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BIOMD0000000373 - Bertram2004_PancreaticBetaCell_modelB

 

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Reference Publication
Publication ID: 15347584
Bertram R, Satin L, Zhang M, Smolen P, Sherman A.
Calcium and glycolysis mediate multiple bursting modes in pancreatic islets.
Biophys. J. 2004 Nov; 87(5): 3074-3087
Department of Mathematics and Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida, USA. bertram@math.fsu.edu  [more]
Model
Original Model: CellML logo
Submitter: Camille Laibe
Submission ID: MODEL1006230042
Submission Date: 23 Jun 2010 09:12:09 UTC
Last Modification Date: 28 May 2014 20:23:16 UTC
Creation Date: 29 Sep 2011 22:04:00 UTC
Encoders:  Ishan Ajmera
   Catherine Lloyd
set #1
bqbiol:isVersionOf Gene Ontology type B pancreatic cell proliferation
Gene Ontology regulation of type B pancreatic cell proliferation
Gene Ontology glycolytic process
set #2
bqbiol:occursIn Brenda Tissue Ontology BTO:0000783
set #3
bqbiol:hasTaxon Taxonomy Homo sapiens
set #4
bqmodel:isDerivedFrom PubMed 15294427
Notes

This a model from the article:
Calcium and glycolysis mediate multiple bursting modes in pancreatic islets.
Bertram R, Satin L, Zhang M, Smolen P, Sherman A. Biophys J2004 Nov;87(5):3074-87 15347584,
Abstract:
Pancreatic islets of Langerhans produce bursts of electrical activity when exposed to stimulatory glucose levels. These bursts often have a regular repeating pattern, with a period of 10-60 s. In some cases, however, the bursts are episodic, clustered into bursts of bursts, which we call compound bursting. Consistent with this are recordings of free Ca2+ concentration, oxygen consumption, mitochondrial membrane potential, and intraislet glucose levels that exhibit very slow oscillations, with faster oscillations superimposed. We describe a new mathematical model of the pancreatic beta-cell that can account for these multimodal patterns. The model includes the feedback of cytosolic Ca2+ onto ion channels that can account for bursting, and a metabolic subsystem that is capable of producing slow oscillations driven by oscillations in glycolysis. This slow rhythm is responsible for the slow mode of compound bursting in the model. We also show that it is possible for glycolytic oscillations alone to drive a very slow form of bursting, which we call "glycolytic bursting." Finally, the model predicts that there is bistability between stationary and oscillatory glycolysis for a range of parameter values. We provide experimental support for this model prediction. Overall, the model can account for a diversity of islet behaviors described in the literature over the past 20 years.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Bertram R, Satin L, Zhang M, Smolen P, Sherman A. (2004) - version=1.0
The original CellML model was created by:
Catherine Lloyd
c.lloyd@auckland.ac.nz
The University of Auckland

