A mathematical model analyzing temperature threshold dependence in cold sensitive neurons

Here we examine a class of neurons that have been recently explored, the somatosensory neuronal subclass of cold thermosensors. We create a mathematical model of a cold sensing neuron that has been formulated to understand the variety of ionic channels involved. In particular this model showcases the role of TRPM8 and voltage gated potassium channels in setting the temperature dependent activation and inactivation threshold level. Bifurcation analysis of the model demonstrates that a Hodgkin-Huxley type model with additional TRPM8 channels is sufficient to replicate observable experimental features of when different threshold level cold thermosensors turn on. Additionally, our analysis gives insight into what is happening at the temperature levels at which these neurons shut off and the role sodium and leak currents may have in this. This type of model construction and analysis provides a framework moving forward that will help tackle less well understood neuronal classes and their important ionic channels.