## 1 Introduction
In one of our previous studies of the role of HH-GLI signaling pathway in breast cancer (BC), we found that SHH co-localize with estrogen receptor alpha (ER\(\alpha\)) in the ER-positive BC cell line MCF-7, but not in the ER-negative cell line SK-BR-3 [18]. Since cholesterol is a precursor to all sex steroid hormones (Figure 1) [19], we have started to hypothesize that SHH-N could physically interact, though its cholesterol PTM, with SHRs, and activate their signaling pathways (i.e., achieve transcription of their target genes). In our more comprehensive study of the role of the HH-GLI signaling pathway in prostate cancer (PC), we have proven, both experimentally and computationally, that in the androgen-dependent prostate cancer cell line LNCaPP, which was made androgen-independent, SHH-N non-canonically binds to AR and activates it, and thus sustains androgen-independent PC cell growth [20]. Furthermore, inhibition of this interaction by statins, the cholesterol-lowering drugs, led to AR signaling downregulation, and this might offer a valuable, new strategy for the treatment of advanced (or so-called \"castration-resistant\"), androgen-independent, or hormone-refractory PC. Considering all available knowledge, progesterone receptor (PR) remains the only member of the nuclear SHRs without any indication of its potential interaction with SHH. Like all the other SHRs, PR acts as a ligand-dependent transcription factor--when activated with progesterone, it regulates gene expression, influencing cell growth, proliferation and differentiation, and other functions. Two PR isoforms, PRA and PRB, are described in humans, where PRB is considered as the canonical isoform, and has 164 amino acids longer N-terminus known as the \"B-upstream segment\" [21]. Both isoforms have similar levels of expression in normal tissues, and their ratio can be altered in BC with a poor prognosis, where the loss of PRB and predominance of PRA are present [22]. Furthermore, with the exception of BC and gynecologic cancers, altered PR expression has also been described in some other non-gynecologic cancers, such as astrocytomas, pituitary adenomas, colorectal and thyroid carcinomas [23; 24; 25; 26]. The presence and activity of PR in tumors can influence their response to hormonal therapies, affecting the prognosis and treatment strategies [27]. In some cases, higher expression of PR might protectively affect tumor development and progression, particularly in hormone-sensitive cancers, like certain subtypes of ovarian cancer, endometrial tumors, and Grade 1 meningiomas [28; 29; 30], where PR signaling can inhibit uncontrolled cell growth and proliferation or is associated with a significantly more favorable prognosis. However, the impact of PR in various tumor types can differ based on the specific biological characteristics and signaling pathways involved in the particular tumor type. In this study we conducted comprehensive molecular docking and molecular dynamics studies to find both binding affinities and molecular modes of interaction between cholesterol moiety of SHH-N and all three types of sex hormone receptors, with particular emphasis on PR. In establishing positive controls for docking studies we used structures of the most potent natural agonists of the respective receptors, which are presented in Figure 1. Free cholesterol was also used as a control molecule to deduce if/how the protein backbone of SHH-N affects the interaction between cholesterol and SHRs.