tang1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000285) Biomodels notes: The model reproduces figure S2 of the Supplementary material of the reference publication. In the paper, figure S2 is generated by picking 3 stochastic simulation runs and plotted the monomer, oligomers and inclusion bodies. There is slight inconsistency between the plots obtained here (curation figure) and that of the paper (figure S2). The curation figure is obtained using deterministic simulation run, whereas in the paper figure S2 is obtained using stochastic simulation run. The inconsistency is due to the difference in the stochastic and deterministic simulation runs. This has been checked with the author. The model was integrated and simulated using Copasi v4.6 (Build 32). JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

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Experimental and computational analysis of polyglutamine-mediated cytotoxicity.

  • Matthew Y Tang
  • Carole J Proctor
  • John Woulfe
  • Douglas A Gray
PLoS Comput. Biol. 2010; 6 (9):
Abstract
Expanded polyglutamine (polyQ) proteins are known to be the causative agents of a number of human neurodegenerative diseases but the molecular basis of their cytoxicity is still poorly understood. PolyQ tracts may impede the activity of the proteasome, and evidence from single cell imaging suggests that the sequestration of polyQ into inclusion bodies can reduce the proteasomal burden and promote cell survival, at least in the short term. The presence of misfolded protein also leads to activation of stress kinases such as p38MAPK, which can be cytotoxic. The relationships of these systems are not well understood. We have used fluorescent reporter systems imaged in living cells, and stochastic computer modeling to explore the relationships of polyQ, p38MAPK activation, generation of reactive oxygen species (ROS), proteasome inhibition, and inclusion body formation. In cells expressing a polyQ protein inclusion, body formation was preceded by proteasome inhibition but cytotoxicity was greatly reduced by administration of a p38MAPK inhibitor. Computer simulations suggested that without the generation of ROS, the proteasome inhibition and activation of p38MAPK would have significantly reduced toxicity. Our data suggest a vicious cycle of stress kinase activation and proteasome inhibition that is ultimately lethal to cells. There was close agreement between experimental data and the predictions of a stochastic computer model, supporting a central role for proteasome inhibition and p38MAPK activation in inclusion body formation and ROS-mediated cell death.

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
1.0 item
Id Name Spatial dimensions Size
cytosol 3.0 1.0
Id Name Initial quantity Compartment Fixed
AggP1 0.0 cytosol
AggP2 0.0 cytosol
AggP3 0.0 cytosol
AggP4 0.0 cytosol
AggP5 0.0 cytosol
AggP_Proteasome 0.0 cytosol
AggPolyQ1 0.0 cytosol
AggPolyQ2 0.0 cytosol
AggPolyQ3 0.0 cytosol
AggPolyQ4 0.0 cytosol
AggPolyQ5 0.0 cytosol
MisP 0.0 cytosol
MisP_Proteasome 0.0 cytosol
NatP 19500.0 cytosol
PIdeath 0.0 cytosol
PolyQ 1000.0 cytosol
PolyQ_Proteasome 0.0 cytosol
Proteasome 1000.0 cytosol
ROS 10.0 cytosol
SeqAggP 0.0 cytosol
Sink 1.0 cytosol
Source 1.0 cytosol
mRFPu 300.0 cytosol
mRFPu_Proteasome 0.0 cytosol
p38 100.0 cytosol
p38_P 0.0 cytosol
p38death 0.0 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
AggP_ProteasomeSequestering AggP_Proteasome + SeqAggP > {2.0}SeqAggP

kseqAggPProt * AggP_Proteasome * SeqAggP * kalive
MisPInclusionGrowth MisP + SeqAggP > {2.0}SeqAggP

kseqMisP * MisP * SeqAggP * kalive
MisP_Aggregation1 {2.0}MisP > AggP1

kaggMisP * MisP * (MisP - 1) * 0.5 * kalive
MisP_Aggregation2 MisP + AggP1 > AggP2

