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BIOMD0000000059 - Fridlyand2003_Calcium_flux

 

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Reference Publication
Publication ID: 12644446
Fridlyand LE, Tamarina N, Philipson LH.
Modeling of Ca2+ flux in pancreatic beta-cells: role of the plasma membrane and intracellular stores.
Am. J. Physiol. Endocrinol. Metab. 2003 Jul; 285(1): E138-54
Department of Medicine, University of Chicago, Illinois 60637, USA.  [more]
Model
Original Model: BIOMD0000000059.xml.origin
Submitter: Harish Dharuri
Submission ID: MODEL0928773489
Submission Date: 23 Jun 2006 16:16:44 UTC
Last Modification Date: 24 May 2014 16:27:04 UTC
Creation Date: 20 Jun 2006 13:12:19 UTC
Encoders:  Harish Dharuri
set #1
bqbiol:occursIn Brenda Tissue Ontology pancreatic beta cell
set #2
bqbiol:hasPart Gene Ontology regulation of calcium-mediated signaling
Gene Ontology regulation of insulin secretion
bqbiol:is KEGG Pathway map04020
bqbiol:hasTaxon Taxonomy Mus musculus
Notes

The model reproduces block A of Fig 5 and also Fig 3 (without the inclusion of Tg action). The model was successfully tested on MathSBML


To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

In summary, you are entitled to use this encoded model in absolutely any manner you deem suitable, verbatim, or with modification, alone or embedded it in a larger context, redistribute it, commercially or not, in a restricted way or not.


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: 12644446 Submission Date: 23 Jun 2006 16:16:44 UTC Last Modification Date: 24 May 2014 16:27:04 UTC Creation Date: 20 Jun 2006 13:12:19 UTC
Mathematical expressions
Reactions
Calcium_cyt_Ivca Calcium_cyt_Inaca Calcium_cyt_Icapump Calcium_cyt_Jerp
Calcium_cyt_Jout Calcium_cyt_sequestration IP3_synthesis IP3_degradation
Na_Inaca Na_Inak Na_Ina Na_Icran
ATP_production ATP_NaKATPase ATP_Capump ATP_Jerp
ATP_Ca_dependent_consumption ATP_consumption    
Rules
Assignment Rule (variable: Cytosolic ADP) Assignment Rule (variable: Vca) Assignment Rule (variable: Vk) Assignment Rule (variable: Vna)
Assignment Rule (variable: Vnaca) Assignment Rule (variable: pvca) Assignment Rule (variable: f_CRAN) Assignment Rule (variable: p_CRAN)
Assignment Rule (variable: pna) Assignment Rule (variable: f_5) Assignment Rule (variable: b_5) Assignment Rule (variable: F1)
Assignment Rule (variable: F4) Assignment Rule (variable: F5) Assignment Rule (variable: B2) Assignment Rule (variable: B3)
Assignment Rule (variable: B4) Assignment Rule (variable: B6) Assignment Rule (variable: D) Assignment Rule (variable: f_Ca)
Assignment Rule (variable: Okatp) Assignment Rule (variable: n_infinity) Assignment Rule (variable: tau_n) Assignment Rule (variable: I_Vca)
Assignment Rule (variable: I_CaPump) Assignment Rule (variable: I_NaCa) Assignment Rule (variable: I_CRAN) Assignment Rule (variable: I_Na)
Assignment Rule (variable: I_NaK) Assignment Rule (variable: I_KDr) Assignment Rule (variable: I_KCa) Assignment Rule (variable: I_KATP)
Assignment Rule (variable: Jerp) Assignment Rule (variable: O_infinity) Assignment Rule (variable: Jout) Rate Rule (variable: n)
Rate Rule (variable: V)      
Physical entities
Compartments Species
cytoplasm Cytosolic Calcium Cytosolic IP3 Cytosolic Sodium
Cytosolic ATP Cytosolic ADP  
endoplasmic reticulum ER Calcium    
Global parameters
n V Vca TV
Ca_ec Vk K_ec K_cyt
Vna Na_ec Vnaca pvca
Vcah Kcah f_CRAN gm_CRAN
Kcar p_CRAN V_CRAN pna
f_5 f5_ast b_5 b5_ast
F1 f_1 F4 f_4
F5 B2 b_2 B3
b_3 B4 b_4 P
B6 b_6 Ksup D
f_2 f_3 f_6 b_1
f_Ca Kkca Okatp Kdd
Ktd Ktt n_infinity Vn
Sn tau_n c Vtau
a b I_Vca gmvca
I_CaPump Pmcap Kcap I_NaCa
gnaca Knaca I_CRAN I_Na
gmna I_NaK Pnak I_KDr
gmKDr I_KCa gmkca I_KATP
gmkatp Jerp Pcaer Kcarp
O_infinity Krca Kip3 Jout
Pleak Pip3 Cm fi
Faraday's constant ksg fer IP3 production rate constant
half activation cytosolic Ca IP3 degradation rate constant ATP production rate constant Ca dependent ATP consumption
Rate constant of ATP consumption      
Reactions (18)
 
