Combined physical and pharmacological anabolic osteoporosis therapies increase bone response and mechanoregulation in female mice

Domain: biology
Published: 2026-03-10
Editorial outcome: major_revision

Abstract
Bone’s ability to adapt to mechanical demands is governed by mechanoregulation, the process by which cells sense and respond to mechanical stimuli to maintain skeletal integrity. In osteoporosis, increased bone resorption activity leads to structural deterioration and elevated fracture risk. While existing pharmacological therapies aim to restore bone mass to reduce fracture risk, it is unclear how they modulate mechanoregulation, especially when combined with physical interventions. Here, we investigate the joint effects of load-bearing physical and pharmacological treatment in a female mouse model of osteoporosis using longitudinal in vivo micro-computed tomography and computational mechanics. We demonstrate that mechanical loading additively and synergistically enhanced predicted strength, bone volume, and mechanoregulation parameters when combined with anabolic therapies (parathyroid hormone and sclerostin antibody) but not with anti-catabolic treatments (bisphosphonates). Increases in predicted strength are associated with reductions in bone resorption rates, shifts in the (re)modeling thresholds as anticipated by Frost in the mechanostat theory, and the modeling capacity of anabolic pharmacological treatments. These findings underscore the therapeutic potential of combining anabolic pharmacological therapies with load-bearing physical activity, particularly in early treatment phases, to optimize bone adaptation and fracture prevention in osteoporosis management.

Introduction
Postmenopausal osteoporosis in women is characterized by increased bone resorption, leading to structural deterioration of the bone micro-architecture and increased susceptibility to fractures1. Exercise is fundamental to bone health, but its role alongside pharmacological treatment remains an area of active inquiry2. Patients with diagnosed osteoporosis often question the compatibility of exercise with pharmacological treatment, some fearing interference with drug efficacy, others assuming that their potent medications obviate the need for physical activity. This highlights the need for evidence on whether mechanical loading improve outcomes for bone strength beyond pharmacological monotherapy.

Mechanical loads are transmitted from the organ to bone cells, where osteocytes act as mechanosensors, osteoblasts form, and osteoclasts resorb bone. This interplay drives both remodeling (formation followed by resorption) and modeling (formation without prior resorption), the latter potentially via lining cell redifferentiation in the absence of sclerostin3. Key signaling pathways between bone cells include Wnt/β-catenin4 (osteocyte-osteoblast) and RANKL/OPG5 (osteoblast-osteoclast). To study these dynamic processes in vivo, high-resolution imaging techniques such as micro-computed tomography (micro-CT) are commonly used. While micro-CT does not resolve individual cells or molecular signals, it captures the net microstructural changes resulting from formation and resorption, which are collectively referred to as bone (re)modeling6.

On the cellular level, anti-resorptive bisphosphonates (BIS) prevent osteoclast attachment and activity by binding to hydroxyapatite crystals in the bone matrix, and are characterized by low osteoanabolic capacity7. We hypothesized that mechanical loading would stimulate bone formation, but bisphosphonates might blunt this response by inhibiting (re)modeling.

Intermittent parathyroid hormone (PTH) exerts anabolic effects by binding to PTH-receptors on osteoblasts and osteocytes, leading to suppression of sclerostin expression and subsequent activation of the Wnt/β-catenin signaling pathway. This promotes osteoblastic activity and indirectly enhances osteoclast recruitment via upregulation of RANKL expression by osteoblasts8. PTH and mechanical loading have shown synergistic effects in cortical bone9, 10. We hypothesized that in trabecular bone, their combination would suppress otherwise increased resorption, and concurrently stimulate bone formation11.

Sclerostin antibodies (SclAB) inhibit a Wnt/β-catenin-signaling antagonist protein, promoting osteoblast activity and suppressing osteoclast activity12. Wnt/β-catenin-signaling is initiated when a Wnt ligand binds to a Frizzled family receptor and its co-receptor LRP5/6 on the surface of a cell, resulting in β-catenin stabilization and target gene transcription inside the cell11. We hypothesized mechanical loading in combination with SclAB would increase formation and decrease resorption further. Synergy may arise because mechanical loading downregulates sclerostin expression in osteocytes13, while SclAB pharmacologically neutralizes it, amplifying the same pathway from two directions, especially in trabecular bone which particularly adapts its microarchitecture to mechanical demands. It should be noted that, similar to mechanical loading, sclerostin antibody effects saturate after a certain time, which limits their long-term use as a standalone therapy14.

Frost’s mechanostat theory15, 16, 17 proposes that bone adapts to maintain mechanical strain within a defined setpoint range - much like a thermostat. The setpoints separate the four following states: the disuse state for bone resorption; the adapted state for quiescence, the overload state for formation, and the fracture state for microdamage and fractures. The mechanostat theory was introduced more than 30 years ago. In this theoretical construct, anti-catabolic bisphosphonates help inhibit increased bone resorption in underloaded areas by raising the mechanical setpoints towards higher strains. Anabolic treatments theoretically promote bone formation by lowering the mechanical setpoints required to initiate formation, provided mechanical loading is also encouraged. Measuring the "setpoints" of osteoporosis medications in the context of Frost's mechanostat theory, however, is not straightforward, as the setpoints themselves are theoretical constructs that describe the mechanical thresholds at which bones adjust their structure, and measuring them experimentally would require complex assessments of both bone volume and mechanical strain under highly controlled conditions.

Here we provide experimental insights into this interaction using in vivo micro-computed tomography (micro-CT) and finite-element modeling in a C57BL/6 mouse model of osteoporosis. The aim of this study was to explore whether combining pharmacological treatments with mechanical loading leads to improved pharmacological treatment outcomes, i.e. stronger bones. We tested short-term effects of BIS, PTH, and SclAB treatment with or without mechanical loading of the 6th caudal vertebra, aiming to maximize bone accrual in early treatment phases. The choice of selected therapies was based on clinical relevance and distinct modes of action in the bone (re)modeling process.

Results
Micro-architectural and (re)modeling differences reveal treatment-specific effects on bone recovery after ovariectomy

As shown in Fig. 1a, C57BL/6 mice were ovariectomized at 15 weeks-of-age, and bone loss was confirmed in all animals (n=105) via in vivo micro-CT of the 6th caudal vertebra (-26.8 ± 0.95% change in bone volume fraction (BV/TV) from baseline). From week 20 to 24, animals received pharmacological and/or mechanical treatment through an established tail vertebra loading model18. In the VEH-group, BV/TV continued to decline from week 20, while all monotreatment groups showed significant increases after four weeks of treatment (p<0.001, Fig. 1b). Trabecular thickness (Tb.Th) did not increase significantly in BIS compared to VEH, whereas all anabolic treatments led to increases, but lower in PTH than in ML and SclAB (p<0.01, Fig. 1c). Trabecular number (Tb.N) was preserved in BIS but was significantly lower in all other groups compared to BIS (p<0.001, Fig. 1d). Connectivity density (Conn.D) was preserved in BIS and PTH and declined in VEH, ML, and SclAB (p<0.05, Fig. 1e). A full summary of these microstructural parameters is provided in Supplementary Dataset S.2. As previously described18, mechanical loading increases BV/TV mainly through trabecular thickening despite a reduction in trabecular number, explainable by a full loss of thin trabeculae - a pattern also seen in the SclAB-group (Fig. 1c,d). In contrast, PTH increased BV/TV through moderate thickening and sustained preservation of trabecular number, resulting in a smaller loss of connectivity. BIS maintained BV/TV by preserving existing trabeculae, including thinner ones, with minimal thickening (Fig. 1, b-e).

The micro-architectural changes resulted from the time course of formation and resorption (Fig. 1f). In week interval w20-22 (see also Supplementary Dataset S.5 for results from the second interval, w22–24), bone formation rate per bone volume (BFR) was significantly increased in ML and PTH compared to VEH, with no significant increases in BIS or SclAB (Fig. 1g). Mineral apposition rate (MAR) did not differ between groups (Fig. 1h), while mineralizing surface per bone surface (MS) was elevated in all treatment groups compared to VEH (p<0.05, Fig. 1i). Bone resorption rate per bone volume (BRR) was significantly reduced in all treatment groups versus VEH (Fig. 1j), where BRR in PTH was the least reduced (significantly higher than VEH, ML, and BIS), consistent with the known anabolic effects of intermittent PTH treatment. Surprisingly, BRR was found to be significantly lower than VEH, while not as low as in ML and BIS. This decrease, even more pronounced in the second time interval (see Supplementary Dataset S.5), may result from micro-CT missing parts of the reversal phase between resorption and formation, thus potentially underrepresenting remodeling at the same sites. As expected, mineral resorption rate (MRR) was significantly lower in the BIS-group compared to VEH and unchanged in the anabolic groups (Fig. 1k), suggesting bisphosphonates preserve Tb.N (Fig. 1d) by preventing full trabecular resorption. Eroded surface per bone surface (ES), reflecting the proportion of bone surface previously affected by resorption, was significantly lower in ML and SclAB compared to VEH, BIS, and PTH (p<0.05, Fig. 1l).

Together, these results confirm that each monotherapy exerted effects consistent with its known mode of action - bisphosphonates preserving trabecular structure by suppressing bone resorption, and anabolic agents increasing bone mass predominantly through formation - while also highlighting treatment-specific differences in trabecular architecture and dynamic turnover.

