The model space 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.
Data is presented in Wang (2001) and applied in Liu and Wang (2008). Four variables are measured in time-series, biomass (X1), glucose (X2), ethanol (X3) and glycerol (X4). Experiment 1 starts from a glucose concentration of 100 g/L, experiment 2 from 150 g/L and experiment 3 from 200 g/L.
Problem ss_ethanolferm1 includes two experiments and was specified in Liu and Wang (2008). Here, a third experiment was used for model validation. Time-series data was calculated from the average of two repetitions. Standard deviations were calculated from the two repetitions individually for each measurement point. Standard deviations equal zero were replaced by a default value of 0.1.
Problem ss_ethanolferm2 includes all 3 experiments presented in Liu and Wang (2008).
Liu,P.K., Wang,F.S. (2008) Inference of biochemical network models in S-system using multiobjective optimization approach. Bioinformatics, 24, 1085-92. PMID:1832\1886
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.
Wang,F.S., Su,T.L., Jang,H.J. (2001) Hybrid Differential Evolution for Problems of Kinetic Parameter Estimation and Dynamic Optimization of an Ethanol Fermentation Process. Ind Eng Chem Res, 40, 2876-85. Ind Eng Chem Res