simpleLin

This test system models a simple metabolic pathway. It is a simplified version of the problem metabol and can preferably be used as a basic test case.

The system has two input variables X₁ and X₂ and three dependent variables X₃-X₅. It can be described by the following equations:

X3'(t) = - k1  X3(t) + k2 X1(t) X4(t)  

X4'(t) = k1  X3(t) - k2 X1(t) X4(t)  +  k3 X5(t) - k4 X2(t) X4(t) 

X5'(t) = - k3 X5(t) + k4 X2(t) X4(t) 

The following rate constants were used: k₁=k₂=k₃=k₄=1.

The system specification in the same format as the problem: simpleLin.

The system specification in SBML format: simpleLin.xml.

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

About the problems

The general problem, in which conservation of mass (in this case X₃+X₄+X₅=const) is not assumed as prior knowledge is considered.

simpleLin1 is designed to be a simple test problem with perfect data.

simpleLin2 adds the complexity of noisy data. Data was simulated for 8 experiments with different combinations of inputs:

  
Exp.    X1     X2     X3     X4     X5
 1     3.0    2.0    1.0    0.0    0.0   
 2     4.0    5.0    1.0    0.0    0.0  
 3     1.0    3.0    1.0    0.0    0.0 
 4     3.0    1.0    1.0    0.0    0.0 
 5     0.5    1.0    1.0    0.0    0.0  
 6     1.0    0.5    1.0    0.0    0.0 
 7     0.5    5.0    1.0    0.0    0.0 
 8     5.0    0,5    1.0    0.0    0.0 

13 data-points were uniformly sampled between t=0 and t=3. Gaussian noise with 10% standard deviation relative to the particular experimental value was added. At t=0, the mean of three repetitions was used.