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 , 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 or 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. 4B how K, and hence channel open increases for both heating and cooling as T departs from the

Table 1. Enthalpies, ΔH, of selected proteins

−1 Protein T range °C Q10 ΔH kcal mol Reference(s)

TRPA1 26–16 ≈10 −40 10 TRPM8 27–18 24 −56 (−112) 11 TRPC5 25–40 ≈10 −40 12 25–15 ≈2 −14 TRPV4 25–45 10, 19 44, 57 13, 14 TRPV3 24–34 33 64 15 TRPV1 41–50 40 75, 90–100 9, 16 TRPV2 50–60 >100 >100 17, 18 Comparators Hemoglobin T → R transition −10 19 K+ channel C-type inactivation −16 20 AdiC arginine agmatine antiporter substrate occlusion 5 21 Hexokinase closing 222

Values of Q10, determined in the indicated temperature range to either heat (red) or cold (blue) for various TRP channels. Corre- sponding ΔH are calculated from Eq. 6B; numbers in parentheses for TRPM8 from Brauchi et al.’s (11) fit of the van’t Hoff plot. We do not list Q10s measured over more moderate deviations from room temperature. Q10s often increased on repeated trials, indicating that proteins become modified by internal changes (e.g., Ca2+), equivalent to failure of the protein to return to its initial conformation between trials. Bottom four rows: For comparison, ΔH values are shown for several systems of carefully studied protein conformational rearrangements near 20 °C. We thank Feng Qing for providing data before publication (18).

2of6 | www.pnas.org/cgi/doi/10.1073/pnas.1117485108 Clapham and Miller Downloaded by guest on September 24, 2021 minimum point. The reason for the U shape is simple: the ΔHo and occur from an altered molecular interactions within the protein). o ΔS components of the overall free energy vary in opposite direc- This dramatic physiological change does not require changing in INAUGURAL ARTICLE tions with T. This U shape will provide a key to understand the any way the channel’s temperature-sensing element ΔCP;itfollows Δ large Q10 that underlies TRP-based T sensing. (If CP is negative, from merely tweaking the modulator element T0.Thefigure the plot is bell-shaped, but this does not alter the points made makes the additional point that according to this mechanism, any below.) These points are identical to long-known aspects of the hot-sensing channel is also a cold-sensing channel. Of course, it thermodynamics of heat- and cold-denaturation of proteins (25). may not be experimentally possible to cover a temperature range wide enough to actually observe both hot-sensing and cold-sensing Application to TRP Channels. The classical protein-folding literature arms of the curve, but thermodynamics demands that in principle is replete with measurements that provide estimates of the both arms must be present. Moreover, it is easy to envision a fur- 10 parameters in Eq. . These allow us to apply the abstract con- ther mechanistic unification regarding the many TRPs that nature siderations above to the real-world problem of TRP temperature does not use to sense temperature. These may open by an identical sensitivity. For this discussion, we envision TRP gating as a simple conformational change, but with a position on the T axis, and closed–open conformational change, as in the “A–B” equilibrium perhaps somewhat lower ΔCP, so that both rising arms