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BIOMD0000000324 - Morris1981_MuscleFibre_Voltage_full

 

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Reference Publication
Publication ID: 7260316
Morris C, Lecar H.
Voltage oscillations in the barnacle giant muscle fiber.
Biophys. J. 1981 Jul; 35(1): 193-213
  [more]
Model
Original Model: BIOMD0000000324.xml.origin
Submitter: Lukas Endler
Submission ID: MODEL1011230001
Submission Date: 23 Nov 2010 22:52:31 UTC
Last Modification Date: 31 Mar 2011 00:49:12 UTC
Creation Date: 31 Mar 2011 00:20:52 UTC
Encoders:  Lukas Endler
set #1
bqbiol:isVersionOf Gene Ontology action potential
set #2
bqbiol:hasVersion Gene Ontology voltage-gated potassium channel activity
Gene Ontology voltage-gated calcium channel activity
set #3
bqbiol:hasProperty Mathematical Modelling Ontology MAMO_0000046
set #4
bqbiol:hasTaxon Taxonomy Balanus nubilus
Notes

This is the full model (eq. 1 and 2) of the voltage oscillations in barnacle muscle fibers described in the article:
Voltage oscillations in the barnacle giant muscle fiber.
Morris C, Lecar H. Biophys J. 1981 Jul;35(1):193-213. PubmedID:7260316; DOI:10.1016/S0006-3495(81)84782-0
Abstract:
Barnacle muscle fibers subjected to constant current stimulation produce a variety of types of oscillatory behavior when the internal medium contains the Ca++ chelator EGTA. Oscillations are abolished if Ca++ is removed from the external medium, or if the K+ conductance is blocked. Available voltage-clamp data indicate that the cell's active conductance systems are exceptionally simple. Given the complexity of barnacle fiber voltage behavior, this seems paradoxical. This paper presents an analysis of the possible modes of behavior available to a system of two noninactivating conductance mechanisms, and indicates a good correspondence to the types of behavior exhibited by barnacle fiber. The differential equations of a simple equivalent circuit for the fiber are dealt with by means of some of the mathematical techniques of nonlinear mechanics. General features of the system are (a) a propensity to produce damped or sustained oscillations over a rather broad parameter range, and (b) considerable latitude in the shape of the oscillatory potentials. It is concluded that for cells subject to changeable parameters (either from cell to cell or with time during cellular activity), a system dominated by two noninactivating conductances can exhibit varied oscillatory and bistable behavior.

The model consists of the differential equations (1) and (2) given on pages 195 and 196 of the article. There is one typo in the equation for I in (1), gL(VL) should be gL(V - VL). This was changed in the SBML file. As there are no current values given, for reproducing the time courses in figure 6 an applied current of 50 uA was assumed. The legend for the broken and the full line in this figure seems to be confounded in the article.

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

Model
Publication ID: 7260316 Submission Date: 23 Nov 2010 22:52:31 UTC Last Modification Date: 31 Mar 2011 00:49:12 UTC Creation Date: 31 Mar 2011 00:20:52 UTC
Mathematical expressions
Rules
Assignment Rule (variable: Minf) Rate Rule (variable: V) Assignment Rule (variable: Ninf) Assignment Rule (variable: lambdaN)
Assignment Rule (variable: lambdaM) Rate Rule (variable: N) Rate Rule (variable: M)  
Physical entities
Compartments Species
musclefibre      
Global parameters
Minf V V1 V2
Ninf V3 V4 lambdaN
lambdaN_bar lambdaM lambdaM_bar I
gL VL gCa VCa
gK N VK C
M      
Reactions (0)
Rules (7)
 
 Assignment Rule (name: Minf) Minf = (1+tanh((V-V1)/V2))/2
 
 Rate Rule (name: V) d [ V] / d t= (Iapp-gL*(V-VL)-gCa*M*(V-VCa)-gK*N*(V-VK))/C
 
 Assignment Rule (name: Ninf) Ninf = (1+tanh((V-V3)/V4))/2
 
 Assignment Rule (name: lambdaN) lambdaN = lambdaN_bar*cosh((V-V3)/(2*V4))
 
 Assignment Rule (name: lambdaM) lambdaM = lambdaM_bar*cosh((V-V1)/(2*V2))
 
 Rate Rule (name: N) d [ N] / d t= lambdaN*(Ninf-N)
 
 Rate Rule (name: M) d [ M] / d t= lambdaM*(Minf-M)
 
  Spatial dimensions: 3.0  Compartment size: 1.0
Global Parameters (21)
 
  Minf
Value: NaN   (Units: dimensionless)
 
 V
Value: -50.0   (Units: mV)
 
 V1
Constant
 
 V2
Value: 15.0   (Units: mV)
Constant
 
  Ninf
Value: NaN   (Units: dimensionless)
 
 V3
Value: 10.0   (Units: mV)
Constant
 
 V4
Value: 10.0   (Units: mV)
Constant
 
  lambdaN
Value: NaN   (Units: per ms)
 
 lambdaN_bar
Value: 0.1   (Units: per ms)
Constant
 
  lambdaM
Value: NaN   (Units: per ms)
 
 lambdaM_bar
Value: 1.0   (Units: per ms)
Constant
 
 I
Value: 50.0   (Units: microA_per_cm2)
Constant
 
 gL
Value: 2.0   (Units: mS_per_cm2)
Constant
 
 VL
Value: -50.0   (Units: mV)
Constant
 
 gCa
Value: 4.0   (Units: mS_per_cm2)
Constant
 
 VCa
Value: 100.0   (Units: mV)
Constant
 
 gK
Value: 8.0   (Units: mS_per_cm2)
Constant
 
 N
Value: NaN   (Units: dimensionless)
 
 VK
Value: -70.0   (Units: mV)
Constant
 
 C
Value: 20.0   (Units: microF per cm2)
Constant
 
 M
Value: NaN   (Units: dimensionless)
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000324

Curator's comment: (updated: 31 Mar 2011 01:20:28 BST)

Time courses calculated with CopasiUI v4.6.33 as in figure 6 of the publication.

As there is no applied current given, I=50 uA/cm2 was taken. gCA and gK where taken as indicated in the graph.

The other parameter values used where: gL = 2, VL = - 50, VCa = 100, VK = -70, lambdaM_bar = 1 -0, lambdaN_bar = 0.1, V1 = 0, V2 = 15, V3 = 10, V4 = 10, C = 20. The legend of the two curves in figure 6 seems to be mixed up in respect to the values of gCA and gK used.

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