On the Modelling of Kainate Receptor Channels

Abstract: Kainate receptor channels are a class of ion channels found on the membrane of nerve cells. These proteins play a key role in the brain, since their properties regulate the strength of the synapses. Their structure and gating mechanisms are still extensively studied by biologists: originally closed, the channel opens upon the binding of kainate, allowing ions to flow inside the cell through the pores and creating thus an electrical current. It undergoes then a desensitization: the channel is closed even if the kainite is still bound. In this Master's Thesis, we put forward a mathematical model that reproduces both qualitatively and quantitatively the observed behaviours of kainate receptor channels. The distinctive feature of the model lies in its original framework ANC, which uses rule-based formalism to model allosteric proteins. We find that compared to traditional kinetic scheme, our model has the advantage of being scalable. We propose furthermore an alternative model. It includes a new hypothesis, namely that the ions that flow through the channel alter its gating properties. We illustrate the modularity of ANC, which enables a straightforward definition of the new model from the former, and an easy switch between these two. Our results suggest finally that this new model agrees with the biological observed behaviours of the channels.