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BIOMD0000000374 - Bertram1995_PancreaticBetaCell_CRAC

 

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Reference Publication
Publication ID: 7647236
Bertram R, Smolen P, Sherman A, Mears D, Atwater I, Martin F, Soria B.
A role for calcium release-activated current (CRAC) in cholinergic modulation of electrical activity in pancreatic beta-cells.
Biophys. J. 1995 Jun; 68(6): 2323-2332
Mathematical Research Branch, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892, USA.  [more]
Model
Original Model: CellML logo
Submitter: Camille Laibe
Submission ID: MODEL1006230051
Submission Date: 23 Jun 2010 09:12:14 UTC
Last Modification Date: 08 Apr 2016 17:07:11 UTC
Creation Date: 29 Sep 2011 22:07:50 UTC
Encoders:  Ishan Ajmera
   Catherine Lloyd
set #1
bqmodel:isDerivedFrom PubMed 3907728
set #2
bqbiol:hasTaxon Taxonomy Homo sapiens
set #3
bqbiol:isVersionOf Gene Ontology type B pancreatic cell proliferation
Gene Ontology calcium-release channel activity
Gene Ontology regulation of type B pancreatic cell proliferation
set #4
bqbiol:occursIn Brenda Tissue Ontology pancreatic beta cell
Notes

This a model from the article:
A role for calcium release-activated current (CRAC) in cholinergic modulation of electrical activity in pancreatic beta-cells.
Bertram R, Smolen P, Sherman A, Mears D, Atwater I, Martin F, Soria B. Biophys J1995 Jun;68(6):2323-32 7647236,
Abstract:
S. Bordin and colleagues have proposed that the depolarizing effects of acetylcholine and other muscarinic agonists on pancreatic beta-cells are mediated by a calcium release-activated current (CRAC). We support this hypothesis with additional data, and present a theoretical model which accounts for most known data on muscarinic effects. Additional phenomena, such as the biphasic responses of beta-cells to changes in glucose concentration and the depolarizing effects of the sarco-endoplasmic reticulum calcium ATPase pump poison thapsigargin, are also accounted for by our model. The ability of this single hypothesis, that CRAC is present in beta-cells, to explain so many phenomena motivates a more complete characterization of this current.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Bertram R, Smolen P, Sherman A, Mears D, Atwater I, Martin F, Soria B. (1995) - 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: 7647236 Submission Date: 23 Jun 2010 09:12:14 UTC Last Modification Date: 08 Apr 2016 17:07:11 UTC Creation Date: 29 Sep 2011 22:07:50 UTC
Mathematical expressions
Rules
Assignment Rule (variable: i_K) Assignment Rule (variable: n_infinity) Assignment Rule (variable: tau_n) Assignment Rule (variable: i_K_ATP)
Assignment Rule (variable: m_f_infinity) Assignment Rule (variable: i_Ca_f) Assignment Rule (variable: m_s_infinity) Assignment Rule (variable: i_Ca_s)
Assignment Rule (variable: i_Ca) Assignment Rule (variable: j) Assignment Rule (variable: jm_infinity) Assignment Rule (variable: tau_j)
Assignment Rule (variable: i_K_Ca) Assignment Rule (variable: r_infinity) Assignment Rule (variable: i_CRAC) Assignment Rule (variable: i_leak)
Assignment Rule (variable: J_er_p) Assignment Rule (variable: a_infinity) Assignment Rule (variable: b_infinity) Assignment Rule (variable: h_infinity)
Assignment Rule (variable: O) Assignment Rule (variable: J_er_IP3) Assignment Rule (variable: J_er_leak) Assignment Rule (variable: J_er_tot)
Assignment Rule (variable: J_mem_tot) Rate Rule (variable: V_membrane) Rate Rule (variable: n) Rate Rule (variable: jm)
Rate Rule (variable: ca_er_ca_equations) Rate Rule (variable: Ca_i)    
Physical entities
Compartments Species
COMpartment V_membrane n jm
ca_er_ca_equations Ca_i  
Global parameters
Cm i_K g_K n_infinity
tau_n lambda_n i_K_ATP g_K_ATP
i_Ca_f V_Ca g_Ca_f m_f_infinity
i_Ca_s g_Ca_s m_s_infinity j
jm_infinity tau_j i_Ca i_K_Ca
g_K_Ca kdkca i_CRAC g_CRAC
V_CRAC r_infinity Ca_er_bar i_leak
g_leak J_er_p IP3 kerp
verp dact dinh dip3
a_infinity b_infinity h_infinity O
J_er_tot J_er_IP3 J_er_leak perl
lambda_er sigma_er k_Ca gamma
J_mem_tot f    
Reactions (0)
Rules (30)
 
