The role of osteocytes in targeted bone remodeling: a mathematical model

Abstract

Until recently many studies of bone remodeling at the cellular level have focused on the behavior of mature osteoblasts and osteoclasts, and their respective precursor cells, with the role of osteocytes and bone lining cells left largely unexplored. This is particularly true with respect to the mathematical modeling of bone remodeling. However, there is increasing evidence that osteocytes play important roles in the cycle of targeted bone remodeling, in serving as a significant source of RANKL to support osteoclastogenesis, and in secreting the bone formation inhibitor sclerostin. Moreover, there is also increasing interest in sclerostin, an osteocyte-secreted bone formation inhibitor, and its role in regulating local response to changes in the bone microenvironment. Here we develop a cell population model of bone remodeling that includes the role of osteocytes, sclerostin, and allows for the possibility of RANKL expression by osteocyte cell populations. We have aimed to give a simple, yet still tractable, model that remains faithful to the underlying system based on the known literature. This model extends and complements many of the existing mathematical models for bone remodeling, but can be used to explore aspects of the process of bone remodeling that were previously beyond the scope of prior modeling work. Through numerical simulations we demonstrate that our model can be used to explore theoretically many of the qualitative features of the role of osteocytes in bone biology as presented in recent literature.

Figure 1. Interactions between bone cell populations.

Figure 2. System of ordinary differential equations constructed, using the biochemical systems analysis formalism –, to model osteocyte-induced targeted bone remodeling.

Figure 3. Dynamics of bone cells during a single event of targeted bone remodeling.

The dynamics of osteocyte (a), pre-osteoblast (b), osteoblast (c), and osteoclast (d) populations during an event of targeted bone remodeling.

Figure 4. Dynamics of bone volume during a single event of targeted bone remodeling.

Figure 5. The steady state bone volume, , as a simultaneous function of the effectiveness of osteocyte paracrine signaling on stromal cell differentiation, , and pre-osteoblast autocrine signaling for pre-osteoblast proliferation, .

Figure 6. The steady state bone volume, , computed as a function of the effectiveness of osteocyte paracrine signaling on stromal cell differentiation, , with all other parameters held at baseline values.

Figure 7. The steady state bone volume, , computed as a function of the effectiveness of pre-osteoblast autocrine signaling for pre-osteoblast proliferation, , with all other parameters held at baseline values.

Figure 8. We simulate the loss of bone mass associated with over resorption in conjunction with a bone degenerative disease, modeled by a slight increase in the value of with all other parameters set to the baseline values listed in table 2.

Figure 9. This figure shows simulation results of treating pathological bone remodeling, as simulated in figure 5, via the addition of an anti-sclerostin drug.

This results in a dose-dependent increase in bone mass. Treatment with an anti-sclerostin drug is modeled by modifying the appropriate signaling mechanisms, that is, by modifying the appropriate exponents and in the power law approximation.