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A simple work flow for biologically inspired model reduction--application to early JAK-STAT signaling.

Quaiser T, Dittrich A, Schaper F, Mönnigmann M - BMC Syst Biol (2011)

Bottom Line: These steps need to be applied iteratively until the resulting model is identifiable, or equivalently, until parameter variances are small.In contrast to related work in systems biology, we do not suggest simplifying a model by fixing some of its parameters, but change the structure of the model.The resulting model is not only identifiable with small parameter variances, but also shows the best trade-off between goodness of fit and model complexity.

View Article: PubMed Central - HTML - PubMed

Affiliation: Automatic Control and Systems Theory, Ruhr University Bochum, D-44801 Bochum, Germany.

ABSTRACT

Background: Modeling of biological pathways is a key issue in systems biology. When constructing a model, it is tempting to incorporate all known interactions of pathway species, which results in models with a large number of unknown parameters. Fortunately, unknown parameters need not necessarily be measured directly, but some parameter values can be estimated indirectly by fitting the model to experimental data. However, parameter fitting, or, more precisely, maximum likelihood parameter estimation, only provides valid results, if the complexity of the model is in balance with the amount and quality of the experimental data. If this is the case the model is said to be identifiable for the given data. If a model turns out to be unidentifiable, two steps can be taken. Either additional experiments need to be conducted, or the model has to be simplified.

Results: We propose a systematic procedure for model simplification, which consists of the following steps: estimate the parameters of the model, create an identifiability ranking for the estimated parameters, and simplify the model based on the identifiability analysis results. These steps need to be applied iteratively until the resulting model is identifiable, or equivalently, until parameter variances are small. We choose parameter variances as stopping criterion, since they are concise and easy to interpret. For both, the parameter estimation and the calculation of parameter variances, multi-start parameter estimations are run on a parallel cluster. In contrast to related work in systems biology, we do not suggest simplifying a model by fixing some of its parameters, but change the structure of the model.

Conclusions: We apply the proposed approach to a model of early signaling events in the JAK-STAT pathway. The resulting model is not only identifiable with small parameter variances, but also shows the best trade-off between goodness of fit and model complexity.

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Related in: MedlinePlus

Simplification of the PPX part leads to model M4. The same notation as in Figure 3 is used. Additionally, a red colored parameter name indicates, the introduction of a new parameter. In this simplification step PPX and all corresponding reactions have been removed from the model. In order to still account for STAT1cPhos_2 dissociation and phosphorylation, we added a new dissociation reaction containing the parameter k11new. The mathematical description of model M4 is given in Additional file 1 table S6a and S6b.
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Figure 4: Simplification of the PPX part leads to model M4. The same notation as in Figure 3 is used. Additionally, a red colored parameter name indicates, the introduction of a new parameter. In this simplification step PPX and all corresponding reactions have been removed from the model. In order to still account for STAT1cPhos_2 dissociation and phosphorylation, we added a new dissociation reaction containing the parameter k11new. The mathematical description of model M4 is given in Additional file 1 table S6a and S6b.

Mentions: kf25 describes the rate of the dephosphorylation of STAT1cPhos_2 by PPX (cf. Figure 4). STAT1cPhos can be dephosphorylated by PPX along either of two routes. 1) PPX binds and dephosphorylates the phosphorylated STAT1c monomer or 2) PPX binds the homodimer of phosphorylated STAT1c and subsequently dephosphorylates one of the two STAT1c proteins. In the second case the heterodimer STAT1c_STAT1cPhos is created. Since neither STAT1c heterodimers, nor the phosphatase PPX have been experimentally validated we propose to considerably simplify this part of the model (see Figure 4). We remove PPX and all its complexes from the model and assume a simple first order kinetic for the conversion of the phosphorylated dimer into two unphosphorylated monomers. We stress that removing PPX is a drastic simplification. The fact that the PPX-related parameters kf12 and k24 are ranked third and fourth in the identifiability ranking (cf. Table 1) further suggests that this simplification is reasonable. Since not only PPX (PPX(0) = 50 nM) but also all PPX bound species are removed, the initial conditions of the remaining species do not change.


