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BIOMD0000000620 - Palmer2014 - Effect of IL-1β-Blocking therapies in T2DM - Disease Condition

 

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Reference Publication
Publication ID: 24918743
Palmér R, Nyman E, Penney M, Marley A, Cedersund G, Agoram B.
Effects of IL-1β-Blocking Therapies in Type 2 Diabetes Mellitus: A Quantitative Systems Pharmacology Modeling Approach to Explore Underlying Mechanisms.
CPT Pharmacometrics Syst Pharmacol 2014; 3: e118
Wolfram MathCore AB, Linköping, Sweden.  [more]
Model
Original Model: BIOMD0000000620.origin
Submitter: Vijayalakshmi Chelliah
Submission ID: MODEL1604270002
Submission Date: 27 Apr 2016 15:02:42 UTC
Last Modification Date: 13 Jan 2017 15:59:54 UTC
Creation Date: 27 Apr 2016 17:38:43 UTC
Encoders:  Vijayalakshmi Chelliah
   Vincent Knight-Schrijver
   Robert Palmér
   Balaji Agoram
set #1
bqmodel:isDerivedFrom BioModels Database Gaetano2008_DiabetesProgressionModel
set #2
bqbiol:isVersionOf Gene Ontology interleukin-1 beta secretion
set #3
bqbiol:hasTaxon Taxonomy Homo sapiens
bqbiol:hasProperty Human Disease Ontology type 2 diabetes mellitus
Notes
Palmer2014 - Effect of IL-1β-Blocking therapies in T2DM - Disease Condition

This is the model with disease state initial conditions. A few changes were made to the model equations in order to bypass the circular dependencies apparent in SBML. Coupled algebraic equations for the species Glucose, Insulin and Proinsulin were changed to reactions which represent the ordinary differential equations found in a previously published model by De Gaetano et al (2008), [MODEL1112110003]. This reference was used by the present authors for the algebraic equations. The original Mathematica code, obtained from the supplementary material of the article can be downloaded from the link below: [Palmer2014_notebook.nb].

This model is described in the article:

Palmér R, Nyman E, Penney M, Marley A, Cedersund G, Agoram B.
CPT Pharmacometrics Syst Pharmacol. 2014 Jun 11;3:e118.

Abstract:

Recent clinical studies suggest sustained treatment effects of interleukin-1β (IL-1β)-blocking therapies in type 2 diabetes mellitus. The underlying mechanisms of these effects, however, remain underexplored. Using a quantitative systems pharmacology modeling approach, we combined ex vivo data of IL-1β effects on β-cell function and turnover with a disease progression model of the long-term interactions between insulin, glucose, and β-cell mass in type 2 diabetes mellitus. We then simulated treatment effects of the IL-1 receptor antagonist anakinra. The result was a substantial and partly sustained symptomatic improvement in β-cell function, and hence also in HbA1C, fasting plasma glucose, and proinsulin-insulin ratio, and a small increase in β-cell mass. We propose that improved β-cell function, rather than mass, is likely to explain the main IL-1β-blocking effects seen in current clinical data, but that improved β-cell mass might result in disease-modifying effects not clearly distinguishable until >1 year after treatment.

This model is hosted on BioModels Database and identified by: MODEL1604270002.

To cite BioModels Database, please use: BioModels: Content, Features, Functionality and Use.

