Phosphatidylinositol-4,5-biphosphate (PIP 2 )-Dependent Thermoring Basis for Cold-Sensing of the Transient Receptor Potential Melastatin-8 (TRPM8) Biothermometer

: The menthol sensor transient receptor potential melastatin-8 (TRPM8) can be activated by cold and, thus, serves as a biothermometer in a primary afferent sensory neuron for innocuous-to-noxious cold detection. However, the precise structural origins of specific temperature thresholds and sensitivity have remained elusive. Here, a grid thermodynamic model was employed, to examine if the temperature-dependent noncovalent interactions found in the 3-dimensional (3D) structures of thermo-gated TRPM8 could assemble into a well-organized fluidic grid-like mesh network, featuring the constrained grids as the thermorings for cold-sensing in response to PIP 2 , Ca 2+ and chemical agents. The results showed that the different interactions of TRPM8 with PIP 2 during the thermal incubation induced the formation of the biggest grids with distinct melting temperature threshold ranges. Further, the overlapped threshold ranges between open and pre-open closed states were required for initial cold activation with the matched thermo-sensitivity and the decrease in the systematic thermal instability. Finally, the intact anchor grid near the lower gate was important for channel opening with the active selectivity filter. Thus, PIP 2 -dependent thermorings in TRPM8 may play a pivotal role in cold sensing.

Recent studies have demonstrated that a biological macromolecule has a thermoring structure to govern its thermal stability and activity.The thermoring can be a DNA hairpin in a single poly-nucleotide chain or a 3D topological grid in a systematic fluidic grid-like noncovalent interaction mesh network of a single polypeptide chain [23][24][25][26][27][28].Such a biochemical or biophysical network can be characterized by a graph theory-based grid thermodynamic model.First, a melting temperature threshold (T m ) for the thermal unfolding of the thermoring from the biggest grid to the smallest one is determined by its strength and size.Second, the grid-based systematic thermal instability (T i ) at a specific temperature is governed by the ratio of the total grid size to the total noncovalent interactions.Third, the structural thermo-sensitivity (Ω 10 ) is controlled by a change in the total grid sizes upon an alteration in the total noncovalent interactions along the same polypeptide chain within a 10 • C interval.Once three calculated parameters match the experimental values, including the functional thermo-sensitivity Q 10 , the specific thermoring can be identified as the structural motif or factor for the structural thermostability or the functional thermoactivity [24][25][26][27][28].Following a success in deciphering the lipid-dependent heat response and sensitivity of the TRP vanilloid 1 or 3 (TRPV1 or TRPV3) channel [27,28], it is attractive to use this graphical method to examine such a hypothesis that the temperature-dependent systematic fluidic grid-like noncovalent interaction mesh networks, once identified in the 3D structures of the TRPM8 channel, can be constrained as a thermoring structure from the biggest grid to the smallest one, to control the PIP 2 -dependent cold-sensing with specific temperature threshold and sensitivity.
In this computational study, the three PIP 2 -dependent biggest grids were first identified near the outer pore loop of mTRPM8.Their melting temperature threshold ranges in turn decreased upon the binding of the chemical agents C3 and AITC together with Ca 2+ .Once the threshold matched the incubation temperature of 20 • C, the channel was open, with the intact anchor grid near the lower S6 gate to secure the active selectivity filter, the decrease in the systematic thermal instability and the matched structural and functional thermo-sensitivities. Taken as a whole, although TRPM8 can be finally opened by chemical agents in the presence of Ca 2+ and PIP 2 , the PIP 2 -dependent thermorings may still serve as the critical structural motif for cold-evoked activation of TRPM8 with the specific temperature threshold and sensitivity.

Data Mining Resources
In this study, cryo-EM structural data of mTRPM8 in three gating states were exploited to prepare the systemic fluidic grid-like noncovalently interacting mesh networks.They included the closed states at 20   C with PIP 2 , Ca 2+ , C3 and AITC bound (PDB ID, 8E4L, model resolution = 3.32 Å) [22].UCSF Chimera was used for the thermoring analyses.

The Definition of the Necessary Gating Pathway
PIP 2 is required for TRPM8 opening [5,6,9,22].The cryo-EM structure indicates that S4b, the TRP domain, and pre-S1 of mTRPM8 form the active PIP 2 binding pocket [22].The primary structural analysis showed that mTRPM8 with PIP 2 bound at 20 • C (PDB ID, 8E4N) had F1013 in the distal C-terminus of the TRP domain to form a π-π interaction with F744 on S1.On the other hand, Q675 in the pre-S1 domain H-bonded with R998 in the TRP domain, in both closed and open states [22].Hence, the segment from Q675 in the pre-S1 domain to F1013 in the distal C-terminus of the TRP domain should be at least included as the necessary minimal PIP 2 -dependent gating pathway for the specific temperature threshold range and sensitivity and the reasonable systematic thermal instability.