Mechanical loading modulates structural and functional responses to pharmacological interventions

We next assessed how additional mechanical loading influenced the response to pharmacological treatment. In the BIS + ML-group, BV/TV gains were significantly less than the expected additive effects (treatment:loading: p<0.05, Fig. 2a), and did not differ significantly from BIS alone (Supplementary Dataset S.2). In contrast, anabolic treatment combined with mechanical loading (PTH + ML, SclAB + ML) resulted in additive increases, as supported by a non-significant treatment:loading interaction (Fig. 2a). ΔTb.Th was significantly higher in all combination groups compared to monotreatments after four weeks (Fig. 2b). ΔTb.N was preserved in BIS + ML, despite the known Tb.N loss with ML alone (Fig. 2c), suggesting BIS blunted this effect. The loss of Tb.N observed in SclAB was not rescued in SclAB + ML (Fig. 2c). Conn.D as a measure of the structural integrity and interconnectedness of the trabecular network, was preserved the most in BIS + ML, and PTH + ML (Fig. 2d). It should be noted that structural parameters such as Tb.Th and Tb.N are interdependent; apparent increases in Tb.Th may arise from the loss of complete thinner trabeculae. Synergy was found in total area (Tt.Ar), leading to additive increases in cortical area fraction (Ct.Ar/Tt.Ar) and cortical thickness (Ct.Th), found in Supplementary Fig. S.1 and Dataset S.4. Predicted strength increased in all treatment groups, with loading-induced increases being additive in the PTH + ML group and synergistic in the SclAB + ML group (p<0.05, Fig. 2e). Strain energy density (SED) decreased in all treatment groups, being most pronounced in the combination groups, with less than the expected additive reduction in BIS + ML (treatment:loading: p<0.05, Fig. 2f). Illustrating the effect of decreasing SED, the visualization of the 6th caudal vertebra in a SclAB + ML animal shows a highly loaded trabecula at week 20, followed by structural reorganization and reduced SED at week 24 (see Fig. 2g). Linear regression analysis revealed that the changes in predicted strength did not correlate with baseline BV/TV (R = 0.010) and moderately with Tb.Th (R = 0.424, Fig. 2h), indicating that initial BV/TV or Tb.Th serve as poor or only moderate predictors of future changes in strength.

Combination treatments affect bone formation and resorption dynamics differentially

Bone formation rate per bone volume (BFR) was lowest in VEH and highest in the anabolic combination groups (p<0.05, Fig. 3a). MAR showed synergy in SclAB + ML (treatment:loading: p<0.05, Fig. 3b). MS increased additively in PTH + ML and SclAB + ML, and antagonistically in BIS + ML (treatment:loading: p<0.01, Fig. 3c). Bone resorption rate per bone volume (BRR) was reduced in all treatment groups (p<0.05, Fig. 3d). In BIS + ML, the BRR reduction was antagonistically affected by mechanical loading (treatment:loading, p<0.05). In contrast, BRR decreased synergistically in PTH+ML (treatment:loading: p<0.05, Fig. 3d) and additively in SclAB + ML (Fig. 3d). MRR remained suppressed in BIS + ML and was unaffected by mechanical loading (Fig. 3e). ES decreased synergistically in PTH + ML treatment:loading: p<0.05, Fig. 3f) and SclAB + ML (treatment:loading: p<0.01, Fig. 3f). This synergistic effect was, at least in SclAB + ML, still present in the second time interval (see Supplementary Fig. S.2 and Dataset S.5 for results from w22–24). Representative trabecular microstructures and insets of the combination groups at both time intervals are depicted in Fig. 3g. Changes in predicted strength correlated linearly with BFR (R = 0.830) and decayed according to a power-law relationship with BRR (ρ = 0.760), indicating that small reductions in bone resorption rates under treatment can result in large increases in predicted strength (Fig. 3h).

Bone formation and resorption occur in mechanically distinct strain windows

To address the question whether pharmacological treatments target bone (re)modeling to the places that mechanically need it, we correlated the underlying mechanical signals in the trabecular compartment with subsequent formation and resorption events. Visually, spatial agreement was found between high SED and regions of subsequent bone formation, and low SED and regions of subsequent bone resorption (Fig. 4a). Quantitative analysis (Fig. 4b) showed that mean SED was significantly higher at formation sites (p<0.05) and significantly lower at resorption sites (p<0.05) compared to quiescent surfaces, when presented as percentage change to the average quiescent SED across all animals per group. The addition of mechanical loading to the monotreatments resulted in marginal changes, indicating that bone formation and resorption continue to occur in mechanically distinct strain windows despite possible influences of pharmacological interventions. Levene’s test revealed significantly smaller variances between BIS and BIS + ML and between VEH and ML (p<0.05), indicative of more consistent mechanosensitive responses in these groups in the presence of mechanical loading.

Conditional probabilities of formation, quiescence, and resorption events for a given SED-value were calculated and fitted with exponential functions. The probability for bone formation increased with increasing SED, and the probability for bone resorption decreased with increasing SED (Fig. 4c, Supplementary Fig. S.3 and Dataset S.6 for results in w22-24). Especially the PTH + ML and SclAB + ML conditional probability curves opened up compared to their monotreatments, indicating a higher responsiveness to mechanical signals (Fig. 4c). The asymptotic resorption probability value minR represents the point at which further increases in local mechanical loading stimulus do not further suppress bone resorption. This value was significantly lower in ML, PTH + ML, and in SclAB + ML than in VEH (p<0.05, Fig. 4d, Supplementary Dataset S.8). Further comparisons of the coefficients from fitted functions to the conditional probabilities are provided in Supplementary Datasets S.7 and S.8. The presence of few significant differences between groups suggests mechanosensitivity of the system is largely preserved regardless of the presence or absence of mechanical loading. Combined anabolic treatments resulted in higher correct classification rate (CCR) values compared to VEH and the BIS groups (Fig. 4e), with CCR being a metric used to evaluate the accuracy of classifying local bone formation or resorption events based on predicted mechanical signals. However, CCR only correlated moderately with the increases in strength, indicating increased mechanosensitivity of the system may not fully explain the ability of bone to increase strength (Fig. 4f).

Frost’s mechanostat setpoints are shifted towards lower values for mono- and combined treatments

To assess potential shifts in the setpoints due to different drug or combination treatments, (re)modeling velocity (RmV) curves and mechanostat parameters19 were calculated for each treatment group as an approximation to the mechanostat theory. These curves show the net RmV for a given surface effective strain, where a negative value means net resorption and a positive value means net formation (Fig. 5a). From these curves, formation saturation levels (FSL), resorption saturation levels (RSL), and (re)modeling thresholds (RmTs) were derived.

FSL was increased in all treatments compared to VEH (p<0.001, Fig. 5b, Supplementary Dataset S.9), and was significantly higher in anabolic combination groups compared to the respective monotreatments (p<0.001). This suggests an increased mechanosensitivity of the cells involved in bone formation. RSL was increased in the BIS and all combination groups compared to VEH (p<0.05, Fig. 5c). The increase in RSL under bisphosphonate treatment may be explained by the suppression of bone turnover: at comparable strain levels, resorption would typically occur, resulting in a lower RSL; however, due to inhibited osteoclast activity, this resorptive response is blunted, making the system appear saturated at a higher RSL value. Regarding the role of additional mechanical loading, only the PTH + ML group showed a significant increase compared to PTH alone (p<0.05, Supplementary Dataset S.9). This suggests that, under strain conditions that would typically lead to bone resorption, the balance has shifted towards bone formation. RmT values, representing the setpoints in the mechanostat theory, were decreased in all pharmacological treatment groups compared to VEH (p<0.05), with no significant improvements observed in the combination groups receiving mechanical loading (Fig. 5d). These results were even more pronounced in the second time interval (Supplementary Fig. 4d and Dataset S.9). The reduction in RmT suggests an upregulation of osteocytic mechanosensitivity, an expected outcome in the anabolic treatment groups, but an unexpected finding in the bisphosphonate-treated groups. This may reflect a compensatory osteocytic response to the suppressed bone resorption induced by bisphosphonate treatment. Furthermore, FSL correlated strongly with predicted strength increases (R = 0.888), while RmT exhibited a moderate inverse correlation (ρ = 0.609) when fitted with a power-law function. These findings suggest that a reduction in RmT may be a prerequisite for strength gains; however, actual increases in strength require anabolic potential (Fig. 5e,f).

The amount of modeling correlates highly with increases in predicted strength for all treatments

Next, we distinguished between the remodeling and the modeling ability of the different treatments. Visually, in several areas in VEH, high SED values decreased over time, but in other areas they increased and the resorption of a single trabecula led to a more heterogeneous SED distribution (Fig. 6a). While SED on average decreased over time for BIS + ML, this did not particularly affect areas with high SED, as there remained several highly strained areas in week 24. In contrast, both PTH + ML and SclAB + ML showed large decreases in SED, especially in areas with high SED values in week 20 (Fig. 6a).

The remodeling ability - as represented by the amount of resorption followed by formation - was in BIS, BIS + ML, PTH and SclAB comparable to VEH, and significantly lower in ML and the anabolic combination groups compared to VEH (p<0.05, Fig. 6b). In contrast, the modeling ability was significantly higher compared to VEH in all but the BIS group, with the highest amount in the anabolic combination treatments (p<0.001, Fig. 6c). Both remodeling and modeling capacity showed antagonistic effects in BIS + ML and additive effects in anabolic combination treatments (Fig. 6b,c). Remodeling showed a moderate inverse correlation with increases in predicted strength when fitted with a power-law function (ρ = 0.476, Fig. 6d), while modeling correlated strongly in a linear fit (R = 0.928, Fig. 6e). Fig. 6f illustrates the distribution of surface events relative to increasing effective strain. Remodeling events appeared strain-independent, and modeling increased with higher mechanical stimuli, particularly in the anabolic combination groups (Fig. 6f). There is also a non-linear increase in modeling with mechanical loading in comparison to the mono-treatment, with a stronger effect for low effective strain regions, especially for SclAB. Fig. 6g summarizes the trabecular bone response across treatments. Bisphosphonates, alone or with mechanical loading, help preserve trabecular interconnectedness. Anabolic treatments combined with mechanical loading effectively enhance predicted strength by promoting formation and suppressing resorption. These additive effects across parameters likely underlie the observed synergistic gains in predicted strength, at least in SclAB.

