S system
S-systems (S for saturation (from saturation) or synergism) are used to describe and simulate biological and biochemical systems that strive towards a limit or saturation state.
You can reliably describe almost all kinetic phenomena of natural reactions. The interactions are described by a set of first-order nonlinear differential equations , which consist of a production and a degradation term:
; for i = 1 .. N
N denotes the number of interacting substances. The concentration variables are designated with x i , the production rate with α and the degradation rate with β . The exponents g ij and h ij correspond to reaction orders of the production and degradation functions of substance i as a function of substance j .
example
The following differential equation system results for a system with 2 substances:
literature
- Feng-Sheng Wang, Chih-Lung Ko, Eberhard O. Voit: Kinetic modeling using S-systems and lin-log approaches. In: Biochemical Engineering Journal. 33, 2007, p. 238, doi: 10.1016 / j.bej.2006.11.002 .
Individual evidence
- ^ Eberhard O. Voit: Computational Analysis of Biochemical Systems. Cambridge University Press, 2000, ISBN 978-0-521-78579-2 , p. 57.