TRPM8-Dependent Dynamic Response in a Mathematical Model of Cold Thermoreceptor

<div><p>Cold-sensitive nerve terminals (CSNTs) encode steady temperatures with regular, rhythmic temperature-dependent firing patterns that range from irregular tonic firing to regular bursting (static response). During abrupt temperature changes, CSNTs show a dynamic response, transiently increasing their firing frequency as temperature decreases and silencing when the temperature increases (dynamic response). To date, mathematical models that simulate the static response are based on two depolarizing/repolarizing pairs of membrane ionic conductance (slow and fast kinetics). However, these models fail to reproduce the dynamic response of CSNTs to rapid changes in temperature and notoriously they lack a specific cold-activated conductance such as the TRPM8 channel. We developed a model that includes TRPM8 as a temperature-dependent conductance with a calcium-dependent desensitization. We show by computer simulations that it appropriately reproduces the dynamic response of CSNTs from mouse cornea, while preserving their static response behavior. In this model, the TRPM8 conductance is essential to display a dynamic response. In agreement with experimental results, TRPM8 is also needed for the ongoing activity in the absence of stimulus (i.e. neutral skin temperature). Free parameters of the model were adjusted by an evolutionary optimization algorithm, allowing us to find different solutions. We present a family of possible parameters that reproduce the behavior of CSNTs under different temperature protocols. The detection of temperature gradients is associated to a homeostatic mechanism supported by the calcium-dependent desensitization.</p></div

Dynamic and static response of three different set of parameters.

<p>Responses to an acute cold pulse (A) and to cooling steps (B) with three different sets of parameters (indicated at the top). Parameters are listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139314#pone.0139314.t001" target="_blank">Table 1</a>. In B, the temperature steps are 31.5°C, 30.0°C, 28.0°C and 26.0°C.</p

Values of free parameters that reproduce satisfactorily both the dynamic and static responses of cold sensitive nerve endings.

<p>Values of free parameters that reproduce satisfactorily both the dynamic and static responses of cold sensitive nerve endings.</p

Dynamic response to heat.

<p>A. Temperature trace (top) and firing rate (bottom) in an experimental recording in mouse cornea. B. Our model subjected to the same temperature trace, showing the firing rate and ISIs obtained with parameter set 293.</p

Dynamic response to cold in CS nerve endings and models.

<p>Experimental recording (A), simulation of the Huber & Braun model (B), and simulation of our model (C) exposed to the same temperature protocol (top). Middle panels show the firing rate (spikes/sec) and the bottom panels show the inter-spike intervals (log scale). Our model reproduces three main features of the experimental recording: The steady-state firing rate at the resting temperature of the skin; the increase in the firing rate in response to a temperature drop; and a silent period when the temperature is rising back. Parameter set is 92 (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139314#pone.0139314.t001" target="_blank">Table 1</a>).</p

Relationship between some model parameters and the dynamic response.

<p>The basal firing rate at 33.5°C (A, D G), the maximum firing rate during the response to cold (B, E, H) and the seconds of silence after the cold pulse (C, F, I) are plotted against the TRPM8 conductance density (A-C), the ratio between depolarizing and repolarizing conductances (D-F) and the sum of the time constants involved in TRPM8 adaptation (G-I). Small black points represent the whole set of 360 parameter sets obtained and the large blue dots correspond to parameter sets listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139314#pone.0139314.t001" target="_blank">Table 1</a>.</p