Temperature gating in thermoTRPs may depend on temperature-dependent heat capacity differences

Comment on: Yeh F, Jara-Oseguera A, Aldrich RW. Implications of a temperature-dependent heat capacity for temperature-gated ion channels. Proc Natl Acad Sci U S A. 2023;120(24):e2301528120

Thermosensitive ion channels are transmembrane proteins that transduce temperature information into physiologically relevant chemical and electrical signals. Many of these thermosensitive ion channels come from the transient receptor potential (TRP) channel family, abbreviated as thermoTRPs. Many studies have investigated the temperature sensitivity of thermoTRPs, but a strong understanding of the thermodynamics that govern the thermoTRPs’ temperature gating has not been achieved. Recently, my colleagues and I have published a theoretical analysis of thermoTRP gating to lay a strong thermodynamic foundation on which experimentalists might be able to build more mechanistically accurate temperature gating models [1].

Temperature sensitivity of thermoTRPs is described by at least two states – closed versus open states (Figure 1a, upper cartoon). The activity of the channel is determined by the proportional occupancy of the closed versus open states and is typically assessed through electrophysiological measurements of channel open probability (P_o). For a two-state model, P_o is determined by the standard free energy difference between the open and closed states (ΔG⁰). The more negative the ΔG⁰, the more channels are in the open state, and vice versa. When ΔG⁰ is zero, there is equal occupancy of the open and closed states. This ΔG⁰ is determined by the temperature (T), measured in Kelvin, and two thermodynamic parameters: the enthalpic difference (ΔH⁰) and the entropic difference (ΔS⁰) (Eq. 1).

1 $\mathrm{\Delta }{G}^o=\mathrm{\Delta }{H}^o-\mathit{T}\cdot \mathrm{\Delta }{S}^o$1

Figure 1. Inclusion of ΔC_p into thermodynamics of thermo-TRPs temperature gating. a. (top) a cartoon depiction of thermoTRP temperature gating equilibrium. (middle) the generalized equation relating the heat capacity (C_p) of the open and closed states to the second order polynomial of ΔC_p(T). (bottom) a representation of some potential ΔC_p(T) relationships. Green is where ΔC_p is 0 and ΔH⁰ is temperature- independent. Brown represents a constant non-zero ΔC_p (ΔC_p,constant). Purple shows a ΔC_p that is linearly dependent on temperature (ΔC_p,linear). Magenta shows a ΔC_p that is parabolically dependent on temperature (ΔC_p,parabolic). b. ΔC_p is 0 and ΔH⁰ is temperature-independent. Two temperature activation curves shown are simulated based on the ΔH⁰ and ΔS⁰ of TRPV1 (ΔH⁰ = 150 kcal/mol, ΔS⁰ = 470 cal/molK [2]) and TRPM8 (ΔH⁰=-112 kcal/mol and ΔS⁰=-384 cal/molK [3];). Note the single temperature-sensitivity per curve. c. ΔC_p displayed with constant value. A single temperature activation curve is shown and is based on Clapham and Miller (2011). Note the U-shape leading to dual temperature-sensitivity curves [4]. d. ΔC_p linearly dependent on temperature as investigated by our recent publication [1]. All the possible temperature activation curves are overlaid upon a parameter space diagram where the parameters of ΔC_p slope (B) and intercept (A) are the Y- and X-axes, respectively. Note that we observe single temperature-sensitivities alongside multiple other types of temperature sensitivities. e. ΔC_p is parabolically dependent on temperature. This could be a likely model if unfolding is indeed an integral part of the thermoTRP gating mechanisms.

These thermodynamic parameters are properties of a protein that can be influenced by ligand-binding, solvent, and possibly temperature. The enthalpic difference of protein function is generally attributed to the differences in bonds (covalent, ionic, and Van der Waals forces) between two states. The entropic difference, on the other hand, is generally attributed to the change in flexibility of the protein and in the ordering of the solvent molecules around the protein. Classically, these thermodynamic parameters were assumed to be temperature-independent, as will be described in the next section.

Temperature-independent thermodynamic parameters

Obtaining values for the ΔH⁰ and ΔS⁰ of thermoTRP temperature-gating are critical to understanding thermoTRP channel function. However, classical methods for obtaining these thermodynamic parameters, such as calorimetry, are very difficult in transmembrane proteins, such as thermoTRP ion channels. Hence, these thermodynamic parameters were estimated from temperature activation curves in initial electrophysiology experiments of thermoTRPs, such as in the canonical heat-sensitive transient receptor potential vanilloid 1 (TRPV1) and in the canonical cold-sensitive transient receptor potential melastatin 8 (TRPM8) channels [2,3]. These estimated thermodynamic parameters generate temperature activation curves with a single temperature-sensitivity (Figure 1b; red for TRPV1, blue for TRPM8). A critical assumption of these experiments is that ΔH⁰ and ΔS⁰ are temperature-independent; models with this assumption will be abbreviated as the ΔH⁰_constant model. The ΔH⁰_constant model has been the prevailing thermodynamic framework utilized to fit experimental data thus far.

A constant ΔC_p framework predicts dual thermosensitivity

Although the ΔH⁰_constant model fits most experimental data well, the assumption of temperature-independent ΔH⁰ and ΔS⁰ might not be biophysically correct. In fact, soluble proteins are known to have temperature-dependent ΔH⁰ due to their high heat capacities (C_p, Eq. 2). Heat capacity is a sum of different contributions. A protein conformation’s side-chain-side-chain interactions, protonation states, and interactions with solvent all influence its total heat capacity. With two conformationally distinct open and closed states, there is likely a substantial heat capacity difference (ΔC_p) that exists. This will make the enthalpic and entropic differences temperature-dependent (Eqs. 2 ,3).

