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BIOMD0000000446 - Erguler2013 - Unfolded protein stress response

 

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Reference Publication
Publication ID: 23433609
Erguler K, Pieri M, Deltas C.
A mathematical model of the unfolded protein stress response reveals the decision mechanism for recovery, adaptation and apoptosis.
BMC Syst Biol 2013; 7: 16
Molecular Medicine Research Center and Laboratory of Molecular and Medical Genetics, Department of Biological Sciences, University of Cyprus, Kallipoleos 75, 1678 Nicosia, Cyprus. erguler.kamil@ucy.ac.cy  [more]
Model
Original Model: BIOMD0000000446.origin
Submitter: Kamil Erguler
Submission ID: MODEL1302180000
Submission Date: 18 Feb 2013 10:06:00 UTC
Last Modification Date: 20 May 2013 11:06:47 UTC
Creation Date: 25 Mar 2013 12:25:08 UTC
Encoders:  Vijayalakshmi Chelliah
   Kamil Erguler
set #1
bqbiol:isVersionOf Gene Ontology endoplasmic reticulum unfolded protein response
set #2
bqbiol:hasTaxon Taxonomy cellular organisms
Notes
Erguler2013 - Unfolded protein stress response

The model investigates the mechanism by which UPR (unfolded protein response) outcome switches between survival and death.

This model is described in the article:

Erguler K, Pieri M, Deltas C.
BMC Syst Biol. 2013 Feb 21;7(1):16.

Abstract:

BACKGROUND: The unfolded protein response (UPR) is a major signalling cascade acting in the quality control ofprotein folding in the endoplasmic reticulum (ER). The cascade is known to play an accessory rolein a range of genetic and environmental disorders including neurodegenerative and cardiovasculardiseases, diabetes and kidney diseases. The three major receptors of the ER stress involved withthe UPR, i.e. IRE1a, PERK and ATF6, signal through a complex web of pathways to convey anappropriate response. The emerging behaviour ranges from adaptive to maladaptive depending on theseverity of unfolded protein accumulation in the ER; however, the decision mechanism for the switchand its timing have so far been poorly understood.

RESULTS: Here, we propose a mechanism by which the UPR outcome switches between survival and death.We compose a mathematical model integrating the three signalling branches, and perform a comprehensivebifurcation analysis to investigate possible responses to stimuli. The analysis reveals threedistinct states of behaviour, low, high and intermediate activity, associated with stress adaptation, tolerance,and the initiation of apoptosis. The decision to adapt or destruct can, therefore, be understoodas a dynamic process where the balance between the stress and the folding capacity of the ER playsa pivotal role in managing the delivery of the most appropriate response. The model demonstratesfor the first time that the UPR is capable of generating oscillations in translation attenuation and theapoptotic signals, and this is supplemented with a Bayesian sensitivity analysis identifying a set ofparameters controlling this behaviour.

CONCLUSIONS: This work contributes largely to the understanding of one of the most ubiquitous signalling pathwaysinvolved in protein folding quality control in the metazoan ER. The insights gained have direct consequenceson the management of many UPR-related diseases, revealing, in addition, an extended listof candidate disease modifiers. Demonstration of stress adaptation sheds light to how preconditioningmight be beneficial in manifesting the UPR outcome to prevent untimely apoptosis, and paves the wayto novel approaches for the treatment of many UPR-related conditions.

In the paper, PERKA refers to the amount of phosphorylated PERK monomer. However, it refers to the active complex in the model. The complex with the model parameterization is formed of 4 monomers (n=4). So, the value of PERKA should be multiplied by 4, in order to generate the figures in the paper (eg. Figure 12).

An additional parameter (tmr=10)) is used in the model. This parameter is not mentioned in the paper. The model values of kf(=10) and kr(=1) are not consistent with that of the paper (kf=100, kr=10, in the paper). However, this is corrected by the introduction of "tmr" in the model, which is multiplied with kf and kr to get the resulting values.

The term "tmr" was missing in the kinetic laws of the reactions reu7 and reu8, in the original model. This has been corrected as per the author's request.

