Mathematical Model of Paracrine Interactions between Osteoclasts and Osteoblasts Predicts Anabolic Action of Parathyroid Hormone on Bone
http://www.100md.com
内分泌学杂志 2005年第8期
McGill University, Montreal, Canada H3A 2B2
Address all correspondence and requests for reprints to: Dr. Svetlana V. Komarova, Faculty of Dentistry, McGill University, 3640 University Street, Montreal, Quebec, Canada H3A 2B2. E-mail: svetlana.komarova@mcgill.ca
Abstract
To restore falling plasma calcium levels, PTH promotes calcium liberation from bone. PTH targets bone-forming cells, osteoblasts, to increase expression of the cytokine receptor activator of nuclear factor B ligand (RANKL), which then stimulates osteoclastic bone resorption. Intriguingly, whereas continuous administration of PTH decreases bone mass, intermittent PTH has an anabolic effect on bone, which was proposed to arise from direct effects of PTH on osteoblastic bone formation. However, antiresorptive therapies impair the ability of PTH to increase bone mass, indicating a complex role for osteoclasts in the process. We developed a mathematical model that describes the actions of PTH at a single site of bone remodeling, where osteoclasts and osteoblasts are regulated by local autocrine and paracrine factors. It was assumed that PTH acts only to increase the production of RANKL by osteoblasts. As a result, PTH stimulated osteoclasts upon application, followed by compensatory osteoblast activation due to the coupling of osteoblasts to osteoclasts through local paracrine factors. Continuous PTH administration resulted in net bone loss, because bone resorption preceded bone formation at all times. In contrast, over a wide range of model parameters, short application of PTH resulted in a net increase in bone mass, because osteoclasts were rapidly removed upon PTH withdrawal, enabling osteoblasts to rebuild the bone. In excellent agreement with experimental findings, increase in the rate of osteoclast death abolished the anabolic effect of PTH on bone. This study presents an original concept for the regulation of bone remodeling by PTH, currently the only approved anabolic treatment for osteoporosis.
Introduction
BONE REMODELING OCCURS in spatially and temporally discrete sites as a coordinated process involving resorption by osteoclasts, followed by formation of new bone by osteoblasts (1). Multiple factors provide paracrine coupling between osteoclasts and osteoblasts as well as autocrine loops for positive and negative feedback regulation of each cell type (Fig. 1A). Among the most important factors are the proresorptive cytokine receptor activator of nuclear factor B ligand (RANKL) and its decoy receptor osteoprotegerin (OPG), which are expressed by osteoblasts and reciprocally regulate osteoclasts (2). Other factors include TGF?, which is released and activated by resorbing osteoclasts and affects osteoclasts and osteoblasts (3, 4), and IGF, secreted by osteoblasts and released from the matrix by resorbing osteoclasts, which stimulate osteoblast formation (5).
FIG. 1. PTH effect on bone mass depends on the amplitude and duration of stimulation. A, Schematic representation of interactions between osteoclasts and osteoblasts included in the model. Black arrows, Cell formation from precursors (parameters 1,2 describe the activities of cell formation for osteoclasts and osteoblasts, respectively) and cell death (parameters ?1,2 describe the activities of cell removal for osteoclasts and osteoblasts, respectively); red and green arrows, effects of autocrine and paracrine regulators on the rates of osteoclast and osteoblast formation, with parameter g11 describing osteoclast autocrine regulation; g12, osteoclast-derived regulation of osteoblasts; g22, osteoblast autocrine regulation; and g21, osteoblast-derived regulation of osteoclasts. The normalized activities of bone resorption and formation are described with parameters k1,2. PTH was assumed to affect osteoblasts, represented by the blue arrow. B and C, Stimulation with PTH was modeled by an increase in g21 from –0.5 to –0.1 (green), 0.1 (blue), or 0.3 (red) as a 1-d burst (B) or continuously (C). OC, Number of osteoclasts; OB, number of osteoblasts. Changes in bone mass are expressed as a percentage of initial bone mass (100%). Decrease of bone mass to zero percent represents thinning and loss of connectivity of single trabeculae.
Bone remodeling plays a major role in mineral homeostasis, by providing access to stores of calcium and phosphate (6, 7). PTH is secreted in response to a drop in plasma Ca2+ levels. With the goal of maintaining plasma Ca2+, PTH increases bone resorption to release Ca2+ stored in bone. Interestingly, PTH mainly stimulates osteoclasts indirectly, first affecting osteoblasts that have receptors for PTH (8, 9). Acting on osteoblasts, PTH alters expression of RANKL and OPG, leading to a large increase in the RANKL/OPG ratio, thus stimulating osteoclastogenesis and bone resorption (10, 11). Most intriguingly, the overall effect of PTH on bone mass depends primarily on its mode of administration. Whereas a continuous increase in PTH levels decreases bone mass, intermittent PTH administration has an anabolic action on bone (8, 12, 13, 14, 15).
When applied intermittently, PTH acts in a number of ways resulting in an overall increase in bone mass. First, it accelerates bone remodeling (16), both by increasing the number of sites undergoing remodeling and by increasing the turnover of individual sites (17). At each site of bone remodeling, increase in formation is higher than increase in resorption, resulting in a positive remodeling balance. In addition, PTH induces renewed modeling (16, 17). The anabolic action of PTH has been attributed to its direct effects on osteoblastic bone formation (14, 18, 19, 20). However, recently, two clinical trials demonstrated that antiresorptive agents, such as alendronate, attenuate and even impair the bone-forming abilities of PTH (21, 22), suggesting the complex role for osteoclasts in the process (23, 24). Although United States Food and Drug Administration has approved PTH as an anabolic treatment for osteoporosis, the mechanisms underlying its actions remain elusive.
Mathematical modeling provides a powerful tool to predict the net outcome of multiple, simultaneous actions of autocrine, paracrine, and endocrine factors on the process of bone remodeling. Although only few attempts have been made to mathematically reconstruct the process of bone remodeling at a cellular level, there is increasing interest in this approach. In the last few years, two models, one of which was created by our group, were published describing the interactions among osteoclasts and osteoblasts (25, 26); one model describes the changes in cellular activities (27), and two other models were aimed specifically to investigate the mechanism for different effects of PTH administration (28, 29).