extend above, with B representing the open state. This is surely a vast beyond the experimental midrange of temperatures. fi oversimpli cation, but it captures the essence of the temperature- The conclusions above are model-free (unless the laws of dependent phenomena outlined here. A natural choice for the thermodynamics would be considered a “model”). Any protein reference temperature, To, is the point of minimum K (i.e., conformational change must behave this way in principle, but Δ o “ ” H o = 0); this set-point of the enthalpy-temperature line is strong T dependence will not be seen unless ΔC is large, on the sensitive to the particulars of all molecular interactions of the P “ ” order of several kcal/mol-K. TRP channels have apparently protein, and so To is a modulation parameter sensitive to mo- evolved to produce a large heat capacity change upon opening. lecular variations such as mutations, sequence and splice variants, fi What might be the molecular origin of this? The answer is not etc. With this simpli cation, we arrive at the working relation: difficult to guess, because it has been studied for many decades as the common molecular basis of heat- and cold-driven unfolding of lnKðTÞ¼ΔS8=R − ΔC ½1 − T =T þ lnðT =TÞ=R: [11] 0 P 0 0 proteins: exposure of hydrophobic groups to water (25, 27, 28). It is Thus, the temperature dependence of K is determined by three firmly established from small-molecule physical chemistry that Δ o a high heat capacity increase accompanies the transfer of nonpolar parameters: T0 and S0, which set the horizontal and vertical NEUROSCIENCE positions of the “U” curve, and ΔCP, which determines the compounds into water, approximately +15 cal/mol-K per methy- steepness of its “arms.” lene group in linear alkanes, slightly less for aromatic carbons (29, Fig.1displaysK(T)fortwovaluesofΔC : 3 and 5 kcal/mol-K, 30). This effect arises from a “tightening” and “straightening” of P fi with T0 set at 25 °C. Most importantly for our purposes, a low H-bonds among the rst-shell waters forced into direct apposition o value (≈0.01) is chosen for K0 (ΔS0 = −9 cal/mol-K), so that the to the nonpolar moiety (31, 32). If, therefore, a TRP domain channel is mostly closed at room temperature, as in a typical ex- containing buried hydrophobic groups were thrust into solvent periment, before applying heat or cold. Fig. 2 illustrates the effect upon channel opening, CP would certainly increase. A little of shifting the K(T) curve and the equivalent open-probability vs. arithmetic shows that a ΔCP of 2–5 kcal/mol-K is easily within the T(“temperature-activation”) curves along the T axis by varying T0; realm of plausibility for a TRP channel. This would require “ ” with the parameters used here, these curves give Q10 values in the unburial of roughly 300 methylene or aromatic carbons, on the midrange of opening of ≈20, as found experimentally (Table 1). order of 50 nonpolar side chains—10 to 20 side chains per subunit The key point to be appreciated is that a channel that operates in the tetrameric channel. No special hand-waving is required to physiologically as a hot sensor (red curve) can be transformed into imagine this amount of nonpolar exposure to water upon the a cold sensor (blue curve) merely by modestly shifting T0 (as would opening of a channel composed of ≈3,000 residues.

