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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - D. Yu. Ignatiev
AU  - M. A. Khanin
TI  - Optimization model of collagen type~IV limited proteolyses
JO  - Matematičeskoe modelirovanie
PY  - 2008
SP  - 92
EP  - 98
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2008_20_1_a7/
LA  - ru
ID  - MM_2008_20_1_a7
ER  - 
%0 Journal Article
%A D. Yu. Ignatiev
%A M. A. Khanin
%T Optimization model of collagen type~IV limited proteolyses
%J Matematičeskoe modelirovanie
%D 2008
%P 92-98
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2008_20_1_a7/
%G ru
%F MM_2008_20_1_a7
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/

[1] Mignatti P. and Rifkin D. B., “Biology and Biochemestry of Proteinases in Tumor Invasion”, Physiological Reviews, 73:1 (1993), 161–195

[2] Nagase H., Woessner J. F., “Matrix Metalloproteinases”, J. Biol. Chem., 274:31 (1999), 21491–21494 | DOI

[3] Ries C. and Petrides P. E., “Cytokine Regulation of Matrix Metalloproteinase Activity and Its Regulatory Dysfunction in Disease”, Biol. Chem. Hoppe-Seyler, 376 (1995), 345–355

[4] Benbow U., Schoenermark M. P., Mitchell T. I. et. al., “A Novel Host/Tumor Cell Interaction Activates Matrix Metalloproteinase 1 and Mediates Invasion the Type 1 Collagen”, J. Biol. Chem., 274 (1999), 25371–25378 | DOI

[5] Will H., Atkinson S. J., Butler G. S. et. al., “The Soluble Catalytic Domain of Membrane Type 1 Matrix Metalloproteinase Cleaves the Propeptide of Progelatinase A and Initiates Autoproteolytic Activation”, J. Biol. Chem., 271:29 (1996), 17119–17123 | DOI

[6] Will H., Atkinson S. J., Butler G. S. et al., J. Biol. Chem., 271 (1996), 17119–17123 | DOI

[7] English W. R., Holtz B., Vogt G. et al., J. Biol. Chem., 276 (2001), 42018–42026 | DOI

[8] Olson M. W., Toth M., Gervasi D. C. et. al., “High Affinity Binding of Latent Matrix Metalloproteinase-9 to the a2(IV) Chain of Collagen IV”, J. Biol. Chem., 273:17 (1998), 10672–10681 | DOI

[9] Murray C. D., “The physiological principle of minimum work I: the vascular system and the cost of blood volume”, Prot. Nat. Acad. Sci., 12 (1926), 207–214 | DOI

[10] Cohn D., “Optimal systems I: the vascular system”, Bull. Math. Biophys., 16 (1955), 59–74 | DOI

[11] Khanin M. A., Dorfman N. L., Bukharov I. B. i dr., Ekstremalnye printsipy v biologii i fiziologii, Nauka, M., 1978 | Zbl

[12] Khanin M. A., Bukharov I. B., “A mathematical model of the functional state of the oxygen transport system”, Bull. Math. Biol., 42 (1980), 627–645 | MR | Zbl

[13] Khanin M. A., Bukharov I. B., “A mathematical model of the pathological functional state of the oxygen transport system”, J. Theor. Biol., 86 (1984), 46115–46125

[14] Khanin M. A., Bukharov I. B., “A mathematical model of the exercise functional state of the oxygen transport system”, J. Theor. Biol., 137 (1989), 191–201 | DOI | MR

[15] Chernousko F. L., “Optimalnye vetvyaschiesya truboprovodnye struktury”, Prikl. Mat. Mekh., 41 (1977), 376–383

[16] Chernousko F. L., “Optimalnye vetvyaschiesya truboprovodnye struktury v biomekhanike”, Mekh. Kompozits. Mater., 16 (1980), 308–311

[17] Kamiya A., Togawa T., “Optimal branching structure of the vascular tree”, Bull. Math. Biophys., 34 (1972), 431–438 | DOI

[18] Horsefield K., Cumming G., “Angles of branching and diameters of branches in the human bronchial tree”, Bull. Math. Biophys., 29 (1967), 245–259 | DOI

[19] Zamir M., “Optimality principles in arterial branching”, J. Theor. Biol., 62 (1976), 227–251 | DOI

[20] Uylings H. B. M., “Optimization of diameters and bifurcation angles in lung and vascular tree structures”, Bull. Math. Biol., 39 (1997), 509–515

[21] Khanin M. A., Bukharov I. B., “Optimal structure of the microcirculatory Bed”, J. Theor. Biol., 169 (1991), 267–273 | DOI

[22] Milsum J. H., “Optimization aspects in biological control theory”, Advances in biomedical engineering and medical physics, V. 1, ed. S. N. Levine, Interscience, New York, 1968, 243–278

[23] Rosen R., Optimality Principles in Biology, Butterworths, London, U.K., 1967 | Zbl