Methods
Study design

The study design is illustrated in Fig. 1a. In total, 120 female 15-week-old C57BL/6 mice (n=60, C57BL/6JRccHsd, RCC/Harlan; Füllinsdorf, Switzerland/ Horst, The Netherlands; n=60, C57BL/6JRj mice (Janvier Labs, Le Genest-Saint-Isle, France) were subjected to bilateral ovariectomy. A basal micro-CT image of the 6th caudal vertebra was obtained (vivaCT 40, Scanco Medical, Brüttisellen, Switzerland). Recovery lasted five weeks after surgery, as in this period, an osteopenic state was established in the trabecular compartment of the 6th caudal vertebra in a previous study43. Pinning of the adjacent vertebrae as preparation for the loading procedure took place in week 17. At week 20, the animals were divided into 8 groups and the following treatments were administered for the following four weeks: BIS (n=9), BIS + ML (n=9), PTH (n=10), PTH + ML (n=9), SclAB (n=9), SclAB + ML (n=8), ML (n=26), VEH (n=25). 10 mice were excluded due to swollen tails or loose pins. In the SclAB study, 4 mice showed a periosteal reaction, possibly due to injury of the periosteum during intravenous injection at the tail vein. One mouse in the BIS + ML group did not lose bone volume after ovariectomy. These mice were excluded from evaluation, resulting in 105 animals included. Micro-CT was performed in weeks 15, 20, 22 and 24. Surgeries, imaging, and loading were performed under isoflurane anesthesia (induction 4%, maintenance 1.5-2.5%, Attane, Piramal Healthcare, India). Vehicle control was an isotonic buffer (pH 5.3). While the data was gained in four experiments (at different times), study and loading parameters were not different except for the administered pharmacological treatments, thus combined in this study. The bone responses of the VEH and the ML groups of both mouse lines (JRccHsd and 6JRj) showed no differences in reactions (ΔBV/TV VEH: p = 0.937; ML: p = 0.206; two-way ANOVA followed by Tukey’s post-hoc test), thus ML groups from all experiments and VEH groups from all experiments were merged, explaining the larger sample size in these groups. The merging was conducted because separate vehicle group presentations would not have yielded additional insights but substantially would have increased data complexity (see Supplementary Dataset S.3). All animal experiments were performed with approval of the local authority (Kantonales Veterinäramt Zürich, Zurich, Switzerland, license number 171/2008, 108/2011, 078/2012) and reported according to ARRIVE 2.0 guidelines.

Animal care and monitoring

Animals were kept in groups of 3-5 mice in filter top cages in Scantainers (Scanbur, Karslunde, Denmark) with ad libitum access to tap water and chow (KLIBA NAFAG 3437, Granivit AG, Kaiseraugst Switzerland), wood chips bedding and a 12h:12h light:dark cycle. Room temperature was 22 ± 2 °C and humidity was not controlled. Cages were changed weekly by the experimenters. Microbiological status of the facility (Animal Imaging Center, ETH Zurich) was not monitored, because it housed only animals during experiments. Animals were checked and scored daily for three days after OVX surgery and pinning and at least three times per week during the further experiment. Meloxicam 2 mg kg-1 was injected s.c. for three days after OVX and pinning.

Mechanical loading

A validated in vivo mouse tail loading model was used to induce trabecular bone adaptation under controlled mechanical conditions43, 44, 45. Stainless steel pins were implanted into adjacent vertebrae under fluoroscopic guidance three weeks prior to loading. An 8N cyclic axial load (3000 cycles, 10 Hz) was applied to the 6th caudal vertebra (CV6) using a custom loading device (caudal vertebra axial loading device, CVAD44) three times a week. Control animals (0N groups) underwent identical procedures, including pin placement and anesthesia but no load was applied. A force of 8 N was used in order to maximize the effect within a short timeframe. It was the maximum force that could be applied based on what the pins within the bone could bear, and represents twice the force exerted on mouse vertebrae under physiological conditions46. Pistoia simulations estimate a maximum failure load of 24.5 N at CV6 in osteoporotic mice at week 20 (predicted trabecular strength, see Supplementary Dataset S.2).

Pharmacological treatment

The BIS group received 100 μg kg-1 zoledronate (Zometa 4 mg/5 ml; Novartis Pharma Schweiz AG, Bern) subcutaneously once in week 20. Corresponding VEH (0.9% NaCl, B. Braun Medical AG, Switzerland) was injected at the same time point. Mice in the PTH study received 40 μg kg-1 PTH (hPTH 1-34, Bachem AG, Switzerland) or the according VEH (0.9% NaCl) subcutaneously daily over four weeks. SclAB (100 mg kg-1, Novartis Pharma AG, Basel, Switzerland) or the corresponding VEH (isotonic buffer, pH 5.3) was injected i.v. weekly into the lateral tail vein over 4 weeks.

BIS and SclAB doses were selected based on established protocols in the literature24, 47. The PTH dose was determined in a dose-response study comparing 10 μg kg-1 d-1 and 40 μg kg-1 d-1, following an initial 80 μg kg-1 d-1 dose proposed in the literature48 that led to excessive increases in bone volume fraction (BV/TV) by the end of the experiment. The 40 μg kg-1 d-1 dose was chosen to obtain BV/TV increases comparable to those observed with BISS and SclAb treatments, enabling a more balanced comparison across treatment groups (see Fig. 1b).

Bone morphometry

Micro-CT images were obtained with a vivaCT 40 (Scanco Medical AG, Brüttisellen, Switzerland) operated at 55 kVp and 146 µA. 1000 projection images were obtained with an integration time of 200 ms. Grayscale images were reconstructed using a Feldkamp algorithm, with automated beam hardening correction, resulting in an isotropic voxel size of 10.5 µm. The image of week 20 was aligned in the main loading direction. Follow up scans were registered to the previous scan. A constrained 3D Gauss filter (sigma 1.2, support 1) and a global thresholding procedure of 22% (approximately 580 mg HA cm-3) were applied. Automated masks were created to extract the trabecular bone volumes (trabecular mask truncated by 10% of length at both ends to exclude epiphyses and primary spongiosa; middle 26% removed because this area is almost void of trabeculae)18. The cortical mask included 75% of the length of the inner mask18. Static trabecular bone morphometric parameters were calculated according to Bouxsein et al.49. Dynamic bone morphometry was performed by registering and superimposing segmented bone volume images of consecutive time points. Bone formation and resorption rates were calculated36 over two two-week periods (w20-22 and w22-24).

Finite element analysis of mechanical properties

Finite-element simulations were used to analyze mechanical properties of the vertebrae. 3D micro-FE models were generated by converting all voxels of the micro-CT image to 8 node hexahedral elements, with each model consisting of approximately 1.8 million elements. A Young’s modulus of 14.8 GPa and a Poisson’s ratio of 0.344 were assigned. Each model was solved with ParOSol50 running on the Euler cluster operated by Scientific IT Services at ETH Zurich. Cylindric intervertebral disks (10% of absolute height) were applied and assigned the same Young’s modulus and Poisson’s ratio as bone. The top of the model was displaced by 1% of the total vertebral length, while the bottom was fixed. The resulting reaction force was rescaled to the value of the force applied in the experimental setup; consequently, all the FE outcomes were rescaled accordingly (4 N for non-loaded46 and 8 N for loaded mice). Strain energy density (SED), defined as the increase in energy associated with the tissue deformation per unit volume, and effective strain were used as the mechanical signal. Trabecular bone strength was estimated for each mouse at each time point by using the Pistoia criterion51 which assumes that bone failure is initiated if a certain percentage of the bone tissue (2%) is strained beyond the tissue yield effective strain (7000 με). This criterion has been shown applicable to the mouse vertebra as well52. For the predicted bone strength estimation, the full bone was modeled but only the effective strains in the trabecular compartment were analyzed.

Local mechanoregulation analysis

The local mechanical environment was derived from micro-FE simulations of the baseline scan. Here, SED is used as a mathematical term to describe the (re)modeling stimulus phenomenologically. To quantify the relationship between the local SED and cellular activity on the bone surface, the bone formation or resorption sites determined by rigid registration were projected onto the surface of the baseline scan, resulting in three masks representing three different clusters of formed (F), quiescent (Q) or resorbed (R) bone surfaces6. In short, the mean SED value was calculated in each of these three masks and for each mouse, and normalized to the mean SED of the quiescent surface as absolute SED values differ per mouse and over time due to differences in BV/TV. To establish a quantitative description of the mechanoregulatory system, the relation between increasing mechanical stimuli and consequent (re)modeling events was assessed by calculating the relative percentage of voxels being formed, quiescent and resorbed for each value of SED binned at 1% step size of the maximum SED, and assuming that each (re)modeling event has the same occurrence probability (i.e., formation, resorption and quiescent regions were virtually rescaled to have the same amount of voxels) to remove dependencies on imbalances in the (re)modeling process due to differences between animals or treatments. The conditional probabilities were fitted per animal by exponential functions. Correct classification rate (CCR) values were calculated from the mean conditional probabilities from all animals, returning a scalar value between 0.33 and 1 assessing overall mechanoregulation, with 0.33 meaning (re)modeling is independent of the mechanical signal and 1 meaning it is entirely dependent on the mechanical signal. (Re)modeling velocities (RmVs) and their mechanostat parameters were calculated according to Marques et al. for each animal19. Minimum and maximum RmV, represented as formation saturation level (FSL) and resorption saturation level (RSL), as well as (re)modeling thresholds (RmTs) were extracted from the resulting curves.

Statistical methods

Statistical analysis was performed using R (R, Auckland, New Zealand53). Data are presented as group means ± standard error unless otherwise specified. P-values lower than 0.05 are considered significant, statistical significance was defined as *p<0.05, **p<0.01, ***p<0.001. Normality was assessed using the Shapiro-Wilk test (in R, with α = 0.05).

Static morphometric and mechanical parameters of trabecular bone in the 6th caudal vertebra were measured at weeks 15, 20, 22, and 24, with Δ representing the percentage change between weeks 20 and 24. Two-way ANOVA followed by Tukey’s post-hoc test was used to compare Δw20-24. Synergy (S) or antagonism (I) between treatment and mechanical loading was evaluated using the interaction term (“treatment:loading”) in a linear model.

A synergistic effect was defined as a combined treatment response that exceeded the sum of the individual effects of treatment and mechanical loading. This implies that the two interventions may act through the same or facilitating biological pathways. Statistically, such synergy is indicated by a significant and positive interaction term between the main effect (treatment) and mechanical loading. An antagonistic effect was defined as a combined treatment response that was less than the expected additive effect of treatment and mechanical loading. Statistically, such antagonism was reflected by a significant and negative interaction term between the main effect (treatment) and mechanical loading. The animal provider from the third (SclAB) and fourth (PTH) experiment was different, therefore we adjusted the model for this.

Dynamic morphometric parameters were analyzed during weeks 20-22 and 22-24. One-way ANOVA followed by Tukey’s post-hoc test was applied to absolute values in each time interval. Synergy or antagonism was assessed using the interaction term from a linear model of log2-transformed values in each time interval.

