ss_cascade
The model is defined as a so called S-system. The S-system formalism (Savageau 1976, Voit 2000) is based on approximating kinetic laws with multivariate power-law functions. A model consists of n non-linear ODEs and the generic form of equation i reads
Xi'(t) = αi ∏j=1..n Xj(t)gij - βi ∏j=1..n Xj(t)hij
where X is a vector (length n) of variables, α and β are vectors (length n) of non-negative rate constants and g and h are matrices (n*n) of kinetic orders, that can be negative as well as positive.
The system was introduced by Voit (2000) and applied in Tsai and Wang (2005). It represents a cascaded pathway with three dependent variables, X1...X3, and one input variable X4.
The parameter values are:
| i | αi | gi1 | gi2 | gi3 | gi4 | βi | hi1 | hi2 | hi3 | hi4 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 10 | -0.1 | -0.05 | 1 | 5 | 0.5 | ||||
| 2 | 2 | 0.5 | 1.44 | 0.5 | ||||||
| 3 | 3 | 0.5 | 7.2 | 0.5 | ||||||
| 4 | Input | |||||||||
Here, an empty element corresponds to 0.0. Each row corresponds to one ODE according to Eq. 1, e.g. the first row gives X1'(t) = 10.0 X2(t)-0.1 X3(t)-0.05 X4(t) - 5.0 X1(t)0.5.
The system specification in the same format as the problem: ss_cascade.
The system specification in SBML format: ss_cascade.xml.
A simple Matlab script for simulating the system is given in ss_cascade.m.
About the problems
ss_cascade1 was presented in Tsai and Wang (2005).ss_cascade2 is similar to ss_cascade1, but with fewer data, only 4 experiments instead of 8.
ss_cascade3 is similar to ss_cascade1, but here Gaussian noise with 5% standard deviation relative to the particular experimental value is added.
pe_ss_cascade1 is the same as ss_cascade but with a fixed correct structure, i.e. a parameter estimation problem.
References
Savageau,M.A. (1976) Biochemical systems analysis: a study of function and design in molecular biology (Addison-Wesley, Reading, Mass).
Tsai,K.Y., Wang,F.S. (2005) Evolutionary optimization with data collocation for reverse engineering of biological networks. Bioinformatics, 21, 1180-8. PMID:15513993
Voit,E.O. (2000) Computational analysis of biochemical systems. A practical guide for biochemists and molecular biologists. Cambridge University Press, Cambridge, 176-184.