RMSD
After embedding TRPV2 in the membrane, molecular dynamics (MD) simulation was done for 50 ns. The value of the root mean square deviations (RMSD) is a good parameter for evaluating structure stability because it make structural comparison between initial structure and following structure during simulations 17. As shown in Fig. 1a, the system reached equilibration with RMSD value around 0.55 nm that indicated the overall stability and good convergence during MD simulations. After that, RMSD value of steered molecular dynamics (SMD) simulation was calculated during 6 ns that was stabilized around 0.4 nm. The results indicated that the channel was stable when calcium passed through it (Fig. 1b). RMSD of MD and SMD were calculated for backbone of TRPV2 channel.
Ion conduction pathway
The molecular architecture and gates region of TRPV2 channel has been described in some previous studies. The length of TRPV2 ion-conduction pathway from the beginning first gate to end of second gate is approximately 50 Å 9,12,15. As shown in Fig. 2a, b, the pore dimensions of TRPV2 were calculated after simulations. The results indicated that radius of first gate had been wide than second gate and showed a big cavity (about a radius of 6.5 Å) between first gate to the second gate. The length of the first gate was about 10 Å that located in range of 9 to19 Å and consisted of four residues (Gly606, Met607, Gly608 and Glu609). Also, the length of the second gate was about 12 Å that located in range of 32 to 44 Å in ion conduction pathway. The second gate contained distal end of S6 that Met640 and Ile642 were identified as important residues 12. Previous studies showed that the first and second gates are open state with van der Vaals radius about 3.5 Å and 3 Å, respectively 16,18. The Results demonstrated that the channel was in the Apo-state and first and second gates were open after simulations.
Radial distribution functions:
Radial distribution function (RDF) is a function of distance from a specific point which describes density of atoms surrounding the point in MD simulation 19. RDF was calculated to investigate the important residues in transport mechanism of calcium ion through the TRPV2 channel. As shown in Fig. 3a, b, RDF showed a sharp peak in monomer C of first gate, and monomer A and D of S6 segments (AA630- AA650) that confirmed ion passed close to these monomers. Moreover, results showed that maximum g (r) in first gate was significantly higher than S6 segments (about 3000 and 70, respectively) because the monomers of first gate had an angle to Z direction (Fig. 3c, d). In the other hand, by placing the ion at a distance of around 1 nanometer from another atoms, they can interact with each other by electrostatic and Van der Waals interactions. So, these results showed that all monomer in first gate and monomer A and D in S6 segments can be considered as effective regions for passing ion through the channel.
Interaction’s energy analysis
To determine which residues were important for passing calcium ion through TRPV2 channel, interactions energy was calculated for each residuein the path of ion transport. Non-bonded energies that describe interactions between different atomsarise due to van der waals and charged (electrostatic) interactions which were modeled using the Lennard-Jones potential and Coulomb's law, respectively. Non-bonded energies between two stationary charged particles are calculated with below formula in equation (1).
Where A and B are Lennard-Jones parameters, r is the interatomic distance, qi,j are the atomic charges and D (= 4εr) is a dielectric function. Moreover, interactions energy can be attractive or repulsive that are shown as negative and positive values, respectively 20–22. Indeed, the net interactions energy between atoms is obtained from the sum of these energies. In first gate, while Lennard-Jones energy was positive in monomers A, C, D but Coulomb energy was extremely negative. These results indicated that, generally, interactions energy between calcium and first gate were attractive. In addition, in the presented residues in calcium ion pathway (S6 segments; AA630 - AA650), Lennard-Jones and coulomb energies were calculated, so that these energies in the monomer D were positive and negative, respectively and the net energy of interactions was negative. A comparison of these results showed that the attraction force (that are determined through interactions energy) between calcium ions and first gate was more than other areas (Fig. 4).
To determine which residues from the channel monomers participate in interactions, Lennard-Jones and coulomb energies were calculated for each residue in first gate and S6 segments (Data not shown). Results demonstrated that the following residues played an important role to conduct the calcium ion through the channel including Gly606, Met607, Gly608, Glu609, Tyr634, Leu637, 638, Met640, Leu641, Ile642, Ala643, Leu644, Met645, Ser646, Gly647, Thr648, Val649 and Asn650.
Diffusion of water in trpv2 channel:
In many channels, diffusion of water molecules play an important role in the transfer of ions 23,24. So, water density and interactions of water with calcium ion were determined during SMD simulation. Our results showed that water density in first gate was lower than the created hole by S6 segments. Indeed, the Lennard-Jones energies between calcium ion and water molecules were positive in first gate and its values were lower than S6 segments. Unlike the Lennard-Jones energies, coulomb energies were negative in first gate and its values were higher than S6 segments. Moreover, fluctuation of coulomb energy during 4000 to 4300 ns can be caused by change of radius in this region, so that radius of this region was found to decrease from 6.5 Å in meddle channel to 2.5 Å in near the end of the channel (second gate region) (Fig. 5). Results in Figs. 4, 5, demonstrated that interactions of water molecules with calcium ion caused to decrease interactions of Ca2+ with residues in the ion pathway. So, interaction of Ca2+ with residues in first gate were more than the rest of the ion path.
Ion permeation in TRPV2 channel
Constant velocity pulling is a method in SMD simulation that an atom, molecule or compound is moved with a constant velocity by applying external forces. The force is calculated below formula in Eq. (2).
where k is the spring constant, x and v are the coordinate and velocity of the pulling atom respectively and t is time 25,26. Absolutely, if we want to keep the velocity constant, the force must change during simulation because there are some interactions that affect the force. In the other hand, the force indicates whether the interactions are attractive or repulsive in direction of coordination 27,28.
As shown in Fig. 1b, first gate was located 1 nm away from the mouth of the channel and its length was about 1 nm. Also, Fig. 6b, showed that the calcium ion had traveled this path about 1.7 ns. Moreover, the force increased to pass ion thought first gate because of steric effect and abundance of interaction between calcium ion and residues. When the ion passed thought first gate, the force slumped and calcium ion traveled a distance of about 1 nm during a few times step because radius in this region (middle of S6 segments) increased to 6.5 Å and interaction between calcium ion and its amino acid decreased. Furthermore, as mentioned earlier, effective residues in this path and second gate caused to fluctuate in the force (Figs. 4, 6). Generally, these results indicated that required forces for passing calcium ion through first gate were more than second gate which their values were about 1000 and 400 KJ/mol/nm, respectively.
Potential of mean force (PMF)
PMF is an important parameter in computational studies that reflects all interactions of the desired molecule with its environment as ion, amino acids and solvent, etc. Moreover, dehydration at the entrance and inside the channel strongly affects PMF. It should be noted that PMF is not an average of interactions and potentials, but is equivalent to the Helmholtz free energy 29,30.
Existence of two gates on path of Ca+ 2 conductions had caused a force fluctuation pattern with two big force jump. (Figs. 1, 6). Therefore, as shown in Fig. 7, there were two large barriers at first and second gates. In the first gate, energies for two main steps of reaction mechanism were about 10 and 15 Kcal/ mol as well as in second gate, which occurred a leap of energy from 3.2 nm to 3.8 nm with energy value about 28 Kcal/ mol and another energy step was about 3 Kcal/ mol. The obtained results indicated that barrier energy in second gate was higher than first gate because in addition to the interactions energy, ion dehydration occurred at time 4000 to 4300 ps in the second gate (Figs. 5e, 7). Also, radius of second gate was less than first gate that was an important parameter in the energy calculation. Ultimately, the large barriers of energy at the gates support this suggestion that calcium ion cannot easily enter and/ or leave the TRPV2 channel.