XPP model

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

# A simplified model of NMDA oscillations in lamprey locomotor network neurons
# Mikael Huss 070315

# Components: NMDA, KCa, Kv, leak, Cav, KCa channels
# KCa gets activated by both NMDA-Ca and Cav.

# Voltage equation (the factor 1000 is to get the time in seconds)

dv/dt= 1000 * (p(v)*gnmda*(enmda-v) + gkca*act_kca(C)*(ek-v) + gk*act_k(v)*(ek-v) + gleak*(eleak-v) + gcav*act_cav(v)*(eca-v) + ibias)

dc/dt= inmda*p(v)*gnmda*(enmda-v) + icav*gcav*act_cav(v)*(eca-v) - C/tau

param gnmda=0.005, gkca=20, gk=8, gcav=0.005, gleak=0.001
param tc=0.02, tau=1, inmda=0.2, icav=0.3, ibias=0
param enmda=0, eleak=-70,   ek=-80, eca=150, 
param vmhalf=-60, vkhalf=-1, vcahalf=-45
param sm=.3, sk=-7, sca=-5

# Magnesium block equation
p(v)=exp(sm*(v-vmhalf))/(1+exp(sm*(v-vmhalf)))

# Kv current (assumed to be a combination of delayed rectifier and A-current)
act_k(v) = 1/(1+exp((v-vkhalf)/sk))

# Assume that we have a calcium component with half-activation at -45 mV
# (Corresponding to the component which "starts to activate between
# -60 and -50 mV"; El Manira and Bussieres 1997)
act_cav(v) = 1/(1+exp((v-vcahalf)/sca))

act_kca(C)=tc*C
aux act=act_kca(C)

init v=-70
param v(0)=-70
c(0)=0

@ METH=cvode, ATOLER=1e-6, TOLER=1e-6, DT=0.02
@ TOTAL=30, XP=t, YP=v, MAXSTOR=500000, BOUND=50000, BELL=0
@ XLO=0, XHI=30, YLO=-80, YHI=0
@ ntst=400, nmax=20000, dsmin=1e-15, dsmax=.1, ds=1e-4
@ epsl=1e-7, epsu=1e-7, epss=1e-5
@ parmin=0, parmax=0.8
@ autoxmin=0, autoxmax=0.8, autoymin=-80, autoymax=0, autovar=v
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Copyright © 2017 Matthias Koenig

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This model is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.


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Access SBML model  L3V1

FunctionDefinitions [8] 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
p v sm vmhalf sm v vmhalf 1 sm v vmhalf
act_k v sk vkhalf 1 1 v vkhalf sk
act_cav v sca vcahalf 1 1 v vcahalf sca
act_kca c tc tc c

Parameters [24] name constant value unit derived unit sbo cvterm
gnmda gnmda = 0.005 0.005 None
gkca gkca = 20 20.0 None
gk gk = 8 8.0 None
gcav gcav = 0.005 0.005 None
gleak gleak = 0.001 0.001 None
tc tc = 0.02 0.02 None
tau tau = 1 1.0 None
inmda inmda = 0.2 0.2 None
icav icav = 0.3 0.3 None
ibias ibias = 0 0.0 None
enmda enmda = 0 0.0 None
eleak eleak = -70 -70.0 None
ek ek = -80 -80.0 None
eca eca = 150 150.0 None
vmhalf vmhalf = -60 -60.0 None
vkhalf vkhalf = -1 -1.0 None
vcahalf vcahalf = -45 -45.0 None
sm sm = .3 0.3 None
sk sk = -7 -7.0 None
sca sca = -5 -5.0 None
v v = -70 -70.0 None
c c = 0 0.0 None
act 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [4]   assignment name derived units sbo cvterm
d v/dt = 1000 p v sm vmhalf gnmda enmda v gkca act_kca c tc ek v gk act_k v sk vkhalf ek v gleak eleak v gcav act_cav v sca vcahalf eca v ibias None
d c/dt = inmda p v sm vmhalf gnmda enmda v icav gcav act_cav v sca vcahalf eca v c tau None
act = act_kca c tc None
t = time None