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BIOMD0000000345 - Koschorreck2008_InsulinClearance

 

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Reference Publication
Publication ID: 18477391
Koschorreck M, Gilles ED.
Mathematical modeling and analysis of insulin clearance in vivo.
BMC Syst Biol 2008; 2: 43
Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr, 1, 39106 Magdeburg, Germany. koschorreck@mpi-magdeburg.mpg.de  [more]
Model
Original Model: BIOMD0000000345.xml.origin
Submitter: Ishan Ajmera
Submission ID: MODEL1108040000
Submission Date: 04 Aug 2011 19:02:08 UTC
Last Modification Date: 09 Mar 2012 16:16:46 UTC
Creation Date: 05 Aug 2011 09:33:47 UTC
Encoders:  Ishan Ajmera
set #1
bqbiol:occursIn Brenda Tissue Ontology BTO:0000575
Brenda Tissue Ontology BTO:0000089
set #2
bqbiol:hasTaxon Taxonomy Homo sapiens
set #3
bqbiol:isVersionOf Gene Ontology insulin-activated receptor activity
Gene Ontology regulation of cellular response to insulin stimulus
Gene Ontology insulin receptor internalization
Notes

This model is from the article:
Mathematical modeling and analysis of insulin clearance in vivo.
Koschorreck M, Gilles ED. BMC Syst Biol. 2008 May 13;2:43. 18477391,
Abstract:
BACKGROUND: Analyzing the dynamics of insulin concentration in the blood is necessary for a comprehensive understanding of the effects of insulin in vivo. Insulin removal from the blood has been addressed in many studies. The results are highly variable with respect to insulin clearance and the relative contributions of hepatic and renal insulin degradation. RESULTS: We present a dynamic mathematical model of insulin concentration in the blood and of insulin receptor activation in hepatocytes. The model describes renal and hepatic insulin degradation, pancreatic insulin secretion and nonspecific insulin binding in the liver. Hepatic insulin receptor activation by insulin binding, receptor internalization and autophosphorylation is explicitly included in the model. We present a detailed mathematical analysis of insulin degradation and insulin clearance. Stationary model analysis shows that degradation rates, relative contributions of the different tissues to total insulin degradation and insulin clearance highly depend on the insulin concentration. CONCLUSION: This study provides a detailed dynamic model of insulin concentration in the blood and of insulin receptor activation in hepatocytes. Experimental data sets from literature are used for the model validation. We show that essential dynamic and stationary characteristics of insulin degradation are nonlinear and depend on the actual insulin concentration.

This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2011 The BioModels.net Team.
For more information see the terms of use.
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

Model
Publication ID: 18477391 Submission Date: 04 Aug 2011 19:02:08 UTC Last Modification Date: 09 Mar 2012 16:16:46 UTC Creation Date: 05 Aug 2011 09:33:47 UTC
Mathematical expressions
Rules
Assignment Rule (variable: mkidney) Assignment Rule (variable: mliver) Assignment Rule (variable: vp) Assignment Rule (variable: vhep)
Assignment Rule (variable: vd) Assignment Rule (variable: I2RPen) Assignment Rule (variable: Kkidney) Assignment Rule (variable: r1)
Assignment Rule (variable: r2) Assignment Rule (variable: r3) Assignment Rule (variable: r4) Assignment Rule (variable: r5)
Assignment Rule (variable: r6) Assignment Rule (variable: r7) Assignment Rule (variable: i1) Assignment Rule (variable: i2)
Assignment Rule (variable: i3) Assignment Rule (variable: i4) Assignment Rule (variable: i5) Assignment Rule (variable: i6)
Assignment Rule (variable: i7) Assignment Rule (variable: f1) Assignment Rule (variable: f2) Assignment Rule (variable: f3)
Assignment Rule (variable: f4) Assignment Rule (variable: f5) Assignment Rule (variable: f6) Assignment Rule (variable: rliv)
Assignment Rule (variable: rkid) Assignment Rule (variable: Ratetotal) Assignment Rule (variable: Fracliver) Assignment Rule (variable: Frackidney)
Assignment Rule (variable: Cliver) Assignment Rule (variable: Ckidney) Assignment Rule (variable: Ctotal) Assignment Rule (variable: ReceptorIns)
Assignment Rule (variable: ReceptorInsPM) Assignment Rule (variable: ReceptorIns2) Assignment Rule (variable: ReceptorIns2PM) Assignment Rule (variable: ReceptorInsEN)
Assignment Rule (variable: ReceptorIns2EN) Rate Rule (variable: R) Rate Rule (variable: IR) Rate Rule (variable: I2R)
Rate Rule (variable: Rp) Rate Rule (variable: IRp) Rate Rule (variable: I2Rp) Rate Rule (variable: Ren)
Rate Rule (variable: IRen) Rate Rule (variable: I2Ren) Rate Rule (variable: RPen) Rate Rule (variable: IRPen)
Physical entities
Compartments Species
compartment1 R ins IR
I2R Rp IRp
I2Rp Ren IRen
I2Ren RPen IRPen
I2RPen    
Global parameters
kins kins1d kins2d kins1den
kins2den kyd kyden kyp
intk1 intk2 reck1 Rtotal
k1ub k2ub pansec Kpan
mliver vp rholiver vhep
vd mkidney Kkidney r1
r2 r3 r4 r5
r6 r7 i1 i2
i3 i4 i5 i6
i7 f1 f2 f3
f4 f5 f6 bw
rliv rkid Ratetotal Fracliver
Frackidney Cliver Ckidney Ctotal
ReceptorIns ReceptorIns2 ReceptorInsPM ReceptorIns2PM
ReceptorInsEN ReceptorIns2EN    
Reactions (0)
Rules (52)
 
