Thermoring basis for the TRPV3 bio-thermometer

The thermosensitive transient receptor potential (TRP) channels are well-known as bio-thermometers with specific temperature thresholds and sensitivity. However, their structural origins are still mysterious. Here, graph theory was used to test how the temperature-dependent non-covalent interactions as identified in the 3D structures of thermo-gated TRPV3 could form a systematic fluidic grid-like mesh network with the thermal rings from the biggest grids to the smallest ones as necessary structural motifs for the variable temperature thresholds and sensitivity. The results showed that the heat-evoked melting of the biggest grids may control temperature thresholds to activate the channel while the smaller grids may act as thermo-stable anchors to secure the channel activity. Together, all the grids along the gating pathway may be necessary for the specific temperature sensitivity. Therefore, this grid thermodynamic model may provide an extensive structural basis for the thermo-gated TRP channels.

Of special interest, TRPV3, which is mainly expressed in skin keratinocytes and oral and nasal epithelia mediating thermal reception and pain sensation [5][6], undergoes sensitization together with TRPV2 while TRPV1 and 4 channels desensitize in response to successive heat stimuli [1,[7][8][17][18][19]. Upon initial short heat stimulation within 100 ms, TRPV3 exhibits the high temperature threshold and sensitivity in the noxious temperature range above 50°C. After that intensive stimulation, it becomes responsive to warm temperatures with the low sensitivity. Further studies showed that the insertion of valine at position 412 dramatically eliminates the use-dependent heat sensitization of TRPV3 [19].
Following those ndings, the primary cryo-electron microscopy (cryo-EM) structural studies indicated that TRPV3 is a homotetramer. Each monomer has S1-S6 as a transmembrane domain (TMD) and a large intracellular amino-(N-) terminal as an ankyrin repeat domain (ARD). S1-S4 form a voltage-sensor-like domain (VSLD) while S5-S6 and the pore helix and two pore loops are folded as a pore domain. Both the VSLD and the pore domain are swapped via a S4-S5 linker. The TRP helices, which are almost parallel to the membrane, interact with both the skirt ARD and the TMD. Several lipid sites were also found in their interfaces [20]. The pre-S1 domain, together with the carboxyl-(C-) terminal loop domain, couples the TMD with the ARD. The residues 638 GLGD 641 in the P-loop-extended region line the selectivity lter to permeate partially hydrated Na + , K + or Ca 2+ ions but not to function as an upper gate. In contrast, the narrowest pore constriction around M677 on S6 may act as a lower gate [20][21]. Although the state-and redox-dependent cryo-EM structures of mouse TRPV3 (mTRPV3) with or without the Y564A mutation at different temperatures are available [22][23], the speci c structural motifs responsible for the usedependent temperature threshold and sensitivity have not been pinpointed.
On the other hand, following the ndings that a nucleic acid hairpin can function as a thermal ring with the number of H-bonds in the stem and the loop length to regulate the melting temperature threshold (T m ) [24][25][26], a graph theory-based grid thermodynamic model has been developed to describe proteins as a systematic uidic grid-like noncovalent interaction mesh network along a single polypeptide chain.
Further, the T m of each grid and the grid-based systematic thermal instability (T i ) have been de ned and calculated and compared with relevant experimental values. In this way, the theoretical and experimental match allows the thermal rings from the biggest grid to the smallest one to be identi ed as the necessary structural motifs for the thermal stability and activity of globular proteins such as two classes of fructose aldolases from psychrophilic to mesophilic and hyperthermophilic [27][28][29]. In this regard, it is necessary to test if membrane proteins such as TRPV3 also use such a series of thermo-rings as necessary structural motifs to achieve the use-dependent thermal sensitization.