Preparation of the Systematic Fluidic Noncovalent Interaction Mesh Network Maps
For the thermoring structural analyses of a systematic fluidic grid-like mesh network of mTRPM8 along the PIP 2 -dependent minimal gating pathway of one subunit, all the potential stereo-or regio-selective inter-domain diagonal and intra-domain lateral noncovalent interactions, such as salt/metal bridges and π interactions, and H-bonds, once filtered as described previously (Tables S1-S3), were geometrically mapped as grids [24][25][26][27][28].By using the Floyd-Warshall algorithm, the grid size was constrained as the minimal number of the total side chains of free residues in protein or atoms in the bound lipid, which did not engage in any noncovalent interaction in a grid [29].In this way, both the shortest direct and reverse paths were obtained to link two ends of a noncovalent interaction.For example, in Figure 1A, based on a grid-like biochemical reaction mesh network, a direct path length from F874 to Y908 was zero, owing to a π-π interaction between them.However, another shortest reverse path directed from Y908 to M878, W877 and back to F874 via three π interactions.Because no free residue participated in any noncovalent interaction during this cycle, the grid size was zero.Once each noncovalent interaction was tracked by a constrained grid size and the unshared sizes were marked in black numbers, a grid with an x-residue or atom size was denoted as Grid x , and then all the noncovalent interactions and grid sizes along the PIP 2 -dependent minimal gating pathway of one subunit were summed in black and cyan circles beside the mesh network map, respectively, for the computation of the melting temperature threshold (T m ), the systematic thermal instability (T i ) and the defined structural thermo-sensitivity (Ω 10 ).

Preparation of the Systematic Fluidic Noncovalent Interaction Mesh Network Maps
For the thermoring structural analyses of a systematic fluidic grid-like mesh network of mTRPM8 along the PIP2-dependent minimal gating pathway of one subunit, all the potential stereo-or regio-selective inter-domain diagonal and intra-domain lateral noncovalent interactions, such as salt/metal bridges and π interactions, and H-bonds, once filtered as described previously (Tables S1-S3), were geometrically mapped as grids [24][25][26][27][28].By using the Floyd-Warshall algorithm, the grid size was constrained as the minimal number of the total side chains of free residues in protein or atoms in the bound lipid, which did not engage in any noncovalent interaction in a grid [29].In this way, both the shortest direct and reverse paths were obtained to link two ends of a noncovalent interaction.For example, in Figure 1A, based on a grid-like biochemical reaction mesh network, a direct path length from F874 to Y908 was zero, owing to a π-π interaction between them.However, another shortest reverse path directed from Y908 to M878, W877 and back to F874 via three π interactions.Because no free residue participated in any noncovalent interaction during this cycle, the grid size was zero.Once each noncovalent interaction was tracked by a constrained grid size and the unshared sizes were marked in black numbers, a grid with an x-residue or atom size was denoted as Gridx, and then all the noncovalent interactions and grid sizes along the PIP2-dependent minimal gating pathway of one subunit were summed in black and cyan circles beside the mesh network map, respectively, for the computation of the melting temperature threshold (Tm), the systematic thermal instability (Ti) and the defined structural thermo-sensitivity (Ω10).