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: 24918743 Submission Date: 27 Apr 2016 15:02:42 UTC Last Modification Date: 13 Jan 2017 15:59:54 UTC Creation Date: 27 Apr 2016 17:38:43 UTC
Mathematical expressions
Reactions
TigB_up TigB_down Bcell_replication Bcell_apoptosis
proinsulin_sec_up proinsulin_sec_down IL1b_treatment IL1b_degradation
IL1b_placebo AnakinraSC_elimination Anakinra_absorption Anakinra_elimination
Glucose_production Basal_glucose_uptake Insulin_dependent_glucose_uptake Proinsulin_dependent_glucose_uptake
Glucose_dependent_insulin_secretion Insulin_elimination Glucose_dependent_proinsulin_secretion Proinsulin_elimination
Rules
Rate Rule (variable: a1c1) Rate Rule (variable: rbc1) Rate Rule (variable: a1c2) Rate Rule (variable: rbc2)
Rate Rule (variable: a1c3) Rate Rule (variable: rbc3) Rate Rule (variable: a1c4) Rate Rule (variable: rbc4)
Rate Rule (variable: a1c5) Rate Rule (variable: rbc5) Rate Rule (variable: a1c6) Rate Rule (variable: rbc6)
Rate Rule (variable: a1c7) Rate Rule (variable: rbc7) Rate Rule (variable: a1c8) Rate Rule (variable: rbc8)
Rate Rule (variable: a1c9) Rate Rule (variable: rbc9) Rate Rule (variable: a1c10) Rate Rule (variable: rbc10)
Rate Rule (variable: a1c11) Rate Rule (variable: rbc11) Rate Rule (variable: a1c12) Rate Rule (variable: rbc12)
Assignment Rule (variable: hba1c) Assignment Rule (variable: apoptosis) Assignment Rule (variable: IL1R) Assignment Rule (variable: replication)
Assignment Rule (variable: PI_I)      
Events
Anakinra_Administration_event      
Physical entities
Compartments Species
default_compartment IL1b IL1Ra Anakinra
Proinsulin Insulin TigB
B f Anakinrasc
Glucose a1c1 rbc1
a1c2 rbc2 a1c3
rbc3 a1c4 rbc4
a1c5 rbc5 a1c6
rbc6 a1c7 rbc7
a1c8 rbc8 a1c9
rbc9 a1c10 rbc10
a1c11 rbc11 a1c12
rbc12 hba1c  
Global parameters
Kxg Kxi Gh vh
Ktr Kin lambda Kglucose
vs kms taus kmf
tauf vfg xfg kmfg
vf vlr kmlr xlr
vhr kmhr xhr vla
kmla xla vha kmha
xha km ki ka
kr kf ks Tgl
Kxgi il1bH il1b0 kplacebo
k1 k2 kab CL
Vp apoptosis IL1R replication
Ana_on placebo_on Anakinra_dose_counter PI_I
Reactions (20)
 
 TigB_up  → [TigB];  
 
 TigB_down [TigB] → ;  
 
 Bcell_replication  → [B];  
 
 Bcell_apoptosis [B] → ;  
 
 proinsulin_sec_up  → [f];   {Glucose}
 
 proinsulin_sec_down [f] → ;  
 
 IL1b_treatment  → [IL1b];  
 
 IL1b_degradation [IL1b] → ;  
 
 IL1b_placebo  → [IL1b];  
 
 AnakinraSC_elimination [Anakinrasc] → ;  
 
 Anakinra_absorption  → [Anakinra];   {Anakinrasc}
 
 Anakinra_elimination [Anakinra] → ;  
 
 Glucose_production  → [Glucose];  
 
 Basal_glucose_uptake [Glucose] → ;  
 
 Insulin_dependent_glucose_uptake [Glucose] → ;   {Insulin}
 
 Proinsulin_dependent_glucose_uptake [Glucose] → ;   {Proinsulin}
 
 Glucose_dependent_insulin_secretion  → [Insulin];   {TigB} , {B} , {Glucose}
 
 Insulin_elimination [Insulin] → ;  
 
 Glucose_dependent_proinsulin_secretion  → [Proinsulin];   {TigB} , {B} , {f} , {Glucose}
 
 Proinsulin_elimination [Proinsulin] → ;  
 
Rules (29)
 
