Osteoprotegerin in Bone Metastases: Mathematical Solution to the Puzzle

Marc D. Ryser, Yiding Qu, Svetlana V. Komarova

Bone is a common site for cancer metastasis. To create space for their growth, cancer cells stimulate bone resorbing osteoclasts. Cytokine RANKL is a key osteoclast activator, while osteoprotegerin (OPG) is a RANKL decoy receptor and an inhibitor of osteoclastogenesis. Consistently, systemic application of OPG decreases metastatic tumor burden in bone. However, OPG produced locally by cancer cells was shown to enhance osteolysis and tumor growth. We propose that OPG produced by cancer cells causes a local reduction in RANKL levels, inducing a steeper RANKL gradient away from the tumor and towards the bone tissue, resulting in faster resorption and tumor expansion. We tested this hypothesis using a mathematical model of nonlinear partial differential equations describing the spatial dynamics of OPG, RANKL, PTHrP, osteoclasts, tumor and bone mass. We demonstrate that at lower expression rates, tumor-derived OPG enhances the chemotactic RANKL gradient and osteolysis, whereas at higher expression rates OPG broadly inhibits RANKL and decreases osteolysis and tumor burden. Moreover, tumor expression of a soluble mediator inducing RANKL in the host tissue, such as PTHrP, is important for correct orientation of the RANKL gradient. A meta-analysis of OPG, RANKL and PTHrP expression in normal prostate, carcinoma and metastatic tissues demonstrated an increase in expression of OPG, but not RANKL, in metastatic prostate cancer, and positive correlation between OPG and PTHrP in metastatic prostate cancer. The proposed mechanism highlights the importance of the spatial distribution of receptors, decoys and ligands, and can be applied to other systems involving regulation of spatially anisotropic processes.