Strain Energy Density (SED) in formation (F), quiescence (Q), and resorption (R) surfaces was reported for each group in each time interval. Differences between F, Q, and R were compared using two-sided Wilcoxon signed-rank tests with Bonferroni correction after testing for normality. For conditional probabilities, exponential curves were fitted to the formation and resorption slopes. For formation, a saturating exponential model f(x) = y0 + a ∙(1− exp (−bx)) was applied to the first 40% of normalized SED data for each animal individually, with parameters y0, a, and b representing level of formation in the absence of mechanical stimulus (i.e. at SED = 0), maximal formation, and sensitivity to mechanical stimulus, respectively. For resorption, a decaying exponential model f(x) = y0 + a ∙exp (− bx)) was used to assess the rate of resorption. Resorption asymptote min represents the saturation level of resorption at high mechanical signal, i.e. the minimum resorption probability (x→∞), indicative of the amount of non-targeted resorption. Coefficient a represents the magnitude of the response, i.e. the difference between the initial and the minimum resorption probability. Coefficient b is the rate of decay, representing how quickly the probability of resorption drops as SED increases. Synergy or antagonism was assessed using the interaction term from a linear model applied to log2-transformed coefficients, with significance determined by two-way ANOVA followed by Tukey’s post-hoc test.

Formation and resorption saturation levels (FSL, RSL) and remodeling thresholds (RmTs) were derived from hyperbola remodeling velocity curves, fitted with the function f(x) = y0 + a/(b−x), where x represents the mechanical signal, y0 the FSL, and a the (re)modeling velocity modulus. The remodeling threshold (RmT) is defined as: RmT = b + a/y0. One-way ANOVA followed by Tukey’s post-hoc test was used for statistical comparisons, with synergy or antagonism assessed using the interaction term from a linear model applied to absolute values in each time interval, because FSL and RSL can obtain negative values.

Modeling and remodeling amounts were calculated by monitoring spatial agreement of voxels over the time intervals w20-22 and w22-24, following the approach presented by Birkhold et al.37. Modeling amount was defined as formation without prior resorption in either the first or the second interval, divided by the amount of surface voxels. Remodeling amount was defined as resorption followed by formation, divided by the amount of surface voxels.

