthSchool of Life Course SciencesKing’s College LondonLondonUK
| | - Craig A. McArdle
- Laboratories for Integrative Neuroscience and EndocrinologySchool of Clinical SciencesUniversity of BristolBristolUK
| | - Kevin T. O’Byrne
- Department of Women and Children’s HealthSchool of Life Course SciencesKing’s College LondonLondonUK
| | - Krasimira Tsaneva‐Atanasova
- Department of Mathematics and Living Systems InstituteCollege of Engineering, Mathematics and Physical SciencesUniversity of ExeterExeterUK
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Duittoz A, Cayla X, Fleurot R, Lehnert J, Khadra A. Gonadotrophin-releasing hormone and kisspeptin: It takes two to tango. J Neuroendocrinol 2021; 33:e13037. [PMID: 34533248 DOI: 10.1111/jne.13037] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Revised: 08/25/2021] [Accepted: 08/26/2021] [Indexed: 01/06/2023]
Abstract
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.
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Affiliation(s)
- Anne Duittoz
- Physiologie de la Reproduction et des Comportements (PRC) UMR7247 INRA, CNRS, Centre INRAe Val de Loire, Université de Tours, IFCE, Nouzilly, France
| | - Xavier Cayla
- Physiologie de la Reproduction et des Comportements (PRC) UMR7247 INRA, CNRS, Centre INRAe Val de Loire, Université de Tours, IFCE, Nouzilly, France
| | - Renaud Fleurot
- Physiologie de la Reproduction et des Comportements (PRC) UMR7247 INRA, CNRS, Centre INRAe Val de Loire, Université de Tours, IFCE, Nouzilly, France
| | - Jonas Lehnert
- Department of Quantitative Life Sciences, McGill University, Montreal, QC, Canada
| | - Anmar Khadra
- Department of Quantitative Life Sciences, McGill University, Montreal, QC, Canada
- Department of Physiology, McGill University, Montréal, QC, Canada
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Lehnert J, Khadra A. How Pulsatile Kisspeptin Stimulation and GnRH Autocrine Feedback Can Drive GnRH Secretion: A Modeling Investigation. Endocrinology 2019; 160:1289-1306. [PMID: 30874725 DOI: 10.1210/en.2018-00947] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/07/2018] [Accepted: 03/09/2019] [Indexed: 02/03/2023]
Abstract
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.
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Affiliation(s)
- Jonas Lehnert
- Department of Quantitative Life Sciences, McGill University, Montreal, Quebec, Canada
| | - Anmar Khadra
- Department of Quantitative Life Sciences, McGill University, Montreal, Quebec, Canada
- Department of Physiology, McGill University, Montreal, Quebec, Canada
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A mathematical model of pulse-coded hormone signal responses in pituitary gonadotroph cells. Math Biosci 2013; 246:38-46. [PMID: 24095971 DOI: 10.1016/j.mbs.2013.09.006] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2013] [Revised: 09/09/2013] [Accepted: 09/20/2013] [Indexed: 11/23/2022]
Abstract
Cells in the pituitary that synthesize luteinizing and follicle-stimulating hormones regulate the relative production of these two key reproductive hormones in response to signals from the hypothalamus. These signals are encoded in the frequency of gonadotrophin-releasing-hormone pulses. In vitro experiments with a murine-derived cell line have identified key elements of the processes that decode the signal to regulate transcription of the subunits encoding these hormones. The mathematical model described in this paper is based on the results of those experiments and advances quantitative understanding of the biochemical decoder. The model consists of non-linear differential equations for each of six processes that lead to the synthesis of follicle-stimulating hormone. Simulations of the model exhibit key characteristics found in the experiments, including a preference for follicle-stimulating hormone synthesis at low pulse frequencies and a loss of this characteristic when a mutation is introduced.
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Alam MJ, Devi GR, Singh RKB, Ramaswamy R, Thakur SC, Sharma BI. Stochastic synchronization of interacting pathways in testosterone model. Comput Biol Chem 2012; 41:10-7. [PMID: 23131789 DOI: 10.1016/j.compbiolchem.2012.08.001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2012] [Revised: 07/13/2012] [Accepted: 08/05/2012] [Indexed: 11/26/2022]
Abstract
We examine the possibilities of various coupling mechanisms among a group of identical stochastic oscillators via Chemical Langevin formalism where each oscillator is modeled by stochastic model of testosterone (T) releasing pathway. Our results show that the rate of synchrony among the coupled oscillators depends on various parameters namely fluctuating factor, coupling constants [symbol; see text], and interestingly on system size. The results show that synchronization is achieved much faster in classical deterministic system rather than stochastic system. Then we do large scale simulation of such coupled pathways using stochastic simulation algorithm and the detection of synchrony is measured by various order parameters such as synchronization manifolds, phase plots etc and found that the proper synchrony of the oscillators is maintained in different coupling mechanisms and support our theoretical claims. We also found that the coupling constant follows power law behavior with the systems size (V) by [symbol; see text] ~ AV(-γ), where γ=1 and A is a constant. We also examine the phase transition like behavior in all coupling mechanisms that we have considered for simulation. The behavior of the system is also investigated at thermodynamic limit; where V → ∞, molecular population, N → ∞ but N/V → finite, to see the role of noise in information processing and found the destructive role in the rate of synchronization.