In this computational, graph theory was used to examine this hypothesis by carefully decrypting each grid in the grid-like non-covalently interacting mesh networks as identi ed in the cryo-EM structures of mTRPV3 with or without the Y564A mutation at different temperatures [22][23]. Once the biggest grid was identi ed, the calculated T m was compared with the experimental threshold. Further, the grid-based systematic thermal instability (T i ) was also calculated as important energetic references to identify different gating states for the use-dependent sensitization. Finally, the systematic structural thermosensitivity (Ω 10 ) between any two gating states was also calculated and compared with the experimental Q 10 once de ned as a heat-evoked change of the total chemical potential of all the grids upon a change in the total enthalpy included in non-covalent interactions along the same gating pathway of one subunit between two gating states within 10°C apart. Once all the three lines of calculated parameters were found to be close to the experimental ones of some redox-and lipid-dependent gating states, a closed and reduced state, a sensitized but oxidized state, and an open and oxidized state were identi ed with a reasonable energetic sequence for the use-dependent heat sensitization of TRPV3.

Results
Reduced and PC-free mTRPV3-Y564A had the biggest Grid 13 in the Pre-S1/TRP interface for a calculated T m 38°C The cryo-EM structures of both closed and open states in detergent-solubilized PC-free mTRPV3-Y564A were rst sampled at 37°C after heat sensitization. Therefore, it is necessary to examine if the release of the phosphatidylcholine (PC) lipid from the vanilloid site by the Y546A mutation is responsible for the lower experimental temperature threshold and sensitivity [22].
The previous chimera studies between rat TRPV1 (rTRPV1) and mTRPV3 indicated that the pre-S1 segment 358-434 plays a critical role in mediating the temperature threshold and sensitivity Q 10 [30]. On the other hand, the chimera investigations between heat-sensing TRPV1 and cold-sensing TRP melastatin 8 (TRPM8) showed that the C-terminal including the TRP domain (693-710) is required for the polarity of thermal sensitivity [31]. In this regard, the segment from D396 in the pre-S1 domain to K705 in the TRP domain should be at least included as the necessary gating pathway for the temperature threshold and sensitivity and the systemic thermal instability. Along such a gating pathway, the diversity of noncovalent interactions between amino acid side chains in the closed and PC-free Y564 mutant was found after heat sensitization (Fig. 1A). They included 9 H-bonds emerged between different hydrophilic residues, twenty-six π interactions between aromatic residues and nearby residues, and 3 salt bridges between several charged pairs (Fig. 1A, Table S1).
When these non-covalent interactions formed a systematic grid-like non-covalent interaction mesh network, the total non-covalent interactions and grid sizes along the gating pathway from D396 to K705 were 38 and 77, respectively (Fig. 1A). Thus, the systemic thermal instability (T i ) was 2.03 (Table 1).
Meanwhile, in addition to the smallest grid with a 0-residue size in the VSLD, the biggest Grid 13 with a 13residue size appeared in the pre-S1/TRP interface via the shortest path from D396 to Y409, R698, R696, W433, K432 and back to D396 to control the D396-K432 salt bridge ( Fig. 1B-D). When 1.0 equivalent Hbond sealed this grid, the removal of the PC lipid from the vanilloid site by the Y564A mutation allowed a calculated T m of 38°C near the experimental T m 37°C (Table 1) [22].
The melting of the biggest Grid 13 at 37°C initiated channel opening of reduced and PC-free mTRPV3-Y564A with a low Ω 10 comparable to the low Q 10 When the mTRPV3-Y564A mutant opened with the melting of Grid 13 in the TRP/pre-S1 interface at 37°C, the disruption of the D396-K432 salt bridge triggered several changes in the systematic grid-like noncovalent interaction mesh network. In addition to one salt bridge, three H-bonds and 17 π interactions were conserved, two salt bridges, six H-bonds and eight π interactions were replaced with three new salt bridges, six new H-bonds and eight new π interactions (Tables S1 and S2). Thus, the total non-covalent interactions along the gating pathway from D396 to K705 had only a minor change from 38 to 39   [22]. In other words, the removal of the PC lipid from the vanilloid site by the Y564A mutation allowed reduced mTRPV3 to have the very low structural and functional thermo-sensitivities.
