Syntheses of 25-Adamantyl-25-alkyl-2-methylidene-1α,25-dihydroxyvitamin D3 Derivatives with Structure–Function Studies of Antagonistic and Agonistic Active Vitamin D Analogs

The active form of vitamin D3, 1α,25-dihydroxyvitamin D3 [1,25(OH)2D3], is a major regulator of calcium homeostasis through activation of the vitamin D receptor (VDR). We have previously synthesized vitamin D derivatives with large adamantane (AD) rings at position 24, 25, or 26 of the side chain to study VDR agonist and/or antagonist properties. One of them—ADTK1, with an AD ring and 23,24-triple bond—shows a high VDR affinity and cell-selective VDR activity. In this study, we synthesized novel vitamin D derivatives (ADKM1-6) with an alkyl group substituted at position 25 of ADTK1 to develop more cell-selective VDR ligands. ADKM2, ADKM4, and ADKM6 had VDR transcriptional activity comparable to 1,25(OH)2D3 and ADTK1, although their VDR affinities were weaker. Interestingly, ADKM2 has selective VDR activity in kidney- and skin-derived cells—a unique phenotype that differs from ADTK1. Furthermore, ADKM2, ADKM4, and ADKM6 induced osteoblast differentiation in human dedifferentiated fat cells more effectively than ADTK1. The development of vitamin D derivatives with bulky modifications such as AD at position 24, 25, or 26 of the side chain is useful for increased stability and tissue selectivity in VDR-targeting therapy.


Introduction
Osteoporosis is a disease in which the density and quality of bone are reduced [1]. The loss of bone occurs silently and progressively, and often there are no symptoms until the first fracture occurs. Worldwide, osteoporosis causes more than 8.9 million fractures annually, and 1 in 3 women and 1 in 5 men over the age of 50 will experience osteoporosis.
Muscle cells, such as cardiac cells, use calcium ions (Ca ++ ) as a messenger for contraction. The extracellular concentration of Ca ++ (1 mM) is tightly regulated and kept as high as 10 4 times that of their intracellular counterpart [2,3]. This concentration difference is important for the proper function of Ca ++ . Bone is a dynamic storehouse of calcium, and the active form of vitamin D 3 -1α,25-dihydroxyvitamin D 3 [1,25(OH) 2 D 3 ] [4,5]-and parathyroid hormone (PTH) [6] are major regulators of calcium homeostasis. Vitamin D 3 analogs, such as 1α-hydroxyvitamin D 3 [7] and eldecalciferol [8][9][10], have been used as good therapeutic agents for osteoporosis. For a long time now, the usefulness of the active vitamin D 3 and its derivatives in the treatment of osteoporosis has not been accepted in the USA and European countries because of the potential adverse effect of hypercalcemia. In these countries, bisphosphonates [11] are the agents most commonly used for osteoporosis. Bisphosphonates are pyrophosphate analogs and bind strongly to hydroxyapatite in bone. Because of their non-hydrolysable P-C-P structure, bisphosphonates accumulate in osteoclasts and can cause significant side effects, such as osteonecrosis of the jaw [12]. Other drugs used for osteoporosis include peptides of the parathyroid hormone family [13], as well as the antibody drug denosumab [14]. Recently, many reports and reviews have recommended the use of vitamin D combined with Ca for the prevention of osteoporosis and bone fractures [15,16]. Bislev et al. [17] reported that vitamin D 3 supplementation (70 µg [2800 IU]/day) improves strength and trabecular thickness in the tibia, as well as volumetric bone mineral density in the trochanter and femoral neck, compared with those given placebo, but does not affect aerialbone mineral density. They also reported increases in the plasma concentrations of both 25-hydroxyvitamin D 3 [25(OH)D 3 ] and 1,25(OH) 2 D 3 in women treated with vitamin D 3 . Vitamin D 3 is produced from 7-dehydrocholesterol (provitamin D 3 ) in the skin via sunlight irradiation [18], followed by thermal isomerization, and converted to 1,25(OH) 2 D 3 via metabolic hydroxylations at position 25 [19], followed by the 1α-position [4,20]. However, the production of vitamin D 3 in the skin [21] and its metabolism to the active form 1,25(OH) 2 D 3 decrease age-dependently [22]. Therefore, supplementation of not only vitamin D 3 but also the active metabolite 1,25(OH) 2 D 3 should be necessary for the prevention of age-related osteoporosis and bone fractures. More broadly, vitamin D has recently been recognized as an important agent in controlling not only bone density [22], but also the rate of aging and age-related diseases [23].