Because bone remodeling is involved in both anabolic and catabolic effects of PTH on bone, we extended our model describing interactions among osteoclasts and osteoblasts at a single remodeling site (25), to analyze changes in bone cell numbers and bone mass after PTH administration. PTH was first assumed only to increase RANKL/OPG ratio by changing the expressions of RANKL and OPG by osteoblasts, and thus augmenting the ability of osteoblasts and their precursors to recruit osteoclasts. It is important to note that the kinetics of increase in RANKL/OPG ratio do not directly reflect the duration or frequency of the PTH administration; therefore, within this model, only the following question was asked: can the duration of increase in RANKL/OPG affect the overall balance of a single remodeling cycle? It was found that over a wide range of model parameters, short PTH administrations resulted in anabolic actions on bone, whereas continuous PTH led to bone loss. Anabolic responses to PTH depended mostly on parameters describing the capacity for osteoblast activation in response to preceding increases in osteoclast numbers (30, 31). In agreement with recent experimental findings (21, 22), increasing the rate of osteoclast death abolished the anabolic action of PTH on bone. Next, PTH was assumed to directly promote osteoblast formation and survival. Although these actions of PTH were clearly beneficial, PTH was able to induce considerable bone gain only if, in addition to its effects on osteoblasts, it simultaneously led to osteoclast stimulation. In summary, this model suggests that the complex actions of PTH on bone remodeling may arise from a strong coupling of osteoblasts to osteoclasts.
Materials and Methods
Using ordinary differential equations, the mathematical model describes changes in osteoclast and osteoblast numbers at a single site of bone remodeling within a basic multicellular unit (1, 32). The changes in cell numbers in the model are determined by the rates of production of each cell population (recruitment and differentiation of precursors), and the rates of cell removal (cell death, migration of osteoclasts from the site, differentiation of osteoblasts into osteocytes). We assumed that local effectors regulate only the processes of osteoblast and osteoclast formation, whereas systemic effectors can regulate both cell formation and cell death. To summarize the net effect of local factors on the rates of cell production, a power-law approximation was employed (25, 33, 34). Populations of osteoclasts and osteoblasts under initial steady-state conditions were assumed to consist of less differentiated cells able only to participate in autocrine and paracrine signaling. Increases in numbers of osteoclasts and osteoblasts above steady-state levels were attributed to the proliferation and differentiation of precursors into mature cells able to remove or build bone. The rates of bone resorption and formation were assumed to be proportional to the numbers of osteoclasts and osteoblasts (respectively) exceeding initial steady-state levels. Because resident bone cells do not have an ability to predict the duration for which the systemic factor is present, it was assumed that locally cells respond to the PTH in the same manner independently of the duration of its administration. First PTH was modeled to induce increases only in the RANKL/OPG ratio, an effect shown to follow both intermittent and continuous PTH administration (14, 35). This effect of PTH was modeled as a step increase in the parameter describing osteoblast-derived osteoclast regulation, g21. Later, PTH was also modeled to promote osteoblast responsiveness to stimulatory factors (as a step increase in osteoblast autocrine regulation, g22), the rate of osteoblast formation (as a step increase in activity of osteoblast production, 2), or osteoblast survival (as a step decrease in activity of osteoblast removal, ?2).
These assumptions resulted in the following system of differential equations:
(1)
(2)
(3)
(4)
(5)
where x1 and x2 are the numbers of osteoclasts and osteoblasts respectively; z is total bone mass; i are activities of cell production; ?i are activities of cell removal; gij are parameters describing osteoclast autocrine regulation (g11), osteoclast-derived regulation of osteoblasts (g12), osteoblast autocrine regulation (g22), and osteoblast-derived regulation of osteoclasts (g21); ki are normalized activities of bone resorption and formation; i are the numbers of cells at initial steady-state; yi are the numbers of cells actively resorbing or forming bone; t0 is the time of PTH application; and d is the duration of changes in RANKL/OPG induced by PTH. With one exception (see Fig. 4B), PTH application was started at t0 = 1 d.
FIG. 4. Role of osteoclasts in the anabolic effects of PTH on bone. A, Effect of PTH at the site undergoing bone remodeling. Local stimulation was assumed to result in a momentary increase in the number of osteoclasts by 10 cells at time zero (red). Stimulation with PTH was modeled by an increase in g21 from –0.5 to 0 for 1 d starting at time = 1 d, either at a quiescent bone (blue) or after stimulation by local stimulus (purple). B, Effect of PTH application at different phases of local stimulus-induced bone remodeling. Changes in bone mass were calculated after increases in g21 for 1 d from –0.5 to 0.2 at d 1, 10, 30, 50, or 80 (black) after local stimulation. The red line indicates the effect of local stimulus alone (same as red line in Fig. 4A). C, Antiresorptive agents impair the ability of PTH to increase bone mass. Stimulation with PTH was modeled by an increase in g21 from –0.5 to 0.3 for 1 d. To model the increase in osteoclast death due to treatment with bisphosphonates (Bisph.) the rate constant of osteoclast removal ?1 was increased from 0.2 (red) to 0.4 (blue) or 0.8 (green). D, Role for direct action of PTH on osteoblasts in the anabolic effect of PTH on bone. Effects of PTH were modeled by an increase for 1 d either in osteoblast autocrine regulation, g22, from 0 to 0.1 (green); or in g22 from 0 to 0.1 and osteoblast-derived osteoclast regulation, g21, from –0.5 to 0.3 (purple); or only in g21 from –0.5 to 0.3 (red). OC, Number of osteoclasts; OB, number of osteoblasts. Changes in bone mass are expressed as a percentage of initial bone mass (100%).
The stability of steady-state solutions of the system of equations 1 and 2 was previously analyzed analytically, and the dynamic behavior of the system of equations 1–4 using numerical integration (25). The parameters of the model in this study were chosen to be the same as those describing a stable node type behavior of a single bone remodeling cycle (25): 1 = 3 cells(d)–1; ?1 = 0.2 (d)–1; 2 = 4 (d)–1; ?2 = 0.02 (d)–1; g11 = 0.5; g21 = –0.5; g12 = 1; g22 = 0; k1 = 0.24% (cell)–1 (d)–1; k2 = 0.0017% (cell)–1 (d)–1. It is important to note that, in keeping with the histomorphometric data (1), the rate of osteoclast turnover in the model is approximately 10 times higher than the rate of turnover of osteoblasts, whereas the normalized activity of bone resorption by single osteoclast is approximately 1000 times higher than the normalized activity of bone formation by a single osteoblast. Model 1–5 was analyzed using numerical integration by a fourth order Runge-Kutta algorithm using Berkeley Madonna version 8.0.1 (R. I. Macey, G. F. Oster, University of California at Berkeley).
