Foliation-Based Parameter Tuning in a Model of the GnRH Pulse and Surge Generator

Abstract

Le manuscrit disponible sur cette page "Clement_Vidal.ps" est une version pré-printWe investigate a model of the GnRH pulse and surge generator, with the definite aim of constraining the model GnRH output with respect to a physiologically relevant list of specifications. The alternating pulse and surge pattern of secretion results from the interaction between a GnRH secreting system and a regulating system exhibiting fast-slow dynamics. The mechanisms underlying the behavior ofInternational audienceWe investigate a model of the GnRH pulse and surge generator, with the definite aim of constraining the model GnRH output with respect to a physiologically relevant list of specifications. The alternating pulse and surge pattern of secretion results from the interaction between a GnRH secreting system and a regulating system exhibiting fast-slow dynamics. The mechanisms underlying the behavior of the model are reminded from the study of the Boundary-Layer System according to the "dissection method" principle. Using singular perturbation theory, we describe the sequence of bifurcations undergone by the regulating (FitzHugh-Nagumo) system, encompassing the rarely investigated case of homoclinic connexion. Basing on pure dynamical considerations, we restrict the space of parameter search for the regulating system and describe a foliation of this restricted space, whose leaves define constant duration ratios between the surge and the pulsatility phase in the whole system. We propose an algorithm to fix the parameter values to also meet the other prescribed ratios dealing with amplitude and frequency features of the secretion signal. We finally apply these results to illustrate the dynamics of GnRH secretion in the ovine species and the rhesus monkey

Modeling the Dynamics of Gonadotropin‐Releasing Hormone (GnRH) Secretion in the Course of an Ovarian Cycle

“…As there is good agreement between GnRH levels in cerebrospinal fluid compared to pituitary portal blood at the time of the GnRH surge (Skinner et al, 1997), we also used cerebrospinal GnRH time series to adapt the specification list to another species, the rhesus monkey (Xia et al, 1992). The algorithm procedure designed to tune the model parameters and based on pure dynamical considerations (Fenichel, 1979) has been described elsewhere (Clément and Vidal, 2009). We just discuss here the role of the parameters impacting most significantly the GnRH secretion pattern and underlying the differences observed between the ewe and the rhesus monkey.…”

Mixed-Mode Oscillations in a piecewise linear system with multiple time scale coupling

“…In [1], we considered a piecewise linear (PWL) version of the system initially proposed in [2,3], a model introduced in a context of mathematical neuroendocrinology. The original smooth model in [2,3] consists of a four dimensional (4D) system made of two coupled FitzHugh-Nagumo subsystems running on different timescales, in which the fast subsystem is forced by the slow subsystem.…”

“…The original smooth model in [2,3] consists of a four dimensional (4D) system made of two coupled FitzHugh-Nagumo subsystems running on different timescales, in which the fast subsystem is forced by the slow subsystem. We replaced in [1] the original FitzHugh-Nagumo subsystems [4,5] by two PWL equivalents (McKean caricatures [6]).…”

Multiscale modelling of endocrine systems: new insight on the gonadotrope axis

“…These specifications deal with the duration of the luteal (progesterone-dominated) and follicular (estradiol-dominated) phases of the ovarian cycle, and the ratios between (i) the surge duration and the whole cycle duration, (ii) the pulse amplitude and the surge amplitude, and (iii) the increase in pulse frequency from the luteal to the follicular phase. Basing on pure dynamical considerations, we have proposed an algorithm-like procedure to tune the model parameters subject to biologically-meaningful specifications [11]. From a more generic dynamical viewpoint, this study indirectly addresses the questions of tracking homoclinic connections, where classical Canard cycles disappear, and Bogdanov-Takens like bifurcations of Relaxation Oscillators that occur on a parameter control manifold.…”

“…The key point is that the regulating system (6c)-(6d) acts as a slow pacemaker. As soon as the parameters b 1 and b 2 are chosen small enough, the regulating system belongs to the class of Lienard systems, for which it can be proved that there exists a limit cycle when ǫ is small enough (see [11,20]). The secreting system (6a)-(6b) is part time excitable, part time fast oscillating.…”