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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 three basic scenarios that will be discussed in the following. Figure A depicts a receptor or scaffold protein with single protein ligands, i.e. each binding domain can recruit single proteins which do not possess further binding domains. A scaffold with multiprotein ligands is shown in Figure B. Some of the ligands are scaffolds themselves. The last scenario additionally includes receptor homodimerization. Heterodimerization on the other site corresponds to the scenario depicted in Figure B.
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Figure 1: The three basic scenarios that will be discussed in the following. Figure A depicts a receptor or scaffold protein with single protein ligands, i.e. each binding domain can recruit single proteins which do not possess further binding domains. A scaffold with multiprotein ligands is shown in Figure B. Some of the ligands are scaffolds themselves. The last scenario additionally includes receptor homodimerization. Heterodimerization on the other site corresponds to the scenario depicted in Figure B.

Mentions: Step 3: The last reduction step is the elimination of the unobservable system states. If the model also comprises uncontrollable states these ODEs can be replaced by the related steady state equations. A suitable transformation pattern that facilitates a Kalman decomposition of models describing scaffolds with multiprotein ligands or scaffold homodimerization is still missing. The term multprotein ligand indicates that the direct binding partners of the considered scaffold can also recruit further proteins or scaffolds (see Figure 1). In the following subsections, we will introduce and discuss transformation patterns for these kind of systems.


Exact model reduction of combinatorial reaction networks.

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

The three basic scenarios that will be discussed in the following. Figure A depicts a receptor or scaffold protein with single protein ligands, i.e. each binding domain can recruit single proteins which do not possess further binding domains. A scaffold with multiprotein ligands is shown in Figure B. Some of the ligands are scaffolds themselves. The last scenario additionally includes receptor homodimerization. Heterodimerization on the other site corresponds to the scenario depicted in Figure B.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: The three basic scenarios that will be discussed in the following. Figure A depicts a receptor or scaffold protein with single protein ligands, i.e. each binding domain can recruit single proteins which do not possess further binding domains. A scaffold with multiprotein ligands is shown in Figure B. Some of the ligands are scaffolds themselves. The last scenario additionally includes receptor homodimerization. Heterodimerization on the other site corresponds to the scenario depicted in Figure B.
Mentions: Step 3: The last reduction step is the elimination of the unobservable system states. If the model also comprises uncontrollable states these ODEs can be replaced by the related steady state equations. A suitable transformation pattern that facilitates a Kalman decomposition of models describing scaffolds with multiprotein ligands or scaffold homodimerization is still missing. The term multprotein ligand indicates that the direct binding partners of the considered scaffold can also recruit further proteins or scaffolds (see Figure 1). In the following subsections, we will introduce and discuss transformation patterns for these kind of systems.

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