 Calcium_cyt_Ivca  → [Cytosolic Calcium];  
 
 Calcium_cyt_Inaca  → [Cytosolic Calcium];  
 
 Calcium_cyt_Icapump [Cytosolic Calcium] → ;  
 
 Calcium_cyt_Jerp 0.01 × [Cytosolic Calcium] → 0.03 × [ER Calcium];  
 
 Calcium_cyt_Jout 0.03 × [ER Calcium] → 0.01 × [Cytosolic Calcium];  
 
 Calcium_cyt_sequestration [Cytosolic Calcium] → ;  
 
 IP3_synthesis  → [Cytosolic IP3];   {Cytosolic Calcium}
 
 IP3_degradation [Cytosolic IP3] → ;  
 
 Na_Inaca [Cytosolic Sodium] → ;  
 
 Na_Inak [Cytosolic Sodium] → ;  
 
 Na_Ina  → [Cytosolic Sodium];  
 
 Na_Icran  → [Cytosolic Sodium];  
 
 ATP_production  → [Cytosolic ATP];   {Cytosolic ADP}
 
 ATP_NaKATPase [Cytosolic ATP] → ;  
 
 ATP_Capump [Cytosolic ATP] → ;  
 
 ATP_Jerp [Cytosolic ATP] → ;  
 
 ATP_Ca_dependent_consumption [Cytosolic ATP] → ;   {Cytosolic Calcium}
 
 ATP_consumption [Cytosolic ATP] → ;  
 
Rules (37)
 
 Assignment Rule (name: ADP_cyt) Cytosolic ADP = 4000-ATP_cyt
 
 Assignment Rule (name: Vca) Vca = TV/2*log(Ca_ec/Ca_cyt)
 
 Assignment Rule (name: Vk) Vk = TV*log(K_ec/K_cyt)
 
 Assignment Rule (name: Vna) Vna = TV*log(Na_ec/Na_cyt)
 
 Assignment Rule (name: Vnaca) Vnaca = TV*(3*log(Na_ec/Na_cyt)-log(Ca_ec/Ca_cyt))
 
 Assignment Rule (name: pvca) pvca = 1/(1+exp((Vcah-V)/Kcah))
 
 Assignment Rule (name: f_CRAN) f_CRAN = (-gm_CRAN)/(1+exp((Ca_er-Kcar)/3))
 
 Assignment Rule (name: p_CRAN) p_CRAN = V-V_CRAN
 
 Assignment Rule (name: pna) pna = 1/(1+exp((104+V)/8))
 
 Assignment Rule (name: f_5) f_5 = f5_ast*exp(V/(2*TV))
 
 Assignment Rule (name: b_5) b_5 = b5_ast*exp((-V)/(2*TV))
 
 Assignment Rule (name: F1) F1 = f_1*Na_cyt^3
 
 Assignment Rule (name: F4) F4 = f_4*K_ec^2
 
 Assignment Rule (name: F5) F5 = f_5*ATP_cyt
 
 Assignment Rule (name: B2) B2 = b_2*ADP_cyt
 
 Assignment Rule (name: B3) B3 = b_3*Na_ec^3
 
 Assignment Rule (name: B4) B4 = b_4*P
 
 Assignment Rule (name: B6) B6 = b_6*Ksup^2
 
 Assignment Rule (name: D) D = f_2*f_3*F4*F5*f_6+b_1*f_3*F4*F5*f_6+b_1*B2*F4*F5*f_6+b_1*B2*B3*F5*f_6+b_1*B2*B3*B4*f_6+b_1*B2*B3*B4*b_5
 
 Assignment Rule (name: f_Ca) f_Ca = Ca_cyt^4/(Ca_cyt^4+Kkca^4)
 
 Assignment Rule (name: Okatp) Okatp = (0.08*(1+0.33*ADP_cyt/Kdd)+0.89*(0.165*ADP_cyt/Kdd)^2)/((1+0.165*ADP_cyt/Kdd)^2*(1+0.135*ADP_cyt/Ktd+0.05*ATP_cyt/Ktt))
 