On the other hand, oxidized mTRPV3 with a disul de bond between C612 and C619 in the outer pore has also been reported to open from a PC-bound closed state at a lower threshold 42°C after repeated heat sensitization from 25°C to 40°C [23]. Therefore, it is exciting to test if oxidation also allows a low structural temperature sensitivity Ω 10 to be responsible for the measured functional temperature sensitivity Q 10 (1.9-3.1) [19].
Closed PC-bound mTRPV3 with the disul de bond in the outer pore had the biggest Grid 17 in the Pre-S1/VSLD interface for a calculated T m 40°C after heat sensitization Regarding the PC-bound closed state of oxidized mTRPV3 after heat sensitization, much more non covalent interactions than those in the PC-free closed state of reduced mTRPV3-Y564A shaped a distinct systematic uidic grid-like non-covalent interaction mesh network (Figs. 1A and 3A). In the presence of the C612-C619 disul de bond in the pore domain, four salt bridges (E610-K614 was merged into the C612-C619 disul de bond), fteen H-bonds and forty π interactions were identi ed between D396 and K705 ( Fig. 3A, Table S3). Since the total non-covalent interactions and grid sizes along the gating pathway from D396 in the pre S1 domain to K705 in the TRP domain were 59 and 72, respectively ( Fig. 3A), the grid-based systemic thermal instability (T i ) was about 1.22 (Table 1). Despite several smallest grids with a zero-residue size, the biggest Grid 17 with a 17-residue size was outstanding in the VSLD/pre-S1 interface to control the D519-R416 salt bridge ( Fig. 3B-D). It started with D519 and went through W521, F522, Y564, Y565, F441, W433 and ended with R416 ( Fig. 3E). When two equivalent Hbonds sealed the grid, the predicted T m was about 40°C (Table 1), which was close to the measured T m 42°C. [23] The melting of the biggest Grid 17 at 42°C drove oxidized mTRPV3 opening with a low Ω 10 comparable to the low Q 10 In the heat-activated open state, following the melting of the R416-D517 salt bridge in the biggest Grid 17 at 42°C as predicted (Fig. 3D) [23], although one salt bridge, ve H-bonds, and 35 π interactions were conserved, three salt bridges, ten H-bonds, and six π interactions were substituted by two new salt bridges, eight new H-bonds, and one new π interaction (Figs. 3A and 4A, Tables S3 and S4). However, two smallest Grid 0 with a zero-residue size were still conserved as anchors near the R416-D519 salt bridge: one via the shortest path from F445 to Y565, Y448, F449, and back to F445, and the other via the shortest path from Y448 to Y565, Y564, F526 and back to Y448 (Figs. 3A and 4A). Therefore, the following gating pathway against these two anchors was proposed.
Third, when the conformational wave extended to the S4-S5/TRP interface, the R567-T699 H-bond was disrupted and the E689-R693 H-bond changed to a salt bridge (Fig. 4A).
Taking all these changes into account, after the biggest Grid 17 in the VSLD/pre-S1 interface melted above the predicted 40°C, the PC lipid was released from nearby W521 and Q695 and thus the new biggest Grid 9 with a 9-residue size was created in the S5-S6 interface, which may be required for channel opening ( Fig. 4B (Table 1), which was close to the experimental Q 10 (1.9-3.1) [19]. Therefore, even if the PC lipid at the corresponding vanilloid site was not released, the presence of the C612-C619 disul de bond in the outer pore may be adequate for mTRPV3 to open with both low T m and Ω 10 to match the measured T th and Q 10 in response to the second heat stimulation [19]. In that regard, it is attractive to test if the disruption of the C612-C619 disul de bond can increase the T m and the Ω 10 upon channel opening from reduced mTRPV3 to meet the requirement of the higher T th (> 50 C) and Ω 10 (16.4-22.6) [19].
