ss_5genes

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 Hlavacek et al. (1996) and employed in Kikuchi et al. (2003). It represents a genetic network with 5 dependent variables, X1...X5, and 3 input variables X6-X8.

The parameters of the system are:

i αi gi1 gi2 gi3 gi4 gi5 gi6 gi7 gi8 βi hi1 hi2 hi3 hi4 hi5 hi6 hi7 hi8
1 5     1   -1 1     10 2              
2 10 2           1   10   2            
3 10   -1           1 10   -1 2          
4 8     2   -1 1     10       2        
5 10       2     1   10         2      

Each row corresponds to one ODE according to Eq. 1, e.g. the first row gives X1'(t) = 5*X3(t)*(X5(t))-1*X6(t) - 10*(X1(t))2.

In most of the test problems, the input variables X6-X8 are not explicitly considered, and hence, a reduced S-system can be used:

i αi gi1 gi2 gi3 gi4 gi5 βi hi1 hi2 hi3 hi4 hi5
1 5     1   -1 10 2        
2 10 2         10   2      
3 10   -1       10   -1 2    
4 8     2   -1 10       2  
5 10       2   10         2

The system specification in the same format as the problem: ss_5genes and ss_5genes_8variables.

The system specification in SBML format: ss_5genes.xml.

A simple Matlab script for simulating the system is given in ss_5genes.m.

About the problems

ss_5genes1 is presented in Kikuchi et al. (2003).

ss_5genes2 and ss_5genes3 are presented in Gennemark and Wedelin (2007).In ss_5genes2, 3 points are sampled at t=0 and the average value is considered.

ss_5genes4 is presented in Kimura et al. (2005).

ss_5genes5 is presented in Daisuke and Horton (2006).

ss_5genes6 is presented in Cho et al. (2006).

ss_5genes7 is presented in Tucker and Moulton (2006).

ss_5genes8 is presented in Tsai et al. (2005).

References

Cho,D.Y., Cho,K.H.,Zhang,B.T. (2006) Identification of biochemical networks by S-tree based genetic programming. Bioinformatics, 22, 1631-40. PMID:16585066

Daisuke,T.,Horton,P. (2006) Inference of scale-free networks from gene expression time series. J Bioinform Comput Biol., 4, 503-14. PMID:16819798

Gennemark,P.,Wedelin,D. (2007) Efficient algorithms for ordinary differential equation model identification of biological systems. IET Syst Biol., 1, 120-9. PMID:17441553

Hlavacek,W.S.,Savageau,M.A. (1996) Rules for coupled expression of regulator and effector genes in inducible circuits. J Mol Biol., 255, 121-39. PMID:8568860

Kikuchi,S., Tominaga,D., Arita,M., Takahashi,K., Tomita,M. (2003) Dynamic modeling of genetic networks using genetic algorithm and S-system, Bioinformatics, 19, 643-50. PMID:12651723

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

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

Tucker,W.,Moulton,V. (2006) Parameter reconstruction for biochemical networks using interval analysis, Reliable Computing, 12, 389-402. http\://www.springerlink.com/content/r5252637515v1qq3/

Voit,E.O. (2000) Computational analysis of biochemical systems. A practical guide for biochemists and molecular biologists. Cambridge University Press, Cambridge, 176-184.