Linear correlations between the %-change in predicted strength and parameter outcomes were assessed using Pearson’s correlation coefficient R. For nonlinear relationships, we employed a power-law model of the form y = a ∙xb, which was linearized via logarithmic transformation to ln(y) = ln(a)+b∙ln (x). Parameters a and b were estimated using linear regression on the transformed data, and the Spearman’s correlation coefficient ρ between the log-transformed observed and predicted values was used to assess the goodness of fit. Since the fitted power-law model adequately described the nonlinear relationships, we did not perform a formal model selection procedure to compare alternative models, such as those based on the Akaike information criterion (AIC).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript by Schulte et al presents a novel comparison of different osteoporosis treatments in ovariectomized mice and put them in addition under mechanical compression loading. The aim of the work is to compare anabolic vs. catabolic osteoporosis treatments with or without loading (as surrogate to training intervention). Compared were bisphosphonate (BIS), parathyroid hormone (PTH), sclerostin antibody (SclAB) or vehicle (VEH) treatment in ovariectomized 20-week-old C57BL/6 mice. In clinical routine treatment of osteoporosis patients and doctors are frequently unsure if an additional physiotherapy or training would help to maintain bone mass and thus a very practical reasoning is behind the here presented study. The work is organized in a sound manner and the question targeted has very practical consequences. While I do like the approach, I do have two main concerns that could eventually be addressed by the authors:\n\n1. Why did you use the selected therapies in this specific comparison? Did you formulate initially more concrete hypothesis for each individual comparison loaded vs. sham in bisphosphonate (BIS), parathyroid hormone (PTH) and sclerostin antibody (SclAB)? E.g. regarding OB or OC or synergistically? A more stringent biological explanation for the comparisons would be helpful.\n\n2. Some treatments come with side effects; not all can be given for a similar (long) period. And not in a similar manner. This is due to substantial biological differences across the therapies selected. This aspect seems to be widely ignored; eventually focusing here on more comparable approaches and eventually only the initial effects (and not long-term consequences) might help?\n\n3. If the work focuses only on osteoblasts and osteoclasts and their activities, I would assume that more in depth analyses on the tissue (histological) level could help confirm the findings from the µCT data.\n\n4. In my eyes very interesting findings are – specifically in the light of the authors reference to Frost – the separation that formation – rest – resorption volumes seen in the PTH + ML and SclAB + ML (Figure 4), while they do overlap in almost all other cases. So maybe Frost was correct in the end – but only in a co-stimulation with PTH or SclAB. What sets these stimuli in respect to mechano-responsiveness apart from the others?\n\n5. The manuscript would benefit from a clear link to biology, here specifically osteoblastic or osteoclastic activities. In one sentence, the authors mention osteocytes. But there is no reasoning given on how specifically Osteoblasts or osteoclasts are affected. Frost referred more to the osteocytes, which are here in analyses and data not at all in the focus. I am a bit surprised that the biology is not really included, even though the therapies analyzed are very distinctly different in their effects on these cell types.\n\n6. Finally, no other cells – such as immune or endothelial cells– are here considered. This limitation needs more discussion.", "reviewer_2": "This work from Schulte et al examines combined effects of experimental mechanical loading with three current therapeutic approaches for osteoporosis in an animal model. This is an important question to test, and the experimental intervention they have carried out is good. The authors report that the combination of two anabolic therapies (anti-sclerostin and intermittent PTH) with mechanical loading has a (numerically) more than additive effect on trabecular bone volume and on cortical thickness. They then carry out a secondary analysis which shows that bone formation occurs where there is high predicted mechanical signal, and bone loss where there is less mechanical signal; this is confirmatory data of a general principle of bone mechanobiology, but they take it one step further in attempting to develop a data-driven theoretical model of whether there is a change in the set-point at which bone surface activity occurs. This latter part of the paper is extremely difficult to critique as it is not very clearly described. The experiments are well planned, and the discussion section of the work is very thorough, but the data presentation is unclear and I disagree strongly with the way the authors have interpreted the combined effects of the treatments they have tested.\n\nMajor concerns:\n\n1. Claims of synergy and interference: The work lays claim to a synergistic effect of mechanical loading and anabolic therapy. This is an overclaim and shows a lack of understanding of synergy. Usually, in pharmacological analysis, proof of synergy depends on showing that the effect of two treatments together is much greater than the addition of the two therapies, and is based on the idea that they work through the same pathway. In this project, they have calculated the average increase of the combined treatment, and compared it numerically to adding together the average effect of each treatment. There is no statistical analysis to determine whether these \"effects\" are significantly different. What is also a problem is that they use this method on parameters, such as trabecular number and trabecular thickness, which are not separable, and each contribute to trabecular bone density. This overlooks the fact that an increase in trabecular thickness is frequently associated with a reduction in trabecular number, since it can reflect a loss of thinner trabeculae, rather than a specific increase in trabecular thickness. It is not possible to test for synergy on such parameters in this context. The meaning of \"interference\" is not clear.\n\n2. Data presentation: The presentation of much of the data as percentage change from baseline obscures the observations being made here; the data is not at all transparent, though I appreciate that an in vivo study allows you to see changes over time. Inclusion of the raw data in Supplementary Figures is needed for data transparency.\n\n3. It seems that three different vehicle groups have been combined into a single vehicle group of samples. This is not good practice, and will have a major effect on the statistics for this study. The vehicle groups should be shown separately, at least to confirm that there was no difference between the three different vehicle groups.\n\n4. It is surprising that, in the single agent treatment groups, that there was a reduction in BRR/BV and ES with PTH treatment, and a reduction in MAR with anti-sclerostin. This needs to be discussed.\n\n5. The paper is not written for a general audience, apart from the introduction. The results section is highly technical and full of jargon, making it extremely challenging to follow. What is the \"natural law\" that you refer to in line 250, for example? I found it almost impossible to understand the final two figures, and their description on the results section, despite being very interested in the outcomes. Part of this is the continuing mis-use of the term \"synergy\", but also these sorts of highly theoretical methods need to have some clear explanation for non-theorists, particularly to justify the mathematical approach being used.\n\n6. Minor points\nThe authors make many comments in the introduction and discussion which are not supported by references (e.g line 58, 78, 82... )\n\n7. The introduction to this paper reads more like an opinion piece rather than a critical review of the literature. This needs attention.\n\n8. Some references are not appropriate - for example, the peculiar term (re)modeling (which is common, but confusing) was not used in reference 9. Also the references used in line 93 do not really support the statement being made here.\n\n9. The use of the term (re)modeling is not really helpful in this manuscript - it is not clear whether you are talking about modeling or remodeling or simply bone surface activity. If you cannot distinguish between the two with this method, I think it is better to say \"bone surface activity\".\n\n10. Use of the term \"pharmaceutical\" is inaccurate - it refers to pharmacological agents used in humans. The correct term here would be \"pharmacological\".\n\n11. The inclusion of data in both the text and the figures is very confusing. It is better to simply report the data, and allow the reader to look at the figures.\n\n12. How were the doses of bisphosphonate, PTH and Anti-sclerostin selected?", "reviewer_3": "Overview of Key Results and Significance\nThe aim of the manuscript was to evaluate the interaction between mechanical loading and osteoporosis drug treatments in the vertebral trabecular bone of osteoporotic female mice, and test whether mechanical loading acts additively or synergistically to improve drug treatment outcomes. The authors have developed, over several years, innovative biomechanical, imaging and statistical modeling approaches that allow them to address this topic in a detailed and rigorous manner. They have selected three relevant osteoporosis drugs (two anabolic, one anti-catabolic), alone and in combination with mechanical loading, which enhances the generalizability of the findings. The main finding is that combining mechanical loading with anabolic osteoporosis drug therapy synergistically enhances bone volume and bone (re)modeling, whereas no such effects were observed with anti-catabolic drug. In addition to addressing this important topic (ie, effects of drugs + loading), the authors have framed the work in the context of the influential “mechanostat model” proposed byHarold Frost. Frostbased the model largely on observations and inference (and little data). Herein, the authors have used their valuable data set to provide a rigorous test of the model, and show that its basic tenets align well with data and are indeed a useful framework for explaining (and predicting) how bone responds to loading, and how osteoporosis drugs shift this response. Further, the data provided by this manuscript is an important addition to the literature as it addresses the clinically relevant question about the role of physical therapy in osteoporotic skeletons undergoing pharmaceutical treatments.\n\nThere are issues with the clarity and presentation of results, figures, etc., which make parts of the paper challenging to follow. Most of the comments below highlight these issues.\n\nMajor Comments:\n\n1. The results section can be difficult to follow, especially with the frequent inclusion of mean+/- SD values for all the groups (which is redundant with same data shown in Figures). Consider stating the % difference between groups, rather than listing the mean/SD values.\n\n2. The results include many statements of difference where it is unclear if the differences are supported by statisticaltesting. Please use the word ‘significant(ly)’ to clarify (e.g., lines 120-122).\n\n3. What is the rationale for limiting the SED/SEDmax range to 0.0-0.4 (eg, Fig 5)?\n\n4. The in vivo micro-CT was done at 20, 22 and 24 wks age. It is not always clear which time interval is used for calculation of dynamic indices – please add this information as a label on the relevant figures. (It is stated in the captions but is hard to find.) If different intervals are used in different sections of the Results, state the rationale and if the results are sensitive to the interval used. This is an important concern that must be addressed. For example, in Fig 1 caption it indicates w22-w24 was used to determine remodeling rates in panels g-l. Figure 3 does not mention the interval for panels a-f, and in Figure 4, it indicates w20-w22 was the interval used to determine formed/quiescent/resorbed bone. Please justify the use of interval used, and state clearly in the figure captions.\n\n5. Addition of supplemental data would enhance the rigor of the paper.\n\n6. Specific Comments:\nIntroduction\nThe Introduction could benefit from additional details about the PTH analog and bisphosphonate, similar to the level of detail provided for the sclerostin-targeting drug.\n\n7. The section of the Introduction from lines 60-97 could be shortened. In general, the Introduction is too long.\n\n8. Lines 53-55: State here that sclerostin is a Wnt antagonist. Wnt binds to the co-receptors LRP5 (or LRP6) and Frizzled.\n\n9. Lines 75-78: The mention of microdamage associated with bisphosphonates requires supporting citations. This is an important issue, albeit with limited clinical data.\n\n10. Results\n‘Dependence of (re)modeling probability on mechanical stimulus’and ‘Synergismsin (re)modeling velocityand mechanostat parameters’ sections could benefit from more descriptive headers and clear summaries or key takeaways at the end of each section to help guide the reader through the findings.\n\n11. In ‘Dependence of(re)modeling probability on mechanical stimulus’section, discussion about Fig. 5e, CCR is missing. Additionally, the implication of changes in non-targeted formation and resorption (Fig. 5i and j) should be discussed in the result. Many readers will not understand whatyou mean by “non-targeted formation/resorption”.\n\n12. Lines 127-131 and Fig 1d,e: The decreases in Tb.N and Conn.D for most groups are surprising to me. Please add some explanation or context. (Is the increase in BV/TV due solely to increased Tb.Th, and despite fewer trabeculae?)\n\n13. Figure 1b-e. The y-axis values do not make sense. Should 100% be 0%, ie., representing change from week 20 (start of treatment)?\n\n14. Fig 1b-e.Inaddition to between group comparisonsnotedby‘o’, consideradding a symbol indicating whether the delta for each group is different from zero (i.e., the treatment increase (or decrease) the parameter).\n\n15. Lines 139-145: Please state how Eroded Surface is defined.\n\n16. Section starting with line 162 and Figure 2: The comparisons of combination groups vs. the sum of the monotherapies to infer Interfering, Additive or Synergistic effects is an excellent concept, but it is unclear how this is implemented and additional justification should be stated in the Results. Is the height of each bar the mean value for that group? It is unclear if these comparisons can be supported with statistical testing to increase rigor. Also state in Figure what the time interval used is for the data in the bar graphs.\n\n17. Lines 184- : The measures of trabecular “strength” estimated/predicted using FEA, and should be referred to as‘Predicted strength’.