XPP model

This model was converted from XPP ode format to SBML using sbmlutils-0.1.5a6.

" ball and stick model w 2 comps
" copied from model_I_long_range_better_offset.ode
" Na params close enough to accept this as wildtype cocktail model.
" Can change only 2 out of 3 passive parameters. The last one is dependent to preserve total input resistance.
#
# conductances in nS, resistances in GOhm
# currents in pA  
# Voltages in mV  
# time in ms  
# capacitances in pF  

# Larger soma capacitance, but still low leak
# 3-steps: 16, 36, 56
# Params: gaxon=1.8, NaP=0.1, NaT=350, gKs=1, gaKs=550, Cm=15, Ca=10, gL=0.1, gaL=3, eleak=-55, ealeak=-59

# principles:
# - good for spike height => gaxon, Cm = (3, 20); (1.6, 15)  
# - gaKs > gNaT makes longer delay
# - lowering gaL increases first spike voltage offset
# - high gaKs makes spike asymmetric with slow depolarization
# - lowering Cm increases spike height
# - decreasing gaxon makes spikes shorter and more asymmetric, but requires more current to fire
# - increasing zi increases offset slightly

# firing rate rules:
# - increasing gl decreases galeak and therefore increases f
# - increasing gaxon increases f
# - increasing zi increases f
# - reducing Ca increases f!

# Params: gaxon=1, NaP=0.14, NaT=350, gKs=1, gaKs=550, Cm=15, Ca=10, gL=0.1, gaL=dep(zi), zi=1.6, eleak=-60, ealeak=-60
# pros: nice spike height, goes up to >-10mV
# cons: threshold @ -50mV, spikes a bit too short

# Params: gaxon=1.6, NaP=0.05, NaT=450, gKs=1, gaKs=500, Cm=15, Ca=10, gL=0.1, gaL=dep(zi), zi=1.6, eleak=-60, ealeak=-60
# pros: nice spike height, goes up to >-10mV, threshold @ -40mV
# cons: initial rate too high, spike shape not nice, too small

# Params: gaxon=1.6, NaP=0.08, NaT=260, gKs=1, gaKs=1000, Cm=15, Ca=10, gL=0.1, gaL=dep(zi), zi=1.6, eleak=-60, ealeak=-60
# pros: nice spike height, asymmetric spike shape, initial rate low
# cons: threshold @ -45mV, offset a bit too small

# Params: NaP=0.08, NaT=300, gKs=1, gaKs=1000, Cm=15, Ca=10, gaxon=1.6, gL=0.1, gaL=dep(zi), zi=1.1, eleak=-60, ealeak=-60
# pros: nice spike height, asymmetric spike shape, initial rate low, threshold @ -40mV
# cons: starts firing at 14 pA, must compare f-I curve to recordings

# TODO: make mlab figure and attach to bif.lyx
  
#dV/dt=-1/c*(gKs*mKs^4*(V-EK) + gKf*mKf^4*(fh*hKf+(1-fh)*hKf2)*(V-EK) + gNa*mNa^3*hNa*(V-ENa) + gleak*(V-Eleak)-I)  

# soma voltage
dVm/dt=-1/Cm*(IksVm+IkfVm+gleak*(Vm-Eleak)-I+gaxon*(Vm-Va))

# axon compartment voltage
dVa/dt=-1/Ca*(IksVa+IkfVa+Ina+Inap+galeak*(Va-Ealeak)+gaxon*(Va-Vm))
  
#slow K  
# orig = 5.1
par gKs=1 gaKs=700
minfKs(V) = 1/(1+exp((V+12.85)/(-19.91)))  
mtauKs(V) = 2.03 + 1.96 /(1+exp((V-29.83)/3.32))  
dmKsVm/dt=(minfKs(Vm)-mKsVm)/mtauKs(Vm)  
dmKsVa/dt=(minfKs(Va)-mKsVa)/mtauKs(Va)  
IksVm=gKs*mKsVm^4*(Vm-EK)  
IksVa=gaKs*mKsVa^4*(Va-EK)  
aux IksVm=IksVm
aux IksVa=IksVa

