Osteoprotegerin in Bone Metastases: Mathematical Solution to the Puzzle
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{"title"=>"Osteoprotegerin in Bone Metastases: Mathematical Solution to the Puzzle", "type"=>"journal", "authors"=>[{"first_name"=>"Marc D.", "last_name"=>"Ryser", "scopus_author_id"=>"26633370000"}, {"first_name"=>"Yiding", "last_name"=>"Qu", "scopus_author_id"=>"55440530300"}, {"first_name"=>"Svetlana V.", "last_name"=>"Komarova", "scopus_author_id"=>"6701498558"}], "year"=>2012, "source"=>"PLoS Computational Biology", "identifiers"=>{"scopus"=>"2-s2.0-84868131986", "pmid"=>"23093918", "sgr"=>"84868131986", "doi"=>"10.1371/journal.pcbi.1002703", "isbn"=>"1553-7358 (Electronic)\\r1553-734X (Linking)", "issn"=>"1553734X", "pui"=>"365953593"}, "id"=>"5daf04c5-08b0-37b0-8cdd-d22a80407050", "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.", "link"=>"http://www.mendeley.com/research/osteoprotegerin-bone-metastases-mathematical-solution-puzzle", "reader_count"=>28, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>3, "Researcher"=>5, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>8, "Student > Postgraduate"=>1, "Student > Master"=>4, "Other"=>4, "Student > Bachelor"=>1, "Professor"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>3, "Researcher"=>5, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>8, "Student > Postgraduate"=>1, "Student > Master"=>4, "Other"=>4, "Student > Bachelor"=>1, "Professor"=>1}, "reader_count_by_subject_area"=>{"Engineering"=>5, "Unspecified"=>1, "Biochemistry, Genetics and Molecular Biology"=>3, "Mathematics"=>5, "Agricultural and Biological Sciences"=>7, "Medicine and Dentistry"=>5, "Physics and Astronomy"=>2}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>5}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>5}, "Physics and Astronomy"=>{"Physics and Astronomy"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>7}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>3}, "Mathematics"=>{"Mathematics"=>5}, "Unspecified"=>{"Unspecified"=>1}}, "reader_count_by_country"=>{"United States"=>1, "United Kingdom"=>1}, "group_count"=>1}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/296269", "https://ndownloader.figshare.com/files/296408", "https://ndownloader.figshare.com/files/296537"], "description"=>"<div><p>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.</p> </div>", "links"=>[], "tags"=>["osteoprotegerin", "mathematical"], "article_id"=>118368, "categories"=>["Physiology"], "users"=>["Marc D. Ryser", "Yiding Qu", "Svetlana V. Komarova"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002703.s001", "https://dx.doi.org/10.1371/journal.pcbi.1002703.s002", "https://dx.doi.org/10.1371/journal.pcbi.1002703.s003"], "stats"=>{"downloads"=>37, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Osteoprotegerin_in_Bone_Metastases_Mathematical_Solution_to_the_Puzzle/118368", "title"=>"Osteoprotegerin in Bone Metastases: Mathematical Solution to the Puzzle", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2012-10-18 02:19:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/556024"], "description"=>"<p>The set of initial conditions used for all simulations of the study. The initial RANKL field consists of host–tissue RANKL only, and is of constant concentration . The initial profile of active osteoclasts (OC) is placed in the middle of the domain. Initially, there is no tumor present. Not shown above are the following fields: the bone tissue is intact, i.e. , and the OPG and PTHrP concentrations are uniformly zero. Note that the initial conditions are consistent with the choice of periodic boundary conditions.</p>", "links"=>[], "tags"=>["physiology"], "article_id"=>226529, "categories"=>["Physiology"], "users"=>["Marc D. Ryser", "Yiding Qu", "Svetlana V. Komarova"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002703.g003", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Initial_conditions_/226529", "title"=>"Initial conditions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-18 01:48:49"}
  • {"files"=>["https://ndownloader.figshare.com/files/556350"], "description"=>"<p><b>A</b> Starting from the initial conditions described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002703#pcbi-1002703-g003\" target=\"_blank\">Figure 3</a>, the PTHrP and RANKL concentrations, the osteoclast population density (OC) and the tumor density (Tumor) are shown at 45 and 90 days, respectively. The initial host–tissue level of RANKL is . For , tumor produces PTHrP at rates . Length of domain is , only the right halves of the symmetric fields are shown, the units of the y-axes are as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002703#pcbi-1002703-g004\" target=\"_blank\">Figure 4</a>, and PTHrP has units . <b>B</b> The simulations in A were repeated for the initial host tissue level of RANKL .</p>", "links"=>[], "tags"=>["physiology"], "article_id"=>226850, "categories"=>["Physiology"], "users"=>["Marc D. Ryser", "Yiding Qu", "Svetlana V. Komarova"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002703.g007", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_PTHrP_production_by_tumor_/226850", "title"=>"PTHrP production by tumor.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-18 01:54:10"}
