Reduced leech heart interneuron (Channell et al. 2009)

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Accession:125125
"Spiking and bursting patterns of neurons are characterized by a high degree of variability. A single neuron can demonstrate endogenously various bursting patterns, changing in response to external disturbances due to synapses, or to intrinsic factors such as channel noise. We argue that in a model of the leech heart interneuron existing variations of bursting patterns are significantly enhanced by a small noise. In the absence of noise this model shows periodic bursting with fixed numbers of interspikes for most parameter values. ..."
Reference:
1 . Channell P, Fuwape I, Neiman AB, Shilnikov AL (2009) Variability of bursting patterns in a neuron model in the presence of noise. J Comput Neurosci 27:527-42 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism: Leech;
Cell Type(s): Leech heart interneuron;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: CONTENT; Dynamics Solver;
Model Concept(s):
Implementer(s):
Version = 181
Identifier      = 
;
[Type]
Single ODE      = No
System of ODEs  = Yes
Map             = No
Dimension/Order = 9
Stack length    = 1000
P-code length   = 10000
Heaviside(0)    = 0.5
;
[Variables]
Independent variable      = t
Dependent variable(s)     = x
Individual names:
V1
m1
h1
V2
m2
h2
V3
m3
h3
Independent variable(0)   = t0
Dependent variable(0)     = x0
Individual names(0):











;
[Parameters]
Parameters                = 13
GK2 = 30
EK = -0.07
ENa = 0.045
GNa = 160
GI = 8
Pol = -0.012
K2shft = -0.02
shftNam = 0.0035
shftNah = 0.0065
tauK2 = 0.9
tauhNa = 0.0405
EI = -0.046
Esyn = -0.0625
Poincare/Bifurcation time = tp
Phase-portrait x min      = 0
Phase-portrait x name     = nx
Phase-portrait x max      = 0
Phase-portrait y min      = 0
Phase-portrait y name     = ny
Phase-portrait y max      = 0
;
[Equations]
Definitions:
-2*(GK2*m1*m1*(V1-EK)+GNa*1/(1+exp(-150*(V1+0.027+shftNam)))^3*h1*(V1-ENa)+GI*(V1-EI)+Pol)
(1/(1+exp(-83*(V1+0.018+K2shft+0.0)))-m1)/tauK2
(1/(1+exp(500*(V1+0.026+shftNah)))-h1)/tauhNa
-2*(GK2*m2*m2*(V2-EK)+GNa*1/(1+exp(-150*(V2+0.027+shftNam)))^3*h2*(V2-ENa)+GI*(V2-EI)+Pol)
(1/(1+exp(-83*(V2+0.018+K2shft+0.0)))-m2)/tauK2
(1/(1+exp(500*(V2+0.026+shftNah)))-h2)/tauhNa
0
0
0
Delay                     = 0
Discontinuities           = 
;
[Initial values]
Independent variable      = 0
Dependent variable(s):
-0.08
1
0
0
0
0
0
0
0
0
0
Initial functions:









Point                     = 0
Iterations                = 0
Error                     = 1e-05
Boundary functions:









;
[Range]
First value               = 0
Last value                = 1e+20
Infinity                  = 1e+20
Interpolate               = Yes
Step                      = 0.002
Backward                  = No
Pause                     = 0
Retarded points           = 100
Real time                 = 0
Auto start                = No
Idle                      = No
Lowest                    = No
Below normal              = No
Normal                    = Yes
Above normal              = No
Highest                   = No
Time critical             = No
;
[Method]
Tolerance                 = 1e-05
h                         = 0.001
h max.                    = 0.001
Integration code          = Runge-Kutta 4
;
[Status line]
First expression          = t
Second expression         = x[1]
Numerical format          = t = %g   x = %g
Frequency                 = 0
;
[Mathematica]
Initialization            = 
;
[Graphics window] = 0.116429,-0.0197095,0.409286,0.595436,0
Title                 = (m,V)
Window                = 
Min. X                = -0.01
X axis                = m1
Max. X                = 0.6
Min. Y                = -0.06
Y axis                = V1
Max. Y                = 0.04
Continuous line       = Yes
Frequency             = 1
Direction field       = No
Cell length           = 24
Mark length           = 12
Axes location         = 
Drawing color         = FF0000
Drawing width         = 0
Grid color            = 0
Grid width            = 0
Direction field color = 0
Direction field width = 0
Background color      = FFFFFF
Width (px)            = 0
Height (px)           = 0
Arbitrary aspect      = Yes
Adjust X range        = No
Adjust Y range        = No
Square                = No
Adjust width          = No
Adjust height         = No
Poincare section      = No
Condition             = 
Error                 = 1e-05
Increasing            = No
Decreasing            = No
Capture               = 1
Select in X axis      = 2
Select in Y axis      = 1
Step in X axis        = 0.0001
Step in Y axis        = 0.0001
Angular step          = 15
Zoom factor           = 10
Fractal order         = 0
Plotter               = No
Frame                 = Yes
Pen                   = 3
Width                 = 0