Fig. 1. Temperature dependence of conformational equilibrium constant. The behavior of Eq. 1 is shown for indicated values of ΔCP (kcal/mol-K), with Ko =0.01andTo = 25 °C (arrow). Dashed line marks the half-activation level of the equilibrium.

Clapham and Miller PNAS Early Edition | 3of6 Downloaded by guest on September 24, 2021 Fig. 2. Modulation of temperature sensing. Temperature dependence of either lnK (Left, Eq. 10) or open probability (Right, Eq. 2B) is plotted for ΔCP =4 kcal/mol-K and two values of To: 21 °C (red, mimicking hot-activating channel) or 29 °C (blue, mimicking cold-activating channel). Dashed regions of the curves mark ranges where channels are likely to be experimentally inaccessible.

Where might such a conformational rearrangement occur in a a thermodynamic approach is that it allows us to ignore mecha- TRP channel? Are there any known domains that could serve this nistic minutiae and predict general constraints, as above. How- temperature-sensing function? First, we state the obvious: that the ever, to fully understand how TRP channels work, we must dig relevant hydrophobic side chains need not cohabit a single domain. more deeply into the protein’sdetails. With only ≈20 side chains per subunit to account for, it is entirely Currently there is no structure of an entire TRP channel, but we possible that channel opening leads to relatively small rearrange- speculate that TRPs resemble Kv channels in their architecture. ments in multiple regions that unbury greasy residues distant in As in Kv channels, an S1–S4 ligand/voltage sensor domain is linked primary sequence and structure. Such a situation would be bad to an S5-P-S6 pore domain within each 6TM subunit. The pore news for biophysicists using mutagenesis to search for a localized domains associate around a central axis, the aqueous channel, with “temperature-sensing domain.” Of course, it is possible that a lo- the S1–S4 domains arranged peripherally behind them. Outside calized domain movement would turn out to be the hydrophobic the core 6TM segments, there are no common domains shared by culprit; the membrane-embedded S1–S4 domains (which in TRP all TRPs. repeats are present in the TRPC, TRPV, and channels are poor voltage sensors because they carry so few TRPA families’ amino termini. High-resolution structures of these charges) might serve this purpose if they would become signifi- cytoplasmic regions have been solved for TRPV1, TRPV2, and – cantly water-exposed upon opening. The large N- and C-terminal TRPV6 (33 37), and comparison of functional and structural data domains are also suspects because both contain regions that suggests that these regions competitively bind ATP and calmod- modulate gating (18). However, we are not confident that tem- ulin in TRPV1, TRPV3, and TRPV4 (36, 37), primarily to regulate “ ” perature-sensing local domains even exist: mutagenesis can cer- inactivation gating. The proximal C-terminal TRP box, con- tainly alter thermal sensing, but such a result does not identify a T- taining the sequence EWKFAR in all TRPC family members, is sensing domain. In particular, it is important to appreciate that the less well conserved in other TRPs and binds PIP2 in TRPV1 and slope of the U-shaped curve steadily increases with temperature; TRPM8 (11, 38). As in many calcium-conducting channels, in- thus, a mutation that merely shifts the curve by a few degrees tracellular (IQ motifs) and potential calcium binding without altering the temperature-sensing domain at all will also sites are common (39). By comparison with Kv channels, TRP activation is poorly understood, but whether activated by ligands change Q10 measured at a particular temperature. To summarize our main point before delving into side issues: if or voltage, these energies must be propagated to the pore, perhaps – — via the S4–S5 linker to an intracellular gate, or from the turret/ 10 20 side chains in a TRP subunit or indeed lipid moieties, which fi are, after all, part of the thermodynamic system—become exposed pore region to a selectivity lter gate. Ligand binding drives state changes by imparting binding energy. to water upon channel opening, the properties discussed here must Voltage-induced and phosphorylation-induced conformational emerge. They are necessary, direct consequences of the First and changes also represent distinct states in TRP channels. Classic Second Laws of thermodynamics. Adding more states to account voltage-gated ion channels carry several charged amino acids in for what is undoubtedly a multistep process does not alter this ar- their S4 transmembrane helices that move in response to an im- gument. As long as the function of hot- and cold-sensing TRPs fi ≈ posed electric eld. For these ion channels, the balance between involves the exposure of 20 nonpolar residues upon gating, then closed vs. open states changes over a narrow range of voltage. thermodynamics requires that a channel activated by high tem- Voltage-dependent activation moves charges (z) across the volt- peratures will also be activated low temperatures (and vice versa). age field in the protein, which for Kv channels is ≈13 and for TRP channels <1. As always, ΔH determines the temperature depen- Multiple States. Up to now, we have considered only a two-state dence of activation, but we should remember that the electrical process. TRP channel gating is much more complicated than this energy of voltage-sensor movement confers voltage dependence idealization. Every protein’s conformational change is an ener- upon ΔH: getically and kinetically “bumpy ride.” Moreover, additional states must be added to account for ligand binding. Binding of exoge- dlnk=dð1=TÞ¼ − ΔHðVÞ=R ¼ − ðΔHð0ÞþzFVÞ=R: nous compounds, cytoplasmic nucleotides, calmodulin, PIP2,cal- cium, and other ions, all linked to conformational changes, yields At resting membrane potentials (e.g., V = −70 mV), the closed many states in any complete reaction scheme. The advantage of state of predominantly voltage-gated channels is lower in energy

