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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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Topology mapping. Example of network topology mapping onto kinetic orders in an S-system [17]. The exponents in the equations directly correspond to effects of metabolites on processes (flux arrows) in the pathway diagram. As an example, the flux out of X3 is affected by X3 as substrate and by X4 as activator. Both variables appear in the corresponding term with their respective kinetic orders. The gray-scale in the g and h matrices reflects the magnitudes of the exponents in the production and degradation terms of the S-system, respectively, with higher values shown in darker hues.
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Figure 1: Topology mapping. Example of network topology mapping onto kinetic orders in an S-system [17]. The exponents in the equations directly correspond to effects of metabolites on processes (flux arrows) in the pathway diagram. As an example, the flux out of X3 is affected by X3 as substrate and by X4 as activator. Both variables appear in the corresponding term with their respective kinetic orders. The gray-scale in the g and h matrices reflects the magnitudes of the exponents in the production and degradation terms of the S-system, respectively, with higher values shown in darker hues.

Mentions: Here, Xi represents the concentration of metabolite i, αi and βi are non-negative rate constants, and gij and hij are real-valued kinetic orders for the production and degradation term, respectively. A considerable amount of information about S-systems can be found in [1-5]. A major advantage of this representation is that it uniquely maps dynamical and topological information onto its parameters; an illustration is given in Figure 1.


Parameter optimization in S-system models.

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

Topology mapping. Example of network topology mapping onto kinetic orders in an S-system [17]. The exponents in the equations directly correspond to effects of metabolites on processes (flux arrows) in the pathway diagram. As an example, the flux out of X3 is affected by X3 as substrate and by X4 as activator. Both variables appear in the corresponding term with their respective kinetic orders. The gray-scale in the g and h matrices reflects the magnitudes of the exponents in the production and degradation terms of the S-system, respectively, with higher values shown in darker hues.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Topology mapping. Example of network topology mapping onto kinetic orders in an S-system [17]. The exponents in the equations directly correspond to effects of metabolites on processes (flux arrows) in the pathway diagram. As an example, the flux out of X3 is affected by X3 as substrate and by X4 as activator. Both variables appear in the corresponding term with their respective kinetic orders. The gray-scale in the g and h matrices reflects the magnitudes of the exponents in the production and degradation terms of the S-system, respectively, with higher values shown in darker hues.
Mentions: Here, Xi represents the concentration of metabolite i, αi and βi are non-negative rate constants, and gij and hij are real-valued kinetic orders for the production and degradation term, respectively. A considerable amount of information about S-systems can be found in [1-5]. A major advantage of this representation is that it uniquely maps dynamical and topological information onto its parameters; an illustration is given in Figure 1.

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