ss_15genes
The model is defined as a so called S-system model. 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 dependent 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.
This test system is a reduced version of test system ss_30genes that was introduced by Maki et al. (2001). The system represents a genetic network with 15 variables. A positive regulation of synthesis is indicated by a black arrow, whereas repression of synthesis is indicated by a red arrow.
The parameters are:
| for all i: αi=1 | ||||
| for all i: βi=1 | ||||
| g1,14=-0.1 | g3,12=-0.2 | g5,1=1.0 | g6,1=1.0 | g7,2=0.5 |
| g7,3=0.4 | g8,4=0.2 | g9,5=1.0 | g9,6=-0.1 | g10,7=0.3 |
| g11,4=0.4 | g11,7=-0.2 | g12,13=0.5 | g13,8=0.6 | g14,9=1.0 |
| g14,15=-0.2 | g15,10=0.2 | other gij=0.0 | ||
| for all i: hii=1.0, other hij=0 | ||||
The ODE of X1 according to Eq. 1: X1'(t) = 1-1*X1(t)*X14(t)-0.1.
The system specification in the same format as the problem: ss_15genes.
The system specification in SBML format: ss_15genes.xml.
A simple Matlab script for simulating the system is given in ss_15genes.m.
About the problems
Problem ss_30genes1 is a reduced version of a problem presented in Kimura et al. (2005).
Problem ss_15genes2 is the same as ss_15genes1, but with the addition of Gaussian noise with a 10% standard deviation relative to the particular experimental value.At t=0, 3 points are sampled and the average value is considered.
References
Kimura,S., Ide,K., Kashihara,A., Kano,M., Hatakeyama,M., Masui,R., Nakagawa,N., Yokoyama,S., Kuramitsu,S., Konagaya,A. (2005) Inference of S-system models of genetic networks using a cooperative coevolutionary algorithm. Bioinformatics, 21, 1154-63. PMID:15514004
Maki,Y., Tominaga,D.,Okamoto,M., Watanabe,S., Eguchi,Y. (2001) Development of a system for the inference of large scale genetic networks. Pac Symp Biocomput. 2001, 446-58. PMID:11262963
Savageau,M.A. (1976) Biochemical systems analysis: a study of function and design in molecular biology (Addison-Wesley, Reading, Mass).
Voit,E.O. (2000) Computational analysis of biochemical systems. A practical guide for biochemists and molecular biologists. Cambridge University Press, Cambridge, 176-184.