4of6 | www.pnas.org/cgi/doi/10.1073/pnas.1117485108 Clapham and Miller Downloaded by guest on September 24, 2021 than the open state and thus is the favored conformation of the models are useful in understanding the contributions of the

protein complex. Depolarization allows the channel protein to parts of the protein machine and may allow interpretation of INAUGURAL ARTICLE relax into its open configuration. TRP channels have few charges calorimetric measurements. Nonetheless, temperature effects (z < 1) in the electric field, and the slope of the conductance/V will be difficult to parse into domains when the output is the curve is shallow. Thus, the voltage term, zFV, is small compared behavior of the complete protein. In this vein, it is improper to with ΔH(0) and can be ignored; irrelevantly high voltages would draw conclusions about energetic interactions that occur during be required to turn TRPM8 (<−2,100 mV) into a heat sensor or gating by applying mutant cycle analysis to measurements of po TRPV1 into a cold sensor (>+2,500 mV) (40). (or fraction of maximal current) to channels that have more The position of the conductance (or po) curve on the voltage than a single closed and single open state (presumably, the vast axis is another matter entirely—it should not be confused with majority of ion channels). As one particularly obvious example, the standard definition of voltage dependence, the steepness of one could consider a channel having two closed states and one the voltage–activation curve. For a two-state channel, the posi- open state; a mutation that simply caused one of the closed tion of this curve, usually measured as the half-point of activation states to become conducting would shift the current–voltage V1/2, simply reflects the purely “chemical” free energy at zero relationship even if it did not have any effect on the underlying voltage, where there is no applied electric field contribution to energetics of gating transitions. In brief, if a channel has more the conformational energy: than two states, then “open” and “closed” are not thermody- namic state variables. ¼ Δ = [12] V1= GV¼0 zF 2 Reality. As pointed out above, if the entire range of energies could These voltage shifts account for many physiological mechanisms. be explored, the U shape of the lnK vs. T curve would emerge. In practice (between 10 °C and 50 °C, ±200 mV), experimentalists see Temperature, ligands, pH, PIP2, and mutagenesis all change the position of the conductance curve on the voltage axis. For Kv only one arm of the U curve and dub the channel either cold- or hot-activated. Indeed, species differences in TRPA1 orthologs channels, temperature shifts the position by relatively small fl amounts (e.g., ≈1 mV/°C) (41). By comparison, this shift is 7 and 9 might underlie why this channel seems to be heat-activated in ies mV/°C for TRPM8 and TRPV1, respectively (42). However, we (43, 44) and snakes (45) but cold-activated in mice (46). However, take issue with the contention of Voets et al. (42), who see a basic, there are important experimental limitations, and these relate to unifying principle in these shifts. In contrast, we point out that the inaccessibility of relevant kinetic parameters. For TRPA1, in