 Assignment Rule (name: i_K) i_K = g_K*n*(V_membrane+70)
 
 Assignment Rule (name: n_infinity) n_infinity = 1/(1+exp(((-15)-V_membrane)/6))
 
 Assignment Rule (name: tau_n) tau_n = 9.09/(1+exp((15+V_membrane)/6))
 
 Assignment Rule (name: i_K_ATP) i_K_ATP = g_K_ATP*(V_membrane+70)
 
 Assignment Rule (name: m_f_infinity) m_f_infinity = 1/(1+exp(((-20)-V_membrane)/7.5))
 
 Assignment Rule (name: i_Ca_f) i_Ca_f = g_Ca_f*m_f_infinity*(V_membrane-V_Ca)
 
 Assignment Rule (name: m_s_infinity) m_s_infinity = 1/(1+exp(((-16)-V_membrane)/10))
 
 Assignment Rule (name: i_Ca_s) i_Ca_s = g_Ca_s*m_s_infinity*(1-jm)*(V_membrane-V_Ca)
 
 Assignment Rule (name: i_Ca) i_Ca = i_Ca_f+i_Ca_s
 
 Assignment Rule (name: j) j = 1-jm
 
 Assignment Rule (name: jm_infinity) jm_infinity = 1-1/(1+exp((53+V_membrane)/2))
 
 Assignment Rule (name: tau_j) tau_j = 50000/(exp((53+V_membrane)/4)+exp(((-53)-V_membrane)/4))+1500
 
 Assignment Rule (name: i_K_Ca) i_K_Ca = g_K_Ca*Ca_i^5/(Ca_i^5+kdkca^5)*(V_membrane+70)
 
 Assignment Rule (name: r_infinity) r_infinity = 1/(1+exp(1*(Ca_er_Ca_equations-Ca_er_bar)))
 
 Assignment Rule (name: i_CRAC) i_CRAC = g_CRAC*r_infinity*(V_membrane-V_CRAC)
 
 Assignment Rule (name: i_leak) i_leak = g_leak*(V_membrane-V_CRAC)
 
 Assignment Rule (name: J_er_p) J_er_p = verp*Ca_i^2/(Ca_i^2+kerp^2)
 
 Assignment Rule (name: a_infinity) a_infinity = 1/(1+dact/Ca_i)
 
 Assignment Rule (name: b_infinity) b_infinity = IP3/(IP3+dip3)
 
 Assignment Rule (name: h_infinity) h_infinity = 1/(1+Ca_i/dinh)
 
 Assignment Rule (name: O) O = a_infinity^3*b_infinity^3*h_infinity^3*1
 
 Assignment Rule (name: J_er_IP3) J_er_IP3 = O*(Ca_er_Ca_equations-Ca_i)
 
 Assignment Rule (name: J_er_leak) J_er_leak = perl*(Ca_er_Ca_equations-Ca_i)
 
 Assignment Rule (name: J_er_tot) J_er_tot = (J_er_leak+J_er_IP3)-J_er_p
 
 Assignment Rule (name: J_mem_tot) J_mem_tot = (-f)*(gamma*i_Ca+k_Ca*Ca_i)
 
