Mathematical modeling of perifusion cell culture experiments on GnRH signaling

The effects of pulsatile GnRH stimulation on anterior pituitary cells are studied using perifusion cell cultures, where constantly moving culture medium over the immobilized cells allows intermittent GnRH delivery. The LH content of the outgoing medium serves as a readout of the GnRH signaling pathway activation in the cells. The challenge lies in relating the LH content of the medium leaving the chamber to the cellular processes producing LH secretion. To investigate this relation we developed and analyzed a mathematical model consisting of coupled partial differential equations describing LH secretion in a perifusion cell culture. We match the mathematical model to three different data sets and give cellular mechanisms that explain the data. Our model illustrates the importance of the negative feedback in the signaling pathway and receptor desensitization. We demonstrate that different LH outcomes in oxytocin and GnRH stimulations might originate from different receptor dynamics and concentration. We analyze the model to understand the influence of parameters, like the velocity of the medium flow or the fraction collection time, on the LH outcomes. We show that slow velocities lead to high LH outcomes. Also, we show that fraction collection times, which do not divide the GnRH pulse period evenly, lead to irregularities in the data. We examine the influence of the rate of binding and dissociation of GnRH on the GnRH movement down the chamber. Our model serves as an important tool that can help in the design of perifusion experiments and the interpretation of results.