## Introduction

During biological activity, body tissues are subjected to various kinds of stimuli outside and inside the body. In order to adapt to such stimuli, body tissues remodel themselves. Bone tissue is remodeled via a repetitive cycle of osteoclastic bone resorption and osteoblastic bone formation on the bone surface. Osteoclasts are large, multinucleated cells that have capacity to degrade bone tissue1,2. Osteoblasts secrete bone matrix molecules, mostly collagen, and mineralize them to construct calcified tissue3. A portion of osteoblasts is embedded in the bone matrix and these cells differentiate into osteocytes. The balance between bone resorption and formation is strictly regulated by various biological systems, including the endocrine, nervous, immune and musculoskeletal system itself1,2.

During the growth period, the jawbone is subjected to certain forces imposed by the surrounding tissues, including the teeth and oro-facial muscles (masticatory, lingual and mimetic muscles). Therefore, the resulting adult facial profile is believed to be closely associated with these forces, especially the ones generated by the masticatory muscles, which play a central role in food ingestion: a brachyofacial pattern (short face) in individuals with strong masticatory force and a dolicofacial pattern (long face) in individuals with weak15. Animal models of reduced mastication, induced by liquid or powder diets, recapitulate the phenotypes seen in humans16,17. However, it is unclear if masticatory force by itself is a sufficient cause in such skeletal phenotypes. The underlying cellular and molecular mechanisms remain elusive as well.

Here, we established a novel increased mastication mouse model by feeding mice with a HD, thus burdening maxillofacial tissues with a higher mechanical load. HD increased mastication frequency and enlarged the masseter muscles. Using a computer simulation, mechanical loading onto the lower jawbone (mandibular bone) by the masseter muscle, the masticatory muscle with the largest muscular force, was indicated to induce extrusion of the masseteric ridge and a shortening of the mandibular ramus. Micro-CT analysis showed that the extrusion and the shortening were more prominent in mice fed with the HD. In the extruded masseteric ridge of these mice, there was an increase of IGF-1 and a decrease of sclerostin in osteocytes, both of which are implicated in the promotion of bone formation. IGF-1 was shown to enhance osteoblastogenesis of the cells in the tendon.

These findings taken together indicate that the osteocytes in the mandibular bone increase IGF-1 and decrease sclerostin expression as the result of mechanical load. The alteration in the local cytokine milieu adjacent to the enthesis leads to bone formation, resulting in morphological change in the mandibular bone so the mechanical stress in the bone can be alleviated.

## Results

### Establishment of a novel increased mastication model

In order to impose a higher mechanical load on the musculoskeletal tissue of the maxillofacial region, we developed a HD in which nutrition component is changed so that the hardness is greater than in a normal diet (ND) (Fig. 1a). The compression strength of the HD was approximately three times higher than that of a ND (Fig. 1b). The change did not result in any significant difference in food intake or body weight between the ND– and HD–fed mice (Supplementary Fig. 1a and b). Analyses on the bone and muscle of the limbs indicated that the difference between the diets did not cause either hypertrophy or atrophy in these tissues (Supplementary Fig. 2a–c).

During the ingestion of the two diets, mastication frequency and time were significantly higher in the mice fed with the HD than the ND (Fig. 1c). The fiber width of the masseter muscle, which is crucial for occlusion and mastication, was larger in the mice fed with the HD than the ND (Fig. 1d–f). The neuronal activity of the primary motor cortex (M1) region of the cerebrum, which controls the masticatory muscles, was assessed according to the expression of cFos, as its expression is related to masticatory stimulation17,18. The M1 activity was higher in the HD–fed mice (Fig. 1g,h). These findings indicate that the newly developed HD increased mastication and the mechanical load imposed on the maxillofacial region.

### Increased mastication results in bone formation at the enthesis of the masseter muscle

Masticatory force is closely related to the shape of the bones in the maxillofacial region, especially the lower jawbone, i.e. the mandibular bone15. However, it is unclear if it is masticatory force itself that changes mandibular morphology. Thus, we predicted the morphological change of the mandibular bone under a mechanical loading condition, using a remodeling simulation. We adopted a computer model in which bone formation occurs at a point where the mechanical stress is higher than in the surrounding area19,20, so that the non-uniformity of the mechanical stress is reduced (Fig. 2a). A voxel finite element (FE) model of the mandibular bone of a mouse was constructed and the muscular force of the masseter muscle was set to tract the masseteric ridge antero–superio–laterally (Fig. 2b). At the initial state, stress distribution exhibited a non-uniformity, which was reduced after the bone remodeling (Fig. 2c). In the mandibular bone after loading, there was a prominent extrusion of the masseteric ridge and a shortening of the mandibular ramus (Fig. 2d).