  • {"files"=>["https://ndownloader.figshare.com/files/556281"], "description"=>"<p>Starting from the initial conditions described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002703#pcbi-1002703-g003\" target=\"_blank\">Figure 3</a>, 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 <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002703#pcbi-1002703-g004\" target=\"_blank\">Figure 4</a>.</p>", "links"=>[], "tags"=>["rankl"], "article_id"=>226787, "categories"=>["Physiology"], "users"=>["Marc D. Ryser", "Yiding Qu", "Svetlana V. Komarova"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002703.g006", "stats"=>{"downloads"=>4, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Direct_RANKL_production_by_tumor_/226787", "title"=>"Direct RANKL production by tumor.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-18 01:53:07"}
  • {"files"=>["https://ndownloader.figshare.com/files/556415"], "description"=>"<p><b>A</b> Starting from the initial conditions described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002703#pcbi-1002703-g003\" target=\"_blank\">Figure 3</a>, the PTHrP, RANKL and OPG concentrations, the osteoclast population density (OC) and the tumor density (Tumor) are shown at 30, 60 and 90 days, respectively. The initial RANKL level is . The growing tumor produces PTHrP at a fixed rate , and three different levels of tumor-derived OPG production are considered. Length of the domain is 15 mm, only the right halves of the symmetric fields are shown. Units of the y-axes are as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002703#pcbi-1002703-g007\" target=\"_blank\">Figure 7</a>, and the OPG field has units of . <b>B</b> The simulation described in panel A is performed for varying values of and , and the total tumor mass at 90 days is presented.</p>", "links"=>[], "tags"=>["opg"], "article_id"=>226919, "categories"=>["Physiology"], "users"=>["Marc D. Ryser", "Yiding Qu", "Svetlana V. Komarova"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002703.g008", "stats"=>{"downloads"=>0, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_PTHrP_and_OPG_production_by_tumor_/226919", "title"=>"PTHrP and OPG production by tumor.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-18 01:55:19"}
  • {"files"=>["https://ndownloader.figshare.com/files/555943"], "description"=>"<p>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.</p>", "links"=>[], "tags"=>["physiology"], "article_id"=>226444, "categories"=>["Physiology"], "users"=>["Marc D. Ryser", "Yiding Qu", "Svetlana V. Komarova"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002703.g002", "stats"=>{"downloads"=>2, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_geometry_/226444", "title"=>"Model geometry.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-18 01:47:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/556585"], "description"=>"<p>Variables and parameters in model (6).</p>", "links"=>[], "tags"=>["parameters"], "article_id"=>227085, "categories"=>["Physiology"], "users"=>["Marc D. Ryser", "Yiding Qu", "Svetlana V. Komarova"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002703.t001", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Variables_and_parameters_in_model_6_/227085", "title"=>"Variables and parameters in model (6).", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-10-18 01:58:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/556067"], "description"=>"<p><b>A</b> Starting from the initial conditions described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002703#pcbi-1002703-g003\" target=\"_blank\">Figure 3</a>, the RANKL concentration, osteoclast population density (OC) and tumor density (Tumor) are shown at 30, 60 and 90 days, respectively. The outcomes for three different values of the host-RANKL level are shown. The computational domain is 15 mm long, but since the fields are symmetric, only the right half is shown. The y-axes have the following units: RANKL in pmol/mm; OC in cells/mm; tumor density is normalized between 0, when there is no tumor per unit length, and 1, when the unit space is fully occupied by tumor. The resorption fronts of osteoclasts either reach wave-like propagation () or die out (). <b>B</b> Starting from the initial conditions described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002703#pcbi-1002703-g003\" target=\"_blank\">Figure 3</a>, the evolution of the RANKL concentration, osteoclast population density (OC) and tumor density (Tumor) is shown after 45 and 90 days, respectively. The initial host-RANKL level is , and between 20 and 90 days, a uniform source of OPG is administered at (green) and (blue), respectively. Compared to the control at (red), the respective tumor burdens are reduced.