The melting of the biggest Grid 12 at the vanilloid PC site above T m 50°C was required to release PC from reduced mTRPV3 for channel opening with a high Ω 10 In the absence of the C612-C619 disul de bond, reduced mTRPV3 had some different noncovalent interactions to form the systematic grid-like non-covalent interaction mesh network at 4°C when compared with the closed and oxidized one at 42°C after heat sensitization (Figs. 4A & 5A, Table S5) [32].
By all account, the disruption of the C612-C619 disul de bond brought about the biggest Grid 12 at the vanilloid PC site (Fig. 5B). When two equivalent H-bonds governed the 12-atom path from W521 to PC to F524 (Figs. 5C-D), the predicted melting temperature was about 50°C (Table 1), which was close to the initial experimental T th 52°C for TRPV3 opening [19]. On the other hand, when compared with oxidized  (Tables S3, S4 and  S5). As the total non-covalent interactions and grid sizes along the gating pathway from D396 to K705 were 55 and 96, respectively (Fig. 5A), the systemic thermal instability (T i ) was 1.75 (Table 1). When the same open state as shown in the oxidized and PC-free mTRPV3 was employed (Fig. 4A)

Discussion
Thermo-sensitive TRPV3 is characterized as the use-dependent heat sensitization. Although several cryo-EM structures of mTRPV3 are available in different gating and redox states and at various temperatures, the speci c structural motifs responsible for this use-dependent heat sensitization are still missing. This computational study rst demonstrated that the calculated melting temperature threshold (T m ) of the biggest grid along the gating pathway in mTRPV3 was comparable to not only the structural T m but also the functional activation threshold T th of mTRPV3. It further con rmed that the functional thermosensitivity Q 10 was also comparable to the grid-based structural thermo-sensitivity Ω 10 . Finally, the grid-based systematic thermal instability values of mTRPV3 in different redox-and lipid-dependent gating states were also compared with each other to establish the energetic relationship of different gating states. Taken as a whole, three gating states were completely identi ed to account for the use-dependent heat sensitization of TRPV3.
First, it was further con rmed that the biggest grid may employ its size and strength to determine the melting temperature threshold (T m ) of TRPV3. At a given salt concentration (150 mM NaCl), for reduced and sensitized mTRPV3-Y564A, when 1.0 equivalent H-bond sealed the biggest Grid 13 Table 1), the biggest grids along the gating pathway may be responsible for the optimal activity temperature range of the mTRPV3 bio-thermometer [19].
Third, increased temperature has been reported to accelerate the dissociation rate (k d ) of enthalpy-driven non-covalent interaction in a biophysical network but to slow down k d of entropy-driven crosslinks to a different extent [34]. In this study, an increase in the opening rate or the open probability (P o ) of TRPV3 has been observed with raised temperatures [23]. If the temperature threshold for TRPV3 opening is governed by a rate-limiting single step to disrupt a non-covalent interaction in the biggest grid along the gating pathway, TRPV3 opening would be initially enthalpy-driven (ΔH < 0). In this case, when thermogated TRPV3 opens from a closed state within 10°C, the functional thermo-sensitivity (Q 10 ) should be comparable to the calculated systematic structural thermo-sensitivity Ω 10 because they both factually re ect the change of the total chemical potentials of all the grids upon the alteration of the total enthalpy included in the non-covalent interactions along the same gating pathway from D396 to K705. In agreement with this proposal, if wild-type mTRPV3 had the same open and oxidized state, the calculated mean Ω 10 of reduced mTRPV3 would be 18.3, which was close to the measured Q 10 (16.4-22.6) ( Table 1) [19]. For oxidized and sensitized mTRPV3, the calculated mean Ω 10 was 4.12, which was similar to the measured Q 10 (1.9-3.1) ( Table 1) [19]. For the reduced mTRPV3-Y564A mutant, the calculated mean Ω 10 was 1.48, which was near to the measured Q 10 1.21 (Table 1) [22]. Thereafter, the functional thermo-sensitivity Q 10 may be governed by the grid-based systematic structural thermosensitivity Ω 10 as de ned. In this regard, when the intensity of a non-covalent interaction was in the range from 0.5 to 3 kJ/mol, the resultant Ω 10 ranges from the minimum to the maximum may be theoretically calculated as 8.76-58.5 for reduced and closed mTRPV3, 1.88-14.3 for sensitized and oxidized mTRPV3, and 0.76-4.3 for reduced and sensitized mTRPV3-Y564A (Table 1).