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Affiliation(s)
- Md Jahoor Alam
- Centre for Interdisciplinary Research in Basic Sciences, Jamia Millia Islamia, New Delhi 110025, India
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Lyles D, Tien JH, McCobb DP, Zeeman ML. Pituitary network connectivity as a mechanism for the luteinising hormone surge. J Neuroendocrinol 2010; 22:1267-78. [PMID: 20961340 DOI: 10.1111/j.1365-2826.2010.02084.x] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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.
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Affiliation(s)
- D Lyles
- Department of Environmental Science and Policy, UC Davis, Davis, CA, USA
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Vetharaniam I, Peterson A, McNatty K, Soboleva T. Modelling female reproductive function in farmed animals. Anim Reprod Sci 2010; 122:164-73. [DOI: 10.1016/j.anireprosci.2010.08.015] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2010] [Revised: 08/12/2010] [Accepted: 08/17/2010] [Indexed: 10/19/2022]
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Veldhuis JD, Keenan DM, Pincus SM. Regulation of Complex Pulsatile and Rhythmic Neuroendocrine Systems: the Male Gonadal Axis as a Prototype. PROGRESS IN BRAIN RESEARCH 2010; 181:79-110. [DOI: 10.1016/s0079-6123(08)81006-0] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
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Krsmanovic LZ, Hu L, Leung PK, Feng H, Catt KJ. The hypothalamic GnRH pulse generator: multiple regulatory mechanisms. Trends Endocrinol Metab 2009; 20:402-8. [PMID: 19740674 PMCID: PMC2769988 DOI: 10.1016/j.tem.2009.05.002] [Citation(s) in RCA: 78] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/26/2009] [Revised: 05/04/2009] [Accepted: 05/05/2009] [Indexed: 12/30/2022]
Abstract
Pulsatile secretion of gonadotropin-releasing hormone (GnRH) release is an intrinsic property of hypothalamic GnRH neurons. Pulse generation has been attributed to multiple specific mechanisms, including spontaneous electrical activity of GnRH neurons, calcium and cAMP signaling, a GnRH receptor autocrine regulatory component, a GnRH concentration-dependent switch in GnRH receptor (GnRH-R) coupling to specific G proteins, the expression of G protein-coupled receptors (GPCRs) and steroid receptors, and homologous and heterologous interactions between cell membrane receptors expressed in GnRH neurons. The coexistence of multiple regulatory mechanisms for pulsatile GnRH secretion provides a high degree of redundancy in maintaining this crucial component of the mammalian reproductive process. These studies provide insights into the basic cellular and molecular mechanisms involved in GnRH neuronal function.
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Affiliation(s)
- Lazar Z Krsmanovic
- Section on Hormonal Regulation, Program on Developmental Endocrinology and Genetics, National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD 20892, USA
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An integrated model of electrical spiking, bursting, and calcium oscillations in GnRH neurons. Biophys J 2009; 96:4514-24. [PMID: 19486674 DOI: 10.1016/j.bpj.2009.03.037] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2008] [Revised: 02/28/2009] [Accepted: 03/11/2009] [Indexed: 11/22/2022] Open
Abstract
The plasma membrane electrical activities of neurons that secrete gonadotropin-releasing hormone (GnRH) have been studied extensively. A couple of mathematical models have been developed previously to explain different aspects of these activities. The goal of this article is to develop a single model that accounts for the previously modeled experimental results and some more recent results that have not been accounted for. The latter includes two types of membrane potential bursting mechanisms and their associated cytosolic calcium oscillations. One bursting mechanism has not been reported in experiments and is thus regarded as a model prediction. Although the model is mainly based on data collected in immortalized GnRH cell lines, it is capable of explaining some properties of GnRH neurons observed in several other preparations including mature GnRH neurons in hypothalamic slices. We present a spatial model that incorporates a detailed description of calcium dynamics in a three-dimensional cell body with the ion channels evenly distributed on the cell surface. A phenomenological reduction of the spatial model into a simplified form is also presented. The simplified model will facilitate the study of the roles of plasma membrane electrical activities in the pulsatile release of GnRH.
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