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: 15347584 Submission Date: 23 Jun 2010 09:12:09 UTC Last Modification Date: 28 May 2014 20:23:16 UTC Creation Date: 29 Sep 2011 22:04:00 UTC
Mathematical expressions
Rules
Assignment Rule (variable: IK) Assignment Rule (variable: IKCa) Assignment Rule (variable: minf) Assignment Rule (variable: ICa)
Assignment Rule (variable: ninf) Assignment Rule (variable: Jmem) Assignment Rule (variable: Jserca) Assignment Rule (variable: Jleak)
Assignment Rule (variable: Jer) Assignment Rule (variable: rgpdh) Assignment Rule (variable: f6p) Assignment Rule (variable: topa2)
Assignment Rule (variable: weight3) Assignment Rule (variable: topa3) Assignment Rule (variable: weight5) Assignment Rule (variable: weight7)
Assignment Rule (variable: mgadp) Assignment Rule (variable: adp3m) Assignment Rule (variable: topo) Assignment Rule (variable: y)
Assignment Rule (variable: fback) Assignment Rule (variable: rad) Assignment Rule (variable: atp) Assignment Rule (variable: weight2)
Assignment Rule (variable: bottom2) Assignment Rule (variable: bottom3) Assignment Rule (variable: weight4) Assignment Rule (variable: topa4)
Assignment Rule (variable: bottom4) Assignment Rule (variable: topa5) Assignment Rule (variable: bottom5) Assignment Rule (variable: weight6)
Assignment Rule (variable: topa6) Assignment Rule (variable: bottom6) Assignment Rule (variable: topa7) Assignment Rule (variable: bottom7)
Assignment Rule (variable: weight8) Assignment Rule (variable: topa8) Assignment Rule (variable: topa9) Assignment Rule (variable: bottom8)
Assignment Rule (variable: topa10) Assignment Rule (variable: atp4m) Assignment Rule (variable: bottomo) Assignment Rule (variable: katpo)
Assignment Rule (variable: IKATP) Assignment Rule (variable: amp) Assignment Rule (variable: weight9) Assignment Rule (variable: bottom9)
Assignment Rule (variable: weight10) Assignment Rule (variable: bottom10) Assignment Rule (variable: weight11) Assignment Rule (variable: topa11)
Assignment Rule (variable: bottom11) Assignment Rule (variable: weight12) Assignment Rule (variable: topa12) Assignment Rule (variable: bottom12)
Assignment Rule (variable: weight13) Assignment Rule (variable: topa13) Assignment Rule (variable: bottom13) Assignment Rule (variable: weight14)
Assignment Rule (variable: topa14) Assignment Rule (variable: bottom14) Assignment Rule (variable: weight15) Assignment Rule (variable: topa15)
Assignment Rule (variable: bottom15) Assignment Rule (variable: weight16) Assignment Rule (variable: topa16) Assignment Rule (variable: bottom16)
Assignment Rule (variable: topb) Assignment Rule (variable: pfk) Assignment Rule (variable: ratio) Rate Rule (variable: V)
Rate Rule (variable: n) Rate Rule (variable: c) Rate Rule (variable: cer) Rate Rule (variable: g6p)
Rate Rule (variable: fbp) Rate Rule (variable: adp)    
Physical entities
Compartments Species
COMpartment V n c
cer g6p fbp
adp    
Global parameters
IK ICa IKCa Cm
gK gKCa kd gCa
minf VCa taun ninf
fcyt Jmem Jer fer
sigmaV pleak Kserca lambdaer
epser alpha kpmca Jserca
Jleak rgpdh Rgk atot
pfkbas f6p lambda pfk
bottom1 topa1 k1 k2
k3 k4 cat weight2
topa2 bottom2 topa3 weight3
bottom3 famp fatp ffbp
fbt fmt weight4 topa4
bottom4 weight5 topa5 bottom5
weight6 topa6 bottom6 weight7
topa7 bottom7 weight8 topa8
bottom8 weight9 topa9 bottom9
weight10 topa10 bottom10 weight11
topa11 bottom11 weight12 topa12
bottom12 weight13 topa13 bottom13
weight14 topa14 bottom14 weight15
topa15 bottom15 weight16 topa16
bottom16 topb mgadp adp3m
atp4m topo bottomo katpo
IKATP VK gkatpbar kdd
ktd ktt atp fback
taua r1 r y
vg kg amp rad
ratio      
Reactions (0)
Rules (78)
 
 Assignment Rule (name: IK) IK = gK*n*(V-VK)
 
 Assignment Rule (name: IKCa) IKCa = gKCa/(1+(kd/c)^2)*(V-VK)
 
 Assignment Rule (name: minf) minf = 1/(1+exp((-(20+V/1))/12))
 
 Assignment Rule (name: ICa) ICa = gCa*minf*(V-VCa)
 
 Assignment Rule (name: ninf) ninf = 1/(1+exp((-(16+V/1))/5))
 
 Assignment Rule (name: Jmem) Jmem = -(alpha*ICa+kpmca*c)
 
 Assignment Rule (name: Jserca) Jserca = Kserca*c
 
 Assignment Rule (name: Jleak) Jleak = pleak*(cer-c)
 
 Assignment Rule (name: Jer) Jer = epser*(Jleak-Jserca)/lambdaer
 
 Assignment Rule (name: rgpdh) rgpdh = 0.2*(abs(fbp*1/1^2))^(1/2)
 
