Limits...
Parameter optimization in S-system models.

Vilela M, Chou IC, Vinga S, Vasconcelos AT, Voit EO, Almeida JS - BMC Syst Biol (2008)

Bottom Line: We tackle this challenge here through the parameterization of S-system models.It was previously shown that parameter identification can be performed as an optimization based on the decoupling of the differential S-system equations, which results in a set of algebraic equations.A procedure was developed that facilitates automated reverse engineering tasks for biological networks using S-systems.

View Article: PubMed Central - HTML - PubMed

Affiliation: Dept. Bioinformatics and Computational Biology, University of Texas M,D, Anderson Cancer Center, 1515 Holcombe Blvd, Houston, TX 77030, USA. mvilela@mdanderson.org

ABSTRACT

Background: The inverse problem of identifying the topology of biological networks from their time series responses is a cornerstone challenge in systems biology. We tackle this challenge here through the parameterization of S-system models. It was previously shown that parameter identification can be performed as an optimization based on the decoupling of the differential S-system equations, which results in a set of algebraic equations.

Results: A novel parameterization solution is proposed for the identification of S-system models from time series when no information about the network topology is known. The method is based on eigenvector optimization of a matrix formed from multiple regression equations of the linearized decoupled S-system. Furthermore, the algorithm is extended to the optimization of network topologies with constraints on metabolites and fluxes. These constraints rejoin the system in cases where it had been fragmented by decoupling. We demonstrate with synthetic time series why the algorithm can be expected to converge in most cases.

Conclusion: A procedure was developed that facilitates automated reverse engineering tasks for biological networks using S-systems. The proposed method of eigenvector optimization constitutes an advancement over S-system parameter identification from time series using a recent method called Alternating Regression. The proposed method overcomes convergence issues encountered in alternate regression by identifying nonlinear constraints that restrict the search space to computationally feasible solutions. Because the parameter identification is still performed for each metabolite separately, the modularity and linear time characteristics of the alternating regression method are preserved. Simulation studies illustrate how the proposed algorithm identifies the correct network topology out of a collection of models which all fit the dynamical time series essentially equally well.

Show MeSH

Related in: MedlinePlus

Flowchart. Flowchart of the proposed algorithm. To perform the optimization process, the algorithm requires only the time series set and an initial β value as input.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC2333970&req=5

Figure 8: Flowchart. Flowchart of the proposed algorithm. To perform the optimization process, the algorithm requires only the time series set and an initial β value as input.

Mentions: where represents all negative slope values from the time series of Xi. A simple linear regression step in logarithmic space thus suffices to determine admissible initial guesses for the kinetic orders hij. In this fashion, for a given βi, small values of kinetic orders hij are provided to the optimization algorithm. As a technical note, it is easier to keep a parameter value than to bring it to zero during the optimization. If the slope vector contains no negative values, the procedure is performed without ε. A flowchart of the proposed algorithm is shown in Figure 8.


Parameter optimization in S-system models.

Vilela M, Chou IC, Vinga S, Vasconcelos AT, Voit EO, Almeida JS - BMC Syst Biol (2008)

Flowchart. Flowchart of the proposed algorithm. To perform the optimization process, the algorithm requires only the time series set and an initial β value as input.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2333970&req=5

Figure 8: Flowchart. Flowchart of the proposed algorithm. To perform the optimization process, the algorithm requires only the time series set and an initial β value as input.
Mentions: where represents all negative slope values from the time series of Xi. A simple linear regression step in logarithmic space thus suffices to determine admissible initial guesses for the kinetic orders hij. In this fashion, for a given βi, small values of kinetic orders hij are provided to the optimization algorithm. As a technical note, it is easier to keep a parameter value than to bring it to zero during the optimization. If the slope vector contains no negative values, the procedure is performed without ε. A flowchart of the proposed algorithm is shown in Figure 8.

Bottom Line: We tackle this challenge here through the parameterization of S-system models.It was previously shown that parameter identification can be performed as an optimization based on the decoupling of the differential S-system equations, which results in a set of algebraic equations.A procedure was developed that facilitates automated reverse engineering tasks for biological networks using S-systems.

View Article: PubMed Central - HTML - PubMed

Affiliation: Dept. Bioinformatics and Computational Biology, University of Texas M,D, Anderson Cancer Center, 1515 Holcombe Blvd, Houston, TX 77030, USA. mvilela@mdanderson.org

ABSTRACT

Background: The inverse problem of identifying the topology of biological networks from their time series responses is a cornerstone challenge in systems biology. We tackle this challenge here through the parameterization of S-system models. It was previously shown that parameter identification can be performed as an optimization based on the decoupling of the differential S-system equations, which results in a set of algebraic equations.

Results: A novel parameterization solution is proposed for the identification of S-system models from time series when no information about the network topology is known. The method is based on eigenvector optimization of a matrix formed from multiple regression equations of the linearized decoupled S-system. Furthermore, the algorithm is extended to the optimization of network topologies with constraints on metabolites and fluxes. These constraints rejoin the system in cases where it had been fragmented by decoupling. We demonstrate with synthetic time series why the algorithm can be expected to converge in most cases.

Conclusion: A procedure was developed that facilitates automated reverse engineering tasks for biological networks using S-systems. The proposed method of eigenvector optimization constitutes an advancement over S-system parameter identification from time series using a recent method called Alternating Regression. The proposed method overcomes convergence issues encountered in alternate regression by identifying nonlinear constraints that restrict the search space to computationally feasible solutions. Because the parameter identification is still performed for each metabolite separately, the modularity and linear time characteristics of the alternating regression method are preserved. Simulation studies illustrate how the proposed algorithm identifies the correct network topology out of a collection of models which all fit the dynamical time series essentially equally well.

Show MeSH
Related in: MedlinePlus