A thermodynamic framework for understanding INAUGURAL ARTICLE temperature sensing by transient receptor potential (TRP) channels David E. Claphama,1 and Christopher Millerb,1 aDepartment of Cardiology, Howard Hughes Medical Institute, Manton Center for Orphan Disease, Children’s Hospital Boston, and Department of Neurobiology, Harvard Medical School, Boston, MA 02115; and bDepartment of Biochemistry, Howard Hughes Medical Institute, Brandeis University, Waltham, MA 02454 This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2006. Contributed by David E. Clapham, October 24, 2011 (sent for review October 15, 2011) The exceptionally high temperature sensitivity of certain transient responses arise from the same type of conformational change upon receptor potential (TRP) family ion channels is the molecular basis of channel opening. Hence, the search for domain differences between hot and cold sensation in sensory neurons. The laws of thermody- hot- and cold-sensing TRPs is an exercise in futility. (ii)Allhot- namics dictate that opening of these specialized TRP channels must sensing TRPs are also cold-sensing TRPs, and vice versa. (iii)The involve an unusually large conformational standard-state enthalpy, source of high temperature sensitivity is a difference in heat capacity ΔHo:positiveΔHo for heat-activated and negative ΔHo for cold-ac- between the channel’s open vs. its closed conformation. tivated TRPs. However, the molecular source of such high-enthalpy changes has eluded neurobiologists and biophysicists. Here we offer Results a general, unifying mechanism for both hot and cold activation that Basic Thermodynamic Considerations. We consider a protein in recalls long-appreciated principles of protein folding. We suggest equilibrium between two conformations, A and B. that TRP channel gating is accompanied by large changes in molar heat capacity, ΔCP. This postulate, along with the laws of thermo- A ⇔ B [1] NEUROSCIENCE dynamics and independent of mechanistic detail, leads to the con- clusion that hot- and cold-sensing TRPs operate by identical con- with equilibrium constant K: formational changes. ¼½ =½ ¼ =ð − Þ [2A] K B A pB 1 pB TRPV | TRPM8 | TRPC5 | hydrophobic interaction ¼ =ð þ Þ [2B] pB K 1 K any membrane proteins are signal integrators evolved to “ ” respond to extracellular ligands, intracellular signal trans- where the bracket form represents concentrations of A or B at M “ ” duction, and transmembrane voltage changes. Our sensory nerves equilibrium, and the probability form represents, equivalently, use specialized ion-channel proteins to report environmental the probability of the appearance of B. We assume that K may temperatures, most notably, but not exclusively, the transient re- be determined experimentally. Stationary-state single-channel re- ceptor potential (TRP) ion channels (1–3). The TRPV1 channels cording, for instance, would provide a direct measure of pB,ifB ’ in sensory nerves respond to heat and also to capsaicin, an alkaloid would represent the channel s open state and A the closed, as in a from “hot” peppers, which binds to open the channel and thus thorough analysis of TRPV1 (9). K is of course a function of both depolarizes the neuron and fires action potentials (4). The brain, temperature and pressure; for this discussion, we consider pressure fi interpreting this information as an increase in ambient tempera- xed and will ask how K is expected to vary with temperature, T. ture, initiates vasodilation and sweating. Conversely, drugs that The fundamental relation of chemical thermodynamics, which block TRPV1 input to the brain provoke hypothalamic-mediated follows from the First and Second Laws, relates the measured Δ o changes in metabolism that elevate body temperature (5). The value of K to the change in standard-state Gibbs free energy, G : cold-sensing counterpart of TRPV1 is TRPM8, which binds ΔG8 ¼ − RT lnK; [3] ligands like menthol or icilin to counterfeit cold sensation (6, 7). When injected into animals, icilin induces shivering to raise body where R is the gas constant and ΔGo is the intrinsic difference in temperature (8). Here we discuss how proteins like TRPV1 and Gibbs free energy between the two conformational states at a given TRPM8 are tuned for robust responses to small differences in temperature and pressure. Because at a given temperature, temperature over a narrow range. This study offers a model-free framework for understanding the ΔG8 ¼ ΔH8 − TΔS8 [4A] temperature sensitivities of various TRP channels. We address two types of questions. First, how can the temperature sensitivity of ¼ − Δ 8= þ Δ 8= : [4B] channel opening be so high? Second, what sorts of differences lnK H RT S R fi should we expect