 Assignment Rule (name: mkidney) mkidney = 2*0.85*bw/230
 
 Assignment Rule (name: mliver) mliver = 0.05*bw
 
 Assignment Rule (name: vp) vp = 0.03375*10^(-3)*bw
 
 Assignment Rule (name: vhep) vhep = mliver/rholiver*0.78
 
 Assignment Rule (name: vd) vd = 0.272*10^(-3)*vhep*rholiver
 
 Assignment Rule (name: I2RPen) I2RPen = Rtotal-R-IR-I2R-Rp-IRp-I2Rp-Ren-IRen-I2Ren-RPen-IRPen
 
 Assignment Rule (name: Kkidney) Kkidney = 0.0225*10^(-3)*mkidney
 
 Assignment Rule (name: r1) r1 = kins*R*ins-kins1d*IR
 
 Assignment Rule (name: r2) r2 = kins*Rp*ins-kins1d*IRp
 
 Assignment Rule (name: r3) r3 = kins*IR*ins-kins2d*I2R
 
 Assignment Rule (name: r4) r4 = kins*IRp*ins-kins2d*I2Rp
 
 Assignment Rule (name: r5) r5 = kyd*Rp
 
 Assignment Rule (name: r6) r6 = kyp*IR-kyd*IRp
 
 Assignment Rule (name: r7) r7 = kyp*I2R-kyd*I2Rp
 
 Assignment Rule (name: i1) i1 = kins1den*IRen
 
 Assignment Rule (name: i2) i2 = kins1den*IRPen
 
 Assignment Rule (name: i3) i3 = kins2den*I2Ren
 
 Assignment Rule (name: i4) i4 = kins2den*I2RPen
 
 Assignment Rule (name: i5) i5 = kyden*RPen
 
 Assignment Rule (name: i6) i6 = kyp*IRen-kyden*IRPen
 
 Assignment Rule (name: i7) i7 = kyp*I2Ren-kyden*I2RPen
 
 Assignment Rule (name: f1) f1 = intk2*R-reck1*Ren
 
 Assignment Rule (name: f2) f2 = intk2*IR
 
 Assignment Rule (name: f3) f3 = intk2*I2R
 
 Assignment Rule (name: f4) f4 = intk1*Rp-reck1*RPen
 
 Assignment Rule (name: f5) f5 = intk1*IRp
 
 Assignment Rule (name: f6) f6 = intk1*I2Rp
 
 Assignment Rule (name: parameter_1) rliv = (-(-r1-r2-r3-r4))*vhep/vp
 
 Assignment Rule (name: parameter_2) rkid = Kkidney*ins/vp
 
 Assignment Rule (name: parameter_3) Ratetotal = parameter_2+parameter_1
 
 Assignment Rule (name: parameter_4) Fracliver = parameter_1/(parameter_1+parameter_2)*100
 
 Assignment Rule (name: parameter_5) Frackidney = parameter_2/(parameter_2+parameter_1)*100
 
 Assignment Rule (name: parameter_6) Cliver = parameter_1*vp*6000/ins
 
 Assignment Rule (name: parameter_7) Ckidney = parameter_2*vp*6000/ins
 
 Assignment Rule (name: parameter_8) Ctotal = parameter_7+parameter_6
 
 Assignment Rule (name: parameter_9) ReceptorIns = (Rtotal-R-Rp-Ren-RPen)/Rtotal
 
 Assignment Rule (name: parameter_11) ReceptorInsPM = (IR+I2R+IRp+I2Rp)/Rtotal
 
 Assignment Rule (name: parameter_10) ReceptorIns2 = (I2R+I2Ren+I2Rp+I2RPen)/Rtotal
 