which activation and inactivation kinetics significantly overlap and NEUROSCIENCE these voltage shifts merely track the effect of temperature on are calcium-dependent, these kinetics are crucial. More generally, ΔG . Furthermore, we note that when temperature is changed, V=0 TRP channel currents do not reach steady state after a change in conductance–voltage curves are measured under different initial temperature during practicable recording times. Estimates of K conditions; the new temperature will change the conformation of a are approximate, and symmetrical temperature “ramps” produce protein before the activation curve is obtained, and this initial state asymmetric responses. In addition, many TRP channels undergo a will differ for each temperature measured. The point at which ≈ fi transition to a new gating regime over extended recording [ 10 channel opening becomes measurable de nes the position of the min; called “I2” states (47)], indicating initiation of a secondary conductance curve on the voltage axis. The energy landscape ex- process driven by opening of the channel. Separation of the two perienced by the channel before this point is opaque to the ex- realms of gating is difficult without extensive single-channel re- perimentalist. Indeed, if we could reliably compute the complex cording. At least for TRPV3 where it has been measured, there is history of molecules in a chemical reaction or protein, we could pronounced hysteresis: the current increases steadily with heating, dispense with Δ and report energies in absolute H, S, and G. When ’ but upon transition from heating to cooling, the current rapidly temperature, pH, ligand, or mutation change a channel s initial collapses, regardless of the temperature reached (15). This last state and it is remeasured under the new condition, we are mea- behavior has many possible interpretations, but one is that at this suring changes from a different initial condition, a new confor- rate of heating, gating is far from equilibrium. Moreover, TRP mation of the protein about which we have no information. The protein temperature dependence is never recorded in isolation. range and linearity of such shifts with temperature are useful for TRP gating is significantly affected by modulators physiologists but are at this point only empirically defined. An (e.g., PIP2), which themselves depend on temperature-dependent additional, subtle problem is that TRP channel gating is generally 2+ enzymes. These should be separated from the primary process, dependent on localized internal Ca levels, levels that depend on perhaps by reconstitution into model membranes. Even so, tem- fi the driving force for calcium (voltage). By de nition, shifts along perature-induced lipid sorting alters protein function (48), and the voltage axis induced purportedly by temperature produce new these effects depend on both the composition of the levels of modulating calcium, thereby setting up a complex feed- as well as the protein. back loop. Mutagenesis is a potent tool in the biologist’s armamentarium, An additional problem concerns a commonly used metric in underpinning much of our understanding of protein function. TRP electrophysiological work related to the activation curve’s However, there are practical difficulties, some of which are unique position: the “threshold temperature” at which channel activation to the understanding of temperature dependence. Plasmids are is first discerned. This term, although of some empirical utility, is transfected into cells, grown overnight at 37 °C, and channels that highly misleading because it carries a strong connotation of abrupt fold properly are inserted into the membrane and the currents switching. No such switching occurs in the framework offered measured the next day. The temperature-dependent folding so- here, because K and po are smooth functions of T. The sense that lution reached by the protein (in the middle of the night!) may TRPs activate at a threshold is a consequence of electrophysio- overlap with gating of the channel. Because membrane proteins logical realities—background leaks or noise below which po is are present in endoplasmic reticulum (ER), Golgi, and vesicular too small to observe TRP current. Only when the channel opens membranes, gating of the channel en route alters the behavior of enough for the current to rise up out of the background “mud” these compartments and may block their delivery or alter post- will the experimenter observe it as a threshold (Fig. 2). translational modifications. Indeed, some TRP channels such as The complexities above have led experimentalists to produce mucolipins (TRPML) function solely to regulate intracellular multistate models of TRP gating. However, multiple states trafficking (3). Most importantly, proteins that do not fold prop- partition ΔH; they do not change the thermodynamic essence of erly are of necessity excluded from analysis. If temperature sen- the U-shaped activation curves of Figs. 1 and 2. Multistate sitivity and protein folding for successful expression are not

Clapham and Miller PNAS Early Edition | 5of6 Downloaded by guest on September 24, 2021 independent, the most interesting mutations are excluded. Thus, capacity changes underlie temperature sensing. Any TRP that would the ubiquitous energy bath we call temperature selects mutants (of show even weak indications of activation at both hot- and cold-going any protein) before they can be studied. For all these reasons, the temperatures would be a powerful indicator of this mechanism. A quest for a potentially few scattered hydrophobic domains exposed nominally “temperature-insensitive” TRP might act in such a way, if during temperature-dependent gating is likely to be arduous in its set-point were positioned around 25 °C and its cold and hot ac- execution and uncertain in interpretation. tivation ranges were accessible from such a midpoint. One would have to get lucky, but even a rough result like this would speak to Discussion heat capacity as a key driving force for temperature sensitivity. The thermodynamic framework introduced here is straightforward on paper, but the welter of these experimental complications limits Materials and Methods our ability to test it. We know of no clean experimental results that All calculations were plotted using MatLab (MathWorks) and Mathematica explicitly support or refute this picture. What, then, might be done to (Wolfram Research). examine whether this mechanism of temperature sensing is actually used by TRPs? While acknowledging the difficulty of quantifying ACKNOWLEDGMENTS. We thank Kene Piasta for provoking this collabora- tion, Brian Matthews for screwing in the light bulb that illuminated ideas conformational equilibrium constants as a function of temperature expressed here, Feng Qin for steering us to appropriate TRP literature, Kurt for these channels, we suggest a phenomenon that, if observed Beam for catalyzing our inclusion of mutant cycle analysis, and Randy even qualitatively, would provide a compelling indication that heat Stockbridge for comments on the manuscript.