Taken together, it is proposed that reduced mTRPV3 may start the rst activation above the calculated T m 50°C upon the fast heat stimulation. Once the channel is opened, it is oxidized to form the C612-C619 disul de bond so that the functional thermo-sensitivity Q 10 (16.4-22.6) can keep consistent with the calculated Ω 10 (18.3) (Fig. 6A, Table 1). It is further proposed that when the temperature declines, oxidized but sensitized mTRPV3 may decrease a T th to 30-40°C and Q 10 to 1.9-3.1 as a result of the formation of the C612-C619 disul de-bond (Fig. 6A, Table 1) [19]. In this way, the lower threshold 30-40°C may increase the open probability in response to the same temperature jump from 32°C to 59°C so that mTRPV3 activation exhibits the use-dependent sensitization upon successive heat stimuli [19]. In direct line with this use-dependent sensitization, the grid-based systemic thermal instability (T i ) in the closed state was 1.75 for reduced mTRPV3, and slightly decreased to 1.22 when oxidized by heat sensitization in favor of the use-dependent heat-sensitization during channel opening with a similar T i of 1.25 (Table 1). In contrast, the Y564A mutation increased the grid-based systemic thermal instability (T i ) from 1.75 to 2.03 for the sensitized but closed state and 1.90 for the open state (Table 1). In other words, the Y564A mutation may increase the systemic thermal instability in favor of spontaneous channel opening [22]. On the other hand, when reduced or Cys-less mTRPV3 is exposed to the long and slow heat stimulation, the channel can be activated above a threshold T th 30°C [33]. Therefore, it is also possible that either the formation of the C612-C619 disul de bond by air oxidation or the Cys-less mutation may increase the length of the R416-D519 salt bridge to account for the declined T th of 30°C so that the PC lipid could be released from the vanilloid site for channel opening (Fig. 6A, Table 1). When the insertion of valine at position 412 disrupts the T411-D519 salt bridge and the related smaller Grid 4 via the shortest path from T411 to R416 and D519 and then back to T411 (Figs. 5A, 6B), the same biggest Grid 17 as shown in oxidized but closed mTRPV3 may be followed in the VSLD/pre-S1 interface in favor of the release of the vanilloid site lipid for channel opening below 40°C in response to the rst fast heat stimulus (Figs. 3A, 5A, Table 1). That may be why the insertion of valine at 412 removes the use-dependent sensitization upon repeated heat stimuli [19]. In support of this proposal, when the Y564A mutation release the PC lipid from the vanilloid site, it also had a low calculated T m (38°C) and Ω 10 (1.48) to keep consistent with the low threshold (< 37°C) and the low Q 10 (1.21), respectively ( Fig. 1-2, Table 1) [22].
In any way, several smaller anchor grids in the pore domain may be important to stablize the common open state in favor of high heat e cacy. In the pore domain, the rst was Grid 7 with the shortest path from F590 to Y594, T636, Y661, T665, L673 and back to F590, and the second was Grid 9 with the shortest path from D586 to F590, L673 and T680 and then back to D586 (Figs. 4A, 4C, 6B). It has been reported that the T636S mutation decreases the temperature threshold [33], and the mutation N643S, I644S, N647Y, L657I, Y661C or T680A is actually less sensitive to heat or slows down the activation rate [30,32,[35][36]. Therefore, it is possible that these mutations may affect the thermostability of these smaller anchor grids in the pore domain.
