Table S1: Data-generating Model:

Transcription

1 Table S1: Data-generating Model: Below are the parameters used for the data-generating model (section 1.5). The model was generated using CNORode. The data generating model is included below (figure S1). Parameters Values map3k7_n_nik map3k7_k_nik tau_nik map3k7_n_mkk map3k7_k_mkk map3k1_n_mkk map3k1_k_mkk tau_mkk traf2_n_ask traf2_k_ask tau_ask traf2_n_map3k traf2_k_map3k tau_map3k ask1_n_mkk ask1_k_mkk map3k1_n_mkk map3k1_k_mkk tau_mkk _n_tnfr _k_tnfr tau_tnfr _n_r _k_r tau_r _n_ph _k_ph tau_ph _n_ex _k_ex tau_ex _n_mek _k_mek 195 tau_mek _n_ras _k_ras tau_ras tnfr_n_traf tnfr_k_traf2 476 tau_traf nik_n_ikk nik_k_ikk tau_ikk _n_akt _k_akt tau_akt r_n_ r_k_ tau_ ex_n_ikb ex_k_ikb ikk_n_ikb ikk_k_ikb tau_ikb ikb_n_ ikb_k_ tau_ jnk_n_cjun jnk_k_cjun tau_cjun mkk7_n_jnk mkk7_k_jnk tau_jnk ras_n_map3k ras_k_map3k tau_map3k mek_n_ mek_k_ tau_ ras_n_ ras_k_ tau_ r_n_ r_k_ ph_n_ ph_k_ tau_ mkk4_n_ mkk4_k_ tau_ akt_n_ akt_k_ tau_ cjun_n_ cjun_k_ tau_

2 tnfr r traf2 ras map3k7 ask1 map3k1 akt nik mkk7 mek ikk jnk mkk4 ikb ph cjun ex Figure S1: The model used to generate the in silico data.

3 Compression and Expansion Figure S2: The prior knowledge network (section 1.5) annotated with stimuli (green), inhibited species (red) and readouts (blue). The graph was exported by Graphviz by the plotmodel function of CellNOptR.

4 Figure S3: The compressed form of the PKN, as described in sections 1.4 and 8.1. Figure S4: The expanded form, accounting for all possible hyperedges of the PKN after compression.

5 Acronyms: Akt - RAC-alpha serine/threonine-protein kinase AP1 - Activator protein 1 ASK-1 - Apoptosis signal-regulating kinase 1 c-jun - Jun proto-oncogene cfl Constrained fuzzy logic EGF Epidermal growth factor EGFR Epidermal growth factor receptor ERK - Extracellular signal-regulated kinase ex Expression GSK-3 Glycogen synthase kinase 3 IκB - Inhibitor of nuclear factor kappa-b IKK - IκB kinase JNK1 - Mitogen-activated protein kinase 8 Map3K1 - Mitogen-activated protein kinase kinase kinase 1 Map3K7 - Mitogen-activated protein kinase kinase kinase 7 MAPK - Mitogen-activated protein kinase MEK 1 - Dual specificity mitogen-activated protein kinase kinase 1 MKK4 - Dual specificity mitogen-activated protein kinase kinase 4 MKK7 - Dual specificity mitogen-activated protein kinase kinase 7 mtor - Mammalian target of rapamycin) NIK - NF-kappa-B-inducing kinase NFκB - Nuclear factor kappa-light-chain-enhancer of activated B cells PDK1-3-phosphoinositide-dependent protein kinase 1 PIN Protein interaction network ODE Ordinary differential equation - P38 mitogen-activated protein kinase ph Phosphatase PI3K - Phosphatidylinositol 3-kinase PKN Prior knowledge network PSN Protein signaling network Rac - FYVE, RhoGEF and PH domain-containing protein 1 Raf-1 - RAF proto-oncogene serine/threonine-protein kinase SBGN Systems Biology Graphical Notation SOS-1 Son of sevenless homolog 1 TNFα - Tumor Necrosis Factor α TNFR - Tumor Necrosis Factor Receptor

6 i i i i Exploring the choice of steady state (CellNOptR, Boolean steady state) The following figures explore the choice of time point on the fitting of model to data, using the Boolean steady state formalism (section 2) Stim Inh Error 0 ikb 1 Figure S5: The optimized model and fit to data using minutes. At this early time point, the system has not reached a steady state and the data does not reflect the underlying network structure. For example, GSK3 deactivation through EGF stimulation is not evident in the data and is hence not added to the model. Stim Inh Error 0 map3k Figure S6: The optimized model and fit to data using 0 minutes. Measuring the system at this time point encounters the problem of secondary feedback interactions (figure 2). The feedback to SOS- 1 has inhibited ERK/Raf1 activation so these interactions cannot be fitted to the data. The fitting process has used alternative pathways to explain AP1 activation (i.e. through TNFα stimulation), which causes errors when fitting the GSK readouts.

7 Testing MSE Selected Deletions MSE i i Stim Inh Error 0 map3k1 1 Figure S7: The optimized model and fit to data using 0 minutes. At this late time point, most of the activation has ceased in the system and only some interactions can be uncovered from the true model. Cross-Validation: Two cross validation techniques were used for each formalism. This first was 5-fold crossvalidation, where 20% of the data was randomly removed and model training was performed on the remaining 80% of the data. The trained model was then fitted against the remaining 20% and the mean squared error was compared between testing and training. The second method selectively removed all data from 2 randomly chosen experiments (or conditions), and 2 randomly chosen readouts. The MSE of the optimized model was then compared against the MSE of the model fitted to the full data Training MSE Full Data MSE Figure S8: Random and selected cross-validation for the Boolean steady state formalism. On the left, there was no significant difference between the MSE of the training data (80%) and the test data (20%) against the optimized model found using the training data (P = 0.43, 2-sided t-test, n = 20). On the right, there was no significant difference in the MSE between the optimized model of the full data and the optimized model of the data missing 2 random conditions/signals (P = 0.06, 2-sided t-test, n = 20).