We then investigated if such morphological changes of the mandibular bone actually occur in vivo using micro-CT images of the mandibular bone. As predicted by the computer simulation (Fig. 2d), the masseteric ridge was more extruded and the mandibular ramus was shorter in the HD–fed than ND–fed mice (Fig. 3a,b). Angular and linear analyses further revealed the extrusion of the masseteric ridge to be related to the thickening of the cortical bone at the site (Fig. 3c,d). In addition, the lingual inclination of the molar was larger and the mandibular height was lower in the HD–fed mice than ND–fed mice (Fig. 3c,d). With the parameters obtained (Fig. 3d), principal component analysis (PCA) indicated that the increased mastication model mice exhibit a distinct mandibular morphology (Fig. 3e).

The extrusion of the masseteric ridge in the HD–fed mice prompted us to analyze the bone formation and resorption around the ridge, a site where the tendon of the masseter muscle inserts into the mandibular bone. Histological analyses showed that there was an increase in the number of osteocalcin–positive cells, osteoblasts, in the enthesis, while osteoclasts were undetectable (Fig. 4a–c). Although large masticatory force may be harmful on the condyle and result in the shortening of the ramus, there was no erosion on the surface of the condyle of mice fed with HD (Fig. 4d,e). No obvious differences in the cartilage and subchondral bone were observed (Fig. 4e), indicating that the increased mastication by the HD affects the mandibular bone morphology without damaging the cartilage in the condyle. Thus, increased mastication was revealed to remodel the mandibular bone by enhancing bone formation in the enthesis of the masseter muscle.

### Osteocytes produce IGF-1 in response to increased mastication, promoting osteoblastogenesis of tendon cells

Next, we examined the mechanism by which increased mastication enhances bone formation. Because osteocytes are known to sense mechanical stress imposed on the bone and release cytokines8,9, we hypothesized that the osteocytes in the masseteric ridge would exhibit this activity. In search of such cytokines, we found a significantly higher expression of Igf1 in the masseteric ridge of the HD–fed than ND–fed mice (Fig. 5a). There was no significant difference in Igf1 expression in the long bone (Supplementary Fig. 3). Immunohistological analysis also showed that the protein level of IGF-1 was higher in the HD–fed mice, especially in the subsurface area of the masseteric ridge but not on the lingual side of the mandibular bone (Fig. 5b,c). The expression of the IGF-1 receptor, Igf1r, in the masseteric ridge was comparable between the mice fed with the HD and ND (Supplementary Fig. 4). Interestingly, in the masseter muscle, Igf1r expression was higher in the mice fed with the HD (Supplementary Fig. 4), suggesting that osteocyte IGF-1 can induce muscle enlargement by increased mastication (Fig. 1d–f).

Based on the findings described above, cells were collected from the tendon and cultured in an osteogenic medium in the presence of IGF-1. Osteoblastogenesis, as indicated by the activity of alkaline phosphatase, was enhanced by IGF-1 (Fig. 6a,b). The expression of osteoblastic genes, including Sp7, Alpl and Bglap1 (encoding Osterix, alkaline phosphatase and osteocalcin, respectively) was upregulated by IGF-1 (Fig. 6c). In order to examine if mechanically–stimulated osteocytes function as a supplier of IGF-1 for tendon cells in the process of bone formation, another in vitro experimental system was established. An osteocyte cell line, IDG-SW3 cells were cultured in a stretch chamber and underwent cyclic stretching and compression stimulation (see Materials and Methods). This mechanical stimulation induced an upregulation of Igf1 expression (Fig. 6d). Supernatant of these cells was collected and added to the tendon cell culture, either in the presence or absence of an anti–IGF-1 antibody. The addition of supernatant of mechanically–stimulated osteocytes enhanced the osteoblastogenesis of the tendon cells, which was cancelled by the anti–IGF-1 antibody (Fig. 6e,f). These results indicate that osteocytes produce IGF-1 in response to increased mastication to induce osteoblastogenesis of tendon cells.