2 $\mathrm{\Delta }{H}^o\left(\mathit{T}\right)=\int \mathrm{\Delta }{C}_p\mathit{dT}$2

3 $\mathrm{\Delta }{S}^o\left(\mathit{T}\right)=\int \frac{\mathrm{\Delta }{C}_p}{\mathit{T}}\mathit{dT}$3

Clapham and Miller (2011) pioneered the incorporation of a temperature-independent heat capacity difference (ΔC_p,constant) into modeling of thermoTRP gating [4]. Critically, this thermodynamic framework predicts a U-shaped temperature activation curve (Figure 1c), resulting in thermosensitivity across two different temperature ranges – one within physiological temperatures and one in an extreme temperature range. The Clapham and Miller analysis requires that a heat-sensitive thermoTRP, like TRPV1, must be cold-sensitive at extremely cold temperatures, and extreme heat-sensitivity must also be present in cold-sensitive channels, such as TRPM8.

This predicted dual temperature-sensitivity is not a commonly observed feature of thermoTRPs, as many are temperature-gated across only a single temperature range [2,3]. The discrepancy between dual temperature-sensitivity of the thermodynamically sound ΔC_p,constant model and single temperature-sensitivity observed from experimental data from thermoTRPs was attributed to the difficulty of data collection at extreme temperatures needed to observe the second temperature sensitivity.

A linear ΔC_p framework results in single, dual, or triple thermosensitivities

The lack of experimental evidence for dual temperature-sensitivity might lead some to discount the validity of the ΔC_p,constant thermodynamic framework. However, if thermoTRPs are similar to other proteins, it is likely that the ΔC_p is nonzero – temperature-dependent ΔH⁰ and ΔS⁰ must be accounted for. Can we resolve the theoretical and experimental difference?

In attempting to resolve this disparity, my colleagues and I relaxed the assumption of a constant, temperature-independent ΔC_p in the ΔC_p,constant model [1], while maintaining the constraint of only to two states (Figure 1a, Top). This relaxation is supported in the soluble protein literature; the heat capacity of protein states and the heat capacity difference between protein states are generally temperature-dependent [5]. We used simulations to investigate linearly temperature-dependent ΔC_p (ΔC_p,linear; Figure 1d [1]), the simplest case of temperature-dependence.

With the ΔC_p,linear model, we are able to predict temperature-sensitivity curves across one, two, or three temperature ranges (Figure 1d). The single temperature-sensitivity curves (Figure 1d, blue, orange) mimic the experimentally observed temperature activation behavior of many thermoTRPs. Although the simulated single temperature-sensitivity curves appear as a single smooth sigmoid, these single temperature-sensitivity curves have a plateau at temperatures where channel activity approaches 0 or 1. This gating behavior has been experimentally observed in thermoTRPs such as TRPV1.

In addition to single temperature-sensitivity curves, we also observed double (Figure 1d, black) and triple temperature-sensitivities (Figure 1d, red, yellow, cyan, dark blue). As stated in the previous section, these multiple temperature sensitivities are not commonly observed experimentally in thermoTRPs.

Both plateaus and multiple temperature sensitivities are gating features that have typically been attributed to multi-state models. However, utilizing only a two-state model, we showed that these complex multi-state models might not be necessary to explain all the thermoTRP gating features; a simple open-closed two state model with a temperature-independent or -dependent ΔC_p can generate the many of same gating features [1,4]. Additionally, we outlined a general mathematical analysis to understand how parameters of different temperature-dependencies of ΔC_p might lead to hypotheses for the temperature gating of thermoTRPs.

Consequences of interpreting unfolding in a temperature-gating model

Results of recent electrophysiology experiments in TRPV1, V2, V3 and possibly TRPM8 support speculations that unfolding might be an important mechanism in thermoTRP temperature gating. Even more recently, Mugo et al. (2023) performed difficult differential scanning calorimetry experiments complemented by electrophysiological recordings of TRPV1 that lend more weight to the possibility of unfolding as a mechanism of temperature-gating in thermoTRPs [6].

If thermoTRPs utilize unfolding in their temperature gating mechanism, the heat capacity difference is likely not zero, not temperature-independent, and not even linear. Instead, the soluble protein literature have noted that the unfolded state of proteins tends to have parabolically temperature-dependent heat capacities [5]. The progression of complexity in temperature activation curves for models assuming constant ΔH⁰, ΔC_p,constant, or ΔC_p,linear [1–4] is quite unexpected. Therefore, it is difficult to intuit the types of temperature activation curves that might exist with models assuming parabolic ΔC_p (ΔC_p,parabolic; Figure 1e).

To fully understand the temperature-gating of thermoTRPs, we will likely need to simulate and analyze the ΔC_p,parabolic model of thermoTRP gating. In our ΔC_p,linear work, we developed a general analysis to relate the thermodynamic parameters to the different types of temperature activation curves [1]. It is straightforward to extend our approach to the ΔC_p,parabolic model to predict different types of temperature activation curves that might exist and to better understand the critical parameters that determine the temperature activation curves. These simulations will help lay the strong thermodynamic foundation on which to build comprehensive thermoTRP temperature-gating models.