To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

Model
Publication ID: 23433609 Submission Date: 18 Feb 2013 10:06:00 UTC Last Modification Date: 20 May 2013 11:06:47 UTC Creation Date: 25 Mar 2013 12:25:08 UTC
Mathematical expressions
Reactions
re2 re3 re4 reu1
reu2 reu3 reu4 reu5
reu6 reu7 reu8 reu9
reu10 reu11 reu12 re5
re6 re8 rew1 re9
re10 re11 rew2 rew3
rew4 rew5 re12 re13
re14 re15 re16 re17
re18 re19 re20 re21
re23 re24 re25 re26
re27 re28 re29 re30
re31 re32 rea1 rea2
rea3 rea4 rea5 rea6
rea7 rea8 rea9 rea10
rea11 rea12 rea13 rea14
rea15 rea16    
Rules
Assignment Rule (variable: UFP) Assignment Rule (variable: BiP) Assignment Rule (variable: IRE1) Assignment Rule (variable: PERK)
Assignment Rule (variable: ATF6) Assignment Rule (variable: spliceRate) Assignment Rule (variable: eIF2a) Assignment Rule (variable: BCL2)
Assignment Rule (variable: BH3) Assignment Rule (variable: BAXm) Assignment Rule (variable: mUFPT)  
Physical entities
Compartments Species
ERlumen UFPT BiUFP BiRE1
BiATF BiPER IRE1A
PERKA BiPT ATF6T
WFS1    
cytoplasm mXbp1u mXbp1s Xbp1s
mBiPT ATF6p50 mWFS1
ATF4 mCHOP CHOP
mGADD34 GADD34 BH3T
     
Golgi ATF6GB    
mitochondria BCL2T BAXmT BAXmBCL2
BH3BCL2    
Global parameters
UFP BiP IRE1 PERK
ATF6 eIF2a spliceRate BCL2
BH3 BAXm tmr IRE1T
PERKT eIF2aT CReP kf
kr n nh extATT
extPERK basalXBP basalBiP krcXU
krcBiP krcWFS krcCHOP krcGADD34
kmXbp kmAtfsXBP kmAtfsBiP kmAtff
kmChop kmAtfs ksplice krcSplice
trcXU trcBiP trcWFS trcCHOP
trcGADD34 ktrUFP ktrXS ktrBiP
ktrATF6 ktrWFS ktrATF4 ktrCHOP
ktrGADD34 kdmXU kdmXS kdmBiP
kdmWFS kdmCHOP kdmGADD34 kdUFP
kdXS kdBiP kdATF6 kdATF6GB
kdATF6p50 kdWFS kdATF4 kdCHOP
kdGADD34 mATF6T mUFPT mATF4
ktrans kcleave kphos kdephos
kdeAW kbu switch kATF4
J K kfbc kdbc
kmbc kstr BAXT kfx
kfxp kbx kasx kdsx
ks3 ks3p kd3 kas3
kds3 kff    
Reactions (62)
 
 re2  → [UFPT];  
 
 re3 [UFPT] → ;   {UFPT}
 
 re4 [UFPT] → ;   {BiUFP} , {BiUFP} , {UFPT}
 
 reu1  → [BiUFP];  
 
 reu2 [BiUFP] → ;   {BiUFP}
 
 reu3  → [BiRE1];  
 
 reu4 [BiRE1] → ;   {BiRE1}
 
 reu5  → [BiATF];  
 
 reu6 [BiATF] → ;   {BiATF}
 
 reu7  → [BiPER];  
 
 reu8 [BiPER] → ;   {BiPER}
 
 reu9  → [IRE1A];  
 
 reu10 [IRE1A] → ;   {IRE1A}
 
 reu11  → [PERKA];  
 
 reu12 [PERKA] → ;   {PERKA}
 
 re5  → [ATF6T];  
 
 re6 [ATF6T] → ;   {ATF6T}
 
 re8 [ATF6T] → [ATF6GB];  
 
 rew1 [ATF6T] → ;   {WFS1} , {WFS1} , {ATF6T}
 
 re9 [ATF6GB] → ;   {ATF6GB}
 
 re10 [ATF6GB] → [ATF6p50];   {ATF6GB}
 
 re11 [ATF6p50] → ;   {ATF6p50}
 
 rew2  → [mWFS1];   {ATF6p50} , {ATF6p50}
 
 rew3 [mWFS1] → ;   {mWFS1}
 
 rew4  → [WFS1];   {mWFS1} , {mWFS1}
 
 rew5 [WFS1] → ;   {WFS1}
 
 re12  → [mXbp1u];   {ATF6p50} , {ATF6p50}
 
 re13 [mXbp1u] → ;   {mXbp1u}
 
 re14 [mXbp1u] → [mXbp1s];  
 
