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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

Simulation results of the generated crosstalk model. The kinetic parameters of the model have been chosen such that the system qualitatively shows the expected behavior. All quantities are depicted in relative concentrations. The overall concentrations of all involved components have been set to 100. The displayed curves show the chosen input signals [EGF], [insulin] and [ERK] as well as the output concentrations [IR(*, SOS, *)], [IR(*, *, SOS)], [EGFR(*, SOS, *).*] and [EGFR(*, *, SOS).*].
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Figure 5: Simulation results of the generated crosstalk model. The kinetic parameters of the model have been chosen such that the system qualitatively shows the expected behavior. All quantities are depicted in relative concentrations. The overall concentrations of all involved components have been set to 100. The displayed curves show the chosen input signals [EGF], [insulin] and [ERK] as well as the output concentrations [IR(*, SOS, *)], [IR(*, *, SOS)], [EGFR(*, SOS, *).*] and [EGFR(*, *, SOS).*].

Mentions: An exactly reduced version of the crosstalk model was generated using the reduced order modeling approach we introduced above. The definition of molecules, processes and process interactions (steps 1–3 of the method) is already given in the previous Model definition section. The process interaction graph corresponds to the arrows drawn in Figure 4. In order to get comparable results for all occurring binding and phosphorylation processes each of them was chosen as output process (step 4). The process interaction graph of the considered system can be dissected into four subgraphs (step 5). Until now this step has not been automatized but an automatization would be possible. Each subgraph describes one intracellular binding domain either of the EGF or the insulin receptor. However, due to the multifunctionality of the Grb2 binding domain all four subgraphs comprise the Grb2-SOS binding process as well as the serine/threonine phosphorylation of SOS. Consequently, the four subgraphs have to be simultaneously modeled and all species have to be simulantiously balanced. We use the modeling tool ALC to model the four submodels [29]. The input file with which ALC generates the ODEs is provided as additional file [see Additional file 2]. A link to a downloadable version of ALC can be found in Koschorreck et al. [29]. The resulting model comprises 1,826 reactions and 391 ODEs which already is a significant reduction compared to the complete model. A further reduction can be achieved by transforming the model to the previously introduced occurrence levels and subsequent elimination of redundant, unobservable and uncontrollable system dynamics (steps 7 and 8). These steps have been performed using MATHEMATICA. The MATHEMATICA code can also be found in the Additional files section [see Additional file 3]. The final and exactly reduced model of the network consists of 87 ODEs, which can be divided into six unidirectionally coupled modules. One of these modules, which consists of four ODEs, describes EGF binding and EGFR homodimerization. Another module specifies insulin binding to the insulin receptor and comprises two ODEs. Six ODEs are required to model IR phosphorylation at the IRS domain and subsequent IRS binding. Shc binding to EGFR as well as IR and the related domain phosphorylations form another module with a total number of 18 ODEs. The largest module consists of 32 ODEs and describes Grb2 binding to the EGF receptor as well as to phosphorylated Shc. The last module comprises all variables describing SOS binding and SOS phosphorylation and consists of 25 ODEs. One simulation run of this exactly reduced model only takes a few seconds. The size of the simulation file is 37.4 KB [see Additional file 4]. In Figure 5 it is shown that both models also provide exactly the same results for the considered output variables.


Exact model reduction of combinatorial reaction networks.

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

Simulation results of the generated crosstalk model. The kinetic parameters of the model have been chosen such that the system qualitatively shows the expected behavior. All quantities are depicted in relative concentrations. The overall concentrations of all involved components have been set to 100. The displayed curves show the chosen input signals [EGF], [insulin] and [ERK] as well as the output concentrations [IR(*, SOS, *)], [IR(*, *, SOS)], [EGFR(*, SOS, *).*] and [EGFR(*, *, SOS).*].
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 5: Simulation results of the generated crosstalk model. The kinetic parameters of the model have been chosen such that the system qualitatively shows the expected behavior. All quantities are depicted in relative concentrations. The overall concentrations of all involved components have been set to 100. The displayed curves show the chosen input signals [EGF], [insulin] and [ERK] as well as the output concentrations [IR(*, SOS, *)], [IR(*, *, SOS)], [EGFR(*, SOS, *).*] and [EGFR(*, *, SOS).*].
Mentions: An exactly reduced version of the crosstalk model was generated using the reduced order modeling approach we introduced above. The definition of molecules, processes and process interactions (steps 1–3 of the method) is already given in the previous Model definition section. The process interaction graph corresponds to the arrows drawn in Figure 4. In order to get comparable results for all occurring binding and phosphorylation processes each of them was chosen as output process (step 4). The process interaction graph of the considered system can be dissected into four subgraphs (step 5). Until now this step has not been automatized but an automatization would be possible. Each subgraph describes one intracellular binding domain either of the EGF or the insulin receptor. However, due to the multifunctionality of the Grb2 binding domain all four subgraphs comprise the Grb2-SOS binding process as well as the serine/threonine phosphorylation of SOS. Consequently, the four subgraphs have to be simultaneously modeled and all species have to be simulantiously balanced. We use the modeling tool ALC to model the four submodels [29]. The input file with which ALC generates the ODEs is provided as additional file [see Additional file 2]. A link to a downloadable version of ALC can be found in Koschorreck et al. [29]. The resulting model comprises 1,826 reactions and 391 ODEs which already is a significant reduction compared to the complete model. A further reduction can be achieved by transforming the model to the previously introduced occurrence levels and subsequent elimination of redundant, unobservable and uncontrollable system dynamics (steps 7 and 8). These steps have been performed using MATHEMATICA. The MATHEMATICA code can also be found in the Additional files section [see Additional file 3]. The final and exactly reduced model of the network consists of 87 ODEs, which can be divided into six unidirectionally coupled modules. One of these modules, which consists of four ODEs, describes EGF binding and EGFR homodimerization. Another module specifies insulin binding to the insulin receptor and comprises two ODEs. Six ODEs are required to model IR phosphorylation at the IRS domain and subsequent IRS binding. Shc binding to EGFR as well as IR and the related domain phosphorylations form another module with a total number of 18 ODEs. The largest module consists of 32 ODEs and describes Grb2 binding to the EGF receptor as well as to phosphorylated Shc. The last module comprises all variables describing SOS binding and SOS phosphorylation and consists of 25 ODEs. One simulation run of this exactly reduced model only takes a few seconds. The size of the simulation file is 37.4 KB [see Additional file 4]. In Figure 5 it is shown that both models also provide exactly the same results for the considered output variables.

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