In contrast, four smallest grids with a zero-residue size in the VSLD may form a basic stable backbone anchor system for mTRPV3 activation or a fuse group to keep a low systemic thermal instability (

CONCLUSION
In this computational study, a graphical grid thermodynamic model has bridged crystallographic static conformations with electrophysiological dynamic ndings together by using graph theory in atomic details. Once the thermal rings in the systematic uidic grid-like mesh network of non-covalent interactions along the gating pathway were tested and identi ed as key deterministic structural factors or motifs for thermo-gated mTRPV3, three gating states could be in turn established to account for the usedependent heat sensitization of TRPV3. Accordingly, this model can be used to predict the thermal stability and activity of cellular biological macromolecules including membrane proteins once highresolution 3D structural data are available.

Data mining resources
In this in silico study, two groups of the temperature-dependent cryo-EM structures of mTRPV3 in different gating and redox states were analyzed by graph theory to abstract the structural bioinformation for the use-dependent temperature thresholds and sensitivity. One included reduced and sensitized mTRPV3-Y564A at 37°C in the detergent (PDB ID, 6PVO, model resolution = 5.18 Å) and reduced and open mTRPV3-Y564A (PDB ID, 6PVP, model resolution = 4.4 Å) at 37°C in the detergent [22]; The other covered oxidized and sensitized WT mTRPV3 in cNW11 at 42°C (PDB ID, 7MIN, model resolution = 3.09 Å), oxidized and open WT mTRPV3 in cNW11 at 42°C (PDB ID, 7MIO, model resolution = 3.48 Å) [23], and reduced and closed WT mTRPV3 in MSP2N2 at 4°C (PDB ID, 6LGP, model resolution = 3.31 Å) [32].

Standards for non-covalent interactions
In order to secure that results could be reproduced with a high sensitivity, the same strict standard de nition as described previously as well as structure visualization software, UCSF Chimera, was exploited to identify stereo-or regio-selective inter-domain diagonal and intra-domain lateral non-covalent interactions in the 3D strcutres of mTRPV3 (Tables S1-S5) [27][28][29]. They included salt-bridges, CH/cation/lone pair/π−π interactions and H-bonds along the gating pathway from D396 to K705 in mTRPV3 with or without the Y564A mutation. Notably, although the hydrophobic effect and residue hydrophobicity are necessary to drive protein folding, their effects on protein stabilization may be rather marginal [37][38].
Preparation of topological grid maps by using graph theory The identi ed non-covalent interactions were geometrically mapped as edges along with marked node arrows to represent the positions of the linked residues in the systematic uidic mesh network according to the same protocol as previously described [27][28][29]. All the grids were then covered in this network after their ring sizes were constrained as the minimal number of the total free side chains of residues or atoms in the bound lipid that did not participate in any non-covalent interction in a grid. The size constraint was completed by using graph theory and the Floyd-Warshall algorithm to calculate the shortest return path from one end of a non-covalent interaction to the start because the direct path from the start to the end was zero. [39]. For example, in the intra-subunit grid-like biochemical reaction mesh network of Fig. 3A, a direct path length from E610 and N647 was zero because of an H-bond between them. However, there was another shortest return path from N647 to K614 and back to E610 via the N647-K614 H-bond and the K614-E610 salt bridge in this grid. Therefore, the grid size was zero. Once all the grid sizes were available, only the uncommon sizes were marked in black, and a grid with an x-residue or atom size was denoted as Grid x . When the total number of all noncovalent interactions and grid sizes along the gating pathway were calculated, they were displayed in black and blue circles beside the mesh network map, respectively, for the calculations of the systematic thermal instability and the structural temperature sensitivity.
Calculation of the temperature threshold of mTRPV3 A DNA hairpin thermo-sensor with a 20-base loop and two G-C base pairs in the stem has a start control melting temperature threshold (T m ) of 34°C to initiate thermal unfolding of the hairpin loop. When an additional G-C base or ve additional bases are included in the hairpin, the T m is increased by 10°C [26].
