Mathematical exploration of pulsatility in cultured gonadotropin-releasing hormone neurons

Pulsatile gonadotropin-releasing hormone (GnRH) release has been demonstrated in cultures of an immortalized line of GnRH expressing neurons (GT1 cells) in experiments by four different research groups. Pulsatile release is known to play a crucial role in GnRH-mediated signaling in vivo, and thus deserves theoretical and quantitative consideration, especially as GT1 cells are presumably genetically homogeneous. Here we have modeled idealized GT1 cells with a differential equation/logic based modeling program, Stella II. We have created a network of 'neurons', with randomized (within the same preset limits for each neuron) thresholds, number and weight of connections to other neurons, and build-up of signal; as well as continuous decay of stored signal. Surprisingly, we found that with this minimal set of assumptions, without any sort of predefined pacemaking cells, it is possible to create pulsatility similar to that observed in the laboratory. A variety of different parameter sets was found to produce these pulses. Network behaviors similar to those of GT1 cells depended on the degree of interconnection between neurons and their functioning within a critical range of network excitability. These findings allow for a clearer consideration of the critical elements of such networks as well as experimental predictions regarding the production of pulsatile behavior.