## 3 Results and Discussion
### Molecular Dynamics Studies  
To further elucidate the binding interactions and ascertain the stability of the peptides upon binding to PHF tau, we carried out molecular dynamics studies. The four optimal peptides in their best binding modes were chosen based on the results of the docking studies. These include KAWVCDGDND (TauRP1-2), WVCDGDNDCE (TauRP1-4) (mode 2), GDNDCEDNSD (Tau RP1-8) and DNSDEENCES (TauRP1-14). The results obtained are shown in Figure 6.  
The C\(\alpha\) RMSDs over 100 ns runs are shown in Figure 6a. Overall, the backbone protein RMSDs appeared to be stable and ranged from 0.35 nm to 0.6 nm, with the highest C\(\alpha\) RMSD seen upon binding to TauRP1-2. All others showed RMSD values between 0.35 nm and 0.45 nm, indicating stability. When bound to Tau RP1-4, the C\(\alpha\) RMSD showed a slight increase of 0.6 nm, observed between 20 ns and 25 ns, after which the RMSD values remained between 0.4 nm and 0.5 nm. The RMSDs of each of the peptides complexed with Tau are shown in Figure S1 of the Supplementary Materials. As can be seen in the figure, the most stable and lowest RMSD value was seen for the peptide GDNDCEDNSD (TauRP1-8),  
Figure 6: (**a**) Comparison of C\(\alpha\) RMSDs of PHF Tau upon binding to each of the TauRP peptides; (**b**) trajectory images of top three conformers based on clustering obtained at the last 25 ns of simulations from left to right for each ligand with PHF Tau. (**i**) TauRP1-2 with PHF Tau; (**ii**) TauRP 1-4 with PHF Tau; (**iii**) TauRP1-8 with PHF Tau; (**iv**) TauRP1-14 with PHF Tau. where the RMSD remained stable between 0.52 and 0.6 nm throughout the 100 ns run. For the peptide DNSDEENCES (TauRP1-14), the RMSD value showed a gradual increase from 0.3 nm to 0.85 nm within the first 25 ns and then gradually increased to 0.92 nm up to 72 ns, after which the RMSD was found to be stable at 0.86 nm for the rest of the simulation. The KAWVCDGDND (TauRP1-2) and WVCDGDNDCE (TauRP1-4) peptides showed similar RMSD patterns after 25 ns. The RMSD value for the KAWVCDGDNDD peptide increased substantially to 1.1 nm within the first 15 ns and then remained fairly stable between 0.78 nm and 0.9 nm for the rest of the simulation. In the case of WVCDGDNDCE, the RMSD values increased at 23 ns and at 78 ns to 1.1 nm; however, once again, it stabilized to 0.82 nm by the end of the simulation. When compared to C\(\alpha\) values, the overall change in RMSD was found to be within 0.4 nm for TauRP1-2 and TauRP1-14 peptides, indicating that those peptides formed relatively more stable complexes compared to TauRP1-4 and TauRP1-8. To further elucidate these results, we conducted clustering analysis of the trajectories over the course of the last 25 ns of the simulations. The top three preferred conformers of each of the TauRP peptides bound to PHF Tau are seen in Figure 6b. The tau filamentous structure consists of four microtubule-binding repeat regions with eight beta strand regions and a cross-\(\beta\) interface formed between \(\beta\)1-2 and \(\beta\)8 regions. The N-terminal end is formed by the hexapeptide VQIVYK between residues 306 and 311, which is well-known to be involved in the aggregation and formation of tau filaments [106]. The \(\beta\)2 and \(\beta\)8 strands pack against each other through a polar-zipper motif while hydrophobic residues L324, I326 and V353 form a cluster. The cross-\(\beta\) interface between \(\beta\)3 and \(\beta\)7 is stabilized by hydrogen bonds between the side-chains of hydrophilic residues H328 and T361. Overall, hydrophobic interactions and aromatic stacking (F346) stabilize the interior of the \(\beta\)-helix, while the charged residues E338 and R349 on the solvent-exposed surface of the \(\beta\)-helix provide intramolecular charge compensation.