\n\n18. Line 189: Suggest that you add a statement explaining what ismeantbyan ‘interfering’ effect, and how you interpret this.\n\n19. Figure 2j not referenced in the text.\n\n20. Line 214: Lowered compared to what?\n\n21. Line 215: Is“beneficial” correct? Graph looks like Interfering.\n\n22. Line 224: Typo “inlets” à “insets”.\n\n23. Fig 3h:the second graph shows ‘stderr’ rather than R^2.\n\n24. Line 240: Word “ranges”is vague here.\n\n25. Lines 250, 252:The term“natural law” is an overstatement. Please find another way to state this.\n\n26. Figure 4: It is unclear what %diff SED is showing; it is explained in the text, but could be also stated in the figure caption. It looks like the average value of %diff SED for quiescent group is not always equal to 0%. If so, can you explain how this can be.\n\n27. Section starting on Line 260 Dependence of (re)modeling probability on mechanical stimulus. This is one of the most interesting aspects of the study, but the presentation is challenging as it lacks quantitative values (Figs 5a-d) and is unclear if statistical testing can be performed to support the comparison of AUC values and probabilities of non-targeted formation and values of RQ and QF.\n\n28. Figure 5a-d: Include equations of these exponential curve fits in Supplemental. Do constants of these eqns have meaning that can support the qualitative descriptions of the curves in the text (e.g, Line 270-271). In general, the qualitative descriptions and the statements referring to steeper slopes, etc, lacks quantitative rigor. Authors should mention the slope values to give the readers the opportunity to better appreciate the magnitude of differences in mechanical sensitivity among the groups.\n\n29. Figure 5e,f,g are not cited in the text.\n\n30. Lines 276-284: If you want to include the AUC values, it would be better in a table than in the text.\n\n31. Line 285: Suggest revise tostate “InML,the probabilities of non-targetedformation…”\n\n32. Fig 6f-h. Unclear that these RmV curves are relative to the VEH curve. State in the caption.\n\n33. Figure 6 and related text (lines 349-357): Values of RmV seem very low (eg, 0.00585 um/day). Are these correct? Why so different from histological mineral apposition rates which are on order of 1 um/day?\n\n34. The implication of changes in RSL and FSL (Fig. 6i and j) should be discussed.\n\n35. Discussion\nAlthough the BIS and BIS+ML groups exhibit the lowest RmT values, suggesting a lower threshold for remodeling, they also demonstrated the least overall response. This apparent discrepancy should be addressed in the discussion section.\n\n36. Fig 5a-d: Since the differences in conditional probabilities between the monotreatment and the loading + treatment groups are relatively small (approximately 1–2%), the authors should consider commenting on the biological or practical significance of these differences in the discussion section.\n\n37. Line 370-71: “this isregulated viathe mechanostat” – can you support this with citations, or qualify it“proposed to be regulated viathe mechanostat”.This studyis themostconvincing I have seen to support that this is true.\n\n38. Line 402: “46-bladed propellers” seemstypo. Usually described as“4-beta propeller structures”\n\n39. The SED maps in Fig. 5m show a reduction in SED over time. Given that the manuscript argues higher SED is associated with increased bone formation, does this observed reduction imply a decrease in bone formation capacity over time?\n\n40. Methods\nLines 552-554: The method for bone strength estimation seems very sound, but is based on assumptions about failure criterion that were developed for human bones (Pistoia #59). Have these been shown accurate for estimation of mouse vertebral strength?\n\n41. Line 577: Define CCR.\n\n42. Lines 607-…: Are thereany citations to supportthe definitions of Synergism, Additivityand Interference? I think these are very clear and reasonable, but perhaps there is supporting literature on this?\n\n43. The mechanical loading protocol should be described in greater detail. Additionally, did the applied 8N supraphysiological load induce any microdamage in the bone? What is the failure load of the 6th caudal vertebra?\n\n44. In ‘Pharmaceuticaltreatment’section, the delivery method for SOSTab isnot specified and should be included.\n\n45. Figures – additional comments\nThe use of ‘o’ inthe color of correspondinggroup to denotestatistical significance is innovative; however, itonly representsp<0.05 and the‘o’s are verysmall. If there areresults with more stringent significance levels (e.g., p < 0.001), the authors should consider denoting these separately to reflect the varying degrees of statistical strength, and consider making the symbols larger.\n\n46. The authors should present the data with individual data points for each mouse, where applicable, to visualize the variability within groups.\n\n47. All figure captions should clearly state what the box-and-whisker plots represent, e.g., whether the box indicates the interquartile range, the line represents the median, and the whiskers show the full range or a specific percentile.\n\n48. Fig 5 is missing the color key for formation, resorption, and quiescence.\n\n49. Minor comments\nThe manuscript primarily discusses changes in trabecular bone; however, were any changes observed in the cortical shell of the vertebral body in response to mechanical loading and/or drug treatments?\n\n50. As Table 1 (list of statistical significances) does not provide any key additional information, this can be moved to the supplementary or consolidated with the figure. Also, a color key in the table will be helpful.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response to Reviewers\n\nResponse to Reviewer 1\n\nReviewer #1 (Remarks to the Author):\n\n1. Why did you use the selected therapies in this specific comparison? Did you formulate initially more concrete hypothesis for each individual comparison loaded vs. sham in bisphosphonate (BIS), parathyroid hormone (PTH) and sclerostin antibody (SclAB)? E.g. regarding OB or OC or synergistically? A more stringent biological explanation for the comparisons would be helpful.\n\nWe have reformulated the hypotheses and believe that reformulation with a more stringent biological explanation of the rationale behind the selection of therapies, with each treatment targeting a different component of the bone cell network, helps strengthen the manuscript.\n\nChanged text (Introduction, l.40-101): ... [Text omitted for brevity] ...\n\n2. Some treatments come with side effects; not all can be given for a similar (long) period. And not in a similar manner. This is due to substantial biological differences across the therapies selected. This aspect seems to be widely ignored; eventually focusing here on more comparable approaches and eventually only the initial effects (and not long-term consequences) might help?\n\nIn response to your suggestion, we have added a discussion paragraph discussing the differences, anabolic windows and their potential impact on interpretation of long-term outcomes. Furthermore, we have clarified in the introduction that our analysis does not aim to directly compare long-term effects across biologically dissimilar therapies, but the focus is on short-term effectiveness. We hope this addresses your concern and improves the clarity and robustness of our interpretation.\n\nChanged text (Abstract, l.37) …, particularly in early treatment phases,\n\n3. If the work focuses only on osteoblasts and osteoclasts and their activities, I would assume that more in depth analyses on the tissue (histological) level could help confirm the findings from the µCT data.\n\nThank you for this valuable comment. We agree that histological analyses would provide important complementary insights to support the cell-specific interpretations derived from the micro-CT data. However, this study was specifically designed to prioritize longitudinal in vivo assessment of dynamic bone (re)modeling, with a focus on surface-level formation and resorption activities. Following animal sacrifice, bone samples were embedded in polymethyl methacrylate (PMMA) for synchrotron radiation-based computed tomography (SR CT). Unfortunately, this embedding protocol precluded subsequent histological processing, and some samples were lost during preparation. This is a limitation of the study and has now been acknowledged in the revised manuscript. We have added the following statement to the Discussion section to clarify this point:\n\nChanged text (Discussion, l.411 - 423): ... [Text omitted for brevity] ...\n\n4. In my eyes very interesting findings are – specifically in the light of the authors reference to Frost – the separation that formation – rest – resorption volumes seen in the PTH + ML and SclAB + ML (Figure 4), while they do overlap in almost all other cases. So maybe Frost was correct in the end – but only in a co-stimulation with PTH or SclAB. What sets these stimuli in respect to mechano-responsiveness apart from the others?\n\nIn response to this comment, we have revised Figure 4 to better visualize differences in remodeling site distributions across groups. To formally assess variability in site-specific responses, we performed a variance analysis between formation, quiescence, and resorption across all treatment groups. Interestingly, while the reviewer highlights PTH and SclAB as visually distinct, the statistical analysis identified significant reductions in variance specifically in the BIS + ML and ML groups, suggesting these groups may exhibit more defined mechanosensitive responses under mechanical loading. We have added this statistical result and interpretation to the revised results sections. We would like to highlight that Figures 5 and 6 now explore in more detail what differentiates the stimuli in PTH + ML and SclAB + ML with respect to mechano-responsiveness from those in other groups.\n\nChanged text (Results, l.244 – 246): ... [Text omitted for brevity] ...\n\n5. The manuscript would benefit from a clear link to biology, here specifically osteoblastic or osteoclastic activities. In one sentence, the authors mention osteocytes. But there is no reasoning given on how specifically Osteoblasts or osteoclasts are affected. Frost referred more to the osteocytes, which are here in analyses and data not at all in the focus. I am a bit surprised that the biology is not really included, even though the therapies analyzed are very distinctly different in their effects on these cell types.\n\nWe agree that stronger biological framing helps interpret imaging-based results. As a first step, we reformulated the hypotheses in a more biological context (see comment 1). Our study relies on in vivo micro-CT, which captures the spatial and temporal output of cellular activity, namely bone formation and resorption surfaces, but not the cells themselves. In the mechanostat framework, osteocytes are thought to serve as the primary mechanosensors, regulating osteoblast and osteoclast behavior via molecular signaling (e.g., sclerostin). While we do not directly visualize osteocytes, our observed remodeling patterns represent the outcome of their regulatory influence. We have clarified this point in both the Introduction and Discussion sections. Moreover, we now explicitly address how the treatments used (PTH, SclAB, BIS) are expected to act on different cellular populations, as stated in comment 1. We have revised the text accordingly to better reflect the cellular context.\n\n6. Finally, no other cells – such as immune or endothelial cells– are here considered. This limitation needs more discussion.\n\nInserted text (Discussion, l.430 - 434): Other cell types, particularly immune cells and endothelial cells, also contribute to bone (re)modeling via inflammatory signaling and vascularization, respectively. Recent work originating from fracture healing highlights the role of immune and vascular interactions, particularly in the context of aging and mechanical loading42. While these cell types were not analyzed here, future multimodal approaches could complement imaging-based assessments.\n\nReviewer #1 (Remarks on code availability):\n\nno further comments\n\nResponse to Reviewer 2\n\nReviewer #2 (Remarks to the Author):\n\n1. Claims of synergy and interference: The work lays claim to a synergistic effect of mechanical loading and anabolic therapy. This is an overclaim and shows a lack of understanding of synergy. Usually, in pharmacological analysis, proof of synergy depends on showing that the effect of two treatments together is much greater than the addition of the two therapies, and is based on the idea that they work through the same pathway. In this project, they have calculated the average increase of the combined treatment, and compared it numerically to adding together the average effect of each treatment. There is no statistical analysis to determine whether these \"effects\" are significantly different. What is also a problem is that they use this method on parameters, such as trabecular number and trabecular thickness, which are not separable, and each contribute to trabecular bone density. This overlooks the fact that an increase in trabecular thickness is frequently associated with a reduction in trabecular number, since it can reflect a loss of thinner trabeculae, rather than a specific increase in trabecular thickness. It is not possible to test for synergy on such parameters in this context. The meaning of \"interference\" is not clear.\n\nWe thank the reviewer for this important and constructive comment regarding our interpretation of synergy and interference effects. We acknowledge that our initial analytical approach was not sufficient to rigorously support claims of synergy. In response to this concern, we have substantially revised our statistical analysis. Specifically, we now assess interaction effects directly within a linear model framework in R, whereby the statistical significance and direction (positive or negative) of the interaction term between treatment and mechanical loading is used to evaluate potential synergy or antagonism. This approach allows for a formal statistical test of whether the combined effect deviates significantly from an additive model, without relying solely on descriptive comparisons of group means. To ensure robustness and appropriate interpretation of these models, we have consulted with a statistical expert with experience in experimental design and interaction modeling. This expert has reviewed and revised the statistical approach and has been added as a co-author of the manuscript. Additionally, we have revised our language throughout the manuscript to avoid overstating claims and now describe the observed interactions more cautiously and mechanistically, without assuming pharmacological synergy in the strictest sense. We also replaced the term interference with the more common term antagonism, which we now define explicitly as a statistically significant negative interaction effect (treatment:loading), suggesting that the combined treatment response is lower than expected additive effect of the individual effects. Regarding the trabecular number and thickness, we agree that these parameters are interrelated and should not be interpreted in isolation. We now address this in the results section and avoid attributing specific mechanistic conclusions to changes in individual parameters without considering their combined effect on trabecular bone volume fraction. We believe the revised statistical rigor and clarity of the manuscript.