## 3 Results
### SHRs in Complex with SHH-N-Cholesterol (PP Complexes)
During the simulation, the N-terminus stabilizes by binding to the SHRs, establishing interactions with E330, L345, N348, D351 and Y537 residues in the complex with ER\(\alpha\); D704, N705, T706 and E904 residues in the complex with PR; and D690 residue in the complex with AR (Figures 3 and S10). The lowest number of amino acids from AR that interact with the N-terminus of SHH-N, as identified by per-residue MM/GBSA analysis, indicates the highest flexibility of that region in the complex with AR (see Figure S7, right). By analyzing native and non-native contacts with the coptraj module of the AMBER program, we observed a generally consistent number of total contacts between the receptor and the SHH-N-cholesterol protein lacking 22 amino acid residues at the N-terminus, during the entire MD simulations of the PR-SHH-N-cholesterol and AR-SHH-N-cholesterol complexes, as well as during the last 0.6 \(\upmu\)s of the MD simulation of the ER\(\alpha\)-SHH-N-cholesterol complex (Figure S14b). The number of these contacts is similar for all three complexes. In addition, analyses have indicated that the total number of contacts between the receptors and SHH-N protein increases as the simulation progresses, which can be explained by the progressively more stable binding of the N-terminus of SHH-N-cholesterol to the body of the SHR protein. The largest number of contacts observed during the last 600 ns of MD simulations in the ER\(\alpha\)-SHH-N-cholesterol (Figure S14a) aligns with the highest binding affinity determined for the complex during this period. (Table 1). At the same time, large fluctuations in the total number of contacts observed for the AR-SHH-N-cholesterol complex agree with the highest flexibility of the SHH-N N-terminus noted for this complex throughout MD simulations (Figure S7, right). Figure 6 illustrates all contacts, encompassing both native and non-native interactions, on the structures of the PP complexes for each amino acid, as calculated during the final 200 ns of the simulations. Notably, it becomes evident that the N- and C-terminal amino acid residues of SHH-N-cholesterol, along with the cholesterol moiety itself, exert the most pronounced impact on PP complex stabilization in all complexes with SHH-N-cholesterol. According to MM/PBSA binding enthalpies (Table 1), the binding of cholesterol attached to the C-terminus of SHH-N to ER\(\alpha\) is more exothermic than the binding of estradiol (\(-12.87\) kcal/mol) or cholesterol alone (\(-17.50\) kcal/mol), which have almost similar binding energies. Apparently, numerous favorable interactions between SHH-N and ER\(\alpha\) proteins contribute to more favorable binding of SHH-N-cholesterol to ER\(\alpha\), than estradiol. Interestingly, calculated MM/PBSA binding energies predict similar enthalpies for progesterone (\(-19.02\) kcal/mol), free cholesterol and cholesterol attached to SHH-N C-terminus to PR. Apparently, MM/PBSA analysis predict no significant difference in cholesterol binding to PR when free or attached to SHH-N C-terminus, suggesting a negligible energy contribution of the SHH-N protein body to the formation of the PP complex. Figure 6: Relative contact strengths for all native and non-native contacts calculated on the last 200 ns of MD simulations (1.8–2.0 \(\upmu\)s in case of ER\(\alpha\)–SHH-N-cholesterol, 0.8–1.0 \(\upmu\)s in case of PR–SHH-N-cholesterol complex simulation with lower binding energy determine, and 0.3–0.5 \(\upmu\)s in case of AR-SHH-N-cholesterol) and shown using B-factor purity representation (for protein residues) and/or color coding (protein and cholesterol moiety). Relative contact strengths calculated per atom are summed for each residue and summed values are shown. A red to white to blue colors (with minimum and maximum values set at 5 and 200, respectively) and a narrower to wider tube indicate regions with lower to higher summed relative contact strength. The complex is oriented so that the SHR is at the top and SHH-N is at the bottom of the figure.