Computational study of flavonoids from Eucommia ulmoides against RANKL-induced osteoclastogenesis using Molecular Docking and molecular dynamics simulation

Computational study of flavonoids from Eucommia ulmoides against RANKL-induced osteoclastogenesis using Molecular Docking and molecular dynamics simulation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Computational study of flavonoids from Eucommia ulmoides against RANKL-induced osteoclastogenesis using Molecular Docking and molecular dynamics simulation Xiaofei Zhang, Lixia Zhang, Dan Li, Qi Wang, Libin Wang, Ziqi Zheng, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5909485/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 May, 2025 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract Osteoporosis is the most common form of bone disease and the RANKL/RANK/OPG has been widely demonstrated to be a critical protein for bone metabolism. Previous studies suggested that flavonoids played an obligatory role in the inhibition process of osteoclast differentiation induced by RANKL. However, the detailed mechanisms were still unknown. Eucommia ulmoides is a popular herb used to treat bone diseases in traditional medicine, in which flavonoids play an important role. Thus, in the present study, the flavonoids in Eucommia ulmoides were specially selected and the molecular recognition mechanisms between flavonoids and RANKL monomer were examined and analyzed by molecular modeling approaches. The in-silico experiments revealed that the selected molecules exhibited variable degrees of affinities toward the RANKL monomer. Among them, cyrtominetin may be used as a lead compound for the development of potent RANKL inhibitors. By analyzing the binding sites of flavonoids to RANKL monomer, we found that most flavonoids interacted with RANKL monomer by forming strong hydrogen bonds with Gly178 and Asn195 to exhibit higher binding affinity, which was assumed to be essential for the activity. Moreover, the MD simulation showed good interactions between the selected molecules and the active site of RANKL monomer. Throughout the all-atom 100 ns MD simulation, flavonoids depicted superior stability at the RANKL binding site for more than 70 ns, where the solvation energy was greatly compensated by the electrostatic and van der Waal binding energies. We believed that the results could help to elucidate the underlying mechanisms of flavonoids to inhibit osteoclast differentiation induced by RANKL at the atomic level and facilitate the development of new medications for bone-related diseases. Biological sciences/Computational biology and bioinformatics Biological sciences/Drug discovery Osteoporosis flavonoids RANKL Molecular docking Molecular dynamics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Introduction Osteoporosis is the most common form of bone disease characterized by low bone density decreased bone mass and increased bone fragility 1 . More than 100 million people worldwide are suffering from osteoporosis, and the World Health Organization (WHO) has identified it as a major public health concern 2 . Bone mass is maintained through a dynamic process, known as bone remodeling, which is generated by the interaction of sustained balance between osteoclast-induced bone resorption and osteoblast-mediated bone formation 3 . Accumulating evidence indicates that the disorder of dynamic balance between bone resorption and bone formation results in osteoporosis. Among them, the overactivation of osteoclasts is considered to be the main reason for excessive bone resorption and bone mass reduction 4 . Therefore, reducing the activity of osteoclasts to restore the balance between bone resorption and bone formation has become a critical strategy for the treatment of osteoporosis 5 . The differentiation and maturation of osteoclasts is a complex and delicate multilevel regulatory process, in which the receptor activator of nuclear factor-κB ligand (RANKL) plays a vital role 6 . Specifically, the binding of RANKL to the receptor activator of nuclear factor-κB (RANK) induces tumor necrosis factor receptor-associated factor 6 (TRAF6) recruitment, which sequentially activates signaling factors nuclear factor kappa-B (NF-κB) and mitogen-activated protein kinases (MAPKs), including p38, c-Jun N-terminal kinase (JNK) and extracellular signal-regulated kinase (ERK) 7, 8 . At the same time, the RANKL-RANK interaction activates the AKT signaling pathway by recruiting c-Src 9, 10 . Subsequently, the activation of these signaling molecules increases the expression of nuclear factor of activated T cell c1 (NFATc1) and c-Fos, which can directly regulate osteoclast differentiation and osteoclast-specific gene expression 11 . In addition, osteoprotegerin (OPG), a natural antagonist of RANKL, inhibits the formation of osteoclasts by preventing RANKL/RANK interaction 12 . Based on the above analysis, targeting RANKL/RANK/OPG system of osteoclast differentiation signaling pathway, especially directly blocking RANKL-RANK interaction, provides the possibility to develop novel therapeutic approaches for treating osteoporosis 13 . Currently, many researchers have been working hard to find effective drugs to antagonize or inhibit RANKL. Unfortunately, most of the drugs that have been found have some drawbacks that limit their administration 14 . For example, denosumab is a RANKL monoclonal antibody inhibitor, which has been developed to treat osteoporosis 15 . It is the first RANKL inhibitor approved by FDA, but its application is limited due to its high price 16 . Besides, recombinant proteins such as Fc-OPG, Fc-osteoprotegerin, and other anti-RANKL antibodies have also been developed as therapeutic agents for osteoporosis 17, 18 . However, the clinical applications of macromolecular drugs are hindered by some shortcomings, including low stability, poor bioavailability, high cost, and difficulties in administration 19 . Nowadays, many researchers have turned to select compounds from natural products to find more specific and safer agents against RANKL. For example, it has been found that ellagic acid, niloticin and epigallocatechin-3-gallate can directly block RANKL-RANK interaction to inhibit RANKL-induced osteoclast differentiation signaling pathway 20, 21 . In fact, many flavonoid compounds also have beneficial activities in inhibiting RANKL-induced osteoclast differentiation and bone resorption 22-24 . Such as, quercetin can affect NF-kB, AP-1 and NFATc1 in RANKL/RANK/OPG system to inhibit osteoclast differentiation 25 . Kaempferol can inhibit RANKL-mediated ERK, JNK and p38 phosphorylation and the expression of c-Fos and NFATc1 26, 27 . Genistein directly inhibits osteoclastic differentiation through inhibiting the expression of two transcription factors c-Fos and NFATc1 induced by NF-kB up regulation 28 . Syringetin is an inhibitor targeting osteoclast differentiation 29 . Moreover, according to the analysis results of the KEGG pathway in previous report, we found that the flavonoids in Eucommia ulmoides (EU) could directly regulate the osteoclast differentiation signaling pathways to treat osteoporosis 30 . Given that flavonoids can inhibit the RANKL-stimulated activation of the AKT, MAPK, and NF-κB signaling pathways and regulate osteoclast differentiation signaling pathways, we speculated that flavonoids could inhibit osteoclast differentiation by binding RANKL to block RANKL–RANK interaction. Here, we described the ability of flavonoids to bind RANKL using molecular docking and molecular dynamic approaches. Molecular simulation could provide detailed information on both quantitative atomic level and thermodynamic descriptions of the interactions between receptor and ligand with ideal resolution, which could not be obtained by experimental approaches 31 . The six flavonoids previously reported in EU, including quercetin, kaempferol, cyrtominetin, syringetin, genistein and ombuin, were specially selected in the present study 30 . We believed that the results of molecular simulation could give more insights into understanding the underlying mechanisms of flavonoids to inhibit RANKL-induced osteoclastogenesis at the atomic level, and help to further development of new medications for osteoporosis. Results Preparation of ligand and protein for Docking The details of six flavonoids with positive ADMET properties in the present study were shown in Table 1 . It could be seen from the radar plot that all the physicochemical properties are in the proper scope. PROCHECK checked the stereochemical quality of protein structure by analyzing residue-by-residue geometry and overall structure geometry. Ramachandran plot showed that 89.1% of residues fall in the most favorable regions, 9.5% in additional allowed regions, 1.5% in generously allowed regions, and 0% in disallowed regions (Fig. 1 ). Binding site prediction 3URF includes two parts, RANKL and its decoy receptor OPG. The binding interface of RANKL/OPG is composed of two binding sites (Fig. 2 ) 32 . The binding site I, composed of relatively small and separate contact patches in both RANKL and OPG, is located on the OPG "50s loop" (His47-Leu65) and nearly parallel to the RANKL along the groove. Whereas at the binding site II, the OPG “90s loop” (Arg90 -Leu98) is deeply within the groove. Compared with separate interactions at the binding site I, more interactions at the binding site II are concentrated around the tip of OPG 90s loop. The binding site II forms a hydrophilic interaction network with RANKL residues by using Glu95 of the OPG "90s loop", which is more important than the binding site I in RANKL/OPG binding. At the same time, this position is also the main binding determinant of RANKL/RANK interaction. In addition, after binding with RANKL active site, it was found that Glu93 and Ile94 residues formed hydrophobic and van der Waals interactions with hydrophobic residues around RANKL. Three amino acids, Glu93, Ile94, and Glu95, from the OPG probe deeply into the concave surface of RANKL, defining the main binding pocket for small molecular inhibitors targeting RANKL/RANK interaction. Residues within a distance of 6 Å around the residues Glu93, Ile94, and Glu95 of OPG were defined as the binding pocket for molecular docking 33 . Molecular interaction In molecular docking, the ligands bind to amino acid residues and interact with each other in the active pocket, participating in the process of conformational changes and energy complementation. The binding sites and binding score values can intuitively reflect the interaction and stability of the docking model. The docking results showed that all flavonoids exhibited notable interactions and docking scores were greater than 4, indicating that the binding between flavonoids and RANKL was relatively stable. Among picked molecules, cyrtominetin and quercetin displayed the best binding affinities compared to other molecules with total scores of 6.5143 and 5.0316 respectively. The control group had a total score of 6.3254. Interestingly, cyrtominetin achieved a superior binding than control group indicating that it has a promising affinity and intrinsic activity towards the RANKL. The binding modes of RANKL with the 6 flavonoids were shown in Fig. 3 . After exploring the molecular interactions, it was perceived that cyrtominetin manifested hydrogen bonds with residues Gly178, His180, Lys181, and Asn295. One amide-Pi stacked with residues Ser179, one Pi-alkyl (His180), and one alkyl interaction (Met239). It also formed van der Waals (vdW) interaction with residues Val182, Thr233, Gln237, Tyr241, Ser294, and Pro296. In the case of quercetin, residue Gly178, Lys181, Gln237, and Asn295 formed hydrogen bonds. Residues Ser179 interacted via Pi-lone pair interactions. Residues His180, Met239, Tyr241, Ser294 and Pro296 formed vdW interactions. In molecule syringetin, residues Gly178, Lys181, Gln237, and Asn295 formed hydrogen bonds. Several residues formed other interactions like Ser179 (Pi-lone pair), Tyr241 (Pi-alkyl), Met239 (Alkyl), and residues His180, Lys257, Ser294 and Pro296 showed vdW interactions. In genistein, hydrogen bonds were formed by residues Gly178, Gln237, Asn295, and C-H bond by Ser294, Leu236. Residues Ser179 also formed amide-Pi stacked. Residues Lys181, Val182, Tyr235, Thr261, Pro296 and Ser294 showed vdW interactions. In the case of ombuin, hydrogen bonds were formed by residues Gly178, Thr233, Asn295, and C-H bond by His180. Residues also formed other interactions, including one amide-Pi stacked (Ser179), and alkyl (Lys181). Residues Tyr235, Leu236, Gln237, Tyr241, Ser294, and Pro296 displayed vdW interactions. Kaempferol exhibited hydrogen bonds with residue His180, Thr233, Tyr235, and Tyr241. It also formed vdW interaction with residues Ser179, Lys181, Leu236, Gln237, Met239, Ser294, and Asn295. In control group, hydrogen bonds were formed by residues Ser179, His180, Gln237, Asn295, and C-H bond by Ser179. Residues also formed other interactions, including one Pi-sigma (Gln237), Pi-alkyl (Lys181), and alkyl (Lys181). Residues Tyr235, Leu236, Met239, Tyr241, Thr261 and Ser294 showed vdW interactions. The binding style contributes a reasonable rationale for the significance of interacting residues in target protein binding. It was observed that there was a high resemblance between the above 6 flavonoids, and they nearly occupied the same active pocket. Furthermore, the binding of flavonoids to RANKL was also significantly mediated by the critical residues and conferred the best interactions. These data indicated that residues Gly178, Asn295, Lys181, Gln237, and Ser179 played a more critical role in the binding process. Molecular dynamics simulations Molecular dynamics simulation is considered to be an efficacious approach, which can explore the stability of protein-ligand complex obtained from previous docking studies and investigate their relative dynamic properties, so as to provide stability information on the predicted binding interactions with important residues 34 . From the result of docking, the protein-ligand complex having the least binding energy with the best configuration was carried out 100ns MD simulation. RMSD analysis RMSD of backbone C-α atoms was measured using the GROMACS “gmx rmsd” tool to quantify the structural stability of protein-ligand complex. Generally, RMSD is a standard measurement of the structural distance between coordinates, which is used to infer the extent of deviation for a group of atoms relative to their initial structures 35 . The RMSD values express how much the conformations of these groups of atoms have changed to indicate the