A network model of the periodic synchronization process in the dynamics of calcium concentration in GnRH neurons

Sheep as a model for neuroendocrinology research

Animal models remain essential to understand the fundamental mechanisms of physiology and pathology. Particularly, the complex and dynamic nature of neuroendocrine cells of the hypothalamus make them difficult to study. The neuroendocrine systems of the hypothalamus are critical for survival and reproduction, and are highly conserved throughout vertebrate evolution. Their roles in controlling body metabolism, growth and body composition, stress, electrolyte balance, and reproduction, have been intensively studied, and have yielded groundbreaking discoveries. Many of these discoveries would not have been feasible without the use of the domestic sheep (Ovis aries). The sheep has been used for decades to study the neuroendocrine systems of the hypothalamus and has become a model for human neuroendocrinology. The aim of this chapter is to review some of the profound biomedical discoveries made possible by the use of sheep. The advantages and limitations of sheep as a neuroendocrine model will be discussed. While no animal model can perfectly recapitulate a human disease or condition, sheep are invaluable for enabling manipulations not possible in human subjects and isolating physiologic variables to garner insight into neuroendocrinology and associated pathologies.

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.

Mechanism of pulsatile GnRH release in primates: Unresolved questions

The pulsatility of GnRH release is essential for reproductive function. The key events in reproductive function, such as puberty onset and ovulatory cycles, are regulated by the frequency and amplitude modulation of pulsatile GnRH release. Abnormal patterns of GnRH pulsatility are seen in association with disease states, such as polycystic ovarian syndrome and anorexia nervosa. Recent studies with physiological, track-tracing, optogenetic and electrophysiological recording experiments indicate that a group of kisspeptin neurons in the arcuate nucleus (ARC) of the hypothalamus are responsible for pulsatile GnRH release. Thus, the kisspeptin neuron in the ARC has been called the "GnRH pulse-generator." However, a few pieces of evidence do not quite fit into this concept. This article reviews some old works and discusses unresolved issues on the mechanism of GnRH pulse generation.

Phase transitions in the multi-cellular regulatory behavior of pancreatic islet excitability

The pancreatic islets of Langerhans are multicellular micro-organs integral to maintaining glucose homeostasis through secretion of the hormone insulin. β-cells within the islet exist as a highly coupled electrical network which coordinates electrical activity and insulin release at high glucose, but leads to global suppression at basal glucose. Despite its importance, how network dynamics generate this emergent binary on/off behavior remains to be elucidated. Previous work has suggested that a small threshold of quiescent cells is able to suppress the entire network. By modeling the islet as a Boolean network, we predicted a phase-transition between globally active and inactive states would emerge near this threshold number of cells, indicative of critical behavior. This was tested using islets with an inducible-expression mutation which renders defined numbers of cells electrically inactive, together with pharmacological modulation of electrical activity. This was combined with real-time imaging of intracellular free-calcium activity [Ca²⁺]_i and measurement of physiological parameters in mice. As the number of inexcitable cells was increased beyond ∼15%, a phase-transition in islet activity occurred, switching from globally active wild-type behavior to global quiescence. This phase-transition was also seen in insulin secretion and blood glucose, indicating physiological impact. This behavior was reproduced in a multicellular dynamical model suggesting critical behavior in the islet may obey general properties of coupled heterogeneous networks. This study represents the first detailed explanation for how the islet facilitates inhibitory activity in spite of a heterogeneous cell population, as well as the role this plays in diabetes and its reversal. We further explain how islets utilize this critical behavior to leverage cellular heterogeneity and coordinate a robust insulin response with high dynamic range. These findings also give new insight into emergent multicellular dynamics in general which are applicable to many coupled physiological systems, specifically where inhibitory dynamics result from coupled networks.

As science has successfully broken down the elements of many biological systems, the network dynamics of large-scale cellular interactions has emerged as a new frontier. One way to understand how dynamical elements within large networks behave collectively is via mathematical modeling. Diabetes, which is of increasing international concern, is commonly caused by a deterioration of these complex dynamics in a highly coupled micro-organ called the islet of Langerhans. Therefore, if we are to understand diabetes and how to treat it, we must understand how coupling affects ensemble dynamics. While the role of network connectivity in islet excitation under stimulatory conditions has been well studied, how connectivity also suppresses activity under fasting conditions remains to be elucidated. Here we use two network models of islet connectivity to investigate this process. Using genetically altered islets and pharmacological treatments, we show how suppression of islet activity is solely dependent on a threshold number of inactive cells. We found that the islet exhibits critical behavior in the threshold region, rapidly transitioning from global activity to inactivity. We therefore propose how the islet and multicellular systems in general can generate a robust stimulated response from a heterogeneous cell population.