 Rate Rule (name: a1c1) d [ a1c1] / d t= Kglucose*Glucose^lambda*rbc1-Ktr*a1c1
 
 Rate Rule (name: rbc1) d [ rbc1] / d t= (Kin-Ktr*rbc1)-Kglucose*Glucose^lambda*rbc1
 
 Rate Rule (name: a1c2) d [ a1c2] / d t= (Kglucose*Glucose^lambda*rbc2+Ktr*a1c1)-Ktr*a1c2
 
 Rate Rule (name: rbc2) d [ rbc2] / d t= (Ktr*rbc1-Ktr*rbc2)-Kglucose*Glucose^lambda*rbc2
 
 Rate Rule (name: a1c3) d [ a1c3] / d t= (Kglucose*Glucose^lambda*rbc3+Ktr*a1c2)-Ktr*a1c3
 
 Rate Rule (name: rbc3) d [ rbc3] / d t= (Ktr*rbc2-Ktr*rbc3)-Kglucose*Glucose^lambda*rbc3
 
 Rate Rule (name: a1c4) d [ a1c4] / d t= (Kglucose*Glucose^lambda*rbc4+Ktr*a1c3)-Ktr*a1c4
 
 Rate Rule (name: rbc4) d [ rbc4] / d t= (Ktr*rbc3-Ktr*rbc4)-Kglucose*Glucose^lambda*rbc4
 
 Rate Rule (name: a1c5) d [ a1c5] / d t= (Kglucose*Glucose^lambda*rbc5+Ktr*a1c4)-Ktr*a1c5
 
 Rate Rule (name: rbc5) d [ rbc5] / d t= (Ktr*rbc4-Ktr*rbc5)-Kglucose*Glucose^lambda*rbc5
 
 Rate Rule (name: a1c6) d [ a1c6] / d t= (Kglucose*Glucose^lambda*rbc6+Ktr*a1c5)-Ktr*a1c6
 
 Rate Rule (name: rbc6) d [ rbc6] / d t= (Ktr*rbc5-Ktr*rbc6)-Kglucose*Glucose^lambda*rbc6
 
 Rate Rule (name: a1c7) d [ a1c7] / d t= (Kglucose*Glucose^lambda*rbc7+Ktr*a1c6)-Ktr*a1c7
 
 Rate Rule (name: rbc7) d [ rbc7] / d t= (Ktr*rbc6-Ktr*rbc7)-Kglucose*Glucose^lambda*rbc7
 
 Rate Rule (name: a1c8) d [ a1c8] / d t= (Kglucose*Glucose^lambda*rbc8+Ktr*a1c7)-Ktr*a1c8
 
 Rate Rule (name: rbc8) d [ rbc8] / d t= (Ktr*rbc7-Ktr*rbc8)-Kglucose*Glucose^lambda*rbc8
 
 Rate Rule (name: a1c9) d [ a1c9] / d t= (Kglucose*Glucose^lambda*rbc9+Ktr*a1c8)-Ktr*a1c9
 
 Rate Rule (name: rbc9) d [ rbc9] / d t= (Ktr*rbc8-Ktr*rbc9)-Kglucose*Glucose^lambda*rbc9
 
 Rate Rule (name: a1c10) d [ a1c10] / d t= (Kglucose*Glucose^lambda*rbc10+Ktr*a1c9)-Ktr*a1c10
 
 Rate Rule (name: rbc10) d [ rbc10] / d t= (Ktr*rbc9-Ktr*rbc10)-Kglucose*Glucose^lambda*rbc10
 
 Rate Rule (name: a1c11) d [ a1c11] / d t= (Kglucose*Glucose^lambda*rbc11+Ktr*a1c10)-Ktr*a1c11
 
 Rate Rule (name: rbc11) d [ rbc11] / d t= (Ktr*rbc10-Ktr*rbc11)-Kglucose*Glucose^lambda*rbc11
 
 Rate Rule (name: a1c12) d [ a1c12] / d t= (Kglucose*Glucose^lambda*rbc12+Ktr*a1c11)-Ktr*a1c12
 