In calculations for Fig. 2A, the parameters for normalized activities of bone resorption and formation were adjusted for illustrative purposes, so that 100% remodeling would be achieved in response to intermediate stimulations. The calculations were performed with the same parameter values except the following: Fig. 2A, left, g12 = 0.5, k2 = 0.005; Fig. 2A, middle, g12 = 0.98, k2 = 0.0017; Fig. 2A, right, g12 = 1.4, k2 = 0.00075.
FIG. 2. Effective coupling of osteoblasts to osteoclasts is essential for anabolic effect of PTH. A, Parameter describing osteoclast-derived regulation of osteoblasts, g12, was 0.5 (left), 0.98 (middle), or 1.4 (right). The model was initially balanced to achieve 100% remodeling in response to intermediate stimulations (see Materials and Methods). Changes in bone mass were calculated in response to PTH application modeled as an increase in g21 for 1 d from –0.5 to 0 (green), 0.1 (blue), or 0.15 (red). Vertical lines indicate time when bone mass reached final value. B, Final bone mass was plotted as a function of stimulus strength, which was determined by a number of osteoclast activated in response to PTH application. C and D, Initial parameters were chosen to be at slightly positively balanced state (g12 = 1). Single parameter was gradually altered, and changes in bone mass were assessed after a momentary increase in the number of osteoclasts at time 0 by 5, 10, or 15 cells. For each parameter value, final bone mass was plotted as a function of initial stimulation, and the slope of the relationship was calculated. This slope was then plotted as a function of parameter value. C, Parameters regulating magnitude and duration of osteoclast activation. D, Parameters regulating magnitude and duration of osteoblast activation.
The model is considerably simplified, which resulted in a number of limitations, including: 1) only two cell types were considered, 2) only formation of osteoclasts and osteoblasts were regulated by local paracrine and autocrine factors, and 3) parameters describing the effectiveness of autocrine and paracrine regulation included the actions of multiple factors. Although, more complex models are clearly needed to address these limitations, the fact that this simplified model predicts intricate patterns of responses to PTH without invoking more complex relationships indicates that these effects may arise from the basic organization of the system.
Results and Discussion
Short application of PTH was found to initiate a bone remodeling cycle (Fig. 1B). First, we assumed that PTH acted on osteoblasts to induce increases in RANKL, which activates osteoclasts. Next, osteoclasts stimulated the slower process of osteoblast formation, leading to an increase in osteoblast numbers. Upon withdrawal of stimulation by PTH/RANKL, osteoclasts were promptly removed from the site. However, because osteoblasts have a much lower turnover rate (1, 25), their numbers were elevated sufficiently long to allow for repair of osteoclast-induced bone loss. Amplitudes of changes in osteoclasts, osteoblasts, and bone mass increased with increases in the amplitude of PTH-induced stimulation. Surprisingly, at high levels of stimulation, osteoblasts overcompensated, resulting in a net gain of bone at the end of the cycle (Fig. 1B). Continuous PTH application was assumed to similarly induce increase in RANKL, resulting in activation of both osteoclasts and osteoblasts. Nevertheless, osteoclastic resorption always preceded bone formation by osteoblasts, resulting in prompt loss of bone (Fig. 1C).
Because the only PTH action in the model was to stimulate osteoclastogenesis, we hypothesized that the anabolic effect of PTH must arise indirectly, as a result of the coupling of osteoblasts to osteoclasts. The parameter describing the coupling, g12, was varied; and the ability of the model to compensate for different levels of PTH-induced increase in RANKL was examined (Fig. 2A). Increasing levels of RANKL ultimately resulted in recruitment of more osteoclasts; therefore the maximal number of osteoclasts recruited was used as a measure of the stimulus strength. Three types of behavior were found in the model. Importantly, at the intermediate level of stimulus, all three types of behavior resulted in a perfect balance, and the difference between different types was evident only when the level of stimulation was changed. In the negatively balanced state, increased stimulation of bone resorption led to progressively insufficient osteoblast activation and net loss of bone. In the perfectly balanced state, any degree of bone resorption resulted in compensatory activation of the precise number of osteoblasts needed to build back as much bone as was resorbed. Finally, in a positively balanced state, osteoblasts were recruited more aggressively than necessary, resulting in net gain of bone. Only when the model was in a positively balanced state, did the increase in proresorptive stimulus result in the overall gain of bone, similar to the anabolic affect of PTH. Interestingly, when the model was in a positively balanced state, insufficient stimulation resulted in negative bone balance, in keeping with known effects of mechanical unloading on bone (36) and recent findings that low levels of RANKL correlate with nontraumatic fractures (37).
To characterize the ability of the system to achieve balance after transient perturbations of different magnitudes, the final bone mass was plotted as a function of the strength of initial stimulation (Fig. 2B). The slope of this relationship characterizes the system as negatively balanced (slope < 0), perfectly balanced (slope = 0), or positively balanced (slope > 0). The role of different parameters in attaining anabolic effects of PTH was further studied.
Alterations in the parameters regulating the magnitude and duration of osteoclast activation were unable to change the anabolic behavior of the system (Fig. 2C; slope > 0 for all parameter values). In contrast, changes in any of the parameters regulating the magnitude and duration of osteoblast activation resulted, at some point, in a switch from positively to negatively balanced behavior of the system (Fig. 2D; at a certain parameter value, the slope becomes negative). These data indicate that, if osteoclast-induced osteoblast activation is hampered, the anabolic effects of PTH on bone can be lost. This prediction is in good agreement with experimental evidence that osteoblast formation, activation, survival, and autocrine regulation through IGF-1 are critical for achieving the anabolic action of PTH (14, 18, 19, 20). Ideally, it would be desirable to have the parameters of the system in a perfectly balanced state. However, if one takes into account age- and disease-related changes in individual factors, it is interesting to speculate that the system is set in a slightly positively balanced state to provide a margin for safety (i.e. to increase the range of changes that would not result in bone loss).
Because the parameters describing the capacity for osteoblast activation appear to be critical in setting the remodeling system in a positively balanced state, the role of a combination of parameters describing the activity of osteoblast production, 2; effectiveness of the osteoblast autocrine regulation, g22; and effectiveness of osteoclast-derived regulation of osteoblasts, g12, in anabolic effects of PTH was further examined. Figure 3 represents a surface that separates the space of parameters where a short increase in resorption above normal levels leads to bone gain from the space of parameters where bone loss results. When parameters take values that belong to the surface itself, the model behaves as perfectly balanced. Inspection of this surface reveals that, whereas anabolic behavior can be achieved at negative values of g22, corresponding to self-inhibition of osteoblasts, only positive values for the activity of osteoblast production and the effectiveness of coupling of osteoblasts to osteoclasts result in anabolic effects of PTH on bone. Thus, the parameters describing activation of osteoblasts are critical in determining whether treatment with PTH will lead to bone gain in an individual remodeling site.