stability of complexes. In the present study, the 6 flavonoids under investigation were successfully converged within the 100 ns MD simulation window. As shown in Fig. 4 , all complexes tended to reach their stable states, and the fluctuation of proteins was within acceptable range with RMSD values of less than 4.00 Å, indicating the stability of the conformational ensemble. The cyrtominetin-bound protein started from C-alpha RMSD (RMSD-Cα) 1.07Å, gradually increasing until it converged at around 15ns. After this, the protein adopted an equilibrium plateau showing minimal fluctuations around its average until the end of the MD run with an average deviation of 2.86Å. This behavior is a typical MD simulation run, in which the protein begins to relax after removing all constraints until reaching its equilibration state, where RMSD-Cα trajectories tends to be stable indicating the stability of the protein. In the case of quercetin-bound protein, the backbone RMSD gradually increased until convergence at around 30ns where RMSD tends to be stable until reaching 50ns, in which RMSD decreased then rose again. The final convergence around an average RMSD (2.66 Å) started from 60ns until the end of MD simulation at 100ns. The simulation of syringetin-bound protein performed well, in which it gradually reached dynamic equilibration at around 25ns, and the average RMSD was 2.33 Å with stable fluctuations until 100 ns. The RMSD-Cα trajectories of genistein-bound protein had a low average value (2.15Å) and lesser fluctuations, indicating its stability. With regard to ombuin and kaempferol, the proteins started at lower RMSD-Cα values (0.71 and 0.78 Å, respectively), and proteins depicted delayed convergences after 30ns from the start of the MD simulation runs. Following convergence, both proteins were dynamically balanced, showing their RMSD-Cα trajectories being maintained around their respective average deviations (1.17 Å and 2.89 Å, respectively). The RANKL apo state was initially stable and maintained structural integrity during most of the simulation time. However, a rise of the RMSD value was observed for 85–95 ns time and returned to the steady state in the final period (average 2.38 Å). The minimal fluctuations in the RMSD trajectories and low difference in average RMSD values showed that the RANKL-flavonoids complexes were stable. Overall results explained that these 6 flavonoids molecules did not significantly influence the structural stability of RANKL, and all systems showed stable internal motion. RMSF analysis We further performed RMSF analysis to evaluate the positional fluctuation of each amino acid around its average mean position. The individual backbone RMSF was calculated using the GROMACS “gmx rmsf” command line to perceive structural stability and flexibility at local levels. In addition, it can also be used to identify the flexible residues in the protein, so that we can explore the conformational flexibility of the protein structure 36 . As depicted in Fig. 5 , all systems showed almost similar patterns. In the case of RANKL apo state, we observed the highest fluctuations in loop regions. The loop regions are very flexible elements of protein, and their flexibility is essential to accommodate the ligand at the binding site appropriately. For the residues (178–181, 237–241, and 293–296) at the binding site, the RMSF had smaller values throughout the simulation, further showing the regions of active site residues were quite stable. Compared with the RANKL apo state, the RMSF values of numerous residues in RANKL-flavonoids complexes increased, especially residues in loop regions, indicating that the flexibility of RANKL monomer increased after binding with flavonoids. Additionally, the majority of the protein residues were stable with RMSF values smaller than 0.3 nm. The active site residues participating in interactions with flavonoids molecules remained highly stable throughout the MD simulation. Radius of gyration Next, we investigated the structural stability of the protein-ligand complex by calculating the Rg to determine the compactness of the protein structure. Rg was calculated using the GROMACS "gmx gyrate" script. Rg reveals the knowledge of folding and unfolding of protein structure upon binding of the ligands. Higher Rg values explain less compactness (more unfolded) with high conformational entropy while low Rg values show high compactness and more stability in the structure (more folded) 37 . As shown in Fig. 6 , all systems of ligand-bound proteins have projected the Rg values between 16 to 17 Å. To some extent, the protein Rg values were comparable among the investigated systems being fluctuated around close averages. In the case of RANKL apo state, the average Rg value was found to be 16.94 Å. The average Rg values of cyrtominetin-bound protein and quercetin-bound protein were 16.76 Å and 16.31 Å, where cyrtominetin exhibited steadier trajectory, indicating significant stability and compactness within the protein active pocket. Similarly, syringetin, genistein, ombuin, and kaempferol bound to the target protein, the average Rg values were found to be 16.56, 16.57, 16.54, and 16.33 Å, respectively. In the whole simulation process, all systems of ligand-bound proteins became more compact than RANKL apo state, which indicated that the RANKL-flavonoids complexes are well converged. Solvent-accessible surface area Moreover, another important quantity that we measure and analyze to probe the conformational stability of the protein-ligand complex is SASA. The SASA values were analyzed to assess the complexes volume change through GROMACS “gmx sasa” script. Generally, SASA correlates for the molecular surface area being assessable to solvent molecules providing a quantitative measurement about the extent of protein/solvent interaction 38 . The decrease of SASA values implies that the relative structures of complexes shrink under the influence of the solvent surface charge, resulting in more compact and stable conformations. As predicted, the SASA values of all RANKL-flavonoids complexes were comparable, and all values were concentrated between 85 to 90 nm 2 (Fig. 7 ). Among them, cyrtominetin-bound protein had a higher SASA trajectory in the initial phase. After this stage, the SASA value gradually decreased to reach min SASA value which was followed by a subsequent increase until reaching the end of the MD simulation run (average 86.68 nm 2 ). The elevated SASA trajectories might confer the migration of cyrtominetin towards the solvent side within the simulation time frames of 60 to 100 ns where the protein pocket became highly solvated and minimally compacted. The quercetin-bound protein showed lower SASA trajectory (average 85.56 nm 2 ), particularly within the last 50 ns. Such dynamic behavior suggested preferential confinement of quercetin within the protein pocket. The syringetin-bound protein and ombuin-bound protein had higher SASA trajectories in the initial phase, followed by a lower value, and then maintained a stable SASA until the end of the simulation. The SASA trajectories of genistein-bound protein and kaempferol-bound protein were similar, with less fluctuation during the simulation, indicating that the stability of these two complexes was less affected by the solvent. On the other hand, the RANKL apo state showed stable SASA trajectorie (average 88.05 nm 2 ) until reaching 100 ns of the simulation run. In the whole simulation process, all systems of ligand-bound proteins became more compact than RANKL apo state. In the presented study, findings from the SASA analysis appeared to ensure the well stability of the RANKL-flavonoids complexes previously presented by the Rg trajectory analysis. Effects of flavonoids on the intra-chain interactions To further explore the roles of flavonoids on the intra-chain interactions, the sidechain-sidechain contact diagrams of the RANKL monomer were calculated by using the GROMACS "gmx mdmat" program. As shown in Fig. 8 , the contact distance between sidechains of residues in the RANKL monomer was represented by distinct colors. Blue and red expressed the distance between sidechains was 0.0 nm and 1.5 nm, respectively. When the color was closer to blue, the distance between the related sidechains was closer. On the contrary, when the color was closer to red, the related sidechains were farther from each other. In all simulation systems, the contact distance changes mainly located in the active pocket. In the absence of flavonoids molecules, it was found that there was some repulsion between the sidechains of residues in the active pocket. In the presence of flavonoids molecules, it was observed that the number of blocks close to red was reduced, demonstrating that the contacts between sidechains were strengthened by flavonoids. To be more specific, the sidechain-sidechain contact distance between residues Ser294-Gln237, Ser294-Met239, Ser294-Tyr241, Asn295-Gln237, Asn295-Met239, Asn295-Tyr241, Gly178-Gln237, Gly178-Met239, Gly178-Tyr241, Ser179-Gln237, Ser179-Met239, and Ser179-Tyr241 was decreased by the presence of flavonoids. In addition, the sidechain-sidechain contact distance between most residues was still kept almost the same as the RANKL monomer without flavonoids molecules. The results of sidechain-sidechain contact maps indicated that flavonoids molecules promoted the sidechain-sidechain contacts in the active pocket, and then led to the formation of more compact conformation in the RANKL monomer, which were in good agreement with the results of Rg and SASA. Hydrogen bonds analysis Hydrogen bond interaction is one of the main parameters to reflect the stability of the ligand at the active pocket in the protein. It provides the basis for molecular recognition and selectivity by imparting directionality and explicitness to molecular interactions 39 . Thus, we performed H-bonds analysis using the GROMACS "gmx hbond" script to calculate the time evolution of hydrogen bonds during the complete run of MD simulations (Fig. 9 ). In complexes with cyrtominetin and quercetin, the most conformations formed 3 to 4 hydrogen bonds during the simulation. A very few conformations showed less than 2 and greater than 5 hydrogen bonds. In the complexes with syringetin and genistein, the conformational changes showed the same trend. However, in complexes with ombuin and kaempferol, the average number of hydrogen bonds formed was 1 to 3. These results provided a good verification for molecular docking. In comparison, compound 1 formed an average number of 2 to 3 hydrogen bonds in the first 50ns, and few conformations showed up to 5 hydrogen bonds. In the last 50ns, the number of hydrogen bonds decreased until reaching the end of the MD simulation run. Most flavonoids formed a higher number of hydrogen bonds inside the binding pocket throughout the simulation than control group. These results showed that the flavonoids were able to maintain strong interaction with the binding pocket of RANKL during the simulation. Free energy analyses Principal component analyses (PCA) of MD simulations is a technique used to reveal various conformations of protein molecules. Protein function is regulated by the transformation between various conformations. To make proteins functional, reasonable flexibility and rigidity are required, especially for the residues in the binding site. Typically, tighter interactions would limit the movement of the protein, so it is not allowed to switch some conformations required for its activity 40 . In order to understand the transformation of protein occupied in the conformational space, we applied PCA to analyze the combined fluctuations in the most unstable regions of the protein molecule into two variables, principal component 1 (PC1) and principal component 2 (PC2), which represent most of the fluctuations observed during MD simulation. Next, FEL plots were generated from the principal PC1 and principal PC2 coordinates. The FEL accurately described the minimum energy conformation ensembles of proteins, which is crucial for understanding the conformational transition underlying protein-ligand interactions. Figure 10 showed that the binding of flavonoids with RANKL occurs through the minimum free energy pathway. The FEL of RANKL-cyrtominetin complex showed that the stably bound conformation was widely filled to a single consolidated energy minimum, which provided favorable evidence for interaction inducing the stable conformational transition of the complex. The FEL of RANKL-quercetin complex showed the appearance of two distinct populations confined to two different energy basins, separated with high transition barrier > 4.8 kcal/mol, which signified the population of loosely and tightly ligand-bound conformations of the protein. The conformational ensemble derived from FEL showed that the complexes of RANKL-syringetin and RANKL-genistein clustered in the different energy basins. However, these energy minima separated through a low transition barrier < 3.0 kcal/mol indicated that the ensemble states of complexes readily transferred from one energy basin to another with a small deviation. The FEL with segmented small energy of complexes with ombuin and kaempferol indicated the presence of loosely bound complexes. The low transition barriers between small energy basins suggested a longer equilibration phase of the complex structure. Contrary to this, RANKL apo state experienced a wide region of phase space. In fact, it explored a large conformational space in comparison to the other RANKL-flavonoids complexes, which represent the overall higher flexibility of the protein. The conformational ensemble occupying the small energy basin represented the population of the equilibration phase, which readily achieved a stable equilibrium. It is apparent from these plots that RANKL-flavonoids complexes are localized in a small conformational space, which may facilitate the vital interactions with flavonoids. Secondary structural characterization Although the above results indicated that the conformation of RANKL monomer was stabilized by the presence of flavonoids, the detailed mechanisms of the interactions between RANKL monomer and flavonoids were still unclear. Therefore, to further explore the influence of flavonoids on the secondary structure of RANKL monomer, the analysis of RANKL monomer was performed by the DSSP algorithm. The secondary structure information for each residue (residues 162–317) during the simulations was given in Fig. 11 . For the RANKL monomer without flavonoids molecules, most of the residues mainly kept the β-sheet structure