Equations
When a 20-base loop and two G-C base pairs in the stem form a DNA hairpin thermosensor, an initial T m for loop unfolding is 34 • C, and then increased by 10 • C with a more G-C base pair or five more bases included [23].Similarly, for the thermorings to undergo rate-limiting thermal unfolding from the biggest grid to the smallest one along the PIP 2dependent minimal gating pathway, the T m of the given grid could be in turn calculated by using the following equation, as described and examined previously [24][25][26][27][28]: where n is the total number of the grid size-controlled basic H-bonds equivalent to the noncovalent interactions in a given grid, and S max is the size of the given grid.Clearly, a smaller grid size or more equivalent H-bonds are necessary for higher heat capacity in a grid.Based on the above equation, the more G-C base pairs in the stem or the shorter poly-A loop, the higher the T m of the DNA hairpin [23].Thus, in either gating state, the systematic thermal instability (T i ) along the PIP 2 -dependent minimal gating pathway was reasonably defined using the following equation, as described and examined previously [24][25][26][27][28]: where along the same PIP 2 -dependent minimal gating pathway of one subunit in a given gating state, S is the total grid sizes and N is the total noncovalent interactions.In this way, the lower the T i , the less the compact conformational entropy in the system.In a temperature range ∆T, for an enthalpy-driven closed-to-open transition, assuming the chemical potential of a grid as the maximal potential for equivalent residues in the grid to form the tightest β-hairpin with the smallest loop via paired noncovalent interactions [30], the grid-based structural thermo-sensitivity (Ω ∆T ) of a single ion channel can be defined and computed using the following equations: where, along the same PIP 2 -dependent minimal gating pathway of one subunit, N c and N o are the total noncovalent interactions, S c and S o are the total grid sizes, and H c and H o are the total enthalpy included in noncovalent interactions in the closed and open states, respectively.E is the energy strength of a noncovalent interaction in a range of 0.5-3 kcal/mol.Usually, E is 1 kcal/mol [31].Thus, Ω ∆T actually mirrors a thermo-induced change in the total chemical potential of grids upon a thermo-evoked change in the total enthalpy included in noncovalent interactions from a closed state to an open one along the same PIP 2 -dependent minimal gating pathway of one subunit.
When ∆T = 10 • C, Ω 10 could be comparable to the functional thermo-sensitivity (Q 10 ) of a single ion channel.Q 10 during thermal activation was computed using the following equation: where X 1 and X 2 are open probability (P o ) values or reaction rates of mTRPM8 at temperatures T 1 and T 2 (measured in kelvin), respectively.For a given PIP 2 -dependent minimal gating pathway from Q675 in the pre-S1 domain to F1013 in the distal C-terminus of the TRP domain of mTRPM8 at 20 • C, nine H-bonds, thirty-four π interactions and six salt bridges shaped a systematic fluidic grid-like mesh network (Figure 1A).When the total noncovalent interactions and grids size were 49 and 95, respectively (Figure 1A, Table S1), the grid-based systematic thermal instability (T i ) was 1.94 (Table 1).Notably, in the presence of 1 mM PIP 2 [22], PIP 2 was packaged by R688 and N692 in the pre-S1, R851 at S4b, and R998 in the TRP domain via three salt bridges and an H-bond (Figure 1B).In this case, the biggest Grid 16 was outstanding at the S5/S6 interface.It had a 16-residue size via the shortest path from F881 to Y963, T967, Y981, F870, F874, W877 and back to F881 (Figure 1C).When 1.0-1.5 equivalent H-bonds sealed this biggest Grid 16 to hold the F881-Y963 π interaction at the S5/S6 interface (Figure 1C), the calculated melting temperature threshold (T m ) ranged from 32 to 37 • C, which was close to the experimental threshold range of 31-37 • C of mTRPM8 for cold activation in the presence of a high concentration of PIP 2 (>500 µM) [5].Thereafter, the biggest Grid 16 may act as a start cooling switch in TRPM8 to initiate channel activation in an optimal temperature range 32-37 • C.However, it could not be broken at 20 • C for channel opening [22].It has been reported that Ca 2+ binding cannot change the temperature threshold for cold-evoked activation of mTRPM8 [32].On the other hand, the C3-evoked TRPM8 activity at room temperature (22-24 • C) is not desensitized by Ca 2+ [22].However, mTRPM8 is not structurally open in the presence of C3, Ca 2+ and PIP 2 at 20 • C [22].Therefore, it is necessary to test the effect of C3 on the activation threshold of mTRPM8.When Ca 2+ bridged E782, Q785, N799 and D802 together, the Y793-N799 π interaction and the E782-Y793-Q785 H-bonds were broken (Figures 1A and 2A).Although C3 was bound against Y745 in the voltage sensor-like domain (VSLD) [22], it did not link any two residues together via a noncovalent interaction (Figure 2A).In contrast, the R851-PIP 2 salt bridge was replaced with the S850-PIP 2 H-bond (Figure 2B).As a result, when the total noncovalent interactions and grid sizes were 49 and 93, respectively, the resultant systematic thermal instability (T i ) decreased from 1.94 to 1.90 (Figure 2A, Table 1).What is more, the biggest Grid 21 appeared at the S5/S6 interface to control the F881-T967 π bridge.It had a 21-residue size via the shortest path from F881 to W877, F874, F870, F869, D866, Y981, T967 and back to F881 (Figure 2C,D).With 1.0-1.5 equivalent H-bonds sealing it, the calculated melting temperature threshold range was 22-27 • C, which was close to the experimental range of 23-29 • C in the presence of 100 µM PIP 2 [5].However, it was still higher than the sampling temperature 20 • C of the structural data, thereby leaving the channel closed [22].In the presence of not only Ca 2+ , PIP 2 and C3 but also AITC at 20 • C, mTRPM8 was open with several changes in the systematic fluidic grid-like noncovalent interaction mesh network (Figure 3A).First, at the Ca 2+ site, W786-Y793-W798 π interactions and the Y793-E782 and D781-R784 H-bonds were formed.Second, C3 and AITC were bound against Y745 and W798 in the VSLD, respectively [22].However, these two chemical agonists failed to connect any two residues together via a noncovalent interaction (Figure 3A).Third, PIP 2 was bound again to R688, R851 and R998, forming a Grid 7 (Figure 3B).Fourth, along with the PIP 2 binding, the D781-F1013 π interaction was disrupted to allow the gating Grid 8 to be born with an 8-residue size via the shortest path from H845 to R851, W994, R998, Y999, F1000, E1004 and back to H845 (Figure 3A,D).Fifth, when R851 formed a π interaction with W994 and an H-bond with D991 in the TRP domain, the D866-T982 H-bond and the F870-L975 π interaction at the S5/S6 interface were created to form the thermo-stable anchor Grid 7 in favor of the active lower S6 gate (Figure 3A).It had a 7-residue size from D866 to F868, F869, F870, L975, T982 and back to D866 (Figure 3D).Meanwhile, the biggest Grid 22 in the pore domain had a 22-residue size to stabilize the open state via the shortest path from F874, W877, F881, Y963, R885, Y908 and back to F874 (Figure 3C,D).When 1.0-1.5 equivalent H-bonds sealed it, the calculated T m ranged from 20 to 25 • C, which matched the sampling temperature 20 • C of the open state [22].As the total noncovalent interactions and grids size were 51 and 74, respectively (Figure 3A, Table S3), the grid-based systematic thermal instability (T i ) further decreased to 1.45 (Table 1).For channel opening upon the addition of AITC, the calculated mean Ω 10 of −8.68 was close to the experimental Q 10 of −9.16 at 100 µM PIP 2 (Table 1) [5].