Vitamin D derivatives with selective modulatory activity on the vitamin D receptor (VDR) [24][25][26] have been developed for the treatment of VDR-related diseases, including bone and calcium diseases, malignancies, immune and inflammatory diseases, and metabolic disease. We have been developing active analogs of vitamin D from the viewpoint of synthetic chemists. We reported for the first time (1) the synthesis of super-high radioactive [ 3 H]-25-OHD 3 and its biological conversion to [ 3 H]-1,25(OH) 2 D 3 to prove the presence of the VDR in various target tissues [27][28][29]; (2) the synthesis of 24F 2 -25(OH)D 3 and 24F 2 -1,25(OH) 2 D 3 [30,31] to examine the importance of 24-hydroxylation in the vitamin D 3 metabolism; (3) the activity of 24F 2 -1,25(OH) 2 D 3 with four to seven times more activity than natural metabolite (1) in HL-60 cell differentiation [32]; and (4) the synthesis of the highly fluorescent dienophile to selectively bind to the s-cis 5,10(19)-diene structure of vitamin D and quantify vitamin D 3 metabolites in biological fluids [33][34][35]. We have been interested in the role of the VDR residues lining the ligand-binding pocket, as understanding this would allow us to clarify which residues are important for ligands to express the VDR activity. To this end, we prepared VDR one-point alanine mutants for all 34 residues lining the ligand-binding pocket (LBP) of the VDR, and the effect of the mutation was evaluated in transactivation assays using an hVDR expression vector and a luciferase reporter gene with the mouse osteopontin VDRE at the promoter in COS7 cells [36,37]. From these studies, we showed which LBP residues are important in expressing the activity of the ligands.
In this paper, we report the synthesis and biological activity of analogs of ADTK1 (5b) with a methyl, ethyl, or n-butyl group (8a, 8b, 9a, 9b, 10a and 10b) at position 25. We expect these compounds to show more selective activities because of the inserted hydrophobic alkyl group. Elevation of hydrophobicity at the side chain of the vitamin D compounds is known to improve their activity. We also investigated the structure-activity relationships of all ADXY compounds on the VDR antagonist and agonist relationships, comparing them with the known antagonists TE-9647 and ZK168281 and agonists KH1060 (15) and 24-carboranyl-1α-(OH)D3 analog (16) via an analysis of their crystal structure (Chart 2). We also carried out computational analyses using the fragment molecular orbital (FMO) computational method and inter-fragment interaction energy (IFIE) as a tool.

VDR Transactivation Activity
The transcriptional activity of the 25-alkylvitamin D analogs on the VDR was evaluated via a luciferase reporter assay in HEK293 human kidney cells transfected with an

Osteogenic Differentiation Activity in Human Dedifferentiated Fat Cells
Mature adipocytes from the adipose tissue of mammals such as humans and rodents can be dedifferentiated into pluripotent cells using ceiling culture [50]. Dedifferentiated fat (DFAT) cells have potential applications in both regenerative medicine and injury healing, as well as mesenchymal stem cells [51,52], embryonic stem cells, and induced pluripotent stem cells [53]. The osteogenic activity of vitamin D derivatives was assessed based on alkaline phosphatase (ALP) activity. In DFAT cells, the addition of natural hormone 1 to the osteogenic medium induced ALP activity (100%) ( Figure 5). Among the derivatives, ADKM2 (8b) was the strongest in inducing ALP activity (98.8%), with ADKM4 (9b) and ADKM6 (10b) showing the next-strongest effects (72.6% and 62.4%, respectively). The other compounds (ADKM1 (8a), ADKM3 (9a), and ADKM5 (10a)) also showed weak activity of less than 50% (41%, 40.4%, and 19%, respectively). ADKM2 (8b), ADKM4 (9b), and ADKM6 (10b) showed stronger activities in inducing bone differentiation than ADTK1 (5b) (45.6%). The results show that alkylated vitamin D analogs with VDR affinity less than that of natural hormone 1 can induce osteoblast differentiation. We previously reported that the vitamin D derivative ADYW2 is more stable than natural hormone 1 in bonederived MG63 cells [44]. The introduction of adamantyl groups may affect the stability of vitamin D analogs.