In a similar way, when a single polypeptide chain in protein carries out rate-limiting thermal unfolding of the thermal rings from the biggest grid to the smallest grid, the T m of thermal unfolding of the given grid along the chain was calculated by using the following equation as described previously [27][28][29]: T m (°C) = 34 + (n-2)×10 + (20-S max )×2 (1) where, n is the total number of the grid size-controlled H-bonds equivalent to non-covalent interactions in the given grid, and S max is the size of the given grid. In this regard, the more grid's heat capacity will be expected with the decreased grid size or the increased equivalent H-bonds.

Calculation of the systemic thermal instability (T i )
On the other hand, the T m of the DNA hairpin will be always increased by the more G-C base pairs in the stem or the shorter the poly-A loop [26]. Thus, the grid-based systemic thermal instability (T i ) along the single polypeptide chain was reasonably de ned using the following equation as described previously [27][28][29]: where, S is the total grid sizes and N is the total non-covalent interactions along the gating pathway of one subunit in a gating state. Usually, the lower T i , the less the conformational entropy in the system.

Calculation of the systematic temperature sensitivity of mTRPV3
For initial enthalpy-driven TRPV3 opening upon decyclization of the biggest grid (ΔH < 0), if a thermosensitive TRPV3 channel changes from a fully closed state to a fully open state within a temperature range ΔT, and if the chemical potential of a grid is de ned as the maximal potential for equivalent residues in the grid to form a tight and ideal β-hairpin with the smallest loop via non-covalent interactions [40], the grid-based systematic structural thermo-sensitivity (Ω ΔT ) of a single ion channel can be de ned and calculated using the following equations:  , temperature threshold; TMD, transmembrane domain; TRP, transient receptor   potential; TRPA, TRP ankyrin; TRPC, TRP canonical; TRPVi, TRP vanilloid i; TRPV3, TRP vanilloid-3;   rTRPV1, rat TRPV1; mTRPV3, mouse TRPV3; TRPMi, TRP melastatin i; TRPM8, TRP melastatin 8; VSLD, voltage-sensor-like domain; WT, wild-type.
Declarations Figure 1 The grid-like non-covalently interacting mesh network along the gating pathway of PC-free reduced mTRPV3-Y564A in the sensitized state at 37 °C after heat sensitization.
A, The topological grids in the systemic uidic grid-like mesh network. The cryo-EM structure of one subunit in detergent-solubilzed mTRPV3-Y564A, which was PC-free, reduced, sensitized but closed at 37 (PDB ID, 6PVO), was used for the model. The pore domain, the S4-S5 linker, the TRP domain, the VSLD and the pre-S1 domain are indicated in black. Salt bridges, p interactions, and H-bonds between pairing amino acid side chains along the gating pathway from D396 to K705 are marked in purple, green, and orange, respectively. The grid sizes required to control the relevant non-covalent interactions were calculated with graph theory and labeled in black. The total grid sizes and grid size-controlled noncovalent interactions along the gating pathway are shown in the blue and black circles, respectively. B, The location of the biggest Grid 13 is marked in a red circle. C, The structure of the biggest Grid 13 with a 13-residue size in the TRP/pre S1 interface to control the D396-K432 salt bridge. D, The sequence of the biggest Grid 13 to control the D396-K432 salt bridge in a blue rectangle. (PDB ID, 6PVP) was used for the model. The pore domain, the S4-S5 linker, the TRP domain, the VSLD and the pre-S1 domain are indicated in black. Salt bridges, p interactions, and H-bonds between pairing amino acid side chains along the gating pathway from D396 to K705 are marked in purple, green, and orange, respectively. The grid sizes required to control the relevant non-covalent interactions were calculated with graph theory and labeled in black. The total grid sizes and grid size-controlled noncovalent interactions along the gating pathway are shown in the blue and black circles, respectively. B, The structure of the smaller Grid 4 with a 4-residue size to control the D519-R698 salt bridge and F526-Y565 p interaction in the grid. C, The location of the biggest Grid 11 is marked in a red circle. D, The structure of the biggest Grid 11 with an 11-residue size in the VSLD/TRP/pre S1 interfaces to control the H417-E689 and T411-S515 H-bonds. E, The sequences of two smaller Grid 4 and Grid 11 to control the aformentioned non-covalent interactions in the blue boxes, respectively. The grid-like non-covalently interacting mesh network along the gating pathway of PC-bound oxidized mTRPV3 in the sensitized state at 42 °C after heat sensitization.
