Data is presented in McKinney et al. (2006). Four variables are measured in time-series, IL-10 (X1), IL-4 (X2), IL-2 (X3) and TNF-α (X4). There is one experiment with 7 sampling points for each variable.
Data is reconstructed semi-automatically (the function ginput in Matlab) from Figure 3 in the paper. Standard deviation is assumed to be 10% of measured values.
Problem cytokine1 uses a model space of linear mass action kinetics.
Problem cytokine2 is similar to cytokine1, but another reaction of Michaelis-Menten type is included in the model space.
McKinney,B.A., Crowe, J.E.Jr., Voss,H.U., Crooke,P.S., Barney,N., Moore,J.H. (2006) Hybrid grammar-based approach to nonlinear dynamical system identification from biological time series. Phys Rev E Stat Nonlin Soft Matter Phys., 73, (2 Pt 1). PMID:16605367