FIG. 3. Parameters regulating the capacity for osteoblast activation determine the overall remodeling balance after PTH administration. The surface separates the space of parameters 2, g22, and g12 into areas where PTH leads to anabolic or catabolic changes in bone mass. The values of parameters 2, g22, and g12 were varied following the grid. For each set of parameters, the changes in bone mass were assessed after a momentary increase in the number of osteoclasts at time 0 by 5, 10, or 15 cells, then final bone mass was plotted as a function of initial stimulation, and the slope of the relationship was calculated. Plotted are the values of 2, g22, and g12 where the slope = 0, and the model demonstrates a perfectly balanced behavior.
We next modeled application of PTH to a site of bone that is already undergoing remodeling. The strength of stimuli for both locally and PTH-induced bone remodeling were chosen at levels that would cause only a balanced change in bone mass (Fig. 4A). PTH application to bone, where remodeling was already in progress, increased both resorption and formation, leading to a net anabolic effect on bone (Fig. 4A). When PTH application was simulated at different stages of bone remodeling, the synergistic effect was most prominent when PTH was applied during the resorption phase (Fig. 4B). Notably, the ability of PTH to induce Ca2+ release from bone was also improved when it was applied to sites already undergoing remodeling. Thus, both actions of PTH (as a proresorptive hormone, inducing rapid release of Ca2+ from bone, and as an anabolic agent) were augmented when bone remodeling was already in progress before PTH administration.
To test the role of osteoclasts in the anabolic actions of PTH on bone, we simulated clinical studies in which PTH was given in combination with antiresorptive agents (21, 22). Bisphosphonates act either by induction of osteoclast apoptosis or by osteoclast inactivation (38, 39). High-amplitude PTH application was chosen, resulting in a prominent anabolic effect on bone mass (Fig. 4C). The simulations were then repeated with increased activity of osteoclast removal, ?1, imitating bisphosphonate-induced osteoclast apoptosis (39). In this case, PTH applications led to smaller increases in osteoclasts, followed by recruitment of fewer osteoblasts; and, as a result, the anabolic effect of PTH on bone was lost (Fig. 4C). Because the coupling of osteoblasts to osteoclasts originates from resorption, suppression of resorptive activity would have the same effect, i.e. decrease in osteoclast-derived paracrine signaling, resulting in inefficient osteoblast stimulation and loss of the anabolic action of PTH. These data are in excellent agreement with seemingly surprising findings that treatment of patients with the antiresorptive agent alendronate impairs the ability of PTH to increase bone mass (21, 22).
Because PTH was also found to affect osteoblast formation, activation, survival, and autocrine regulation through IGF-1 (14, 18, 19, 20), we considered the role for these PTH actions in inducing the anabolic effect on bone. These effects of PTH were modeled as step increases in the values of corresponding parameters (see Materials and Methods). When PTH acted on osteoblasts to simultaneously induce autocrine activation by IGF and production of RANKL, its application resulted in larger net bone gain, compared with effects achieved when the single PTH action was to induce RANKL production (Fig. 4D). However, when PTH acted only to induce autocrine activation of osteoblasts by IGF, negligible effects on bone were observed (Fig. 4D, green line), because much fewer osteoblasts were available to produce IGF and to benefit from its actions. Similarly, when PTH was considered to induce osteoblast formation (by increasing the activity of osteoblast production, 2) or promote osteoblast survival (by decreasing in activity of osteoblast removal, ?2) it was found to be effective only if it simultaneously induced RANKL-mediated stimulation of osteoclasts (data not shown). Therefore, activation of osteoclasts by PTH, either indirectly by RANKL or directly by PTH (40), allows for consequent efficient recruitment of large numbers of osteoblasts, due to the strong coupling between these cell types (30, 31). Thus, the interdependency of these two cell types creates an amplification circuit, where the osteoclasts drive recruitment of osteoblasts, which further benefit from direct actions of PTH on their formation, activation, survival, and autocrine regulation.
Conclusion
In summary, this study proposes a new hypothesis for the role of PTH in the regulation of bone turnover. Here, PTH acts as a proresorptive agent, which stimulates osteoclasts to quickly restore plasma calcium levels. Locally, osteoblasts are effectively coupled to osteoclasts through paracrine factors, therefore PTH application results in activation of both osteoclasts and osteoblasts. Continuous PTH stimulation results in bone loss because bone resorption by more active osteoclasts always precedes bone formation. However, upon PTH withdrawal, osteoclasts are promptly removed, and osteoblasts rebuild bone back to normal levels. Importantly, at certain levels of PTH activation, osteoblasts overcompensate, leading to net gain of bone mass. Thus, the model predicts that the bone cells interact in such a manner that the duration of PTH application can give rise to qualitatively different outcomes, i.e. net bone loss in the one case, and gain of bone mass in the other, without having to assume that bone cells respond differently to continuous and intermittent PTH.
The model identified different roles for parameters important in the anabolic action of PTH on bone remodeling. Parameters describing osteoblast (but not osteoclast) activation were found to be critical in determining whether or not remodeling will result in a gain of bone. Interestingly, different parameters were found to be most effective in initiating the changes that result in the positive remodeling balance. When PTH first activated osteoclasts, due to effective coupling of osteoblasts to osteoclasts in the remodeling unit, PTH-induced osteoclasts intensely recruited osteoblasts, which further benefited from the direct stimulatory actions of PTH.
The present model predicts that, at a single remodeling site, initial loss of bone follows application of PTH, whereas increase in bone formation occurs later. Such a pattern of changes is not commonly observed in vivo after intermittent PTH application (41). In this regard, it is important to note that in vivo PTH affects many sites, which asynchronously undergo remodeling. As shown on Fig. 4A, when PTH is applied to a site already under remodeling: first, much less stimulation by PTH is needed to achieve anabolic effect on bone; and second, the preexisting resorption is stimulated, followed by overcompensation by osteoblasts and positive remodeling balance. Therefore, first the effect of PTH would be seen from the remodeling sites, which existed before PTH application, and later from the newly activated bone remodeling units. Averaging the outcome of remodeling events over the whole skeleton will then result in a continuous, rather than delayed, increase in bone formation, consistent with clinical observations.
Overall, this model provides a simple, coherent explanation for a series of otherwise surprising experimental findings, offering a conceptual framework to explore novel options for anabolic therapies for bone diseases.
Acknowledgments
The author is grateful to Drs. S. Jeffrey Dixon (University of Western Ontario), Eugene V. Mosharov (Columbia University), Lindi M. Wahl (University of Western Ontario), and Peter M. Siegel (McGill University) for their helpful discussions and comments on the manuscript.
