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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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OPG production by tumor.A Starting from the initial conditions described in Figure 3, the RANKL and OPG concentrations, the osteoclast population density (OC) and the tumor density (Tumor) are shown after 30, 60 and 90 days, respectively. The growing tumor produces OPG at rates  (green) and  (blue), with a control case  (red). Length of domain is , and only the right halves of the symmetric fields are shown. Scales are as in Figure 4, and OPG is in pmol/mm. BLeft: zoom in on RANKL at 90 days in panel A. Right: the RANKL gradients are obtained by taking the spatial derivatives of the respective fields. C The simulation described in panel A is repeated for different initial RANKL levels , and different levels of OPG production by cancer cells . After 90 days, the following quantities are shown: distance traveled by osteoclasts (Distance), total number of active osteoclasts (OC), and total tumor mass (Tumor).
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pcbi-1002703-g005: OPG production by tumor.A Starting from the initial conditions described in Figure 3, the RANKL and OPG concentrations, the osteoclast population density (OC) and the tumor density (Tumor) are shown after 30, 60 and 90 days, respectively. The growing tumor produces OPG at rates (green) and (blue), with a control case (red). Length of domain is , and only the right halves of the symmetric fields are shown. Scales are as in Figure 4, and OPG is in pmol/mm. BLeft: zoom in on RANKL at 90 days in panel A. Right: the RANKL gradients are obtained by taking the spatial derivatives of the respective fields. C The simulation described in panel A is repeated for different initial RANKL levels , and different levels of OPG production by cancer cells . After 90 days, the following quantities are shown: distance traveled by osteoclasts (Distance), total number of active osteoclasts (OC), and total tumor mass (Tumor).

Mentions: Next, we assess how the local production of OPG by cancer cells affects the progression of bone metastases. We consider system (6) in absence of the PTHrP equation, set , and repeat the same scenario for varying levels of osteoprotegerin production , see Figure 5-A (a dynamic representation of these simulations is found in Video S1). In comparison to the control case with no OPG expression (), higher levels of OPG production by cancer cells ( and ) lead to an increase in osteoclast advance (see OC after 90 days), and hence a bigger resorption area. A closer look at the RANKL field after 90 days in Figure 5-B reveals that tumor-produced OPG removes residual RANKL left behind the remodeling front, resulting in the formation of steeper RANKL gradients, and hence increased speed of osteoclast migration. Note that the RANKL gradients of in our simulations are consistent with the gradients of which were shown to induce osteoclast chemotaxis in experimental studies [16]. In Figure 5-C, we present a systematic study of the effect of OPG production by cancer cells on osteoclast migration, the number of active osteoclasts and tumor mass. These results demonstrate that the interplay of two main factors is important in determining the overall outcome of OPG action. First, the OPG-induced increase in RANKL gradient and osteoclast speed (evident by the distance traveled in 90 days) is accompanied by a decrease in the number of active osteoclasts. This results in a non-trivial dependence of the tumor mass on the rate of OPG production by cancer cells. While low and intermediate expression of osteoprotegerin by cancer cells correlates with an increase in osteolysis and hence tumor burden, at high OPG expression, the remodeling front is too small to completely resorb all bone tissue, leading to an overall decrease in tumor mass. Second, the effect of tumor-produced OPG strongly depends on the levels of RANKL in the bone tissue: at low RANKL levels, OPG is predominantly inhibitory, while at high RANKL levels, tumor-produced OPG becomes more effective in inducing osteolysis (Figure 5-C, compare and ). Thus, the model predicts the existence of two different regimes for the impact of tumor-produced OPG, which correspond well to experimental findings of inhibition of osteolysis by cancer cell–produced OPG [9], and stimulation of osteolysis by cancer cell–produced OPG [12].


Osteoprotegerin in bone metastases: mathematical solution to the puzzle.

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

OPG production by tumor.A Starting from the initial conditions described in Figure 3, the RANKL and OPG concentrations, the osteoclast population density (OC) and the tumor density (Tumor) are shown after 30, 60 and 90 days, respectively. The growing tumor produces OPG at rates  (green) and  (blue), with a control case  (red). Length of domain is , and only the right halves of the symmetric fields are shown. Scales are as in Figure 4, and OPG is in pmol/mm. BLeft: zoom in on RANKL at 90 days in panel A. Right: the RANKL gradients are obtained by taking the spatial derivatives of the respective fields. C The simulation described in panel A is repeated for different initial RANKL levels , and different levels of OPG production by cancer cells . After 90 days, the following quantities are shown: distance traveled by osteoclasts (Distance), total number of active osteoclasts (OC), and total tumor mass (Tumor).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1002703-g005: OPG production by tumor.A Starting from the initial conditions described in Figure 3, the RANKL and OPG concentrations, the osteoclast population density (OC) and the tumor density (Tumor) are shown after 30, 60 and 90 days, respectively. The growing tumor produces OPG at rates (green) and (blue), with a control case (red). Length of domain is , and only the right halves of the symmetric fields are shown. Scales are as in Figure 4, and OPG is in pmol/mm. BLeft: zoom in on RANKL at 90 days in panel A. Right: the RANKL gradients are obtained by taking the spatial derivatives of the respective fields. C The simulation described in panel A is repeated for different initial RANKL levels , and different levels of OPG production by cancer cells . After 90 days, the following quantities are shown: distance traveled by osteoclasts (Distance), total number of active osteoclasts (OC), and total tumor mass (Tumor).
Mentions: Next, we assess how the local production of OPG by cancer cells affects the progression of bone metastases. We consider system (6) in absence of the PTHrP equation, set , and repeat the same scenario for varying levels of osteoprotegerin production , see Figure 5-A (a dynamic representation of these simulations is found in Video S1). In comparison to the control case with no OPG expression (), higher levels of OPG production by cancer cells ( and ) lead to an increase in osteoclast advance (see OC after 90 days), and hence a bigger resorption area. A closer look at the RANKL field after 90 days in Figure 5-B reveals that tumor-produced OPG removes residual RANKL left behind the remodeling front, resulting in the formation of steeper RANKL gradients, and hence increased speed of osteoclast migration. Note that the RANKL gradients of in our simulations are consistent with the gradients of which were shown to induce osteoclast chemotaxis in experimental studies [16]. In Figure 5-C, we present a systematic study of the effect of OPG production by cancer cells on osteoclast migration, the number of active osteoclasts and tumor mass. These results demonstrate that the interplay of two main factors is important in determining the overall outcome of OPG action. First, the OPG-induced increase in RANKL gradient and osteoclast speed (evident by the distance traveled in 90 days) is accompanied by a decrease in the number of active osteoclasts. This results in a non-trivial dependence of the tumor mass on the rate of OPG production by cancer cells. While low and intermediate expression of osteoprotegerin by cancer cells correlates with an increase in osteolysis and hence tumor burden, at high OPG expression, the remodeling front is too small to completely resorb all bone tissue, leading to an overall decrease in tumor mass. Second, the effect of tumor-produced OPG strongly depends on the levels of RANKL in the bone tissue: at low RANKL levels, OPG is predominantly inhibitory, while at high RANKL levels, tumor-produced OPG becomes more effective in inducing osteolysis (Figure 5-C, compare and ). Thus, the model predicts the existence of two different regimes for the impact of tumor-produced OPG, which correspond well to experimental findings of inhibition of osteolysis by cancer cell–produced OPG [9], and stimulation of osteolysis by cancer cell–produced OPG [12].

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