to nd between heat-activated TRPs like TRPV1 ΔGo and K in general vary with T. In the simplest case, with ΔHo and cold-activated TRPs like TRPM8, or indeed between these and ΔSo temperature-independent, ΔGo changes linearly with T, and the many TRPs that are relatively insensitive to temperature? By increasing or decreasing depending on the sign of ΔSo, and lnK “model-free,” we mean that the conclusions here emerge directly from the laws of thermodynamics, with a few conventional auxiliary assumptions. The behavior to be described is therefore necessary Author contributions: D.E.C. and C.M. designed research, performed research, and wrote and inescapable—the only question is whether the particular pa- the paper. rameters involved are of such magnitude to be relevant to temper- The authors declare no conflict of interest. ature-sensing TRP channels. The main conclusions of this thermo- 1To whom correspondence may be addressed. E-mail: [email protected] dynamic treatment are as follows. (i) Hot-sensing and cold-sensing or [email protected]. www.pnas.org/cgi/doi/10.1073/pnas.1117485108 PNAS Early Edition | 1of6 Downloaded by guest on September 24, 2021 varies inversely with T, increasing or decreasing depending on the probability, would vary with T. However, as has been long appre- sign of ΔHo. Although Eqs. 4A and 4B are equivalent, we focus ciated by physical biochemists (23, 24), proteins do not generally here on the T-dependence of K, because this is so closely related behave this way. It is a fundamental error to assume that ΔHo and to measurables like TRP channel activity. Notice from Eq. 4 that ΔSo are T-independent for processes involving proteins—confor- as T increases, the relative contribution of ΔHo to the value of K mational change, folding, etc. (25)—because proteins can exhibit diminishes and that of ΔSo becomes increasingly dominant. high molar heat capacity. Thermodynamic laws demand that The temperature sensitivity of K follows from Eq. 4B: whenever a conformational change is accompanied by a change in o o molar heat capacity (ΔCP), ΔH and ΔS must both vary with T: dlnK=dð1=TÞ¼ − ΔH8=R [5A] ΔH8ðTÞ¼ΔH8ðT0ÞþΔCPðT − T0Þ¼ΔH80 þ ΔCPðT − T0Þ o Thus, if ΔH is T-independent, as customarily assumed in analysis [7A] of TRP channels, a van’tHoffplot—lnK vs. 1/T—will be linear, with slope yielding ΔHo. An alternative measure of T sensitivity is Δ 8ð Þ¼Δ 8ð ÞþΔ ð = Þ¼Δ 8 þ Δ ð = Þ often used: S T S T0 CP ln T T0 S0 CP ln T T0 [7B] dlnK=dT ¼ ΔH8=RT2: [5B] Here, T0 represents an arbitrarily chosen reference temperature, o Δ o Δ o Δ o Δ o If the reaction is energetically unfavorable (ΔH positive), the and H 0 and S 0 are the particular values of H and S at T0. slope of lnK with respect to T will be positive: K increases with T. Therefore, K will vary with T in a more complicated way than the ’ Δ — This happens because the unfavorable contribution of ΔHo to ΔGo van t Hoff line above. As long as CP itself is independent of T becomes less influential at higher T, as indicated in Eq. 4.An a good approximation for protein behavior under typical physio- — fi empirical measure of T sensitivity, often used in TRP channel logical conditions (26) we can predict with con dence the ex- plicit form of K(T): electrophysiology, is Q10, the ratio of K (or of activation rates, which do not concern us here) at two temperatures 10° apart lnKðTÞ¼ − ΔH8=RT − ΔC ð1 − T =TÞ=R (usually measured at 20 °C and 30 °C, but sometimes over varying 0 P 0 [8] temperature ranges): þ ΔS80=R − ðΔCP=RÞlnðT0=TÞ: Q10 ¼ KðT þ 10Þ=KðTÞ: [6A] We also note that K0, the value of K at the reference temperature, is: o Q10 is related to ΔH : À Á lnK0 ¼ − ΔH80=RT0 þ ΔS80=R: [9] 2 ΔH8 ¼ RT lnQ10 10 ≈ 20lnQ10 [6B] Substituting this into Eq. 8 gives us a practical, working relation at physiological temperatures (kcal/mol). for K(T): o Table 1 reports Q10 and corresponding ΔH values for various — lnKðTÞ¼lnK þðΔH8=T − ΔC Þð1 − T =TÞ=R TRP channels. These enthalpies 100 kcal/mol is not un- 0 0 0 P 0 [10] — common are unusually large values for protein conformational − ðΔCP=RÞlnðT0=TÞ: changes; they challenge us to understand why these TRPs re- quire such large energies to open or close. It is this challenge that This rather opaque function has a remarkable property: regardless motivates the following analysis. of the parameter values, it is always nonmonotonic. If ΔCP is positive (greater heat capacity in conformation B than in A), the Crucial Role of Heat Capacity. If ΔHo and ΔSo for the conforma- plot must be U-shaped, as in Fig. 1. In other words, K(T) will have tional change were both independent of temperature, we would a minimum value, and the steepness of the K–T curve continually immediately know from Eq.