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Address all correspondence and requests for reprints to: Dr. Svetlana V. Komarova, Faculty of Dentistry, McGill University, 3640 University Street, Montreal, Quebec, Canada H3A 2B2. E-mail: svetlana.komarova@mcgill.ca
Abstract
To restore falling plasma calcium levels, PTH promotes calcium liberation from bone. PTH targets bone-forming cells, osteoblasts, to increase expression of the cytokine receptor activator of nuclear factor B ligand (RANKL), which then stimulates osteoclastic bone resorption. Intriguingly, whereas continuous administration of PTH decreases bone mass, intermittent PTH has an anabolic effect on bone, which was proposed to arise from direct effects of PTH on osteoblastic bone formation. However, antiresorptive therapies impair the ability of PTH to increase bone mass, indicating a complex role for osteoclasts in the process. We developed a mathematical model that describes the actions of PTH at a single site of bone remodeling, where osteoclasts and osteoblasts are regulated by local autocrine and paracrine factors. It was assumed that PTH acts only to increase the production of RANKL by osteoblasts. As a result, PTH stimulated osteoclasts upon application, followed by compensatory osteoblast activation due to the coupling of osteoblasts to osteoclasts through local paracrine factors. Continuous PTH administration resulted in net bone loss, because bone resorption preceded bone formation at all times. In contrast, over a wide range of model parameters, short application of PTH resulted in a net increase in bone mass, because osteoclasts were rapidly removed upon PTH withdrawal, enabling osteoblasts to rebuild the bone. In excellent agreement with experimental findings, increase in the rate of osteoclast death abolished the anabolic effect of PTH on bone. This study presents an original concept for the regulation of bone remodeling by PTH, currently the only approved anabolic treatment for osteoporosis.
Introduction
BONE REMODELING OCCURS in spatially and temporally discrete sites as a coordinated process involving resorption by osteoclasts, followed by formation of new bone by osteoblasts (1). Multiple factors provide paracrine coupling between osteoclasts and osteoblasts as well as autocrine loops for positive and negative feedback regulation of each cell type (Fig. 1A). Among the most important factors are the proresorptive cytokine receptor activator of nuclear factor B ligand (RANKL) and its decoy receptor osteoprotegerin (OPG), which are expressed by osteoblasts and reciprocally regulate osteoclasts (2). Other factors include TGF?, which is released and activated by resorbing osteoclasts and affects osteoclasts and osteoblasts (3, 4), and IGF, secreted by osteoblasts and released from the matrix by resorbing osteoclasts, which stimulate osteoblast formation (5).
FIG. 1. PTH effect on bone mass depends on the amplitude and duration of stimulation. A, Schematic representation of interactions between osteoclasts and osteoblasts included in the model. Black arrows, Cell formation from precursors (parameters 1,2 describe the activities of cell formation for osteoclasts and osteoblasts, respectively) and cell death (parameters ?1,2 describe the activities of cell removal for osteoclasts and osteoblasts, respectively); red and green arrows, effects of autocrine and paracrine regulators on the rates of osteoclast and osteoblast formation, with parameter g11 describing osteoclast autocrine regulation; g12, osteoclast-derived regulation of osteoblasts; g22, osteoblast autocrine regulation; and g21, osteoblast-derived regulation of osteoclasts. The normalized activities of bone resorption and formation are described with parameters k1,2. PTH was assumed to affect osteoblasts, represented by the blue arrow. B and C, Stimulation with PTH was modeled by an increase in g21 from –0.5 to –0.1 (green), 0.1 (blue), or 0.3 (red) as a 1-d burst (B) or continuously (C). OC, Number of osteoclasts; OB, number of osteoblasts. Changes in bone mass are expressed as a percentage of initial bone mass (100%). Decrease of bone mass to zero percent represents thinning and loss of connectivity of single trabeculae.
Bone remodeling plays a major role in mineral homeostasis, by providing access to stores of calcium and phosphate (6, 7). PTH is secreted in response to a drop in plasma Ca2+ levels. With the goal of maintaining plasma Ca2+, PTH increases bone resorption to release Ca2+ stored in bone. Interestingly, PTH mainly stimulates osteoclasts indirectly, first affecting osteoblasts that have receptors for PTH (8, 9). Acting on osteoblasts, PTH alters expression of RANKL and OPG, leading to a large increase in the RANKL/OPG ratio, thus stimulating osteoclastogenesis and bone resorption (10, 11). Most intriguingly, the overall effect of PTH on bone mass depends primarily on its mode of administration. Whereas a continuous increase in PTH levels decreases bone mass, intermittent PTH administration has an anabolic action on bone (8, 12, 13, 14, 15).
When applied intermittently, PTH acts in a number of ways resulting in an overall increase in bone mass. First, it accelerates bone remodeling (16), both by increasing the number of sites undergoing remodeling and by increasing the turnover of individual sites (17). At each site of bone remodeling, increase in formation is higher than increase in resorption, resulting in a positive remodeling balance. In addition, PTH induces renewed modeling (16, 17). The anabolic action of PTH has been attributed to its direct effects on osteoblastic bone formation (14, 18, 19, 20). However, recently, two clinical trials demonstrated that antiresorptive agents, such as alendronate, attenuate and even impair the bone-forming abilities of PTH (21, 22), suggesting the complex role for osteoclasts in the process (23, 24). Although United States Food and Drug Administration has approved PTH as an anabolic treatment for osteoporosis, the mechanisms underlying its actions remain elusive.
Mathematical modeling provides a powerful tool to predict the net outcome of multiple, simultaneous actions of autocrine, paracrine, and endocrine factors on the process of bone remodeling. Although only few attempts have been made to mathematically reconstruct the process of bone remodeling at a cellular level, there is increasing interest in this approach. In the last few years, two models, one of which was created by our group, were published describing the interactions among osteoclasts and osteoblasts (25, 26); one model describes the changes in cellular activities (27), and two other models were aimed specifically to investigate the mechanism for different effects of PTH administration (28, 29).