A, The topological grids in the systemic uidic grid-like mesh network. The cryo-EM structure of one subunit in sensitized and oxidized mTRPV3 with PC bound in cNW11 at 42 °C (PDB ID, 7MIN) was used for the model. The pore domain, the S4-S5 linker, the TRP domain, the VSLD and the pre-S1 domain are indicated in black. Salt bridges, p interactions, and H-bonds between pairing amino acid side chains along the gating pathway from D396 to K705 are marked in purple, green, and orange, respectively. The grid sizes required to control the relevant non-covalent interactions were calculated with graph theory and labeled in black. The total grid sizes and grid size-controlled non-covalent interactions along the gating pathway from D396 to K705 are shown in the blue and black circles, respectively. C, The location of the biggest Grid 17 is marked in a red circle. D, The structure of the biggest Grid 17 with a 17-residue size in the VSLD/pre S1 interface to control the strong R416-D519 salt bridge. E, The sequence of the biggest Gird 17 to control the R416-D519 salt bridge in a blue box.

Figure 4
The grid-like non-covalently interacting mesh network along the gating pathway of PC-free oxidized mTRPV3 in the open state at 42 °C after heat sensitization.
A, The topological grids in the systemic uidic grid-like mesh network. The cryo-EM structure of one subunit in open and oxidized mTRPV3 without PC bound in cNW11 at 42 °C (PDB ID, 7MIO) was used for the model. The pore domain, the S4-S5 linker, the TRP domain, the VSLD and the pre-S1 domain are indicated in black. Salt bridges, p interactions, and H-bonds between pairing amino acid side chains along the gating pathway from D396 to K705 are marked in purple, green, and orange, respectively. The grid sizes required to control the relevant non-covalent interactions were calculated with graph theory and labeled in black. The total grid sizes and grid size-controlled non-covalent interactions along the gating pathway are shown in the blue and black circles, respectively. B, The location of the biggest Grid 9 is marked in a red circle. C, The structure of the biggest Grid 9 with a 9-residue size in the S5-S6 interface to control the D586-T680 H-bond. D, The structure of the putative smaller Grid 3 with a 3-residue size for the lower gate. E, The sequences of two smaller gating Grid 9 and Grid 3 to control the D586-T680 H-bond and a group of crtitical cation-p interactions in the blue boxes, respectively.
Page 26/28 The grid-like non-covalently interacting mesh network along the gating pathway of PC-bound reduced mTRPV3 in the closed state at 4 °C without heat sensitization.
A, The topological grids in the systemic uidic grid-like mesh network. The cryo-EM structure of one subunit in reduced and closed mTRPV3 with PC bound in MSP2N at 4 °C (PDB ID, 6LGP) was used for the model. The pore domain, the S4-S5 linker, the TRP domain, the VSLD and the pre-S1 domain are indicated in black. Salt bridges, p interactions, and H-bonds between pairing amino acid side chains along the gating pathway from D396 to K705 are marked in purple, green, and orange, respectively. The grid sizes required to control the relevant non-covalent crosslinking interactions were calculated with graph theory and labeled in black. The total grid sizes and grid size-controlled non-covalent crosslinking interactions along the gating pathway are shown in the blue and black circles, respectively. The T411-D519 H-bond, which is marked in a dashed line, may be disrupted by the insertion of valine or serine at position 412. B, The location of the biggest Grid 12 is marked in a red circle. C, The structure of the biggest Grid 12 with a 12-atom size at the PC site to control the W521-PC-F524 bridge. D, The sequence of the biggest Grid 12 to control the W521-PC-F524 bridge in a blue box.