Since we do not have crystal structures of ADKM1-6 (8a, 8b, 9a, 9b, 10a and 10b)/VDR complexes, we constructed the three-dimensional structures of those rVDR complexes via a computational method using the X-ray crystal structure data (3vtb) of ADTK1 (5b) [42] as a model (see the Materials and Methods section). The calculated model structures of the three compounds ADKM2, ADKM4, and ADKM6 (8b, 9b, and 10b, respectively) complexed with rat VDR are shown in Figure 6. In all of the computational structures, the two His residues 301 and 393 are placed within hydrogen-bonding distance with respect to the 25-hydroxy group. The three Leu residues (Leu223, Leu400, and Leu410) and the adamantane ring of the ligand are situated in the agonistic positions, interacting with one another similarly to the rVDR/1,25(OH) 2 D 3 (1) complex ( Figure 7A). The 25-methyl and ethyl groups were inserted into a pocket of the VDR where they did not interfere with nearby residues. Only the n-butyl group of ADKM6 (10b) interfered with Phe418, which then would change the conformation to adopt the n-butyl group in the pocket, as shown in Figure 6D. The introduction of methyl, ethyl, and n-butyl groups at C-25 increases the hydrophobic interaction energy (FMO, inter-fragment interaction energies (IFIEs)) of Phe418 in ADTK2 (8b), ADKM4 (9b), and ADKM6 (10b) to -6.34, -7.40, and -10.95 kcal/mol, respectively, when given -3.64 kcal/mol of ADTK1 (5b) via the FMO IFIE calculation (Supplementary Materials). ADKM6 (10b) showed the highest activity in an assay to examine the effects of the ligands on the VDR to bind to RXR. The 25S-ethyl substitution had the highest effect on the CYP24A1 induction in kidney (HEK293), intestine (SW480), and lung (H292) cell lines. mammary glands and uterus [49]. In contrast, we previously reported the non-alkylated vitamin D derivative ADTK1 (5b), like compound 1, strongly interacts with SRC1 and induces CYP24A1 expression most strongly in HEK293 cells, which express high levels of SRC1, but less than 50% in HaCaT cells, which express less SRC1 [42]. The cell-selective VDR activity of ADTK1 (5b) is suggested to be determined by the expression of cofactors, such as SRC1, in each cell. In this study, despite the compound ADKM2 (8b) interacting with SRC1 as strongly as natural hormone 1 and ADTK1 (5b), the induction of CYP24A1 expression in HEK293 cells was weaker than in HaCaT cells. The cell-selective VDR activation mechanism of ADKM2 (8b) may be affected by intracellular stability and/or interaction with coactivators other than SRC1. The analogs ADKM4 (9b, 27%) and ADKM6 (10b, 23%), with elongated alkyl groups at C-25, had weaker VDR affinities than ADKM2 (8b, 67%) but similar VDR transcriptional activation efficacies (104% and 95%, respectively), and their ability to induce CYP24A1 expression in all cell lines was comparable to that of natural hormone 1. These results indicate that the elongation of the 25-alkyl group masks the cell selectivity of ADKM2 (8b). ADKM4 (9b) and ADKM6 (10b), which have weaker affinities for the VDR, may be more stable in cells than natural hormone 1 or ADKM2 (8b).  and ADKM6 (10b) showed stronger activities in inducing bone differentiation than ADTK1 (5b) (45.6%). The results show that alkylated vitamin D analogs with VDR affinity less than that of natural hormone 1 can induce osteoblast differentiation. We previously reported that the vitamin D derivative ADYW2 is more stable than natural hormone 1 in bone-derived MG63 cells [44]. The introduction of adamantyl groups may affect the stability of vitamin D analogs. Figure 5. Effects of ADKM1-6 (8a, 8b, 9a, 9b, 10a and 10b) and ADTK1 (5b) on the ALP activity in human DFAT cells. Cells were treated with an osteogenic medium and vitamin D analogs (5b, 8a, 8b, 9a, 9b, 10a and 10b) or 1,25(OH)2D3 (1) (100 nM) for 7 days, and then ALP activity was determined in cell lysates and normalized to protein content. One-way ANOVA followed by Turkey's multiple comparisons: ※※※ p < 0.001 versus CNT.
