## 3 Results and Discussion
### Molecular Dynamics Studies
The number of contacts increased to 38 contacts by the end of the simulation, implying that this peptide remained in contact with higher numbers of residues throughout the entire simulation and had more binding interactions. To further assess the interactions, we examined the root mean square fluctuations (RMSF), radius of gyration (Rg) and the solvent-accessible surface area (SASA) of the PHF Tau-bound peptides (Figure 7). The RMSF results are indicative of relative fluctuations of the tau protein backbone over the 100 ns simulation upon interacting with each of the ligands. Overall, tau protein showed fluctuations in the same regions for all four peptides, which included residues F378 in the C-terminal region, and T377, G323, L376, K311 and V306. Upon binding to the TauRP1-2 peptide, interactions are seen in the region between D348 and S352 from the B chain as well as R349 to K353 of the D and F chains. Large fluctuations are seen in the C-terminal region, and interactions with TauRP (1-2) are also seen in this region. It is to be noted that L376, F378 and T377 are at or near the C-terminal ends of the tau protein and therefore, higher fluctuations of those residues are expected. Interestingly, TauRP (1-4) binding resulted in similar regional fluctuations in addition to His 362. Upon binding to TauRP (1-8), as seen from the regions showing the vertical lines, binding occurs in the binding pocket making interactions with R349, Q351, K369, K353 and I371. Peptide TauRP (1-14) binding leads to fluctuations in similar regions as those of the other peptides; however, relatively fewer fluctuations are seen in the C-terminal region compared to TauRP (1-2) and TauRP (1-4). To examine the compactness of the peptides upon interacting with the PHF Tau [107], we analyzed the changes in the radius of gyration over the entire 100 ns simulation. As seen in (Figure 7e), TauRP1-8 and TauRP1-2 showed higher compactness, and their Rgyr values showed very little variation during the simulation. In the case of TauRP1-2, the Rgyr changed from 0.54 nm to 0.58 nm, while for TauRP1-8, the Rgyr changed from 0.68 nm to 0.64 nm by the end of the simulation. For the TauRP1-14, the Rgyr value remained at 0.64 nm for the first 50 ns, after which there was a gradual increase in value to 0.72 nm up to 75 ns, and it remained constant up to 90 ns and showed a decrease to 0.64 nm at the end of the simulation. This implies that the TauRP1-14 underwent conformational changes between 50 ns and 75 ns but then returned to a relatively compact form by the end of the simulation. The highest Rgyr was seen for TauRP1-4 (0.74 nm initially), which increased to 0.83 nm for the first 20 ns and then came down to 0.7 nm for the rest of the simulation, once again implying that this particular peptide underwent conformation changes during the initial part of the simulation and returned to a stable, compact conformation. All four peptides displayed low pI values due to the presence of several aspartate or glutamate groups. Of the four peptides, Tau RP1-2 had a relatively higher pI (3.53) due to the presence of lysine residue at the N-terminal, while all others displayed pI values in the range of 2.64 to 2.74. Because each of the peptides contain a number of charged groups, we also investigated the SASA (solvent-accessible surface area) values obtained over the course of the simulation. As seen in Figure 7f, the SASA value for TauRP1-4 was found to be the highest and showed very little change over time (100.1 nm\({}^{2}\) initially to 99.8 nm\({}^{2}\) at the end of the simulation). TauRP1-8, which displayed an initial SASA value of 50.8 nm\({}^{2}\), showed a decrease to 38.8 nm\({}^{2}\) by the end of the simulation. Similarly, both TauRP1-14 and TauRP1-2 also showed a decrease in SASA values over time. In the case of TauRP1-14, the value decreased from 59.0 nm\({}^{2}\) to 40.0 nm\({}^{2}\), while for TauRP1-2, the value remained steady at 77.2 nm\({}^{2}\) up to 65 ns, after which the value decreased gradually to 50.3 nm\({}^{2}\).