### Increased mastication reduces sclerostin expression in osteocytes

Osteocytes are known to produce the inhibitor of Wnt signaling sclerostin (encoded by the Sost gene), the expression of which is decreased by mechanical loading21,22. Thus, we analyzed its expression in the mandibular bone. The expression of Sost was significantly lower in HD–fed mice than in ND–fed mice (Fig. 7a). There was no significant difference in the expression of Tnfsf11 or Tnfrsf11b (encoding RANKL and OPG, respectively) (Fig. 7a). There were no significant differences in the long bone (Supplementary Fig. 3). In immunohistological analysis, sclerostin–positive osteocytes were detected in the inner compartment of the mandibular bone of both the HD–fed and ND–fed mice (Fig. 7b,c). The ratio of sclerostin–expressing cells in the masseteric ridge was significantly lower in the HD–fed mice (Fig. 7d). The frequency of osteocytes that highly expressed sclerostin (sclerostinhi osteocytes), as indicated by high fluorescence intensity, was lower in the HD–fed mice (Fig. 7e,f). In the lingual side, where morphological difference was not detected (Fig. 3d), sclerostin expression was almost comparable between the mice fed with ND and HD (Fig. 7b,c). These findings indicate that increased mastication reduces the expression of sclerostin in the osteocytes, which can result in the promotion of bone formation.

## Discussion

“Adaptation to the environment” is a universal dogma in biological systems. In bone homeostasis, it is well known that bones under mechanical loading remodel themselves so that they become able to endure the loaded force. Variation in the facial profile is believed to be in part the result of differences in the force of mastication and occlusion15. However, the evidence for the causation was unclear, despite the apparent correlation. Although this correlation was well observed in experimental animal models16,17,23,24,25, the precise mechanism linking mechanical stimulation and mandibular morphology was unclear. The absence of a proper increased mastication animal model might have stagnated investigations on such mechanisms. In this study, we indicated that mechanical loading onto the jawbone itself can induce bone remodeling, using a novel hard diet. Furthermore, we found that the loading induces IGF-1 and suppresses sclerostin in osteocytes so as to enhance bone formation in the enthesis, leading to morphological change of the bone (Supplementary Fig. 5).

Because bone remodeling is affected not only by mechanical loading but also many other stimuli inside and outside the body, it is extremely difficult to isolate the effect of mechanical load from those of other factors. Computer simulation is one of the means by which the effects of a single factor can be isolated: Our in silico remodeling simulation showed that a mechanical load imposed by the masseter muscle results in a bone phenotype similar to that of a human exhibiting strong occlusal force (Fig. 2c,d), indicating masticatory force is a causative factor in different facial patterns. Subsequent in vivo micro-CT analysis revealed that increased mastication leads to a mandibular bone phenotype that highly resembles the one that was simulated (Fig. 3a–d). With the theoretical rationale acquired by the simulation, our experimental results have become more reliable than results obtained by statistical analyses alone.

The jawbone is exposed to mechanical loading by mastication, occlusion and orthodontic forces. Because osteocytes are considered to act as a mechanosensor in bone, it has been speculated that these cells are active in jawbone remodeling. This study has underscored the significance of osteocytes by demonstrating that they upregulate the expression of IGF-1, which enhances bone formation in the enthesis so as to alleviate the disparity of the stress in the mandibular bone during mastication (Figs 2c, 5a–c).

Increased mastication suppressed sclerostin expression in the mandibular bone at the same time as an increase in IGF-1 expression (Figs 57). It is reported in humans that the serum levels of these factors are negatively correlated26. It is also reported that osteocyte–specific Igf1 deficiency relieves the suppression of sclerostin expression induced by mechanical loading, suggesting the regulation of sclerostin by IGF-127, although the underlying mechanism has yet to be identified. The IGF-1 induced in osteocytes by increased mastication may regulate bone formation not only by enhancing osteoblastogenesis, but also by suppressing a bone formation inhibitor.

Clinicians have expected that masticatory force might serve a promising target in the treatment of skeletal anomalies such as skeletal open bite. However, there have been very few reports on clinical trials for such therapies28,29, possibly because of the lack of insight into their molecular basis. This study has indicated that masticatory force results in morphological change in the facial profile by modifying the function of osteocytes. Concerns about the adverse effects on the condyle might have distanced clinicians from such therapies. Our data suggests that increased mastication, within a certain extent, can alter the shape of the jawbone without damaging the condyle. Thus, there would be an opportunity for targeting masticatory force in the treatment and prevention of skeletal anomalies in the oro-maxillofacial region.