throughout the whole simulation. Among them, the residues Gly178-Lys181 in the N-terminal of RANKL monomer were converted into short β-sheet structure connected with bend structure. The residues Gln237-Tyr241 always kept the β-sheet structure throughout the whole 100 ns simulation. In the C-terminal of RANKL monomer, the residues Val293-Pro296 kept the 3-helix structure, with occasional local deviations that converted the 3-helix to turn structure. By comparison, the time evolution of the secondary structures of RANKL monomer in the presence of flavonoids molecules is not significantly different from that of RANKL monomer alone, indicating that the RANKL-flavonoids complexes are rather stable, which is well consistent with the previous analysis. Effects of flavonoids on the binding free energy of RANKL monomer The binding free energy is a relatively comprehensive evaluation of the binding affinity between receptors and ligands, which takes various interaction forces into account 41 . The previous study indicated that negative of the binding free energy represented the binding of ligands to receptors was beneficial 42 . To obtain quantitative insight into the interactions between RANKL monomer and flavonoids molecules, the binding free energy for RANKL-flavonoids complexes was calculated using the MMPBSA method. The binding free energy and various contribution terms for RANKL-flavonoids complexes were summarized in Table 2 . It was clearly observed that both non-bonded electrostatics interactions (∆E elec ) and non-bonded van der Waals interactions (∆E vdW ) favored the interactions between RANKL monomer and flavonoids molecules. And the nonpolar solvation free energy (∆G nonpolar−sol ) was also favorable for the formation of RANKL-flavonoids complexes. However, the polar solvation free energy (∆G polar−sol ) was unfavorable. The polar binding free energy ∆G polar was the sum of ∆G polar−sol and ∆E elec , and the nonpolar binding free energy ∆G nonpolar was the sum of ∆G nonpolar−sol and ∆E vdW . The ∆G polar and ∆G nonpolar represented the net results of polar interactions and nonpolar interactions, respectively. Hence, the results indicated that the nonpolar interactions were involved in the stabilization of RANKL-flavonoids complexes. Although, ∆G polar impaired the binding, the unfavorable change in the polar binding free energy was completely compensated by ∆G nonpolar . Table 2 Binding free energy between RANKL monomer and flavonoids. Energy terms control group Cyrtominetin Quercetin Syringetin Genistein Ombuin Kaempferol △E elec (kJ/mol) -31.173 ± 15.451 -122.668 ± 14.010 -104.110 ± 20.859 -137.866 ± 20.612 -136.358 ± 22.337 -66.541 ± 11.696 -80.534 ± 11.510 △E vdW (kJ/mol) -102.152 ± 16.511 -85.806 ± 19.310 -64.291 ± 16.876 -87.556 ± 14.752 -72.592 ± 14.764 -52.015 ± 14.495 -78.970 ± 13.591 △E MM (kJ/mol) -133.325 -208.474 -168.401 -225.423 -208.950 -118.556 -159.504 △G polar−sol (kJ/mol) 101.112 ± 24.155 171.266 ± 19.677 135.083 ± 18.764 209.349 ± 21.194 180.071 ± 20.034 66.493 ± 14.658 125.323 ± 11.237 △G nonpolar−sol (kJ/mol) -13.262 ± 2.024 -12.997 ± 0.853 -11.020 ± 2.102 -13.656 ± 0.930 -13.219 ± 0.879 -8.374 ± 2.694 -12.320 ± 0.655 △G polar (kJ/mol) 69.939 48.599 30.974 71.482 43.713 -0.049 44.789 △G nonpolar (kJ/mol) -115.414 -98.803 -75.311 -101.212 -85.811 -60.388 -91.290 △G binding (kJ/mol) -45.475 ± 19.837 -50.205 ± 15.845 -44.338 ± 18.939 -29.730 ± 10.821 -42.098 ± 16.920 -60.437 ± 13.605 -46.502 ± 11.988 To further quantify the contribution of binding pocket residues to the interaction of flavonoids molecules with RANKL monomer, the free energy decomposition of per residue was employed (Fig. 12 ). The binding interaction with cyrtominetin showed that the amino acid residues, Gly178, Ser179, His180, Met239, Tyr241, Ser294, and Pro296, contributed the most to the total ∆Gbinding. Although the vdW interaction primarily stabilized the cyrtominetin at the binding pocket, the electrostatic interaction also contributed to the observed stability by His180 (− 3.21 kcal/mol), Lys181 (-3.89 kcal/mol), and Ser294 (− 8.63 kcal/mol), respectively. Quercetin was predominantly stabilized in the binding pocket through the electrostatic interaction, which was mostly contributed by the residues Ser179 (− 2.21 kcal/mol), Gln237 (− 2.85 kcal/mol), Ser294 (− 6.72 kcal/mol), and Asn295 (− 9.48 kcal/mol), respectively. The free energy decomposition plot of syringetin indicated that amino acids Gly178, His180, Met239, and Tyr241 were important for the binding of syringetin at the binding pocket. Surprisingly, it is noted that Lys181 contributed to both electrostatic energy (− 13.24 kcal/mol) and vdW energy (− 7.40 kcal/mol). The favorable binding of genistein showed the significant contribution of residues, Gly178, Lys181, Ser294, and Pro296. It is noted that Gln237 and Asn295 contributed higher electrostatic energy (− 5.83 and − 5.67 kcal/mol, respectively). The plot of free energy decomposition analysis showed that the active site residues, Gly178, Ser179, His180, Lys181, Met239, Tyr241, and Asn295 favored the binding stability of ombuin. The binding interaction with kaempferol showed that the amino acid residues, Gly178, Ser179, His180, Met239, Tyr241, and Asn295, were important for the interaction in the binding pocket. Interestingly, it is noted that Tyr241 contributed higher electrostatic energy (− 5.67 kcal/mol), whereas the maximum vdW energy (− 7.97 kcal/mol) was contributed by His180. control group was predominantly stabilized in the binding pocket through the vdW interaction, which was mostly contributed by the residues Ser179 (− 5.36 kcal/mol), His180 (− 4.68 kcal/mol), Lys181 (− 4.66kcal/mol) Gln237 (− 10.88kcal/mol) and Asn295 (− 4.07 kcal/mol), respectively. However, the binding pocket of RANKL consisted of hydrophilic and hydrophobic residues. Thus, we observed that both electrostatic energy and vdW energy were major contributions to stabilizing the ligand interaction. Conclusion In summary, using molecular docking and classical MD simulation, we have explored the potential of 6 flavonoids to bind in the active site of the RANKL protein. The selected molecules exhibited variable degrees of affinities toward the RANKL monomer through molecular docking simulation. We found that most flavonoids interacted with RANKL monomer by forming strong hydrogen bonds with Gly178 and Asn195 to exhibit higher binding affinity, which was assumed to be essential for the activity, as well as significant extra interactions with other binding residues. The existence of critical RANKL residues suggested that designing small molecules that could target these critical residues in RANKL is a potential way in targeting the RANKL monomer. Besides, cyrtominetin may be used as a lead compound for the development of potent RANKL inhibitors. This information could help the development of therapeutic agents targeting the RANKL monomer for the treatment of bone-related diseases. Furthermore, the MD simulation showed good interactions between the selected molecules and the active site of RANKL monomer. Throughout the all-atom 100 ns MD simulation, flavonoids depicted superior stability at the RANKL binding site for more than 70 ns, where the solvation energy was greatly compensated by the electrostatic and van der Waal binding energies. Materials and Methods Ligand preparation The ADMET properties of all flavonoids were determined by the online in-silico prediction model ADMETlab 2.0 ( https://admetmesh.scbdd.com/ ), such as absorption, distribution, metabolism, excretion, toxicity and physicochemical properties, and drug similarity properties were evaluated using the Lipinski rule. Then, the 2D structures of compounds meeting the rules were retrieved from PubChem in SDF file format, while the 3D structures conversion and energy minimization were performed by applying standard geometric parameters of the molecular modeling software package Sybyl-X (version 2.1.1, Tripos Inc.). Tripos force field and Powell conjugate gradient algorithm were employed to minimize the energy of each compound using 0.05 kcal/ mol Å and Gasteiger- Huckel charges as convergence criteria 43 . Protein preparation Based on the analysis of the interaction surface of all published RANKL crystal structures, the crystal structure with a concave pocket (PDB ID: 3URF—resolution: 2.70 Å) was most suitable for molecular docking. Next, the crystal structure of 3URF was extracted from Protein Data Bank (PDB https://www.rcsb.org ) in PDB file format. In the process of protein preparation, water molecules were removed from the structure, H atoms were added, and side chains were fixed. Protein structure minimization was performed using Tripos force field and partial atomic charges were calculated the Gasteiger- Huckel method. Finally, the optimal protein structure was verified by PROCHECK tool ( https://saves.mbi.ucla.edu/ ) to determine the allowable regions for torsion angles ψ against φ of amino acid residues. Binding site prediction Based on the analysis of the interaction surface, the most suitable concave pocket for molecular docking was chosen as the binding site 32 33 . Sybyl-x was used to generate the binding site of the protein, which provides a pocket for binding the ligand molecule and offers the expected active region. Molecular docking The Surflex-Dock module in Sybyl-X was used to evaluate the interactions of the flavonoids against RANKL, where 20 possible conformations for each docked ligand were produced. The docked conformations were evaluated and ranked using the Total_Score function, which was expressed in -log10(Kd) units to represent binding affinities. Conformations at the binding site were selected according to the values of Total_Score, and the conformation with the highest score was selected as the optimal conformation to study its docking mode. In general, Total_Score > 4.0 indicates certain binding activity, Total_Score > 5.0 indicates good binding activity, while Total_Score > 7.0 indicates strong binding activity 44 . Additionally, previous studies identified a lead compound, which can directly bind to RANKL and has the property of inhibiting RANKL/RANK protein interaction 33 . Therefore, it was used as a control group for comparison with flavonoids. Subsequently, PyMOL 2.4 program and Discovery Studio Visualizer 2021 were employed to visualize the binding mode between the protein and ligand. Molecular dynamics simulations Molecular docking provides static position of the most favorable conformations of molecules in the protein binding pocket to present a stable complex. However, static images are not able to present other crucial features involved in protein stability, including the flexibility of residues and secondary structural elements 45 . Likewise, the conformational changes caused by the dynamic behavior of proteins may affect their actual biological functions 46 . In order to gain insight into the dynamic behavior of flavonoids at the binding pocket of RANKL, the molecular dynamic (MD) simulation was executed. Before MD simulation, the selected compounds were prepared using ATB online server ( https://atb.uq.edu.au/ ) to generate the initial topology. The simulation was performed using the GROMACS 2019.6. GROMOS96 54a7 force field was applied to the system, and a dodecahedron water box composed of TIP3P water model was used to solvate the system. Na + and Cl − ions were also solvated in the box to maintain the overall neutrality of the system. Next, the steepest descent minimization algorithm was used to carry out energy minimization at 50,000 steps. The process of energy minimization was to eliminate the negative interaction in the system. Then, the system was heated gradually at 300 K using 100 ps in the NVT canonical ensemble with 2 fs time step. For the NPT isothermal–isobaric ensemble, the atoms were relaxed at 300 K and 1 bar using 100 ps with 2 fs time step. To treat long-range electrostatic interactions, the Particle Mesh Ewald (PME) method was used. After equilibrating the system at 300 K temperature and 1 bar pressure, the MD run for the system was carried out at 100 ns with 2 fs time step at 50,000,000 steps. Various structural parameters, including root mean square deviation (RMSD), root mean square fluctuation (RMSF), radius of gyration (Rg), solvent accessible surface area (SASA), intermolecular hydrogen bonds (H-bonds), intra-chain interactions, secondary structural characterization, and free energy landscape (FEL), were calculated by GROMACS built-in tools to explore the structural behavior of the protein-ligand complexes. Binding free energy estimation Free energy calculation analysis is a useful method to quantitatively estimate the binding affinity between bio-macromolecules and ligands 47 . In the present study, the binding free energy of protein-ligand complex was evaluated using molecular mechanics Poisson Boltzmann surface area (MM-PBSA), which described the structural and molecular stability of the ligand in the active site. According to the MM-PBSA method, the calculation principle of the binding free energy of protein-ligand complex was summarized as following: ΔG binding =G complex −G receptor −G ligand , where G complex , G receptor and G ligand were the binding free energy for RANKL-flavonoids complexes, RANKL monomer, and flavonoids molecules, respectively. Excluding the entropy term (TΔS), the above equation for the binding free energy could be approximately written as, ΔG binding = ΔE MM + ΔG solvation , where ΔE MM was the change in the average molecular mechanics interaction energy upon ligand binding and ΔG solvation was the change in solvation free energy upon ligand binding. The change of average molecular mechanics potential energy (ΔE MM ) in vacuum was estimated by: ΔE MM = ΔE intern + ΔE elec + ΔE vdw , where ΔE intern was the change of molecular internal energy, including the energy of bond, angle, dihedral, and improper interactions. Generally, ∆E intern was considered to be zero. The ΔE elec and ΔE vdw were electrostatic interaction energy and van der Waals interaction energy, respectively. Further, ΔG solvation could be written as, ΔG solvation = ΔG polar−sol + ΔG nonpolar−sal , where ΔG polar−sol was the change in the polar part of the solvation free energy, and ΔG nonpolar−sal was the change in the non-polar part of the solvation free energy as a result of ligand binding to the proteins. G polar−sol was calculated by using the PB equation and G nonpolar−sol was estimated as a function of the SASA as the equation following: G nonpolar−sol = γSASA + b, where γ was the coefficient related to the surface tension of the solvent and b was the fitting parameter. The binding free energy was calculated by the g_mmpbsa tool of GROMACS. The default parameters for γ and b were used in the g_mmpbsa tool. In the equilibrium phase of molecular dynamics simulation, the binding free energy was calculated by extracting 20 snapshots from 60 to 80 ns in a time interval of 1ns. Declarations Author Contribution Conceptualization, X.F.Z. and L.X.Z.; methodology, X.F.Z., D.L. and Q.W.; software,L.X.Z., L.B.W. and Z.Q.Z.; investigation, Q.W.; resources, L.X.Z. and Z.Q.Z.; data curation, D.L.; writing—original draft preparation, X.F.Z.; writing—review and editing, L.X.Z.; visualization, D.L.and L.B.W.; supervision, Z.Q.Z. and Y.X.; project administration, Y.X.; funding acquisition, Y.X. All authors have read and agreed to the published version of the manuscript. Data Availability The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request. Competing interests The authors declare no competing interests. References Gullberg, B., Johnell, O. & Kanis, J. A. World-Wide Projections for Hip Fracture. Osteoporos. Int. 7 , 407–413 (1997). Kanis, J. A. Assessment of Fracture Risk and its Application to Screening for Postmenopausal Osteoporosis: Synopsis of a WHO Report. WHO Study Group. Osteoporos. 