Since we do not have crystal structures of ADKM1-6 (8a, 8b, 9a, 9b, 10a and 10b)/VDR complexes, we constructed the three-dimensional structures of those rVDR complexes via a computational method using the X-ray crystal structure data (3vtb) of ADTK1 (5b) [42] as a model (see the Materials and Methods section). The calculated model structures of the three compounds ADKM2, ADKM4, and ADKM6 (8b, 9b, and 10b, respectively) complexed with rat VDR are shown in Figure 6. In all of the computational structures, the two His residues 301 and 393 are placed within hydrogen-bonding distance with respect to the 25-hydroxy group. The three Leu residues (Leu223, Leu400, and Leu410) and the Figure 5. Effects of ADKM1-6 (8a, 8b, 9a, 9b, 10a and 10b) and ADTK1 (5b) on the ALP activity in human DFAT cells. Cells were treated with an osteogenic medium and vitamin D analogs (5b, 8a, 8b, 9a, 9b, 10a and 10b) or 1,25(OH) 2 D 3 (1) (100 nM) for 7 days, and then ALP activity was determined in cell lysates and normalized to protein content. One-way ANOVA followed by Turkey's multiple comparisons: ※※※ p < 0.001 versus CNT.

OR PEER REVIEW 10 of 22
adamantane ring of the ligand are situated in the agonistic positions, interacting with one another similarly to the rVDR/1,25(OH)2D3 (1) complex ( Figure 7A). The 25-methyl and ethyl groups were inserted into a pocket of the VDR where they did not interfere with nearby residues. Only the n-butyl group of ADKM6 (10b) interfered with Phe418, which then would change the conformation to adopt the n-butyl group in the pocket, as shown in Figure 6D.   We postulate that three Leu residues-Leu223, Leu400, and Leu410 (rVDR)-are the key residues for the VDR to form the active conformation and direct a VDR ligand to act as an agonist or antagonist. We reported this motif [41], without recognizing its importance, back in 2008 in an X-ray crystallographic analysis of new-type vitamin D antagonist compounds 25-or 26-adamantyl-22,23-didehydro1α,25-dihydroxyvitamin D analogs ADTT (3b) [40,41] and ADMI3 (4b) [38]. However, we later found that ADVD analogs have a variety of biological properties, ranging from antagonist to agonist activities (Table 1). We reported that the 25-adamantyl-1α,25-dihydroxy-23,23,24,24-tetradehydro-VD analog ADTK1 5b [42] showed partial agonistic activity, with VDR affinity IC 50 0.5 × 10 -9 M and transcriptional activity EC 50 1 × 10 -10 M (69% efficacy)-a higher potency than that of the natural hormone (1). In the present study, we examined and suggested a structure-activity relationship with active vitamin D analogs, focusing on agonist and antagonist activities. We analyzed antagonistic and agonistic VD compounds complexed with VDR, whose structures were unequivocally determined via crystallographic analysis, such as with the antagonists ADTT (3b), TEI-9647 (15) [45,54], and ZK168281 (16) [46,47] and the agonists ADTK1 (5b), KH1060 (17) [55], and carborane VD (18) [48], as shown in Table 1. In addition, we analyzed the physicochemical properties of VDR complexes of adamantane VD compounds with agonistic and antagonistic properties, using a theoretical ab initio FMO computational method and FMO IFIE as a tool.
When a ligand binds with a VDR (rat), Leu400 at the N-terminal part of helix 11 and Leu410 at loops 11-12 link to the C-26 of the ligand; then, loops 11-12 bend, and both Leu residues bind to Leu227 at the N-terminal of helix 3, thereby closing up the VDR to form the active conformation ( Figure 7A). The 23,23,24,24-tetradehydro-VD analog ADTK1 (5b) showed partial agonistic activity, in contrast to the 22,23-didehydro analog ADTT (3b) ( Table 1), which had antagonistic properties. ADTK1 (5b)/rVDR is shown in Figure 7D at the position of the three Leu's. Here, Leu223 and Leu400 strongly interact at their Cδ, with Å distances of 3.985, 4.481, and 4.195; in addition, Leu223, Leu400, and a secondary AD carbon of the ligand interact at Å distances of 3.985, 3.525, and 3.493, respectively, forming a rigid triangular relationship. Figure 7F shows the hVDR complex of the superagonist 1,25-dihydroxy-20-epi-22-oxa-24,26,27-trihomo vitamin D analog KH1060 (15), overlaid with 1,25(OH) 2 D 3 (1)/hVDR. The two VDR complexes are well overlapped, regardless of the bulky side chain of 15. This shows that the bulky-but-flexible side chain can be sufficiently placed within the VDR pocket. Carboranyl VD (16) is a superagonistic analog with a carborane cluster at C-24 in the place of the adamantane ring of the ADVD compounds [55]. Carborane (C 2 B 10 H 12 ) is a boron cluster molecule, and in the 24-carboranyl VD/zVDR complex it interacts with two His residues, His301 and His393, instead of the 25-hydroxyl group of the natural ligand. The VDR complexes of carboranyl VD (15)and ADTK1 (5b) are well overlapped, as shown in Figure 7G. The VDR affinity and transcriptional activity of carboranyl VD (15) are reported to be similar to those of 1,25(OH) 2 D 3 (1), but its calcemic effect is smaller than that of 1,25(OH) 2 D 3 (1) [48].
