## 3 Results
### SHRs in Complex with SHH-N-Cholesterol (PP Complexes)  
The RMSD profiles of individual proteins within the PP complexes (red and green curves in Figure S3, left) indicate that protein structures remained preserved during MD simulations. Furthermore, the globularity of each protein (ER\(\alpha\), PR, AR or SHH-N-cholesterol) has not changed during the production phase (red and green curves in Figure S3, middle). Similarly, the RMSD and R\({}_{\text{g}}\) profiles calculated for the entire PR-SHH-N-cholesterol and AR-SHH-N-cholesterol complexes suggest that these structures remained stable throughout the production phase, showing minimal deviation from their initial configurations (black curves in Figure S3, left and middle, and Figures S7 and S8). The final PR-SHH-N-cholesterol complex structures derived from two separate 1 \(\upmu\)s-long MD simulations are almost identical (Figure 5a), with RMSD of C\(\alpha\) atoms (not considering SHH-N unstructured N- and C-termini) of 1.22 A (see structures show in Figure 5b). This indicates the high stability of the PR-SHH-N-cholesterol, as well as AR-SHH-N-cholesterol, complex structure initially predicted by docking. The alignment of the final structure of the AR-SHH-N-cholesterol complex obtained in this study with those from our previous work [20] reveals the formation of similar PP complexes (see Figure S9). The most notable difference lies in the position of the SHH-N-cholesterol N-terminus, which is shown to be the most flexible part of the protein (as discussed below). The consistent binding energies calculated throughout the production phase, as outlined in Table 1 for each complex, further affirm the stability of the initially predicted PR-SHH-N-cholesterol and AR-SHH-N-cholesterol complex structures. Figure 4: Binding of estradiol (green) and progesterone (cyan) with ER\(\alpha\) and PR (SHR proteins in light gray), respectively, in the optimized structures obtained after 0.5 \(\upmu\)s of simulation. Residues that, according to per-residue MM/GBSA analysis (Figure 3), interact with the ligand are indicated. Non-polar hydrogens and main chain atoms are not shown. Hydrogen bonds are indicated as yellow dashed lines. Figure 5: The PR-SHH-N-cholesterol structures obtained from the molecular modeling study: (**a**) aligned structures obtained by the Hdock server (violet) and after 1 \(\upmu\)s of MD simulations (green and yellow), (**b**) aligned optimized complex structures obtained after 1 \(\upmu\)s of MD simulations, where PR  
is colored in gray, and SHH-cholesterol in lime. Furthermore, residues of SSH-N-cholesterol found within 4 A of PR are colored magenta, and residues of PR found within 4 A of SHH-N-cholesterol are colored cyan. In the middle and bottom rows, an enlarged view is provided, highlighting the residues that, based on per-residue MM/GBSA analysis, contribute to the complex stabilization. More precisely, PR residues that: (**c**) interact with cholesterol moiety, (**d**) stabilize binding of the unstructured C-terminus of SHH-N, and (**e**) stabilize binding of the unstructured N-terminus of SHH-N, as well as its more structured central part, are shown. Hydrogen bonds are indicated with a dashed yellow line. Non-polar hydrogen atoms are not shown. Cholesterol moiety is shown as a sphere (and sticks) and colored magenta in (**b-e**). During MD simulations, a significant structural deviation from its initially docked configuration was observed in the ER\(\alpha\)-SHH-N-cholesterol complex, as evidenced by the complex RMSD profile (black curve in Figure S3, middle). This structural rearrangement can be described as a shift in the mutual orientation of individual proteins (see Figures S7 and S8). The reorganization of protein subunits is concomitant with changes in binding energies (refer to Table 1). Specifically, after 300 ns of MD simulations, the energy of the ER\(\alpha\)-SHH-N-cholesterol complex becomes more negative, signifying an increase in binding affinity. The most stable complex is formed after 1.4 us of MD simulation (Table 1).