\n\n2. Data presentation: The presentation of much of the data as percentage change from baseline obscures the observations being made here; the data is not at all transparent, though I appreciate that an in vivo study allows you to see changes over time. Inclusion of the raw data in Supplementary Figures is needed for data transparency.\n\nThe raw data are now included in Supplementary Tables. Also, where appropriate, we show changes in the figures in the original units (dynamic bone morphometry and mechanoregulation analysis).\n\n3. It seems that three different vehicle groups have been combined into a single vehicle group of samples. This is not good practice, and will have a major effect on the statistics for this study. The vehicle groups should be shown separately, at least to confirm that there was no difference between the three different vehicle groups.\n\nThe VEH groups were drawn from the same underlying population and conducted under identical experimental conditions at different time points; they were therefore combined to improve clarity and interpretability of the results, as separate presentation would not yield additional insights but substantially increase data complexity. Nevertheless, we understand the reviewer's concern and provide a table in the Supplementary Material which lists the absolute and %-change values in bone volume fraction in the three vehicle groups (Table S.3), showing that significant differences in absolute values exist in weeks 15 and 24. No significant differences were found in %-change values. In consultation with the statistics expert we therefore test synergy on the change in bone response. We include the information about the animal provider and adjust for this in the statistical evaluation (lm(Diff ~ group x treatment + provider).\n\n4. It is surprising that, in the single agent treatment groups, that there was a reduction in BRR/BV and ES with PTH treatment, and a reduction in MAR with anti-sclerostin. This needs to be discussed.\n\nThis response happens in the second time interval more pronounced than in the first time interval. As more questions arose regarding the time intervals presented (see Reviewer 3, comment 4), we decided to show the first instead of the second time interval of the bone response. PTH has a higher response in the first time interval. ES is not significantly different in this time interval from VEH. Still, bone resorption rate BRR is lower than VEH but not as low as BIS and SclAB. We address this now in the text.\n\n5. The paper is not written for a general audience, apart from the introduction. The results section is highly technical and full of jargon, making it extremely challenging to follow. What is the \"natural law\" that you refer to in line 250, for example? I found it almost impossible to understand the final two figures, and their description on the results section, despite being very interested in the outcomes. Part of this is the continuing mis-use of the term \"synergy\", but also these sorts of highly theoretical methods need to have some clear explanation for non-theorists, particularly to justify the mathematical approach being used.\n\nWe have revised the results sections to improve clarity with a short concluding summary in the end of each section. Figures 5 and 6 have been substantially updated, and we removed the term natural law from the text. We agree with the reviewer's comment on the use of the term synergy and agree that it requires a clearer definition. To address this, we have added a paragraph in the Statistical Methods section that formally defines synergy, distinguishes it from antagonism, and explains our choice of mathematical interaction modeling for readers less familiar with theoretical approaches. Additionally, we have introduced new subheadings in the Results section to help summarize key findings for non-specialist readers.\n\n6. Minor points\nThe authors make many comments in the introduction and discussion which are not supported by references (e.g line 58, 78, 82... )\n\n7. The introduction to this paper reads more like an opinion piece rather than a critical review of the literature. This needs attention.\n\n8. Some references are not appropriate - for example, the peculiar term (re)modeling (which is common, but confusing) was not used in reference 9. Also the references used in line 93 do not really support the statement being made here.\n\n9. The use of the term (re)modeling is not really helpful in this manuscript - it is not clear whether you are talking about modeling or remodeling or simply bone surface activity. If you cannot distinguish between the two with this method, I think it is better to say \"bone surface activity\".\n\nWe appreciate the reviewer's concern regarding the clarity of the term (re)modeling. We have previously received requests to change the terms we used before to this terminology and would very much prefer to be consistent with publications in this field (Schulte et al., PLoSOne, 2013, Birkhold et al., Bone, 2015, Marques et al., 2023, Shyu et al., Front. Med. Eng, 2025). In the meantime, new quantification parameters have followed the nomenclature of (re)modeling, e.g. (Marques et al., 2023, 'remodeling velocity'). To alleviate the reviewer's concern, we have now clarified in the manuscript what is specifically meant by (re)modeling. Additionally, we explicitly present the differences between modeling and remodeling within the treatment groups, using methods established in prior studies that employed micro-computed tomography to distinguish these processes (e.g. Birkhold et al., Bone, 2015).\n\n10. Use of the term \"pharmaceutical\" is inaccurate - it refers to pharmacological agents used in humans. The correct term here would be \"pharmacological\".\n\nThe term pharmaceutical was replaced by pharmacological throughout the manuscript.\n\n11. The inclusion of data in both the text and the figures is very confusing. It is better to simply report the data, and allow the reader to look at the figures.\n\nWe have changed the results text. As few as possible data are shown in the text, and the data are now listed in the Supplementary Material. See also Reviewer 3, comment 1.\n\n12. How were the doses of bisphosphonate, PTH and Anti-sclerostin selected?\n\nChanged text (Methods, l.514 - 519): BIS and SclAB doses were selected based on established protocols in the literature24,47. The PTH dose was determined in a dose-response study comparing 10, 20, 40 µg/kg/d, following the 40 µg/kg/d dose proposed in the literature48 that led to significant increases in bone formation (Fig. 1b) by the end of the experiment. The 40 µg/kg/d dose was chosen to obtain BV/TV increases comparable to those observed with BIS and SclAb treatments, enabling a more balanced comparison across treatment groups (see Fig. 1b).\n\nReviewer #2 (Remarks on code availability):\n\nI did not see any supporting code.\n\nChanged text:\n\nCode availability\nAll data and code are available in a Zenodo repository: 10.5281/zenodo.17256047. Please find below the link for reviewer access: [Link provided]\n\nResponse to Reviewer 3\n\nReviewer #3 (Remarks to the Author):\n\n1. The results section can be difficult to follow, especially with the frequent inclusion of mean+/- SD values for all the groups (which is redundant with same data shown in Figures). Consider stating the % difference between groups, rather than listing the mean/SD values.\n\nAs we are now providing the raw data as well as %-differences in the Supplementary Material, we removed them from the text in the results section.\n\n2. The results include many statements of difference where it is unclear if the differences are supported by statisticaltesting. Please use the word ‘significant(ly)’ to clarify (e.g., lines 120-122).\n\nWe have inserted the word significant throughout the results section to clarify statistical significance. Significance levels are now found in Supplementary Material.\n\n3. What is the rationale for limiting the SED/SEDmax range to 0.0-0.4 (eg, Fig 5)?\n\nAdded text (Figure 4 legend): Values are cropped at 40% of the full interval due to the small number of voxels above this threshold as was described previously19.\n\n4. The in vivo micro-CT was done at 20, 22 and 24 wks age. It is not always clear which time interval is used for calculation of dynamic indices – please add this information as a label on the relevant figures. (It is stated in the captions but is hard to find.) If different intervals are used in different sections of the Results, state the rationale and if the results are sensitive to the interval used. This is an important concern that must be addressed. For example, in Fig 1 caption it indicates w22-w24 was used to determine remodeling rates in panels g-l. Figure 3 does not mention the interval for panels a-f, and in Figure 4, it indicates w20-w22 was the interval used to determine formed/quiescent/resorbed bone. Please justify the use of interval used, and state clearly in the figure captions.\n\nThank you for raising this issue. We provide now the raw data in the Supplementary material in all time intervals. In the figure captions and in the figure panels, we state explicitly (as a subscript of each readout) which time interval is shown. For consistency, we now also show the first time interval in figure 1.\n\n5. Addition of supplemental data would enhance the rigor of the paper.\n\nThe authors acknowledge this comment. Supplementary material containing raw data is now provided. The addition of Supplementary material also helped in addressing several of the other reviewer comments.\n\n6. Specific Comments:\nIntroduction\nThe Introduction could benefit from additional details about the PTH analog and bisphosphonate, similar to the level of detail provided for the sclerostin-targeting drug.\n\nWe provide now additional details about PTH and bisphosphonate to be consistent amongst the three investigated drugs.\n\n7. The section of the Introduction from lines 60-97 could be shortened. In general, the Introduction is too long.\n\nThe introduction was shortened, especially with respect to the lines 60-97.\n\n8. Lines 53-55: State here that sclerostin is a Wnt antagonist. Wnt binds to the co-receptors LRP5 (or LRP6) and Frizzled.\n\nWe state now that sclerostin is a Wnt antagonist.\n\n9. Lines 75-78: The mention of microdamage associated with bisphosphonates requires supporting citations. This is an important issue, albeit with limited clinical data.\n\nThe introduction was shortened and this section was deleted. In the discussion, the reference was inserted:\n\nChanged text (Discussion, l.424 - 426): Regions with high local strain are linked to higher occurrences of microscopic tissue damage38 of which even small amounts can lead to large reductions in strength39 and increase fracture risk40.\n\n10. Results\n‘Dependence of (re)modeling probability on mechanical stimulus’and ‘Synergismsin (re)modeling velocityand mechanostat parameters’ sections could benefit from more descriptive headers and clear summaries or key takeaways at the end of each section to help guide the reader through the findings.\n\nChanged headers: See Reviewer 2, comment 5.\n\n11. In ‘Dependence of(re)modeling probability on mechanical stimulus’section, discussion about Fig. 5e, CCR is missing. Additionally, the implication of changes in non-targeted formation and resorption (Fig. 5i and j) should be discussed in the result. Many readers will not understand whatyou mean by “non-targeted formation/resorption”.\n\nGiven the feedback of Reviewers 2 and 3, we have substantially revised Figures 4 - 6. Non-targeted formation/resorption is not used any more in the manuscript. In Fig. 4d), min provides now the information that could be connected with non-targeted resorption, but on a more conceptual level. Furthermore, we have inserted a description of CCR.\n\n12. Lines 127-131 and Fig 1d,e: The decreases in Tb.N and Conn.D for most groups are surprising to me. Please add some explanation or context. (Is the increase in BV/TV due solely to increased Tb.Th, and despite fewer trabeculae?)\n\nWe inserted the following text as explanation.\n\nChanged text (Results, l.118 - 123): As previously described18, mechanical loading increases BV/TV mainly through trabecular thickening despite a reduction in trabecular number, explainable by a full loss of thin trabeculae - a pattern also seen in the SclAB-group (Fig. 1c,d). In contrast, PTH increased BV/TV through moderate thickening and sustained preservation of trabecular number, resulting in a smaller loss of connectivity. BIS maintained BV/TV by preserving existing trabeculae, including thinner ones, with minimal thickening (Fig. 1, b-e).\n\n13. Figure 1b-e. The y-axis values do not make sense. Should 100% be 0%, ie., representing change from week 20 (start of treatment)?\n\nFigure 1-f represents now the change from week 20, with 0% denoting no change from start of treatment.\n\n14. Fig 1b-e.Inaddition to between group comparisonsnotedby‘o’, consideradding a symbol indicating whether the delta for each group is different from zero (i.e., the treatment increase (or decrease) the parameter).\n\nWe have now inserted a symbol (#) to indicate when the delta for each group was different from zero.\n\n15. Lines 139-145: Please state how Eroded Surface is defined.\n\nInserted text (Results, l.139 - 142): Eroded surface per bone surface (ES), reflecting the proportion of bone surface previously affected by resorption, was significantly lower in ML and SclAB compared to VEH, BIS, and PTH (p<0.05, Fig. 1l).\n\n16. Section starting with line 162 and Figure 2: The comparisons of combination groups vs. the sum of the monotherapies to infer Interfering, Additive or Synergistic effects is an excellent concept, but it is unclear how this is implemented and additional justification should be stated in the Results. Is the height of each bar the mean value for that group? It is unclear if these comparisons can be supported with statistical testing to increase rigor. Also state in Figure what the time interval used is for the data in the bar graphs.\n\nThe same concern was also raised by Reviewer 2 (Comment 1). In response, we have reanalyzed synergy and antagonism by statistically using the interaction term treatment:loading of a linear model. In addition, we describe now in the figure legends what the height of each bar represents. We also insert the time interval used for the data in the bar graphs. In addition, we provide all time intervals in the Supplementary Material.