We have used a model reduction technique specifically adapted to discrete systems, which mainly consists in iteratively “hiding” some variables, while keeping track of underlying regulatory processes [47] . The main dynamical properties of the master model, including stable states and other attractors are conserved in the reduced model. Thanks to the computation of the reduced asynchronous transition graph, relevant qualitative dynamical properties of the model can be compared to experimental results for wild type and in different mutant cases.
To reduce the number of species in the master model, each logical rule is considered. For each removed component, the information contained in its rule is included in the rules of its targets such that no effective regulation is lost.
Many intermediate components could easily be replaced by a proper rewriting of the logical rules associated with their target nodes. For example, IKK has only one input (RIP1ub) and one output (NFκB). Since its role in our model merely consists in transmitting the signal from RIP1ub to NFκB, it can be easily replaced by a straightforward change in the logical rule associated with NFκB (implementing a direct activation from RIP1ub instead of IKK). We also relied on the results of the clustering of stable states and their associations with biologically plausible phenotypes to select the key components to keep in the reduced model: NFκB is the principal survival actor, while caspases-3 and -8, together with the mitochondrial membrane permeability variables (MOMP and MPT), determine apoptotic and non-apoptotic cell deaths.
Let us consider the example of the removal of BAX and BCL2 (Figure 1 A and B). The regulators (or inputs) of these variables are NFκB for BCL2 and CASP8 for BAX while their regulating targets (or outputs) are MPT for BCL2 and MOMP for BAX. BCL2 is directly activated by NFκB, and has two targets: MPT and BAX. Therefore, BCL2 removal is performed by replacing BCL2 by NFκB into the rules of the two targets, leading to the two new logical rules: MPT′ = ROS AND NOT NFkB and BAX′ = C8 AND NOT NFkB. Applying the same process to remove BAX, one obtains the following new rule for MOMP: MOMP′ = MPT OR (C8 AND NOT NFkB).
The variables MOMP and MPT have now as inputs the variables NFκB and CASP8. One can see that, in spite of the disappearance of variables BAX and BCL2, their regulating roles are still indirectly coded in the reduced system, ensuring that no “logical interaction” of the master model (i.e. activation or inhibition) is actually lost during the reduction process.Table S3 lists the variables of the master model that are removed to obtain the reduced model.
Some hypotheses were made when reducing the model. First, FADD is considered to be constantly ON in wild type simulations. Second, since the two complexes TNFR and DISC-TNF have been removed together with the input FADD, the two deaths ligands TNF and L have the exact same action in the reduced model. Indeed, we consider that, in response to FAS death receptor engagement as well as that of TNF; the activations of both the survival and necrotic pathways RIP1-dependent. In this case, one could then merge these variables and consider only one input that could be called “external death receptor”. However, we choose to keep the two variables TNF and FASL, in the FADD deletion mutant, the phenotype differs for TNF and FAS signal: actually, only for that mutant is the symmetry of TNF and FAS broken.
To reduce the number of species in the master model, each logical rule is considered. For each removed component, the information contained in its rule is included in the rules of its targets such that no effective regulation is lost.
Many intermediate components could easily be replaced by a proper rewriting of the logical rules associated with their target nodes. For example, IKK has only one input (RIP1ub) and one output (NFκB). Since its role in our model merely consists in transmitting the signal from RIP1ub to NFκB, it can be easily replaced by a straightforward change in the logical rule associated with NFκB (implementing a direct activation from RIP1ub instead of IKK). We also relied on the results of the clustering of stable states and their associations with biologically plausible phenotypes to select the key components to keep in the reduced model: NFκB is the principal survival actor, while caspases-3 and -8, together with the mitochondrial membrane permeability variables (MOMP and MPT), determine apoptotic and non-apoptotic cell deaths.
Let us consider the example of the removal of BAX and BCL2 (
The variables MOMP and MPT have now as inputs the variables NFκB and CASP8. One can see that, in spite of the disappearance of variables BAX and BCL2, their regulating roles are still indirectly coded in the reduced system, ensuring that no “logical interaction” of the master model (i.e. activation or inhibition) is actually lost during the reduction process.
Some hypotheses were made when reducing the model. First, FADD is considered to be constantly ON in wild type simulations. Second, since the two complexes TNFR and DISC-TNF have been removed together with the input FADD, the two deaths ligands TNF and L have the exact same action in the reduced model. Indeed, we consider that, in response to FAS death receptor engagement as well as that of TNF; the activations of both the survival and necrotic pathways RIP1-dependent. In this case, one could then merge these variables and consider only one input that could be called “external death receptor”. However, we choose to keep the two variables TNF and FASL, in the FADD deletion mutant, the phenotype differs for TNF and FAS signal: actually, only for that mutant is the symmetry of TNF and FAS broken.
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