 re15 [mXbp1s] → ;   {mXbp1s}
 
 re16  → [Xbp1s];   {mXbp1s} , {mXbp1s}
 
 re17 [Xbp1s] → ;   {Xbp1s}
 
 re18  → [mBiPT];   {Xbp1s} , {ATF6p50} , {Xbp1s} , {ATF6p50}
 
 re19 [mBiPT] → ;   {mBiPT}
 
 re20  → [BiPT];   {mBiPT} , {mBiPT}
 
 re21 [BiPT] → ;   {BiPT}
 
 re23  → [ATF4];  
 
 re24 [ATF4] → ;   {ATF4}
 
 re25  → [mCHOP];   {ATF4} , {ATF6p50} , {ATF4} , {ATF6p50}
 
 re26 [mCHOP] → ;   {mCHOP}
 
 re27  → [CHOP];   {mCHOP} , {mCHOP}
 
 re28 [CHOP] → ;   {CHOP}
 
 re29  → [mGADD34];   {CHOP} , {CHOP}
 
 re30 [mGADD34] → ;   {mGADD34}
 
 re31  → [GADD34];   {mGADD34} , {mGADD34}
 
 re32 [GADD34] → ;   {GADD34}
 
 rea1  → [BCL2T];   {CHOP} , {CHOP}
 
 rea2 [BCL2T] → ;   {BCL2T}
 
 rea3  → [BAXmT];  
 
 rea4  → [BAXmT];  
 
 rea5 [BAXmT] → ;   {BAXmT}
 
 rea6 [BAXmT] → ;   {BAXmT}
 
 rea7 [BAXmT] → ;   {BAXmT}
 
 rea8  → [BH3T];  
 
 rea9  → [BH3T];   {CHOP} , {CHOP}
 
 rea10 [BH3T] → ;   {BH3T}
 
 rea11  → [BAXmBCL2];  
 
 rea12 [BAXmBCL2] → ;   {BAXmBCL2}
 
 rea13 [BAXmBCL2] → ;   {BAXmBCL2}
 
 rea14  → [BH3BCL2];  
 
 rea15 [BH3BCL2] → ;   {BH3BCL2}
 
 rea16 [BH3BCL2] → ;   {BH3BCL2}
 
Rules (11)
 
 Assignment Rule (name: UFP) UFP = UFPT-BiUFP
 
 Assignment Rule (name: BiP) BiP = (((BiPT-BiRE1)-BiATF)-BiPER)-BiUFP
 
 Assignment Rule (name: IRE1) IRE1 = (IRE1T-BiRE1)-n*IRE1A
 
 Assignment Rule (name: PERK) PERK = (PERKT-BiPER)-n*PERKA
 
 Assignment Rule (name: ATF6) ATF6 = ATF6T-BiATF
 
 Assignment Rule (name: spliceRate) spliceRate = EMM(mXbp1u, 0.5*n*IRE1A, krcSplice, ksplice)
 
 Assignment Rule (name: eIF2a) eIF2a = eIF2aT*fGK(kphos*0.5*n*PERKA, kdephos*(GADD34+CReP), J/eIF2aT, K/eIF2aT)
 
 Assignment Rule (name: BCL2) BCL2 = (BCL2T-BH3BCL2)-BAXmBCL2
 
 Assignment Rule (name: BH3) BH3 = BH3T-BH3BCL2
 
 Assignment Rule (name: BAXm) BAXm = BAXmT-BAXmBCL2
 
 Assignment Rule (name: mUFPT) mUFPT = 13
 
Functions (3)
 
 EMM lambda(St, Et, Km, kcat, 0.5*kcat*((St+Et+Km)-((St+Et+Km)^2-4*St*Et)^(0.5)))
 
 Gamma lambda(v, u, J, K, (v-u)+v*J+u*K)
 
 fGK lambda(v, u, J, K, piecewise(0, (v == 0) && (u == 0), 2*u*K/(Gamma(v, u, J, K)+(Gamma(v, u, J, K)^2-4*(v-u)*u*K)^(0.5))))
 
   Spatial dimensions: 3.0  Compartment size: 1.0  (Units: volume)
 
   UFPT
Compartment: ERlumen
Initial amount: 0.0  (Units: substance)
 
   BiUFP
Compartment: ERlumen
Initial amount: 0.0  (Units: substance)
 
   BiRE1
Compartment: ERlumen
Initial amount: 0.0  (Units: substance)
 
   BiATF
Compartment: ERlumen
Initial amount: 0.0  (Units: substance)
 
   BiPER
Compartment: ERlumen
Initial amount: 0.0  (Units: substance)
 