 Assignment Rule (name: f6p) f6p = 0.3*g6p
 
 Assignment Rule (name: topa2) topa2 = topa1
 
 Assignment Rule (name: weight3) weight3 = f6p^2/(k3*1)
 
 Assignment Rule (name: topa3) topa3 = topa2+weight3
 
 Assignment Rule (name: weight5) weight5 = fbp/k2
 
 Assignment Rule (name: weight7) weight7 = fbp*f6p^2/(k2*k3*ffbp*1)
 
 Assignment Rule (name: mgadp) mgadp = 0.165*adp
 
 Assignment Rule (name: adp3m) adp3m = 0.135*adp
 
 Assignment Rule (name: topo) topo = 0.08*(1+2*mgadp/(kdd*1))+0.89*(mgadp/(kdd*1))^2
 
 Assignment Rule (name: y) y = vg*rgpdh/(kg+rgpdh)
 
 Assignment Rule (name: fback) fback = r+y
 
 Assignment Rule (name: rad) rad = (abs((adp-atot)^2-4*adp^2))^(1/2)/1
 
 Assignment Rule (name: atp) atp = 0.5*(atot-adp+rad*1)
 
 Assignment Rule (name: weight2) weight2 = atp^2/(k4*1)
 
 Assignment Rule (name: bottom2) bottom2 = bottom1+weight2
 
 Assignment Rule (name: bottom3) bottom3 = bottom2+weight3
 
 Assignment Rule (name: weight4) weight4 = (f6p*atp)^2/(fatp*k3*k4*1^2)
 
 Assignment Rule (name: topa4) topa4 = topa3+weight4
 
 Assignment Rule (name: bottom4) bottom4 = bottom3+weight4
 
 Assignment Rule (name: topa5) topa5 = topa4
 
 Assignment Rule (name: bottom5) bottom5 = bottom4+weight5
 
 Assignment Rule (name: weight6) weight6 = fbp*atp^2/(k2*k4*fbt*1)
 
 Assignment Rule (name: topa6) topa6 = topa5
 
 Assignment Rule (name: bottom6) bottom6 = bottom5+weight6
 
 Assignment Rule (name: topa7) topa7 = topa6+weight7
 
 Assignment Rule (name: bottom7) bottom7 = bottom6+weight7
 
 Assignment Rule (name: weight8) weight8 = fbp*f6p^2*atp^2/(k2*k3*k4*ffbp*fbt*fatp*1^2)
 
 Assignment Rule (name: topa8) topa8 = topa7+weight8
 
 Assignment Rule (name: topa9) topa9 = topa8
 
 Assignment Rule (name: bottom8) bottom8 = bottom7+weight8
 
 Assignment Rule (name: topa10) topa10 = topa9
 
 Assignment Rule (name: atp4m) atp4m = 0.05*atp
 
 Assignment Rule (name: bottomo) bottomo = (1+mgadp/(kdd*1))^2*(1+adp3m/(ktd*1)+atp4m/(ktt*1))
 
 Assignment Rule (name: katpo) katpo = topo/bottomo
 
 Assignment Rule (name: IKATP) IKATP = gkatpbar*katpo*(V-VK)
 
 Assignment Rule (name: amp) amp = adp*adp/atp
 
 Assignment Rule (name: weight9) weight9 = amp/k1
 
 Assignment Rule (name: bottom9) bottom9 = bottom8+weight9
 
 Assignment Rule (name: weight10) weight10 = amp*atp^2/(k1*k4*fmt*1)
 
 Assignment Rule (name: bottom10) bottom10 = bottom9+weight10
 
 Assignment Rule (name: weight11) weight11 = amp*f6p^2/(k1*k3*famp*1)
 
 Assignment Rule (name: topa11) topa11 = topa10+weight11
 
 Assignment Rule (name: bottom11) bottom11 = bottom10+weight11
 
 Assignment Rule (name: weight12) weight12 = amp*f6p^2*atp^2/(k1*k3*k4*famp*fmt*fatp*1^2)
 
 Assignment Rule (name: topa12) topa12 = topa11+weight12
 
 Assignment Rule (name: bottom12) bottom12 = bottom11+weight12
 
 Assignment Rule (name: weight13) weight13 = amp*fbp/(k1*k2)
 
