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Exact model reduction of combinatorial reaction networks.

Conzelmann H, Fey D, Gilles ED - BMC Syst Biol (2008)

Bottom Line: Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable.A novel model reduction technique allows the significant reduction and modularization of these models.Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures.

View Article: PubMed Central - HTML - PubMed

Affiliation: Max-Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr, 1, 39106, Magdeburg, Germany. Conzelmann@isr.uni-stuttgart.de

ABSTRACT

Background: Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models.

Results: We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs) to a model with 87 ODEs.

Conclusion: The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.

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Exemplification of the developed reduced order modeling technique. The considered example is very similar to the previously discussed insulin example. Only the interaction pattern is a bit different. The depicted steps of the reduced order modeling technique are explained in the text.
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Figure 3: Exemplification of the developed reduced order modeling technique. The considered example is very similar to the previously discussed insulin example. Only the interaction pattern is a bit different. The depicted steps of the reduced order modeling technique are explained in the text.

Mentions: The enormous complexity of most real signal transduction networks often impedes the application of common model reduction techniques discussed in literature as well as the previously proposed model reduction concept. New alternative techniques are required that allow the direct generation of reduced model equations. The already introduced concepts of process interactions, interaction graphs as well as process controllability and observability serve as a basis for the following considerations. The fundamental idea is that at the macroscopic level a mathematical description of a certain process merely requires the incorporation of those other processes that exert some influence on the considered one. A detailed specification of the method will be given in the following and is structured in nine elementary steps. Each step will be illustrated considering the example shown in Figure 3.


Exact model reduction of combinatorial reaction networks.

Conzelmann H, Fey D, Gilles ED - BMC Syst Biol (2008)

Exemplification of the developed reduced order modeling technique. The considered example is very similar to the previously discussed insulin example. Only the interaction pattern is a bit different. The depicted steps of the reduced order modeling technique are explained in the text.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2570670&req=5

Figure 3: Exemplification of the developed reduced order modeling technique. The considered example is very similar to the previously discussed insulin example. Only the interaction pattern is a bit different. The depicted steps of the reduced order modeling technique are explained in the text.
Mentions: The enormous complexity of most real signal transduction networks often impedes the application of common model reduction techniques discussed in literature as well as the previously proposed model reduction concept. New alternative techniques are required that allow the direct generation of reduced model equations. The already introduced concepts of process interactions, interaction graphs as well as process controllability and observability serve as a basis for the following considerations. The fundamental idea is that at the macroscopic level a mathematical description of a certain process merely requires the incorporation of those other processes that exert some influence on the considered one. A detailed specification of the method will be given in the following and is structured in nine elementary steps. Each step will be illustrated considering the example shown in Figure 3.

Bottom Line: Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable.A novel model reduction technique allows the significant reduction and modularization of these models.Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures.

View Article: PubMed Central - HTML - PubMed

Affiliation: Max-Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr, 1, 39106, Magdeburg, Germany. Conzelmann@isr.uni-stuttgart.de

ABSTRACT

Background: Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models.

Results: We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs) to a model with 87 ODEs.

Conclusion: The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.

Show MeSH
Related in: MedlinePlus