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BIOMD0000000342 - Zi2011_TGF-beta_Pathway

 

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Reference Publication
Publication ID: 21613981
Zi Z, Feng Z, Chapnick DA, Dahl M, Deng D, Klipp E, Moustakas A, Liu X.
Quantitative analysis of transient and sustained transforming growth factor-β signaling dynamics.
Mol. Syst. Biol. 2011 May; 7: 492
BIOSS Centre for Biological Signalling Studies and Center for Biological Systems Analysis (ZBSA), University of Freiburg, Freiburg, Germany. zhike.zi@bioss.uni-freiburg.de  [more]
Model
Original Model: BIOMD0000000342.origin
Submitter: Zhike Zi
Submission ID: MODEL1104050000
Submission Date: 05 Apr 2011 15:06:13 UTC
Last Modification Date: 24 Feb 2014 17:00:59 UTC
Creation Date: 14 Jul 2011 12:23:21 UTC
Encoders:  Vijayalakshmi Chelliah
   Zhike Zi
set #1
bqbiol:isPartOf KEGG Pathway TGF-beta signaling pathway
Reactome REACT_6844
set #2
bqbiol:occursIn Brenda Tissue Ontology motoneuron
set #3
bqbiol:hasTaxon Taxonomy Homo sapiens
set #4
bqbiol:isVersionOf Gene Ontology transforming growth factor beta receptor signaling pathway
Notes

This model is from the article:
Quantitative analysis of transient and sustained transforming growth factor-β signaling dynamics.
Zhike Zi, Zipei Feng, Douglas A Chapnick, Markus Dahl, Difan Deng, Edda Klipp, Aristidis Moustakas & Xuedong Liu Molecular Systems Biology 2011 May 24;7:492. 21613981 ,
Abstract:
Mammalian cells can decode the concentration of extracellular transforming growth factor-β (TGF-β) and transduce this cue into appropriate cell fate decisions. How variable TGF-β ligand doses quantitatively control intracellular signaling dynamics and how continuous ligand doses are translated into discontinuous cellular fate decisions remain poorly understood. Using a combined experimental and mathematical modeling approach, we discovered that cells respond differently to continuous and pulsating TGF-β stimulation. The TGF-β pathway elicits a transient signaling response to a single pulse of TGF-β stimulation, whereas it is capable of integrating repeated pulses of ligand stimulation at short time interval, resulting in sustained phospho-Smad2 and transcriptional responses. Additionally, the TGF-β pathway displays different sensitivities to ligand doses at different time scales. While ligand-induced short-term Smad2 phosphorylation is graded, long-term Smad2 phosphorylation is switch-like to a small change in TGF-β levels. Correspondingly, the short-term Smad7 gene expression is graded, while long-term PAI-1 gene expression is switch-like, as is the long-term growth inhibitory response. Our results suggest that long-term switch-like signaling responses in the TGF-β pathway might be critical for cell fate determination.

Note:

Developer of the model: Zhike Zi

Reference: Zi Z. et al., Quantitative Analysis of Transient and Sustained Transforming Growth Factor-beta Signaling Dynamics, Molecular Systems Biology, 2011

1. The global parameter that set the type of stimulation

(a) for sustained TGF-beta stimulation: set stimulation_type = 1.

(b) for single pulse of TGF-beta stimulation: set stimulation_type = 2.

parameter "single_pulse_duration" is for the duration of stimulation, for example,

single_pulse_duration = 0.5, for 0.5 min (30 seconds) of TGF-beta stimulation.

*Note: make sure that the time course cover the time point when the event is triggered.

(c) for single pulse of TGF-beta stimulation in COPASI

change the trigger of event "single_pulse_TGF_beta_washout"

from

"and(eq(stimulation_type, 2), eq(time, single_pulse_duration))" (for SBML-SAT)

to

"and(eq(stimulation_type, 2), gt(time, single_pulse_duration))" (for COPASI)

2. Notes for TGF-beta dose in terms of molecules per cell

(a) The following equation applies for conversion of TGF-beta dose in molecules per cell

TGF_beta_dose_mol_per_cell = initial TGF_beta_ex*1e-9*Vmed*6e23

(b) for standard experimental setup 1e6 cells in 2 mL medium

0.001 nM initial TGF_beta_ex is approximately equal to the dose of 1200 TGF-beta molecules/cell

0.050 nM initial TGF_beta_ex is approximately equal to the dose of 60000 TGF-beta molecules/cell

(c) For 1e6 cells in 10 mL medium, please change the initial compartment size of Vmed and the corresponding assignment rule for Vmed.

initial Vmed = 1e-8 (1e6 cells in 10 mL medium)

Vmed = 0.010/(1e6*exp(log(1.45)*time/1440)) (1e6 cells in 10 mL medium)

