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BIOMD0000000346 - FitzHugh1961_NerveMembrane

 

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Reference Publication
Publication ID: 19431309
Fitzhugh R.
Impulses and Physiological States in Theoretical Models of Nerve Membrane.
Biophys. J. 1961 Jul; 1(6): 445-466
  [more]
Model
Original Model: BIOMD0000000346.origin
Submitter: Vijayalakshmi Chelliah
Submission ID: MODEL0911929415
Submission Date: 28 Apr 2009 13:20:23 UTC
Last Modification Date: 20 Apr 2012 21:37:02 UTC
Creation Date: 28 Apr 2009 13:20:23 UTC
Encoders:  Nicolas Le Novère
set #1
bqbiol:hasTaxon Taxonomy cellular organisms
bqbiol:isVersionOf Gene Ontology transmission of nerve impulse
bqbiol:occursIn Brenda Tissue Ontology nerve
Notes

This is the original model from Richard FitzHugh, which led the famous FitzHugh–Nagumo model, still used for instance in computational neurosciences.
Impulses and Physiological States in Theoretical Models of Nerve Membrane
FitzHugh R Biophysical Journal, 1961 July:1(6):445-466 doi:10.1016/S0006-3495(61)86902-6 ,
Abstract:
Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle. The resulting BVP model has two variables of state, representing excitability and refractoriness, and qualitatively resembles Bonhoeffer's theoretical model for the iron wire model of nerve. This BVP model serves as a simple representative of a class of excitable-oscillatory systems including the Hodgkin-Huxley (HH) model of the squid giant axon. The BVP phase plane can be divided into regions corresponding to the physiological states of nerve fiber (resting, active, refractory, enhanced, depressed, etc.) to form a physiological state diagram, with the help of which many physiological phenomena can be summarized. A properly chosen projection from the 4-dimensional HH phase space onto a plane produces a similar diagram which shows the underlying relationship between the two models. Impulse trains occur in the BVP and HH models for a range of constant applied currents which make the singular point representing the resting state unstable.

This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2012 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: 19431309 Submission Date: 28 Apr 2009 13:20:23 UTC Last Modification Date: 20 Apr 2012 21:37:02 UTC Creation Date: 28 Apr 2009 13:20:23 UTC
Mathematical expressions
Rules
Rate Rule (variable: x) Rate Rule (variable: y)    
Physical entities
Compartments Species
compartment x y  
Global parameters
a b c z
Reactions (0)
Rules (2)
 
 Rate Rule (name: x) d [ x] / d t= c*(x+(-x^3/3)+y+z)
 
 Rate Rule (name: y) d [ y] / d t= (-1/c)*(x+(-a)+b*y)
 
   compartment Spatial dimensions: 3.0  Compartment size: 1.0
 
   x
Compartment: compartment
Initial concentration: -1.0
 
   y
Compartment: compartment
Initial concentration: 0.5
 
Global Parameters (4)
 
 a
Value: 0.7   (Units: dimensionless)
Constant
 
 b
Value: 0.8   (Units: dimensionless)
Constant
 
 c
Value: 3.0   (Units: dimensionless)
Constant
 
 z
Value: -0.4   (Units: dimensionless)
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000346

Curator's comment: (updated: 09 Aug 2011 00:39:06 BST)

Reproduction of the timecourse shown on Figure 2 of the original paper. The right panel present the phase-plane, equivalent to Figure 1 of the paper but with z=-0.4. Simulations ran in Copasi 4.7.

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