#fast K with 2 inactivation time constants
dmKfVm/dt=(minfKf(Vm)-mKfVm)/mtauKf(Vm)  
dhKfVm/dt=(hinfK(Vm)-hKfVm)/htauK(Vm)  
dhKf2Vm/dt=(hinfK2(Vm)-hKf2Vm)/116  
IkfVm=gKf*mKfVm^4*(fh*hKfVm + (1-fh)*hKf2Vm)*(Vm-EK)  
dmKfVa/dt=(minfKf(Va)-mKfVa)/mtauKf(Va)  
dhKfVa/dt=(hinfK(Va)-hKfVa)/htauK(Va)  
dhKf2Va/dt=(hinfK2(Va)-hKf2Va)/116  
IkfVa=gaKf*mKfVa^4*(fh*hKfVa + (1-fh)*hKf2Va)*(Va-EK)  
minfKf(V) = 1/(1+exp((V+17.55)/(-7.27)))  
mtauKf(V) = 1.94+2.66/(1+exp((V-8.12)/7.96))  
hinfK(V) = 1/(1+exp((V+45)/6))  
htauK(V) = 1.79+515.8/(1+exp((V+147.4)/(28.66)))  
# mistake; should be hinfK == hinfK2
hinfK2(V) = 1/(1+exp((V+44.2)/1.5))
aux IkfVm=IkfVm
aux IkfVa=IkfVa
  
#na  
# from O'Dowd and Aldrich (1988)
dmNa/dt=(minfNa(Va)-mNa)/mtauNa(Va)
dhNa/dt=(hinfNa(Va)-hNa)/htauNa(Va)
Ina=gNa*mNa^3*hNa*(Va-ENa)
# gNa reported as 500 pS/pF, multiply with C=20 pF
par gNa=180
minfNa(V) = 1/(1+exp((V+29.13)/(-8.922)))
mtauNa(V) = 0.1270 + 3.434/(1+exp((V+45.35)/(5.98)))
hinfNa(V) = 1/(1+exp((V+47)/5))
htauNa(V) = 0.36 + exp(-(V+20.65)/(10.47))
aux Ina=Ina

# NaP from DmNav10 of WHL oocyte #1
dmNaP/dt=(minfNaP(Va)-mNaP)/mtauNaP(Va)
Inap=(gNaP+modgNaP)*mNaP*(Va-ENa)
par gNaP=.01
minfNap(V) = 1/(1+exp((V+48.77)/(-3.68)))
mtauNap(V) = 1
aux Inap=Inap

global 1 t {I=Ihold}    
global 1 t-10 {I=Ipulse}  
global 1 t-510 {I=Ihold}  

# initial conditions for settled at I=-6.5
# easiest way is to get this is to save "info" from File menu 
# after running for a long while and then doing a "run last"
init VM=-68.81670299025546 VA=-64.34801596094069 MKSVM=0.05673345401938218 MKSVA=0.07000969210752514 MKFVM=0.0008650853390965969 HKFVM=0.9814660312384692 HKF2VM=0.9839995279862832 MKFVA=0.001598416867905559 HKFVA=0.961752460873017 HKF2VA=0.9900602079074428 MNA=0.01894063272630685 HNA=0.9695223296922046 MNAP=0.01429909346846636

@ total=600,bounds=10000000000,meth=euler,dt=.001, nout=100, maxstor=10000000  

# window ranges
@ xlo=0, xhi=600, ylo=-65, yhi=0

# do a I range from -9 to +51 with 7 steps

# do a I range from 5 to +45 with 2 steps

par Cm=10 Ca=1.8 Ipulse=-6.5

# conserve total input resistance
par zi=2.1

# connection strength
par gaxon=1.3 gleak=0.05

# make some parameters dependent to preserve zi
gad=1/zi-gleak
galeak=1/(1/gad-1/gaxon)

par eleak=-55 ealeak=-55 Ihold=-6.5 

# unneeded pars at the end
par gKf=1 gaKf=200
par ENa=45 EK=-80  I=0 fh=.95 modNaAct=0 modNaInact=0 modgNaP=0

done 
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Copyright © 2017 Matthias Koenig

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Model :

