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BIOMD0000000304 - Plant1981_BurstingNerveCells

 

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Reference Publication
Publication ID: 7252375
Plant RE.
Bifurcation and resonance in a model for bursting nerve cells.
J Math Biol 1981 Jan; 11(1): 15-32
  [more]
Model
Original Model: BIOMD0000000304.xml.origin
Submitter: Harish Dharuri
Submission ID: MODEL6762427183
Submission Date: 30 Sep 2006 17:30:12 UTC
Last Modification Date: 19 Aug 2011 12:02:24 UTC
Creation Date: 24 May 2006 10:35:07 UTC
Encoders:  Vijayalakshmi Chelliah
set #1
bqbiol:isVersionOf Gene Ontology potassium ion transport
Gene Ontology sodium ion transport
Gene Ontology calcium ion transport
Gene Ontology neuronal action potential
bqbiol:hasTaxon Taxonomy Aplysia
Brenda Tissue Ontology BTO:0000938
Brenda Tissue Ontology BTO:0000022
set #2
bqbiol:hasProperty Mathematical Modelling Ontology MAMO_0000046
Notes

This a model from the article:
Bifurcation and resonance in a model for bursting nerve cells.
Plant RE J Math Biol1981 Jan; 11(1): 15-32 7252375,
Abstract:
In this paper we consider a model for the phenomenon of bursting in nerve cells. Experimental evidence indicates that this phenomenon is due to the interaction of multiple conductances with very different kinetics, and the model incorporates this evidence. As a parameter is varied the model undergoes a transition between two oscillatory waveforms; a corresponding transition is observed experimentally. After establishing the periodicity of the subcritical oscillatory solution, the nature of the transition is studied. It is found to be a resonance bifurcation, with the solution branching at the critical point to another periodic solution of the same period. Using this result a comparison is made between the model and experimental observations. The model is found to predict and allow an interpretation of these observations.

Also, look at http://www.scholarpedia.org/article/Plant_model

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: 7252375 Submission Date: 30 Sep 2006 17:30:12 UTC Last Modification Date: 19 Aug 2011 12:02:24 UTC Creation Date: 24 May 2006 10:35:07 UTC
Mathematical expressions
Rules
Assignment Rule (variable: Vs) Assignment Rule (variable: alpha_m) Assignment Rule (variable: beta_m) Assignment Rule (variable: m_infinity)
Assignment Rule (variable: alpha_h) Assignment Rule (variable: beta_h) Assignment Rule (variable: h_infinity) Assignment Rule (variable: tau_h)
Rate Rule (variable: h1) Assignment Rule (variable: i_Na) Assignment Rule (variable: x_infinity) Rate Rule (variable: x1)
Assignment Rule (variable: i_Ca) Assignment Rule (variable: alpha_n) Assignment Rule (variable: beta_n) Assignment Rule (variable: n_infinity)
Assignment Rule (variable: tau_n) Rate Rule (variable: n1) Assignment Rule (variable: i_K) Rate Rule (variable: c)
Assignment Rule (variable: i_K_Ca) Assignment Rule (variable: i_L) Rate Rule (variable: V)  
Physical entities
Compartments Species
COMpartment V h1 x1
n1 c  
Global parameters
i_Na V_I V_K V_L
V_Ca g_I g_K g_T
g_K_Ca g_L K_p K_c
f tau_x a b
Vs m_infinity alpha_m beta_m
h_infinity alpha_h beta_h tau_h
g_Ca x_infinity i_Ca n_infinity
i_K alpha_n beta_n tau_n
i_K_Ca i_L    
Reactions (0)
Rules (23)
 
 Assignment Rule (name: Vs) Vs = a*V_membrane+b
 
 Assignment Rule (name: alpha_m) alpha_m = 0.1*(50-Vs)/(exp((50-Vs)/10)-1)
 
 Assignment Rule (name: beta_m) beta_m = 4*exp((25-Vs)/18)
 
 Assignment Rule (name: m_infinity) m_infinity = alpha_m/(alpha_m+beta_m)
 
 Assignment Rule (name: alpha_h) alpha_h = 0.07*exp((25-Vs)/20)
 
 Assignment Rule (name: beta_h) beta_h = 1/(exp((55-Vs)/10)+1)
 
