Abstract
Mathematical neuroendocrinology is a branch of mathematical neurosciences that is specifically interested in endocrine neurons, which have the uncommon ability of secreting neurohormones into the blood. One of the most striking features of neuroendocrine networks is their ability to exhibit very slow rhythms of neurosecretion, on the order of one or several hours. A prototypical instance is that of the pulsatile secretion pattern of GnRH (gonadotropin releasing hormone), the master hormone controlling the reproductive function, whose origin remains a puzzle issue since its discovery in the seventies. In this paper, we investigate the question of GnRH neuron synchronization on a mesoscopic scale, and study how synchronized events in calcium dynamics can arise from the average electric activity of individual neurons. We use as reference seminal experiments performed on embryonic GnRH neurons from rhesus monkeys, where calcium imaging series were recorded simultaneously in tens of neurons, and which have clearly shown the occurrence of synchronized calcium peaks associated with GnRH pulses, superposed on asynchronous, yet oscillatory individual background dynamics. We design a network model by coupling 3D individual dynamics of FitzHugh–Nagumo type. Using phase-plane analysis, we constrain the model behavior so that it meets qualitative and quantitative specifications derived from the experiments, including the precise control of the frequency of the synchronization episodes. In particular, we show how the time scales of the model can be tuned to fit the individual and synchronized time scales of the experiments. Finally, we illustrate the ability of the model to reproduce additional experimental observations, such as partial recruitment of cells within the synchronization process or the occurrence of doublets of synchronization.
Highlights
GnRH plays a prominent role in the control of reproductive processes in mammals
GnRH neurons are sparsely located in the hypothalamus, they all have an extracerebral origin in the nasal placode, where they develop and from where they migrate to the brain during the development of the embryo
We have presented a network model capable of reproducing the salient features of calcium oscillations that were observed by Terasawa and coworkers [3,4,5] in their experiments on GnRH neurons in placode cultures
Summary
GnRH (gonadotropin releasing hormone) plays a prominent role in the control of reproductive processes in mammals. We introduce a three-dimensional model based on the FitzHugh–Nagumo system that reproduces the average electric activity and the intracellular calcium oscillations in individual neurons This model has a mathematical structure that makes it possible to explain, study and control the dynamics by means of phase plane analysis. Our model is inspired by the work of [16], who considered the so-called PING model of gamma oscillations, consisting of a population of excitatory cells and a population of interneurons, with the interneurons delivering inhibition simultaneously to all excitatory cells, creating a synchronizing effect We have adapted this idea to the context of our model, creating a global variable which would have a similar, strong effect on all the members of the population, giving rise to a synchronous calcium peak. We show how to mimic partial recruitment of the cells in the synchronization episodes and how to reproduce synchronization doublets
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