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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.

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Linear system topology. Linear pathway with precursor-product constraints.
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Figure 6: Linear system topology. Linear pathway with precursor-product constraints.

Mentions: The proposed method was extended to address the parameter identification for systems with topological constraints. This extension allows the algorithm to account for precursor-product relationships problems, which mandate that the degradation term of the precursor is equivalent to the production term of the product [28]. Thus, instead of optimizing the parameters for each metabolite separately, a set of terms is optimized simultaneously, consisting of one of the parameter vectors (production or degradation vector) of each metabolite. As an illustrative, simple example, consider a linear pathway with feedback, where we have to account for constraints between the production and degradation terms of subsequent metabolites (Figure 6). Specifically in the example system, the efflux from X1 is identical to the influx into X2, and the efflux from X2 is identical to the influx into X3. Consequently, the degradation term of X1 is exactly the same as the production term of X2, and the degradation term of X2 must be the same as the production term of X3. The amendment of the proposed method toward simultaneous estimation readily satisfies these types of constraints.


Parameter optimization in S-system models.

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

Linear system topology. Linear pathway with precursor-product constraints.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 6: Linear system topology. Linear pathway with precursor-product constraints.
Mentions: The proposed method was extended to address the parameter identification for systems with topological constraints. This extension allows the algorithm to account for precursor-product relationships problems, which mandate that the degradation term of the precursor is equivalent to the production term of the product [28]. Thus, instead of optimizing the parameters for each metabolite separately, a set of terms is optimized simultaneously, consisting of one of the parameter vectors (production or degradation vector) of each metabolite. As an illustrative, simple example, consider a linear pathway with feedback, where we have to account for constraints between the production and degradation terms of subsequent metabolites (Figure 6). Specifically in the example system, the efflux from X1 is identical to the influx into X2, and the efflux from X2 is identical to the influx into X3. Consequently, the degradation term of X1 is exactly the same as the production term of X2, and the degradation term of X2 must be the same as the production term of X3. The amendment of the proposed method toward simultaneous estimation readily satisfies these types of constraints.

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