## Materials and Methods

### Experimental animals

C57BL/6 J mice 3 weeks of age were obtained from Clea Japan, Inc. These mice were maintained at Tokyo Medical and Dental University under specific pathogen–free conditions and fed with a normal diet (AIN93M: ND) or hard (AIN93M: HD) containing the same nutrition components except a modified cornstarch ratio. The body weight of the mice and their food intake were measured once a week. At 14 weeks of age, mice were sacrificed and the bone, muscle and brain tissues extracted were used for the subsequent analyses. The weight of the soleus muscle was measured after extraction. The number of the mice used in each experiment is described in the corresponding figure legend. All of the animal experiments were approved by the Institutional Animal Care and Use Committee and Genetically Modified Organisms Safety Committee of Tokyo Medical and Dental University (approval No. A2018-024A and 2015-007C, respectively) and conducted in accordance with the guidelines concerning the management and handling of experimental animals.

### Measurement of compression strength

The compression strength of the ND and HD was measured using a universal tester (Autograph AG-IS 5 kN, Shimazu). In the testing process, a pellet of ND or HD was set between 100 mm metal disks and underwent the compression process. The test was performed at the temperature of 23 ± 2 °C and humidity of 50 ± 5%. The maximum strength was measured during compression.

### Determination of mastication frequency

After fasting for 24 hours, a subject mouse was placed in a transparent box in which a ND or HD pellet was fixed on the wall. The mastication activity of the mouse was monitored and recorded for 5 minutes. The weight of the ingested pellet was expressed as the difference between the weights before and after the experiment. The number of mastication cycles and biting time were obtained from the recorded data, and the mastication frequency required for the ingestion of 1 mg pellet was calculated.

### Histological analyses of paraffin–embedded sections

Histological analyses of paraffin–embedded sections were performed as previously described11,30. Excised tissues were fixed by immersion in 4% paraformaldehyde (PFA) at 4 °C over night. Tissues containing bone further underwent decalcification in OSTEOSOFT (Merck Millipore) at 4 °C for 3 weeks. Fixed (and decalcified) tissues were dehydrated and embedded in paraffin. 6–μm–thick sections were cut.

Hematoxylin and eosin staining was carried out by staining deparaffinized sections with hematoxylin (Muto Pure Chemicals) for 3 minutes followed by 2 minutes of staining with eosin (Wako). The muscle fiber width (minor axis) was measured using measurement software (BZ–X analyzer, Keyence). The sections of the condyle were sequentially stained with Weigert’s iron hematoxylin solution (SIGMA) for 10 minutes, 0.05% Fast Green FCF solution (Wako) for 5 minutes and 0.1% Safranin O solution (Nacalai Tesque) for 5 minutes.

For immunohistological analyses of the expression of osteocalcin, IGF-1 and sclerostin in the mandibular bone and enthesis, deparaffinized sections were incubated with primary antibodies at 4 °C overnight: rabbit anti–osteocalcin antibody (1:100, TaKaRa); goat anti–IGF-1 antibody (1:40, R&D systems); and goat anti–sclerostin antibody (1:100, R&D systems). Sections were further incubated with secondary antibodies for 1 hour at room temperature: donkey anti-rabbit IgG Alexa Fluor (1:250, Invitrogen); chicken anti-goat IgG Alexa Fluor 594 (1:250, Thermo Fisher Scientific); and donkey anti-goat IgG Alexa Fluor 594 (1:250, Thermo Fisher Scientific). Nuclei were stained with Hoechst33342. The fluorescence intensity of sclerostin was analyzed using measurement software (BZ–X analyzer, Keyence).

### Histological analyses of frozen sections

Histological analyses of frozen sections were performed as previously described17. The excised brains underwent 4% PFA fixation overnight and followed by immersion in 30% sucrose for 3 days at 4 °C. Fixed tissues were embedded in optimal cutting temperature (O.C.T) compound (Sakura Finetek) and sliced into 20 μm–thick sections using a CM 3050S microtome (Leica Microsystems). Sections were incubated with primary antibodies at 4 °C overnight: mouse anti–NeuN antibody (1:100, Merck Millipore); and rabbit anti-cFos antibody (1:200, Merck millipore). They were then stained with secondary antibodies for 1 hour at room temperature: donkey anti–mouse IgG Alexa Fluor 488 (1:250, Thermo Fisher Scientific); and donkey anti-goat IgG Alexa Fluor 594 (1:250, Thermo Fisher Scientific). Nuclei were stained with Hoechst33342. The fluorescence intensity of cFos was analyzed using measurement software (BZ–X analyzer, Keyence).