Because bone remodeling is involved in both anabolic and catabolic effects of PTH on bone, we extended our model describing interactions among osteoclasts and osteoblasts at a single remodeling site (25), to analyze changes in bone cell numbers and bone mass after PTH administration. PTH was first assumed only to increase RANKL/OPG ratio by changing the expressions of RANKL and OPG by osteoblasts, and thus augmenting the ability of osteoblasts and their precursors to recruit osteoclasts. It is important to note that the kinetics of increase in RANKL/OPG ratio do not directly reflect the duration or frequency of the PTH administration; therefore, within this model, only the following question was asked: can the duration of increase in RANKL/OPG affect the overall balance of a single remodeling cycle? It was found that over a wide range of model parameters, short PTH administrations resulted in anabolic actions on bone, whereas continuous PTH led to bone loss. Anabolic responses to PTH depended mostly on parameters describing the capacity for osteoblast activation in response to preceding increases in osteoclast numbers (30, 31). In agreement with recent experimental findings (21, 22), increasing the rate of osteoclast death abolished the anabolic action of PTH on bone. Next, PTH was assumed to directly promote osteoblast formation and survival. Although these actions of PTH were clearly beneficial, PTH was able to induce considerable bone gain only if, in addition to its effects on osteoblasts, it simultaneously led to osteoclast stimulation. In summary, this model suggests that the complex actions of PTH on bone remodeling may arise from a strong coupling of osteoblasts to osteoclasts.
Materials and Methods
Using ordinary differential equations, the mathematical model describes changes in osteoclast and osteoblast numbers at a single site of bone remodeling within a basic multicellular unit (1, 32). The changes in cell numbers in the model are determined by the rates of production of each cell population (recruitment and differentiation of precursors), and the rates of cell removal (cell death, migration of osteoclasts from the site, differentiation of osteoblasts into osteocytes). We assumed that local effectors regulate only the processes of osteoblast and osteoclast formation, whereas systemic effectors can regulate both cell formation and cell death. To summarize the net effect of local factors on the rates of cell production, a power-law approximation was employed (25, 33, 34). Populations of osteoclasts and osteoblasts under initial steady-state conditions were assumed to consist of less differentiated cells able only to participate in autocrine and paracrine signaling. Increases in numbers of osteoclasts and osteoblasts above steady-state levels were attributed to the proliferation and differentiation of precursors into mature cells able to remove or build bone. The rates of bone resorption and formation were assumed to be proportional to the numbers of osteoclasts and osteoblasts (respectively) exceeding initial steady-state levels. Because resident bone cells do not have an ability to predict the duration for which the systemic factor is present, it was assumed that locally cells respond to the PTH in the same manner independently of the duration of its administration. First PTH was modeled to induce increases only in the RANKL/OPG ratio, an effect shown to follow both intermittent and continuous PTH administration (14, 35). This effect of PTH was modeled as a step increase in the parameter describing osteoblast-derived osteoclast regulation, g21. Later, PTH was also modeled to promote osteoblast responsiveness to stimulatory factors (as a step increase in osteoblast autocrine regulation, g22), the rate of osteoblast formation (as a step increase in activity of osteoblast production, 2), or osteoblast survival (as a step decrease in activity of osteoblast removal, ?2).
These assumptions resulted in the following system of differential equations:
(1)
(2)
(3)
(4)
(5)
where x1 and x2 are the numbers of osteoclasts and osteoblasts respectively; z is total bone mass; i are activities of cell production; ?i are activities of cell removal; gij are parameters describing osteoclast autocrine regulation (g11), osteoclast-derived regulation of osteoblasts (g12), osteoblast autocrine regulation (g22), and osteoblast-derived regulation of osteoclasts (g21); ki are normalized activities of bone resorption and formation; i are the numbers of cells at initial steady-state; yi are the numbers of cells actively resorbing or forming bone; t0 is the time of PTH application; and d is the duration of changes in RANKL/OPG induced by PTH. With one exception (see Fig. 4B), PTH application was started at t0 = 1 d.
FIG. 4. Role of osteoclasts in the anabolic effects of PTH on bone. A, Effect of PTH at the site undergoing bone remodeling. Local stimulation was assumed to result in a momentary increase in the number of osteoclasts by 10 cells at time zero (red). Stimulation with PTH was modeled by an increase in g21 from –0.5 to 0 for 1 d starting at time = 1 d, either at a quiescent bone (blue) or after stimulation by local stimulus (purple). B, Effect of PTH application at different phases of local stimulus-induced bone remodeling. Changes in bone mass were calculated after increases in g21 for 1 d from –0.5 to 0.2 at d 1, 10, 30, 50, or 80 (black) after local stimulation. The red line indicates the effect of local stimulus alone (same as red line in Fig. 4A). C, Antiresorptive agents impair the ability of PTH to increase bone mass. Stimulation with PTH was modeled by an increase in g21 from –0.5 to 0.3 for 1 d. To model the increase in osteoclast death due to treatment with bisphosphonates (Bisph.) the rate constant of osteoclast removal ?1 was increased from 0.2 (red) to 0.4 (blue) or 0.8 (green). D, Role for direct action of PTH on osteoblasts in the anabolic effect of PTH on bone. Effects of PTH were modeled by an increase for 1 d either in osteoblast autocrine regulation, g22, from 0 to 0.1 (green); or in g22 from 0 to 0.1 and osteoblast-derived osteoclast regulation, g21, from –0.5 to 0.3 (purple); or only in g21 from –0.5 to 0.3 (red). OC, Number of osteoclasts; OB, number of osteoblasts. Changes in bone mass are expressed as a percentage of initial bone mass (100%).
The stability of steady-state solutions of the system of equations 1 and 2 was previously analyzed analytically, and the dynamic behavior of the system of equations 1–4 using numerical integration (25). The parameters of the model in this study were chosen to be the same as those describing a stable node type behavior of a single bone remodeling cycle (25): 1 = 3 cells(d)–1; ?1 = 0.2 (d)–1; 2 = 4 (d)–1; ?2 = 0.02 (d)–1; g11 = 0.5; g21 = –0.5; g12 = 1; g22 = 0; k1 = 0.24% (cell)–1 (d)–1; k2 = 0.0017% (cell)–1 (d)–1. It is important to note that, in keeping with the histomorphometric data (1), the rate of osteoclast turnover in the model is approximately 10 times higher than the rate of turnover of osteoblasts, whereas the normalized activity of bone resorption by single osteoclast is approximately 1000 times higher than the normalized activity of bone formation by a single osteoblast. Model 1–5 was analyzed using numerical integration by a fourth order Runge-Kutta algorithm using Berkeley Madonna version 8.0.1 (R. I. Macey, G. F. Oster, University of California at Berkeley).
In calculations for Fig. 2A, the parameters for normalized activities of bone resorption and formation were adjusted for illustrative purposes, so that 100% remodeling would be achieved in response to intermediate stimulations. The calculations were performed with the same parameter values except the following: Fig. 2A, left, g12 = 0.5, k2 = 0.005; Fig. 2A, middle, g12 = 0.98, k2 = 0.0017; Fig. 2A, right, g12 = 1.4, k2 = 0.00075.