Addition of Ca
the active lower S6 gate (Figure 3A).It had a 7-residue size from D866 to F868, F869, F870, L975, T982 and back to D866 (Figure 3D).Meanwhile, the biggest Grid22 in the pore domain had a 22-residue size to stabilize the open state via the shortest path from F874, W877, F881, Y963, R885, Y908 and back to F874 (Figure 3C,D).When 1.0-1.5 equivalent H-bonds sealed it, the calculated Tm ranged from 20 to 25 °C, which matched the sampling temperature 20 °C of the open state [22].As the total noncovalent interactions and grids size were 51 and 74, respectively (Figure 3A, Table S3), the grid-based systematic thermal instability (Ti) further decreased to 1.45 (Table 1).For channel opening upon the addition of AITC, the calculated mean Ω10 of −8.68 was close to the experimental Q10 of −9.16 at 100 µM PIP2 (Table 1) [5].

Discussion
The release of the lipid phosphatidylcholine (PC) or phosphatidylinositol (PI) from the vanilloid site of TRPV3 or TRPV1 is required for heat activation, respectively [33,34].In contrast, the cold activation of TRPM8 needs the lipid PIP2 [5,6,9,22].Although the role of PC or PI in heat response and sensitivity of TRPV3 or TRPV1 has been illuminated recently [27,28], much less is known about how the interaction of TRPM8 with PIP2 governs the specific temperature threshold and sensitivity for cold sensing.In this computational study, the three

Discussion
The release of the lipid phosphatidylcholine (PC) or phosphatidylinositol (PI) from the vanilloid site of TRPV3 or TRPV1 is required for heat activation, respectively [33,34].In contrast, the cold activation of TRPM8 needs the lipid PIP 2 [5,6,9,22].Although the role of PC or PI in heat response and sensitivity of TRPV3 or TRPV1 has been illuminated recently [27,28], much less is known about how the interaction of TRPM8 with PIP 2 governs the specific temperature threshold and sensitivity for cold sensing.In this computational study, the three PIP 2 -dependent biggest grids at or near the S5/S6 interface of mTRPM8 were identified in the presence of the high concentration of 1 mM PIP 2 .Further studies showed that the different interactions of mTRPM8 with PIP 2 , in response to the addition of Ca 2+ and the chemical agents C3 and AITC, created declined melting temperature threshold ranges, which were calculated from those PIP 2 -dependent biggest grids.When two threshold ranges in both open and pre-open closed states were similar, the channel could be opened with the matched thermosensitivity and the decrease in the systematic thermal instability.Finally, the intact anchor near the lower gate was necessary for channel opening with the active selectivity filter.Therefore, this study may promote our understanding about the role of the lipids in regulating distinct thermorings for specific temperature thresholds and sensitivity in thermo-gated TRP channels.The temperature threshold ranges increased from 23-29 • C to 31-37 • C when the concentration of PIP 2 raised from 0.1 to 0.5 mM [5].However, the underlying structural motif is unknown.This computational study identified two biggest grids in the systemic fluidic grid-like noncovalently interacting mesh networks of mTRPM8 in the presence of 1 mM PIP 2 .In the absence of the cooling agent C3, PIP 2 was found tightly bound with R688 and N692 in the pre-S1 domain, R851 at S4b, and R998 in the TRP domain via three salt bridges or one H-bond (Figure 1B).In this case, the biggest Grid 16 at the S5/S6 interface generated the calculated melting temperature threshold range from 32 to 37 • C, which was similar to the measured activation threshold range from 31 to 37 • C (Table 1) [5].In the presence of the cooling agent C3, the salt bridge between R851 and PIP 2 was substituted by the S850-PIP 2 H-bond (Figure 2B).In that case, another biggest Grid 21 at the S5/S6 interface had the calculated melting temperature threshold range from 22 to 27 • C, which was close to the experimental threshold range from 23 to 29 • C (Table 1) [5].Thus, it is possible that PIP 2 may have a similar interaction with TRPM8 for the biggest Grid 21 to be a temperature sensor in the pore domain when the concentration declines to 0.1 mM.
On the other hand, the temperature sensation of mammalian TRPM8 is reportedly regulated by the initial or ambient temperature [32].For example, the rise in the exposed temperature from 30 to 40 • C can increase the temperature threshold for the activation of human or rat TRPM8 (hTRPM8 or rTRPM8, respectively) from 28.3 • C to 33.8 • C in HEK293 cells expressing hTRPM8 [32].Furthermore, reducing the level of cellular PIP 2 or the R1008Q mutation in the TRP domain attenuates or eliminates the ambient temperatureinduced changes in the cold temperature threshold [32].Therefore, the interaction of TRPM8 with PIP 2 plays a pivotal role in modifying the temperature threshold for channel activation.At the ambient temperature 40 • C, the higher level of cellular PIP 2 may allow the tight interaction at the pre-S1/S4b/TRP interfaces to produce the biggest Grid 16 or the similar one with a higher temperature threshold 33.8 • C (Figure 1B,D, Table 1).In contrast, at lower pre-determined temperature 30 • C, cellular PIP 2 may decrease the level so that the relatively loose binding to the pre-S1/S4b/TRP interfaces could trigger the formation of another biggest Grid 21 or the similar one with the lower threshold of 28.3 • C (Figure 2B,D, Table 1).In good agreement with this proposal, in the former case, R1008 in the TRP domain interacted with both D781 in the VSLD and nearby E1004 via the salt bridges (Figure 1A).However, in the latter case, the D781-R1008 salt bridge was replaced by the D781-F1013 π interaction (Figure 2A).Thereafter, the R1008Q mutation may allow the loose binding of PIP 2 to TRPM8 to have a similar lower threshold for channel activation, no matter whether the exposed temperature increased from 30 to 40 • C [32].Since the cellular PIP 2 level did decline upon a temperature decrease from 25 to 10 • C [35], it is reasonable that the open state of TRPM8 could be stabilized at the maximal activity temperature of 8.2 • C [1,2].In that case, the stimulatory H-bond between H845 in the VSLD and E1004 in the TRP domain may be enough to allow the gating Grid 8 to hold the open state even at the lower PIP 2 level once TRPM8 has been activated (Figure 3A,D).