kagg2MisP * MisP * AggP1 * kalive
MisP_Aggregation3 MisP + AggP2 > AggP3

kagg2MisP * MisP * AggP2 * kalive
MisP_Aggregation4 MisP + AggP3 > AggP4

kagg2MisP * MisP * AggP3 * kalive
MisP_Aggregation5 MisP + AggP4 > AggP5

kagg2MisP * MisP * AggP4 * kalive
MisP_Degradation MisP_Proteasome > Proteasome

kdegMisP * MisP_Proteasome * kalive * kproteff
MisP_Disaggregation1 AggP1 > {2.0}MisP

kdisaggMisP1 * AggP1 * kalive
MisP_Disaggregation2 AggP2 > MisP + AggP1

kdisaggMisP2 * AggP2 * kalive
MisP_Disaggregation3 AggP3 > MisP + AggP2

kdisaggMisP3 * AggP3 * kalive
MisP_Disaggregation4 AggP4 > MisP + AggP3

kdisaggMisP4 * AggP4 * kalive
MisP_Disaggregation5 AggP5 > MisP + AggP4

kdisaggMisP5 * AggP5 * kalive
MisP_InclusionFormation MisP + AggP5 > {7.0}SeqAggP

kagg2MisP * MisP * AggP5 * kalive
MisP_ProteasomeBinding MisP + Proteasome > MisP_Proteasome

kbinMisPProt * MisP * Proteasome * kalive
MisP_ProteasomeRelease MisP_Proteasome > MisP + Proteasome

krelMisPProt * MisP_Proteasome * kalive
MisP_ProteasomeSequestering MisP_Proteasome + SeqAggP > {2.0}SeqAggP

kseqMisPProt * MisP_Proteasome * SeqAggP * kalive
Misfolding NatP + ROS > MisP + ROS

kmisfold * NatP * ROS * kalive
P38DeathPathway p38_P > p38_P + p38death

kp38death * p38_P * kalive * kp38act
PIDeathPathway AggP_Proteasome > AggP_Proteasome + PIdeath

kPIdeath * AggP_Proteasome * kalive
PolyQAggregation1 {2.0}PolyQ + ROS > AggPolyQ1 + ROS

kaggPolyQ * PolyQ * (PolyQ - 1) * 0.5 * (pow(ROS, 2) / (pow(10, 2) + pow(ROS, 2))) * kalive
PolyQAggregation2 PolyQ + AggPolyQ1 + ROS > AggPolyQ2 + ROS

kaggPolyQ * PolyQ * AggPolyQ1 * (pow(ROS, 2) / (pow(10, 2) + pow(ROS, 2))) * kalive
PolyQAggregation3 PolyQ + AggPolyQ2 + ROS > AggPolyQ3 + ROS

kaggPolyQ * PolyQ * AggPolyQ2 * (pow(ROS, 2) / (pow(10, 2) + pow(ROS, 2))) * kalive
PolyQAggregation4 PolyQ + AggPolyQ3 + ROS > AggPolyQ4 + ROS

kaggPolyQ * PolyQ * AggPolyQ3 * (pow(ROS, 2) / (pow(10, 2) + pow(ROS, 2))) * kalive
PolyQAggregation5 PolyQ + AggPolyQ4 + ROS > AggPolyQ5 + ROS

kaggPolyQ * PolyQ * AggPolyQ4 * (pow(ROS, 2) / (pow(10, 2) + pow(ROS, 2))) * kalive
PolyQDegradation PolyQ_Proteasome > Proteasome

kdegPolyQ * PolyQ_Proteasome * kalive * kproteff
PolyQDisaggregation1 AggPolyQ1 > {2.0}PolyQ

kdisaggPolyQ1 * AggPolyQ1 * kalive
PolyQDisaggregation2 AggPolyQ2 > PolyQ + AggPolyQ1

kdisaggPolyQ2 * AggPolyQ2 * kalive
PolyQDisaggregation3 AggPolyQ3 > PolyQ + AggPolyQ2

kdisaggPolyQ3 * AggPolyQ3 * kalive
PolyQDisaggregation4 AggPolyQ4 > PolyQ + AggPolyQ3

