The plasma membrane electrical activities of neurons that secrete gonadotropin releasing hormone (GnRH), referred to as GnRH neurons hereafter, have been studied extensively. A couple of mathematical models have been developed previously to explain different aspects of these activities including spontaneous spiking and responses to stimuli such as current injections, GnRH, thapsigargin (Tg) and apamin. The goal of this paper is to develop one single, minimal model that accounts for the experimental results reproduced by previously existing models and results that were not accounted for by these models. The latter includes two types of membrane potential bursting mechanisms and the associated calcium oscillations in the cytosol. One of them has not been reported in experimental literatures on GnRH neurons and is thus regarded as a model prediction. Other improvements achieved in this model include the incorporation of a more detailed description of calcium dynamics in a three dimensional cell body with the ion channels evenly distributed on the cell surface. Although the model is mainly based on data collected in cultured GnRH cell lines, we show that it is capable of explaining some properties of GnRH neurons observed in several of other preparations including mature GnRH neurons in hypothalamic slices. One potential explanation is suggested. A phenomenological reduction of this model into a simplified form is presented. The simplified model will facilitate the study of the roles of plasma membrane electrical activities on the pulsatile release of GnRH by these neurons when it is coupled with a model of pulsatile GnRH release based on the autoregulation mechanism.

The plasma membrane electrical activities of neurons that secrete gonadotropin releasing hormone (GnRH), referred to as GnRH neurons hereafter, have been studied extensively. A couple of mathematical models have been developed previously to explain different aspects of these activities including spontaneous spiking and responses to stimuli such as current injections, GnRH, thapsigargin (Tg) and apamin. The goal of this paper is to develop one single, minimal model that accounts for the experimental results reproduced by previously existing models and results that were not accounted for by these models. The latter includes two types of membrane potential bursting mechanisms and the associated calcium oscillations in the cytosol. One of them has not been reported in experimental literatures on GnRH neurons and is thus regarded as a model prediction. Other improvements achieved in this model include the incorporation of a more detailed description of calcium dynamics in a three dimensional cell body with the ion channels evenly distributed on the cell surface. Although the model is mainly based on data collected in cultured GnRH cell lines, we show that it is capable of explaining some properties of GnRH neurons observed in several of other preparations including mature GnRH neurons in hypothalamic slices. One potential explanation is suggested. A phenomenological reduction of this model into a simplified form is presented. The simplified model will facilitate the study of the roles of plasma membrane electrical activities on the pulsatile release of GnRH by these neurons when it is coupled with a model of pulsatile GnRH release based on the autoregulation mechanism.

The plasma membrane electrical activities of neurons that secrete gonadotropin releasing hormone (GnRH), referred to as GnRH neurons hereafter, have been studied extensively. A couple of mathematical models have been developed previously to explain different aspects of these activities including spontaneous spiking and responses to stimuli such as current injections, GnRH, thapsigargin (Tg) and apamin. The goal of this paper is to develop one single, minimal model that accounts for the experimental results reproduced by previously existing models and results that were not accounted for by these models. The latter includes two types of membrane potential bursting mechanisms and the associated calcium oscillations in the cytosol. One of them has not been reported in experimental literatures on GnRH neurons and is thus regarded as a model prediction. Other improvements achieved in this model include the incorporation of a more detailed description of calcium dynamics in a three dimensional cell body with the ion channels evenly distributed on the cell surface. Although the model is mainly based on data collected in cultured GnRH cell lines, we show that it is capable of explaining some properties of GnRH neurons observed in several of other preparations including mature GnRH neurons in hypothalamic slices. One potential explanation is suggested. A phenomenological reduction of this model into a simplified form is presented. The simplified model will facilitate the study of the roles of plasma membrane electrical activities on the pulsatile release of GnRH by these neurons when it is coupled with a model of pulsatile GnRH release based on the autoregulation mechanism. / Science, Faculty of / Mathematics, Department of / Graduate