950468
constant: true
value: 2.67818
name: alfa10
type: Parameter

950492
constant: true
value: 4.19449
name: alfa12
type: Parameter

950760
constant: true
value: 16.8985
name: RecTINFstim_c
type: Parameter

951690
stoichiometry: 1.0
species: 950142
type: SpeciesReference

950736
constant: true
value: 0.0
name: RecTINFstim_a
type: Parameter

951666
kinetic law: 951702
reactant: 951690
reactant: 951678
fast: false
reversible: false
name: B_clean_oxLDL
type: Reaction

950154
constant: false
boundary condition: false
has only substance units: false
initial concentration: 0.0
initial amount: NaN
in compartment: 950118
name: HDL
type: Species

950820
constant: true
value: 0.347323
name: RecTAINFstim_b
type: Parameter

950674
constant: true
value: 1.00266
name: ForFoamstim_b
type: Parameter

950588
constant: true
value: 0.0
name: oxLDLstim_a
type: Parameter

950118
constant: true
size: 1.0
spatial dimensions: 3.0
name: compartment
type: Compartment

951026
constant: true
value: 0.147264
name: ActEndConstant
type: Parameter

950953
constant: true
value: 0.196692
name: Kdeg_MP
type: Parameter

950202
constant: false
boundary condition: false
has only substance units: false
initial concentration: 0.0
initial amount: NaN
in compartment: 950118
name: TAINF
type: Species

951365
kinetic law: 951401
product: 951389
reactant: 951377
fast: false
reversible: false
name: TINF_deg
type: Reaction

951099
constant: true
value: 0.150145
name: KBcleanoxLDL
type: Parameter

950892
constant: true
value: 2.78714
name: RecBcellsstim_b
type: Parameter

950322
constant: false
boundary condition: true
has only substance units: false
initial concentration: 0.0
initial amount: NaN
in compartment: 950118
name: SUMACT_END
type: Species

950748
constant: true
value: 2.27905
name: RecTINFstim_b
type: Parameter

950407
constant: true
value: 1.83425
name: alfa5
type: Parameter

950552
constant: true
value: 0.0
name: ActEndinh_a
type: Parameter

950916
constant: true
value: 0.555078
name: Kdeg_Bcells
type: Parameter

951497
kinetic law: 951533
product: 951521
reactant: 951509
fast: false
reversible: false
name: InLDL
type: Reaction

950868
constant: true
value: 14.549
name: RecTAINFinh_c
type: Parameter

951738
stoichiometry: 1.0
species: 950178
type: SpeciesReference

950625
constant: true
value: 0.0
name: oxLDLinh_a
type: Parameter

951786
stoichiometry: 1.0
species: 950178
type: SpeciesReference

951822
kinetic law: 951870
modifier: 951858
modifier: 951846
product: 951834
fast: false
reversible: false
name: MP_Recruitment
type: Reaction

950286
constant: false
boundary condition: true
has only substance units: false
initial concentration: 2.67523886569906E-7
initial amount: NaN
in compartment: 950118
name: SUMRecBcells
type: Species

951882
reactant: 951906
fast: false
product: 951918
name: ForFoam
modifier: 951942
reversible: false
type: Reaction
kinetic law: 951955
modifier: 951930
reactant: 951894