Speed                 = 0
Line type             = 0
Device                = 
Driver                = 
No bitmap             = No
Copy bitmap           = No
Stretch bitmap        = Yes
Phi                   = 30
Theta                 = 60
Psi                   = 90
Origin                = 0
Distance              = 0
Print Info            = No
Total X               = 0
Total Y               = 0
Left margin           = 0
Print width           = 0
Top margin            = 0
Print height          = 0
Print unit            = 0
Print mode            = 0
Pixels per point      = 0
Basic width           = 0
Frame width           = 0
Min. distance         = 0
Print EPSF            = No
Invert print          = No
Include elements      = No
Preserve aspect       = No
Rotate PS             = No
EPSF File             = 
Post process          = No
Post program          = 
Post arguments        = 
Post delete           = No
;
[Graphics window] = 0.543571,-0.00414938,0.27,0.353734,0
Title                 = (h,V)
Window                = 
Min. X                = -0.02
X axis                = h1
Max. X                = 1.02
Min. Y                = -0.07
Y axis                = V1
Max. Y                = 0.04
Continuous line       = Yes
Frequency             = 1
Direction field       = No
Cell length           = 24
Mark length           = 12
Axes location         = 
Drawing color         = FF0000
Drawing width         = 0
Grid color            = 0
Grid width            = 0
Direction field color = 0
Direction field width = 0
Background color      = FFFFFF
Width (px)            = 0
Height (px)           = 0
Arbitrary aspect      = Yes
Adjust X range        = No
Adjust Y range        = No
Square                = No
Adjust width          = No
Adjust height         = No
Poincare section      = No
Condition             = 
Error                 = 1e-05
Increasing            = No
Decreasing            = No
Capture               = 1
Select in X axis      = 1
Select in Y axis      = 2
Step in X axis        = 0.01
Step in Y axis        = 0.01
Angular step          = 15
Zoom factor           = 10
Fractal order         = 0
Plotter               = No
Frame                 = Yes
Pen                   = 1
Width                 = 0
Speed                 = 0
Line type             = 0
Device                = 
Driver                = 
No bitmap             = No
Copy bitmap           = No
Stretch bitmap        = Yes
Phi                   = 30
Theta                 = 60
Psi                   = 90
Origin                = 0
Distance              = 0
Print Info            = No
Total X               = 0
Total Y               = 0
Left margin           = 0
Print width           = 0
Top margin            = 0
Print height          = 0
Print unit            = 0
Print mode            = 0
Pixels per point      = 0
Basic width           = 0
Frame width           = 0
Min. distance         = 0
Print EPSF            = No
Invert print          = No
Include elements      = No
Preserve aspect       = No
Rotate PS             = No
EPSF File             = 
Post process          = No
Post program          = 
Post arguments        = 
Post delete           = No
;
[Graphics window] = -0.00571429,0.603734,0.93,0.328838,0
Title                 = (t,  V)
Window                = 
Min. X                = 0
X axis                = t
Max. X                = 200
Min. Y                = -0.1
Y axis                = V1+.034
Max. Y                = 0.1
Continuous line       = Yes
Frequency             = 1
Direction field       = No
Cell length           = 24
Mark length           = 12
Axes location         = 
Drawing color         = FF0000
Drawing width         = 0
Grid color            = 0
Grid width            = 0
Direction field color = 0
Direction field width = 0
Background color      = FFFFFF
Width (px)            = 0
Height (px)           = 0
Arbitrary aspect      = Yes
Adjust X range        = No
Adjust Y range        = No
Square                = No
Adjust width          = No
Adjust height         = No
Poincare section      = No
Condition             = 
Error                 = 1e-05
Increasing            = No
Decreasing            = No
Capture               = 1
Select in X axis      = 1
Select in Y axis      = 2
Step in X axis        = 0.0001
Step in Y axis        = 0.0001
Angular step          = 15
Zoom factor           = 10
Fractal order         = 0
Plotter               = No
Frame                 = Yes
Pen                   = 1
Width                 = 0
Speed                 = 0
Line type             = 0
Device                = 
Driver                = 
No bitmap             = No
Copy bitmap           = No
Stretch bitmap        = Yes
Phi                   = 30
Theta                 = 60
Psi                   = 90
Origin                = 0
Distance              = 0
Print Info            = No
