## 3 Results
### Complexes with Estradiol and Progesterone  
Complexes in which estradiol and progesterone were bonded with ER\(\alpha\) and PR, respectively, remained stable during simulations (see protein RMSD and Rg profiles in Figure S3), with no significant change in the orientation of the ligand molecules in the rather tight binding pocket of the receptor proteins (Figure S4). Ligands' RMSF profiles indicate low fluctuations of estradiol and progesterone heavy atoms during the production phase (Figure 2).  
Strong hydrogen bonds formed between the hydroxyl groups (oxygen atoms O3 and O17) of estradiol and E353 and H524 residues of ER\(\alpha\), and the carbonyl groups (oxygen atoms O3 and O20) of progesterone and R766, Q725 and C891 residues of PR, greatly contributing to ligand stabilization in the interior of the protein during simulations  
Figure 2: Ligands’ heavy atoms RMSF profile calculated throughout the entire MD simulation after RMSD alignment of the ER\(\alpha\), PR or AR backbone to the first structure obtained from the production phase was performed. The O1 atom of cholesterol is covalently bonded with G197 residue from the SHH-N C-terminal. Atom names are indicated in Figure 1.  
(Figure S5). Interestingly, salt bridge interaction between E353 and R394 residues of ER\(\alpha\) found at the entrance to the ligand binding site, and present in the ligand-free protein structure (e.g., in ER\(\alpha\) structure deposit under PDB code 2B23), is mostly preserved upon complexation (Figure S6). By referring to overlaying SHR structures it can be seen that amino acids Q725 and R766 in PR protein (and Q711 and R752 in AR protein) are located at the equivalent position as E353 and R394 in ER\(\alpha\). Although intra-molecular hydrogen bonds between Q725 and R766 residues of PR rarely form in complexes with progesterone (Figure S6), they more frequently engage in inter-molecular hydrogen bonding with progesterone (Figure S5).  
In addition to these hydrogen bonding interactions, the MM/GBSA per-residue analysis highlights the importance of non-polar amino acid residues of ER\(\alpha\) (L346, A350, L387, M388, L391, F404, M421, and L525) and PR residues (L715, L718, L721, Q725, M756, M759, V760, L763, R766, F778, L887, and Y890) in the stabilization of the gonane core of estradiol and progesterone (respectively) within the interior of the receptor binding site (residues indicated with red dots in Figure 3 and depicted in Figure 4).  
Figure 3: The MM/GBSA per-residue energy decomposition was performed for ER\(\alpha\), PR, and SHH-N proteins in the studied complexes. The energies were calculated based on 0.5 \(\upmu\)s-long MD simulations for complexes with sex steroid hormones and cholesterol. For complexes involving SHH-N, the last 0.5 and 0.6 \(\upmu\)s-long trajectories were considered, corresponding to complexes with PR and ER\(\alpha\), respectively. Values are given for residues with energy contributions larger than \(\pm\)1.5 kcal/mol. The amino acid residues from the unstructured N- and C-terminus of SHH-N protein (residues C24-K45 and V185-G197, respectively) are indicated. Residues highlighted with a red dot interact with estradiol, progesterone or cholesterol (moiety), while residues highlighted with a green or gray dot interact with unstructured C- or the N-terminus of the SHH-N protein, respectively. The Glu353 residue of ER\(\alpha\) and Gln725 residue of PR have red and green dots assigned, as in complexes with SHH-N-cholesterol they interact both with sterols and the SHH-N C-terminus.