Benchmarks for identification of ODEs from time series data

3genes, 4genes, 5genes and 6genes

We prepare the problems from a generalised version of the gene regulatory network, 3genes. The generalised gene network based on the n=3 case considered in Moles et al. (2003). The size of the system is determined by a constant n corresponding to the number of different mRNA species and enzymes in the system.

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+(M_n/K_{I_i})^z_i+(K_{A_i}/M_i-1)^w_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
 M₀ and M₀ corresponds to the input variables
 V^G_i, K_{I_i}, z_i, K_{A_i}, w_i, k^G_i, V^E_i, K^E_i, k^E_i  are parameters defined for i = 1...n
 k^M1_i, k^M2_i, k^M3_i are parameters defined for i = 1...n-1.

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

Using this system with n = 3, 4, 5 and 6, we have created parameter estimation problems with 36, 48, 60 and 72 parameters, respectively. The original problem presented in Moles et al. (2003) corresponds to n = 3. For each model, we have generated data with the same sampling schedules as the benchmark problem given for the n = 3 system, and we have also used the same parameter bounds. In this way, the four problems have basically the same properties but for the size. We refer to the problems as pe_3genes1, pe_4genes1, pe_5genes1, and pe_6genes1, respectively.

The system specification in the same format as the problem: 4genes.

The system specification in SBML format: 4genes.xml.

A simple Matlab script for simulating the system is given in (UNDER CONSTRUCTION)

About the problems

The problem 4genes1 is for n=4.

The problem 5genes1 is for n=5.

The problem 6genes1 is for n=6.

All problmes consider the same number of experiments and number of time-points as in a parameter estimation problem presented in Moles et al. (2003).

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