 Assignment Rule (name: h_infinity) h_infinity = alpha_h/(alpha_h+beta_h)
 
 Assignment Rule (name: tau_h) tau_h = 12.5/(alpha_h+beta_h)
 
 Rate Rule (name: h1) d [ h1] / d t= (h_infinity-h1)/tau_h
 
 Assignment Rule (name: i_Na) i_Na = g_I*m_infinity^3*h1*(V_I-V_membrane)
 
 Assignment Rule (name: x_infinity) x_infinity = 1/(exp(0.15*(-V_membrane-50))+1)
 
 Rate Rule (name: x1) d [ x1] / d t= (x_infinity-x1)/tau_x
 
 Assignment Rule (name: i_Ca) i_Ca = g_T*x1*(V_I-V_membrane)
 
 Assignment Rule (name: alpha_n) alpha_n = 0.01*(55-Vs)/(exp((55-Vs)/10)-1)
 
 Assignment Rule (name: beta_n) beta_n = 0.125*exp((45-Vs)/80)
 
 Assignment Rule (name: n_infinity) n_infinity = alpha_n/(alpha_n+beta_n)
 
 Assignment Rule (name: tau_n) tau_n = 12.5/(alpha_n+beta_n)
 
 Rate Rule (name: n1) d [ n1] / d t= (n_infinity-n1)/tau_n
 
 Assignment Rule (name: i_K) i_K = g_K*n1^4*(V_K-V_membrane)
 
 Rate Rule (name: c) d [ c] / d t= f*(K_c*x1*(V_Ca-V_membrane)-c)
 
 Assignment Rule (name: i_K_Ca) i_K_Ca = g_K_Ca*c/(K_p+c)*(V_K-V_membrane)
 
 Assignment Rule (name: i_L) i_L = g_L*(V_L-V_membrane)
 
 Rate Rule (name: V_membrane) d [ V] / d t= i_Na+i_Ca+i_K+i_K_Ca+i_L
 
   Spatial dimensions: 3.0  Compartment size: 1.0
 
 V
Compartment: COMpartment
Initial concentration: -55.0
 
 h1
Compartment: COMpartment
Initial concentration: 0.9
 
 x1
Compartment: COMpartment
Initial concentration: 0.27
 
 n1
Compartment: COMpartment
Initial concentration: 0.03
 
 c
Compartment: COMpartment
Initial concentration: 0.4
 
Global Parameters (34)
 
   i_Na
Value: NaN
 
   V_I
Value: 30.0
Constant
 
   V_K
Value: -75.0
Constant
 
   V_L
Value: -40.0
Constant
 
   V_Ca
Value: 140.0
Constant
 
   g_I
Value: 4.0
Constant
 
   g_K
Value: 0.3
Constant
 
   g_T
Value: 0.01
Constant
 
   g_K_Ca
Value: 0.03
Constant
 
   g_L
Value: 0.0030
Constant
 
   K_p
Value: 0.5
Constant
 
   K_c
Value: 0.0085
Constant
 
   f
Value: 3.0E-4
Constant
 
   tau_x
Value: 235.0
Constant
 
   a
Value: 1.209
Constant
 
   b
Value: 78.714
Constant
 
   Vs
Value: NaN
 
   m_infinity
Value: NaN
 
   alpha_m
Value: NaN
 
   beta_m
Value: NaN
 
   h_infinity
Value: NaN
 
   alpha_h
Value: NaN
 
   beta_h
Value: NaN
 
   tau_h
Value: NaN
 
   g_Ca
Value: 0.0040
 
   x_infinity
Value: NaN
 
   i_Ca
Value: NaN
 
   n_infinity
Value: NaN
 
   i_K
Value: NaN
 
   alpha_n
Value: NaN
 
   beta_n
Value: NaN
 
   tau_n
Value: NaN
 
   i_K_Ca
Value: NaN
 
   i_L
Value: NaN
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000304

Curator's comment: (updated: 19 Aug 2011 12:41:21 BST)

Figures 1 and 2 (here A and B, respectively) of the reference publication has been reproduced here. The model as such reproduces figure 1. Figure 2 can be obtained by setting g_I to 0. The model was integrated and simulated using Copasi v4.6 (Build 32).

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