A simple integrative electrophysiological model of bursting GnRH neurons

Abstract

In this paper a modular model of the GnRH neuron is presented. For the aim of simplicity, the currents corresponding to fast time scales and action potential generation are described by an impulsive system, while the slower currents and calcium dynamics are described by usual ordinary differential equations (ODEs). The model is able to reproduce the depolarizing afterpotentials, afterhyperpolarization, periodic bursting behavior and the corresponding calcium transients observed in the case of GnRH neurons.

A unified model for two modes of bursting in GnRH neurons

“…Some previous models of the GnRH neuron assume compartmental calcium dynamics (LeBeau et al 2000; Duan et al 2011; Csercsik et al 2012) but in order to minimize the number of free parameters, a single compartment model was used here. The Ca 2+ submodel assumes influx of Ca 2+ through voltage-gated calcium channels and efflux of Ca 2+ via membrane pumps.…”

“…To date, no other published models for the GnRH neuron have captured both modes of bursting, while keeping the set of kinetic parameters for ionic currents invariant. The model developed for this study extends previous bursting models (LeBeau et al 2000; Fletcher and Li 2009; Duan et al 2011; Csercsik et al 2012) by using an updated set of ionic currents that are based on more recent electrophysiological data. The new set of currents includes the previously excluded I A and I h , as well as updates to the delayed rectifier potassium current I K , the high-voltage activated calcium current I HVA , and the fast and persistent sodium currents I NaF / I NaP .…”

A Mathematical Model of Gonadotropin‐Releasing Hormone Neurons

“…Possibly the most comprehensive model to date of GnRH neurons in vivo is that of Csercsik et al (2012). They incorporated the earlier models of van Goor and LeBeau with the later model of Lee et al (2010) to provide a single integrated model that reproduced the shape of the action potentials in detail, as well as incorporating the mechanisms that controlled burst length and interburst interval.…”

“…The earlier models of Van and LeBeau et al (2000), as well as the model of Fletcher and Li (2009), are based on data from GT1 cells, while the later models of Roberts and Suter (Roberts et al, 2006(Roberts et al, , 2008bRoberts and Suter, 2008), Csercsik et al (2012), and Lee et al (2010) are based on data from hypothalamic slices, and are, thus, presumably, more applicable to GnRH neurons in vivo. Nevertheless, the later models still rely to a large extent on the earlier modeling work based on GT1 cells, as there are few detailed measurements of electrophysiological parameters of the ion channels in GnRH neurons in brain slices.…”

“…• In the same vein, neither our original full model, nor the simplified model presented here, provide an accurate quantitative description of the action potentials. For a model that does a better job in this respect, the reader is referred to the work of Roberts and Suter (2008) or Csercsik et al (2012). Although such quantitative accuracy is not necessary for the questions we pose here, the differences between our model and the data may well yet prove to be important, and should not be forgotten.…”