3. Please note that this model contains events and the medium compartment size is varied.

4. For the model simulation in SBML-SAT, please remove initialAssignments and save it as SBML Level 2 Verion 1 file.

Model
Publication ID: 21613981 Submission Date: 05 Apr 2011 15:06:13 UTC Last Modification Date: 24 Feb 2014 17:00:59 UTC Creation Date: 14 Jul 2011 12:23:21 UTC
Mathematical expressions
Reactions
T1R production T1R internalization to early endosome T1R recycling from early endosome T1R constitutive degradation
T2R production T2R internalization to early endosome T2R recycling from early endosome T2R constitutive degradation
LRC activation LRC internalization to early endosome LRC constitutive degradation dissociation of LRC in endosome
TGF-beta constitutive degradation Smad2 nuclear import Smad2 nuclear export Smad4 nuclear import
Smad4 nuclear export Smad2 phosphorylation PSmad2 nuclear import PSmad2 nuclear export
Smad2-Smad4 complex formation Smad2-Smad4 nuclear import Smad2-Smad4 dissociation Smad2 dephosphorylation
PSmad2 dimer formation PSmad2 dimer nuclear import PSmad2 dimmer dissociation negative feedback induced LRC degradation
non-specific binding of TGF-beta      
Rules
Assignment Rule (variable: Medium) Assignment Rule (variable: totalNumPSmad2) Assignment Rule (variable: totalNuclearPSmad2) Assignment Rule (variable: totalNumT1R)
Assignment Rule (variable: totalNumT2R) Assignment Rule (variable: totalNumLRC) Assignment Rule (variable: totalSmad2c) Assignment Rule (variable: totalSmad2n)
Assignment Rule (variable: koff_ns) Assignment Rule (variable: medium_TGF_beta_amount)    
Events
TGF-beta washout in singel pulse stimulation      
Physical entities
Compartments Species
default      
Medium TGF_beta_ex TGF_beta_ns  
Cytoplasm T1R_surf T1R_endo T2R_surf
T2R_endo LRC_surf LRC_endo
Smad2c Smad4c PSmad2c
PSmad2_PSmad2_c PSmad2_Smad4_c TGF_beta_endo
AA empty_degraded  
Nucleus Smad2n Smad4n PSmad2n
PSmad2_PSmad2_n PSmad2_Smad4_n  
Global parameters
stimulation_type single_pulse_duration totalNumT1R totalNumT2R
totalNumLRC totalNumPSmad2 totalNuclearPSmad2 totalSmad2c
totalSmad2n medium_TGF_beta_amount TGF_beta_dose_mol_per_cell ki
kr k_T1R k_T2R kdeg_T1R
kdeg_T2R kdeg_LRC kdeg_TGF_beta klid
ka_LRC kdiss_LRC kimp_Smad2 kexp_Smad2
kimp_Smad4 kexp_Smad4 kpho_Smad2 kon_Smads
koff_Smads kimp_Smads kdepho_Smad2 kon_ns
koff_ns KD_ns    
Reactions (29)
 
 T1R production [AA] → [T1R_surf];  
 
 T1R internalization to early endosome [T1R_surf] → [T1R_endo];  
 
 T1R recycling from early endosome [T1R_endo] → [T1R_surf];  
 
 T1R constitutive degradation [T1R_endo] → [empty_degraded];  
 
 T2R production [AA] → [T2R_surf];  
 
 T2R internalization to early endosome [T2R_surf] → [T2R_endo];  
 
 T2R recycling from early endosome [T2R_endo] → [T2R_surf];  
 
 T2R constitutive degradation [T2R_endo] → [empty_degraded];  
 
 LRC activation [TGF_beta_ex] + [T2R_surf] + [T1R_surf] → [LRC_surf];  
 
 LRC internalization to early endosome [LRC_surf] → [LRC_endo];  
 
 LRC constitutive degradation [LRC_endo] → [empty_degraded];  
 
 dissociation of LRC in endosome [LRC_endo] → [T1R_endo] + [T2R_endo] + [TGF_beta_endo];  
 
 TGF-beta constitutive degradation [TGF_beta_endo] → [empty_degraded];  
 
 Smad2 nuclear import [Smad2c] → [Smad2n];  
 
 Smad2 nuclear export [Smad2n] → [Smad2c];  
 
 Smad4 nuclear import [Smad4c] → [Smad4n];  
 
 Smad4 nuclear export [Smad4n] → [Smad4c];  
 
 Smad2 phosphorylation [Smad2c] → [PSmad2c];   {LRC_endo}
 
 PSmad2 nuclear import [PSmad2c] → [PSmad2n];  
 
 PSmad2 nuclear export [PSmad2n] → [PSmad2c];  
 