FIG. 2. Effective coupling of osteoblasts to osteoclasts is essential for anabolic effect of PTH. A, Parameter describing osteoclast-derived regulation of osteoblasts, g12, was 0.5 (left), 0.98 (middle), or 1.4 (right). The model was initially balanced to achieve 100% remodeling in response to intermediate stimulations (see Materials and Methods). Changes in bone mass were calculated in response to PTH application modeled as an increase in g21 for 1 d from –0.5 to 0 (green), 0.1 (blue), or 0.15 (red). Vertical lines indicate time when bone mass reached final value. B, Final bone mass was plotted as a function of stimulus strength, which was determined by a number of osteoclast activated in response to PTH application. C and D, Initial parameters were chosen to be at slightly positively balanced state (g12 = 1). Single parameter was gradually altered, and changes in bone mass were assessed after a momentary increase in the number of osteoclasts at time 0 by 5, 10, or 15 cells. For each parameter value, final bone mass was plotted as a function of initial stimulation, and the slope of the relationship was calculated. This slope was then plotted as a function of parameter value. C, Parameters regulating magnitude and duration of osteoclast activation. D, Parameters regulating magnitude and duration of osteoblast activation.
The model is considerably simplified, which resulted in a number of limitations, including: 1) only two cell types were considered, 2) only formation of osteoclasts and osteoblasts were regulated by local paracrine and autocrine factors, and 3) parameters describing the effectiveness of autocrine and paracrine regulation included the actions of multiple factors. Although, more complex models are clearly needed to address these limitations, the fact that this simplified model predicts intricate patterns of responses to PTH without invoking more complex relationships indicates that these effects may arise from the basic organization of the system.
Results and Discussion
Short application of PTH was found to initiate a bone remodeling cycle (Fig. 1B). First, we assumed that PTH acted on osteoblasts to induce increases in RANKL, which activates osteoclasts. Next, osteoclasts stimulated the slower process of osteoblast formation, leading to an increase in osteoblast numbers. Upon withdrawal of stimulation by PTH/RANKL, osteoclasts were promptly removed from the site. However, because osteoblasts have a much lower turnover rate (1, 25), their numbers were elevated sufficiently long to allow for repair of osteoclast-induced bone loss. Amplitudes of changes in osteoclasts, osteoblasts, and bone mass increased with increases in the amplitude of PTH-induced stimulation. Surprisingly, at high levels of stimulation, osteoblasts overcompensated, resulting in a net gain of bone at the end of the cycle (Fig. 1B). Continuous PTH application was assumed to similarly induce increase in RANKL, resulting in activation of both osteoclasts and osteoblasts. Nevertheless, osteoclastic resorption always preceded bone formation by osteoblasts, resulting in prompt loss of bone (Fig. 1C).
Because the only PTH action in the model was to stimulate osteoclastogenesis, we hypothesized that the anabolic effect of PTH must arise indirectly, as a result of the coupling of osteoblasts to osteoclasts. The parameter describing the coupling, g12, was varied; and the ability of the model to compensate for different levels of PTH-induced increase in RANKL was examined (Fig. 2A). Increasing levels of RANKL ultimately resulted in recruitment of more osteoclasts; therefore the maximal number of osteoclasts recruited was used as a measure of the stimulus strength. Three types of behavior were found in the model. Importantly, at the intermediate level of stimulus, all three types of behavior resulted in a perfect balance, and the difference between different types was evident only when the level of stimulation was changed. In the negatively balanced state, increased stimulation of bone resorption led to progressively insufficient osteoblast activation and net loss of bone. In the perfectly balanced state, any degree of bone resorption resulted in compensatory activation of the precise number of osteoblasts needed to build back as much bone as was resorbed. Finally, in a positively balanced state, osteoblasts were recruited more aggressively than necessary, resulting in net gain of bone. Only when the model was in a positively balanced state, did the increase in proresorptive stimulus result in the overall gain of bone, similar to the anabolic affect of PTH. Interestingly, when the model was in a positively balanced state, insufficient stimulation resulted in negative bone balance, in keeping with known effects of mechanical unloading on bone (36) and recent findings that low levels of RANKL correlate with nontraumatic fractures (37).
To characterize the ability of the system to achieve balance after transient perturbations of different magnitudes, the final bone mass was plotted as a function of the strength of initial stimulation (Fig. 2B). The slope of this relationship characterizes the system as negatively balanced (slope < 0), perfectly balanced (slope = 0), or positively balanced (slope > 0). The role of different parameters in attaining anabolic effects of PTH was further studied.
Alterations in the parameters regulating the magnitude and duration of osteoclast activation were unable to change the anabolic behavior of the system (Fig. 2C; slope > 0 for all parameter values). In contrast, changes in any of the parameters regulating the magnitude and duration of osteoblast activation resulted, at some point, in a switch from positively to negatively balanced behavior of the system (Fig. 2D; at a certain parameter value, the slope becomes negative). These data indicate that, if osteoclast-induced osteoblast activation is hampered, the anabolic effects of PTH on bone can be lost. This prediction is in good agreement with experimental evidence that osteoblast formation, activation, survival, and autocrine regulation through IGF-1 are critical for achieving the anabolic action of PTH (14, 18, 19, 20). Ideally, it would be desirable to have the parameters of the system in a perfectly balanced state. However, if one takes into account age- and disease-related changes in individual factors, it is interesting to speculate that the system is set in a slightly positively balanced state to provide a margin for safety (i.e. to increase the range of changes that would not result in bone loss).
Because the parameters describing the capacity for osteoblast activation appear to be critical in setting the remodeling system in a positively balanced state, the role of a combination of parameters describing the activity of osteoblast production, 2; effectiveness of the osteoblast autocrine regulation, g22; and effectiveness of osteoclast-derived regulation of osteoblasts, g12, in anabolic effects of PTH was further examined. Figure 3 represents a surface that separates the space of parameters where a short increase in resorption above normal levels leads to bone gain from the space of parameters where bone loss results. When parameters take values that belong to the surface itself, the model behaves as perfectly balanced. Inspection of this surface reveals that, whereas anabolic behavior can be achieved at negative values of g22, corresponding to self-inhibition of osteoblasts, only positive values for the activity of osteoblast production and the effectiveness of coupling of osteoblasts to osteoclasts result in anabolic effects of PTH on bone. Thus, the parameters describing activation of osteoblasts are critical in determining whether treatment with PTH will lead to bone gain in an individual remodeling site.