Implication of Transient Receptor Potential Melastatin-8 (TRPM8) Activation by Lysophospholipids (LPLs) and Menthol
In addition to PIP 2 , a small dose (3 µM) of long-chain intracellular LPLs can also directly activate TRPM8 even at normal body temperature.This activation has prominent prolongation of channel openings and can be suppressed by protons at pH 6 but not by Mg 2+ [10,11].In this case, PIP 2 may not be involved, so that either or both of free PIP 2 and AITC sites may hold LPLs with smaller head groups, stabilizing the stimulatory interaction between S4b and the TRP domain for channel opening at elevated temperature (Figure 3B) [6,22].
In contrast, menthol may share the same pocket with C3.The binding of a single menthol molecule to R841 on S4 has been proposed to stimulate TRPM8 activity [36].However, that model cannot explain the Y1005-dependent menthol upregulation of TRPM8 with a low efficacy but a high coefficient of a dose response at membrane hyperpolarization [19,37,38], and the ligand stereoselectivity of the LNI1009PAA mutant [19].Thus, in addition to H-bonding with R841, an H-bonded homochiral menthol dimer with head-tohead or head-to-tail is still required to push Y1005 against the anchors L841 and I844 on S4 of mTRPM8 for those experimental observations [20].In this way, the tighter interaction between PIP 2 and TRPM8 may be allowed to increase the melting temperature threshold for channel opening.Further structural data are necessary to reveal the LPLs or menthol sites and their roles in stimulating TRPM8 opening at higher temperature.The open state of mTRPM8 in the presence of high concentration of PIP 2 at 20 • C had the biggest Grid 22 for the melting temperature threshold range of 20-25 • C (Figure 1, Table 1).Therefore, even if the channel can be opened at 32-37 • C in the presence of 0.5 mM PIP 2 [5], the biggest Grid 22 would have melted at 32-37 • C and, hence, another biggest grid may be necessary to match the higher T m of 32-37 • C for channel opening.In contrast, the pre-open closed state of mTRPM8 with Ca 2+ and C3 bound in the presence of 1 mM PIP 2 had the biggest Grid 21 for the calculated T m range from 22 to 27 • C (Figure 2C,D).Therefore, the biggest Grid 22 in the open state could adapt a temperature range from 22 to 25 • C even if AITC was absent (Figure 4).In other words, the overlapped thresholds between open and pre-open closed states may be necessary for cold activation of TRPM8.Given that the threshold is 25 • C at the cellular PIP 2 concentration of 10 µM [5,39], further structural investigations of closed and open mTRPM8 at 10 µM PIP 2 around 25 • C may be required for the detailed understanding about how the TRPM8 bio-thermometer senses cold under the native physiological condition.1).The grid sizes (cyan) are shown in the red circles, along with equivalent basic H-bond numbers (orange) to control them.

Thermostable F874-Y908 π Interaction in the Pore Domain Was Needed for the Active Selectivity Filter
A previous chimera study of TRPM8 in a cold-sensitive mouse, rat or African elephant versus a cold-insensitive squirrel, hamster, chicken or emperor penguin showed that the outer pore loop is thermosensitive [40][41][42].Notably, the R897E mutation in mTRPM8 inhibits the cold response but does not alter the menthol response [41].Further, the Y908A mutation, rather than the Y908W/F mutation, in the P-helix suppresses the cold-sensing, although their response to icilin or menthol is not affected [43].Because Y908 is close to the selectivity filter [22], this residue is crucial for the cold-evoked activity.This study indicated that the F874-Y908 π interaction was highly conserved in both closed and open states (Figures 1A and 3A,Tables S1 and S3).In this regard, such a π interaction may be required to secure the active selectivity filter, although the segment from Y925 to P950 of the outer pore loop was unstructured in both closed and open states in the absence of the C929-C940 disulfide bond (Figures 1A-3A) [22,44].

