Implications of a temperature-dependent heat capacity for temperature-gated ion channels

Abstract

Temperature influences dynamics and state-equilibrium distributions in all molecular processes, and only a relatively narrow range of temperatures is compatible with life-organisms must avoid temperature extremes that can cause physical damage or metabolic disruption. Animals evolved a set of sensory ion channels, many of them in the family of transient receptor potential cation channels that detect biologically relevant changes in temperature with remarkable sensitivity. Depending on the specific ion channel, heating or cooling elicits conformational changes in the channel to enable the flow of cations into sensory neurons, giving rise to electrical signaling and sensory perception. The molecular mechanisms responsible for the heightened temperature-sensitivity in these ion channels, as well as the molecular adaptations that make each channel specifically heat- or cold-activated, are largely unknown. It has been hypothesized that a heat capacity difference (ΔC_p) between two conformational states of these biological thermosensors can drive their temperature-sensitivity, but no experimental measurements of ΔC_p have been achieved for these channel proteins. Contrary to the general assumption that the ΔC_p is constant, measurements from soluble proteins indicate that the ΔC_p is likely to be a function of temperature. By investigating the theoretical consequences for a linearly temperature-dependent ΔC_p on the open-closed equilibrium of an ion channel, we uncover a range of possible channel behaviors that are consistent with experimental measurements of channel activity and that extend beyond what had been generally assumed to be possible for a simple two-state model, challenging long-held assumptions about ion channel gating models at equilibrium.

Keywords: TRP channels; heat capacity; temperature-gating; thermodynamics.

Fig. 1.

Change in open probability as a function of temperature with no change in heat capacity ( $\Delta C_p=0$ ). (A) Single heat- and single cold-sensitive curves. Parameters estimated from single TRPV1 channel measurements: $\Delta H_{constant}=150\frac{kcal}{mol},\Delta S=470\frac{cal}{mol\cdot K}$ (35). Parameters estimated for TRPM8 channels: $\Delta H_{constant}=-112\frac{kcal}{mol},\Delta S=-384\frac{cal}{mol\cdot K}$ (36). Dotted lines denote $T_{50}$ for TRPV1 (red) and TRPM8 (blue). (B) Slope of $P_o$ as a function of temperature ( $\frac{d{P}_o}{dT}\left(T\right)$).

Fig. 2.

Change in open probability as a function of temperature with constant $\Delta C_p$ . The gray curves have parameters: $\begin{array}{c}{T}_0=298K\left({25}^{o}C\right),\Delta S_o^o=-9\frac{cal}{mol\cdot K},\end{array}\Delta C_{p,cons\tan t}=3\frac{kcal}{mol\cdot k}.$ (A) Change in $T_0$ primarily determines the temperature of minimum $P_o$ . Red: $T_0=308K\left({35}^{o}C\right)$ . Changes in $T_0$ shift the curves along the temperature axis. (B) Change in $\Delta S_o^o$ primarily determines the value of the minimum $P_o$ . Yellow: $\Delta S_o^o=-20\frac{cal}{mol\cdot K}$ . (C) Change in $\Delta C_{p,constant}$ determines the slope of the two halves of the temperature-sensitive curve. Blue: $\Delta C_{p,constant}=5\frac{kcal}{mol\cdot K}$ . This parameter determines the temperature-sensitivity (slope) of the $P_o\left(T\right)$ curves without affecting the temperature location and value of the minimum $P_o$.

Fig. 3.

Parameters that control the number of sensitivities in temperature-dependent $P_o$ vs. T relations. Example simulations showing the range of possible $P_o\left(T\right)$ relationships and the parameters that determine them. $T_0$ is held at $250K\left(-23{}^{o}C\right)$ . Black diamonds are $T_0$ ; empty circles are $T_{stat.\beta }$ . The cells are also labeled as in Figs. 4 and 5.

Fig. 4.

Parameter space associated with $\Delta C_{p,linear}\left(T\right)$ and the implications for $P_o$ as a function of temperature. Possible $P_o\left(T\right)$ behaviors across a subset of intercept and slope values when $T_0=250K\left(-{23}^{o}C\right)$ and $\Delta S_o^o=0\frac{cal}{molK}$ . Each region is labeled as in Figs. 3 and 5 with a representative curve shape. In these example traces, $T_0$ is the stationary point where $P_o=0.5$ . The $P_o$ value at $T_0$ is determined by $\text{Δ}{S}_o^o$ and changes in $\text{Δ}{S}_o^o$ are explored in Fig. 5. Regions I and III: only double temperature-sensitive curves can be obtained. Regions IIa and IVa: triple temperature-sensitive curves are observed. If $\Delta S_o^o<0\frac{cal}{molK}$ , regions IIa and IVa could appear singly temperature-sensitive on a linear $P_o\left(T\right)$ scale (Fig. 5). Regions IIb and IVb: $P_o\left(T\right)$ is monotonic, but has a plateau at $T_0$ . Regions IIc and IVc: triple temperature-sensitive curves are observed. If $\Delta S_o^o>0\frac{cal}{molK}$ , regions IIa and IVa could appear singly temperature-sensitive on a linear $P_o\left(T\right)$ scale (Fig. 5). The squares are data fits compiled from DNA–protein binding in the study by Liu et al. (57). The triangles are data fits from protein unfolding from the study by Gomez et al. (24). Since protein unfolding was best fit by a parabolic fit, the slopes and the intercepts of the line of best fit at $298K\left({25}^{o}C\right)$ were used. Peptide–peptide interactions are mapped by stars. Most peptide–peptide interaction slopes and intercepts were much greater than what we used for our simulations.

Fig. 5.

$\Delta S_o^o$ values affect the number of temperature-sensitivities observable on a linear $P_o\left(T\right)$ scale. $T_0$ is held at $250K\left(-{23}^{o}C\right)$ . Each graph is labeled as in Figs. 3 and 4. The $\Delta S_o^o$ = $-9,0,9\frac{cal}{molK}$ . The black diamonds are $T_o,$ whereas the empty circles are $T_{stat.\text{β}}$ . When $\Delta S_o^o$ is negative, $P_o$ at $T_o$ is less than 0.5. In this case, IIa and IVa might appear as single temperature-sensitivities. This will also make region III appear as not temperature-sensitive. Contrarily, when $\Delta S_o^o$ is positive, $P_o$ at $T_0$ is greater than 0.5. This will result in IIc and IVc to seem singly temperature-sensitive, while making region I appear not temperature-sensitive.