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Supplementary Files Table1.docx Cite Share Download PDF Status: Published Journal Publication published 17 May, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 31 Mar, 2025 Reviews received at journal 24 Mar, 2025 Reviews received at journal 09 Mar, 2025 Reviewers agreed at journal 26 Feb, 2025 Reviewers agreed at journal 26 Feb, 2025 Reviewers invited by journal 26 Feb, 2025 Editor assigned by journal 22 Feb, 2025 Editor invited by journal 31 Jan, 2025 Submission checks completed at journal 31 Jan, 2025 First submitted to journal 27 Jan, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5909485","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":409599773,"identity":"f68a45c3-fbe9-45d9-9258-a7ce7c58000f","order_by":0,"name":"Xiaofei Zhang","email":"","orcid":"","institution":"Northwest Women's and Children's Hospital","correspondingAuthor":false,"prefix":"","firstName":"Xiaofei","middleName":"","lastName":"Zhang","suffix":""},{"id":409599774,"identity":"d1a6f972-0834-498c-9f3e-253f19b9c5fe","order_by":1,"name":"Lixia Zhang","email":"","orcid":"","institution":"Shaanxi Provincial People’s Hospital","correspondingAuthor":false,"prefix":"","firstName":"Lixia","middleName":"","lastName":"Zhang","suffix":""},{"id":409599775,"identity":"75634ce6-0534-4da7-8695-8801c727d621","order_by":2,"name":"Dan Li","email":"","orcid":"","institution":"Northwest Women's and Children's Hospital","correspondingAuthor":false,"prefix":"","firstName":"Dan","middleName":"","lastName":"Li","suffix":""},{"id":409599776,"identity":"328a82ac-a894-4d41-a25d-cdf0a428cd92","order_by":3,"name":"Qi Wang","email":"","orcid":"","institution":"Second Affiliated Hospital of Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Qi","middleName":"","lastName":"Wang","suffix":""},{"id":409599777,"identity":"051978ab-69bc-4def-9595-2dd926351991","order_by":4,"name":"Libin Wang","email":"","orcid":"","institution":"Northwest Women's and Children's Hospital","correspondingAuthor":false,"prefix":"","firstName":"Libin","middleName":"","lastName":"Wang","suffix":""},{"id":409599778,"identity":"016662b9-1f47-4bd5-8652-4742c06d65b9","order_by":5,"name":"Ziqi Zheng","email":"","orcid":"","institution":"Northwest University","correspondingAuthor":false,"prefix":"","firstName":"Ziqi","middleName":"","lastName":"Zheng","suffix":""},{"id":409599779,"identity":"a67db299-208d-4caf-bc9e-8d753fc65b46","order_by":6,"name":"Yun Xie","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1UlEQVRIiWNgGAWjYDACZjB5AMQ6wJBAoha2BCK1MMC18BgQp9bgOPMxad4dd+TM23s+f3i4w46Bv70bv2WSzWxp0rxnnhnLnDm7TSLxTDKDxJmzG/Bq4WfmMZPmbTucOEMidxtDYhszg4FELn4tbMz830Ba6mdI5Dz+kNhWT1gL0BY2kJYECYkcBonEtsOEtQD9Ymw5t+2w4QyeY2ZALcd5CPrF4Pzhhzfeth2Wl2BvfvzxZ1u1HH97L34tQMAigczjIaQcBJg/EKNqFIyCUTAKRjAAAHXSQxCNk4O+AAAAAElFTkSuQmCC","orcid":"","institution":"Northwest Women's and Children's Hospital","correspondingAuthor":true,"prefix":"","firstName":"Yun","middleName":"","lastName":"Xie","suffix":""}],"badges":[],"createdAt":"2025-01-27 05:23:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5909485/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5909485/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-01913-3","type":"published","date":"2025-05-17T15:57:05+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":75314665,"identity":"f331cc56-e5c6-4559-a14b-ec9a30eb65a2","added_by":"auto","created_at":"2025-02-03 09:32:30","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":72107,"visible":true,"origin":"","legend":"\u003cp\u003e(A) Overall structure of RANKL/OPG complex. (B) The Ramachandran plot of RANKL. Red, yellow, light yellow, and white are the most favorable, additional allowed, generously allowed, and disallowed regions in conformation, respectively.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5909485/v1/a80b944d974128d0130e44a6.jpg"},{"id":75313714,"identity":"e76cf02b-bf38-4b41-8eff-69bd3ef1d147","added_by":"auto","created_at":"2025-02-03 09:24:29","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":66798,"visible":true,"origin":"","legend":"\u003cp\u003eOverall view of RANKL/OPG binding interface. (A) Sites I and II in the binding interface. The OPG is shown in surface colored with violet. The RANKL is colored with blue. (B) An open-book view of the contact residues in binding sites I and II. The contact residues in binding sites I and II are colored with grey and orange, respectively.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5909485/v1/57a538d3dcbdf74d2b441fcb.jpg"},{"id":75313712,"identity":"fc3771d5-07b7-40cd-a417-9554f8cc213a","added_by":"auto","created_at":"2025-02-03 09:24:29","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":355672,"visible":true,"origin":"","legend":"\u003cp\u003eBinding mode of flavonoids in the active site of RANKL. (A) Cyrtominetin (orange), (B) Quercetin (blue), (C) Syringetin (cyan), (D) Genistein (purple), (E) Ombuin (yellow), (F) Kaempferol (green), and (G) control group (pink). Protein residues are shown in pale gold sticks.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5909485/v1/299f34975e84748a65c70b2d.jpg"},{"id":75313748,"identity":"4e601564-0424-415a-b5db-2e098bae247f","added_by":"auto","created_at":"2025-02-03 09:24:30","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":94689,"visible":true,"origin":"","legend":"\u003cp\u003eTime evolution RMSD trajectories of the RANKL-flavonoids complexes over 100 ns all-atom MD simulation. (A) The RMSD of backbone Cα-atoms. (B) The relative frequency distribution of RMSD.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5909485/v1/23ea0df80f9575820b098b2d.jpg"},{"id":75314661,"identity":"449df14f-30c0-4a54-b5f3-b58ccd4e6962","added_by":"auto","created_at":"2025-02-03 09:32:29","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":93494,"visible":true,"origin":"","legend":"\u003cp\u003eAnalysis of RMSF trajectories versus residue number of the RANKL-flavonoids complexes over 100 ns all-atom MD simulation.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5909485/v1/f581f9ca63d471d20f54a748.jpg"},{"id":75316443,"identity":"d0d41129-d5e2-437f-9354-355b335f4895","added_by":"auto","created_at":"2025-02-03 09:40:30","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":103889,"visible":true,"origin":"","legend":"\u003cp\u003eTime evolution Rg trajectories of the RANKL-flavonoids complexes over 100 ns all-atom MD simulation. (A) The Rg of the RANKL-flavonoids complexes. (B) The relative frequency distribution of Rg.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5909485/v1/a4c7895cf1557ce5eac3d4fb.jpg"},{"id":75314658,"identity":"32baa82b-213d-43c0-8940-05563dc3bb0d","added_by":"auto","created_at":"2025-02-03 09:32:29","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":98972,"visible":true,"origin":"","legend":"\u003cp\u003eTime evolution SASA trajectories of the RANKL-flavonoids complexes over 100 ns all-atom MD simulation. (A) The SASA of the RANKL-flavonoids complexes. (B) The relative frequency distribution of SASA.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5909485/v1/de5c5e4af8c8e3bcd0d03c6b.jpg"},{"id":75314659,"identity":"b5b59be7-161a-4fb1-a645-a8c5b7a687c2","added_by":"auto","created_at":"2025-02-03 09:32:29","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":176498,"visible":true,"origin":"","legend":"\u003cp\u003eThe sidechain-sidechain contact maps for RANKL monomer of all flavonoids simulation systems. (A) Cyrtominetin, (B) Quercetin, (C) Syringetin, (D) Genistein (E) Ombuin (F) Kaempferol (G) control group and (H) apo. The distance is given in nm and indicated by the color code.\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5909485/v1/10e88d0a15c3e4b7ce3ebc40.jpg"},{"id":75313732,"identity":"aeec0c81-df27-4ca2-90df-472e8bb4f379","added_by":"auto","created_at":"2025-02-03 09:24:30","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":98513,"visible":true,"origin":"","legend":"\u003cp\u003eTime evolution plot of hydrogen bond interaction between the RANKL and flavonoids over 100 ns all-atom MD simulation.\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5909485/v1/3c2df18c4878ac9c3a8f9976.jpg"},{"id":75313721,"identity":"cca6bd71-e298-4270-ac7e-2d008e00ccda","added_by":"auto","created_at":"2025-02-03 09:24:29","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":102127,"visible":true,"origin":"","legend":"\u003cp\u003eFEL of RANKL-flavonoids complexes. (A) Cyrtominetin, (B) Quercetin, (C) Syringetin, (D) Genistein, (E) Ombuin, (F) Kaempferol, (G) control group, and (H) apo. The free energy is given in kcal/mol and indicated by the color code, from lower to higher energy in the right panel.\u003c/p\u003e","description":"","filename":"10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5909485/v1/7b7917193afc93cf801e73e4.jpg"},{"id":75313742,"identity":"8831cd16-709d-46de-8cd0-674a8655e485","added_by":"auto","created_at":"2025-02-03 09:24:30","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":158046,"visible":true,"origin":"","legend":"\u003cp\u003eTime evolution secondary structures of the RANKL-flavonoids complexes over 100 ns all-atom MD simulation. (A) Cyrtominetin, (B) Quercetin, (C) Syringetin, (D) Genistein, (E) Ombuin, (F) Kaempferol, (G) control group, and (H) apo.\u003c/p\u003e","description":"","filename":"11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5909485/v1/ad343664fcd2243dff12f928.jpg"},{"id":75313716,"identity":"65c2f77f-f903-4932-893c-ea87860b45e3","added_by":"auto","created_at":"2025-02-03 09:24:29","extension":"jpg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":78419,"visible":true,"origin":"","legend":"\u003cp\u003eThe residue decomposition plot (MM-PBSA) representing the binding energy contribution of the residues energetically stabilizing the flavonoids at binding pocket. (A) Cyrtominetin, (B) Quercetin, (C) Syringetin, (D) Genistein, (E) Ombuin, (F) Kaempferol and (G) control group.\u003c/p\u003e","description":"","filename":"12.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5909485/v1/bf425d4599dffe330bb665bc.jpg"},{"id":83068674,"identity":"8e88908c-b1f0-4ec1-9d62-087bb35f1310","added_by":"auto","created_at":"2025-05-19 16:10:48","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2462562,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5909485/v1/e4ac8390-0b4a-439f-86ef-6bd2f77e4250.pdf"},{"id":75316442,"identity":"7905c535-7800-4d9b-92d8-e518843e92d9","added_by":"auto","created_at":"2025-02-03 09:40:30","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":386619,"visible":true,"origin":"","legend":"","description":"","filename":"Table1.docx","url":"https://assets-eu.researchsquare.com/files/rs-5909485/v1/0dbd338eec11da7681eecf63.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Computational study of flavonoids from Eucommia ulmoides against RANKL-induced osteoclastogenesis using Molecular Docking and molecular dynamics simulation","fulltext":[{"header":"Introduction","content":"\u003cp\u003eOsteoporosis is the most common form of bone disease characterized by low bone density decreased bone mass and increased bone fragility\u003csup\u003e1\u003c/sup\u003e. More than 100 million people worldwide are suffering from osteoporosis, and the World Health Organization (WHO) has identified it as a major public health concern\u003csup\u003e2\u003c/sup\u003e. Bone mass is maintained through a dynamic process, known as bone remodeling, which is generated by the interaction of sustained balance between osteoclast-induced bone resorption and osteoblast-mediated bone formation\u003csup\u003e3\u003c/sup\u003e. Accumulating evidence indicates that the disorder of dynamic balance between bone resorption and bone formation results in osteoporosis. Among them, the overactivation of osteoclasts is considered to be the main reason for excessive bone resorption and bone mass reduction\u003csup\u003e4\u003c/sup\u003e. Therefore, reducing the activity of osteoclasts to restore the balance between bone resorption and bone formation has become a critical strategy for the treatment of osteoporosis\u003csup\u003e5\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eThe differentiation and maturation of osteoclasts is a complex and delicate multilevel regulatory process, in which the receptor activator of nuclear factor-\u0026kappa;B ligand (RANKL) plays a vital role\u003csup\u003e6\u003c/sup\u003e. Specifically, the binding of RANKL to the receptor activator of nuclear factor-\u0026kappa;B (RANK) induces tumor necrosis factor receptor-associated factor 6 (TRAF6) recruitment, which sequentially activates signaling factors nuclear factor kappa-B (NF-\u0026kappa;B) and mitogen-activated protein kinases (MAPKs), including p38, c-Jun N-terminal kinase (JNK) and extracellular signal-regulated kinase (ERK)\u003csup\u003e7,\u003c/sup\u003e \u003csup\u003e8\u003c/sup\u003e. At the same time, the RANKL-RANK interaction activates the AKT signaling pathway by recruiting c-Src\u003csup\u003e9,\u003c/sup\u003e \u003csup\u003e10\u003c/sup\u003e. Subsequently, the activation of these signaling molecules increases the expression of nuclear factor of activated T cell c1 (NFATc1) and c-Fos, which can directly regulate osteoclast differentiation and osteoclast-specific gene expression\u003csup\u003e11\u003c/sup\u003e. In addition, osteoprotegerin (OPG), a natural