\n\n17. Lines 184- : The measures of trabecular “strength” estimated/predicted using FEA, and should be referred to as‘Predicted strength’.\n\nThe term predicted strength has been used throughout the manuscript.\n\n18. Line 189: Suggest that you add a statement explaining what ismeantbyan ‘interfering’ effect, and how you interpret this.\n\nThank you for pointing out the need for clarification. We now include a more explicit explanation of what is meant by synergy and antagonism. The word \"interfering\" was replaced with antagonistic.\n\n19. Figure 2j not referenced in the text.\n\nFigure 2j (now Figure 2g) is now referenced in the text.\n\n20. Line 214: Lowered compared to what?\n\nChanged text (Results, l.137): As expected, mineral resorption rate (MRR) was significantly lower in the BIS-group compared to VEH and unchanged in the anabolic groups (Fig. 1k), suggesting bisphosphonates preserve Tb.N (Fig. 1d) by preventing full trabecular resorption. Eroded surface per bone surface (ES), reflecting the proportion of bone surface previously affected by resorption, was significantly lower in ML and SclAB compared to VEH, BIS, and PTH (p<0.05, Fig. 1l).\n\n21. Line 215: Is“beneficial” correct? Graph looks like Interfering.\n\nAs we have been suggested, we replaced the term interfering with antagonistic.\n\n22. Line 224: Typo “inlets” à “insets”.\n\nThe typo has been corrected to insets.\n\n23. Fig 3h:the second graph shows ‘stderr’ rather than R^2.\n\nWe thank the reviewer for pointing out the confusion regarding the use of standard error. Our intention was to distinguish between linear and non-linear regression analyses, where R² is not always appropriate. To clarify this, we have revised the figures to distinguish between linear regressions and the correlation coefficient for non-linear regressions based on log-transformed models.\n\n24. Line 240: Word “ranges”is vague here.\n\nThe word ranges was replaced by strain windows (l.233 and l.243).\n\n25. Lines 250, 252:The term“natural law” is an overstatement. Please find another way to state this.\n\nDeleted text: [Text omitted for brevity]\n\n26. Figure 4: It is unclear what %diff SED is showing; it is explained in the text, but could be also stated in the figure caption. It looks like the average value of %diff SED for quiescent group is not always equal to 0%. If so, can you explain how this can be.\n\nChanged Figure 4 legend: (b) SED at formation, resorption, and quiescent sites6, normalized to the group mean of quiescence to allow statistical testing with this group.\n\n27. Section starting on Line 260 Dependence of (re)modeling probability on mechanical stimulus. This is one of the most interesting aspects of the study, but the presentation is challenging as it lacks quantitative values (Figs 5a-d) and is unclear if statistical testing can be performed to support the comparison of AUC values and probabilities of non-targeted formation and values of RQ and QF.\n\nWe acknowledge that the presentation of Figure 5 was challenging to interpret. We have reframed Figures 4 and 5 and present now slightly other parameters to describe mechanoregulation and its implications on bone strength. We follow the publication of Marques et al. (2023) who formally assessed the ability of time-lapsed micro-computed tomography scans and finite-element-analysis to extract mechanostat parameters from experimental data. Furthermore, as this reviewer suggested, we quantify and test statistically, the coefficients of the fits of the conditional probability curves. Min represents non-targeted resorption, CCR the amount of mechanoregulated (re)modeling, summarizing AUC and AUC in one variable. The (re)modeling threshold is a representation of the intersection values RQ and QF. With this, we hope that the presentation of Figure 5 becomes clearer.\n\n28. Figure 5a-d: Include equations of these exponential curve fits in Supplemental. Do constants of these eqns have meaning that can support the qualitative descriptions of the curves in the text (e.g, Line 270-271). In general, the qualitative descriptions and the statements referring to steeper slopes, etc, lacks quantitative rigor. Authors should mention the slope values to give the readers the opportunity to better appreciate the magnitude of differences in mechanical sensitivity among the groups.\n\nSupplementary material contains now a table for the coefficients derived from the conditional probabilities of formation and resorption. The curves were fitted per animal which allows statistical testing of the resulting coefficients. The asymptotic value of the conditional probability for bone resorption is used to characterize the basal level of resorption and is presented in Fig. 4d.\n\n29. Figure 5e,f,g are not cited in the text.\n\nFigure 5 has been rearranged. All subpanels are now cited in the text.\n\n30. Lines 276-284: If you want to include the AUC values, it would be better in a table than in the text.\n\nWe decided to remove the AUC values. All parameter values are now presented in the Supplementary Material.\n\n31. Line 285: Suggest revise tostate “InML,the probabilities of non-targetedformation…”\n\nThe text regarding non-targeted formation has been deleted to alleviate understandability of the last two figures (see Reviewer 2, comment 1 and Reviewer 3, comment 27).\n\n32. Fig 6f-h. Unclear that these RmV curves are relative to the VEH curve. State in the caption.\n\nThe RmV curve comparisons have been deleted to improve understandability of Figure 6 (see Reviewer 2, comment 1). Instead, we use now consistently the graphs showing the sum of monotreatments compared to the combination treatments.\n\n33. Figure 6 and related text (lines 349-357): Values of RmV seem very low (eg, 0.00585 um/day). Are these correct? Why so different from histological mineral apposition rates which are on order of 1 um/day?\n\nThank you for pointing this out. In fact, the values had to be rescaled by a factor of 1000 to convert into the right unit [kPa]. We have now corrected this.\n\n34. The implication of changes in RSL and FSL (Fig. 6i and j) should be discussed.\n\nAdded text (Results, l.299 - 310): FSL was increased in all treatments compared to VEH (p<0.001, Fig. 5b, Supplementary Table S.9), and was significantly higher in anabolic combination groups compared to the respective monotreatments (p<0.001). This suggests an increased mechanosensitivity of the cells involved in bone formation. RSL was increased in the BIS and all combination groups compared to VEH (p<0.05, Fig. 5c). The increase in RSL under bisphosphonate treatment may be explained by the suppression of bone turnover: at comparable strain levels, resorption would typically occur, resulting in a lower RSL; however, due to inhibited osteoclast activity, this resorptive response is blunted, making the system appear saturated at a higher RSL value. Regarding the role of additional mechanical loading, only the PTH + ML group showed a significant increase compared to PTH alone (p<0.05, Supplementary Table S.9). This suggests that, under strain conditions that would typically lead to bone resorption, the balance has shifted towards bone formation.\n\n35. Discussion\nAlthough the BIS and BIS+ML groups exhibit the lowest RmT values, suggesting a lower threshold for remodeling, they also demonstrated the least overall response. This apparent discrepancy should be addressed in the discussion section.\n\nAdded text (Results, l.310 - 321): RmT values, representing the setpoints in the mechanostat theory, were decreased in all pharmacological treatment groups compared to VEH (p<0.05), with no significant improvements observed in the combination groups receiving mechanical loading (Fig. 5d). These results were even more pronounced in the second time interval (Supplementary Fig. 4d, Table S.9). The reduction in RmT suggests an upregulation of osteocytic mechanosensitivity, an expected outcome in the anabolic treatment groups, but an unexpected finding in the bisphosphonate-treated groups. This may reflect a compensatory osteocytic response to the suppressed bone resorption induced by bisphosphonate treatment. Furthermore, FSL correlated strongly with predicted strength increases (R = 0.888), while RmT exhibited a moderate inverse correlation (R = -0.36) when fitted with a power-law function. These findings suggest that a reduction in RmT may be a prerequisite for strength gains; however, actual increases in strength require anabolic potential (Fig. 5e,f).\n\n36. Fig 5a-d: Since the differences in conditional probabilities between the monotreatment and the loading + treatment groups are relatively small (approximately 1–2%), the authors should consider commenting on the biological or practical significance of these differences in the discussion section.\n\nAs we provide in the revision also quantitative data to assess differences in conditional probabilities, it is now even easier to comment on the biological significance of these differences. We have added this to the results section where the findings are presented.\n\n37. Line 370-71: “this isregulated viathe mechanostat” – can you support this with citations, or qualify it“proposed to be regulated viathe mechanostat”.This studyis themostconvincing I have seen to support that this is true.\n\nWe decided to use the phrasing proposed to be regulated via the mechanostat and inserted citations.\n\n38. Line 402: “46-bladed propellers” seemstypo. Usually described as“4-beta propeller structures”\n\nRenamed to four beta-propeller domains but then deleted in the latest version. Thank you.\n\n39. The SED maps in Fig. 5m show a reduction in SED over time. Given that the manuscript argues higher SED is associated with increased bone formation, does this observed reduction imply a decrease in bone formation capacity over time?\n\nThank you for your insightful comment. The observed reduction in Strain Energy Density (SED) over time in Fig. 5m (now: Figure 6a) does not necessarily imply a decrease in bone formation capacity. Rather, it reflects the dynamic nature of the mechanical loading and treatment effects, which contribute to a saturation window. Specifically, reductions in SED during the loading and treatment periods are consistent with the model of mechanostat theory, where bone formation is responsive to mechanical stimuli up to a certain threshold. Once this threshold is reached, the system enters a saturation phase, where the rate of bone formation stabilizes despite continued mechanical loading. This plateau is a natural result of the system's regulatory mechanisms, which aim to maintain bone homeostasis and prevent over-formation, rather than a decline in bone formation capacity. Thus, the reduction in SED is indicative of the system stabilizing within this saturation window, rather than a loss of formation potential over time.\n\n40. Methods\nLines 552-554: The method for bone strength estimation seems very sound, but is based on assumptions about failure criterion that were developed for human bones (Pistoia #59). Have these been shown accurate for estimation of mouse vertebral strength?\n\nWe included the following reference (Nyman et al. 2015):\n\nChanged text (Methods, l.553): This criterion has been shown applicable to the mouse vertebra as well52.\n\n41. Line 577: Define CCR.\n\nChanged text (Results, l.574): Correct classification rate (CCR) values were calculated from the mean conditional probabilities from all animals, returning a scalar value between 0.33 and 1 assessing overall mechanoregulation, with 0.33 meaning (re)modeling is independent of the mechanical signal and 1 meaning it is entirely dependent on the mechanical signal.\n\n42. Lines 607-…: Are thereany citations to supportthe definitions of Synergism, Additivityand Interference? I think these are very clear and reasonable, but perhaps there is supporting literature on this?\n\nPlease see Reviewer 2, comment 1 who has requested to use another concept of assessing synergy, additivity or interference using statistical methods.\n\n43. The mechanical loading protocol should be described in greater detail. Additionally, did the applied 8N supraphysiological load induce any microdamage in the bone? What is the failure load of the 6th caudal vertebra?\n\nThe mechanical loading protocol is now described in greater detail. We have added an explanation regarding the occurrence of microdamage and predicted failure load.\n\n44. In ‘Pharmaceuticaltreatment’section, the delivery method for SOSTab isnot specified and should be included.\n\nChanged text (Discussion, l.512 - 513): [Text omitted for brevity]\n\n45. Figures – additional comments\nThe use of ‘o’ inthe color of correspondinggroup to denotestatistical significance is innovative; however, itonly representsp<0.05 and the‘o’s are verysmall. If there areresults with more stringent significance levels (e.g., p < 0.001), the authors should consider denoting these separately to reflect the varying degrees of statistical strength, and consider making the symbols larger.\n\nAll statistical significances are now also reported in the Supplementary Material. We have there the possibility to show more stringent significance levels (e.g. p<0.001). With the possibility to lookup the significance levels in the Supplementary Material, we hope it is not necessary any more to indicate separately in the figures. All symbols in Figures 1, 3, 5, and 6 have been made slightly larger.\n\n46. The authors should present the data with individual data points for each mouse, where applicable, to visualize the variability within groups.\n\nWe have changed the figures to present the data with individual data points for each mouse to visualize the variability within groups.\n\n47. All figure captions should clearly state what the box-and-whisker plots represent, e.g., whether the box indicates the interquartile range, the line represents the median, and the whiskers show the full range or a specific percentile.\n\nThe figure captions now state more clearly what the box-and-whisker plots represent.\n\n48. Fig 5 is missing the color key for formation, resorption, and quiescence.\n\nFig. 5 (conditional probabilities) has been merged with Fig. 4 which now contains the color key for formation, resorption and quiescence.\n\n49. Minor comments\nThe manuscript primarily discusses changes in trabecular bone; however, were any changes observed in the cortical shell of the vertebral body in response to mechanical loading and/or drug treatments?\n\nWe provide now values of the cortical shell in the Supplementary material to provide a more holistic picture of the changes occurring in the caudal vertebra (Table S.3, Figure S.1).\n\n50. As Table 1 (list of statistical significances) does not provide any key additional information, this can be moved to the supplementary or consolidated with the figure. Also, a color key in the table will be helpful.\n\nTable 1 has been deleted. A color key has been inserted in Supplementary Table S.1. Supplementary Tables S.2-S.9 yield now the absolute values and significance values in the Supplementary material."}]

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