 Assignment Rule (name: parameter_12) ReceptorIns2PM = (I2R+I2Rp)/Rtotal
 
 Assignment Rule (name: parameter_13) ReceptorInsEN = parameter_9-parameter_11
 
 Assignment Rule (name: parameter_14) ReceptorIns2EN = parameter_10-parameter_12
 
 Rate Rule (name: R) d [ R] / d t= -r1+r5-f1
 
 Rate Rule (name: IR) d [ IR] / d t= r1-r3-r6-f2
 
 Rate Rule (name: I2R) d [ I2R] / d t= r3-r7-f3
 
 Rate Rule (name: Rp) d [ Rp] / d t= -r2-r5-f4
 
 Rate Rule (name: IRp) d [ IRp] / d t= r2-r4+r6-f5
 
 Rate Rule (name: I2Rp) d [ I2Rp] / d t= r4+r7-f6
 
 Rate Rule (name: Ren) d [ Ren] / d t= i1+i5+f1
 
 Rate Rule (name: IRen) d [ IRen] / d t= -i1+i3-i6+f2
 
 Rate Rule (name: I2Ren) d [ I2Ren] / d t= -i3-i7+f3
 
 Rate Rule (name: RPen) d [ RPen] / d t= i2-i5+f4
 
 Rate Rule (name: IRPen) d [ IRPen] / d t= -i2+i4+i6+f5
 
   compartment1 Spatial dimensions: 3.0  Compartment size: 1.0
 
 R
Compartment: compartment1
Initial concentration: 35.3837
 
 ins
Compartment: compartment1
Initial concentration: 100.0
Constant
 
 IR
Compartment: compartment1
Initial concentration: 0.0
 
 I2R
Compartment: compartment1
Initial concentration: 0.0
 
 Rp
Compartment: compartment1
Initial concentration: 0.0
 
 IRp
Compartment: compartment1
Initial concentration: 0.0
 
 I2Rp
Compartment: compartment1
Initial concentration: 0.0
 
 Ren
Compartment: compartment1
Initial concentration: 4.6163
 
 IRen
Compartment: compartment1
Initial concentration: 0.0
 
 I2Ren
Compartment: compartment1
Initial concentration: 0.0
 
 RPen
Compartment: compartment1
Initial concentration: 0.0
 
 IRPen
Compartment: compartment1
Initial concentration: 0.0
 
  I2RPen
Compartment: compartment1
Initial concentration: -4.44089209850063E-15
 
Global Parameters (58)
 
 kins
Value: 0.0010
Constant
 
 kins1d
Value: 4.0E-4
Constant
 
 kins2d
Value: 0.04
Constant
 
 kins1den
Value: 0.001925
Constant
 
 kins2den
Value: 0.00385
Constant
 
 kyd
Value: 0.00385
Constant
 
 kyden
Value: 0.00722
Constant
 
 kyp
Value: 0.0231
Constant
 
 intk1
Value: 5.5E-4
Constant
 
 intk2
Value: 2.0E-4
Constant
 
 reck1
Value: 0.001533
Constant
 
 Rtotal
Value: 40.0
Constant
 
 k1ub
Value: 0.35
Constant
 
 k2ub
Value: 0.2
Constant
 
 pansec
Value: 0.0016976
Constant
 
 Kpan
Value: 0.5
Constant
 
  mliver
Value: 10.0
 
  vp
Value: 0.00675
 
 rholiver
Value: 1051.0
Constant
 
  vhep
Value: 0.00742150333016175
 
  vd
Value: 0.0021216
 
  mkidney
Value: 1.47826086956522
 
  Kkidney
Value: 3.32608695652174E-5
 
  r1
Value: 3.53837
 
  r2  
 
  r3  
 
  r4  
 
  r5  
 
  r6  
 
  r7  
 
  i1  
 
  i2  
 
  i3  
 
  i4
Value: -1.70974345792274E-17
 
  i5  
 
  i6  
 
  i7
Value: 3.20632409511745E-17
 
  f1
Value: -4.78999999985533E-8
 
  f2  
 
  f3  
 
  f4  
 
  f5  
 
  f6  
 
 bw
Value: 200.0
Constant
 
  rliv
Value: 3.89037403531029
 
  rkid
Value: 0.492753623188406
 
  Ratetotal
Value: 4.38312765849869
 
  Fracliver
Value: 88.757944974909
 
  Frackidney
Value: 11.242055025091
 
  Cliver
Value: 1.57560148430067
 
  Ckidney
Value: 0.199565217391304
 
  Ctotal
Value: 1.77516670169197
 
  ReceptorIns
Value: -1.11022302462516E-16
 
  ReceptorIns2
Value: -1.11022302462516E-16
 
  ReceptorInsPM  
 
  ReceptorIns2PM  
 
  ReceptorInsEN
Value: -1.11022302462516E-16
 
  ReceptorIns2EN
Value: -1.11022302462516E-16
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000345

Curator's comment: (updated: 05 Aug 2011 11:19:52 BST)

The model reproduce figure 6 and 7 of the referenced publication representing insulin degradation and clearance respectively.
(A and B belongs to figure 6 and C belongs to Figure 7 of the reference publication)
The model was integrated and simulated using Copasi v4.7 (Build 34).

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