Geodesic
Mathematical modeling of biochemical reactions on the example of caoutchouc biosynthesis
Matematičeskaâ biologiâ i bioinformatika, Tome 1 (2006) no. 1, pp. 41-57.

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In the present work the biosynthesis process of natural caoutchouc is considered. This process is a part of metabolic pathway of biosynthesis of sterol, vitamin K, vitamin E and carotenoids. A mathematic model describing the process in the form of a differential equation system has been suggested. Quasi-stationary states, in which rates of intermediate reactions in a chain do not change through time, have been described. Convergence to these states has been determined. Since the process has not been investigated entirely, various possible variations of caoutchouc metabolism have been discussed in the work presented here. For these variations, formulae for calculation of the rate of caoutchouc formation for various initial data have been derived. These formulae allow calculating impact of alteration of characteristics of individual enzymes on the entire metabolic process. 
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A. A. Vasin; A. K. Gaponenko; A. E. Teplov; A. N. Markeev. Mathematical modeling of biochemical reactions on the example of caoutchouc biosynthesis. Matematičeskaâ biologiâ i bioinformatika, Tome 1 (2006) no. 1, pp. 41-57. http://geodesic.mathdoc.fr/item/MBB_2006_1_1_a4/