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BIOMD0000000020 - Hodgkin-Huxley1952 squid-axon

 

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Reference Publication
Publication ID: 12991237
HODGKIN AL, HUXLEY AF.
A quantitative description of membrane current and its application to conduction and excitation in nerve.
J. Physiol. (Lond.) 1952 Aug; 117(4): 500-544
  [more]
Model
Original Model: BIOMD0000000020.xml.origin
Submitter: Nicolas Le Novère
Submission ID: MODEL6617668482
Submission Date: 13 Sep 2005 13:22:40 UTC
Last Modification Date: 02 Feb 2011 23:00:36 UTC
Creation Date: 31 Mar 2005 13:09:21 UTC
Encoders:  Maria Schilstra
   Catherine Lloyd
   Lukas Endler
set #1
bqbiol:occursIn Taxonomy Loligo forbesi
Gene Ontology giant axon
bqbiol:isVersionOf Gene Ontology voltage-gated potassium channel activity
Gene Ontology voltage-gated sodium channel activity
Gene Ontology neuronal action potential propagation
Notes

This is an implementation of the Hodgkin-Huxley model of the electrical behavior of the squid axon membrane from:
A quantitative description of membrane current and its application to conduction and excitation in nerve.
A. L. Hodgkin and A. F. Huxley. (1952 ) Journal of Physiology 119(4): pp 500-544; pmID: 12991237 .

Abstract:
This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre (Hodgkin,Huxley & Katz, 1952; Hodgkin & Huxley, 1952 a-c). Its general object is to discuss the results of the preceding papers (Part I), to put them into mathematical form (Part II) and to show that they will account for conduction and excitation in quantitative terms (Part III).

This SBML model uses the same formalism as the one described in the paper, contrary to modern versions:
* V describes the the membrane depolarisation relative to the resting potential of the membrane
* opposing to modern practice, depolarization is negative , not positive , so the sign of V is different
* inward transmembrane currents are considered positive (inward current positive), contrary to modern use
The changeable parameters are the equilibrium potentials( E_R, E_K, E_L, E_Na ), the membrane depolarization ( V ) and the initial sodium and potassium channel activation and inactivation coefficients ( m,h,n ). The initial values of m,h,n for the model were calculated for V = 0 using the equations from the article: n t=0 = α_n V=0 /(α_n V=0 + β_n V=0 ) and equivalent expressions for h and m .
For single excitations apply a negative membrane depolarization (V < 0). To achieve oscillatory behavior either change the resting potential to a more positive value or apply a constant negative ionic current (I < 0).
Two assignments for parameters in the model, alpha_n and alpha_m, are not defined at V=-10 resp. -25 mV. We did not change this to keep the formulas similar to the original publication and as most integrators seem not to have any problem with it. The limits at V=-10 and -25 mV are 0.1 for alpha_n resp. 1 for alpha_m.
We thank Mark W. Johnson for finding a bug in the model and his helpful comments.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2009 The BioModels Team.
For more information see the terms of use .
To cite BioModels Database, please use Le Novère N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

Model
Publication ID: 12991237 Submission Date: 13 Sep 2005 13:22:40 UTC Last Modification Date: 02 Feb 2011 23:00:36 UTC Creation Date: 31 Mar 2005 13:09:21 UTC
Mathematical expressions
Rules
Assignment Rule (variable: V_neg) Assignment Rule (variable: E) Assignment Rule (variable: V_L) Assignment Rule (variable: beta_n)
Assignment Rule (variable: auxiliary alpha_h) Assignment Rule (variable: V_Na) Assignment Rule (variable: V_K) Assignment Rule (variable: i_K)
Assignment Rule (variable: i_Na) Assignment Rule (variable: i_L) Assignment Rule (variable: beta_m) Assignment Rule (variable: alpha_n)
Assignment Rule (variable: alpha_m) Assignment Rule (variable: beta_h) Rate Rule (variable: V) Rate Rule (variable: m)
Rate Rule (variable: h) Rate Rule (variable: n)    
Physical entities
Compartments Species
unit_compartment      
Global parameters
V V_neg E I
i_Na i_K i_L m
h n E_R Cm
g_Na g_K g_L E_Na
E_K E_L V_Na V_K
V_L alpha_m beta_m auxiliary alpha_h
beta_h alpha_n beta_n  
Reactions (0)
Rules (18)
 
 Assignment Rule (name: V_neg) V_neg = -V
 
 Assignment Rule (name: E) E = V+E_R
 
 Assignment Rule (name: V_L) V_L = E_L-E_R
 
 Assignment Rule (name: beta_n) beta_n = 0.125*exp(V/80)
 
 Assignment Rule (name: alpha_h) auxiliary alpha_h = 0.07*exp(V/20)
 
 Assignment Rule (name: V_Na) V_Na = E_Na-E_R
 
 Assignment Rule (name: V_K) V_K = E_K-E_R
 
 Assignment Rule (name: i_K) i_K = g_K*n^4*(V-V_K)
 
 Assignment Rule (name: i_Na) i_Na = g_Na*m^3*h*(V-V_Na)
 
 Assignment Rule (name: i_L) i_L = g_L*(V-V_L)
 
 Assignment Rule (name: beta_m) beta_m = 4*exp(V/18)
 
 Assignment Rule (name: alpha_n) alpha_n = 0.01*(V+10)/(exp((V+10)/10)-1)
 
 Assignment Rule (name: alpha_m) alpha_m = 0.1*(V+25)/(exp((V+25)/10)-1)
 
 Assignment Rule (name: beta_h) beta_h = 1/(exp((V+30)/10)+1)
 
 Rate Rule (name: V) d [ V] / d t= (I-(i_Na+i_K+i_L))/Cm
 
 Rate Rule (name: m) d [ m] / d t= alpha_m*(1-m)-beta_m*m
 
 Rate Rule (name: h) d [ h] / d t= alpha_h*(1-h)-beta_h*h
 
 Rate Rule (name: n) d [ n] / d t= alpha_n*(1-n)-beta_n*n
 
   unit_compartment Spatial dimensions: 3.0  Compartment size: 1.0
Global Parameters (27)
 
 V  
 
  V_neg
Value: NaN   (Units: mV)
 
  E
Value: NaN   (Units: mV)
 
 I
Constant
 
  i_Na
Value: NaN
 
  i_K
Value: NaN
 
  i_L
Value: NaN
 
 m
Value: 0.052932
 
 h
Value: 0.59612
 
 n
Value: 0.31768
 
 E_R
Value: -75.0   (Units: mV)
Constant
 
 Cm
Value: 1.0
Constant
 
 g_Na
Value: 120.0
Constant
 
 g_K
Value: 36.0
Constant
 
 g_L
Value: 0.3
Constant
 
 E_Na
Value: -190.0   (Units: mV)
Constant
 
 E_K
Value: -63.0   (Units: mV)
Constant
 
 E_L
Value: -85.613   (Units: mV)
Constant
 
  V_Na
Value: -115.0   (Units: mV)
 
  V_K
Value: 12.0   (Units: mV)
 
  V_L
Value: -10.613   (Units: mV)
 
  alpha_m
Value: NaN
 
  beta_m
Value: NaN
 
  auxiliary alpha_h
Value: NaN
 
  beta_h
Value: NaN
 
  alpha_n
Value: NaN
 
  beta_n
Value: NaN
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000020

Curator's comment: (updated: 30 Jun 2009 17:34:39 BST)

Reproduction of fig. 12 from the original publication, Calculations performed using SBML ODESolver with the -j option to suppress analytic Jacobian Matrix derivation.

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