Benchmarks for identification of ODEs from time series data

3genes

This test system models a gene network originally considered in Moles et al. (2003).

S, M and P are metabolites, E are enzymes, and G are mRNAs. The system can be described by the following equations:

            
G_i'(t)  = V^G_i / (1+(P/K_{I_i})^n_i+(K_{A_i}/M_i-1)^m_i ) - k^G_i G_i                 i=1...N
 
E_i'(t)  = V^E_i G_i / (K^E_i+G_i) - k^E_i E_i                                  i=1...N

M_i'(t) = k^M1_i E_i (k^M2_i)^-1 (M_i-1 - M_i) / (1+M_i-1/k^M2_i+M_i/k^M3_i) - 

       k^M1_i+1 E_i+1 (k^M2_i+1)^-1 (M_i - M_i+1) / (1+M_i/k^M2_i+1+M_i+1/k^M3_i+1)    i=1...N-1

where 

 N is the size of the model,
 M₀ refers to the input signal S,
 M_N refers to the input signal P.

The following parameter values are used:


 V^G_i = K_{I_i} = K_{A_i} = k^G_i =  K^E_i  = k^M1_i = k^M2_i = k^M3_i = 1
 n_i = m_i  = 2
 V^E_i = k^E_i = 0.1

Note that conservation of mass (in this case S+M₁+M₂+P=const) can not be generally assumed and hence, should not be assumed as prior knowledge in this test problem.

The system specification in the same format as the problem: 3genes.

The system specification in SBML format: 3genes.xml.

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

About the problems

The problem 3genes1 considers the same data as in a parameter estimation problem presented in Moles et al. (2003). The structure is unknown.

The problems pe_3genes1/2/3 are parameter estimation problems with various noise levels.

pe_3genes1: no noise.

pe_3genes2f: 3% noise. The initial value for the variable in each time series is considered fixed.

pe_3genes2: 3% noise. The initial value of the variable in each time series is considered a parameter that is estimated.

pe_3genes3f: 5% noise. The initial value for the variable in each time series is considered fixed.

pe_3genes3: 5% noise. The initial value of the variable in each time series is considered a parameter that is estimated.

Reference

Moles,C.G., Mendes,P.,Banga,J.R. (2003) Parameter estimation in biochemical pathways: a comparison of global optimization methods. Genome Res., 13, 2467-74. PMID:14559783