Lee2003 - Roles of APC and Axin in Wnt Pathway (without regulatory loop)
This model is described in the article:
Abstract:
Wnt signaling plays an important role in both oncogenesis and development. Activation of the Wnt pathway results in stabilization of the transcriptional coactivator beta-catenin. Recent studies have demonstrated that axin, which coordinates beta-catenin degradation, is itself degraded. Although the key molecules required for transducing a Wnt signal have been identified, a quantitative understanding of this pathway has been lacking. We have developed a mathematical model for the canonical Wnt pathway that describes the interactions among the core components: Wnt, Frizzled, Dishevelled, GSK3beta, APC, axin, beta-catenin, and TCF. Using a system of differential equations, the model incorporates the kinetics of protein-protein interactions, protein synthesis/degradation, and phosphorylation/dephosphorylation. We initially defined a reference state of kinetic, thermodynamic, and flux data from experiments using Xenopus extracts. Predictions based on the analysis of the reference state were used iteratively to develop a more refined model from which we analyzed the effects of prolonged and transient Wnt stimulation on beta-catenin and axin turnover. We predict several unusual features of the Wnt pathway, some of which we tested experimentally. An insight from our model, which we confirmed experimentally, is that the two scaffold proteins axin and APC promote the formation of degradation complexes in very different ways. We can also explain the importance of axin degradation in amplifying and sharpening the Wnt signal, and we show that the dependence of axin degradation on APC is an essential part of an unappreciated regulatory loop that prevents the accumulation of beta-catenin at decreased APC concentrations. By applying control analysis to our mathematical model, we demonstrate the modular design, sensitivity, and robustness of the Wnt pathway and derive an explicit expression for tumor suppression and oncogenicity.
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To cite BioModels Database, please use: Chelliah V et al. BioModels: ten-year anniversary. Nucl. Acids Res. 2015, 43(Database issue):D542-8.
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The roles of APC and Axin derived from experimental and theoretical analysis of the Wnt pathway.
- Lee E, Salic A, Krüger R, Heinrich R, Kirschner MW
- PLoS Biology , 10/ 2003 , Volume 1 , Issue 1 , pages: E10 , PubMed ID: 14551908
- Department of Cell Biology, Harvard Medical School, Boston, Massachusetts, USA.
- Wnt signaling plays an important role in both oncogenesis and development. Activation of the Wnt pathway results in stabilization of the transcriptional coactivator beta-catenin. Recent studies have demonstrated that axin, which coordinates beta-catenin degradation, is itself degraded. Although the key molecules required for transducing a Wnt signal have been identified, a quantitative understanding of this pathway has been lacking. We have developed a mathematical model for the canonical Wnt pathway that describes the interactions among the core components: Wnt, Frizzled, Dishevelled, GSK3beta, APC, axin, beta-catenin, and TCF. Using a system of differential equations, the model incorporates the kinetics of protein-protein interactions, protein synthesis/degradation, and phosphorylation/dephosphorylation. We initially defined a reference state of kinetic, thermodynamic, and flux data from experiments using Xenopus extracts. Predictions based on the analysis of the reference state were used iteratively to develop a more refined model from which we analyzed the effects of prolonged and transient Wnt stimulation on beta-catenin and axin turnover. We predict several unusual features of the Wnt pathway, some of which we tested experimentally. An insight from our model, which we confirmed experimentally, is that the two scaffold proteins axin and APC promote the formation of degradation complexes in very different ways. We can also explain the importance of axin degradation in amplifying and sharpening the Wnt signal, and we show that the dependence of axin degradation on APC is an essential part of an unappreciated regulatory loop that prevents the accumulation of beta-catenin at decreased APC concentrations. By applying control analysis to our mathematical model, we demonstrate the modular design, sensitivity, and robustness of the Wnt pathway and derive an explicit expression for tumor suppression and oncogenicity.