951050
constant: true
value: 0.571007
name: ForFoamConstant
type: Parameter

950480
constant: true
value: 0.313487
name: alfa11
type: Parameter

950724
constant: true
value: 20.0861
name: ForFoaminh_c
type: Parameter

950772
constant: true
value: 0.0
name: RecTINFinh_a
type: Parameter

951111
constant: true
value: 0.431588
name: KBcleanPLAQUE
type: Parameter

950456
constant: true
value: 2.36282
name: alfa9
type: Parameter

951606
stoichiometry: 1.0
species: 950130
type: SpeciesReference

951521
stoichiometry: 1.0
species: 950130
type: SpeciesReference

950612
constant: true
value: 15.8416
name: oxLDLstim_c
type: Parameter

950106
exponent: 1.0
scale: 0
multipler: 1.0
kind: DIMENSIONLESS
type: SBMLUnit

951377
stoichiometry: 1.0
species: 950190
type: SpeciesReference

950941
constant: true
value: 0.191241
name: Kdeg_TAINF
type: Parameter

951014
constant: true
value: 1.0
name: MCblood
type: Parameter

MODEL1002160000
reaction: 951497
species: 950250
function def: 949938
species: 950310
species: 950214
parameter: 950612
species: 950322
function def: 950010
parameter: 950880
parameter: 950528
rule: 951135
notes: This model is from the article: Workflow for generating competing hypothesis from models with parameter uncertainty. David Gomez-Cabrero, Albert Compte and Jesper Tegner Interface Focus 6 June 2011 vol. 1 no. 3 438-449; doi: 10.1098/rsfs.2011.0015 Abstract: Mathematical models are increasingly used in life sciences. However, contrary to other disciplines, biological models are typically over-parametrized and loosely constrained by scarce experimental data and prior knowledge. Recent efforts on analysis of complex models have focused on isolated aspects without considering an integrated approach-ranging from model building to derivation of predictive experiments and refutation or validation of robust model behaviours. Here, we develop such an integrative workflow, a sequence of actions expanding upon current efforts with the purpose of setting the stage for a methodology facilitating an extraction of core behaviours and competing mechanistic hypothesis residing within underdetermined models. To this end, we make use of optimization search algorithms, statistical (machine-learning) classification techniques and cluster-based analysis of the state variables' dynamics and their corresponding parameter sets. We apply the workflow to a mathematical model of fat accumulation in the arterial wall (atherogenesis), a complex phenomena with limited quantitative understanding, thus leading to a model plagued with inherent uncertainty. We find that the mathematical atherogenesis model can still be understood in terms of a few key behaviours despite the large number of parameters. This result enabled us to derive distinct mechanistic predictions from the model despite the lack of confidence in the model parameters. We conclude that building integrative workflows enable investigators to embrace modelling of complex biological processes despite uncertainty in parameters. This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/bi…
parameter: 950796
parameter: 950953
parameter: 951099
reaction: 951822
species: 950334
time units: 950070
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rule: 951243
reaction: 951762
parameter: 951087
parameter: 950941
units def: 950046
parameter: 950540
rule: 951219
substance units: 950094
function def: 949950
name: SIGMOID_1_VAR
name: TWO_TO_NOTHING
species: 950262
species: 950190
parameter: 950588
name: TWO_TO_ONE
function def: 949986
name: INFLUX
parameter: 950965
function def: 949926
species: 950274
parameter: 950928
parameter: 950516
name: OUTFLUX
reaction: 951329
volume units: 950046
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reaction: 951449
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reaction: 951593
species: 950298
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reaction: 951882
parameter: 951075
parameter: 950576
species: 950346
parameter: 950649
species: 950226
function def: 950022
species: 950178
parameter: 950868
name: Gomez-Cabrero2011_Atherogenesis
parameter: 951062
parameter: 950637
function def: 949998
species: 950238
parameter: 951026
parameter: 950711
parameter: 950358
parameter: 950661
name: DEGRADATION
parameter: 951002
parameter: 950978
reaction: 951967
is described by: rsfs.2011.0015
parameter: 951014

950166
constant: false
boundary condition: false
has only substance units: false
initial concentration: 0.0
initial amount: NaN
in compartment: 950118
name: MP
type: Species

950528
constant: true
value: 3.51949
name: ActEndstim_b
type: Parameter

951569
stoichiometry: 1.0
species: 950154
type: SpeciesReference

950334
constant: false
boundary condition: true
has only substance units: false
initial concentration: 7.69164659200097E-7
initial amount: NaN
in compartment: 950118
name: SIGMOID_ACTENDstim
type: Species

950600
constant: true
value: 0.229015
name: oxLDLstim_b
type: Parameter

951509
stoichiometry: 1.0
species: 950310
type: SpeciesReference

951087
constant: true
value: 1.14614
name: RecBcellsConstant
type: Parameter

951798
stoichiometry: 1.0
species: 950166
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950298
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name: HDL_blood
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951449
kinetic law: 951485
product: 951473
reactant: 951461
fast: false
reversible: false
name: MP_deg
type: Reaction

950856
constant: true
value: 0.160629
name: RecTAINFinh_b
type: Parameter

950928
constant: true
value: 0.0882042
name: Kdeg_TINF
type: Parameter

950238
constant: false
boundary condition: true
has only substance units: false
initial concentration: 1.76022162286916E-7
initial amount: NaN
in compartment: 950118
name: SUMoxidLDL
type: Species

951726
stoichiometry: 1.0
species: 950214
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950687
constant: true
value: 4.39941
name: ForFoamstim_c
type: Parameter

950540
constant: true
value: 1.98699
name: ActEndstim_c
type: Parameter

951894
stoichiometry: 1.0
species: 950166
type: SpeciesReference

951714
kinetic law: 951750
reactant: 951738
reactant: 951726
fast: false
reversible: false
name: B_clean_PLAQUE
type: Reaction

