2.1 Data mining resources
The systemic fluidic grid-like non-covalently interacting mesh networks of rTRPV1 in different gating states were based on the cryo-electronic microscopy (cryo-EM) structural data of closed rTRPV1 in MSP2N2 with PI-bound at 4°C (PDB ID, 7LP9, model resolution = 2.63 Å) and 48°C (PDB ID, 7LPC, model resolution = 3.07 Å), capsaicin (Cap)-bound at 4°C (PDB ID, 7LPA, model resolution = 3.37 Å), 25°C (PDB ID, 7LPB, model resolution = 3.54 Å), and 48°C for 10 s (EMD ID, 23477, model resolution = 3.70 Å) and 30 s (EMD 23478; PDB ID, 7LPD, model resolution = 3.55 Å) [13]. Meanwhile, open rTRPV1 with Cap-bound at 48°C (PDB ID, 7LPE, model resolution = 3.72 Å) and the the pre-open state of rTRPV1 with resiniferatoxin (RTx) bound at 25°C (PDB ID, 7RQX, model resolution = 3.73 Å) were used as important controls [13, 19].
2.4 Preparation of topological grid maps by using graph theory
Once the non-covalent interactions were filtered, all the grids as defined previously were geometrically mapped along the PI-dependent gating pathway in the different gating states and at distinct temperatures [15–18]. The grid size (S) was constrained by the Floyd-Warshall algorithm as the minimal number of the total side chains of residues in protein or atoms in the bound lipid that did not involve any non-covalent interaction in a grid [20]. As a consequence, the shortest direct or reverse path between two ends of a noncovalent interaction was available. For example, in the grid-like biochemical reaction mesh network of Fig. 1A, a direct path length from Y627 and E636 was zero because there was an H-bond between them. However, there was another shortest reverse path from E636 to F649 and back to Y627 via two π interactions. Because nothing but these three residues was involved in the non-covalent interactions, the grid size was zero. Once each non-covalent interaction was tracked with a grid size, the unshared sizes were then marked in black. Taken as a whole, a grid with an x-residue or atom size was denoted as Gridx, and the total non-covalent interactions and grid sizes along the PI-dependent gating pathway of one subunit were calculated and shown in black and cyan circles beside the mesh network map, respectively, in favor of the calculation of the systematic thermal instability (Ti) and the structural thermosensitivity (Ω10).
2.5 Equations
Following the report that thermal unfolding of the DNA hairpin was controlled by the G-C base pairs or the H-bonds in the stem and the loop length [14], the same equation as described and examined previously was used to calculate the melting temperature threshold (Tm) for thermal unfolding of the given grid [15–18]:
Tm (°C) = 34 + (n − 2) × 10 + (20 - Smax) × 2 (1)
where, n is the total number of simple H-bonds energetically equivalent to the non-covalent interactions controlled by the given grid, and Smax is the size of the given grid. Accordingly, a decrease in the grid size or an increase in equivalent H-bonds will raise the grid’s heat capacity.
Similarly, the same equation as described and examined previously was employed to define and to calculate the systematic thermal instability (Ti) along the PI-dependent gating pathway [15–18]:
Ti = S/N (2)
where, S and N are the total grid sizes and the total non-covalent interactions along the PI-dependent gating pathway of one subunit in a given gating state. On the ground of this definition, the lower Ti means the less conformational entropy in the system.
For enthalpy-driven TRPV1 opening from the pre-open closed state within a temperature range ΔT as a result of the broken biggest grid, if the chemical potential of a grid is theoretically defined as the maximal potential for equivalent residues in the grid to form the tightest β-hairpin with the smallest loop via non-covalent interactions [21], the grid-based structural thermo-sensitivity (ΩΔT) of a single ion channel can be defined and calculated using the following equations:
ΩΔT = [(Sc - So)E/2](Hc/Ho) = [(Sc - So)E/2][(ENc)/(ENo)] = [(Sc - So)E/2](Nc/No) (3)
where, along the same PI-dependent gating pathway of one subunit, Nc and No are the total non-covalent interactions, Hc and Ho are the total enthalpy included in them, and Sc and So are the total grid sizes in the closed and open states, respectively. E is the energy intensity of a non-covalent interaction in a range of 0.5-3 kJ/mol. Usually, E is 1 kJ/mol [22]. Thus, ΩΔT factually reflects a thermo-evoked change in the total chemical potential of grids upon a thermo-evoked change in the total enthalpy included in the non-covalent interactions from a closed state to an open state along the same PI-dependent gating pathway of one subunit. For the enthalpy-driven TRPV1 inactivation from the pre-open state within a temperature range ΔT as a result of the broken biggest grid, the same equation was used to calculate the apparent ΩΔT value between open and inactivated states after the closed state was replaced with the inactivated state.
When ΔT = 10°C, Ω10 could be comparable to the functional thermo-sensitivity (Q10) of a single ion channel. Q10 during the thermal activation was calculated using the following equation:
Q10 = (X2/X1)10/(T2−T1 ) (4)
However, during the thermal inactivation, it was calculated using the following equation:
Q10 = -(X1/X2)10/(T2−T1) (5)
where, X1 and X2 are open probability (Po) values or reaction rates obtained at temperatures T1 and T2 (measured in kelvin), respectively.