## 2 Results and Discussion
### Potential Use of FEYNF Self-Assembling Aggregates in Polyplex Formation  
Polyplexes are a special type of macromolecular complex that have garnered significant attention in recent decades owing to their potential applications in gene therapy. These specialized complexes arise through the interaction of (macro)molecular entities, such as polypeptides and polycations, with nucleic acids (DNA or RNA) [60]. Gene delivery systems are currently divided into two primary directions: viral and non-viral vector systems. Given the substantial risks associated with viral vectors, increased focus has shifted toward non-viral systems, predominantly relying on the use of cationic lipids, cationic polymers, or cationic polypeptides [61]. For example, it was demonstrated the efficiency of dendritic amino acid-conjugated polyamidoamines as carriers for human adipose-derived mesenchymal stem cells (AD-MSCs), as they exhibit lower immunogenicity and cytotoxicity, as well as higher transfection efficiency [62]. Peptide-based non-viral vectors are also considered ideal candidates for gene therapy, mainly due to their cell-penetrating capacity [63]. In this context, the polyplex formation capacity of the FEYNF peptide was investigated by molecular docking simulations (in silico study). Hence, the optimized protonated FEYNF@FEYNF dimer complex (shown in Figure 8) was employed in a second molecular docking simulation study using a DNA oligonucleotide sequence as the receptor. To this end, the Drew-Dickerson dodecamer d(CGCGAAT TCGCG)2 was used as a model for the short DNA helix simulation [60; 64]. Details regarding the molecular structure of the dodecamer are given in Figure S8 (in Supplementary Materials). Hence, the protonated peptide dimer (FEYNF@FEYNF(+2)) was modeled as a rigid ligand, while the negatively charged Drew-Dickerson dodecamer (DDD (\(-\)25)) was modeled as \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**FEYNF Peptide** & \multicolumn{6}{c}{**Torsion Angles 1**} \\ \cline{2-7}
**Chain** & \(\Phi_{1}\) & \(\Psi_{1}\) & \(\Phi_{2}\) & \(\Psi_{2}\) & \(\Phi_{3}\) & \(\Psi_{3}\) \\ \hline Chain-1 & \(-137.069^{\circ}\) & \(144.980^{\circ}\) & \(-137.509^{\circ}\) & \(123.895^{\circ}\) & \(-126.403^{\circ}\) & \(151.016^{\circ}\) \\ Chain-2 & \(-81.123^{\circ}\) & \(132.445^{\circ}\) & \(-139.163^{\circ}\) & \(116.446^{\circ}\) & \(-43.919^{\circ}\) & \(-52.269^{\circ}\) \\ \hline \hline \end{tabular} \({}^{\dagger}\) The determined torsion angles (dihedrals) correspond to the ones represented in Figure 1a.  
\end{table} 
Table 1: Values of the torsion angles (\(\Phi\)—_Phi_ and \(\Psi\)—_Psi_) for the two FEYNF peptide chains in the optimized dimer conformation. a rigid receptor. In this instance, after running 100 poses for the polyplex conformation, 12 representative docked models (clusters) were identified. The results of the molecular docking calculations, encompassing information on binding energy, dissociation constant, and contact residues, are comprehensively presented in the Supplementary Material (Table S4 and Figure S9). The optimal docking pose between the protonated dimer complex (FEYNF@FEYNF(+2)) and the DNA oligonucleotide sequence (DDD (\(-\)25)) is shown in Figure 9. Consequently, the most favorable affinity was observed at the lowest binding energy (\(E_{b}=-12.49\) kcal/ mol) and the smallest dissociation constant (\(K_{d}=0.694\) nM). Notably, the nanometric order of the dissociation constant value indicates the formation of a highly stable docked complex, affirming the successful formation of the polyplex. As illustrated in Figure 9, polyplex formation relies on noncovalent interactions, such as hydrophobic interactions, inter- and intramolecular H-bonds, \(\pi\)-\(\pi\) stacking, and cation-\(\pi\) interactions. The attractive \(\pi\)-\(\pi\) interactions primarily occur between the \(\pi\) bonds of the PHE1 aromatic ring in the peptide dimer and the fused-ring molecules of the DNA purine nucleobases (G4-guanine and A5-adenine).