BioModels Database logo

BioModels Database

spacer

BIOMD0000000375 - Mears1997_CRAC_PancreaticBetaCells

 

 |   |   |  Send feedback
Reference Publication
Publication ID: 9002424
Mears D, Sheppard NF Jr, Atwater I, Rojas E, Bertram R, Sherman A.
Evidence that calcium release-activated current mediates the biphasic electrical activity of mouse pancreatic beta-cells.
J. Membr. Biol. 1997 Jan; 155(1): 47-59
Department of Biomedical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA.  [more]
Model
Original Model: CellML logo
Submitter: Camille Laibe
Submission ID: MODEL1006230074
Submission Date: 23 Jun 2010 09:12:25 UTC
Last Modification Date: 08 Mar 2012 12:52:27 UTC
Creation Date: 29 Sep 2011 22:10:36 UTC
Encoders:  Ishan Ajmera
   Catherine Lloyd
set #1
bqbiol:isVersionOf Gene Ontology calcium-release channel activity
Gene Ontology type B pancreatic cell proliferation
Gene Ontology regulation of type B pancreatic cell proliferation
set #2
bqbiol:hasTaxon Taxonomy Homo sapiens
set #3
bqbiol:occursIn Brenda Tissue Ontology BTO:0000783
Notes

This a model from the article:
Evidence that calcium release-activated current mediates the biphasic electrical activity of mouse pancreatic beta-cells.
Mears D, Sheppard NF Jr, Atwater I, Rojas E, Bertram R, Sherman A. J Membr Biol1997 Jan 1;155(1):47-59 9002424,
Abstract:
The electrical response of pancreatic beta-cells to step increases in glucose concentration is biphasic, consisting of a prolonged depolarization with action potentials (Phase 1) followed by membrane potential oscillations known as bursts. We have proposed that the Phase 1 response results from the combined depolarizing influences of potassium channel closure and an inward, nonselective cation current (ICRAN) that activates as intracellular calcium stores empty during exposure to basal glucose (Bertram et al., 1995). The stores refill during Phase 1, deactivating ICRAN and allowing steady-state bursting to commence. We support this hypothesis with additional simulations and experimental results indicating that Phase 1 duration is sensitive to the filling state of intracellular calcium stores. First, the duration of the Phase 1 transient increases with duration of prior exposure to basal (2.8 mM) glucose, reflecting the increased time required to fill calcium stores that have been emptying for longer periods. Second, Phase 1 duration is reduced when islets are exposed to elevated K+ to refill calcium stores in the presence of basal glucose. Third, when extracellular calcium is removed during the basal glucose exposure to reduce calcium influx into the stores, Phase 1 duration increases. Finally, no Phase 1 is observed following hyperpolarization of the beta-cell membrane with diazoxide in the continued presence of 11 mm glucose, a condition in which intracellular calcium stores remain full. Application of carbachol to empty calcium stores during basal glucose exposure did not increase Phase 1 duration as the model predicts. Despite this discrepancy, the good agreement between most of the experimental results and the model predictions provides evidence that a calcium release-activated current mediates the Phase 1 electrical response of the pancreatic beta-cell.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Mears D, Sheppard NF Jr, Atwater I, Rojas E, Bertram R, Sherman A. (1997) - version=1.0
The original CellML model was created by:
Tessa Paris
tpar054@aucklanduni.ac.uk
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: 9002424 Submission Date: 23 Jun 2010 09:12:25 UTC Last Modification Date: 08 Mar 2012 12:52:27 UTC Creation Date: 29 Sep 2011 22:10:36 UTC
Mathematical expressions
Rules
Assignment Rule (variable: tau_n) Assignment Rule (variable: i_K) Assignment Rule (variable: n_infinity) Assignment Rule (variable: g_K_ATP)
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: jm_infinity) Assignment Rule (variable: tau_j) Assignment Rule (variable: i_Ca)
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: Jmp) 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 V_K g_K
n_infinity tau_n Vn Sn
lambda_n i_K_ATP g_K_ATP i_Ca_f
V_Ca g_Ca_f m_f_infinity Vm_f
Sm_f i_Ca_s g_Ca_s m_s_infinity
Vm_s Sm_s jm_infinity Vj
tau_j Sj i_Ca i_K_Ca
g_K_Ca kdkca i_CRAC g_CRAC
V_CRAC r_infinity Ca_er_bar sloper
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 kmp
vmp gamma J_mem_tot Jmp
f      
Reactions (0)
Rules (31)
 
 Assignment Rule (name: tau_n) tau_n = 9.09/(1+exp((V_membrane+15)/6))
 