### Micro-computed tomography (micro-CT) analyses of the bone

Micro-CT images were obtained with a micro-CT system (ScanXmate–D090S105) and Xsys software (Comscantecno)17. For the mandibular bone morphometric analysis, lateral images of the whole mandibular bone and coronal section images at the middle of the first molars were constructed and the parameters were calculated using ImageJ (National Institutes of Health). Principal component analysis was conducted using the web tool Easy PCA (http://hoxom-hist.appspot.com/pca.html). In the bone morphometric analysis of the femur, parameters were obtained using a 3–dimensional (3D) morphometry system (White Rabbit; Ratoc System Engineering).

### Mathematical model for bone remodeling

The mathematical model for bone remodeling simulation used in this study is based on the hypothesis that remodeling progresses so as to achieve a locally uniform mechanical state. This is a generic model to represent bone adaptation to mechanical loading, the validity of which has been shown previously19,20. In this model, bone remodeling was assumed to be driven by the local stress non-uniformity Γ, which is defined as the natural logarithm of the ratio of the stress at an arbitrary point on the bone surface, σc, to the weighted average surface stress within the sensing distance lL, σd.

### Incorporation into voxel based modeling

The mechanical stress (von Mises equivalent stress) in bone was numerically computed by means of a voxel finite element method (FEM). A voxel FE model of the mandibular bone was reconstructed from serial micro-CT images. The whole bone was discretized by using cubic voxel finite elements with an edge size of 37.2 μm. This voxel size is sufficiently small compared to the scale of mandibular bone that the dependency of simulated stress distribution on the voxel size is negligible. Because heterogeneous distribution of material properties does not drastically change the stress distribution, and therefore will not essentially influence bone morphological changes by remodeling, the bone was assumed to be a homogeneous and isotropic elastic material, with Young’s modulus E = 20 GPa and Poisson’s ratio ν = 0.3.

In the framework of voxel modeling, the changes of bone morphology can be expressed by the removal/addition of voxel elements from/to the bone surface. Here, we considered only bone formation, i.e. the addition of voxel elements. Despite the fact that bone formation is discretely expressed, the rate of bone formation on the bone surface $$\dot{M}$$ can be described as the continuous function of Γ by taking $$\dot{M}$$ as the probability of bone formation. The following continuous function was introduced in order to describe the relationship between $$\dot{M}$$ and Γ: $$\dot{M}=0$$ when $$\Gamma < 0$$; $$\dot{M}=({\dot{M}}_{{\rm{\max }}}/{\Gamma }_{{\rm{u}}})\Gamma$$ when $$0\le \Gamma < {\Gamma }_{{\rm{u}}}$$; and $$\dot{M}={\dot{M}}_{{\rm{\max }}}$$ when $$\Gamma \ge {\Gamma }_{{\rm{u}}}$$, where Γu indicates the threshold value of bone formation. The parameters for remodeling simulation were set as follows: lL = 1.12 mm, Γu = 0.6 and $${\dot{M}}_{{\rm{\max }}}=1$$ (element/simulation step).

### In vitro osteoblastogenesis of tendon cells

The calcaneal, tail and masseteric tendons were dissected and cut into small pieces. The tissue fragments were digested with 0.1% collagenase (Wako) and 0.2% dispase II (GODO SHUSEI) at 37 °C with shaking at 150 rpm for 30 minutes. After filtration with a nylon filter, the cells were cultured and expanded for one to two days. The cells were plated on 48-well plate (3.0 × 104 cells per well) and stimulated with an osteogenic medium (50 μg ml−1 ascorbic acid, 10 nM dexamethasone and 10 mM β-glycerophosphate in Dulbecco’s modified Eagle medium (DMEM)) supplemented with recombinant mouse IGF-1 (1 ng ml−1) 24 hours after the plating. Supernatant from mechanically–stimulated IDG-SW3 cells (see below) was added to the tendon cell culture at 25% of total volume, in which the cells were plated on 96-well plate (1.0 × 104 cells in 100 μl per well). Either goat anti–IGF-1 antibody (1 μg ml−1, R&D systems) or control goat IgG (1 μg ml−1, R&D systems) was added to the culture.

Alkaline phosphatase staining was performed as previously described30. 7 days after the induction of osteoblastogenesis, cultured cells were fixed with 4% PFA for 15 minutes on ice. Alkaline phosphatase staining solution containing Napthol AS-MX phosphatase, 0.06 mg ml−1; N, N-dimethylformamide, 1%; and Fast blue BB salt, 1 mg ml−1 in 0.1 M Tris-HCl pH 8.0 was added after rinsing with PBS, and the cells were stained for 15 minutes at room temperature. The staining solution was washed away, and the stained cells were air dried. The color intensity was analyzed using measurement software (BZ–X analyzer, Keyence).