   IRE1A
Compartment: ERlumen
Initial amount: 0.0  (Units: substance)
 
   PERKA
Compartment: ERlumen
Initial amount: 0.0  (Units: substance)
 
   BiPT
Compartment: ERlumen
Initial amount: 0.0  (Units: substance)
 
   ATF6T
Compartment: ERlumen
Initial amount: 0.0  (Units: substance)
 
 WFS1
Compartment: ERlumen
Initial amount: 0.0  (Units: substance)
 
   Spatial dimensions: 3.0  Compartment size: 1.0  (Units: volume)
 
   mXbp1u
Compartment: cytoplasm
Initial amount: 0.0  (Units: substance)
 
   mXbp1s
Compartment: cytoplasm
Initial amount: 0.0  (Units: substance)
 
 Xbp1s
Compartment: cytoplasm
Initial amount: 0.0  (Units: substance)
 
   mBiPT
Compartment: cytoplasm
Initial amount: 0.0  (Units: substance)
 
   ATF6p50
Compartment: cytoplasm
Initial amount: 0.0  (Units: substance)
 
   mWFS1
Compartment: cytoplasm
Initial amount: 0.0  (Units: substance)
 
 ATF4
Compartment: cytoplasm
Initial amount: 0.0  (Units: substance)
 
   mCHOP
Compartment: cytoplasm
Initial amount: 0.0  (Units: substance)
 
 CHOP
Compartment: cytoplasm
Initial amount: 0.0  (Units: substance)
 
   mGADD34
Compartment: cytoplasm
Initial amount: 0.0  (Units: substance)
 
 GADD34
Compartment: cytoplasm
Initial amount: 0.0  (Units: substance)
 
   BH3T
Compartment: cytoplasm
Initial amount: 0.0  (Units: substance)
 
   Spatial dimensions: 3.0  Compartment size: 1.0  (Units: volume)
 
   ATF6GB
Compartment: Golgi
Initial amount: 0.0  (Units: substance)
 
   Spatial dimensions: 3.0  Compartment size: 1.0  (Units: volume)
 
   BCL2T
Compartment: mitochondria
Initial amount: 0.0  (Units: substance)
 
   BAXmT
Compartment: mitochondria
Initial amount: 0.0  (Units: substance)
 
   BAXmBCL2
Compartment: mitochondria
Initial amount: 0.0  (Units: substance)
 
   BH3BCL2
Compartment: mitochondria
Initial amount: 0.0  (Units: substance)
 
Global Parameters (94)
 
   UFP  
 
  BiP  
 
  IRE1  
 
  PERK  
 
  ATF6  
 
  eIF2a  
 
   spliceRate  
 
   BCL2  
 
   BH3  
 
   BAXm  
 
   tmr
Value: 10.0   (Units: dimensionless)
Constant
 
   IRE1T
Value: 1.0   (Units: acu)
Constant
 
   PERKT
Value: 1.0   (Units: acu)
Constant
 
   eIF2aT
Value: 1.0   (Units: acu)
Constant
 
 CReP
Value: 0.1   (Units: acu)
Constant
 
   kf
Value: 10.0   (Units: aru2 = acu^-1.atu^-1)
Constant
 
   kr
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   n
Value: 4.0   (Units: dimensionless)
Constant
 