 Rate Rule (name: rbc12) d [ rbc12] / d t= (Ktr*rbc11-Ktr*rbc12)-Kglucose*Glucose^lambda*rbc12
 
 Assignment Rule (name: hba1c) hba1c = 100*(a1c1+a1c2+a1c3+a1c4+a1c5+a1c6+a1c7+a1c8+a1c9+a1c10+a1c11+a1c12)/(a1c1+a1c2+a1c3+a1c4+a1c5+a1c6+a1c7+a1c8+a1c9+a1c10+a1c11+a1c12+rbc1+rbc2+rbc3+rbc4+rbc5+rbc6+rbc7+rbc8+rbc9+rbc10+rbc11+rbc12)
 
 Assignment Rule (name: apoptosis) apoptosis = ka*((1+vha*IL1R^xha/(kmha^xha+IL1R^xha))-vla*IL1R^xla/(kmla^xla+IL1R^xla))
 
 Assignment Rule (name: IL1R) IL1R = IL1b/(IL1b+km*(1+(IL1Ra+Anakinra)/ki))
 
 Assignment Rule (name: replication) replication = kr*((1-vhr*IL1R^xhr/(kmhr^xhr+IL1R^xhr))+vlr*IL1R^xlr/(kmlr^xlr+IL1R^xlr))
 
 Assignment Rule (name: PI_I) PI_I = Proinsulin/Insulin
 
Events (1)
 
 Anakinra_Administration_event
Anakinrasc = Anakinrasc+100000*Ana_on
Anakinra_dose_counter = Anakinra_dose_counter+1
 
