legewie2

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000103) Biomodels notes: This model represents the non-competitive binding of XIAP to Casapase-3 and Caspase-9. In other words, XIAP mediated feedback is abolished in this model. The authors state that this leads to bistable-reversible behaviour as depicted in Fig 4C. The wild-type model displays a bistable-irreversible profile. This shows that irreversibility requires XIAP mediated feedback. The model was tested on MathSBML. However, please note that the paper does not contain any figure that corresponds to simulation of the Non-Competitive model.

None

None

None

None

None

None

Mathematical modeling identifies inhibitors of apoptosis as mediators of positive feedback and bistability.

  • Stefan Legewie
  • Nils Blüthgen
  • Hanspeter Herzel
PLoS Comput. Biol. 2006; 2 (9):
Abstract
The intrinsic, or mitochondrial, pathway of caspase activation is essential for apoptosis induction by various stimuli including cytotoxic stress. It depends on the cellular context, whether cytochrome c released from mitochondria induces caspase activation gradually or in an all-or-none fashion, and whether caspase activation irreversibly commits cells to apoptosis. By analyzing a quantitative kinetic model, we show that inhibition of caspase-3 (Casp3) and Casp9 by inhibitors of apoptosis (IAPs) results in an implicit positive feedback, since cleaved Casp3 augments its own activation by sequestering IAPs away from Casp9. We demonstrate that this positive feedback brings about bistability (i.e., all-or-none behaviour), and that it cooperates with Casp3-mediated feedback cleavage of Casp9 to generate irreversibility in caspase activation. Our calculations also unravel how cell-specific protein expression brings about the observed qualitative differences in caspase activation (gradual versus all-or-none and reversible versus irreversible). Finally, known regulators of the pathway are shown to efficiently shift the apoptotic threshold stimulus, suggesting that the bistable caspase cascade computes multiple inputs into an all-or-none caspase output. As cellular inhibitory proteins (e.g., IAPs) frequently inhibit consecutive intermediates in cellular signaling cascades (e.g., Casp3 and Casp9), the feedback mechanism described in this paper is likely to be a widespread principle on how cells achieve ultrasensitivity, bistability, and irreversibility.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
1e-09 mole
1e-09 mole litre^(-1.0) second^(-1.0)
1000000000.0 mole^(-1.0) litre second^(-1.0)
1e-09 mole litre^(-1.0)
1.0 second^(-1.0)
Id Name Spatial dimensions Size
cytosol Cytosol 3.0 1.0
Id Name Initial quantity Compartment Fixed
A APAF-1 20.0 cytosol (Cytosol)
AC9 APAF-1-Caspase 9 complex 0.0 cytosol (Cytosol)
AC9X APAF-1-Caspase 9-XIAP complex 0.0 cytosol (Cytosol)
AC9X_C3_star Apaf-1-Caspase 9 cleaved -XIAP complex 0.0 cytosol (Cytosol)
AC9_star APAF-1-Caspase 9 cleaved complex 0.0 cytosol (Cytosol)
AC9_starX Apaf-1-Caspase 9 cleaved -XIAP complex 0.0 cytosol (Cytosol)
AC9_starX_C3_star Apaf-1-Caspase 9 cleaved -XIAP complex 0.0 cytosol (Cytosol)
C3 Caspase 3 200.0 cytosol (Cytosol)
C3_star Caspase 3 cleaved 0.0 cytosol (Cytosol)
C3_starX Caspase 3 cleaved - XIAP complex 0.0 cytosol (Cytosol)
C9 Caspase 9 20.0 cytosol (Cytosol)
C9X Caspase 9-XIAP complex 0.0 cytosol (Cytosol)
C9X_C3_star Apaf-1-Caspase 9 cleaved -XIAP complex 0.0 cytosol (Cytosol)
C9_star Caspase 9 cleaved 0.0 cytosol (Cytosol)
C9_starX Caspase 9 cleaved-XIAP complex 0.0 cytosol (Cytosol)
C9_starX_C3_star Apaf-1-Caspase 9 cleaved -XIAP complex 0.0 cytosol (Cytosol)
X XIAP 40.0 cytosol (Cytosol)