Thermostable Anchor Grid7 at the S5/S6 interface Was Necessary for the Active Lower S6 Gate
D866, T982, F870, and L975 are highly conserved in thermosensitive TRPM2-5 and TRPV1-4 [22,33].The equivalent T680A mutation (T982 in mTRPM8) has been reported to suppress heat activation of TRPV3 [45].Moreover, both equivalent D576-T680 H-bond and F590-L673 π interaction in rTRPV1, or both equivalent D586-T685 H-bond and F580-L678 π interaction in mTRPV3, are always highly conserved in a thermo-stable anchor grid in both closed and open states [27,28].On the other hand, L975 is close to the lower S6 gate of mTRPM8 [22,44].Accordingly, the D866-T982 H-bond and the F870-L975 π interaction in the anchor Grid7 at the S5/S6 interface may be required to secure the active lower S6 gate of mTRPM8 (Figure 3A,D).In consonance with this proposal, the Y981F mutation near T982 in rTRPM8 is not functional but the Y981K/E mutation destabilizes the lower gate, rendering  1).The grid sizes (cyan) are shown in the red circles, along with equivalent basic H-bond numbers (orange) to control them.

Thermostable F874-Y908 π Interaction in the Pore Domain Was Needed for the Active Selectivity Filter
A previous chimera study of TRPM8 in a cold-sensitive mouse, rat or African elephant versus a cold-insensitive squirrel, hamster, chicken or emperor penguin showed that the outer pore loop is thermosensitive [40][41][42].Notably, the R897E mutation in mTRPM8 inhibits the cold response but does not alter the menthol response [41].Further, the Y908A mutation, rather than the Y908W/F mutation, in the P-helix suppresses the cold-sensing, although their response to icilin or menthol is not affected [43].Because Y908 is close to the selectivity filter [22], this residue is crucial for the cold-evoked activity.This study indicated that the F874-Y908 π interaction was highly conserved in both closed and open states (Figures 1A and 3A, Tables S1 and S3).In this regard, such a π interaction may be required to secure the active selectivity filter, although the segment from Y925 to P950 of the outer pore loop was unstructured in both closed and open states in the absence of the C929-C940 disulfide bond (Figures 1A-3A) [22,44].4.5.Thermostable Anchor Grid 7 at the S5/S6 interface Was Necessary for the Active Lower S6 Gate D866, T982, F870, and L975 are highly conserved in thermosensitive TRPM2-5 and TRPV1-4 [22,33].The equivalent T680A mutation (T982 in mTRPM8) has been reported to suppress heat activation of TRPV3 [45].Moreover, both equivalent D576-T680 H-bond and F590-L673 π interaction in rTRPV1, or both equivalent D586-T685 H-bond and F580-L678 π interaction in mTRPV3, are always highly conserved in a thermo-stable anchor grid in both closed and open states [27,28].On the other hand, L975 is close to the lower S6 gate of mTRPM8 [22,44].Accordingly, the D866-T982 H-bond and the F870-L975 π interaction in the anchor Grid 7 at the S5/S6 interface may be required to secure the active lower S6 gate of mTRPM8 (Figure 3A,D).In consonance with this proposal, the Y981F mutation near T982 in rTRPM8 is not functional but the Y981K/E mutation destabilizes the lower gate, rendering rTRPM8 constitutively active [46].Since these two noncovalent interactions only appeared in the open state of mTRPM8 (Figure 3A,D), the gating rearrangement at the temperature threshold may be necessary to keep the intact anchor Grid 7 at the S5/S6 interface for channel opening with the active selectivity filter.

Transient Receptor Potential Melastatin-8 (TRPM8) Opened with the Matched Thermosensitivity and the Decrease in the Systematic Thermal Instability
Although the cold sensitivity of TRPM8 in response to a native PIP 2 environment is high (Q 10 , 24-35) [11,12,21,32], the calculated structural thermosensitivity for channel opening from the pre-open closed state, upon the addition of the chemical agent AITC, was still lower in the presence of 1 mM PIP 2 (Ω 10 , −8.68) (Table 1).As this value was similar to the experimental Q 10 of −9.16 at 0.1 mM PIP 2 or the temperature coefficient (Q 10 , 9) of the rundown rate of cold response upon excision of the membrane patch into the PIP 2 -free bath solution [5,6], the physiological PIP 2 concentration for the cold detection of TRPM8 may be dynamic [6,9].On the other hand, although a simple two-state model or an allosteric model has been proposed for single-channel gating mechanisms of TRPM8 activation by cold and membrane depolarization [13,21], a more complex seven-state model may be needed for the high temperature sensitivity of TRPM8 [47], which cannot be figured out by two closed states and one open state in this study.In fact, in addition to the VSLD [40], the side-chain hydrophobicity in the pore domain has been shown to play a critical role in the thermosensitivity of TRPM8 in different vertebrates [42].However, the segment from Y925 to P950 of the outer pore loop in these three states were mostly unstructured (Figures 1A-3A).Hence, the alteration in the heat capacity as a result of the changes in not only the total grid sizes along the PIP 2 -dependent minimal gating pathway but also the side-chain hydrophobicity in the pore domain, along with multiple gating transitions, may be required for such high temperature sensitivity.In addition, recent behavioral studies have shown that phosphoinositide-interacting regulator of TRPs (PIRT) can bind to PIP 2 and is required for normal TRPM8-mediated cold-sensing [48].Therefore, further structural and functional examinations of the PIP 2 -dependent thermosensitivity, with or without PIRT bound along with the hydrophobic or hydrophilic change in the pore domain, are expected under the physiological condition.
In any way, it is interesting that the similar decrease in the systematic thermal instability (T i , from 1.90 to 1.45) was observed upon cold-evoked TRPM8 opening just it was as heat-evoked TRPV1 opening (T i , from 1.91 to 1.65) or TRPV3 opening (T i , from 1.88 to 1.20) [27,28].In that regard, the thermo-gated TRP channel opening may be driven by the minimization of the systematic thermal instability.Further cross-examinations of other thermo-sensitive TRP channels may be required.

