Fig. 1. The Frenet frame vectors (t_i, n_i, b_i) at the i-th C_α atom.

Fig. 2. The virtual bond and torsion angles (κ_i, τ_i) along the backbone C_α chain.

Fig. 3. The radius of gyration evolution with temperature increasing. The gray, red, yellow dashed lines are corresponding to the real temperatures of 25 °C, 75 °C, and 90 °C, respectively. Reproduced with permission from Ref. [46].

Fig. 4. The susceptibility of helical denucleation. Three transition temperatures are labeled as T₁, T₂, T_E, representing the two transition temperatures for the radius of gyration and for the energy, respectively. The colored thick dash lines are the same as in Fig. 3. Reproduced with permission from Ref. [46].

Fig. 5. The superimposition of the soliton model and PDB structures. Left panel is for 2L86 and right panel is for 3DXC. The light blue is from PDB structure and the red is from soliton model. Reproduced with permission from Refs. [35,36].

Fig. 6. The conformational clusters for 2L86 at low temperature. Panel (a) is the conformational landscape, and panel (b) is the representative structures. Reproduced with permission from Ref. [35].

Fig. 7. The conformational clusters for 3DXC at low temperature. Panel (a) is the energy landscape of the conformational ensemble, where the red triangle denotes the initial structure in PDB. Panel (b) is the representative structures whose energies are lower than the initial structures. Reproduced with permission from Ref. [36].

Fig. 8. The corresponding soliton mobility of the clusters in 3DXC. Reproduced with permission from Ref. [36].

Fig. 9. The conformational clusters for 1NKP at low temperature. Top panel is the energy landscape of the conformational ensemble, where the red triangle denotes the initial structure in PDB. The bottom panel is the corresponding conformational landscape projected from top panel. Reproduced with permission from Ref. [38].

Fig. 10. The stability comparison among clusters in 1NKP, (a) comparison of the RMSD evolutions in MD simulations with initial conformations in clusters 1, 4, and 5 (denoted as PDB in the legend), (b) a comparison of the radius of gyration evolutions in MD simulations with initial conformations in clusters 1, 4, and 5 (denoted as PDB in the legend), (c) the conformational landscape evolution for MD simulations with initial conformation from cluster 1, (d) the conformational landscape evolution for MD simulations with initial conformation from cluster 5. Reproduced with permission from Ref. [38].

Fig. 11. The folding index evolution in MD simulation. The top panel is the folding index in the entire MD simulation process, and bottom panel is a zoom in of top panel in frame 3950–4000. Reproduced with permission from Ref. [37].

Fig. 12. The sidechain soliton motion in the N-terminal of the protein during the MD simulation. The two panels show the same data, but from different perspectives, for the first ten residues. Reproduced with permission from Ref. [37].

Table 1. The proteins that have been fitted using topological soliton model.