We next discuss VD antagonists and/or partial agonists. The 25-adamantyl-22,23didehydro analog ADTT (3b) has a high VDR affinity (IC 50 1.3 × 10 -10 M) similar to that of 1,25(OH) 2 D 3 (1), and a high transcriptional activity (EC 50 1 × 10 -9 M), but with low efficacy 15%, in addition to a high antagonistic activity (IC 50 3 × 10 -9 M). These activity patterns should be typical for antagonists. In the crystallographic structure of ADTT (3b)/rVDR, the three Leu residues do not interact with one another and are placed away from one another at a longer distance than 6 Å ( Figure 7H). Each of the three Leu residues interacts with the ligand's adamantane ring. The lack of interactions among the three Leu residues was considered to be a reason for the antagonistic activity of ADTT (3b). TEI-9647 (17) was reported as the first antagonist of the VDR. For this compound, it was suggested that the α, β-unsaturated lactone structure of the TEI compound can be a target for Cys and His residues, and the nucleophilic attack of these residues was assumed to be the reason for the antagonistic activity. However, this hypothesis has not been supported. We suggest a reason for the antagonistic activity of TEI-9647 on the reduced interactions around the three Leu residues and ligands, as shown below ( Figure 7I). Firstly, the position of Leu400 is significantly changed when compared with that of 1,25(OH) 2 D 3 (1) and other agonist (ADTK1) VDR complexes. The distances between δ and δ' of Leu400 and Leu223 are longer than 6.0 Å, and those from the ligand are 6.904 and 4.227 Å, respectively; thus, the interaction energies would be considerably smaller than those of the agonists. The interaction distance between Leu410 and Leu223 is 4.248 Å, and for Leu410 and the ligand it is 4.843 Å which seems to be insufficient to obtain strong binding energy.
In Figure 7J, we show the ZK168281/zVDR complex overlaid with 1,25(OH) 2 D 3 /rVDR. Here, again, Leu430 (rVDR Leu400) changes its position significantly, but Leu255 and Leu440 do not. The interaction between each Cδ and Cδ' of Leu255 and Leu430 are 5.408 and 4.305 Å, respectively, and these interaction energies are not expected to be strong. Other interactions take place between Leu 255 Cδ and the double bond of the 25-propenoate ethyl ester (4.090 and 4.606 Å), Leu430 and the ethyl propenoate methylene carbon (3.608 Å), and Leu400 and the C(25) cyclopropane ring (4.182 Å). Thus, the interactions are not concentrated, and the total interaction energies between three Leu residues and the ligand are not expected to be strong enough to keep the active conformation.

Chemistry
We carried out all reactions under an argon atmosphere. We distilled dimethoxymethane from Na/benzophenone. Reaction temperatures refer to external bath temperatures. We recorded UV spectra on a Hewlett-Packard spectrophotometer (model 8452A). We recorded the 1 H NMR spectra in a CDCl 3 solution on a Bruker 600 MHz spectrometer. Chemical shifts are reported in the δ scale (ppm) downfield from tetramethylsilane (δ = 0.0 ppm), using the residual solvent signal at δ = 7.26 ppm ( 1 H, CDCl 3 ) as the internal standard. We performed high-resolution mass spectrometric analysis (HRMS) via the atmosphericpressure chemical ionization (APCI) method on a JMS-T100LP AccuTOF TM LC-Express. We conducted high-pressure liquid chromatography (HPLC) by using Jasco PU-980 intelligent pumps equipped with an 801-SC solvent programmer and a Jasco UV-970 detector, along with a YMC Pack ODS-AM column (20 × 150 mm, particle size 5 mm, pore size 12 nm).