950130
constant: false
boundary condition: false
has only substance units: false
initial concentration: 0.0
initial amount: NaN
in compartment: 950118
name: LDL
type: Species

950250
constant: false
boundary condition: true
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initial concentration: 7.69116738046758E-8
initial amount: NaN
in compartment: 950118
name: SUMForFoam
type: Species

950564
constant: true
value: 1.9416
name: ActEndinh_b
type: Parameter

951389
stoichiometry: 1.0
species: 950178
type: SpeciesReference

950808
constant: true
value: 0.0
name: RecTAINFstim_a
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950978
constant: true
value: 0.375371
name: KoutHDL
type: Parameter

950058
exponent: 1.0
scale: 0
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kind: DIMENSIONLESS
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951918
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species: 950178
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951255
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fast: false
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name: oxidLDL
type: Reaction

951979
stoichiometry: 1.0
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950346
constant: false
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name: SIGMOID_ACTENDinh
type: Species

951123
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value: 0.302073
name: KRCT
type: Parameter

951642
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species: 950154
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952099
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species: 950214
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950844
constant: true
value: 0.0
name: RecTAINFinh_a
type: Parameter

950226
constant: false
boundary condition: true
has only substance units: false
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in compartment: 950118
name: ACT_END
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951413
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952039
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species: 950202
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950516
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value: 0.0
name: ActEndstim_a
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950178
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name: PLAQUE
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951473
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species: 950178
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950262
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name: SUMRecTINF
type: Species

951762
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product: 951798
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fast: false
reversible: false
name: RCT
type: Reaction

950990
constant: true
value: 4.06157
name: KinLDL
type: Parameter

951341
stoichiometry: 1.0
species: 950214
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950649
constant: true
value: 4.47565
name: oxLDLinh_c
type: Parameter

951329
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reactant: 951341
fast: false
reversible: false
name: Bcell_deg
type: Reaction

951075
constant: true
value: 3.20264
name: RecTAINFConstant
type: Parameter

950661
constant: true
value: 0.0
name: ForFoamstim_a
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950431
constant: true
value: 2.8067
name: alfa7
type: Parameter

950395
constant: true
value: 0.969185
name: alfa4
type: Parameter

951593
kinetic law: 951618
reactant: 951606
fast: false
reversible: false
name: OutLDL
type: Reaction

950190
constant: false
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950904
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value: 2.23629
name: RecBcellsstim_c
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951557
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species: 950298
type: SpeciesReference

950711
constant: true
value: 1.84577
name: ForFoaminh_b
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950784
constant: true
value: 0.24317
name: RecTINFinh_b
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950370
constant: true
value: 4.37096
name: alfa2
type: Parameter

950576
constant: true
value: 16.8895
name: ActEndinh_c
type: Parameter

951038
constant: true
value: 0.28495
name: oxLDLConstant
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951062
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value: 2.04297
name: RecTINFConstant
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952087
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product: 952099
fast: false
reversible: false
name: Recrut_Bcells
type: Reaction

950699
constant: true
value: 0.0
name: ForFoaminh_a
type: Parameter

950142
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boundary condition: false
has only substance units: false
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name: oxLDL
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951280
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species: 950142
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951630
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reactant: 951642
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name: OutHDL
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950082
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951906
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951967
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name: Recrut_TINF
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951268
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950358
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value: 1.55466
name: alfa1
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value: 0.55296
name: KoutLDL
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950274
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951834
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species: 950202
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950214
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name: Bcells
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950637
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name: oxLDLinh_b
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952027
kinetic law: 952075
modifier: 952063
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product: 952039
fast: false
reversible: false
name: Recrut_TAINF
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950504
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name: alfa13
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950832
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name: RecTAINFstim_c
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951461
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species: 950166
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951002
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value: 1.0614
name: KinHDL
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950310
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boundary condition: true
has only substance units: false
initial concentration: 2.5
initial amount: NaN
in compartment: 950118
name: LDL_blood
type: Species

950382
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value: 0.679298
name: alfa3
type: Parameter

950419
constant: true
value: 1.14028
name: alfa6
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950796
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value: 14.4186
name: RecTINFinh_c
type: Parameter

950880
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value: 0.0
name: RecBcellsstim_a
type: Parameter

950443
constant: true
value: 1.90407
name: alfa8
type: Parameter

951678
stoichiometry: 1.0
species: 950214
type: SpeciesReference

951545
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product: 951569
reactant: 951557
fast: false
reversible: false
name: InHDL
type: Reaction