simpleFb

The system is taken from McKinney et al. (2006).

The system consists of 3 dependent variables X₁...X₃ and 7 parameters k₁...k₇.

X1'(t) = k1*h-(X3(t),k2) -  k3*X1(t)

X2'(t) = k4*X1(t) - k5*X2(t)

X3'(t) = k6*X2(t) - k7*X3(t)

where

h⁺(X_i(t),k_j) = X_i(t) / (X_i(t)+k_j)

and

h^-(X_i(t),k_j) = 1 - h⁺(X_i(t),k_j)

The following parameter values are used: k=[0.9,0.9,1.0,1.0,0.6,0.6,0.8].

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

The system specification in SBML format: simpleFb.xml.

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

About the problems

The four problems below are given in an increased order of difficulty. The first, simpleFb1, considers 4 experiments with noise-free data,

Problem simpleFb2 considers the same 4 experiments and sampling rates as defined in problem simpleFb1, but with the addition of Gaussian noise with a 5% standard deviation relative to the particular experimental value. 3 points are sampled at t=0 and the average value is considered.

Problem simpleFb3 includes only a single experiment and the difficulty lies in the sparsity of data.

Problem simpleFb4 is based on simpleFb3 but with noisy data. It is similar to a problem presented in McKinney et al. (2006).

Reference

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