Closing Remark
The TRPM8 channel can be activated by either cold or chemical agents such as C3 and AITC.This computational study demonstrated that both physical and chemical stimuli may share a similar gating pathway.Although Ca 2+ binding was not necessary, PIP 2 was required to induce the stimulatory interaction at the pre-S1/voltage sensor/TRP domain interfaces.Further, the overlapped thresholds between open and pre-open closed states may favor the cold-evoked channel activation.Finally, the intact thermal anchor grid near the lower gate was required to secure the active selectivity filter for channel opening.Accordingly, this study may provide important clues as to how the TRPM8 biothermometer uses the PIP 2 -dependent thermorings, from the biggest grids to the smallest ones, to achieve innocuous-to-noxious cold detection with specific matched temperature thresholds and sensitivity.This study further confirmed the existence of a lipid-dependent temperature sensor in thermo-gated TRP channels.The proposed mechanisms and thermoring concept in this study may facilitate our understanding of the activation of TRPM8 by lysophospholipids and menthol.

Figure 1 .
Figure 1.The grid-like non-covalently interacting mesh network along the PIP2-dependent minimal gating pathway of closed mTRPM8 with PIP2 bound at 20 °C.(A) The topological grids in the systemic fluidic grid-like mesh network.The cryo-EM structure of one subunit in homotetrameric closed mTRPM8 with PIP2 bound at 20 °C (PDB ID, 8E4N) was used for the model.The pore domain, the selectivity filter, S4b, the TRP domain, the voltage sensor-like domain (VSLD) and the pre-S1 domain are indicated in black arrows.Salt bridges, π interactions and H-bonds between paired amino acid side chains along the PIP2-dependent minimal gating pathway from Q675 to F1013 are marked in purple, green and orange, respectively.The grid sizes required to control the relevant noncovalent interactions were constrained with graph theory and labeled in black numbers.The F881-Y963 bridge in the biggest Grid16 was highlighted.The calculated total grid sizes and noncovalent interactions are shown in the cyan and black circles, respectively.(B) The structure of the PIP2 pocket.The grid size of the pocket is shown in a red circle.(C) The structure of the biggest Grid16 at the S5/S6 interface.The

Figure 1 .
Figure 1.The grid-like non-covalently interacting mesh network along the PIP 2 -dependent minimal gating pathway of closed mTRPM8 with PIP 2 bound at 20 • C. (A) The topological grids in the systemic fluidic grid-like mesh network.The cryo-EM structure of one subunit in homotetrameric closed mTRPM8 with PIP 2 bound at 20 • C (PDB ID, 8E4N) was used for the model.The pore domain, the selectivity filter, S4b, the TRP domain, the voltage sensor-like domain (VSLD) and the pre-S1 domain are indicated in black arrows.Salt bridges, π interactions and H-bonds between paired amino acid side chains along the PIP 2 -dependent minimal gating pathway from Q675 to F1013 are marked in purple, green and orange, respectively.The grid sizes required to control the relevant noncovalent interactions were constrained with graph theory and labeled in black numbers.The F881-Y963 bridge in the biggest Grid 16 was highlighted.The calculated total grid sizes and noncovalent interactions are shown in the cyan and black circles, respectively.(B) The structure of the PIP 2 pocket.The grid size of the pocket is shown in a red circle.(C) The structure of the biggest Grid 16 at the S5/S6 interface.The grid size is shown in a red circle.(D) The sequence of the biggest Grid 16 to control the F881-Y963 π interaction in the blue box.

Figure 2 .
Figure 2. The grid-like noncovalently interacting mesh network along the PIP 2 -dependent minimal gating pathway of closed mTRPM8 with Ca 2+ , PIP 2 and C3 bound at 20 • C. (A) The topological grids in the systemic fluidic grid-like mesh network.The cryo-EM structure of one subunit in homotetrameric closed mTRPM8 with Ca 2+ , PIP 2 and C3 bound at 20 • C (PDB ID, 8E4M) was used for the model.The C3 binding residue (Y745) is marked by an asterisk.The pore domain, the selectivity filter, S4b, the TRP domain, the VSLD and the pre-S1 domain are indicated in black arrows.Salt bridges, π interactions, H-bonds and metal bridges between paired amino acid side chains along the PIP 2 -dependent minimal gating pathway from Q675 to F1013 are marked in purple, green, orange and blue, respectively.The grid sizes required to control the relevant noncovalent interactions were constrained with graph theory and labeled in black numbers.The F881-T967 π bridge in the biggest Grid 21 was highlighted.The calculated total grid sizes and noncovalent interactions are shown in the cyan and black circles, respectively.(B) The structure of the PIP 2 binding site.The grid size of the pocket is shown in a red circle.(C) The structure of the biggest Grid 21 at the S5/S6 interface.The grid size is shown in a red circle.(D) The sequence of the biggest Grid 21 to control the F881-T967 π interaction in the blue box.