1. Ramsey IS, Delling M, Clapham DE (2006) An introduction to TRP channels. Annu Rev 25. Schellman JA, Lindorfer M, Hawkes R, Grutter M (1981) Mutations and protein sta- Physiol 68:619–647. bility. Biopolymers 20:1989–1999. 2. Nilius B, Owsianik G, Voets T, Peters JA (2007) Transient receptor potential cation 26. Privalov PL (1997) Thermodynamics of protein folding. J Chem Thermo 29:447–474. channels in disease. Physiol Rev 87:165–217. 27. Dias CL, et al. (2010) The hydrophobic effect and its role in cold denaturation. 3. Wu LJ, Sweet TB, Clapham DE (2010) International Union of Basic and Clinical Phar- Cryobiology 60:91–99. macology. LXXVI. Current progress in the mammalian TRP ion channel family. Phar- 28. Edsall JT (1935) Apparent molar heat capacities of amino acids and other organic macol Rev 62:381–404. compounds. J Am Chem Soc 54:1506–1507. 4. Caterina MJ, Rosen TA, Tominaga M, Brake AJ, Julius D (1999) A capsaicin-receptor 29. Gill SJ, Wadsö I (1976) An equation of state describing hydrophobic interactions. Proc homologue with a high threshold for noxious heat. Nature 398:436–441. Natl Acad Sci USA 73:2955–2958. 5. Gavva NR, et al. (2008) Pharmacological blockade of the vanilloid receptor TRPV1 30. Matulis D (2001) Thermodynamics of the hydrophobic effect. III. Condensation and elicits marked hyperthermia in humans. Pain 136:202–210. aggregation of alkanes, alcohols, and alkylamines. Biophys Chem 93:67–82. 6. McKemy DD, Neuhausser WM, Julius D (2002) Identification of a cold receptor reveals 31. Nemethy G, Scheraga HA (1962) Structure of water and hydrophobic bonding in a general role for TRP channels in thermosensation. Nature 416:52–58. proteins. 1. A model for the thermodynamic properties of liquid water. J Chem Phys 7. Peier AM, et al. (2002) A TRP channel that senses cold stimuli and menthol. Cell 108: 36:3382–3400. – 705 715. 32. Gallager KR, Sharp KA (2002) A new angle on heat capacity changes in hydrophobic 8. Andersson DA, Chase HW, Bevan S (2004) TRPM8 activation by menthol, icilin, and solvation. J Am Chem Soc 125:9853–9860. – cold is differentially modulated by intracellular pH. J Neurosci 24:5364 5369. 33. Jin X, Touhey J, Gaudet R (2006) Structure of the N-terminal ankyrin repeat domain of 9. Liu B, Hui K, Qin F (2003) Thermodynamics of heat activation of single capsaicin ion the TRPV2 ion channel. J Biol Chem 281:25006–25010. – channels VR1. Biophys J 85:2988 3006. 34. McCleverty CJ, Koesema E, Patapoutian A, Lesley SA, Kreusch A (2006) Crystal struc- 10. Karashima Y, et al. (2009) TRPA1 acts as a cold sensor in vitro and in vivo. Proc Natl ture of the human TRPV2 channel ankyrin repeat domain. Protein Sci 15:2201–2206. – Acad Sci USA 106:1273 1278. 35. Phelps CB, Huang RJ, Lishko PV, Wang RR, Gaudet R (2008) Structural analyses of the 11. Brauchi S, Orio P, Latorre R (2004) Clues to understanding cold sensation: Thermo- ankyrin repeat domain of TRPV6 and related TRPV ion channels. Biochemistry 47: dynamics and electrophysiological analysis of the cold receptor TRPM8. Proc Natl 2476–2484. Acad Sci USA 101:15494–15499. 36. Lishko PV, Procko E, Jin X, Phelps CB, Gaudet R (2007) The ankyrin repeats of TRPV1 12. Zimmermann K, et al. (2011) Transient receptor potential cation channel, subfamily C, bind multiple ligands and modulate channel sensitivity. Neuron 54:905–918. member 5 (TRPC5) is a cold-transducer in the peripheral nervous system. Proc Natl 37. Phelps CB, Wang RR, Choo SS, Gaudet R (2010) Differential regulation of TRPV1, Acad Sci USA 108:18114–18119. TRPV3, and TRPV4 sensitivity through a conserved binding site on the ankyrin repeat 13. Guler AD, et al. (2002) Heat-evoked activation of the ion channel, TRPV4. J Neurosci domain. J Biol Chem 285:731–740. 