 Assignment Rule (name: topa13) topa13 = topa12
 
 Assignment Rule (name: bottom13) bottom13 = bottom12+weight13
 
 Assignment Rule (name: weight14) weight14 = amp*fbp*atp^2/(k1*k2*k4*fbt*fmt*1)
 
 Assignment Rule (name: topa14) topa14 = topa13
 
 Assignment Rule (name: bottom14) bottom14 = bottom13+weight14
 
 Assignment Rule (name: weight15) weight15 = amp*fbp*f6p^2/(k1*k2*k3*ffbp*famp*1)
 
 Assignment Rule (name: topa15) topa15 = topa14
 
 Assignment Rule (name: bottom15) bottom15 = bottom14+weight15
 
 Assignment Rule (name: weight16) weight16 = amp*fbp*f6p^2*atp^2/(k1*k2*k3*k4*ffbp*famp*fbt*fmt*fatp*1^2)
 
 Assignment Rule (name: topa16) topa16 = topa15+weight16
 
 Assignment Rule (name: bottom16) bottom16 = bottom15+weight16
 
 Assignment Rule (name: topb) topb = weight15
 
 Assignment Rule (name: pfk) pfk = 1*(pfkbas*cat*topa16+cat*topb)/bottom16
 
 Assignment Rule (name: ratio) ratio = atp/adp
 
 Rate Rule (name: V) d [ V] / d t= (-(IK+ICa+IKCa+IKATP))/Cm
 
 Rate Rule (name: n) d [ n] / d t= (ninf-n)/taun
 
 Rate Rule (name: c) d [ c] / d t= fcyt*(Jmem+Jer)
 
 Rate Rule (name: cer) d [ cer] / d t= (-fer)*sigmaV*Jer
 
 Rate Rule (name: g6p) d [ g6p] / d t= lambda*(Rgk-pfk)
 
 Rate Rule (name: fbp) d [ fbp] / d t= lambda*(pfk/1-0.5*rgpdh)
 
 Rate Rule (name: adp) d [ adp] / d t= (atp-adp*exp(fback*(1-c/r1)))/(taua*1)
 
   COMpartment Spatial dimensions: 3.0  Compartment size: 1.0
 
 V
Compartment: COMpartment
Initial amount: -60.0
 
 n
Compartment: COMpartment
Initial amount: 0.025
 
 c
Compartment: COMpartment
Initial amount: 0.25
 
 cer
Compartment: COMpartment
Initial amount: 185.0
 
 g6p
Compartment: COMpartment
Initial amount: 200.0
 
 fbp
Compartment: COMpartment
Initial amount: 40.0
 
 adp
Compartment: COMpartment
Initial amount: 780.0
 
Global Parameters (113)
 