 Assignment Rule (name: n_infinity) n_infinity = 1/(1+exp((Vn-V)/Sn))
 
 Assignment Rule (name: tau_n) tau_n = c/(exp((V-Vtau)/a)+exp((Vtau-V)/b))
 
 Assignment Rule (name: I_Vca) I_Vca = gmvca*pvca*(V-Vca)
 
 Assignment Rule (name: I_CaPump) I_CaPump = Pmcap*Ca_cyt^2/(Kcap^2+Ca_cyt^2)
 
 Assignment Rule (name: I_NaCa) I_NaCa = gnaca*Ca_cyt^5*(V-Vnaca)/(Ca_cyt^5+Knaca^5)
 
 Assignment Rule (name: I_CRAN) I_CRAN = f_CRAN*p_CRAN*(V-Vna)
 
 Assignment Rule (name: I_Na) I_Na = gmna*pna*(V-Vna)
 
 Assignment Rule (name: I_NaK) I_NaK = Pnak*(F1*f_2*f_3*F4*F5*f_6-b_1*B2*B3*B4*b_5*B6)/D
 
 Assignment Rule (name: I_KDr) I_KDr = gmKDr*n*(V-Vk)
 
 Assignment Rule (name: I_KCa) I_KCa = gmkca*f_Ca*(V-Vk)
 
 Assignment Rule (name: I_KATP) I_KATP = gmkatp*Okatp*(V-Vk)
 
 Assignment Rule (name: Jerp) Jerp = Pcaer*Ca_cyt^2/(Ca_cyt^2+Kcarp^2)
 
 Assignment Rule (name: O_infinity) O_infinity = Ca_cyt*IP3_cyt^3/((Ca_cyt+Krca)*(IP3_cyt^3+Kip3^3))
 
 Assignment Rule (name: Jout) Jout = (Pleak+Pip3*O_infinity)*(Ca_er-Ca_cyt)
 
 Rate Rule (name: n) d [ n] / d t= (n_infinity-n)/tau_n
 
 Rate Rule (name: V) d [ V] / d t= (0-(I_Vca+I_CaPump+I_NaCa+I_CRAN+I_Na+I_NaK+I_KDr+I_KCa+I_KATP))/Cm
 
 cytoplasm Spatial dimensions: 3.0  Compartment size: 7.64E-13
 
 Cytosolic Calcium
Compartment: cytoplasm
Initial concentration: 0.085
 
 Cytosolic IP3
Compartment: cytoplasm
Initial concentration: 0.33
 
 Cytosolic Sodium
Compartment: cytoplasm
Initial concentration: 9858.0
 
 Cytosolic ATP
Compartment: cytoplasm
Initial concentration: 932.1
 
  Cytosolic ADP
Compartment: cytoplasm
Initial concentration: 3067.9
 
 endoplasmic reticulum Spatial dimensions: 3.0  Compartment size: 2.8E-13
 
 ER Calcium
Compartment: endoplasmic reticulum
Initial concentration: 22.8
 
Global Parameters (97)
 
   n
Value: 0.00123
 
   V
Value: -60.9   (Units: Voltage)
 
