334192
constant: false
boundary condition: false
has only substance units: true
initial concentration: NaN
initial amount: 0.0
in compartment: 334188
type: Species

145039
stoichiometry: 1.0
species: 334189
type: SpeciesReference

144614
exponent: 1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit

334218
constant: true
units: metaid_0000071
value: 5.0E7
type: Parameter

334224
constant: true
units: metaid_0000074
value: 1000.0
type: Parameter

334204
kinetic law: 144978
reactant: 144966
fast: false
reversible: false
name: r7: R death
type: Reaction

144820
stoichiometry: 1.0
species: 334191
type: SpeciesReference

334230
constant: true
units: metaid_0000074
value: 5.0
type: Parameter

145015
stoichiometry: 1.0
species: 334194
type: SpeciesReference

metaid_0000074
unit: 144626
name: per_day
type: SBMLUnitsDef

144699
exponent: 1.0
scale: 0
multipler: 1.0
kind: ITEM
type: SBMLUnit

144857
stoichiometry: 1.0
species: 334191
type: SpeciesReference

334220
constant: true
units: dimensionless
value: 1.0E-4
type: Parameter

334225
constant: true
units: metaid_0000074
value: 0.25
type: Parameter

334234
constant: false
units: metaid_0000074
value: NaN
type: Parameter

144990
stoichiometry: 1.0
species: 334192
type: SpeciesReference

145063
stoichiometry: 1.0
species: 334189
type: SpeciesReference

BIOMD0000000290
parameter: 334221
reaction: 334208
created:
  W3 CDTF: Wed Dec 22 02:02:17 GMT 2010
parameter: 334218
is version of: DOID:417
parameter: 334231
length unit: 879216
parameter: 334228
compartment: 334188
reaction: 334201
species: 334189
parameter: 334225
units def: 144639
reaction: 334204
name: Alexander2010_Tcell_Regulation_Sys2
time units: metaid_0000072
area units: metaid_0000005
units def: metaid_0000072
species: 334195
units def: metaid_0000071
units def: metaid_0000074
is: MODEL1012220001
rule: 334214
parameter: 334224
notes: This is system 2, the model with Michelis Menten type antigen uptake by pAPCs, described in the article: Self-tolerance and Autoimmunity in a Regulatory T Cell Model. Alexander HK, Wahl LM. Bull Math Biol. 2010 Mar 2. PMID: 20195912 , doi: 10.1007/s11538-010-9519-2 ; Abstract: The class of immunosuppressive lymphocytes known as regulatory T cells (Tregs) has been identified as a key component in preventing autoimmune diseases. Although Tregs have been incorporated previously in mathematical models of autoimmunity, we take a novel approach which emphasizes the importance of professional antigen presenting cells (pAPCs). We examine three possible mechanisms of Treg action (each in isolation) through ordinary differential equation (ODE) models. The immune response against a particular autoantigen is suppressed both by Tregs specific for that antigen and by Tregs of arbitrary specificities, through their action on either maturing or already mature pAPCs or on autoreactive effector T cells. In this deterministic approach, we find that qualitative long-term behaviour is predicted by the basic reproductive ratio R (0) for each system. When R (0) < 1, only the trivial equilibrium exists and is stable; when R (0)>1, this equilibrium loses its stability and a stable non-trivial equilibrium appears. We interpret the absence of self-damaging populations at the trivial equilibrium to imply a state of self-tolerance, and their presence at the non-trivial equilibrium to imply a state of chronic autoimmunity. Irrespective of mechanism, our model predicts that Tregs specific for the autoantigen in question play no role in the system's qualitative long-term behaviour, but have quantitative effects that could potentially reduce an autoimmune response to sub-clinical levels. Our results also suggest an important role for Tregs of arbitrary specificities in modulating the qualitative outcome. A stochastic treatment of the same model demonstrates that the probability of developing a chro…
units def: 144675
parameter: 334236
parameter: 334230
is version of: GO:0002667
parameter: 334227
curated: true
rule: 334213
reaction: 334198
species: 334191
reaction: 334206
type: SBMLModel
occurs in: http://identifiers.org/taxonomy/33208
reaction: 334200
is described by: http://identifiers.org/pubmed/20195912
reaction: 334203
modified:
  W3 CDTF: Fri Apr 20 23:09:32 BST 2012
parameter: 334235
parameter: 334234
parameter: 334223
creator:
  ORG:
    orgname: EMBL-EBI
  n:
    given: Lukas
    family: Endler
parameter: 334222
rule: 334216
species: 334192
parameter: 334220
reaction: 334199
parameter: 334217
substance units: metaid_0000071
reaction: 334202
reaction: 334207
species: 334194
reaction: 334197
volume units: 982936
reaction: 334205
parameter: 334233

