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Osteoprotegerin in bone metastases: mathematical solution to the puzzle.

Ryser MD, Qu Y, Komarova SV - PLoS Comput. Biol. (2012)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Statistics, McGill University, Montréal, Québec, Canada.

ABSTRACT
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.

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Model geometry.Active osteoclasts () resorb bone () along the gradient (red) of the RANKL field (), and move from left to right. The tumor () invades the space previously resorbed by active osteoclasts. Cancer cells produce PTHrP (), which diffuses and induces the expression of additional RANKL by osteoblastic bone cells. Cancer cells also produce OPG () which diffuses, inhibits RANKL, and hence modifies the RANKL–gradient.
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pcbi-1002703-g002: Model geometry.Active osteoclasts () resorb bone () along the gradient (red) of the RANKL field (), and move from left to right. The tumor () invades the space previously resorbed by active osteoclasts. Cancer cells produce PTHrP (), which diffuses and induces the expression of additional RANKL by osteoblastic bone cells. Cancer cells also produce OPG () which diffuses, inhibits RANKL, and hence modifies the RANKL–gradient.

Mentions: We model a single trabecula exposed to bone marrow and pre-existing cancer cells. Hemi-osteonal, trench-like remodeling of trabecular bone [4] reduces the geometry of the problem from three to two spatial dimensions, and assuming that the trabecula is locally flat, the model domain becomes a bounded subset of . Assuming that the growing tumor induces a radially symmetric front of resorbing osteoclasts, we further reduce the model to one spatial dimension along the radial direction of movement (Figure 2). By choosing a unidirectional model of osteoclast propagation, we do not account for potential irregularities in the resorption path. In applied mathematics, it is a well-established methodology to study lower-dimensional versions of a model in question, especially because geometric complexity, potential blow-up phenomena and computational costs make the study of higher-dimensional versions much more involved. Even though the current one-dimensional framework is expected to be sufficient to test our hypothesis, it represents a significant simplication, and a two-dimensional evaluation of the model should be considered in the future.


Osteoprotegerin in bone metastases: mathematical solution to the puzzle.

Ryser MD, Qu Y, Komarova SV - PLoS Comput. Biol. (2012)

Model geometry.Active osteoclasts () resorb bone () along the gradient (red) of the RANKL field (), and move from left to right. The tumor () invades the space previously resorbed by active osteoclasts. Cancer cells produce PTHrP (), which diffuses and induces the expression of additional RANKL by osteoblastic bone cells. Cancer cells also produce OPG () which diffuses, inhibits RANKL, and hence modifies the RANKL–gradient.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3475686&req=5

pcbi-1002703-g002: Model geometry.Active osteoclasts () resorb bone () along the gradient (red) of the RANKL field (), and move from left to right. The tumor () invades the space previously resorbed by active osteoclasts. Cancer cells produce PTHrP (), which diffuses and induces the expression of additional RANKL by osteoblastic bone cells. Cancer cells also produce OPG () which diffuses, inhibits RANKL, and hence modifies the RANKL–gradient.
Mentions: We model a single trabecula exposed to bone marrow and pre-existing cancer cells. Hemi-osteonal, trench-like remodeling of trabecular bone [4] reduces the geometry of the problem from three to two spatial dimensions, and assuming that the trabecula is locally flat, the model domain becomes a bounded subset of . Assuming that the growing tumor induces a radially symmetric front of resorbing osteoclasts, we further reduce the model to one spatial dimension along the radial direction of movement (Figure 2). By choosing a unidirectional model of osteoclast propagation, we do not account for potential irregularities in the resorption path. In applied mathematics, it is a well-established methodology to study lower-dimensional versions of a model in question, especially because geometric complexity, potential blow-up phenomena and computational costs make the study of higher-dimensional versions much more involved. Even though the current one-dimensional framework is expected to be sufficient to test our hypothesis, it represents a significant simplication, and a two-dimensional evaluation of the model should be considered in the future.

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Statistics, McGill University, Montréal, Québec, Canada.

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus