Fig 1.
Decision tree for state classification based on indices.
See text for details.
Fig 2.
Simple reaction cycle model and scenario-specific parameter values.
(A) Reaction network, and (B) parameter values for the three scenarios, for which the model system was studied. The time span was t ∈ [0, T] min with T = 0.01 or 0.1 (depending on the scenario), the input variable A, and the response variable D. The initial conditions were identical in all three scenarios: (A, B, C, D)0 = (0, 100, 5, 0) nM and input u0 = (2, 0, 0, 0) nM. Units: kon in 1/nM/min; all other reaction rate constants in 1/min.
Fig 3.
Scenario 1 of the simple reaction cycle model: Time course of state variables (Panel A), and normalised ir-indices (Panel B).
For details on the model, see Fig 2.
Fig 4.
Scenario 1, states B (left) and C (right) of the simple reaction cycle model: State classification indices (Panels A, B), relative state approximation error (Panels C, D) and modified dynamics (Panels E, F).
Panels E and F: Comparison of reference dynamics and modified dynamics from t* = 0 (dashed lines) for B as environmental state and for C in partial steady state. For details on the model, see Fig 2.
Fig 5.
Scenario 2 (left) & 3 (right) of the simple reaction model: Time course of state variables (Panels A,B), and normalised ir-indices (Panels C,D).
For details on the model, see Fig 2.
Fig 6.
Scenario 3, states B (left) and C (right) of the simple reaction model: Normalised state classification indices (Panels A, B) and relative state approximation errors (Panels C, D).
For details on the model, see Fig 2.
Fig 7.
Output signal (left) and sum of ir-indices evolving over time (right).
A: Transient increase of ERK-PP (output) in response to the EGF (input) stimulus. Inset zoom: signal activation occurs within 3 min. B: Sum of ir-indices over time, showing three phases: initial peak (0–0.3 min), high plateau (0.3–3 min), and low plateau including decay (3–100 min).
Fig 8.
Normalised ir-indices over time and ordered maximal value.
A, B and C: Normalised ir-indices for the three phases (0–0.3 min, 0.3–3 min, 3–100 min). Shown are all 20 indices with a maximal value exceeding δy = 10%. D: Order of decay of maximum value of the normalised ir-indices. All 20 states above the threshold of 10% are membrane-bound or free cytosolic forms and (as far as applicable) belong to the Shc-dependent pathway—as opposed to internalised forms and the Shc-independent pathway; see Table I in S6 Supplementary Material. The state just below the threshold is (EGF-EGFR*)2-GAP-Shc*-Grb2-Sos.
Fig 9.
Schematic with state classification of the signal transduction network focussing on the Shc dependent pathway for membrane EGFR signalling (Panel A) and internalised EGFR signalling (Panel B).
The schematics include the 20 state variables with largest maximum input-response index (light blue, see Fig 8D), environmental state variables (purple), state variables in quasi-steady state (green) and further state variables (dark blue). States being part of the membrane-bound and internalised pathway are coloured orange in panel (B). The red boxes mark the input and output state variables; coloured dots as part of reaction arrows indicate intermediate complexes. A similar graphic for the Shc-independent pathway is Fig I in S6 Supplementary Material.
Fig 10.
A: concentration-time profiles of Phosphatase3 and relevant cytosolic ERK species during signal activation. B: comparison of the output ERK-PP for the reference simulation (solid lines) and a modified model (dashed lines) with no Phosphatase3. As a result, signal activation speeds up by roughly 1 min, in addition to lack of signal deactivation.
Fig 11.
Analyses of Phosphatase1 (top) & 2 (bottom).
A: State classification indices for Phosphatase1; B: comparison of the output ERK-PP and Phosphatase1 for the reference simulation (solid lines) and a modified model (dashed lines) with constant Phosphatase1 levels. C: State classification indices for Phosphatase2; D: comparison of the output ERK-PP, Phosphatase2 and two MEK-PP species for the reference simulation (solid lines) and a modified model (dashed lines) without MEK internalisation. Absence of internalised MEK increases free Phosphatase2 levels and thereby deactivates the signal more quickly.
Fig 12.
A: State classification indices for Raf*; B: comparison of the output ERK-PP and Raf* for the reference simulation (solid lines) and a modified model (dashed lines, visually indistinguishable from the solid lines) with Raf* in partial-steady state. C: State classification indices for Ras-GTP*; D: comparison of the output ERK-PP and Ras-GTP* for the reference simulation (solid lines) and a modified model (dashed lines) with partially neglected Ras-GTP* (pneg).
Fig 13.
Analyses of receptor degradation.
Comparison of the output ERK-PP and Raf* for the reference simulation (solid lines) and a modified model (dashed lines) with no degradation from six internalised receptor species (those with degradation reaction in Fig 9, realised by classifying the degradation products as cneg).