</p>", "links"=>[], "tags"=>["rankl", "systemic"], "article_id"=>226575, "categories"=>["Physiology"], "users"=>["Marc D. Ryser", "Yiding Qu", "Svetlana V. Komarova"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002703.g004", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Host_tissue_RANKL_and_systemic_OPG_/226575", "title"=>"Host tissue RANKL and systemic OPG.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-18 01:49:35"}
  • {"files"=>["https://ndownloader.figshare.com/files/555899"], "description"=>"<p>Two cell types are considered: cancer cells and osteoclasts. Osteoclasts positively affect cancer cells by providing space for tumor growth. Parathyroid hormone-related protein (PTHrP) produced by metastasizing cancer cells induces the expression of receptor activator of nuclear factor kappa-B ligand (RANKL) in bone tissue. RANKL in turn is a potent stimulator of osteoclasts and bone resorption. Osteoprotegerin (OPG) is a decoy receptor of RANKL which binds and eliminates RANKL.</p>", "links"=>[], "tags"=>["taken"], "article_id"=>226396, "categories"=>["Physiology"], "users"=>["Marc D. Ryser", "Yiding Qu", "Svetlana V. Komarova"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002703.g001", "stats"=>{"downloads"=>0, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Interactions_taken_into_account_in_the_study_/226396", "title"=>"Interactions taken into account in the study.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-18 01:46:36"}
  • {"files"=>["https://ndownloader.figshare.com/files/556537"], "description"=>"<p>Data from nine gene expression data sets <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002703#pcbi.1002703-Lapointe1\" target=\"_blank\">[47]</a>–<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002703#pcbi.1002703-Yu1\" target=\"_blank\">[55]</a> were combined and analyzed. <b>A–C</b> Expression of OPG (A), RANKL (B) and PTHrP (C) are shown in the box-plots where the lower whisker indicates the 1st percentile, the limits of the box indicate the 25th and 75th percentiles, and the upper whisker indicates the 99th percentile. Statistical significance is indicated by , , calculated using one-way ANOVA. <b>D–F</b> Data for the metastatic prostate samples were analyzed for the correlation in the expression of OPG and PTHrP (D), OPG and RANKL (E), and RANKL and PTHrP (F).</p>", "links"=>[], "tags"=>["rankl", "pthrp", "prostate"], "article_id"=>227037, "categories"=>["Physiology"], "users"=>["Marc D. Ryser", "Yiding Qu", "Svetlana V. Komarova"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002703.g009", "stats"=>{"downloads"=>4, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_OPG_RANKL_and_PTHrP_expression_in_prostate_cancer_/227037", "title"=>"OPG, RANKL and PTHrP expression in prostate cancer.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-18 01:57:17"}
  • {"files"=>["https://ndownloader.figshare.com/files/556183"], "description"=>"<p><b>A</b> Starting from the initial conditions described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002703#pcbi-1002703-g003\" target=\"_blank\">Figure 3</a>, 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 <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002703#pcbi-1002703-g004\" target=\"_blank\">Figure 4</a>, and OPG is in pmol/mm. <b>B </b><i>Left:</i> zoom in on RANKL at 90 days in panel A. <i>Right:</i> the RANKL gradients are obtained by taking the spatial derivatives of the respective fields. <b>C</b> 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).</p>", "links"=>[], "tags"=>["physiology"], "article_id"=>226687, "categories"=>["Physiology"], "users"=>["Marc D. Ryser", "Yiding Qu", "Svetlana V. Komarova"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1002703.g005", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_OPG_production_by_tumor_/226687", "title"=>"OPG production by tumor.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-10-18 01:51:27"}

PMC Usage Stats | Further Information

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Relative Metric

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