Vitamin D Receptor-Binding Assay
The pGEX-hVDR and pGEX were expressed for a GST-VDR fusion protein and a control GST protein, respectively, in Escherichia coli BL21 (Merck, Darmstadt, Germany). The bacteria were lysed by sonication in a sonication buffer (50 mM Tris-HCl, pH 8.0, 50 mM NaCl, 1 mM EDTA, and 1 mM DTT). The supernatant proteins (1 µg) were diluted in a binding buffer (25 mM Tris, pH 7.5, 100 mM KCl, 25 mM DTT, 4 mM CHAPS, pH 7.5) containing bovine serum albumin (100 µg/mL). A solution containing each test compound in 15 µL of EtOH was added to 570 µL of the GST protein solution in each tube. After being vortexed 2-3 times, the mixture was incubated for 30 min at room temperature. Then, [26,27-methyl-3 H]-1,25(OH) 2 D 3 (PerkinElmer, Waltham, MA, USA) in 15 µL of ethanol was added. After being vortexed 2-3 times, the whole mixture was allowed to stand at 4 • C for 20 h, and 400 µL of dextran-coated charcoal solution (Sigma) was added to remove free ligands. After 30 min at room temperature, bound and free [ 3 H]-1,25(OH) 2 D 3 were separated via centrifugation at 3000 rpm for 10 min at 0 • C, and aliquots (800 µL) of the supernatant were mixed with 9.2 mL of Bio Fluor (PerkinElmer) and submitted for radioactivity counting.

Reverse Transcription and Quantitative Real-Time PCR Analysis
For gene expression analysis, 1 × 10 4 cells per well were plated in a 24-well plate. After 24 h, the cells were treated with an ethanol control or 100 nM of each test compound for 24 h. The total RNAs from the samples were extracted using the acid guanidine thiocyanate phenol/chloroform method [57], and cDNAs were synthesized using the ImProm-II reverse transcription system (Promega, Madison, WI) [43]. Real-time PCR was performed on the ABI PRISM 7000 sequence detection system (Thermo Fisher Scientific, Waltham, MA, USA) using Power SYBR Green PCR master mix (Thermo Fisher Scientific). The primer sequences were as follows: CYP24A1 5 -TGAACGTTGGCTTCAGGAGAA-3 and 5 -AGGGTGCCTGAGTGTAGCATCT-3 ; GAPDH 5 -ACTTCGCTCAGACACCATGG-3 and 5 -GTAGTTGAGGTCAATGAAGGG-3 . The mRNA values were normalized to the mRNA levels of GAPDH and calculated relative to those in the 1,25(OH) 2 D 3 treatment.

Human Dedifferentiated Fat Cell Isolation and Culture
Samples of human subcutaneous adipose tissue were obtained from patients who underwent surgery in the Department of Pediatric Surgery at Nihon University Itabashi Hospital (Tokyo, Japan). The patients gave their written informed consent, and the Ethics Committee of Nihon University School of Medicine approved this study. We prepared dedifferentiated fat (DFAT) cells using the ceiling culture method, as described previously [50]. Briefly, the adipose tissue (approximately 1 g) was cut into small pieces and digested with a 0.1% type I collagenase solution (Koken Co., Ltd., Tokyo, Japan). Cell samples were filtered and centrifuged at 135 Times g for 3 min, followed by collection of the floating cell layer containing mature adipocytes. The isolated adipocytes were washed with phosphatebuffered saline (PBS) and plated in 25 cm 2 culture flasks (Thermo Fisher Scientific) filled completely with CSTI-303MSC (Cell Science and Technology Institute, Miyagi, Japan) containing 20% FBS with 5 × 10 4 cells per flask. The cells that adhered to the upper surface of the flasks were cultured for conversion to dedifferentiated fat cells. Fibroblast-like adhered cells (dedifferentiated fat cells) were cultured in 5 mL of CSTI-303MSC containing 20% FBS. Cells at passages 2-4 were used for differentiation experiments.

