Mathematical Modeling of TRPM8 and the Cold Thermoreceptors

The role of TRPM8 channel in thermotransduction involves several aspects of complexity that make it difficult to understand intuitively. First, it is activated by several stimuli (cold, voltage, agonists and intracellular signaling) that interact with each other, raising the question of how these interactions occur. Experimental evidence in this type of polymodal channel may be misinterpreted if the consequences of a working hypothesis are not considered carefully. Second, in parallel with the identification of TRPM8 as the main molecular transducer of cold temperatures in cold thermoreceptors of the somatosensory system, a list of other ion channels have been shown to be involved in the activity of cold-sensitive neurons and nerve endings. The variety of firing patterns observed at cold sensitive nerve endings arises from a complex interaction of ion channels that operate on different time scales. Mathematical modeling has been instrumental in understanding these phenomena, showing the consequences of the hypotheses raised. Here we review some of the models that have been proposed in these two areas: the activation of TRPM8 and TRPV1 by voltage and temperature, and the generation of firing patterns of cold thermoreceptors. We finish this chapter with a mathematical model showing how the calcium-dependent adaptation of TRPM8 may account for the response of cold thermoreceptors to rapid changes in temperature.