22:6408–6414. 38. Rohács T, Lopes CM, Michailidis I, Logothetis DE (2005) PI(4,5)P2 regulates the acti- 14. Watanabe H, et al. (2002) Heat-evoked activation of TRPV4 channels in a HEK293 cell vation and desensitization of TRPM8 channels through the TRP domain. Nat Neurosci expression system and in native mouse aorta endothelial cells. J Biol Chem 277: 8:626–634. 47044–47051. 39. Latorre R, Zaelzer C, Brauchi S (2009) Structure-functional intimacies of transient 15. Xu H, et al. (2002) TRPV3 is a calcium-permeable temperature-sensitive cation chan- receptor potential channels. Q Rev Biophys 42:201–246. nel. Nature 418:181–186. 40. Nilius B, et al. (2005) Gating of TRP channels: A voltage connection? J Physiol 567: 16. Yao J, Liu B, Qin F (2010) Kinetic and energetic analysis of thermally activated TRPV1 – channels. Biophys J 99:1743–1753. 35 44. 17. Leffler A, Linte RM, Nau C, Reeh P, Babes A (2007) A high-threshold heat-activated 41. Beam KG, Donaldson PL (1983) A quantitative study of kinetics in – channel in cultured rat dorsal root ganglion neurons resembles TRPV2 and is blocked rat skeletal muscle from 1 to 37 degrees C. J Gen Physiol 81:485 512. by gadolinium. Eur J Neurosci 26:12–22. 42. Voets T, et al. (2004) The principle of temperature-dependent gating in cold- and – 18. Yao J, Liu B, Qin F (2011) Modular thermal sensors in temperature-gated transient heat-sensitive TRP channels. Nature 430:748 754. receptor potential (TRP) channels. Proc Natl Acad Sci USA 108:11109–11114. 43. Hamada FN, et al. (2008) An internal thermal sensor controlling temperature pref- – 19. Brittain T, Hofmann OM, Watmough NJ, Greenwood C, Weber RE (1997) A two-state erence in Drosophila. Nature 454:217 220. analysis of co-operative oxygen binding in the three human embryonic haemoglo- 44. Gallio M, Ofstad TA, Macpherson LJ, Wang JW, Zuker CS (2011) The coding of tem- – bins. Biochem J 326:299–303. perature in the Drosophila brain. Cell 144:614 624. 20. Meyer R, Heinemann SH (1997) Temperature and pressure dependence of Shaker K+ 45. Gracheva EO, et al. (2010) Molecular basis of infrared detection by snakes. Nature channel N- and C-type inactivation. Eur Biophys J 26:433–445. 464:1006–1011. 21. Fang Y, Kolmakova-Partensky L, Miller C (2007) A bacterial arginine-agmatine ex- 46. del Camino D, et al. (2010) TRPA1 contributes to cold hypersensitivity. J Neurosci 30: change transporter involved in extreme acid resistance. J Biol Chem 282:176–182. 15165–15174. 22. Takahashi K, Casey JL, Sturtevant JM (1981) Thermodynamics of the binding of 47. Chung MK, Guler AD, Caterina MJ (2005) Biphasic currents evoked by chemical or D- to yeast hexokinase. Biochemistry 20:4693–4697. thermal activation of the heat-gated ion channel, TRPV3. J Biol Chem 280: 23. Baldwin RL (1986) Temperature dependence of the hydrophobic interaction in pro- 15928–15941. tein folding. Proc Natl Acad Sci USA 83:8069–8072. 48. Toombes GE, Finnefrock AC, Tate MW, Gruner SM (2002) Determination of L(alpha)- 24. Kauzmann W (1959) Some factors in the interpretation of protein denaturation. Adv H(II) phase transition temperature for 1,2-dioleoyl-sn-glycero-3-phosphatidyletha- Prot Chem 14:1–63. nolamine. Biophys J 82:2504–2510.

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