kdisaggPolyQ4 * AggPolyQ4 * kalive
PolyQDisaggregation5 AggPolyQ5 > PolyQ + AggPolyQ4

kdisaggPolyQ5 * AggPolyQ5 * kalive
PolyQInclusionFormation PolyQ + AggPolyQ5 > {7.0}SeqAggP

kaggPolyQ * PolyQ * AggPolyQ5 * kalive
PolyQInclusionGrowth PolyQ + SeqAggP > {2.0}SeqAggP

kseqPolyQ * PolyQ * SeqAggP * kalive
PolyQ_ProteasomeSequestering PolyQ_Proteasome + SeqAggP > {2.0}SeqAggP

kseqPolyQProt * PolyQ_Proteasome * SeqAggP * kalive
ProteasomeInhibition1 AggPolyQ1 + Proteasome > AggP_Proteasome

kinhprot * AggPolyQ1 * Proteasome * kalive
ProteasomeInhibition2 AggPolyQ2 + Proteasome > AggP_Proteasome

kinhprot * AggPolyQ2 * Proteasome * kalive
ProteasomeInhibition3 AggPolyQ3 + Proteasome > AggP_Proteasome

kinhprot * AggPolyQ3 * Proteasome * kalive
ProteasomeInhibition4 AggPolyQ4 + Proteasome > AggP_Proteasome

kinhprot * AggPolyQ4 * Proteasome * kalive
ProteasomeInhibition5 AggPolyQ5 + Proteasome > AggP_Proteasome

kinhprot * AggPolyQ5 * Proteasome * kalive
ProteasomeInhibitionAggP1 AggP1 + Proteasome > AggP_Proteasome

kinhprot * AggP1 * Proteasome * kalive
ProteasomeInhibitionAggP2 AggP2 + Proteasome > AggP_Proteasome

kinhprot * AggP2 * Proteasome * kalive
ProteasomeInhibitionAggP3 AggP3 + Proteasome > AggP_Proteasome

kinhprot * AggP3 * Proteasome * kalive
ProteasomeInhibitionAggP4 AggP4 + Proteasome > AggP_Proteasome

kinhprot * AggP4 * Proteasome * kalive
ProteasomeInhibitionAggP5 AggP5 + Proteasome > AggP_Proteasome

kinhprot * AggP5 * Proteasome * kalive
ProteinSynthesis Source > NatP

ksynNatP * Source * kalive
ROSgenerationAggPProteasome AggP_Proteasome > AggP_Proteasome + ROS

kgenROSAggP * AggP_Proteasome * kalive
ROSgenerationBasal Source > ROS

kgenROS * Source * kalive
ROSgenerationSeqAggP SeqAggP > SeqAggP + ROS

kgenROSSeqAggP * SeqAggP * kalive
ROSgenerationSmallAggP1 AggP1 > AggP1 + ROS

kgenROSAggP * AggP1 * kalive
ROSgenerationSmallAggP2 AggP2 > AggP2 + ROS

kgenROSAggP * AggP2 * kalive
ROSgenerationSmallAggP3 AggP3 > AggP3 + ROS

kgenROSAggP * AggP3 * kalive
ROSgenerationSmallAggP4 AggP4 > AggP4 + ROS

kgenROSAggP * AggP4 * kalive
ROSgenerationSmallAggP5 AggP5 > AggP5 + ROS

kgenROSAggP * AggP5 * kalive
ROSgenerationSmallAggPolyQ1 AggPolyQ1 > AggPolyQ1 + ROS

kgenROSAggP * AggPolyQ1 * kalive
ROSgenerationSmallAggPolyQ2 AggPolyQ2 > AggPolyQ2 + ROS

kgenROSAggP * AggPolyQ2 * kalive
ROSgenerationSmallAggPolyQ3 AggPolyQ3 > AggPolyQ3 + ROS

kgenROSAggP * AggPolyQ3 * kalive
ROSgenerationSmallAggPolyQ4 AggPolyQ4 > AggPolyQ4 + ROS