  Spatial dimensions: 3.0  Compartment size: 1.0
 
 IL1b
Compartment: default_compartment
Initial concentration: 5.0
 
 IL1Ra
Compartment: default_compartment
Initial concentration: 40.0
 
 Anakinra
Compartment: default_compartment
Initial concentration: 0.0
 
 Proinsulin
Compartment: default_compartment
Initial concentration: 43.0
 
 Insulin
Compartment: default_compartment
Initial concentration: 100.0
 
 TigB
Compartment: default_compartment
Initial concentration: 0.1865
 
 B
Compartment: default_compartment
Initial concentration: 40.0
 
 f
Compartment: default_compartment
Initial concentration: 0.0427776
 
 Anakinrasc
Compartment: default_compartment
Initial concentration: 0.0
 
 Glucose
Compartment: default_compartment
Initial concentration: 10.8
 
 a1c1
Compartment: default_compartment
Initial concentration: 0.122997
 
 rbc1
Compartment: default_compartment
Initial concentration: 8.627
 
 a1c2
Compartment: default_compartment
Initial concentration: 0.244266
 
 rbc2
Compartment: default_compartment
Initial concentration: 8.50573
 
 a1c3
Compartment: default_compartment
Initial concentration: 0.363829
 
 rbc3
Compartment: default_compartment
Initial concentration: 8.38617
 
 a1c4
Compartment: default_compartment
Initial concentration: 0.481712
 
 rbc4
Compartment: default_compartment
Initial concentration: 8.26829
 
 a1c5
Compartment: default_compartment
Initial concentration: 0.597938
 
 rbc5
Compartment: default_compartment
Initial concentration: 8.15206
 
 a1c6
Compartment: default_compartment
Initial concentration: 0.71253
 
 rbc6
Compartment: default_compartment
Initial concentration: 8.03747
 
 a1c7
Compartment: default_compartment
Initial concentration: 0.825512
 
 rbc7
Compartment: default_compartment
Initial concentration: 7.92449
 
 a1c8
Compartment: default_compartment
Initial concentration: 0.936905
 
 rbc8
Compartment: default_compartment
Initial concentration: 7.8131
 
 a1c9
Compartment: default_compartment
Initial concentration: 1.04673
 
 rbc9
Compartment: default_compartment
Initial concentration: 7.70327
 
 a1c10
Compartment: default_compartment
Initial concentration: 1.15502
 
 rbc10
Compartment: default_compartment
Initial concentration: 7.59498
 
 a1c11
Compartment: default_compartment
Initial concentration: 1.26178
 
 rbc11
Compartment: default_compartment
Initial concentration: 7.48822
 
 a1c12
Compartment: default_compartment
Initial concentration: 1.36704
 
 rbc12
Compartment: default_compartment
Initial concentration: 7.38296
 
  hba1c
Compartment: default_compartment
Initial concentration: 8.7
 
Global Parameters (52)
 
 Kxg
Value: 1.6E-5
Constant
 
 Kxi
Value: 0.05
Constant
 
 Gh
Value: 9.0
Constant
 
   vh
Value: 4.0
Constant
 
   Ktr
Value: 0.12
Constant
 
   Kin
Value: 1.05
Constant
 
   lambda
Value: 0.743
Constant
 
   Kglucose
Value: 2.92E-4
Constant
 
   vs
Value: 0.7
Constant
 
   kms
Value: 0.021
Constant
 
 taus
Value: 0.5
Constant
 
   kmf
Value: 0.021
Constant
 
 tauf
Value: 0.5
Constant
 
   vfg
Value: 4.0
Constant
 
   xfg
Value: 4.0
Constant
 
 kmfg
Value: 9.0
Constant
 
   vf
Value: 0.4
Constant
 
   vlr
Value: 1.8
Constant
 
   kmlr
Value: 0.0011
Constant
 
   xlr
Value: 3.0
Constant
 
   vhr
Value: 2.7
Constant
 
   kmhr
Value: 0.018
Constant
 
   xhr
Value: 0.5
Constant
 
   vla
Value: 0.65
Constant
 
   kmla
Value: 1.8E-4
Constant
 
   xla
Value: 3.0
Constant
 
   vha
Value: 4.6
Constant
 
   kmha
Value: 0.155
Constant
 
   xha
Value: 0.6666666667
Constant
 
 km
Value: 8.5
Constant
 
 ki
Value: 1.7
Constant
 
 ka
Value: 5.52022E-4
Constant
 
 kr
Value: 3.76393E-4
Constant
 
   kf
Value: 0.00957754
Constant
 
 ks
Value: 0.291008
Constant
 
 Tgl
Value: 0.025405
Constant
 
 Kxgi
Value: 2.24E-5
Constant
 
 il1bH
Value: 0.05
Constant
 
 il1b0
Value: 5.0
 
 kplacebo
Value: 0.00137
Constant
 
 k1
Value: 0.2
Constant
 
 k2
Value: 0.0025
Constant
 
 kab
Value: 3.94
Constant
 
 CL
Value: 432.0
Constant
 
 Vp
Value: 48.0
Constant
 
   apoptosis
Value: 7.543653797E-4
 
  IL1R
Value: 0.02341920375
 
   replication
Value: 5.12314779E-4
 
 Ana_on
Value: 1.0
Constant
 
 placebo_on
Constant
 
 Anakinra_dose_counter
Value: 0.5
 
  PI_I
Value: 0.43
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000620

Curator's comment: (updated: 04 Nov 2016 17:02:28 GMT)

Above. Figure 3. A reproduction of figure 3.
Instead of interpolation of the mean daily anakinra concentration as seen in the original figure, the curated model uses the subcutaneous administration equations available in the supplementary materials. This results in an oscillating anakinra concentration (top left panel) and IL1R modulation (middle left panel).

Below. Reproductions of figures 4 and 5a.
The Glucose, Insulin and Proinsulin reactions were modelled through ODEs instead of algebraic assignments. This removed circular dependencies in the model. As a result however, the curves are slightly different to the original. The peak effect is reached later than observed in the original simulations.

Simulations were carried out in Copasi and plotted in R.

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