Total X               = 0
Total Y               = 0
Left margin           = 0
Print width           = 0
Top margin            = 0
Print height          = 0
Print unit            = 0
Print mode            = 0
Pixels per point      = 0
Basic width           = 0
Frame width           = 0
Min. distance         = 0
Print EPSF            = No
Invert print          = No
Include elements      = No
Preserve aspect       = No
Rotate PS             = No
EPSF File             = 
Post process          = No
Post program          = 
Post arguments        = 
Post delete           = No
;
[Graphics window] = 0.191429,0.370332,0.265714,0.35166,-1
Title                 = (m2,V2)
Window                = 
Min. X                = 0
X axis                = m2
Max. X                = 0.5
Min. Y                = -0.07
Y axis                = V2
Max. Y                = 0.04
Continuous line       = Yes
Frequency             = 1
Direction field       = No
Cell length           = 24
Mark length           = 12
Axes location         = 
Drawing color         = FF
Drawing width         = 0
Grid color            = 0
Grid width            = 0
Direction field color = 0
Direction field width = 0
Background color      = FFFFFF
Width (px)            = 0
Height (px)           = 0
Arbitrary aspect      = Yes
Adjust X range        = No
Adjust Y range        = No
Square                = No
Adjust width          = No
Adjust height         = No
Poincare section      = No
Condition             = 
Error                 = 1e-05
Increasing            = No
Decreasing            = No
Capture               = 1
Select in X axis      = 2
Select in Y axis      = 1
Step in X axis        = 0.0001
Step in Y axis        = 0.0001
Angular step          = 15
Zoom factor           = 10
Fractal order         = 0
Plotter               = No
Frame                 = Yes
Pen                   = 1
Width                 = 0
Speed                 = 0
Line type             = 0
Device                = 
Driver                = 
No bitmap             = No
Copy bitmap           = No
Stretch bitmap        = Yes
Phi                   = 30
Theta                 = 60
Psi                   = 90
Origin                = 0
Distance              = 0
Print Info            = No
Total X               = 0
Total Y               = 0
Left margin           = 0
Print width           = 0
Top margin            = 0
Print height          = 0
Print unit            = 0
Print mode            = 0
Pixels per point      = 0
Basic width           = 0
Frame width           = 0
Min. distance         = 0
Print EPSF            = No
Invert print          = No
Include elements      = No
Preserve aspect       = No
Rotate PS             = No
EPSF File             = 
Post process          = No
Post program          = 
Post arguments        = 
Post delete           = No
;
[Graphics window] = 0.0207143,0.56639,0.292857,0.379668,-1
Title                 = (m',V)
Window                = (m,V)
Min. X                = -0
X axis                = 1/(1+exp(-83*(t+0.018+K2shft)))
Max. X                = 0.5
Min. Y                = -0.07
Y axis                = t
Max. Y                = 0.04
Continuous line       = Yes
Frequency             = 1
Direction field       = No
Cell length           = 24
Mark length           = 12
Axes location         = 
Drawing color         = FFFF
Drawing width         = 0
Grid color            = 0
Grid width            = 0
Direction field color = 0
Direction field width = 0
Background color      = FFFFFF
Width (px)            = 0
Height (px)           = 0
Arbitrary aspect      = Yes
Adjust X range        = No
Adjust Y range        = No
Square                = No
Adjust width          = No
Adjust height         = No
Poincare section      = No
Condition             = 
Error                 = 1e-05
Increasing            = No
Decreasing            = No
Capture               = 1
Select in X axis      = 1
Select in Y axis      = 2
Step in X axis        = 0.01
Step in Y axis        = 0.01
Angular step          = 15
Zoom factor           = 10
Fractal order         = 0
Plotter               = No
Frame                 = Yes
Pen                   = 1
Width                 = 0
Speed                 = 0
Line type             = 0
Device                = 
Driver                = 
No bitmap             = No
Copy bitmap           = No
Stretch bitmap        = Yes
Phi                   = 30
Theta                 = 60
Psi                   = 90
Origin                = 0
Distance              = 0
Print Info            = No
Total X               = 0
Total Y               = 0
Left margin           = 0
Print width           = 0
Top margin            = 0
Print height          = 0
Print unit            = 0
Print mode            = 0
Pixels per point      = 0
Basic width           = 0
Frame width           = 0
Min. distance         = 0