### Mechanical stimulation of IDG-SW3 cells

An osteocyte cell line, IDG-SW3 cells were maintained as previously described31. Cells were incubated in minimum essential medium α (MEM α) containing 10% FCS, 100 units ml−1 of penicillin, and 50 µg ml−1 of streptomycin on type I collagen (Corning) coated polydimethylsiloxane chambers (SC4Ha, Menicon Life Science) for 2 days at 33 °C. Osteogenic differentiation was induced in MEM α and 10% FCS supplemented with 50 μg ml−1 ascorbic acid and 4 mM β–glycerophosphate at 37 °C. On day 21 after differentiation, cells were subjected to mechanical loading using a cyclic unidirectional stretching device (ShellPa Pro, Menicon Life Science) as follows: stretch ratio, 5%; stretch frequency, 1 cycle per second; and stretch time, 4 hours. Total RNA and culture supernatant were collected after mechanical stimulation.

### Quantitative Reverse Transcriptase Polymerase Chain Reaction Analysis

The total RNA of the samples was extracted using a Maxwell RSC simply RNA Tissue Kit (Promega) according to the manufacturer’s instructions17. cDNA was synthesized with Superscript III reverse transcriptase (Thermo Fisher Scientific). Quantitative reverse transcriptase polymerase chain reaction analysis was performed with SYBR Green Realtime PCR Master Mix (TOYOBO) using a Light Cycler apparatus (Bio-Rad Laboratories). Gene expression was calculated with the ΔΔCt method and Gapdh expression was used for normalization. The primer sequences are listed below. Gapdh, 5′-ACCCAGAAGACTGTGGATGG-3′ and 5′-CACATTGGGGGTAGGAACAC-3′; Igf1, 5′-CTGGTGGATGCTCTTCAGTTCG-3′ and 5′-TGCTTTTGTAGGCTTCAGTGGG-3′; Bmp2, 5′-CAGGAAGCTTTGGGAAACAG-3′ and 5′-GTCGAAGCTCTCCCACTGAC-3′; Tgfb1, 5′-CCCTATATTTGGAGCCTGGA-3′ and 5′-CTTGCGACCCACGTAGTAGA-3′; Tgfb2, 5′-ATCGATGGCACCTCCACATATG-3′ and 5′-GCGAAGGCAGCAATTATGCTG-3′; Fgf2, 5′-CAACCGGTACCTTGCTATGA-3′ and 5′-TCCGTGACCGGTAAGTATTG-3′; Runx2, 5′-CCCAGCCACCTTTACCTACA-3′ and 5′-TATGGAGTGCTGCTGGTCTG-3′; Sp7, 5′-ATGGCGTCCTCTCTGCTTG-3′ and 5′-TGAAGGTCAGCGTATGGCTT-3′; Alpl, 5′-AACCCAGACACAAGCATTCC-3′ and 5′-GCCTTTGAGGTTTTTGGTCA-3′; Bglap, 5′-GCGCTCTGTCTCTGACCT-3′ and 5′-ACCTTATTGCCCTCCTGCTT-3′; Col1a1, 5′-GAGCGGAGAGTACTGGATCG-3′ and 5′-GTTAGGGCTGATGTACCAGT; Sost, 5′-TCCTGAGAACAACCAGACCA-3′ and 5′-CAGCTGTACTCGGACACAT-3′; Tnfsf11, 5′-AGCCATTTGCACACCTCAC-3′ and 5′-CGTGGTACCAAGAGGACAGAGT-3′; Tnfrsf11b, 5′-GTTTCCCGAGGACCACAAT-3′ and 5′-CCATTCAATGATGTCCAGGAG-3′; and Igf1r, 5′-GGAGAAGCCCATGTGTGAG-3′ and 5′-GTCGTGGATAACGAAGCCATC-3′.

### Statistical analysis

P-values were calculated using Student’s t-test or Tukey’s multiple–comparison test. Differences with a p-value of <0.05 were considered significant (*p < 0.05; **p < 0.01; ***p < 0.001; ****p < 0.0001; n.s., not significant, throughout the paper). Error bars show the mean ± standard error of the mean (s.e.m.). All statistical analyses were performed with GraphPad Prism 6.08 (GraphPad Software).