334223
constant: true
units: 144639
value: 0.016
type: Parameter

334205
kinetic law: 145003
reactant: 144990
fast: false
reversible: false
name: r8: E death
type: Reaction

144905
stoichiometry: 1.0
species: 334192
type: SpeciesReference

144687
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit

144711
stoichiometry: 1.0
species: 334194
type: SpeciesReference

334197
kinetic law: 144724
reactant: 144711
fast: false
reversible: false
name: r1a: self-antigen uptake
type: Reaction

334200
kinetic law: 144844
modifier: 144832
product: 144820
fast: false
reversible: false
name: r3: R activation by A
type: Reaction

144602
exponent: 1.0
scale: 0
multipler: 1.0
kind: ITEM
type: SBMLUnit

144663
exponent: -1.0
scale: 0
multipler: 1.0
kind: ITEM
type: SBMLUnit

334233
constant: true
units: 144639
value: 3.0E-6
type: Parameter

334228
constant: true
units: metaid_0000074
value: 0.25
type: Parameter

334188
constant: true
size: 1.0
spatial dimensions: 3.0
type: Compartment

144626
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit

metaid_0000072
unit: 144614
name: days
type: SBMLUnitsDef

334206
kinetic law: 145027
reactant: 145015
fast: false
reversible: false
name: r9: G clearance
type: Reaction

334227
constant: true
units: metaid_0000074
value: 0.25
type: Parameter

334222
constant: true
units: metaid_0000074
value: 200.0
type: Parameter

144736
stoichiometry: 1.0
species: 334195
type: SpeciesReference

334198
kinetic law: 144772
modifier: 144760
product: 144748
reactant: 144736
fast: false
reversible: false
name: r1b: pAPC maturation
type: Reaction

334194
constant: false
boundary condition: false
has only substance units: true
initial concentration: NaN
initial amount: 1.0E8
in compartment: 334188
type: Species

144942
stoichiometry: 1.0
species: 334189
type: SpeciesReference

334201
kinetic law: 144893
modifier: 144881
modifier: 144869
product: 144857
fast: false
reversible: false
name: r4: R activation by A and E
type: Reaction

334189
constant: false
boundary condition: false
has only substance units: true
initial concentration: NaN
initial amount: 1.0
in compartment: 334188
type: Species

334203
kinetic law: 144954
reactant: 144942
fast: false
reversible: false
name: r6: A death
type: Reaction

144639
unit: 144663
unit: 144651
name: per_day_per_item
type: SBMLUnitsDef

334235
constant: false
units: metaid_0000074
value: NaN
type: Parameter

334217
constant: true
units: 144675
value: 125000.0
type: Parameter

144675
unit: 144699
unit: 144687
name: items_per_day
type: SBMLUnitsDef

334191
constant: false
boundary condition: false
has only substance units: true
initial concentration: NaN
initial amount: 0.0
in compartment: 334188
type: Species

144748
stoichiometry: 1.0
species: 334189
type: SpeciesReference

metaid_0000071
unit: 144602
name: number
type: SBMLUnitsDef

144784
stoichiometry: 1.0
species: 334194
type: SpeciesReference

144966
stoichiometry: 1.0
species: 334191
type: SpeciesReference

334207
kinetic law: 145051
reactant: 145039
fast: false
reversible: false
name: r10: A suppression by Tregs of other specificity
type: Reaction

334195
constant: false
boundary condition: true
has only substance units: true
initial concentration: NaN
initial amount: 0.0
in compartment: 334188
type: Species

144651
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit

334221
constant: true
units: metaid_0000074
value: 2000.0
type: Parameter

334231
constant: true
units: metaid_0000074
value: 0.25
type: Parameter

334202
kinetic law: 144930
modifier: 144917
product: 144905
fast: false
reversible: false
name: r5: E generation by A
type: Reaction

334199
kinetic law: 144808
modifier: 144796
product: 144784
fast: false
reversible: false
name: r2: self-antigen release triggered by E
type: Reaction

334236
constant: false
units: dimensionless
value: NaN
type: Parameter

334208
kinetic law: 145087
modifier: 145075
reactant: 145063
fast: false
reversible: false
name: r11: A suppression by R
type: Reaction