Flowchart of the proposed method. Starting with experimental time series, the data are smoothed and balanced for mass conservation, if necessary. The slopes of the time series at each time point are estimated. Combined with the knowledge of the system topology, substitution of the derivatives in the ODE with slope information yields a linear system of fluxes. If the system has full rank, solve the system with techniques from linear algebra. If the system is underdetermined, use auxiliary steps, as proposed in this article, to solve a subset of the fluxes until the system is of full rank. The results are the dynamic profiles of all extra- and intra-cellular fluxes in the system. If desired, make assumptions regarding the functional forms of the fluxes. These functions correspond to symbolic flux representations that can be independently fitted to the respective dynamic flux profiles and result in a fully parameterized kinetic model. As an alternative each process may be approximated as a piecewise function, for instance using spline methods.
Chou and Voit BMC Systems Biology 2012 6:84 doi:10.1186/1752-0509-6-84