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首页> 外文期刊>SIAM journal on applied dynamical systems >Coupled Multiple Timescale Dynamics in Populations of Endocrine Neurons: Pulsatile and Surge Patterns of GnRH Secretion
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Coupled Multiple Timescale Dynamics in Populations of Endocrine Neurons: Pulsatile and Surge Patterns of GnRH Secretion

机译：耦合多个时间尺度动态，在内分泌神经元种群中：GnRH分泌的脉动和喘振图案

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摘要

The gonadotropin-releasing hormone (GnRH) is secreted by hypothalamic neurons into the pituitary portal blood in a pulsatile manner. The alternation between a frequency-modulated pulsatile regime and the ovulatory surge is the hallmark of the GnRH secretion pattern in ovarian cycles of female mammals. In this work, we aim at modeling additional features of the GnRH secretion pattern: the possible occurrence of a two-bump surge ("camel surge") and an episode of partial desynchronization before the surge. We propose a six-dimensional extension of a former four-dimensional model with three timescales and introduce two mutually coupled, slightly heterogenous GnRH subpopulations (secretors) regulated by the same slow oscillator (regulator). We consider two types of coupling functions between the secretors, including dynamic state-dependent coupling, and we use numerical and analytic tools to characterize the coupling parameter values leading to the generation of a two bump surge in both coupling cases. We reveal the impact of the slowly varying control exerted by the regulator onto the pulsatile dynamics of the secretors, which leads to dynamic bifurcations and gives rise to desynchronization. To assess the occurrence time of desynchronization during the pulsatile phase, we introduce asymptotic tools based on quasi-static and geometric approaches, as well as analytic tools based on the H-function derived from the phase equation and numerical tracking of period-doubling bifurcations. We discuss the role of coupling parameters in the two-bump surge generation and the speed of desynchronization.
机译：促胆量释放激素（GnRH）被下丘脑神经元分泌到垂直方式中的垂体血液中。频率调制的脉动状态和排卵浪涌之间的交替是雌性哺乳动物卵巢循环中GNRH分泌模式的标志。在这项工作中，我们的目标是建模GNRH分泌模式的附加功能：在浪涌之前可能发生双凸起浪涌（“驼峰浪涌”）和部分去异步的一集。我们提出了具有三个时间尺度的前四维模型的六维延伸，并引入由相同慢振荡器（调节器）调节的两个相互耦合的略微异质的GNRH亚步骤（分泌器）。我们考虑秘密器之间的两种类型的耦合功能，包括动态状态依赖性耦合，并且我们使用数字和分析工具来表征耦合参数值，这导致耦合例中的两个凸块浪涌产生了两种凸起浪涌。我们揭示了调节器施加到分泌器的脉动动力学上的缓慢变化控制的影响，这导致动态分叉并产生了去同步。为了评估在脉动阶段期间去同步的发生时间，我们引入基于准静态和几何方法的渐近工具，以及基于来自相位方程的H函数的分析工具以及周期加倍分叉的分叉的数值跟踪。我们讨论了耦合参数在双凸起浪涌生成和去同步速度中的作用。

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