Model structure and control of bone remodeling: A theoretical study

It is generally accepted that RANKL is highly expressed in osteoblast precursor cells while OPG is highly expressed in mature osteoblasts, but to date no functional utility to the BMU has been proposed for this particular ligand–decoy–receptor expression profile. As discovered in the mid 90s, the RANK–RANKL–OPG signaling cascade is a major signaling pathway regulating bone remodeling. In this paper we study theoretically the functional implications of particular RANKL/OPG expression profiles on bone volume. For this purpose we formulate an extended bone–cell dynamics model describing functional behaviour of basic multicellular units (BMUs) responsible for bone resorption and formation. This model incorporates the RANK–RANKL–OPG signaling together with the regulating action of TGF-β on bone cells. The bone–cell population model employed here builds on the work of Lemaire et al. (2004) [1], but incorporates the following significant modifications: (i) addition of a rate equation describing changes in bone volume with time as the key ‘output function’ tracking functional behaviour of BMUs, (ii) a rate equation describing release of TGF-β from the bone matrix, (iii) expression of OPG and RANKL on both osteoblastic cell lines, and (iv) modified activator/repressor functions. Using bone volume as a functional selection criterion, we find that there is a preferred arrangement for ligand expression on particular cell types, and further, that this arrangement coincides with biological observations. We then investigate the model parameter space combinatorially, searching for preferred ‘groupings’ of changes in differentiation rates of various cell types. Again, a criterion of bone volume change is employed to identify possible ways of optimally controlling BMU responses. While some combinations of changes in differentiation rates are clearly unrealistic, other combinations of changes in differentiation rates are potentially functionally significant. Most importantly, the combination of parameter changes representing the signaling pathway for TGF-β gives a unique result that appears to have a clear biological rationale. The methodological approach for the investigation of model structure described here offers a theoretical explanation as to why TGF-β has its particular suite of biological effects on bone–cell differentiation rates.