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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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Related in: MedlinePlus

The shown part of the EGF and insulin receptor network is modeled. The process interactions are depicted by arrows. Black arrows represent uni- and bidirectional interactions, while grey arrows describe all-or-none interactions. A complete mechanistic model of this network comprises 5,182 ODEs, while the exactly reduced one consists of only 87 ODEs.
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Figure 4: The shown part of the EGF and insulin receptor network is modeled. The process interactions are depicted by arrows. Black arrows represent uni- and bidirectional interactions, while grey arrows describe all-or-none interactions. A complete mechanistic model of this network comprises 5,182 ODEs, while the exactly reduced one consists of only 87 ODEs.

Mentions: The main advantage of the proposed method is the direct generation of a reduced, but exact, system of equations, circumventing a unsuitable large model of full combinatorial complexity. Admittedly, the number of equations that has to be set up in step six mostly include redundant information about processes which can be observed at numerous outputs. However, the absolute number of ODEs that have to be generated is usually much lower than if a complete mechanistic model is created. In the considered example one only has to set up 27 ODEs using the described procedure. A complete combinatorial model would comprise 77 states. The method has to be slightly modified if one of the output variables is a higher order occurrence level which is not contained in any of the submodels. Let us assume that one of the output variables in the example is [B(*, P(*), P(*), *)] which describes both process 2 and process 3. Since none of the three subgraphs depicted in Figure 4C comprises both processes simultaneously the quantity [B(*, P(*), P(*), *)] will not be a state of the reduced 22 ODE model. This problem can be overcome by the fusion of two subgraphs. This will necessarily increase the number of ODEs that has to be generated as well as the final size of the reduced model. However, the number of ODEs would still be smaller than 77. Furthermore, the inclusion of production and degradation into the mathematical model necessitates another extension of this method. The same holds true if the regarded system includes multifunctional protein binding domains, i.e. that certain binding domains are involved in several binding processes. Both cases shall be discussed in the following. Note, that these problems do not occur if a the method described in Section Exact Model Reduction is used.


Exact model reduction of combinatorial reaction networks.

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

The shown part of the EGF and insulin receptor network is modeled. The process interactions are depicted by arrows. Black arrows represent uni- and bidirectional interactions, while grey arrows describe all-or-none interactions. A complete mechanistic model of this network comprises 5,182 ODEs, while the exactly reduced one consists of only 87 ODEs.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: The shown part of the EGF and insulin receptor network is modeled. The process interactions are depicted by arrows. Black arrows represent uni- and bidirectional interactions, while grey arrows describe all-or-none interactions. A complete mechanistic model of this network comprises 5,182 ODEs, while the exactly reduced one consists of only 87 ODEs.
Mentions: The main advantage of the proposed method is the direct generation of a reduced, but exact, system of equations, circumventing a unsuitable large model of full combinatorial complexity. Admittedly, the number of equations that has to be set up in step six mostly include redundant information about processes which can be observed at numerous outputs. However, the absolute number of ODEs that have to be generated is usually much lower than if a complete mechanistic model is created. In the considered example one only has to set up 27 ODEs using the described procedure. A complete combinatorial model would comprise 77 states. The method has to be slightly modified if one of the output variables is a higher order occurrence level which is not contained in any of the submodels. Let us assume that one of the output variables in the example is [B(*, P(*), P(*), *)] which describes both process 2 and process 3. Since none of the three subgraphs depicted in Figure 4C comprises both processes simultaneously the quantity [B(*, P(*), P(*), *)] will not be a state of the reduced 22 ODE model. This problem can be overcome by the fusion of two subgraphs. This will necessarily increase the number of ODEs that has to be generated as well as the final size of the reduced model. However, the number of ODEs would still be smaller than 77. Furthermore, the inclusion of production and degradation into the mathematical model necessitates another extension of this method. The same holds true if the regarded system includes multifunctional protein binding domains, i.e. that certain binding domains are involved in several binding processes. Both cases shall be discussed in the following. Note, that these problems do not occur if a the method described in Section Exact Model Reduction is used.

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