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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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Direct RANKL production by tumor.Starting from the initial conditions described in Figure 3, the RANKL concentration, the osteoclast population density (OC) and the tumor density (Tumor) are shown at 30 and 60 days, respectively. The initial host-tissue level of RANKL is . For , RANKL is produced by the tumor at varying rates . Length of domain is , only the right halves of the symmetric fields are shown, the units of the y-axes are as in Figure 4.
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pcbi-1002703-g006: Direct RANKL production by tumor.Starting from the initial conditions described in Figure 3, the RANKL concentration, the osteoclast population density (OC) and the tumor density (Tumor) are shown at 30 and 60 days, respectively. The initial host-tissue level of RANKL is . For , RANKL is produced by the tumor at varying rates . Length of domain is , only the right halves of the symmetric fields are shown, the units of the y-axes are as in Figure 4.

Mentions: Since high levels of RANKL in the tissue are important for the osteolysis-enhancing effects of OPG, we assess now if cancer cells could promote osteolysis by directly producing RANKL. We model this situation by adding a tumor-derived RANKL source to the -equation, i.e. we solve system (6) in absence of the OPG and PTHrP fields, set , and repeat the same scenario for varying values of . Note in particular that for this scenario it is necessary to model the osteoclast-stimulation rate to be dependent on the bone density (see Text S1 for details), i.e. we replace the reaction term in the osteoclast equation of (6) byAs shown in Figure 6, the tumor-derived production of RANKL leads to a reversal of the RANKL gradient. Rather than moving away from the tumor and resorbing more bone to provide new space for proliferating cancer cells, osteoclasts move towards the tumor. Consequently, no traveling remodeling front is formed, osteolysis is disrupted, and tumor growth decreases with increase in RANKL production rate . Although the RANK-RANKL dynamics are known to play an important role in bone metastases [16], [39], there is uncertainty regarding the actual source of RANKL. While some studies report direct expression of RANKL by metastasizing squamuous cell carcinoma and prostate cancer cells [42], [43], others suggest that there is no direct production of RANKL by cancer cells [44], [45]. In addition, it has been shown that breast cancer cells cease to express RANKL upon embedding into the bone environment [46]. Our simulations suggest that expression of RANKL does not provide cancer cells with an advantage in the bone microenvironment.


Osteoprotegerin in bone metastases: mathematical solution to the puzzle.

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

Direct RANKL production by tumor.Starting from the initial conditions described in Figure 3, the RANKL concentration, the osteoclast population density (OC) and the tumor density (Tumor) are shown at 30 and 60 days, respectively. The initial host-tissue level of RANKL is . For , RANKL is produced by the tumor at varying rates . Length of domain is , only the right halves of the symmetric fields are shown, the units of the y-axes are as in Figure 4.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002703-g006: Direct RANKL production by tumor.Starting from the initial conditions described in Figure 3, the RANKL concentration, the osteoclast population density (OC) and the tumor density (Tumor) are shown at 30 and 60 days, respectively. The initial host-tissue level of RANKL is . For , RANKL is produced by the tumor at varying rates . Length of domain is , only the right halves of the symmetric fields are shown, the units of the y-axes are as in Figure 4.
Mentions: Since high levels of RANKL in the tissue are important for the osteolysis-enhancing effects of OPG, we assess now if cancer cells could promote osteolysis by directly producing RANKL. We model this situation by adding a tumor-derived RANKL source to the -equation, i.e. we solve system (6) in absence of the OPG and PTHrP fields, set , and repeat the same scenario for varying values of . Note in particular that for this scenario it is necessary to model the osteoclast-stimulation rate to be dependent on the bone density (see Text S1 for details), i.e. we replace the reaction term in the osteoclast equation of (6) byAs shown in Figure 6, the tumor-derived production of RANKL leads to a reversal of the RANKL gradient. Rather than moving away from the tumor and resorbing more bone to provide new space for proliferating cancer cells, osteoclasts move towards the tumor. Consequently, no traveling remodeling front is formed, osteolysis is disrupted, and tumor growth decreases with increase in RANKL production rate . Although the RANK-RANKL dynamics are known to play an important role in bone metastases [16], [39], there is uncertainty regarding the actual source of RANKL. While some studies report direct expression of RANKL by metastasizing squamuous cell carcinoma and prostate cancer cells [42], [43], others suggest that there is no direct production of RANKL by cancer cells [44], [45]. In addition, it has been shown that breast cancer cells cease to express RANKL upon embedding into the bone environment [46]. Our simulations suggest that expression of RANKL does not provide cancer cells with an advantage in the bone microenvironment.

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