Mathematical Model for TRPM8 Dynamics in Cold Sensory Neurons

The primary channel responsible for cold thermo-transduction in mammals is the transient receptor potential melastatin 8 (TRPM8) channel. TRPM8 is a polymodal, nonselective cation channel with an activation that is dependent on a variety of signals, including the membrane potential, calcium concentration, temperature, and ligands such as menthol. Mathematical modeling provides valuable insight into biochemical phenomena, such as the activity of these channels, which are difficult to observe experimentally. Here, we propose a TRPM8 gating model, represented as a system of ordinary differential equations with menthol, calcium, voltage, and temperature dependencies. We use voltage-clamp data from transfected HEK293 cells in the presence of menthol to create a menthol-dependent voltage shift of activation. We fit the parameters of the TRPM8 gating model to replicate experimental TRPM8 transfected HEK293 cell voltage clamp electrophysiology data using a genetic algorithm. Using k-means clustering, we note eight clusters within 110 total parameter sets consisting of parameter solutions that provide a good fit to the experimental data. We then replicate novel fixed-voltage temperature ramp and fixed-temperature voltage ramp experimental data, demonstrating that our model can replicate the dynamic behaviors of TRPM8. With this TRPM8 gating model, we analyze the various parameter sets obtained from the genetic algorithm and find that different parameter combinations of calcium decay, calcium voltage shift of activation, and temperature sensitivity are able to match static voltage clamp data although differ in their effects on hysteresis and maximal current within prolonged temperature ramp simulations.