   IK
Value: 1012.5
 
   ICa
Value: -2927.84163162795
 
   IKCa
Value: 1800.0
 
 Cm
Value: 5300.0
Constant
 
 gK
Value: 2700.0
Constant
 
 gKCa
Value: 600.0
Constant
 
 kd
Value: 0.5
Constant
 
 gCa
Value: 1000.0
Constant
 
   minf
Value: 0.0344451956662112
 
 VCa
Value: 25.0
Constant
 
   taun
Value: 20.0
Constant
 
   ninf
Value: 1.50710358059757E-4
 
 fcyt
Value: 0.01
Constant
 
   Jmem
Value: -0.0368247126576742
 
   Jer
Value: -0.06305
 
 fer
Value: 0.01
Constant
 
 sigmaV
Value: 31.0
Constant
 
 pleak
Value: 2.0E-4
Constant
 
 Kserca
Value: 0.4
Constant
 
   lambdaer
Value: 1.0
Constant
 
 epser
Value: 1.0
Constant
 
 alpha
Value: 4.5E-6
Constant
 
 kpmca
Value: 0.2
Constant
 
   Jserca
Value: 0.1
 
   Jleak
Value: 0.03695
 
   rgpdh
Value: 1.26491106406735
 
 Rgk
Value: 0.2
Constant
 
   atot
Value: 3000.0
Constant
 
 pfkbas
Value: 0.06
Constant
 
   f6p
Value: 60.0
 
 lambda
Value: 0.0050
Constant
 
   pfk
Value: 0.550829288131395
 
   bottom1
Value: 1.0
Constant
 
 topa1
Constant
 
 k1
Value: 30.0
Constant
 
 k2
Value: 1.0
Constant
 
 k3
Value: 50000.0
Constant
 
 k4
Value: 1000.0
Constant
 
 cat
Value: 2.0
Constant
 
   weight2
Value: 3609.03788460095
 
   topa2  
 
   bottom2
Value: 3610.03788460095
 
   topa3
Value: 0.072
 
   weight3
Value: 0.072
 
   bottom3
Value: 3610.10988460095
 
 famp
Value: 0.02
Constant
 
 fatp
Value: 20.0
Constant
 
 ffbp
Value: 0.2
Constant
 
 fbt
Value: 20.0
Constant
 
 fmt
Value: 20.0
Constant
 
   weight4
Value: 12.9925363845634
 
   topa4
Value: 13.0645363845634
 
   bottom4
Value: 3623.10242098551
 
   weight5
Value: 40.0
 
   topa5
Value: 13.0645363845634
 
   bottom5
Value: 3663.10242098551
 
   weight6
Value: 7218.07576920189
 
   topa6
Value: 13.0645363845634
 
   bottom6
Value: 10881.1781901874
 
   weight7
Value: 14.4
 
   topa7
Value: 27.4645363845634
 
   bottom7
Value: 10895.5781901874
 
   weight8
Value: 129.925363845634
 
   topa8
Value: 157.389900230198
 
   bottom8
Value: 11025.503554033
 
   weight9
Value: 10.6751068378236
 
   topa9
Value: 157.389900230198
 
   bottom9
Value: 11036.1786608709
 
   weight10
Value: 1926.34324999341
 
   topa10
Value: 157.389900230198
 
   bottom10
Value: 12962.5219108643
 
   weight11
Value: 38.4303846161651
 
   topa11
Value: 195.820284846363
 
   bottom11
Value: 13000.9522954804
 
   weight12
Value: 346.741784998813
 
   topa12
Value: 542.562069845176
 
   bottom12
Value: 13347.6940804792
 
   weight13
Value: 427.004273512945
 
   topa13
Value: 542.562069845176
 
   bottom13
Value: 13774.6983539922
 
   weight14
Value: 3852.68649998681
 
   topa14
Value: 542.562069845176
 
   bottom14
Value: 17627.384853979
 
   weight15
Value: 7686.07692323301
 
   topa15
Value: 542.562069845176
 
   bottom15
Value: 25313.461777212
 
   weight16
Value: 3467.41784998813
 
   topa16
Value: 4009.9799198333
 
   bottom16
Value: 28780.8796272001
 
   topb
Value: 7686.07692323301
 
   mgadp
Value: 128.7
 
   adp3m
Value: 105.3
 
   atp4m
Value: 94.9873397432646
 
   topo
Value: 52.3005816608997
 
   bottomo
Value: 7348.24106009167
 
   katpo
Value: 0.00711742867894527
 
   IKATP
Value: 2669.03575460448
 
 VK
Value: -75.0
Constant
 
 gkatpbar
Value: 25000.0
Constant
 
   kdd
Value: 17.0
Constant
 
 ktd
Value: 26.0
Constant
 
 ktt
Value: 1.0
Constant
 
   atp
Value: 1899.74679486529
 
   fback
Value: 1.24703296147847
 
 taua
Value: 300000.0
Constant
 
 r1
Value: 0.35
Constant
 
 r
Value: 1.0
Constant
 
   y
Value: 0.247032961478473
 
   vg
Value: 2.2
Constant
 
 kg
Value: 10.0
Constant
 
   amp
Value: 320.253205134709
 
   rad
Value: 1579.49358973058
 
   ratio
Value: 2.43557281392986
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000373

Curator's comment: (updated: 30 Sep 2011 12:47:06 BST)

The model reproduces fig 5 of the reference publication.
The model was integrated and simulated using Copasi v4.7 (Build 34).

Additional file(s)
  • Figure 5:
    This is the COPASI file for the model reproducing fig 5 of the reference publication.
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