 Smad2-Smad4 complex formation [PSmad2c] + [Smad4c] ↔ [PSmad2_Smad4_c];  
 
 Smad2-Smad4 nuclear import [PSmad2_Smad4_c] → [PSmad2_Smad4_n];  
 
 Smad2-Smad4 dissociation [PSmad2_Smad4_n] ↔ [PSmad2n] + [Smad4n];  
 
 Smad2 dephosphorylation [PSmad2n] → [Smad2n];  
 
 PSmad2 dimer formation 2.0 × [PSmad2c] ↔ [PSmad2_PSmad2_c];  
 
 PSmad2 dimer nuclear import [PSmad2_PSmad2_c] → [PSmad2_PSmad2_n];  
 
 PSmad2 dimmer dissociation [PSmad2_PSmad2_n] ↔ 2.0 × [PSmad2n];  
 
 negative feedback induced LRC degradation [LRC_surf] → [empty_degraded];  
 
 non-specific binding of TGF-beta [TGF_beta_ex] ↔ [TGF_beta_ns];  
 
Rules (10)
 
 Assignment Rule (name: Vmed) Medium = 2E-3/(1E6*exp(ln(1.45)*time/1440))
 
 Assignment Rule (name: totalNumPSmad2) totalNumPSmad2 = (PSmad2c+PSmad2_PSmad2_c*2+PSmad2_Smad4_c)*2.3*602+(PSmad2n+PSmad2_PSmad2_n*2+PSmad2_Smad4_n)*602
 
 Assignment Rule (name: totalNuclearPSmad2) totalNuclearPSmad2 = PSmad2n+2*PSmad2_PSmad2_n+PSmad2_Smad4_n
 
 Assignment Rule (name: totalNumT1R) totalNumT1R = (T1R_surf+T1R_endo+LRC_surf+LRC_endo)*2.3*602
 
 Assignment Rule (name: totalNumT2R) totalNumT2R = (T2R_surf+T2R_endo+LRC_surf+LRC_endo)*2.3*602
 
 Assignment Rule (name: totalNumLRC) totalNumLRC = (LRC_surf+LRC_endo)*2.3*602
 
 Assignment Rule (name: totalSmad2c) totalSmad2c = Smad2c+PSmad2c+2*PSmad2_PSmad2_c+PSmad2_Smad4_c
 
 Assignment Rule (name: totalSmad2n) totalSmad2n = Smad2n+PSmad2n+2*PSmad2_PSmad2_n+PSmad2_Smad4_n
 
 Assignment Rule (name: koff_ns) koff_ns = kon_ns*KD_ns
 
 Assignment Rule (name: medium_TGF_beta_amount) medium_TGF_beta_amount = TGF_beta_ex*1E-9*Vmed*6E23
 
Events (1)
 
 TGF-beta washout in singel pulse stimulation
TGF_beta_ex = 0
 
   Spatial dimensions: 3.0  Compartment size: 1.0  (Units: volume)
  Medium Spatial dimensions: 3.0  Compartment size: 2.0E-9  (Units: volume)
 
 TGF_beta_ex
Compartment: Medium
Initial concentration: 0.05  (Units: nM)
 
 TGF_beta_ns
Compartment: Medium
Initial concentration: 0.0  (Units: nM)
 
 Cytoplasm Spatial dimensions: 3.0  Compartment size: 2.3E-12  (Units: volume)
 
 T1R_surf
Compartment: Cytoplasm
Initial concentration: 0.702494  (Units: nM)
 
 T1R_endo
Compartment: Cytoplasm
Initial concentration: 6.52344  (Units: nM)
 
 T2R_surf
Compartment: Cytoplasm
Initial concentration: 0.201077  (Units: nM)
 
 T2R_endo
Compartment: Cytoplasm
Initial concentration: 1.43997  (Units: nM)
 
 LRC_surf
Compartment: Cytoplasm
Initial concentration: 0.0  (Units: nM)
 
 LRC_endo
Compartment: Cytoplasm
Initial concentration: 0.0  (Units: nM)
 
 Smad2c
Compartment: Cytoplasm
Initial concentration: 60.6  (Units: nM)
 
 Smad4c
Compartment: Cytoplasm
Initial concentration: 50.8  (Units: nM)
 
 PSmad2c
Compartment: Cytoplasm
Initial concentration: 0.0  (Units: nM)
 
 PSmad2_PSmad2_c
Compartment: Cytoplasm
Initial concentration: 0.0  (Units: nM)
 
 PSmad2_Smad4_c
Compartment: Cytoplasm
Initial concentration: 0.0  (Units: nM)
 
 TGF_beta_endo
Compartment: Cytoplasm
Initial concentration: 0.0  (Units: nM)
 
 AA
Compartment: Cytoplasm
Initial concentration: 0.0  (Units: nM)
Constant
 
 empty_degraded
Compartment: Cytoplasm
Initial concentration: 0.0  (Units: nM)
Constant
 
