TITLE type21v02.mod a second version of a simple planar type-1/type-2 model
COMMENT
Reduce planar model for Hodgkin-Huxley model
with can be witched between Type-1 and Type-2 dynamics.
In both modes model has approximately the same resting potential,
input resistance, spike shape and frequencies (where F-I curves aren't zero).
--- Model equations ---
C dv/dt = I + g_L(E_L-v)+ g_{Na}m^3_\infty(v)(a + bn)(E_{Na}-v)-g_Kn^4(E_K-v)\\
dn/dt = (n_\infty(v) - n)/\tau_n(v)
m_\infty(v) = 1/( 1+e^(-(v+40)/9.5) )
n_\infty(v) = n_0 + (1-n_0)/(1+e^( -(v-v_{1/2})/\theta ) )
\tau_n(v) = \tau_0+ s_\tau e^( -( (v - v_0)/\sigma )^2 )
--- The map of the model parameters into parameter names in the mod-file ---
: : Type I : Type II :
----------:------:---------:---------:
g_L : gl : 0.3 : 0.1 :
E_L : el : -54.3 : -39.0 :
g_{Na} : gna : 120.0 :
a : a : 0.906483183915 :
b : b : -1.10692947808 :
E_{Na} : ena : 50.0 :
g_K : gk : 36.0 :
E_K : ek : -77.0 :
n_0 : n0 : 0.35 : 0.28 :
v_{1/2} : v12 : -40.0 : -44.5 :
\theta : sl : 4.0 : 9.0 :
\tau_0 : t0 : 0.46 : 0.5 :
s_\tua : st : 3.5 : 5.0 :
v_0 : v0 : -60.5 : -60.0 :
\iota : sg : 35.9 : 30.0 :
--- USAGE ---
The type-1/type-2 modes can be switched by variable type21.
If type21 = 1, the model is set into type 1 dynamics, and
any other parameters are ignored.
If type21 = 2, the model is set into type 2 dynamics.
To gain an access to other parameters, set type21 to zero.
--- Neuron parameters for 1000 um2 membrane and 1 uF/cm2 capacitance. ---
Resting potential (mV)
Type-1 : -67.78432212370292
Type-2 : -67.91262149648327
difference : 0.1282993727803472
Input resistance (MOhm) for 1000 um2 compartment
----------------------: Type-1:Type-2
for positive current : 174 : 203
for negative current : 176 : 203
Input resistance (Ohm cm2)
----------------------: Type-1:Type-2
for positive current : 1741 : 2032
for negative current : 1761 : 2027
Steady-state values for zero input current
type21 = 1, vinit = -67.78432212370292, ninit = 0.35062495845399
type21 = 2, vinit = -67.91262149648327, ninit = 0.32971471805597
-----
Spike Threshold:
Type-I : -44.3427953154(mV)
Type-II : -44.8076699075(mV)
Spike duration:
Type-I : 0.39(ms)
Type-II : 0.4(ms)
Spike Height:
Type-I : 88.002566626(mV)
Type-II : 88.3969740276(mV)
AHP:
Type-I : 31.0120287902(mV)
Type-II : 30.547154198(mV)
--- --- ---
Developed by Ruben A. Tikidji-Hamburyan, LSU HSC, 2018-11-21
ENDCOMMENT
UNITS {
(mA) = (milliamp)
(mV) = (millivolt)
(mS) = (millisiemens)
}
NEURON {
SUFFIX type21
NONSPECIFIC_CURRENT i
RANGE ninit : initial conditions for n
: if negative, it uses stady-state for given
: voltage
RANGE type21 : 1 - for type-1
: 2 - for type-2,
: 0 - to enable parameters below
:>> THIS PARAMETERS ARE PRESET BY type21 AT INIT
RANGE gl,el,v12,sl
RANGE n0,sn,t0,st,v0,sg
:<<
:>> Parameters below have default velues
RANGE gk,ek,gna,ena,a,b
:<<
:GLOBAL minf, ninf, ntau
}
PARAMETER {
v (mV)
type21=2 (1)
gna= 120. (mS/cm2)
ena= 50. (mV)
gk = 36. (mS/cm2)
ek = -77. (mV)
gl (mS/cm2)
el (mV)
n0 (1)
sn (1)
t0 (ms)
st (ms)
v0 (mV)
sg (mV)
v12 (mV)
sl (mV)
a = 0.906483183915
b = -1.10692947808
ninit = 0.34
: type21 = 1, vinit = -67.78432212370292, ninit = 0.35062495845399
: type21 = 2, vinit = -67.91262149648327, ninit = 0.32971471805597
}
STATE {
n
}
ASSIGNED {
i (mA/cm2)
minf
ninf
ntau (ms)
}
BREAKPOINT {
SOLVE states METHOD cnexp
:----vvvv-- is needed to convert uA/cm2 to mA/cm2
i = (1e-3)*( gna*minf*minf*minf*(a+n*b)*(v-ena)+gk*n*n*n*n*(v-ek)+gl*(v-el) )
}
DERIVATIVE states {
rates(v)
n'= (ninf- n)/ ntau
}
INITIAL {
if ( fabs(type21 - 1.) < 1e-6 ){
: Paramters for type 1
gl = 0.3 (mS/cm2)
el = -54.3 (mV)
n0 = 0.35
sn = 1. - n0
v12 = -40. (mV)
sl = 4. (mV)
t0 = .46 (ms)
st = 3.5 (ms)
v0 = -60.5 (mV)
sg = 35.9 (mV)
:printf("Type - I\n")
}
if ( fabs(type21 - 2.) < 1e-6 ){
: Paramters for type 2
gl = 0.1 (mS/cm2)
el = -39. (mV)
n0 = 0.28
sn = 1. - n0
v12 = -44.5 (mV)
sl = 9. (mV)
t0 = .5 (ms)
st = 5. (ms)
v0 = -60. (mV)
sg = 30. (mV)
:printf("Type - II\n")
}
rates(v)
if (ninit < 0 || ninit > 1){
n = ninf
} else {
n = ninit
}
}
PROCEDURE rates(v (mV)) {
UNITSOFF
:TABLE minf, ninf, ntau FROM -100 TO 100 WITH 200
minf = 1./(1.+exp(-(v+40.)/9.5))
ninf = n0 + sn/(1.+exp(-(v-v12)/sl ))
ntau = t0 + st*exp(-((v-v0)/sg)*((v-v0)/sg))
UNITSON
}