A theoretical model of type I collagen proteolysis by matrix metalloproteinase (MMP) 2 and membrane type 1 MMP in the presence of tissue inhibitor of metalloproteinase 2
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This version of the model has been checked in COR and PCEnv and it runs to replicate the published results. The model is valid CellML and has consistent units. Thank you to Lucie Gatterpaille, Eric Fanchon and Philippe Tracqui for all the time and effort they invested in the final stages of curating this model. Also note they have provided supporting text and model simulation graphs which can be found as two additional files in the model workspace.
Model Structure
The formation of new biological vessels requires the coordinated assembly of a proliferating syncytium of endothelial cells (EC) at different developmental stages. Angiogenesis may also be an essential mechanism of blood vessel remodelling which occurs during a diverse range of physiological processes; including tissue regeneration following injury and new vessel formation during muscle exercise. It can also occur under pathological conditions such as atherosclerosis and the vascularisation of cancerous tumours.
Matrix metalloproteinases (MMPs) are a family of enzymes responsible for the proteolytic processing of extracellular matrix (ECM) structural proteins. During angiogenesis MMPs are expressed by a single endothelial cell at the tip of the new vessel. These enzymes manifest a proteolytic activity that allows the cells of the new vessle to penetrate the ECM. In the mathematical model presented here, Karagiannis and Popel investigate the proteolytic potential of such a tip endothelial cell. The model authors suggest this model provides a foundation for future quantitative studies of angiogenesis in ECMs of different compositions. The model is described in more detail in the figure below:
The complete original paper reference is cited below:
A theoretical model of type I collagen proteolysis by matrix metalloproteinase (MMP) 2 and membrane type 1 MMP in the presence of tissue inhibitor of metalloproteinase 2, Emmanouil D. Karagiannis and Aleksander S. Popel, 2004, The Journal of Biological Chemistry, 279, 39105-39114. PubMed ID: 15252025
model diagram
A schematic diagram of the signalling pathway.
$\mathrm{v1}=\mathrm{kshed\_eff}\mathrm{MT1}\mathrm{MT1}\mathrm{v2}=\mathrm{kon\_MT1T2}\mathrm{MT1}\mathrm{T2}-\mathrm{ki\_MT1T2}\mathrm{kon\_MT1T2}\mathrm{MT1T2}\mathrm{v3}=\mathrm{kon\_MT1T2M2P}\mathrm{MT1T2}\mathrm{M2P}-\mathrm{koff\_MT1T2M2P}\mathrm{MT1T2M2P}\mathrm{v4}=\mathrm{kact\_eff\_m2}\mathrm{MT1}\mathrm{MT1T2M2P}\mathrm{v5}=\mathrm{kon\_M2T2}\mathrm{M2}\mathrm{T2}-\mathrm{kon\_M2T2}\mathrm{ki\_M2T2}\mathrm{M2T2}\mathrm{v6}=\mathrm{kiso\_M2T2}\mathrm{M2T2}-\mathrm{k\_iso\_M2T2}\mathrm{M2T2star}\mathrm{v7}=\mathrm{kon\_M2C1}\mathrm{M2}\mathrm{C1}-\mathrm{koff\_M2C1}\mathrm{M2C1}\mathrm{v8}=\mathrm{kcat\_M2C1}\mathrm{M2C1}\mathrm{v9}=\frac{\mathrm{kcat\_MT1C1}}{\mathrm{km\_MT1C1}}\mathrm{MT1}\mathrm{C1}\frac{d \mathrm{MT1}}{d \mathrm{time}}=-\mathrm{v1}-\mathrm{v2}\frac{d \mathrm{MT1cat}}{d \mathrm{time}}=\mathrm{v1}\frac{d \mathrm{MT1T2}}{d \mathrm{time}}=\mathrm{v2}-\mathrm{v3}\frac{d \mathrm{MT1T2M2P}}{d \mathrm{time}}=\mathrm{v3}-\mathrm{v4}\frac{d \mathrm{M2P}}{d \mathrm{time}}=-\mathrm{v3}\frac{d \mathrm{M2}}{d \mathrm{time}}=\mathrm{v4}-\mathrm{v5}-\mathrm{v7}\frac{d \mathrm{M2T2}}{d \mathrm{time}}=\mathrm{v5}-\mathrm{v6}\frac{d \mathrm{M2T2star}}{d \mathrm{time}}=\mathrm{v6}\frac{d \mathrm{M2C1}}{d \mathrm{time}}=\mathrm{v7}-\mathrm{v8}\frac{d \mathrm{C1}}{d \mathrm{time}}=-\mathrm{v7}-\mathrm{v9}\frac{d \mathrm{C1dmt1}}{d \mathrm{time}}=\mathrm{v9}\frac{d \mathrm{C1dm2}}{d \mathrm{time}}=\mathrm{v8}\frac{d \mathrm{T2}}{d \mathrm{time}}=-\mathrm{v2}-\mathrm{v5}$
collagen
matrix metalloproteinase
signal transduction
cerebral aneurysm
15252025
The University of Auckland, Bioengineering Institute
Journal of Biological Chemistry
The University of Auckland
The Bioengineering Institute
c.lloyd@auckland.ac.nz
Emmanouil
Karagiannis
D
Catherine
Lloyd
May
keyword
This is a CellML description of Karagiannis and Popel's 2004 mathematical model of collagen type I proteolysis by matrix metalloproteinase (MMP) 2 and membrane type I MMP during the migration of a tip endothelial cell.
A theoretical model of type I collagen proteolysis by matrix metalloproteinase (MMP) 2 and membrane type 1 MMP in the presence of tissue inhibitor of metalloproteinase 2
279
39105
39114
Aleksander
Popel
S
2004-09-10
Karagiannis and Popel's 2004 mathematical model of collagen type I proteolysis by matrix metalloproteinase (MMP) 2 and membrane type I MMP during the migration of a tip endothelial cell.
2007-12-11
Catherine Lloyd
The CellML model was curated to ensure the results it generates are the same as those generated by the original published model. A full desceription of the curation comments can be found in the associated file "Explanations".
Gattepaille
Lucie
2009-09-30