 Nucleus Spatial dimensions: 3.0  Compartment size: 1.0E-12  (Units: volume)
 
 Smad2n
Compartment: Nucleus
Initial concentration: 28.5  (Units: nM)
 
 Smad4n
Compartment: Nucleus
Initial concentration: 50.8  (Units: nM)
 
 PSmad2n
Compartment: Nucleus
Initial concentration: 0.0  (Units: nM)
 
 PSmad2_PSmad2_n
Compartment: Nucleus
Initial concentration: 0.0  (Units: nM)
 
 PSmad2_Smad4_n
Compartment: Nucleus
Initial concentration: 0.0  (Units: nM)
 
Global Parameters (34)
 
   stimulation_type
Value: 1.0   (Units: dimensionless)
Constant
 
   single_pulse_duration
Value: 0.5   (Units: minute)
Constant
 
   totalNumT1R
Value: 10005.0   (Units: molecules per cell)
 
   totalNumT2R
Value: 2272.0   (Units: molecules per cell)
 
   totalNumLRC  
 
   totalNumPSmad2  
 
   totalNuclearPSmad2  
 
   totalSmad2c
Value: 60.6   (Units: nanomolar)
 
   totalSmad2n
Value: 28.5   (Units: nanomolar)
 
   medium_TGF_beta_amount  
 
   TGF_beta_dose_mol_per_cell  
 
   ki
Value: 0.333   (Units: per min)
Constant
 
   kr
Value: 0.0333   (Units: per min)
Constant
 
   k_T1R
Value: 0.0167   (Units: nM per min)
Constant
 
   k_T2R
Value: 0.0190076   (Units: nM per min)
Constant
 
   kdeg_T1R
Value: 0.00256   (Units: per min)
Constant
 
   kdeg_T2R
Value: 0.0132   (Units: per min)
Constant
 
   kdeg_LRC
Value: 0.00256   (Units: per min)
Constant
 
   kdeg_TGF_beta
Value: 0.347   (Units: per min)
Constant
 
   klid
Value: 0.0233678   (Units: per min)
Constant
 
   ka_LRC
Value: 117.897   (Units: third order rate constant)
Constant
 
   kdiss_LRC
Value: 0.0438111   (Units: per min)
Constant
 
   kimp_Smad2
Value: 0.156   (Units: per min)
Constant
 
   kexp_Smad2
Value: 0.763   (Units: per min)
Constant
 
   kimp_Smad4
Value: 0.156   (Units: per min)
Constant
 
   kexp_Smad4
Value: 0.359   (Units: per min)
Constant
 
   kpho_Smad2
Value: 0.0488268   (Units: second order rate constant)
Constant
 
   kon_Smads
Value: 0.198472   (Units: second order rate constant)
Constant
 
   koff_Smads
Value: 1.0   (Units: per min)
Constant
 
   kimp_Smads
Value: 0.889   (Units: per min)
Constant
 
   kdepho_Smad2
Value: 0.394   (Units: per min)
Constant
 
   kon_ns
Value: 0.0505413   (Units: per min)
Constant
 
   koff_ns
Value: 2.03306   (Units: per min)
 
   KD_ns
Value: 40.2257   (Units: dimensionless)
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000342

Curator's comment: (updated: 18 Jul 2011 14:25:12 BST)

Figure 1C of the reference publication has been reproduced here. The parameters defined are in minutes.
So, to get simulation result for 8hours, the model should be run for 480mins (8x60).

The model as such reproduces the plot corresponding to "Sustained TGF-? stimulation (blue plot).
refer supporting file: Zi2011_fig1Cblue.cps [COPASI file].

In order to obtain the plot corresponding to "Single pulse of 30 s TGF-? stimulation (red plot),
the following changes are to be made in the model.
1) set "stimulation_type=2" instead of "1".
2) set the Trigger Expression as "Time > single_pulse_duration and stimulation_type = 2".
refer supporting file: Zi2011_fig1Cred.xml [SBML file], Zi2011_fig1Cred.cps [COPASI file].

The model was integrated and simulated using Copasi v4.6 (Build 32). The curation figure was generated using Gnuplot, data being obtained from Copasi.

Additional file(s)
  • Zi (2011) - Sustained TGF-β stimulation (Figure 1C - blue plot):
    The model as such reproduces this plot.
  • Zi (2011) - Single pulse of 30 s TGF-β stimulation (Figure 1C - red plot):
    In order to obtain this plot the following changes are to be made in the model:
    1) Set "stimulation type = 2", instead of "1".
    2) Event: Set the Trigger Expression as "{Time} gt {Values[single_pulse_duration]} and {Values[stimulation_type]} eq 2".
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