A simple work flow for biologically inspired model reduction--application to early JAK-STAT signaling.

Quaiser T, Dittrich A, Schaper F, Mönnigmann M - BMC Syst Biol (2011)

Simplification of the PPX part leads to model M4. The same notation as in Figure 3 is used. Additionally, a red colored parameter name indicates, the introduction of a new parameter. In this simplification step PPX and all corresponding reactions have been removed from the model. In order to still account for STAT1cPhos_2 dissociation and phosphorylation, we added a new dissociation reaction containing the parameter k11new. The mathematical description of model M4 is given in Additional file 1 table S6a and S6b.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3050741&req=5

Figure 4: Simplification of the PPX part leads to model M4. The same notation as in Figure 3 is used. Additionally, a red colored parameter name indicates, the introduction of a new parameter. In this simplification step PPX and all corresponding reactions have been removed from the model. In order to still account for STAT1cPhos_2 dissociation and phosphorylation, we added a new dissociation reaction containing the parameter k11new. The mathematical description of model M4 is given in Additional file 1 table S6a and S6b.
Mentions: kf25 describes the rate of the dephosphorylation of STAT1cPhos_2 by PPX (cf. Figure 4). STAT1cPhos can be dephosphorylated by PPX along either of two routes. 1) PPX binds and dephosphorylates the phosphorylated STAT1c monomer or 2) PPX binds the homodimer of phosphorylated STAT1c and subsequently dephosphorylates one of the two STAT1c proteins. In the second case the heterodimer STAT1c_STAT1cPhos is created. Since neither STAT1c heterodimers, nor the phosphatase PPX have been experimentally validated we propose to considerably simplify this part of the model (see Figure 4). We remove PPX and all its complexes from the model and assume a simple first order kinetic for the conversion of the phosphorylated dimer into two unphosphorylated monomers. We stress that removing PPX is a drastic simplification. The fact that the PPX-related parameters kf12 and k24 are ranked third and fourth in the identifiability ranking (cf. Table 1) further suggests that this simplification is reasonable. Since not only PPX (PPX(0) = 50 nM) but also all PPX bound species are removed, the initial conditions of the remaining species do not change.

Bottom Line: These steps need to be applied iteratively until the resulting model is identifiable, or equivalently, until parameter variances are small.In contrast to related work in systems biology, we do not suggest simplifying a model by fixing some of its parameters, but change the structure of the model.The resulting model is not only identifiable with small parameter variances, but also shows the best trade-off between goodness of fit and model complexity.

View Article: PubMed Central - HTML - PubMed

Affiliation: Automatic Control and Systems Theory, Ruhr University Bochum, D-44801 Bochum, Germany.

ABSTRACT

Background: Modeling of biological pathways is a key issue in systems biology. When constructing a model, it is tempting to incorporate all known interactions of pathway species, which results in models with a large number of unknown parameters. Fortunately, unknown parameters need not necessarily be measured directly, but some parameter values can be estimated indirectly by fitting the model to experimental data. However, parameter fitting, or, more precisely, maximum likelihood parameter estimation, only provides valid results, if the complexity of the model is in balance with the amount and quality of the experimental data. If this is the case the model is said to be identifiable for the given data. If a model turns out to be unidentifiable, two steps can be taken. Either additional experiments need to be conducted, or the model has to be simplified.

Results: We propose a systematic procedure for model simplification, which consists of the following steps: estimate the parameters of the model, create an identifiability ranking for the estimated parameters, and simplify the model based on the identifiability analysis results. These steps need to be applied iteratively until the resulting model is identifiable, or equivalently, until parameter variances are small. We choose parameter variances as stopping criterion, since they are concise and easy to interpret. For both, the parameter estimation and the calculation of parameter variances, multi-start parameter estimations are run on a parallel cluster. In contrast to related work in systems biology, we do not suggest simplifying a model by fixing some of its parameters, but change the structure of the model.

Conclusions: We apply the proposed approach to a model of early signaling events in the JAK-STAT pathway. The resulting model is not only identifiable with small parameter variances, but also shows the best trade-off between goodness of fit and model complexity.

Show MeSH
Related in: MedlinePlus