antagonist of RANKL, inhibits the formation of osteoclasts by preventing RANKL/RANK interaction\u003csup\u003e12\u003c/sup\u003e. Based on the above analysis, targeting RANKL/RANK/OPG system of osteoclast differentiation signaling pathway, especially directly blocking RANKL-RANK interaction, provides the possibility to develop novel therapeutic approaches for treating osteoporosis\u003csup\u003e13\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eCurrently, many researchers have been working hard to find effective drugs to antagonize or inhibit RANKL. Unfortunately, most of the drugs that have been found have some drawbacks that limit their administration\u003csup\u003e14\u003c/sup\u003e. For example, denosumab is a RANKL monoclonal antibody inhibitor, which has been developed to treat osteoporosis\u003csup\u003e15\u003c/sup\u003e. It is the first RANKL inhibitor approved by FDA, but its application is limited due to its high price\u003csup\u003e16\u003c/sup\u003e. Besides, recombinant proteins such as Fc-OPG, Fc-osteoprotegerin, and other anti-RANKL antibodies have also been developed as therapeutic agents for osteoporosis\u003csup\u003e17,\u003c/sup\u003e \u003csup\u003e18\u003c/sup\u003e. However, the clinical applications of macromolecular drugs are hindered by some shortcomings, including low stability, poor bioavailability, high cost, and difficulties in administration\u003csup\u003e19\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eNowadays, many researchers have turned to select compounds from natural products to find more specific and safer agents against RANKL. For example, it has been found that ellagic acid, niloticin and epigallocatechin-3-gallate can directly block RANKL-RANK interaction to inhibit RANKL-induced osteoclast differentiation signaling pathway\u003csup\u003e20,\u003c/sup\u003e \u003csup\u003e21\u003c/sup\u003e. In fact, many flavonoid compounds also have beneficial activities in inhibiting RANKL-induced osteoclast differentiation and bone resorption\u003csup\u003e22-24\u003c/sup\u003e. Such as, quercetin can affect NF-kB, AP-1 and NFATc1 in RANKL/RANK/OPG system to inhibit osteoclast differentiation\u003csup\u003e25\u003c/sup\u003e. Kaempferol can inhibit RANKL-mediated ERK, JNK and p38 phosphorylation and the expression of c-Fos and NFATc1\u003csup\u003e26,\u003c/sup\u003e \u003csup\u003e27\u003c/sup\u003e. Genistein directly inhibits osteoclastic differentiation through inhibiting the expression of two transcription factors c-Fos and NFATc1 induced by NF-kB up regulation\u003csup\u003e28\u003c/sup\u003e. Syringetin is an inhibitor targeting osteoclast differentiation\u003csup\u003e29\u003c/sup\u003e. Moreover, according to the analysis results of the KEGG pathway in previous report, we found that the flavonoids in Eucommia ulmoides (EU) could directly regulate the osteoclast differentiation signaling pathways to treat osteoporosis\u003csup\u003e30\u003c/sup\u003e. Given that flavonoids can inhibit the RANKL-stimulated activation of the AKT, MAPK, and NF-\u0026kappa;B signaling pathways and regulate osteoclast differentiation signaling pathways, we speculated that flavonoids could inhibit osteoclast differentiation by binding RANKL to block RANKL\u0026ndash;RANK interaction.\u003c/p\u003e\n\u003cp\u003eHere, we described the ability of flavonoids to bind RANKL using molecular docking and molecular dynamic approaches. Molecular simulation could provide detailed information on both quantitative atomic level and thermodynamic descriptions of the interactions between receptor and ligand with ideal resolution, which could not be obtained by experimental approaches\u003csup\u003e31\u003c/sup\u003e. The six flavonoids previously reported in EU, including quercetin, kaempferol, cyrtominetin, syringetin, genistein and ombuin, were specially selected in the present study\u003csup\u003e30\u003c/sup\u003e. We believed that the results of molecular simulation could give more insights into understanding the underlying mechanisms of flavonoids to inhibit RANKL-induced osteoclastogenesis at the atomic level, and help to further development of new medications for osteoporosis.\u0026nbsp;\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003ch2\u003ePreparation of ligand and protein for Docking\u003c/h2\u003e \u003cp\u003eThe details of six flavonoids with positive ADMET properties in the present study were shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. It could be seen from the radar plot that all the physicochemical properties are in the proper scope. PROCHECK checked the stereochemical quality of protein structure by analyzing residue-by-residue geometry and overall structure geometry. Ramachandran plot showed that 89.1% of residues fall in the most favorable regions, 9.5% in additional allowed regions, 1.5% in generously allowed regions, and 0% in disallowed regions (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eBinding site prediction\u003c/h2\u003e \u003cp\u003e3URF includes two parts, RANKL and its decoy receptor OPG. The binding interface of RANKL/OPG is composed of two binding sites (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e)\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. The binding site I, composed of relatively small and separate contact patches in both RANKL and OPG, is located on the OPG \"50s loop\" (His47-Leu65) and nearly parallel to the RANKL along the groove. Whereas at the binding site II, the OPG \u0026ldquo;90s loop\u0026rdquo; (Arg90 -Leu98) is deeply within the groove. Compared with separate interactions at the binding site I, more interactions at the binding site II are concentrated around the tip of OPG 90s loop. The binding site II forms a hydrophilic interaction network with RANKL residues by using Glu95 of the OPG \"90s loop\", which is more important than the binding site I in RANKL/OPG binding. At the same time, this position is also the main binding determinant of RANKL/RANK interaction. In addition, after binding with RANKL active site, it was found that Glu93 and Ile94 residues formed hydrophobic and van der Waals interactions with hydrophobic residues around RANKL. Three amino acids, Glu93, Ile94, and Glu95, from the OPG probe deeply into the concave surface of RANKL, defining the main binding pocket for small molecular inhibitors targeting RANKL/RANK interaction. Residues within a distance of 6 \u0026Aring; around the residues Glu93, Ile94, and Glu95 of OPG were defined as the binding pocket for molecular docking\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eMolecular interaction\u003c/h3\u003e\n\u003cp\u003eIn molecular docking, the ligands bind to amino acid residues and interact with each other in the active pocket, participating in the process of conformational changes and energy complementation. The binding sites and binding score values can intuitively reflect the interaction and stability of the docking model. The docking results showed that all flavonoids exhibited notable interactions and docking scores were greater than 4, indicating that the binding between flavonoids and RANKL was relatively stable. Among picked molecules, cyrtominetin and quercetin displayed the best binding affinities compared to other molecules with total scores of 6.5143 and 5.0316 respectively. The control group had a total score of 6.3254. Interestingly, cyrtominetin achieved a superior binding than control group indicating that it has a promising affinity and intrinsic activity towards the RANKL. The binding modes of RANKL with the 6 flavonoids were shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eAfter exploring the molecular interactions, it was perceived that cyrtominetin manifested hydrogen bonds with residues Gly178, His180, Lys181, and Asn295. One amide-Pi stacked with residues Ser179, one Pi-alkyl (His180), and one alkyl interaction (Met239). It also formed van der Waals (vdW) interaction with residues Val182, Thr233, Gln237, Tyr241, Ser294, and Pro296. In the case of quercetin, residue Gly178, Lys181, Gln237, and Asn295 formed hydrogen bonds. Residues Ser179 interacted via Pi-lone pair interactions. Residues His180, Met239, Tyr241, Ser294 and Pro296 formed vdW interactions. In molecule syringetin, residues Gly178, Lys181, Gln237, and Asn295 formed hydrogen bonds. Several residues formed other interactions like Ser179 (Pi-lone pair), Tyr241 (Pi-alkyl), Met239 (Alkyl), and residues His180, Lys257, Ser294 and Pro296 showed vdW interactions. In genistein, hydrogen bonds were formed by residues Gly178, Gln237, Asn295, and C-H bond by Ser294, Leu236. Residues Ser179 also formed amide-Pi stacked. Residues Lys181, Val182, Tyr235, Thr261, Pro296 and Ser294 showed vdW interactions. In the case of ombuin, hydrogen bonds were formed by residues Gly178, Thr233, Asn295, and C-H bond by His180. Residues also formed other interactions, including one amide-Pi stacked (Ser179), and alkyl (Lys181). Residues Tyr235, Leu236, Gln237, Tyr241, Ser294, and Pro296 displayed vdW interactions. Kaempferol exhibited hydrogen bonds with residue His180, Thr233, Tyr235, and Tyr241. It also formed vdW interaction with residues Ser179, Lys181, Leu236, Gln237, Met239, Ser294, and Asn295. In control group, hydrogen bonds were formed by residues Ser179, His180, Gln237, Asn295, and C-H bond by Ser179. Residues also formed other interactions, including one Pi-sigma (Gln237), Pi-alkyl (Lys181), and alkyl (Lys181). Residues Tyr235, Leu236, Met239, Tyr241, Thr261 and Ser294 showed vdW interactions.\u003c/p\u003e \u003cp\u003eThe binding style contributes a reasonable rationale for the significance of interacting residues in target protein binding. It was observed that there was a high resemblance between the above 6 flavonoids, and they nearly occupied the same active pocket. Furthermore, the binding of flavonoids to RANKL was also significantly mediated by the critical residues and conferred the best interactions. These data indicated that residues Gly178, Asn295, Lys181, Gln237, and Ser179 played a more critical role in the binding process.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eMolecular dynamics simulations\u003c/h3\u003e\n\u003cp\u003eMolecular dynamics simulation is considered to be an efficacious approach, which can explore the stability of protein-ligand complex obtained from previous docking studies and investigate their relative dynamic properties, so as to provide stability information on the predicted binding interactions with important residues\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. From the result of docking, the protein-ligand complex having the least binding energy with the best configuration was carried out 100ns MD simulation.\u003c/p\u003e\n\u003ch3\u003eRMSD analysis\u003c/h3\u003e\n\u003cp\u003eRMSD of backbone C-α atoms was measured using the GROMACS \u0026ldquo;gmx rmsd\u0026rdquo; tool to quantify the structural stability of protein-ligand complex. Generally, RMSD is a standard measurement of the structural distance between coordinates, which is used to infer the extent of deviation for a group of atoms relative to their initial structures\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. The RMSD values express how much the conformations of these groups of atoms have changed to indicate the stability of complexes. In the present study, the 6 flavonoids under investigation were successfully converged within the 100 ns MD simulation window. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, all complexes tended to reach their stable states, and the fluctuation of proteins was within acceptable range with RMSD values of less than 4.00 \u0026Aring;, indicating the stability of the conformational ensemble.\u003c/p\u003e \u003cp\u003eThe cyrtominetin-bound protein started from C-alpha RMSD (RMSD-Cα) 1.07\u0026Aring;, gradually increasing until it converged at around 15ns. After this, the protein adopted an equilibrium plateau showing minimal fluctuations around its average until the end of the MD run with an average deviation of 2.86\u0026Aring;. This behavior is a typical MD simulation run, in which the protein begins to relax after removing all constraints until reaching its equilibration state, where RMSD-Cα trajectories tends to be stable indicating the stability of the protein. In the case of quercetin-bound protein, the backbone RMSD gradually increased until convergence at around 30ns where RMSD tends to be stable until reaching 50ns, in which RMSD decreased then rose again. The final convergence around an average RMSD (2.66 \u0026Aring;) started from 60ns until the end of MD simulation at 100ns. The simulation of syringetin-bound protein performed well, in which it gradually reached dynamic equilibration at around 25ns, and the average RMSD was 2.33 \u0026Aring; with stable fluctuations until 100 ns. The RMSD-Cα trajectories of genistein-bound protein had a low average value (2.15\u0026Aring;) and lesser fluctuations, indicating its stability. With regard to ombuin and kaempferol, the proteins started at lower RMSD-Cα values (0.71 and 0.78 \u0026Aring;, respectively), and proteins depicted delayed convergences after 30ns from the start of the MD simulation runs. Following convergence, both proteins were dynamically balanced, showing their RMSD-Cα trajectories being maintained around their respective average deviations (1.17 \u0026Aring; and 2.89 \u0026Aring;, respectively). The RANKL apo state was initially stable and maintained structural integrity during most of the simulation time. However, a rise of the RMSD value was observed for 85\u0026ndash;95 ns time and returned to the steady state in the final period (average 2.38 \u0026Aring;). The minimal fluctuations in the RMSD trajectories and low difference in average RMSD values showed that the RANKL-flavonoids complexes were stable. Overall results explained that these 6 flavonoids molecules did not significantly influence the structural stability of RANKL, and all systems showed stable internal motion.