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BIOMD0000000289 - Alexander2010_Tcell_Regulation_Sys1

 

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Reference Publication
Publication ID: 20195912
Alexander HK, Wahl LM.
Self-tolerance and autoimmunity in a regulatory T cell model.
Bull. Math. Biol. 2011 Jan; 73(1): 33-71
Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada.  [more]
Model
Original Model: BIOMD0000000289.xml.origin
Submitter: Lukas Endler
Submission ID: MODEL1012220000
Submission Date: 22 Dec 2010 01:12:13 UTC
Last Modification Date: 18 Mar 2014 11:31:13 UTC
Creation Date: 22 Dec 2010 01:15:33 UTC
Encoders:  Nick Juty
   Lukas Endler
set #1
bqbiol:hasProperty Mathematical Modelling Ontology MAMO_0000046
set #2
bqbiol:hasTaxon Taxonomy Metazoa
set #3
bqbiol:isVersionOf Gene Ontology regulation of T cell anergy
Human Disease Ontology DOID:417
Notes

This is system 1, the model with linear 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 chronic autoimmune response increases with the initial exposure to self antigen or autoreactive effector T cells. The three different mechanisms we consider, while leading to a number of similar predictions, also exhibit key differences in both transient dynamics (ODE approach) and the probability of chronic autoimmunity (stochastic approach).

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

Model
Publication ID: 20195912 Submission Date: 22 Dec 2010 01:12:13 UTC Last Modification Date: 18 Mar 2014 11:31:13 UTC Creation Date: 22 Dec 2010 01:15:33 UTC
Mathematical expressions
Reactions
r1a: self-antigen uptake r1b: pAPC maturation r2: self-antigen release triggered by E r3: R activation by A
r4: R activation by A and E r5: E generation by A r6: A death r7: R death
r8: E death r9: G clearance r10: A suppression by Tregs of other specificity r11: A suppression by R
Rules
Assignment Rule (variable: mA) Assignment Rule (variable: mG) Assignment Rule (variable: R0)  
Physical entities
Compartments Species
body A R E
G A_im  
Global parameters
v f gamma beta
pi1 lambdaE muA muR
muE muG b1 sigma1
mA mG R0  
Reactions (12)
 
 r1a: self-antigen uptake [G] → ;  
 
 r1b: pAPC maturation [A_im] → [A];   {G}
 
 r2: self-antigen release triggered by E  → [G];   {E}
 
 r3: R activation by A  → [R];   {A}
 
 r4: R activation by A and E  → [R];   {A} , {E}
 
 r5: E generation by A  → [E];   {A}
 
 r6: A death [A] → ;  
 
 r7: R death [R] → ;  
 
 r8: E death [E] → ;  
 
 r9: G clearance [G] → ;  
 
 r10: A suppression by Tregs of other specificity [A] → ;  
 
 r11: A suppression by R [A] → ;   {R}
 
Rules (3)
 
 Assignment Rule (name: mA) mA = b1+muA
 
 Assignment Rule (name: mG) mG = muG+v
 
 Assignment Rule (name: R0) R0 = f*v*lambdaE*gamma/(mG*mA*muE)
 
   Spatial dimensions: 3.0  Compartment size: 1.0
 
 A
Compartment: body
Initial amount: 1.0
 
 R
Compartment: body
Initial amount: 0.0
 
 E
Compartment: body
Initial amount: 0.0
 
 G
Compartment: body
Initial amount: 1.0E8
 
 A_im
Compartment: body
Initial amount: 0.0
 
Global Parameters (15)
 
   v
Value: 0.0025   (Units: per_day)
Constant
 
   f
Value: 1.0E-4   (Units: dimensionless)
Constant
 
   gamma
Value: 2000.0   (Units: per_day)
Constant
 
   beta
Value: 200.0   (Units: per_day)
Constant
 
   pi1
Value: 0.016   (Units: per_day_per_item)
Constant
 
   lambdaE
Value: 1000.0   (Units: per_day)
Constant
 
   muA
Value: 0.25   (Units: per_day)
Constant
 
   muR
Value: 0.25   (Units: per_day)
Constant
 
   muE
Value: 0.25   (Units: per_day)
Constant
 
   muG
Value: 5.0   (Units: per_day)
Constant
 
   b1
Value: 0.25   (Units: per_day)
Constant
 
   sigma1
Value: 3.0E-6   (Units: per_day_per_item)
Constant
 
   mA
Value: NaN   (Units: per_day)
 
   mG
Value: NaN   (Units: per_day)
 
   R0
Value: NaN   (Units: dimensionless)
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000289

Curator's comment: (updated: 22 Dec 2010 01:15:12 GMT)

Reproduction of the results in the first row of Fig. 2 of the original publication. The time course was integrated using Copasi 4.6.

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