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
v1 Caspase 9 / Apaf-1 binding A + C9 = AC9

cytosol * (k1 * A * C9 - kb1 * AC9)
v10 Caspase 9-Apaf-1 Xiap binding AC9 + X = AC9X

cytosol * (k10 * AC9 * X - k10b * AC9X)
v11 cleaved Caspase 9 XIAP binding C9_star + X = C9_starX

cytosol * (k11 * C9_star * X - k11b * C9_starX)
v12 cleaved Caspase 9-Apaf-1 XIAP binding AC9_star + X = AC9_starX

cytosol * (k12 * AC9_star * X - k12b * AC9_starX)
v13 Caspase 9-Xiap Apaf-1 binding C9X + A = AC9X

cytosol * (k13 * C9X * A - k13b * AC9X)
v14 cleaved Caspase 9-Xiap Apaf-1 binding C9_starX + A = AC9_starX

cytosol * (k14 * C9_starX * A - k14b * AC9_starX)
v15 cleaved Caspase 3-Xiap binding C3_star + X = C3_starX

cytosol * (k15 * C3_star * X - k15b * C3_starX)
v16 Apaf-1 turnover ∅ > A

cytosol * (k16prod - k16 * A)
v17 Caspase 9 turnover ∅ > C9

cytosol * (k17prod - k17 * C9)
v18 Xiap turnover ∅ > X

cytosol * (k18prod - k18 * X)
v19 Caspase 9-Xiap degradation C9X > ∅

cytosol * k19 * C9X
v2 Caspase 3 cleavage by Caspase 9 C3 + C9 > C3_star + C9

cytosol * k2 * C3 * C9
v20 Apaf-1-Caspase 9-Xiap degradation AC9X > ∅

cytosol * k20 * AC9X
v21 Apaf-1-Caspase 9 degradation AC9 > ∅

cytosol * k21 * AC9
v22 Caspase 3 turnover ∅ > C3

cytosol * (k22prod - k22 * C3)
v23 Caspase 3 cleaved degradation C3_star > ∅

cytosol * k23 * C3_star
v24 Caspase 3 cleaved-Xiap degradation C3_starX > ∅

cytosol * k24 * C3_starX
v25 Caspase 9 cleaved-Xiap degradation C9_starX > ∅

cytosol * k25 * C9_starX
v26 Caspase 9 cleaved degradation C9_star > ∅

cytosol * k26 * C9_star
v27 Apaf-1 Caspase 9 cleaved degradation AC9_star > ∅

cytosol * k27 * AC9_star
v28 Apaf-1 Caspase 9 cleaved-Xiap degradation AC9_starX > ∅

cytosol * k28 * AC9_starX
v29 Caspase9-Xiap-Caspase3_star degradation C9X_C3_star > ∅

cytosol * k29 * C9X_C3_star
v3 Caspase 3 cleavage by Caspase 9-Apaf-1 C3 + AC9 > C3_star + AC9

cytosol * k3 * C3 * AC9
v30 Apaf-1-Caspase9-Xiap-Caspase3_star degradation AC9_starX_C3_star > ∅

cytosol * k30 * AC9_starX_C3_star
v31 Caspase9_star-Xiap-Caspase3_star degradation C9_starX_C3_star > ∅

cytosol * k31 * C9_starX_C3_star
v32 Apaf-1-Caspase9_star-Xiap-Caspase3_star degradation AC9_starX_C3_star > ∅

cytosol * k32 * AC9_starX_C3_star
v33 Cleaved-Caspase 3 binding with Xiap-Caspase 9 C3_star + C9X = C9X_C3_star

cytosol * (a * k15 * C3_star * C9X - d * k15b * C9X_C3_star)
v34 Cleaved-Caspase 3 binding with Apaf-Xiap-Caspase 9 C3_star + AC9X = AC9X_C3_star