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eRMSF analysis\u003c/h3\u003e\n\u003cp\u003eWe further performed RMSF analysis to evaluate the positional fluctuation of each amino acid around its average mean position. The individual backbone RMSF was calculated using the GROMACS \u0026ldquo;gmx rmsf\u0026rdquo; command line to perceive structural stability and flexibility at local levels. In addition, it can also be used to identify the flexible residues in the protein, so that we can explore the conformational flexibility of the protein structure\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAs depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, all systems showed almost similar patterns. In the case of RANKL apo state, we observed the highest fluctuations in loop regions. The loop regions are very flexible elements of protein, and their flexibility is essential to accommodate the ligand at the binding site appropriately. For the residues (178\u0026ndash;181, 237\u0026ndash;241, and 293\u0026ndash;296) at the binding site, the RMSF had smaller values throughout the simulation, further showing the regions of active site residues were quite stable. Compared with the RANKL apo state, the RMSF values of numerous residues in RANKL-flavonoids complexes increased, especially residues in loop regions, indicating that the flexibility of RANKL monomer increased after binding with flavonoids. Additionally, the majority of the protein residues were stable with RMSF values smaller than 0.3 nm. The active site residues participating in interactions with flavonoids molecules remained highly stable throughout the MD simulation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eRadius of gyration\u003c/h2\u003e \u003cp\u003eNext, we investigated the structural stability of the protein-ligand complex by calculating the Rg to determine the compactness of the protein structure. Rg was calculated using the GROMACS \"gmx gyrate\" script. Rg reveals the knowledge of folding and unfolding of protein structure upon binding of the ligands. Higher Rg values explain less compactness (more unfolded) with high conformational entropy while low Rg values show high compactness and more stability in the structure (more folded)\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, all systems of ligand-bound proteins have projected the Rg values between 16 to 17 \u0026Aring;. To some extent, the protein Rg values were comparable among the investigated systems being fluctuated around close averages. In the case of RANKL apo state, the average Rg value was found to be 16.94 \u0026Aring;. The average Rg values of cyrtominetin-bound protein and quercetin-bound protein were 16.76 \u0026Aring; and 16.31 \u0026Aring;, where cyrtominetin exhibited steadier trajectory, indicating significant stability and compactness within the protein active pocket. Similarly, syringetin, genistein, ombuin, and kaempferol bound to the target protein, the average Rg values were found to be 16.56, 16.57, 16.54, and 16.33 \u0026Aring;, respectively. In the whole simulation process, all systems of ligand-bound proteins became more compact than RANKL apo state, which indicated that the RANKL-flavonoids complexes are well converged.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eSolvent-accessible surface area\u003c/h3\u003e\n\u003cp\u003eMoreover, another important quantity that we measure and analyze to probe the conformational stability of the protein-ligand complex is SASA. The SASA values were analyzed to assess the complexes volume change through GROMACS \u0026ldquo;gmx sasa\u0026rdquo; script. Generally, SASA correlates for the molecular surface area being assessable to solvent molecules providing a quantitative measurement about the extent of protein/solvent interaction\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. The decrease of SASA values implies that the relative structures of complexes shrink under the influence of the solvent surface charge, resulting in more compact and stable conformations.\u003c/p\u003e \u003cp\u003eAs predicted, the SASA values of all RANKL-flavonoids complexes were comparable, and all values were concentrated between 85 to 90 nm\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). Among them, cyrtominetin-bound protein had a higher SASA trajectory in the initial phase. After this stage, the SASA value gradually decreased to reach min SASA value which was followed by a subsequent increase until reaching the end of the MD simulation run (average 86.68 nm\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e). The elevated SASA trajectories might confer the migration of cyrtominetin towards the solvent side within the simulation time frames of 60 to 100 ns where the protein pocket became highly solvated and minimally compacted. The quercetin-bound protein showed lower SASA trajectory (average 85.56 nm\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e), particularly within the last 50 ns. Such dynamic behavior suggested preferential confinement of quercetin within the protein pocket. The syringetin-bound protein and ombuin-bound protein had higher SASA trajectories in the initial phase, followed by a lower value, and then maintained a stable SASA until the end of the simulation. The SASA trajectories of genistein-bound protein and kaempferol-bound protein were similar, with less fluctuation during the simulation, indicating that the stability of these two complexes was less affected by the solvent. On the other hand, the RANKL apo state showed stable SASA trajectorie (average 88.05 nm\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e) until reaching 100 ns of the simulation run. In the whole simulation process, all systems of ligand-bound proteins became more compact than RANKL apo state. In the presented study, findings from the SASA analysis appeared to ensure the well stability of the RANKL-flavonoids complexes previously presented by the Rg trajectory analysis.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eEffects of flavonoids on the intra-chain interactions\u003c/h3\u003e\n\u003cp\u003eTo further explore the roles of flavonoids on the intra-chain interactions, the sidechain-sidechain contact diagrams of the RANKL monomer were calculated by using the GROMACS \"gmx mdmat\" program. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e, the contact distance between sidechains of residues in the RANKL monomer was represented by distinct colors. Blue and red expressed the distance between sidechains was 0.0 nm and 1.5 nm, respectively. When the color was closer to blue, the distance between the related sidechains was closer. On the contrary, when the color was closer to red, the related sidechains were farther from each other. In all simulation systems, the contact distance changes mainly located in the active pocket. In the absence of flavonoids molecules, it was found that there was some repulsion between the sidechains of residues in the active pocket. In the presence of flavonoids molecules, it was observed that the number of blocks close to red was reduced, demonstrating that the contacts between sidechains were strengthened by flavonoids. To be more specific, the sidechain-sidechain contact distance between residues Ser294-Gln237, Ser294-Met239, Ser294-Tyr241, Asn295-Gln237, Asn295-Met239, Asn295-Tyr241, Gly178-Gln237, Gly178-Met239, Gly178-Tyr241, Ser179-Gln237, Ser179-Met239, and Ser179-Tyr241 was decreased by the presence of flavonoids. In addition, the sidechain-sidechain contact distance between most residues was still kept almost the same as the RANKL monomer without flavonoids molecules. The results of sidechain-sidechain contact maps indicated that flavonoids molecules promoted the sidechain-sidechain contacts in the active pocket, and then led to the formation of more compact conformation in the RANKL monomer, which were in good agreement with the results of Rg and SASA.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eHydrogen bonds analysis\u003c/h2\u003e \u003cp\u003eHydrogen bond interaction is one of the main parameters to reflect the stability of the ligand at the active pocket in the protein. It provides the basis for molecular recognition and selectivity by imparting directionality and explicitness to molecular interactions\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. Thus, we performed H-bonds analysis using the GROMACS \"gmx hbond\" script to calculate the time evolution of hydrogen bonds during the complete run of MD simulations (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn complexes with cyrtominetin and quercetin, the most conformations formed 3 to 4 hydrogen bonds during the simulation. A very few conformations showed less than 2 and greater than 5 hydrogen bonds. In the complexes with syringetin and genistein, the conformational changes showed the same trend. However, in complexes with ombuin and kaempferol, the average number of hydrogen bonds formed was 1 to 3. These results provided a good verification for molecular docking. In comparison, compound 1 formed an average number of 2 to 3 hydrogen bonds in the first 50ns, and few conformations showed up to 5 hydrogen bonds. In the last 50ns, the number of hydrogen bonds decreased until reaching the end of the MD simulation run. Most flavonoids formed a higher number of hydrogen bonds inside the binding pocket throughout the simulation than control group. These results showed that the flavonoids were able to maintain strong interaction with the binding pocket of RANKL during the simulation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eFree energy analyses\u003c/h2\u003e \u003cp\u003ePrincipal component analyses (PCA) of MD simulations is a technique used to reveal various conformations of protein molecules. Protein function is regulated by the transformation between various conformations. To make proteins functional, reasonable flexibility and rigidity are required, especially for the residues in the binding site. Typically, tighter interactions would limit the movement of the protein, so it is not allowed to switch some conformations required for its activity\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn order to understand the transformation of protein occupied in the conformational space, we applied PCA to analyze the combined fluctuations in the most unstable regions of the protein molecule into two variables, principal component 1 (PC1) and principal component 2 (PC2), which represent most of the fluctuations observed during MD simulation. Next, FEL plots were generated from the principal PC1 and principal PC2 coordinates. The FEL accurately described the minimum energy conformation ensembles of proteins, which is crucial for understanding the conformational transition underlying protein-ligand interactions. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e showed that the binding of flavonoids with RANKL occurs through the minimum free energy pathway. The FEL of RANKL-cyrtominetin complex showed that the stably bound conformation was widely filled to a single consolidated energy minimum, which provided favorable evidence for interaction inducing the stable conformational transition of the complex. The FEL of RANKL-quercetin complex showed the appearance of two distinct populations confined to two different energy basins, separated with high transition barrier\u0026thinsp;\u0026gt;\u0026thinsp;4.8 kcal/mol, which signified the population of loosely and tightly ligand-bound conformations of the protein. The conformational ensemble derived from FEL showed that the complexes of RANKL-syringetin and RANKL-genistein clustered in the different energy basins. However, these energy minima separated through a low transition barrier\u0026thinsp;\u0026lt;\u0026thinsp;3.0 kcal/mol indicated that the ensemble states of complexes readily transferred from one energy basin to another with a small deviation. The FEL with segmented small energy of complexes with ombuin and kaempferol indicated the presence of loosely bound complexes. The low transition barriers between small energy basins suggested a longer equilibration phase of the complex structure. Contrary to this, RANKL apo state experienced a wide region of phase space. In fact, it explored a large conformational space in comparison to the other RANKL-flavonoids complexes, which represent the overall higher flexibility of the protein. The conformational ensemble occupying the small energy basin represented the population of the equilibration phase, which readily achieved a stable equilibrium. It is apparent from these plots that RANKL-flavonoids complexes are localized in a small conformational space, which may facilitate the vital interactions with flavonoids.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eSecondary structural characterization\u003c/h2\u003e \u003cp\u003eAlthough the above results indicated that the conformation of RANKL monomer was stabilized by the presence of flavonoids, the detailed mechanisms of the interactions between RANKL monomer and flavonoids were still unclear. Therefore, to further explore the influence of flavonoids on the secondary structure of RANKL monomer, the analysis of RANKL monomer was performed by the DSSP algorithm.\u003c/p\u003e \u003cp\u003eThe secondary structure information for each residue (residues 162\u0026ndash;317) during the simulations was given in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e. For the RANKL monomer without flavonoids molecules, most of the residues mainly kept the β-sheet structure throughout the whole simulation. Among them, the residues Gly178-Lys181 in the N-terminal of RANKL monomer were converted into short β-sheet structure connected with bend structure. The residues Gln237-Tyr241 always kept the β-sheet structure throughout the whole 100 ns simulation. In the C-terminal of RANKL monomer, the residues Val293-Pro296 kept the 3-helix structure, with occasional local deviations that converted the 3-helix to turn structure. By comparison, the time evolution of the secondary structures of RANKL monomer in the presence of flavonoids molecules is not significantly different from that of RANKL monomer alone, indicating that the RANKL-flavonoids complexes are rather stable, which is well consistent with the previous analysis.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eEffects of flavonoids on the binding free energy of RANKL monomer\u003c/h2\u003e \u003cp\u003eThe binding free energy is a relatively comprehensive evaluation of the binding affinity between receptors and ligands, which takes various interaction forces into account\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. The previous study indicated that negative of the binding free energy represented the binding of ligands to receptors was beneficial\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. To obtain quantitative insight into the interactions between RANKL monomer and flavonoids molecules, the binding free energy for RANKL-flavonoids complexes was calculated using the MMPBSA method. The binding free energy and various contribution terms for RANKL-flavonoids complexes were summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. It was clearly observed that both non-bonded electrostatics interactions (∆E\u003csub\u003eelec\u003c/sub\u003e) and non-bonded van der Waals interactions (∆E\u003csub\u003evdW\u003c/sub\u003e) favored the interactions between RANKL monomer and flavonoids molecules. And the nonpolar solvation free energy (∆G\u003csub\u003enonpolar\u0026minus;sol\u003c/sub\u003e) was also favorable for the formation of RANKL-flavonoids complexes. However, the polar solvation free energy (∆G\u003csub\u003epolar\u0026minus;sol\u003c/sub\u003e) was unfavorable. The polar binding free energy ∆G\u003csub\u003epolar\u003c/sub\u003e was the sum of ∆G\u003csub\u003epolar\u0026minus;sol\u003c/sub\u003e and ∆E\u003csub\u003eelec\u003c/sub\u003e, and the nonpolar binding free energy ∆G\u003csub\u003enonpolar\u003c/sub\u003e was the sum of ∆G\u003csub\u003enonpolar\u0026minus;sol\u003c/sub\u003e and ∆E\u003csub\u003evdW\u003c/sub\u003e. The ∆G\u003csub\u003epolar\u003c/sub\u003e and ∆G\u003csub\u003enonpolar\u003c/sub\u003e represented the net results of polar interactions and nonpolar interactions, respectively. Hence, the results indicated that the nonpolar interactions were involved in the stabilization of RANKL-flavonoids complexes. Although, ∆G\u003csub\u003epolar\u003c/sub\u003e impaired the binding, the unfavorable change in the polar binding free energy was completely compensated by ∆G\u003csub\u003enonpolar\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBinding free energy between RANKL monomer and flavonoids.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnergy terms\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003econtrol group\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCyrtominetin\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eQuercetin\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSyringetin\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGenistein\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eOmbuin\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eKaempferol\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e△E\u003csub\u003eelec\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(kJ/mol)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-31.173\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e15.451\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-122.668\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e14.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-104.110\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e20.859\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-137.866\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e20.612\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-136.358\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e22.337\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-66.541\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e11.696\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-80.534\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e11.510\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e△E\u003csub\u003evdW\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(kJ/mol)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-102.152\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e16.511\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-85.806\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e19.310\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-64.291\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e16.876\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-87.556\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e14.752\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-72.592\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e14.764\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-52.015\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e14.495\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-78.970\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e13.591\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e△E\u003csub\u003eMM\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(kJ/mol)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-133.325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-208.474\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-168.401\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-225.423\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-208.950\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-118.556\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-159.504\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e△G\u003csub\u003epolar\u0026minus;sol\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(kJ/mol)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e101.112\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e24.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e171.266\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e19.677\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e135.083\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e18.764\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e209.349\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e21.194\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e180.071\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e20.034\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e66.493\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e14.658\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e125.323\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e11.237\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e△G\u003csub\u003enonpolar\u0026minus;sol\u003c/sub\u003e (kJ/mol)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-13.262\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e2.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-12.997\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e0.853\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-11.020\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e2.102\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-13.656\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e0.930\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-13.219\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e0.879\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-8.374\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e2.694\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-12.320\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e0.655\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e△G\u003csub\u003epolar\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(kJ/mol)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e69.939\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e48.599\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30.974\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e71.482\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e43.713\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.049\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e44.789\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e△G\u003csub\u003enonpolar\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(kJ/mol)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-115.414\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-98.803\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-75.311\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-101.212\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-85.811\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-60.388\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-91.290\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e△G\u003csub\u003ebinding\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(kJ/mol)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-45.475\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e19.837\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-50.205\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e15.845\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-44.338\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e18.939\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-29.730\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e10.821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-42.098\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e16.920\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-60.437\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e13.605\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-46.502\u003c/p\u003e \u003cp\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e11.988\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo further quantify the contribution of binding pocket residues to the interaction of flavonoids molecules with RANKL monomer, the free energy decomposition of per residue was employed (Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e). The binding interaction with cyrtominetin showed that the amino acid residues, Gly178, Ser179, His180, Met239, Tyr241, Ser294, and Pro296, contributed the most to the total ∆Gbinding. Although the vdW interaction primarily stabilized the cyrtominetin at the binding pocket, the electrostatic interaction also contributed to the observed stability by His180 (\u0026minus;\u0026thinsp;3.21 kcal/mol), Lys181 (-3.89 kcal/mol), and Ser294 (\u0026minus;\u0026thinsp;8.63 kcal/mol), respectively. Quercetin was predominantly stabilized in the binding pocket through the electrostatic interaction, which was mostly contributed by the residues Ser179 (\u0026minus;\u0026thinsp;2.21 kcal/mol), Gln237 (\u0026minus;\u0026thinsp;2.85 kcal/mol), Ser294 (\u0026minus;\u0026thinsp;6.72 kcal/mol), and Asn295 (\u0026minus;\u0026thinsp;9.48 kcal/mol), respectively. The free energy decomposition plot of syringetin indicated that amino acids Gly178, His180, Met239, and Tyr241 were important for the binding of syringetin at the binding pocket. Surprisingly, it is noted that Lys181 contributed to both electrostatic energy (\u0026minus;\u0026thinsp;13.24 kcal/mol) and vdW energy (\u0026minus;\u0026thinsp;7.40 kcal/mol). The favorable binding of genistein showed the significant contribution of residues, Gly178, Lys181, Ser294, and Pro296. It is noted that Gln237 and Asn295 contributed higher electrostatic energy (\u0026minus;\u0026thinsp;5.83 and \u0026minus;\u0026thinsp;5.67 kcal/mol, respectively). The plot of free energy decomposition analysis showed that the active site residues, Gly178, Ser179, His180, Lys181, Met239, Tyr241, and Asn295 favored the binding stability of ombuin. The binding interaction with kaempferol showed that the amino acid residues, Gly178, Ser179, His180, Met239, Tyr241, and Asn295, were important for the interaction in the binding pocket. Interestingly, it is noted that Tyr241 contributed higher electrostatic energy (\u0026minus;\u0026thinsp;5.67 kcal/mol), whereas the maximum vdW energy (\u0026minus;\u0026thinsp;7.97 kcal/mol) was contributed by His180. control group was predominantly stabilized in the binding pocket through the vdW interaction, which was mostly contributed by the residues Ser179 (\u0026minus;\u0026thinsp;5.36 kcal/mol), His180 (\u0026minus;\u0026thinsp;4.68 kcal/mol), Lys181 (\u0026minus;\u0026thinsp;4.66kcal/mol) Gln237 (\u0026minus;\u0026thinsp;10.88kcal/mol) and Asn295 (\u0026minus;\u0026thinsp;4.07 kcal/mol), respectively. However, the binding pocket of RANKL consisted of hydrophilic and hydrophobic residues. Thus, we observed that both electrostatic energy and vdW energy were major contributions to stabilizing the ligand interaction.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eIn summary, using molecular docking and classical MD simulation, we have explored the potential of 6 flavonoids to bind in the active site of the RANKL protein. The selected molecules exhibited variable degrees of affinities toward the RANKL monomer through molecular docking simulation. We found that most flavonoids interacted with RANKL monomer by forming strong hydrogen bonds with Gly178 and Asn195 to exhibit higher binding affinity, which was assumed to be essential for the activity, as well as significant extra interactions with other binding residues. The existence of critical RANKL residues suggested that designing small molecules that could target these critical residues in RANKL is a potential way in targeting the RANKL monomer. Besides, cyrtominetin may be used as a lead compound for the development of potent RANKL inhibitors. This information could help the development of therapeutic agents targeting the RANKL monomer for the treatment of bone-related diseases. Furthermore, the MD simulation showed good interactions between the selected molecules and the active site of RANKL monomer. Throughout the all-atom 100 ns MD simulation, flavonoids depicted superior stability at the RANKL binding site for more than 70 ns, where the solvation energy was greatly compensated by the electrostatic and van der Waal binding energies.\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eLigand preparation\u003c/h2\u003e \u003cp\u003eThe ADMET properties of all flavonoids were determined by the online in-silico prediction model ADMETlab 2.0 (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://admetmesh.scbdd.com/\u003c/span\u003e\u003cspan address=\"https://admetmesh.scbdd.com/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e), such as absorption, distribution, metabolism, excretion, toxicity and physicochemical properties, and drug similarity properties were evaluated using the Lipinski rule. Then, the 2D structures of compounds meeting the rules were retrieved from PubChem in SDF file format, while the 3D structures conversion and energy minimization were performed by applying standard geometric parameters of the molecular modeling software package Sybyl-X (version 2.1.1, Tripos Inc.). Tripos force field and Powell conjugate gradient algorithm were employed to minimize the energy of each compound using 0.05 kcal/ mol \u0026Aring; and Gasteiger- Huckel charges as convergence criteria\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003eProtein preparation\u003c/h2\u003e \u003cp\u003eBased on the analysis of the interaction surface of all published RANKL crystal structures, the crystal structure with a concave pocket (PDB ID: 3URF\u0026mdash;resolution: 2.70 \u0026Aring;) was most suitable for molecular docking. Next, the crystal structure of 3URF was extracted from Protein Data Bank (PDB \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.rcsb.org\u003c/span\u003e\u003cspan address=\"https://www.rcsb.org\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) in PDB file format. In the process of protein preparation, water molecules were removed from the structure, H atoms were added, and side chains were fixed. Protein structure minimization was performed using Tripos force field and partial atomic charges were calculated the Gasteiger- Huckel method. Finally, the optimal protein structure was verified by PROCHECK tool (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://saves.mbi.ucla.edu/\u003c/span\u003e\u003cspan address=\"https://saves.mbi.ucla.edu/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) to determine the allowable regions for torsion angles ψ against φ of amino acid residues.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003eBinding site prediction\u003c/h2\u003e \u003cp\u003eBased on the analysis of the interaction surface, the most suitable concave pocket for molecular docking was chosen as the binding site\u003csup\u003e32 33\u003c/sup\u003e. Sybyl-x was used to generate the binding site of the protein, which provides a pocket for binding the ligand molecule and offers the expected active region.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003eMolecular docking\u003c/h2\u003e \u003cp\u003eThe Surflex-Dock module in Sybyl-X was used to evaluate the interactions of the flavonoids against RANKL, where 20 possible conformations for each docked ligand were produced. The docked conformations were evaluated and ranked using the Total_Score function, which was expressed in -log10(Kd) units to represent binding affinities. Conformations at the binding site were selected according to the values of Total_Score, and the conformation with the highest score was selected as the optimal conformation to study its docking mode. In general, Total_Score\u0026thinsp;\u0026gt;\u0026thinsp;4.0 indicates certain binding activity, Total_Score\u0026thinsp;\u0026gt;\u0026thinsp;5.0 indicates good binding activity, while Total_Score\u0026thinsp;\u0026gt;\u0026thinsp;7.0 indicates strong binding activity\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e. Additionally, previous studies identified a lead compound, which can directly bind to RANKL and has the property of inhibiting RANKL/RANK protein interaction\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. Therefore, it was used as a control group for comparison with flavonoids. Subsequently, PyMOL 2.4 program and Discovery Studio Visualizer 2021 were employed to visualize the binding mode between the protein and ligand.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003eMolecular dynamics simulations\u003c/h2\u003e \u003cp\u003eMolecular docking provides static position of the most favorable conformations of molecules in the protein binding pocket to present a stable complex. However, static images are not able to present other crucial features involved in protein stability, including the flexibility of residues and secondary structural elements\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e. Likewise, the conformational changes caused by the dynamic behavior of proteins may affect their actual biological functions\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e. In order to gain insight into the dynamic behavior of flavonoids at the binding pocket of RANKL, the molecular dynamic (MD) simulation was executed. Before MD simulation, the selected compounds were prepared using ATB online server (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://atb.uq.edu.au/\u003c/span\u003e\u003cspan address=\"https://atb.uq.edu.au/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) to generate the initial topology. The simulation was performed using the GROMACS 2019.6. GROMOS96 54a7 force field was applied to the system, and a dodecahedron water box composed of TIP3P water model was used to solvate the system. Na\u003csup\u003e+\u003c/sup\u003e and Cl\u003csup\u003e\u0026minus;\u003c/sup\u003e ions were also solvated in the box to maintain the overall neutrality of the system. Next, the steepest descent minimization algorithm was used to carry out energy minimization at 50,000 steps. The process of energy minimization was to eliminate the negative interaction in the system. Then, the system was heated gradually at 300 K using 100 ps in the NVT canonical ensemble with 2 fs time step. For the NPT isothermal\u0026ndash;isobaric ensemble, the atoms were relaxed at 300 K and 1 bar using 100 ps with 2 fs time step. To treat long-range electrostatic interactions, the Particle Mesh Ewald (PME) method was used. After equilibrating the system at 300 K temperature and 1 bar pressure, the MD run for the system was carried out at 100 ns with 2 fs time step at 50,000,000 steps. Various structural parameters, including root mean square deviation (RMSD), root mean square fluctuation (RMSF), radius of gyration (Rg), solvent accessible surface area (SASA), intermolecular hydrogen bonds (H-bonds), intra-chain interactions, secondary structural characterization, and free energy landscape (FEL), were calculated by GROMACS built-in tools to explore the structural behavior of the protein-ligand complexes.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003eBinding free energy estimation\u003c/h2\u003e \u003cp\u003eFree energy calculation analysis is a useful method to quantitatively estimate the binding affinity between bio-macromolecules and ligands\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. In the present study, the binding free energy of protein-ligand complex was evaluated using molecular mechanics Poisson Boltzmann surface area (MM-PBSA), which described the structural and molecular stability of the ligand in the active site.\u003c/p\u003e \u003cp\u003eAccording to the MM-PBSA method, the calculation principle of the binding free energy of protein-ligand complex was summarized as following:\u003c/p\u003e \u003cp\u003eΔG\u003csub\u003ebinding\u003c/sub\u003e=G\u003csub\u003ecomplex\u003c/sub\u003e\u0026minus;G\u003csub\u003ereceptor\u003c/sub\u003e\u0026minus;G\u003csub\u003eligand\u003c/sub\u003e,\u003c/p\u003e \u003cp\u003ewhere G\u003csub\u003ecomplex\u003c/sub\u003e, G\u003csub\u003ereceptor\u003c/sub\u003e and G\u003csub\u003eligand\u003c/sub\u003e were the binding free energy for RANKL-flavonoids complexes, RANKL monomer, and flavonoids molecules, respectively. Excluding the entropy term (TΔS), the above equation for the binding free energy could be approximately written as,\u003c/p\u003e \u003cp\u003eΔG\u003csub\u003ebinding\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;ΔE\u003csub\u003eMM\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;ΔG\u003csub\u003esolvation\u003c/sub\u003e,\u003c/p\u003e \u003cp\u003ewhere ΔE\u003csub\u003eMM\u003c/sub\u003e was the change in the average molecular mechanics interaction energy upon ligand binding and ΔG\u003csub\u003esolvation\u003c/sub\u003e was the change in solvation free energy upon ligand binding. The change of average molecular mechanics potential energy (ΔE\u003csub\u003eMM\u003c/sub\u003e) in vacuum was estimated by:\u003c/p\u003e \u003cp\u003eΔE\u003csub\u003eMM\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;ΔE\u003csub\u003eintern\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;ΔE\u003csub\u003eelec\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;ΔE\u003csub\u003evdw\u003c/sub\u003e,\u003c/p\u003e \u003cp\u003ewhere ΔE\u003csub\u003eintern\u003c/sub\u003e was the change of molecular internal energy, including the energy of bond, angle, dihedral, and improper interactions. Generally, ∆E\u003csub\u003eintern\u003c/sub\u003e was considered to be zero. The ΔE\u003csub\u003eelec\u003c/sub\u003e and ΔE\u003csub\u003evdw\u003c/sub\u003e were electrostatic interaction energy and van der Waals interaction energy, respectively. Further, ΔG\u003csub\u003esolvation\u003c/sub\u003e could be written as,\u003c/p\u003e \u003cp\u003eΔG\u003csub\u003esolvation\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;ΔG\u003csub\u003epolar\u0026minus;sol\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;ΔG\u003csub\u003enonpolar\u0026minus;sal\u003c/sub\u003e,\u003c/p\u003e \u003cp\u003ewhere ΔG\u003csub\u003epolar\u0026minus;sol\u003c/sub\u003e was the change in the polar part of the solvation free energy, and ΔG\u003csub\u003enonpolar\u0026minus;sal\u003c/sub\u003e was the change in the non-polar part of the solvation free energy as a result of ligand binding to the proteins. G\u003csub\u003epolar\u0026minus;sol\u003c/sub\u003e was calculated by using the PB equation and G\u003csub\u003enonpolar\u0026minus;sol\u003c/sub\u003e was estimated as a function of the SASA as the equation following:\u003c/p\u003e \u003cp\u003eG\u003csub\u003enonpolar\u0026minus;sol\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;γSASA\u0026thinsp;+\u0026thinsp;b,\u003c/p\u003e \u003cp\u003ewhere γ was the coefficient related to the surface tension of the solvent and b was the fitting parameter.\u003c/p\u003e \u003cp\u003eThe binding free energy was calculated by the g_mmpbsa tool of GROMACS. The default parameters for γ and b were used in the g_mmpbsa tool. In the equilibrium phase of molecular dynamics simulation, the binding free energy was calculated by extracting 20 snapshots from 60 to 80 ns in a time interval of 1ns.\u003c/p\u003e "},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eConceptualization, X.F.Z. and L.X.Z.; methodology, X.F.Z., D.L. and Q.W.; software,L.X.Z., L.B.W. and Z.Q.Z.; investigation, Q.W.; resources, L.X.Z. and Z.Q.Z.; data curation, D.L.; writing\u0026mdash;original draft preparation, X.F.Z.; writing\u0026mdash;review and editing, L.X.Z.; visualization, D.L.and L.B.W.; supervision, Z.Q.Z. and Y.X.; project administration, Y.X.; funding acquisition, Y.X. All authors have read and agreed to the published version of the manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eGullberg, B., Johnell, O. \u0026amp; Kanis, J. A. World-Wide Projections for Hip Fracture. \u003cem\u003eOsteoporos. Int.\u003c/em\u003e \u003cb\u003e7\u003c/b\u003e, 407\u0026ndash;413 (1997).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKanis, J. A. Assessment of Fracture Risk and its Application to Screening for Postmenopausal Osteoporosis: Synopsis of a WHO Report. WHO Study Group. \u003cem\u003eOsteoporos. 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Protoc.\u003c/em\u003e \u003cb\u003e15\u003c/b\u003e, 2837\u0026ndash;2866 (2020).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Table 1","content":"\u003cp\u003eTable 1 is available in the Supplementary Files section.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Osteoporosis, flavonoids, RANKL, Molecular docking, Molecular dynamics","lastPublishedDoi":"10.21203/rs.3.rs-5909485/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5909485/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eOsteoporosis is the most common form of bone disease and the RANKL/RANK/OPG has been widely demonstrated to be a critical protein for bone metabolism. Previous studies suggested that flavonoids played an obligatory role in the inhibition process of osteoclast differentiation induced by RANKL. However, the detailed mechanisms were still unknown. Eucommia ulmoides is a popular herb used to treat bone diseases in traditional medicine, in which flavonoids play an important role. Thus, in the present study, the flavonoids in Eucommia ulmoides were specially selected and the molecular recognition mechanisms between flavonoids and RANKL monomer were examined and analyzed by molecular modeling approaches. The in-silico experiments revealed that the selected molecules exhibited variable degrees of affinities toward the RANKL monomer. Among them, cyrtominetin may be used as a lead compound for the development of potent RANKL inhibitors. By analyzing the binding sites of flavonoids to RANKL monomer, we found that most flavonoids interacted with RANKL monomer by forming strong hydrogen bonds with Gly178 and Asn195 to exhibit higher binding affinity, which was assumed to be essential for the activity. Moreover, the MD simulation showed good interactions between the selected molecules and the active site of RANKL monomer. Throughout the all-atom 100 ns MD simulation, flavonoids depicted superior stability at the RANKL binding site for more than 70 ns, where the solvation energy was greatly compensated by the electrostatic and van der Waal binding energies. We believed that the results could help to elucidate the underlying mechanisms of flavonoids to inhibit osteoclast differentiation induced by RANKL at the atomic level and facilitate the development of new medications for bone-related diseases.\u003c/p\u003e","manuscriptTitle":"Computational study of flavonoids from Eucommia ulmoides against RANKL-induced osteoclastogenesis using Molecular Docking and molecular dynamics simulation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-02-03 09:24:23","doi":"10.21203/rs.3.rs-5909485/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-03-31T07:58:44+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-03-24T07:10:05+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-03-09T15:45:21+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"262761201196249564296791645331331246528","date":"2025-02-27T04:57:38+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"46905593938641946664222207792517300840","date":"2025-02-26T11:41:38+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-02-26T07:03:06+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-02-22T12:32:50+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-01-31T14:32:25+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-01-31T06:26:57+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-01-27T05:11:31+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"4a37d828-9ece-42f8-bbf3-ad14dae601b0","owner":[],"postedDate":"February 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":43678656,"name":"Biological sciences/Computational biology and bioinformatics"},{"id":43678657,"name":"Biological sciences/Drug discovery"}],"tags":[],"updatedAt":"2025-05-19T16:09:36+00:00","versionOfRecord":{"articleIdentity":"rs-5909485","link":"https://doi.org/10.1038/s41598-025-01913-3","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-05-17 15:57:05","publishedOnDateReadable":"May 17th, 2025"},"versionCreatedAt":"2025-02-03 09:24:23","video":"","vorDoi":"10.1038/s41598-025-01913-3","vorDoiUrl":"https://doi.org/10.1038/s41598-025-01913-3","workflowStages":[]},"version":"v1","identity":"rs-5909485","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5909485","identity":"rs-5909485","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}