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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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Noisy time series. Noisy time series data (symbols) and results of the numerical integration of the estimated model (solid lines; cf. Eq. (3)). In spite of slight numerical discrepancies between the estimated parameters and their target values (see Additional file 1), the estimated model accurately predicts the dynamics of the target system, indicating quasi-redundancy [e.g., [27] and [25] ] or "sloppiness" [26] among the parameters.
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Figure 2: Noisy time series. Noisy time series data (symbols) and results of the numerical integration of the estimated model (solid lines; cf. Eq. (3)). In spite of slight numerical discrepancies between the estimated parameters and their target values (see Additional file 1), the estimated model accurately predicts the dynamics of the target system, indicating quasi-redundancy [e.g., [27] and [25] ] or "sloppiness" [26] among the parameters.

Mentions: Initially, all experiments were performed with noise-free time series, but in a second set of experiments, we added noise. Because the proposed algorithm uses the decoupled, algebraic form, a signal extraction procedure was employed for the noisy data to provide smooth time series and slopes [22]. The results show that combining the two strategies (smoother and proposed algorithm) generate accurate dynamical responses for the case studies used in this report (Figure 2).


Parameter optimization in S-system models.

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

Noisy time series. Noisy time series data (symbols) and results of the numerical integration of the estimated model (solid lines; cf. Eq. (3)). In spite of slight numerical discrepancies between the estimated parameters and their target values (see Additional file 1), the estimated model accurately predicts the dynamics of the target system, indicating quasi-redundancy [e.g., [27] and [25] ] or "sloppiness" [26] among the parameters.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: Noisy time series. Noisy time series data (symbols) and results of the numerical integration of the estimated model (solid lines; cf. Eq. (3)). In spite of slight numerical discrepancies between the estimated parameters and their target values (see Additional file 1), the estimated model accurately predicts the dynamics of the target system, indicating quasi-redundancy [e.g., [27] and [25] ] or "sloppiness" [26] among the parameters.
Mentions: Initially, all experiments were performed with noise-free time series, but in a second set of experiments, we added noise. Because the proposed algorithm uses the decoupled, algebraic form, a signal extraction procedure was employed for the noisy data to provide smooth time series and slopes [22]. The results show that combining the two strategies (smoother and proposed algorithm) generate accurate dynamical responses for the case studies used in this report (Figure 2).

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