   Vca  
 
   TV
Value: 26.73   (Units: Voltage)
Constant
 
   Ca_ec
Value: 2600.0   (Units: Concentration)
Constant
 
   Vk  
 
   K_ec
Value: 8000.0   (Units: Concentration)
Constant
 
   K_cyt
Value: 132400.0   (Units: Concentration)
Constant
 
   Vna  
 
   Na_ec
Value: 140000.0   (Units: Concentration)
Constant
 
   Vnaca  
 
   pvca  
 
   Vcah
Value: -19.0   (Units: Voltage)
Constant
 
   Kcah
Value: 9.5   (Units: Voltage)
Constant
 
   f_CRAN  
 
   gm_CRAN
Value: 0.7   (Units: Conductance coefficient)
Constant
 
   Kcar
Value: 200.0   (Units: Concentration)
Constant
 
   p_CRAN  
 
   V_CRAN
Constant
 
   pna  
 
   f_5  
 
   f5_ast
Value: 0.0020   (Units: per concentration per time)
Constant
 
   b_5  
 
   b5_ast
Value: 0.03   (Units: Time inverse)
Constant
 
   F1  
 
   f_1
Value: 2.5E-10   (Units: per concentration cubed per time)
Constant
 
   F4  
 
   f_4
Value: 1.5E-8   (Units: per Concentration square per time)
Constant
 
   F5  
 
   B2  
 
   b_2
Value: 1.0E-4   (Units: per concentration per time)
Constant
 
   B3  
 
   b_3
Value: 1.72E-17   (Units: per concentration cubed per time)
Constant
 
   B4  
 
   b_4
Value: 2.0E-4   (Units: per concentration per time)
Constant
 
   P
Value: 4950.0   (Units: Concentration)
Constant
 
   B6  
 
   b_6
Value: 6.0E-7   (Units: per concentration per time)
Constant
 
   Ksup
Value: 150400.0   (Units: Concentration)
Constant
 
   D  
 
   f_2
Value: 10.0   (Units: Time inverse)
Constant
 
   f_3
Value: 0.172   (Units: Time inverse)
Constant
 
   f_6
Value: 11.5   (Units: Time inverse)
Constant
 
   b_1
Value: 100.0   (Units: Time inverse)
Constant
 
   f_Ca  
 
   Kkca
Value: 0.1   (Units: Concentration)
Constant
 
   Okatp  
 
   Kdd
Value: 17.0   (Units: Concentration)
Constant
 
   Ktd
Value: 26.0   (Units: Concentration)
Constant
 
   Ktt
Value: 1.0   (Units: Concentration)
Constant
 
   n_infinity  
 
   Vn
Value: -14.0   (Units: Voltage)
Constant
 
   Sn
Value: 7.0   (Units: Voltage)
Constant
 
   tau_n  
 
   c
Value: 20.0   (Units: milliseconds)
Constant
 
   Vtau
Value: -75.0   (Units: Voltage)
Constant
 
   a
Value: 65.0   (Units: Voltage)
Constant
 
   b
Value: 20.0   (Units: Voltage)
Constant
 
   I_Vca  
 
   gmvca
Value: 770.0   (Units: Conductance)
Constant
 
   I_CaPump  
 
   Pmcap
Value: 2000.0   (Units: Current)
Constant
 
   Kcap
Value: 0.1   (Units: Concentration)
Constant
 
   I_NaCa  
 
   gnaca
Value: 271.0   (Units: Conductance)
Constant
 
   Knaca
Value: 0.75   (Units: Concentration)
Constant
 
   I_CRAN  
 
   I_Na  
 
   gmna
Value: 1200.0   (Units: Conductance)
Constant
 
   I_NaK  
 
   Pnak
Value: 600.0   (Units: Current)
Constant
 
   I_KDr  
 
   gmKDr
Value: 3000.0   (Units: Conductance)
Constant
 
   I_KCa  
 
   gmkca
Value: 130.0   (Units: Conductance)
Constant
 
   I_KATP  
 
   gmkatp
Value: 24000.0   (Units: Conductance)
Constant
 
   Jerp  
 
   Pcaer
Value: 0.105   (Units: concentration per time)
 
   Kcarp
Value: 0.5   (Units: Concentration)
Constant
 
   O_infinity  
 
   Krca
Value: 0.077   (Units: Concentration)
Constant
 
   Kip3
Value: 3.2   (Units: Concentration)
Constant
 
   Jout  
 
   Pleak
Value: 1.0E-16   (Units: volume per time)
Constant
 
   Pip3
Value: 1.2E-15   (Units: volume per time)
Constant
 
   Cm
Value: 6158.0   (Units: Capacitance)
Constant
 
   fi
Value: 0.01   (Units: dimensionless)
Constant
 
   Faraday's constant
Value: 9.6485E16   (Units: Faraday constant)
Constant
 
   ksg
Value: 1.0E-4   (Units: Time inverse)
Constant
 
   fer
Value: 0.03   (Units: dimensionless)
Constant
 
   IP3 production rate constant
Value: 3.0E-4   (Units: concentration per time)
Constant
 
   half activation cytosolic Ca
Value: 0.4   (Units: Concentration)
Constant
 
   IP3 degradation rate constant
Value: 4.0E-5   (Units: Time inverse)
Constant
 
   ATP production rate constant
Value: 3.7E-4   (Units: Time inverse)
Constant
 
   Ca dependent ATP consumption
Value: 5.0E-5   (Units: per concentration per time)
Constant
 
   Rate constant of ATP consumption
Value: 5.0E-5   (Units: Time inverse)
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000059

Curator's comment: (updated: 19 Feb 2008 07:49:10 GMT)

Simulation result obtained by MathSBML reproduces block A of Fig 5 and Fig 3 without Tg action.

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