Submitter of this revision: administrator
Modellers: administrator, Emma Fairbanks
Metadata information
isDescribedBy (1 statement)
hasTaxon (1 statement)
hasProperty (2 statements)
KEGG Pathway Wnt signaling pathway - Xenopus laevis (African clawed frog)
Connected external resources
SBGN view in Newt Editor
| Name | Description | Size | Actions |
|---|---|---|---|
Model files |
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| BIOMD0000000658_url.xml | SBML L2V4 representation of Lee2003 - Roles of APC and Axin in Wnt Pathway (without regulatory loop) | 98.16 KB | Preview | Download |
Additional files |
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| BIOMD0000000658-biopax2.owl | Auto-generated BioPAX (Level 2) | 25.92 KB | Preview | Download |
| BIOMD0000000658-biopax3.owl | Auto-generated BioPAX (Level 3) | 41.63 KB | Preview | Download |
| BIOMD0000000658.m | Auto-generated Octave file | 8.94 KB | Preview | Download |
| BIOMD0000000658.pdf | Auto-generated PDF file | 196.64 KB | Preview | Download |
| BIOMD0000000658.png | Auto-generated Reaction graph (PNG) | 81.37 KB | Preview | Download |
| BIOMD0000000658.sci | Auto-generated Scilab file | 154.00 Bytes | Preview | Download |
| BIOMD0000000658.svg | Auto-generated Reaction graph (SVG) | 34.95 KB | Preview | Download |
| BIOMD0000000658.vcml | Auto-generated VCML file | 897.00 Bytes | Preview | Download |
| BIOMD0000000658.xpp | Auto-generated XPP file | 7.17 KB | Preview | Download |
| BIOMD0000000658_urn.xml | Auto-generated SBML file with URNs | 97.65 KB | Preview | Download |
| MODEL1708310000_edited.cps | Curated and annotated model COPASI file | 114.49 KB | Preview | Download |
| MODEL1708310000_edited.sedml | SED-ML file for figure 6 | 2.33 KB | Preview | Download |
- Model originally submitted by : Emma Fairbanks
- Submitted: Aug 31, 2017 3:36:56 PM
- Last Modified: Mar 21, 2018 11:03:19 AM
Revisions
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Version: 3
- Submitted on: Mar 21, 2018 11:03:19 AM
- Submitted by: administrator
- With comment: Current version of Lee2003 - Roles of APC and Axin in Wnt Pathway (without regulatory loop)
-
Version: 2
- Submitted on: Aug 31, 2017 4:42:09 PM
- Submitted by: Emma Fairbanks
- With comment: Current version of Lee2003 - Wnt Pathway
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Version: 1
- Submitted on: Aug 31, 2017 3:36:56 PM
- Submitted by: Emma Fairbanks
- With comment: Original import of Wnt Pathway
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: Variable used inside SBML models
| Species | Initial Concentration/Amount |
|---|---|
| APC axin GSK3 Axin-1 ; Glycogen synthase kinase-3 beta ; Adenomatous polyposis coli homolog |
0.00483 μmol |
| GSK3 Glycogen synthase kinase-3 beta |
50.0 μmol |
| APC Adenomatous polyposis coli homolog |
98.0 μmol |
| B catenin APC axin GSK3 Axin-1 ; Catenin beta-1 ; Adenomatous polyposis coli homolog ; Glycogen synthase kinase-3 beta |
0.00202 μmol |
| Dsh i Segment polarity protein dishevelled homolog DVL-2 |
100.0 μmol |
| APC axin Axin-1 ; Adenomatous polyposis coli homolog |
9.8065E-4 μmol |
| B catenin APC axin GSK3 Adenomatous polyposis coli homolog ; Catenin beta-1 ; Axin-1 ; Glycogen synthase kinase-3 beta |
0.00202 μmol |
| B catenin Catenin beta-1 |
1.0 μmol |
| Reactions | Rate | Parameters |
|---|---|---|
| APC__axin__GSK3 => APC_axin_GSK3 | Cytoplasm*k5*APC__axin__GSK3 | k5 = 0.133 |
| GSK3 + APC_axin => APC_axin_GSK3 | Cytoplasm*(k6*GSK3*APC_axin-k_6*APC_axin_GSK3) | k6 = 0.0909; k_6 = 0.909 |
| APC + B_catenin_0 => B_catenin_APC | k17*APC*B_catenin_0-k_17*B_catenin_APC | k_17 = 600000.0; k17 = 500.0 |
| APC_axin_GSK3 => APC__axin__GSK3 | Cytoplasm*k4*APC_axin_GSK3 | k4 = 0.267 |
| B_catenin_APC__axin__GSK3 => B_catenin__APC__axin__GSK3 | Cytoplasm*k9*B_catenin_APC__axin__GSK3 | k9 = 206.0 |
| Dsh_a => Dsh_i | Cytoplasm*k2*Dsh_a | k2 = 0.0182 |
| APC + Axin => APC_axin | Cytoplasm*(k7*APC*Axin-k_7*APC_axin) | k7 = 500.0; k_7 = 25000.0 |
| APC__axin__GSK3 + B_catenin_0 => B_catenin_APC__axin__GSK3 | k8*APC__axin__GSK3*B_catenin_0-k_8*B_catenin_APC__axin__GSK3 | k_8 = 60000.0; k8 = 500.0 |
| B_catenin__APC__axin__GSK3 => B_catenin + APC__axin__GSK3 | Cytoplasm*k10*B_catenin__APC__axin__GSK3 | k10 = 206.0 |
(added: 21 Mar 2018, 11:31:47, updated: 21 Mar 2018, 11:31:47)