 Rate Rule (name: V_membrane) d [ V_membrane] / d t= (-(i_Ca+i_K+i_K_ATP+i_K_Ca+i_CRAC+i_leak))/Cm
 
 Rate Rule (name: n) d [ n] / d t= lambda_n*(n_infinity-n)/tau_n
 
 Rate Rule (name: jm) d [ jm] / d t= (jm_infinity-jm)/tau_j
 
 Rate Rule (name: Ca_er_Ca_equations) d [ ca_er_ca_equations] / d t= (-J_er_tot)/(lambda_er*sigma_er)
 
 Rate Rule (name: Ca_i) d [ Ca_i] / d t= J_er_tot/lambda_er+J_mem_tot
 
   COMpartment Spatial dimensions: 3.0  Compartment size: 1.0
 
 V_membrane
Compartment: COMpartment
Initial amount: -61.0
 
 n
Compartment: COMpartment
Initial amount: 5.0E-4
 
 jm
Compartment: COMpartment
Initial amount: 0.25
 
 ca_er_ca_equations
Compartment: COMpartment
Initial amount: 9.0
 
 Ca_i
Compartment: COMpartment
Initial amount: 0.11
 
Global Parameters (50)
 
 Cm
Value: 6158.0
Constant
 
   i_K
Value: 17.55
 
 g_K
Value: 3900.0
Constant
 
   n_infinity
Value: 4.67956725632935E-4
 
   tau_n
Value: 9.085746273364
 
 lambda_n
Value: 1.85
Constant
 
   i_K_ATP
Value: 1350.0
 
   g_K_ATP
Value: 150.0
Constant
 
   i_Ca_f
Value: -548.702035891578
 
 V_Ca
Value: 100.0
Constant
 
 g_Ca_f
Value: 810.0
Constant
 
   m_f_infinity
Value: 0.00420751503635901
 
   i_Ca_s
Value: -793.881316270245
 
 g_Ca_s
Value: 510.0
Constant
 
   m_s_infinity
Value: 0.0109869426305932
 
   j
Value: 0.88
 
   jm_infinity
Value: 0.0179862099620915
 
   tau_j
Value: 8145.05572085199
 
   i_Ca
Value: -1342.58335216182
 
   i_K_Ca
Value: 3.45489443378119
 
 g_K_Ca
Value: 1200.0
Constant
 
 kdkca
Value: 0.55
Constant
 
   i_CRAC
Value: -11.3122509416041
 
 g_CRAC
Value: 75.0
Constant
 
 V_CRAC
Constant
 
   r_infinity
Value: 0.00247262315663477
 
 Ca_er_bar
Value: 3.0
Constant
 
   i_leak  
 
 g_leak
Constant
 
   J_er_p
Value: 0.131402714932127
 
 IP3
Constant
 
 kerp
Value: 0.1
Constant
 
 verp
Value: 0.24
Constant
 
 dact
Value: 0.1
Constant
 
 dinh
Value: 0.4
Constant
 
 dip3
Value: 0.2
Constant
 
   a_infinity
Value: 0.523809523809524
 
   b_infinity  
 
   h_infinity
Value: 0.784313725490196
 
   O  
 
   J_er_tot
Value: 0.0463972850678733
 
   J_er_IP3  
 
   J_er_leak
Value: 0.1778
 
 perl
Value: 0.02
Constant
 
 lambda_er
Value: 250.0
Constant
 
 sigma_er
Value: 5.0
Constant
 
 k_Ca
Value: 0.07
Constant
 
 gamma
Value: 3.607E-6
Constant
 
   J_mem_tot
Value: -2.8573018487523E-5
 
 f
Value: 0.01
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000374

Curator's comment: (updated: 30 Sep 2011 12:47:46 BST)

The model reproduces fig 1 of the reference publication.
The model was integrated and simulated using Copasi v4.7 (Build 34).

Additional file(s)
  • Figure 1:
    This COPASI file reproduces figure 1 of the reference publication.
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