Geodesic
Optimization model of collagen type~IV limited proteolyses
Matematičeskoe modelirovanie, Tome 20 (2008) no. 1, pp. 92-98

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The mathematical model of dynamics of collagen type IV limited proteolyses is proposed. The processes of collagen type IV degradation on cellular membrane are considered. Are the processes of metalloproteinases MT1-MMP and MMP-2 complexes are participated. Inhibitor of metalloproteinases TIMP-2 is also participated. Because many kinetic of enzyme reaction and reactions of second order have not yet measured optimization model that is permitted this constant is proposed. The cost function is minimum protein consumption. The constrained base on physiological purpose of process: basal membrane degradation for a given time. 
@article{MM_2008_20_1_a7,
     author = {D. Yu. Ignatiev and M. A. Khanin},
     title = {Optimization model of collagen {type~IV} limited proteolyses},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {92--98},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2008_20_1_a7/}
}
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D. Yu. Ignatiev; M. A. Khanin. Optimization model of collagen type~IV limited proteolyses. Matematičeskoe modelirovanie, Tome 20 (2008) no. 1, pp. 92-98. http://geodesic.mathdoc.fr/item/MM_2008_20_1_a7/