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Access SBML model  L3V1

FunctionDefinitions [17] name math sbo cvterm
max minimum x y x x y y
min maximum x y x x y y
heav heavyside x 0 x 0 0.5 x 0 1 x 0 0
mod modulo x y x y x y x 0 y 0 x y x y
minfks v 1 1 v 12.85 19.91
mtauks v 2.03 1.96 1 v 29.83 3.32
minfkf v 1 1 v 17.55 7.27
mtaukf v 1.94 2.66 1 v 8.12 7.96
hinfk v 1 1 v 45 6
htauk v 1.79 515.8 1 v 147.4 28.66
hinfk2 v 1 1 v 44.2 1.5
minfna v 1 1 v 29.13 8.922
mtauna v 0.127 3.434 1 v 45.35 5.98
hinfna v 1 1 v 47 5
htauna v 0.36 v 20.65 10.47
minfnap v 1 1 v 48.77 3.68
mtaunap v 1

Parameters [44] name constant value unit derived unit sbo cvterm
gks gks = 1 1.0 None
gaks gaks = 700 700.0 None
gna gna = 180 180.0 None
gnap gnap = .01 0.01 None
vm vm = -68.81670299025546 -68.8167029902555 None
va va = -64.34801596094069 -64.3480159609407 None
mksvm mksvm = 0.05673345401938218 0.0567334540193822 None
mksva mksva = 0.07000969210752514 0.0700096921075251 None
mkfvm mkfvm = 0.0008650853390965969 0.000865085339096597 None
hkfvm hkfvm = 0.9814660312384692 0.981466031238469 None
hkf2vm hkf2vm = 0.9839995279862832 0.983999527986283 None
mkfva mkfva = 0.001598416867905559 0.00159841686790556 None
hkfva hkfva = 0.961752460873017 0.961752460873017 None
hkf2va hkf2va = 0.9900602079074428 0.990060207907443 None
mna mna = 0.01894063272630685 0.0189406327263069 None
hna hna = 0.9695223296922046 0.969522329692205 None
mnap mnap = 0.01429909346846636 0.0142990934684664 None
cm cm = 10 10.0 None
ca ca = 1.8 1.8 None
ipulse ipulse = -6.5 -6.5 None
zi zi = 2.1 2.1 None
gaxon gaxon = 1.3 1.3 None
gleak gleak = 0.05 0.05 None
eleak eleak = -55 -55.0 None
ealeak ealeak = -55 -55.0 None
ihold ihold = -6.5 -6.5 None
gkf gkf = 1 1.0 None
gakf gakf = 200 200.0 None
ena ena = 45 45.0 None
ek ek = -80 -80.0 None
i i = 0 0.0 None
fh fh = .95 0.95 None
modnaact modnaact = 0 0.0 None
modnainact modnainact = 0 0.0 None
modgnap modgnap = 0 0.0 None
iksvm 0.0 dimensionless None
iksva 0.0 dimensionless None
ikfvm 0.0 dimensionless None
ikfva 0.0 dimensionless None
ina 0.0 dimensionless None
inap 0.0 dimensionless None
gad 0.0 dimensionless None
galeak 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [22]   assignment name derived units sbo cvterm
d vm/dt = 1 cm iksvm ikfvm gleak vm eleak i gaxon vm va None
d va/dt = 1 ca iksva ikfva ina inap galeak va ealeak gaxon va vm None
d mksvm/dt = minfks vm mksvm mtauks vm None
d mksva/dt = minfks va mksva mtauks va None
d mkfvm/dt = minfkf vm mkfvm mtaukf vm None
d hkfvm/dt = hinfk vm hkfvm htauk vm None
d hkf2vm/dt = hinfk2 vm hkf2vm 116 None
d mkfva/dt = minfkf va mkfva mtaukf va None
d hkfva/dt = hinfk va hkfva htauk va None
d hkf2va/dt = hinfk2 va hkf2va 116 None
d mna/dt = minfna va mna mtauna va None
d hna/dt = hinfna va hna htauna va None
d mnap/dt = minfnap va mnap mtaunap va None
iksvm = gks mksvm 4 vm ek None
iksva = gaks mksva 4 va ek None
ikfvm = gkf mkfvm 4 fh hkfvm 1 fh hkf2vm vm ek None
ikfva = gakf mkfva 4 fh hkfva 1 fh hkf2va va ek None
ina = gna mna 3 hna va ena None
inap = gnap modgnap mnap va ena None
gad = 1 zi gleak None
galeak = 1 1 gad 1 gaxon None
t = time None

Events [3] name trigger priority delay assignments sbo cvterm
e0 t 0
initialValue = False
persistent = True
i = ihold
e1 t 10 0
initialValue = False
persistent = True
i = ipulse
e2 t 510 0
initialValue = False
persistent = True
i = ihold