kgenROSAggP * AggPolyQ4 * kalive
ROSgenerationSmallAggPolyQ5 AggPolyQ5 > AggPolyQ5 + ROS

kgenROSAggP * AggPolyQ5 * kalive
ROSremoval ROS > Sink

kremROS * ROS * kalive
Refolding MisP > NatP

krefold * MisP * kalive
mRFPuDegradation mRFPu_Proteasome > Proteasome

kdegmRFPu * mRFPu_Proteasome * kalive * kproteff
mRFPuProteasomeBinding mRFPu + Proteasome > mRFPu_Proteasome

kbinmRFPu * mRFPu * Proteasome * kalive
mRFPuProteasomeRelease mRFPu_Proteasome > mRFPu + Proteasome

krelmRFPu * mRFPu_Proteasome * kalive
mRFPuProteasomeSequestering mRFPu_Proteasome + SeqAggP > {2.0}SeqAggP

kseqmRFPuProt * mRFPu_Proteasome * SeqAggP * kalive
mRFPuSequestering mRFPu + SeqAggP > {2.0}SeqAggP

kseqmRFPu * mRFPu * SeqAggP * kalive
mRFPuSynthesis Source > mRFPu

ksynmRFPu * Source * kalive
p38_P_ROS_Generation p38_P > p38_P + ROS

kgenROSp38 * p38_P * kp38act * kalive
p38activation ROS + p38 > ROS + p38_P

kactp38 * ROS * p38 * kalive
p38inactivation p38_P > p38

kinactp38 * p38_P * kalive
polyQSynthesis Source > PolyQ

ksynPolyQ * Source * kalive
polyqProteasomeBinding PolyQ + Proteasome > PolyQ_Proteasome

kbinPolyQ * PolyQ * Proteasome * kalive
polyqProteasomeRelease PolyQ_Proteasome > PolyQ + Proteasome

krelPolyQ * PolyQ_Proteasome * kalive

Global parameters

Id Value
kPIdeath 0.000000025
kactp38 0.000005
kagg2MisP 0.0000000001
kaggMisP 0.00000000001
kaggPolyQ 0.00000005
kalive 1.0
kbinMisPProt 0.00000005
kbinPolyQ 0.00000005
kbinmRFPu 0.0000005
kdegMisP 0.01
kdegPolyQ 0.0025
kdegmRFPu 0.005
kdisaggMisP1 0.0000005
kdisaggMisP2 0.0000004
kdisaggMisP3 0.0000003
kdisaggMisP4 0.0000002
kdisaggMisP5 0.0000001
kdisaggPolyQ1 0.0000005
kdisaggPolyQ2 0.0000004
kdisaggPolyQ3 0.0000003
kdisaggPolyQ4 0.0000002
kdisaggPolyQ5 0.0000001
kgenROS 0.0017
kgenROSAggP 0.000005
kgenROSSeqAggP 0.0000001
kgenROSp38 0.0007
kinactp38 0.002
kinhprot 0.000000005
kmisfold 0.000002
kp38act 1.0
kp38death 0.00000009
kproteff 1.0
krefold 0.00008
krelMisPProt 0.00000001
krelPolyQ 0.000000001
krelmRFPu 0.00000001
kremROS 0.0002
kseqAggPProt 0.0000005
kseqMisP 0.000000001
kseqMisPProt 0.0000005
kseqPolyQ 0.0000008
kseqPolyQProt 0.0000005
kseqmRFPu 0.0000000001
kseqmRFPuProt 0.0000005
ksynNatP 2.4
ksynPolyQ 0.007
ksynmRFPu 0.138
oligomers 0.0

Local parameters

Id Value Reaction

Assignment rules

Definition
oligomers = AggPolyQ1 + AggPolyQ2 + AggPolyQ3 + AggPolyQ4 + AggPolyQ5

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments
gt(PIdeath, 0) kalive = 0
gt(p38death, 0) kalive = 0