FIG. 3. Parameters regulating the capacity for osteoblast activation determine the overall remodeling balance after PTH administration. The surface separates the space of parameters 2, g22, and g12 into areas where PTH leads to anabolic or catabolic changes in bone mass. The values of parameters 2, g22, and g12 were varied following the grid. For each set of parameters, the changes in bone mass were assessed after a momentary increase in the number of osteoclasts at time 0 by 5, 10, or 15 cells, then final bone mass was plotted as a function of initial stimulation, and the slope of the relationship was calculated. Plotted are the values of 2, g22, and g12 where the slope = 0, and the model demonstrates a perfectly balanced behavior.
We next modeled application of PTH to a site of bone that is already undergoing remodeling. The strength of stimuli for both locally and PTH-induced bone remodeling were chosen at levels that would cause only a balanced change in bone mass (Fig. 4A). PTH application to bone, where remodeling was already in progress, increased both resorption and formation, leading to a net anabolic effect on bone (Fig. 4A). When PTH application was simulated at different stages of bone remodeling, the synergistic effect was most prominent when PTH was applied during the resorption phase (Fig. 4B). Notably, the ability of PTH to induce Ca2+ release from bone was also improved when it was applied to sites already undergoing remodeling. Thus, both actions of PTH (as a proresorptive hormone, inducing rapid release of Ca2+ from bone, and as an anabolic agent) were augmented when bone remodeling was already in progress before PTH administration.
To test the role of osteoclasts in the anabolic actions of PTH on bone, we simulated clinical studies in which PTH was given in combination with antiresorptive agents (21, 22). Bisphosphonates act either by induction of osteoclast apoptosis or by osteoclast inactivation (38, 39). High-amplitude PTH application was chosen, resulting in a prominent anabolic effect on bone mass (Fig. 4C). The simulations were then repeated with increased activity of osteoclast removal, ?1, imitating bisphosphonate-induced osteoclast apoptosis (39). In this case, PTH applications led to smaller increases in osteoclasts, followed by recruitment of fewer osteoblasts; and, as a result, the anabolic effect of PTH on bone was lost (Fig. 4C). Because the coupling of osteoblasts to osteoclasts originates from resorption, suppression of resorptive activity would have the same effect, i.e. decrease in osteoclast-derived paracrine signaling, resulting in inefficient osteoblast stimulation and loss of the anabolic action of PTH. These data are in excellent agreement with seemingly surprising findings that treatment of patients with the antiresorptive agent alendronate impairs the ability of PTH to increase bone mass (21, 22).
Because PTH was also found to affect osteoblast formation, activation, survival, and autocrine regulation through IGF-1 (14, 18, 19, 20), we considered the role for these PTH actions in inducing the anabolic effect on bone. These effects of PTH were modeled as step increases in the values of corresponding parameters (see Materials and Methods). When PTH acted on osteoblasts to simultaneously induce autocrine activation by IGF and production of RANKL, its application resulted in larger net bone gain, compared with effects achieved when the single PTH action was to induce RANKL production (Fig. 4D). However, when PTH acted only to induce autocrine activation of osteoblasts by IGF, negligible effects on bone were observed (Fig. 4D, green line), because much fewer osteoblasts were available to produce IGF and to benefit from its actions. Similarly, when PTH was considered to induce osteoblast formation (by increasing the activity of osteoblast production, 2) or promote osteoblast survival (by decreasing in activity of osteoblast removal, ?2) it was found to be effective only if it simultaneously induced RANKL-mediated stimulation of osteoclasts (data not shown). Therefore, activation of osteoclasts by PTH, either indirectly by RANKL or directly by PTH (40), allows for consequent efficient recruitment of large numbers of osteoblasts, due to the strong coupling between these cell types (30, 31). Thus, the interdependency of these two cell types creates an amplification circuit, where the osteoclasts drive recruitment of osteoblasts, which further benefit from direct actions of PTH on their formation, activation, survival, and autocrine regulation.
Conclusion
In summary, this study proposes a new hypothesis for the role of PTH in the regulation of bone turnover. Here, PTH acts as a proresorptive agent, which stimulates osteoclasts to quickly restore plasma calcium levels. Locally, osteoblasts are effectively coupled to osteoclasts through paracrine factors, therefore PTH application results in activation of both osteoclasts and osteoblasts. Continuous PTH stimulation results in bone loss because bone resorption by more active osteoclasts always precedes bone formation. However, upon PTH withdrawal, osteoclasts are promptly removed, and osteoblasts rebuild bone back to normal levels. Importantly, at certain levels of PTH activation, osteoblasts overcompensate, leading to net gain of bone mass. Thus, the model predicts that the bone cells interact in such a manner that the duration of PTH application can give rise to qualitatively different outcomes, i.e. net bone loss in the one case, and gain of bone mass in the other, without having to assume that bone cells respond differently to continuous and intermittent PTH.
The model identified different roles for parameters important in the anabolic action of PTH on bone remodeling. Parameters describing osteoblast (but not osteoclast) activation were found to be critical in determining whether or not remodeling will result in a gain of bone. Interestingly, different parameters were found to be most effective in initiating the changes that result in the positive remodeling balance. When PTH first activated osteoclasts, due to effective coupling of osteoblasts to osteoclasts in the remodeling unit, PTH-induced osteoclasts intensely recruited osteoblasts, which further benefited from the direct stimulatory actions of PTH.
The present model predicts that, at a single remodeling site, initial loss of bone follows application of PTH, whereas increase in bone formation occurs later. Such a pattern of changes is not commonly observed in vivo after intermittent PTH application (41). In this regard, it is important to note that in vivo PTH affects many sites, which asynchronously undergo remodeling. As shown on Fig. 4A, when PTH is applied to a site already under remodeling: first, much less stimulation by PTH is needed to achieve anabolic effect on bone; and second, the preexisting resorption is stimulated, followed by overcompensation by osteoblasts and positive remodeling balance. Therefore, first the effect of PTH would be seen from the remodeling sites, which existed before PTH application, and later from the newly activated bone remodeling units. Averaging the outcome of remodeling events over the whole skeleton will then result in a continuous, rather than delayed, increase in bone formation, consistent with clinical observations.
Overall, this model provides a simple, coherent explanation for a series of otherwise surprising experimental findings, offering a conceptual framework to explore novel options for anabolic therapies for bone diseases.
Acknowledgments
The author is grateful to Drs. S. Jeffrey Dixon (University of Western Ontario), Eugene V. Mosharov (Columbia University), Lindi M. Wahl (University of Western Ontario), and Peter M. Siegel (McGill University) for their helpful discussions and comments on the manuscript.
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