cytosol * (a * k15 * C3_star * AC9X - d * k15b * AC9X_C3_star)
v35 Cleaved-Caspase 3 binding with Cleaved-Xiap-Caspase 9 C3_star + C9_starX = C9_starX_C3_star

cytosol * (a * k15 * C3_star * C9_starX - d * k15b * C9_starX_C3_star)
v36 Apaf-Xiap-cleaved Caspase 9 binding with cleaved Caspase 3 C3_star + AC9_starX = AC9_starX_C3_star

cytosol * (a * k15 * C3_star * AC9_starX - d * k15b * AC9_starX_C3_star)
v37 Binding of Caspase 9 to cleaved Caspase 3-Xiap C9 + C3_starX = C9X_C3_star

cytosol * (a * k9 * C9 * C3_starX - d * k9b * C9X_C3_star)
v38 Binding of Apaf-Caspase 9 to cleaved Caspase 3-Xiap AC9 + C3_starX = AC9X_C3_star

cytosol * (a * k9 * AC9 * C3_starX - d * k9b * AC9X_C3_star)
v39 Binding of cleaved Caspase 9 to cleaved Caspase 3-Xiap C9_star + C3_starX = C9_starX_C3_star

cytosol * (a * k9 * C9_star * C3_starX - d * k9b * C9_starX_C3_star)
v4 Caspase 9 cleavage by cleaved caspase 3 C9 + C3_star > C9_star + C3_star

cytosol * k4 * C9 * C3_star
v40 Binding of cleaved Caspase 9-Apaf-1 to cleaved Caspase 3-Xiap AC9_star + C3_starX = AC9_starX_C3_star

cytosol * (a * k9 * AC9_star * C3_starX - d * k9b * AC9_starX_C3_star)
v41 Binding of Caspase 9-Xiap-cleaved Caspase 3 with Apaf C9X_C3_star + A = AC9X_C3_star

cytosol * (a * k1 * C9X_C3_star * A - d * kb1 * AC9X_C3_star)
v42 Binding of cleaved Caspase 9-Xiap-cleaved Caspase 3 with Apaf C9_starX_C3_star + A = AC9_starX_C3_star

cytosol * (a * k1 * C9_starX_C3_star * A - d * kb1 * AC9_starX_C3_star)
v5 Caspase 9 cleavage by cleaved caspase 3 when Apaf-1 is bound AC9 + C3_star > AC9_star + C3_star

cytosol * k5 * AC9 * C3_star
v6 Caspase 3 cleavage by cleaved Caspase 9 C3 + C9_star > C3_star + C9_star

cytosol * k6 * C3 * C9_star
v7 Caspase 3 cleavage by cleaved Caspase 9 - Apaf-1 C3 + AC9_star > C3_star + AC9_star

cytosol * k7 * C3 * AC9_star
v8 cleaved Caspase 9 Apaf-1 binding C9_star + A = AC9_star

cytosol * (k8 * C9_star * A - k8b * AC9_star)
v9 Caspase 9 Xiap binding C9 + X = C9X

cytosol * (k9 * C9 * X - k9b * C9X)

Global parameters

Id Value
a 1.0
d 1.0
k1 0.002
k10 0.001
k10b 0.001
k11 0.001
k11b 0.001
k12 0.001
k12b 0.001
k13 0.002
k13b 0.1
k14 0.002
k14b 0.1
k15 0.003
k15b 0.001
k16 0.001
k16prod 0.02
k17 0.001
k17prod 0.02
k18 0.001
k18prod 0.04
k19 0.001
k2 0.000005
k20 0.001
k21 0.001
k22 0.001
k22prod 0.2
k23 0.001
k24 0.001
k25 0.001
k26 0.001
k27 0.001
k28 0.001
k29 0.001
k3 0.00035
k30 0.001
k31 0.001
k32 0.001
k4 0.0002
k41 1.0
k42 1.0
k5 0.0002
k6 0.00005
k7 0.0035
k8 0.002
k8b 0.1
k9 0.001
k9b 0.001
kb1 0.1

Local parameters

Id Value Reaction

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments