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BIOMD0000000378 - Chay1997_CalciumConcentration

 

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Reference Publication
Publication ID: 9284334
Chay TR.
Effects of extracellular calcium on electrical bursting and intracellular and luminal calcium oscillations in insulin secreting pancreatic beta-cells.
Biophys. J. 1997 Sep; 73(3): 1673-1688
Department of Biological Sciences, University of Pittsburgh, Pennsylvania 15260, USA. trc1@vms.cis.pitt.edu  [more]
Model
Original Model: CellML logo
Submitter: Vijayalakshmi Chelliah
Submission ID: MODEL0491199816
Submission Date: 24 Apr 2009 12:55:59 UTC
Last Modification Date: 28 May 2014 20:53:14 UTC
Creation Date: 29 Sep 2011 22:17:54 UTC
Encoders:  Ishan Ajmera
   Catherine Lloyd
set #1
bqbiol:isVersionOf Gene Ontology calcium-mediated signaling
Gene Ontology type B pancreatic cell proliferation
Gene Ontology regulation of type B pancreatic cell proliferation
set #2
bqbiol:occursIn Brenda Tissue Ontology BTO:0000783
set #3
bqbiol:hasTaxon Taxonomy Homo sapiens
Notes

This a model from the article:
Effects of extracellular calcium on electrical bursting and intracellular and luminal calcium oscillations in insulin secreting pancreatic beta-cells.
Chay TR Biophys J.1997 Sep;73(3):1673-88. 9284334,
Abstract:
The extracellular calcium concentration has interesting effects on bursting of pancreatic beta-cells. The mechanism underlying the extracellular Ca2+ effect is not well understood. By incorporating a low-threshold transient inward current to the store-operated bursting model of Chay, this paper elucidates the role of the extracellular Ca2+ concentration in influencing electrical activity, intracellular Ca2+ concentration, and the luminal Ca2+ concentration in the intracellular Ca2+ store. The possibility that this inward current is a carbachol-sensitive and TTX-insensitive Na+ current discovered by others is discussed. In addition, this paper explains how these three variables respond when various pharmacological agents are applied to the store-operated model.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Chay TR (1997) - version05
The original CellML model was created by:
Lloyd, Catherine, May
c.lloyd@aukland.ac.nz
The University of Auckland
The Bioengineering Institute

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: 9284334 Submission Date: 24 Apr 2009 12:55:59 UTC Last Modification Date: 28 May 2014 20:53:14 UTC Creation Date: 29 Sep 2011 22:17:54 UTC
Mathematical expressions
Rules
Assignment Rule (variable: m_infinity) Assignment Rule (variable: i_fast) Assignment Rule (variable: tau_h) Assignment Rule (variable: h_infinity)
Assignment Rule (variable: tau_d) Assignment Rule (variable: f_infinity) Assignment Rule (variable: i_Ca) Assignment Rule (variable: d_infinity)
Assignment Rule (variable: i_NS) Assignment Rule (variable: i_K_dr) Assignment Rule (variable: n_infinity) Assignment Rule (variable: tau_n)
Assignment Rule (variable: i_K_ATP) Assignment Rule (variable: i_K_Ca) Assignment Rule (variable: i_NaL) Rate Rule (variable: V_membrane)
Rate Rule (variable: h) Rate Rule (variable: d) Rate Rule (variable: n) Rate Rule (variable: Ca_i_cytosolic_calcium)
Rate Rule (variable: Ca_lum)      
Physical entities
Compartments Species
Compartment V_membrane h d
n Ca_i_cytosolic_calcium Ca_lum
Global parameters
R T F Cm
i_fast g_fast V_fast m_infinity
Vm Sm lamda_h tau_h
h_infinity Vh Sh i_Ca
K_Ca P_Ca Ca_o lamda_d
tau_d d_infinity Vd Sd
f_infinity Ca_i i_NS g_NS
K_NS VNS i_K_dr V_K
g_K_dr lamda_n Vn Sn
n_infinity tau_n i_K_Ca g_K_Ca
i_K_ATP g_K_ATP i_NaL g_NaL
V_Na k_rel k_Ca k_pump
omega      
Reactions (0)
Rules (21)
 
 Assignment Rule (name: m_infinity) m_infinity = 1/(1+exp((Vm-V_membrane)/Sm))
 
 Assignment Rule (name: i_fast) i_fast = g_fast*m_infinity^3*h*(V_membrane-V_fast)
 
 Assignment Rule (name: tau_h) tau_h = 1/(lamda_h*(exp((Vh-V_membrane)/(2*Sh))+exp((V_membrane-Vh)/(2*Sh))))
 
 Assignment Rule (name: h_infinity) h_infinity = 1/(1+exp((Vh-V_membrane)/Sh))
 
 Assignment Rule (name: tau_d) tau_d = 1/(lamda_d*(exp((Vd-V_membrane)/(2*Sd))+exp((V_membrane-Vd)/(2*Sd))))
 
 Assignment Rule (name: f_infinity) f_infinity = K_Ca/(K_Ca+Ca_i_calcium_current_f_gate)
 
 Assignment Rule (name: i_Ca) i_Ca = P_Ca*d*f_infinity*2*F*V_membrane/(R*T)*(Ca_o-Ca_i_cytosolic_calcium*exp(2*F*V_membrane/(R*T)))/(1-exp(2*F*V_membrane/(R*T)))
 
 Assignment Rule (name: d_infinity) d_infinity = 1/(1+exp((Vd-V_membrane)/Sd))
 
 Assignment Rule (name: i_NS) i_NS = g_NS*K_NS^2/(K_NS^2+Ca_lum^2)*((V_membrane-VNS)/(1-exp(0.1*(VNS-V_membrane)))-10)
 
 Assignment Rule (name: i_K_dr) i_K_dr = g_K_dr*n^4*(V_membrane-V_K)
 
 Assignment Rule (name: n_infinity) n_infinity = 1/(1+exp((Vn-V_membrane)/Sn))
 
 Assignment Rule (name: tau_n) tau_n = 1/(lamda_n*(exp((Vn-V_membrane)/(2*Sn))+exp((V_membrane-Vn)/(2*Sn))))
 
 Assignment Rule (name: i_K_ATP) i_K_ATP = g_K_ATP*(V_membrane-V_K)
 
 Assignment Rule (name: i_K_Ca) i_K_Ca = g_K_Ca*Ca_i_cytosolic_calcium^3/(K_Ca^3+Ca_i_cytosolic_calcium^3)*(V_membrane-V_K)
 
 Assignment Rule (name: i_NaL) i_NaL = g_NaL*(V_membrane-V_Na)
 
 Rate Rule (name: V_membrane) d [ V_membrane] / d t= (-(i_K_dr+i_K_Ca+i_K_ATP+i_fast+i_Ca+i_NS+i_NaL))/Cm
 
 Rate Rule (name: h) d [ h] / d t= (h_infinity-h)/tau_h
 
 Rate Rule (name: d) d [ d] / d t= (d_infinity-d)/tau_d
 
 Rate Rule (name: n) d [ n] / d t= (n_infinity-n)/tau_n
 
 Rate Rule (name: Ca_i_cytosolic_calcium) d [ Ca_i_cytosolic_calcium] / d t= k_rel*(Ca_lum-Ca_i_cytosolic_calcium)-(omega*i_Ca+k_Ca*Ca_i_cytosolic_calcium+k_pump*Ca_i_cytosolic_calcium)
 
 Rate Rule (name: Ca_lum) d [ Ca_lum] / d t= (-k_rel)*(Ca_lum-Ca_i_cytosolic_calcium)+k_pump*Ca_i_cytosolic_calcium
 
   Compartment Spatial dimensions: 3.0  Compartment size: 1.0
 
 V_membrane
Compartment: Compartment
Initial amount: -38.34146
 
 h
Compartment: Compartment
Initial amount: 0.214723
 
 d
Compartment: Compartment
Initial amount: 0.0031711238
 
 n
Compartment: Compartment
Initial amount: 0.1836403
 
 Ca_i_cytosolic_calcium
Compartment: Compartment
Initial amount: 0.6959466
 
 Ca_lum
Compartment: Compartment
Initial amount: 102.686
 
Global Parameters (49)
 
 R
Value: 8314.0
Constant
 
 T
Value: 310.0
Constant
 
 F
Value: 96485.0
Constant
 
 Cm
Value: 1.0
Constant
 
   i_fast
Value: -96.6401171990526
 
 g_fast
Value: 600.0
Constant
 
 V_fast
Value: 80.0
Constant
 
  m_infinity
Value: 0.185067533162422
 
 Vm
Value: -25.0
Constant
 
 Sm
Value: 9.0
Constant
 
   lamda_h
Value: 12.5
Constant
 
  tau_h
Value: 0.0320623804770684
 
  h_infinity
Value: 0.201042499324815
 
 Vh
Value: -48.0
Constant
 
 Sh
Value: -7.0
Constant
 
  i_Ca
Value: -24.1248530333721
 
 K_Ca
Value: 1.0
Constant
 
 P_Ca
Value: 2.0
Constant
 
 Ca_o
Value: 2500.0
Constant
 
 lamda_d
Value: 2.5
Constant
 
   tau_d
Value: 0.0234265674250627
 
   d_infinity
Value: 0.00344187186519272
 
 Vd
Value: -10.0
Constant
 
 Sd
Value: 5.0
Constant
 
   f_infinity
Value: 0.5
 
   Ca_i
Value: 1.0
Constant
 
  i_NS
Value: -6.24107017458029
 
 g_NS
Value: 5.0
Constant
 
 K_NS
Value: 50.0
Constant
 
 VNS
Value: -20.0
Constant
 
   i_K_dr
Value: 25.014877991785
 
 V_K
Value: -75.0
Constant
 
 g_K_dr
Value: 600.0
Constant
 
 lamda_n
Value: 12.5
Constant
 
 Vn
Value: -18.0
Constant
 
 Sn
Value: 14.0
Constant
 
   n_infinity
Value: 0.189546217642834
 
   tau_n
Value: 0.0313553515963197
 
   i_K_Ca
Value: 46.2079655277309
 
   g_K_Ca
Value: 5.0
Constant
 
   i_K_ATP
Value: 73.31708
 
   g_K_ATP
Value: 2.0
Constant
 
   i_NaL
Value: -35.502438
 
 g_NaL
Value: 0.3
Constant
 
 V_Na
Value: 80.0
Constant
 
 k_rel
Value: 0.2
Constant
 
 k_Ca
Value: 7.0
Constant
 
 k_pump
Value: 30.0
Constant
 
 omega
Value: 0.2
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000378

Curator's comment: (updated: 30 Sep 2011 12:38:57 BST)

The model reproduces fig 3 of the reference publication.
The model was integrated and simulated using Copasi v4.7 (Build 34).

Additional file(s)
  • Figure 3:
    This COPASI file reproduces fig 3 of the reference publication,but the time scale needs to be adjusted to get the curation figure
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