Figure 3 .
Figure 3.The grid-like noncovalently interacting mesh network along the PIP2-dependent minimal gating pathway of open mTRPM8 with Ca 2+ , PIP2, C3 and AITC bound at 20 °C.(A) The topological grids in the systemic fluidic grid-like mesh network.The cryo-EM structure of one subunit in homotetrameric open mTRPM8 with Ca 2+ , PIP2, C3 and AITC bound at 20 °C (PDB ID, 8E4L) was used for the model.The C3 binding residue (Y745) and the AITC binding residue (W798) are marked by asterisks.The pore domain, the selectivity filter, S4b, the TRP domain, the VSLD and the pre-S1 domain are indicated in black arrows.Salt bridges, π interactions, H-bonds and metal bridges between paired amino acid side chains along the PIP2-dependent minimal gating pathway from Q675 to F1013 are marked in purple, green, orange and blue, respectively.The grid sizes required to control the relevant non-covalent interactions were constrained with graph theory and labeled in black numbers.The F874-Y908 bridge in the biggest Grid22 at 20 °C was highlighted.The calculated total grid sizes and noncovalent interactions are shown in the cyan and black circles, respectively.(B) The structure of the PIP2 binding site.The grid size of the pocket is shown in a red circle.(C) The structure of the biggest Grid22 in the pore domain.The grid size is shown in a red circle.(D) The sequence of the biggest Grid22 to control the F874-Y908 π interaction in the blue box; the sequence of the gating Grid8 to control the H845-E1004 H-bond in the blue box; and the sequence of the anchor Grid7 in the pore domain to control the D866-T982 H-bond and the F870-L975 π interaction in the blue boxes.

Figure 3 .
Figure 3.The grid-like noncovalently interacting mesh network along the PIP 2 -dependent minimal gating pathway of open mTRPM8 with Ca 2+ , PIP 2 , C3 and AITC bound at 20 • C. (A) The topological grids in the systemic fluidic grid-like mesh network.The cryo-EM structure of one subunit in homotetrameric open mTRPM8 with Ca 2+ , PIP 2 , C3 and AITC bound at 20 • C (PDB ID, 8E4L) was used for the model.The C3 binding residue (Y745) and the AITC binding residue (W798) are marked by asterisks.The pore domain, the selectivity filter, S4b, the TRP domain, the VSLD and the pre-S1 domain are indicated in black arrows.Salt bridges, π interactions, H-bonds and metal bridges between paired amino acid side chains along the PIP 2 -dependent minimal gating pathway from Q675 to F1013 are marked in purple, green, orange and blue, respectively.The grid sizes required to control the relevant non-covalent interactions were constrained with graph theory and labeled in black numbers.The F874-Y908 bridge in the biggest Grid 22 at 20 • C was highlighted.The calculated total grid sizes and noncovalent interactions are shown in the cyan and black circles, respectively.(B) The structure of the PIP 2 binding site.The grid size of the pocket is shown in a red circle.(C) The structure of the biggest Grid 22 in the pore domain.The grid size is shown in a red circle.(D) The sequence of the biggest Grid 22 to control the F874-Y908 π interaction in the blue box; the sequence of the gating Grid 8 to control the H845-E1004 H-bond in the blue box; and the sequence of the anchor Grid 7 in the pore domain to control the D866-T982 H-bond and the F870-L975 π interaction in the blue boxes.

4. 3 .
Overlapped Temperature Thresholds between Open and Pre-Open Closed States Were Required for Cold-Sensing

Figure 4 .
Figure 4. Tentative cold switches in the TRPM8 biothermometer.A, the homo-tetrameric cryo-EM structure of mTRPM8 with (PDB ID, 8E4L) or without (PDB ID, 8E4M) AITC bound in the presence of Ca 2+ , PIP2 and C3 at 20 °C was used for the model of the open or pre-open closed state, respectively.For convenience, only two opposite subunits are shown.The dashed rectangle is the membrane area.The PIP2-dependent biggest Grid21 in the pre-open closed state and the biggest Grid22 in the open state have the overlapped Tm range of 22-25 °C for channel opening with the matched temperature threshold range and sensitivity (Table1).The grid sizes (cyan) are shown in the red circles, along with equivalent basic H-bond numbers (orange) to control them.

Figure 4 .
Figure 4. Tentative cold switches in the TRPM8 biothermometer.A, the homo-tetrameric cryo-EM structure of mTRPM8 with (PDB ID, 8E4L) or without (PDB ID, 8E4M) AITC bound in the presence of Ca 2+ , PIP 2 and C3 at 20 • C was used for the model of the open or pre-open closed state, respectively.For convenience, only two opposite subunits are shown.The dashed rectangle is the membrane area.The PIP 2 -dependent biggest Grid 21 in the pre-open closed state and the biggest Grid 22 in the open state have the overlapped T m range of 22-25 • C for channel opening with the matched temperature threshold range and sensitivity (Table1).The grid sizes (cyan) are shown in the red circles, along with equivalent basic H-bond numbers (orange) to control them.

Table 1 .
New PIP 2 -dependent parameters of the TRPM8 bio-thermometer, based on the grid thermodynamic model.The comparative parameters are highlighted in bold.