 Assignment Rule (name: i_K) i_K = g_K*n*(V_membrane-V_K)
 
 Assignment Rule (name: n_infinity) n_infinity = 1/(1+exp((-15-V_membrane)/6))
 
 Assignment Rule (name: g_K_ATP) g_K_ATP = piecewise(2000, (time > 60000) and (time < 660000), 150)
 
 Assignment Rule (name: i_K_ATP) i_K_ATP = g_K_ATP*(V_membrane-V_K)
 
 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: jm_infinity) jm_infinity = 1-1/(1+exp((V_membrane+53)/2))
 
 Assignment Rule (name: tau_j) tau_j = 50000/(exp((V_membrane+53)/4)+exp((-53-V_membrane)/4))+1500
 
 Assignment Rule (name: i_Ca) i_Ca = i_Ca_f+i_Ca_s
 
 Assignment Rule (name: i_K_Ca) i_K_Ca = g_K_Ca*Ca_i^5/(Ca_i^5+kdkca^5)*(V_membrane-V_K)
 
 Assignment Rule (name: r_infinity) r_infinity = 1/(1+exp((Ca_er_Ca_equations-Ca_er_bar)/sloper))
 
 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: Jmp) Jmp = vmp*Ca_i^2/(Ca_i^2+kmp^2)
 
 Assignment Rule (name: J_mem_tot) J_mem_tot = (-f)*(gamma*i_Ca+Jmp)
 
 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: 0.12
 
 Ca_er_Ca_equations
Compartment: COMpartment
Initial amount: 60.0
 
 Ca_i
Compartment: COMpartment
Initial amount: 0.11
 
Global Parameters (61)
 
 Cm
Value: 6158.0
Constant
 
   i_K
Value: 17.55
 
 V_K
Value: -70.0
Constant
 
 g_K
Value: 3900.0
Constant
 
   n_infinity
Value: 4.67956725632935E-4
 
   tau_n
Value: 9.085746273364
 
 Vn
Value: -15.0
Constant
 
 Sn
Value: 6.0
Constant
 
 lambda_n
Value: 1.85
Constant
 
   i_K_ATP
Value: 1350.0
 
   g_K_ATP
Value: 150.0
 
   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
 
 Vm_f
Value: -20.0
Constant
 
 Sm_f
Value: 7.5
Constant
 
   i_Ca_s
Value: -793.881316270245
 
 g_Ca_s
Value: 510.0
Constant
 
   m_s_infinity
Value: 0.0109869426305932
 
 Vm_s
Value: -16.0
Constant
 
 Sm_s
Value: 10.0
Constant
 
   jm_infinity
Value: 0.0179862099620915
 
 Vj
Value: -53.0
Constant
 
   tau_j
Value: 8145.05572085199
 
 Sj
Value: 2.0
Constant
 
   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: -5.81489940359721
 
 g_CRAC
Value: 75.0
Constant
 
 V_CRAC
Constant
 
   r_infinity
Value: 0.00127101626308136
 
 Ca_er_bar
Value: 40.0
Constant
 
 sloper
Value: 3.0
Constant
 
   i_leak  
 
 g_leak
Constant
 
   J_er_p
Value: 0.143762376237624
 
 IP3
Constant
 
 kerp
Value: 0.09
Constant
 
 verp
Value: 0.24
Constant
 
 dact
Value: 0.35
Constant
 
 dinh
Value: 0.4
Constant
 
 dip3
Value: 0.2
Constant
 
   a_infinity
Value: 0.239130434782609
 
   b_infinity  
 
   h_infinity
Value: 0.784313725490196
 
   O  
 
   J_er_tot
Value: 0.0359076237623762
 
   J_er_IP3  
 
   J_er_leak
Value: 0.17967
 
 perl
Value: 0.0030
Constant
 
 lambda_er
Value: 250.0
Constant
 
 sigma_er
Value: 1.0
Constant
 
 kmp
Value: 0.35
Constant
 
 vmp
Value: 0.08
Constant
 
 gamma
Value: 3.607E-6
Constant
 
   J_mem_tot
Value: -2.34898089778648E-5
 
   Jmp
Value: 0.00719167904903418
 
 f
Value: 0.01
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000375

Curator's comment: (updated: 30 Sep 2011 12:48:26 BST)

The model reproduces fig 2 of the reference publication.
The model was integrated and simulated using Copasi v4.7 (Build 34).

Additional file(s)
  • Figure 2:
    This COPASI file reproduces fig 2 of the reference publication,but the time scale new to be adjusted to get the curation figure
spacer
spacer