   nh
Value: 2.0   (Units: dimensionless)
Constant
 
   extATT
Constant
 
   extPERK
Constant
 
   basalXBP
Value: 1.0   (Units: acu)
Constant
 
   basalBiP
Value: 1.0   (Units: acu)
Constant
 
   krcXU
Value: 5.0   (Units: acu)
Constant
 
   krcBiP
Value: 5.0   (Units: acu)
Constant
 
   krcWFS
Value: 1.0   (Units: acu)
Constant
 
   krcCHOP
Value: 1.0   (Units: acu)
Constant
 
   krcGADD34
Value: 1.0   (Units: acu)
Constant
 
   kmXbp
Value: 10.0   (Units: dimensionless)
Constant
 
   kmAtfsXBP
Value: 10.0   (Units: dimensionless)
Constant
 
   kmAtfsBiP
Value: 1.0   (Units: dimensionless)
Constant
 
   kmAtff
Value: 0.05   (Units: dimensionless)
Constant
 
   kmChop
Value: 0.05   (Units: dimensionless)
Constant
 
   kmAtfs
Value: 0.1   (Units: dimensionless)
Constant
 
   ksplice
Value: 10.0   (Units: aru1 = atu^-1)
Constant
 
   krcSplice
Value: 1.0   (Units: acu)
Constant
 
   trcXU
Value: 1.0   (Units: aru = acu.atu^-1)
Constant
 
   trcBiP
Value: 1.0   (Units: aru = acu.atu^-1)
Constant
 
   trcWFS
Value: 1.0   (Units: aru = acu.atu^-1)
Constant
 
   trcCHOP
Value: 1.0   (Units: aru = acu.atu^-1)
Constant
 
   trcGADD34
Value: 1.0   (Units: aru = acu.atu^-1)
Constant
 
   ktrUFP
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   ktrXS
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   ktrBiP
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   ktrATF6
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   ktrWFS
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   ktrATF4
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   ktrCHOP
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   ktrGADD34
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   kdmXU
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   kdmXS
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   kdmBiP
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   kdmWFS
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   kdmCHOP
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   kdmGADD34
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   kdUFP
Value: 0.1   (Units: aru1 = atu^-1)
Constant
 
   kdXS
Value: 0.1   (Units: aru1 = atu^-1)
Constant
 
   kdBiP
Value: 0.01   (Units: aru1 = atu^-1)
Constant
 
   kdATF6
Value: 0.1   (Units: aru1 = atu^-1)
Constant
 
   kdATF6GB
Value: 0.1   (Units: aru1 = atu^-1)
Constant
 
   kdATF6p50
Value: 0.1   (Units: aru1 = atu^-1)
Constant
 
   kdWFS
Value: 0.1   (Units: aru1 = atu^-1)
Constant
 
   kdATF4
Value: 0.1   (Units: aru1 = atu^-1)
Constant
 
   kdCHOP
Value: 0.1   (Units: aru1 = atu^-1)
Constant
 
   kdGADD34
Value: 0.1   (Units: aru1 = atu^-1)
Constant
 
   mATF6T
Value: 5.0   (Units: acu)
Constant
 
   mUFPT  
 
   mATF4
Value: 1.0   (Units: acu)
Constant
 
   ktrans
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   kcleave
Value: 10.0   (Units: aru1 = atu^-1)
Constant
 
   kphos
Value: 5.0   (Units: aru1 = atu^-1)
Constant
 
   kdephos
Value: 0.5   (Units: aru1 = atu^-1)
Constant
 
   kdeAW
Value: 1.0   (Units: aru2 = acu^-1.atu^-1)
Constant
 
   kbu
Constant
 
   switch
Constant
 
   kATF4
Value: 0.1   (Units: acu)
Constant
 
   J
Value: 0.001   (Units: acu)
Constant
 
   K
Value: 0.001   (Units: acu)
Constant
 
   kfbc
Value: 10.0   (Units: aru = acu.atu^-1)
Constant
 
   kdbc
Value: 0.1   (Units: aru1 = atu^-1)
Constant
 
   kmbc
Value: 0.03   (Units: acu1 = acu^-1)
Constant
 
   kstr
Value: 0.2   (Units: dimensionless)
Constant
 
   BAXT
Value: 100.0   (Units: acu)
Constant
 
   kfx
Value: 1.0   (Units: aru1 = atu^-1)
Constant
 
   kfxp
Value: 3.0   (Units: aru2 = acu^-1.atu^-1)
Constant
 
   kbx
Value: 2.0   (Units: aru1 = atu^-1)
Constant
 
   kasx
Value: 90.0   (Units: aru2 = acu^-1.atu^-1)
Constant
 
   kdsx
Value: 0.05   (Units: aru1 = atu^-1)
Constant
 
   ks3
Value: 0.1   (Units: aru = acu.atu^-1)
Constant
 
   ks3p
Value: 0.6   (Units: aru1 = atu^-1)
Constant
 
   kd3
Value: 0.01   (Units: aru1 = atu^-1)
Constant
 
   kas3
Value: 10.0   (Units: aru2 = acu^-1.atu^-1)
Constant
 
   kds3
Value: 0.01   (Units: aru1 = atu^-1)
Constant
 
   kff
Value: 10.0   (Units: aru3 = acu^-3.atu^-1)
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000446

Curator's comment: (updated: 02 Apr 2013 16:27:54 BST)

Figure 12 of the reference publication has been reproduced here. The figure shows the activation of unfolded protein response (UPR) following the rate of total unfolded protein accumulation (mUFPT). Set mUFPT to 12, 15 and 18 for mild, moderate and severe stress conditions.
The model was simulated using Copasi v4.8 (Build 38). Figures were generated using Gnuplot.

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