Coupled multiple timescale dynamics in populations of endocrine neurons: Pulsatile and surge patterns of GnRH secretion

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 timescale 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 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.