## 3 Results
### SHRs in Complex with SHH-N-Cholesterol (PP Complexes)
Specifically, according to MM/GBSA analysis (Figure 3), these residues interact with cholesterol as strongly as they do with estradiol or progesterone. However, in complexes with the latter, hydrogen bonding with these residues predominantly contributes to ligand stabilization, while in complexes with cholesterol, van der Waal's interactions with these amino acids play a key role in stabilizing ligand binding. A salt bridge interaction between E353 and R394 residues, located at the entrance to the ER\(\alpha\) buried binding site, is observed in the complex with SHH-N, as in the complex with estradiol (Figures S6 and S12). However, in the ER\(\alpha\)-SHH-N-cholesterol complex, E353 does not form a hydrogen bond with the hydroxyl group of the cholesterol molecule (oxygen atom O1), as it does with the hydroxyl (O3) group of estradiol (Figure S5). Instead, it more frequently engages in hydrogen bonding with the amino acid residues from the unstructured C-terminus of the SHH-N protein (Figure S13, middle). In complexes with PR, residues Q725 and R766 (found at the entrance to the PR binding site) are more frequently engaged in hydrogen bonding with the ligand (Figures 5d and S5) than with each other (Figures S6 and S12). Similar to the complex with progesterone, R766, and frequently Q725, residues make a hydrogen bond with the hydroxyl group of the cholesterol molecule (oxygen atom O1) that corresponds to carbonyl (O3) groups of progesterone, but also with amino acid residues from the unstructured C-terminus of the SHH-N protein (Figures 5d and S12). Residues R572 and Q711 from AR also make hydrogen bonds with amino acid residues from the unstructured C-terminus of the SHH-N protein (Figures S12 and S13). A higher number of hydrogen bonds between these residues near the entrance of the SHRs' binding site and the C-terminus of SHH-N is observed in the complex with ER\(\alpha\), than with PR and AR (Figure S12). In addition to the aforementioned hydrogen bonds, the per-residue MM/GBSA analysis identified other residues from SHRs that interact with the tetra-peptide motif K194-G197 at the C-terminus of SHH-N and contribute to PP complexes stabilization (highlighted with green dots in Figures 3 and S10). Favorable interactions involve receptor residues E323, I326, E353, H356, R394, L403, and P406 in the complex with ER\(\alpha\); V698, I699, Y700, Q725, H770, Y777, and P780 in the complex with PR; and E681, Q711, A748, W751, R752, and T755 in the complex with AR. Apart from the residues from the unstructured C-terminus of SHH-N, which are in direct contact with SHR due to cholesterol binding in the interior of the receptor, the unstructured N-terminus and the more structured central part of the SHH-N protein also participate in the formation of stable PP complexes with ER\(\alpha\), AR or PR (Figures 3 and S10). According to MM/GBSA analysis, the residues from the structured central part of the SHH-N protein that stabilize PP complexes are: N69, K74 and E75 in the complex with ER\(\alpha\); T77, P78, N79, Y80, P82, D83, N107 and I111 in the complex with PR; and Y80, P82, D83, Q100, A108 and I111 in the complex with AR (Figures 3 and S10). Residues within SHRsthat establish favorable interactions with SHH-N include: P325 and Y328 of ER\(\alpha\); S693, E695, D697, Y700 and R724 of PR; and V676, A679 and V685 of AR (Figures 3 and S10). It can be noticed that chemically different amino acid residues contribute to the stabilization of the PP complex, and that more amino acids from the central part of the SHH-N protein contribute to the stabilization of the complex with PR and AR, than ER\(\alpha\). As expected, MD simulation indicated that the most flexible part of the SHH-N-cholesterol protein in PP complexes is its N-terminus (Figure S7).