Print EPSF            = No
Invert print          = No
Include elements      = No
Preserve aspect       = No
Rotate PS             = No
EPSF File             = 
Post process          = No
Post program          = 
Post arguments        = 
Post delete           = No
;
[Graphics window] = -0.00642857,0.771784,0.894286,0.190871,-1
Title                 = (t,  V2)
Window                = (t,  V)
Min. X                = 0
X axis                = t
Max. X                = 1000
Min. Y                = -5
Y axis                = V2-0.05
Max. Y                = 15
Continuous line       = Yes
Frequency             = 1
Direction field       = No
Cell length           = 24
Mark length           = 12
Axes location         = 
Drawing color         = FF00
Drawing width         = 0
Grid color            = 0
Grid width            = 0
Direction field color = 0
Direction field width = 0
Background color      = FFFFFF
Width (px)            = 0
Height (px)           = 0
Arbitrary aspect      = Yes
Adjust X range        = No
Adjust Y range        = No
Square                = No
Adjust width          = No
Adjust height         = No
Poincare section      = No
Condition             = 
Error                 = 1e-05
Increasing            = No
Decreasing            = No
Capture               = 1
Select in X axis      = 1
Select in Y axis      = 2
Step in X axis        = 0.01
Step in Y axis        = 0.01
Angular step          = 15
Zoom factor           = 10
Fractal order         = 0
Plotter               = No
Frame                 = Yes
Pen                   = 1
Width                 = 0
Speed                 = 0
Line type             = 0
Device                = 
Driver                = 
No bitmap             = No
Copy bitmap           = No
Stretch bitmap        = Yes
Phi                   = 30
Theta                 = 60
Psi                   = 90
Origin                = 0
Distance              = 0
Print Info            = No
Total X               = 0
Total Y               = 0
Left margin           = 0
Print width           = 0
Top margin            = 0
Print height          = 0
Print unit            = 0
Print mode            = 0
Pixels per point      = 0
Basic width           = 0
Frame width           = 0
Min. distance         = 0
Print EPSF            = No
Invert print          = No
Include elements      = No
Preserve aspect       = No
Rotate PS             = No
EPSF File             = 
Post process          = No
Post program          = 
Post arguments        = 
Post delete           = No
;
[Graphics window] = 0.422143,0.0809129,0.299286,0.509336,-1
Title                 = (m2,V2)
Window                = (m,V)
Min. X                = 0
X axis                = m2
Max. X                = 0.5
Min. Y                = -0.07
Y axis                = V2
Max. Y                = 0.04
Continuous line       = Yes
Frequency             = 1
Direction field       = No
Cell length           = 24
Mark length           = 12
Axes location         = 
Drawing color         = FF00
Drawing width         = 0
Grid color            = 0
Grid width            = 0
Direction field color = 0
Direction field width = 0
Background color      = FFFFFF
Width (px)            = 0
Height (px)           = 0
Arbitrary aspect      = Yes
Adjust X range        = No
Adjust Y range        = No
Square                = No
Adjust width          = No
Adjust height         = No
Poincare section      = No
Condition             = 
Error                 = 1e-05
Increasing            = No
Decreasing            = No
Capture               = 1
Select in X axis      = 5
Select in Y axis      = 4
Step in X axis        = 0.01
Step in Y axis        = 0.01
Angular step          = 15
Zoom factor           = 10
Fractal order         = 0
Plotter               = No
Frame                 = Yes
Pen                   = 1
Width                 = 0
Speed                 = 0
Line type             = 0
Device                = 
Driver                = 
No bitmap             = No
Copy bitmap           = No
Stretch bitmap        = Yes
Phi                   = 30
Theta                 = 60
Psi                   = 90
Origin                = 0
Distance              = 0
Print Info            = No
Total X               = 0
Total Y               = 0
Left margin           = 0
Print width           = 0
Top margin            = 0
Print height          = 0
Print unit            = 0
Print mode            = 0
Pixels per point      = 0
Basic width           = 0
Frame width           = 0
Min. distance         = 0
Print EPSF            = No
Invert print          = No
Include elements      = No
Preserve aspect       = No
Rotate PS             = No
EPSF File             = 
Post process          = No
Post program          = 
Post arguments        = 
Post delete           = No
;
[Notes]

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