Osteogenic Differentiation Assay
Cells were grown to confluency in 24-well plates and incubated for a week in DMEM containing 10% FBS, 100 nM dexamethasone (Merk), 10 mM β-glycerophosphate (Merk), and 50 mM L-ascorbic acid-2-phosphate (Merk), with 100 nM of each compound. The induction medium was replaced on day 4. The alkaline phosphatase (ALP) activity in the cell lysates was determined on day 7 with a lab assay ALP kit (Fujifilm wako). The total protein content was determined with the BCA protein assay kit (Thermo Fisher Scientific). ALP levels were normalized to the total protein content.

Statistical Analysis
Data are presented as means ± S.D. We performed one-way ANOVA followed by Tukey's multiple comparisons to assess significant differences using Prism 8 (GraphPad Software, La Jolla, CA, USA).
We refined and rebuilt the atomic coordinates of the crystal structures of the hVDR-LBD complex with natural ligand 1. The protocols [60] of our refinement and rebuilding of the crystal structures of the protein-ligand complex were as follows: (i) the refinement of the target complex structures was optimized using the PDB_REDO web server [61]. This server optimizes various refinement parameters (including B-factor weight, X-ray weight, TLS groups, and bulk solvent modeling), chooses between an anisotropic or isotropic B-factor model, rebuilds side chains in rotamer conformations, flips side-chains to optimize hydrogen bond networks, checks peptides for 'flipping', re-evaluates the water model, and validates all of the present ligands. The R and R-free values of the complexes improved from 0.1910 and 0.2140 to 0.1501 and 0.1826, respectively. (ii) The missing hydrogen atoms were added by using the Protonate 3D module [62] within the Molecular Operating Environment (MOE) program [63] under the standard conditions (pH = 7.0, 25 • C). The orientations of the added hydrogen atoms were then optimized by using an energy minimization scheme through molecular mechanics (MMs) calculations utilizing an Amber10 EHT force field under the generalized Born solvation, which uses Amber10 parameters for macromolecules and extended Hückel theory parameterization for small molecules, which takes electronic effects into account and is incorporated in the MOE program [63].
The positions of important hydrogens in the hydrogen network associated with the three OH groups in ligand 1 were determined as in our previous procedure [64,65] and were optimized using QM calculations at the standard B3LYP/6-31G** level using the Gaussian09 program [66] for the sub-model system of the corresponding six amino acid residues (Ser237, Arg274, Tyr143, Ser278, His305, and His397) and ligand 1.
Since the structures of the VDR-LBD complex bound by ADKM2 (8b), ADKM4 (9b), and ADKM6 (10b) have not been experimentally determined, computational modeling structures of ADKM2 (8b), ADKM4 (9b), and ADKM6 (10b) were constructed as follows: Firstly, the model structures of ADKM2 (8b), ADKM4 (9b), and ADKM6 (10b) were constructed by replacing a hydrogen with a methyl, ethyl, and n-Bu group, respectively. The model structure of the ligand was computationally determined in an isolated system via partial optimization for only the position 25 substituent, in which the absolute conformation at position 25 was maintained at the B3LYP/6-31G** level using the Gaussian09 program [66].
In this study, all FMO calculations for the ligand-bound VDR-LBD complexes were carried out with the correlated resolution-of-identity (RI)-MP2 method [67,68] subjected to counterpoise corrections with the correlation-consistent double ζ(cc-pVDZ) basis set [69] level, using the PAICS program package [70].
The correlated FMO calculation can estimate the interaction energy quantitatively, including not only electrostatic interactions but also London dispersion forces (van der Waals interactions), such as CH/π-π stacking. Utilizing this calculation, FMO-IFIEs were obtained for the various ligand-bound VRD-LBD complexes. The correlated FMO-IFIEs at the MP2 level are represented as the sum of the HF-IFIEs (mainly electrostatic energies) and the ∆MP2-IFIEs (mainly dispersion force) (see the Supplementary Materials).
The ∆MP2-IFIE was adopted to evaluate the stable/unstable interaction between a hydrophilic and/or hydrophobic amino acid residue and the ligand in the VDR-LBD complex.
The root-mean-square deviations (RMSDs) of all of the atoms/Cα of each residue pair were calculated by using the plugin script RmsdByResidue [71] of the molecular graphics software package PyMOL [72].
of Medicine for the osteoblast differentiation assay; and Kaori Umeda and other members of the Makishima lab for technical assistance and helpful comments.