XPP model

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

% SkM_AP_KCa.ode 
% Simulations for skeletal muscle fiber
% 
% ICa(S) and IK(Ca) were  incorporated to simulate AP for human skeletal muscle cells.
% 
% "Wang YJ, Lin MW, Lin AA, Wu SN. Riluzole-induced block of voltage-gated Na(+) 
% current and activation of BK(Ca) channels in cultured differentiated human
% skeletal muscle cell. Life Sci 2007;82:11-20."

% UNITS: millivolts, milliseconds, nanosiemens,  microfarads

% INITIAL VALUES
Initial Vm=-75, m=0.0, h=1.0, n=0.0, Vt=-70, c=0.15, o=0.15, cer=200

% VALUES OF THE MODEL PARAMETERS
Parm gNa_max=0.9, gcabar=0.05, gK_max=0.415, gL_max=0.0024, gkca=0.5
Parm ENa=50.0, EK=-70.0, EL=-75.0, ECa=50
Parm En=-40.0, Em=-42.0, Eh=-41.0
Parm Ct=0.04, Cm=0.0090, Rs=15.0, Am=200.0
Parm alpha_n_max=0.0229, beta_n_max=0.09616
Parm v_alpha_m=10.0, v_alpha_n=7.0, v_alpha_h=14.7
Parm alpha_m_max=0.208, beta_m_max=2.081
Parm v_beta_n=40.0, v_beta_m=18.0, v_beta_h=7.6
Parm alpha_h_max=0.0156, beta_h_max=3.382

Parm kd=0.18, alpha=4.5e-6, kpmca=0.2, pleak=0.0005,  kserca=0.4
Parm d1=0.84, d2=1.0, k1=0.18, k2=0.011, bbar=0.28, abar=0.48
Parm fer=0.01, vcytver=5, fcyt=0.01

% STIMULUS
Parm period=50, iStim_mag=2, iStim_beg=5, iStim_dur=1
iStim=  iStim_mag * heav(mod(t,period)-iStim_beg) * heav(iStim_beg+iStim_dur-mod(t,period))

beta_n= (beta_n_max * exp(((En - Vm) / v_beta_n)))
beta_m= (beta_m_max * exp(((Em - Vm) / v_beta_m)))
beta_h= (beta_h_max / (1.0 + exp(((Eh - Vm) / v_beta_h))))
alpha_n= (alpha_n_max * (Vm - En) / (1.0 - exp(((En - Vm) / v_alpha_n))))
alpha_m= (alpha_m_max * (Vm - Em) / (1.0 - exp(((Em - Vm) / v_alpha_m))))
alpha_h= (alpha_h_max * exp(((Eh - Vm) / v_alpha_h)))

% IK(Ca) PARAMETERS
alp(Vm) = abar/(1+k1*exp(-2*d1*96.485*Vm/8.313424/(310))/c)
beta(Vm) = bbar/(1+c/(k2*exp(-2*d2*96.485*Vm/8.313424/310)))
tau(Vm) = 1/(alp(Vm)+beta(Vm))
ooinf(Vm) = alp(Vm)*tau(Vm)
dinf = 1/(1 + exp((-24.6-Vm)/11.3))
taud = 80*(1/(cosh(-0.031*(Vm+37.1))))
alphad = dinf/taud
betad = (1-dinf)/taud
gca = -gcabar*Vm/(exp(0.117*Vm)-1)

% CA HANDLING MECHANISMS
w=c^5/(c^5+kd^5)
jmem=-(alpha*ICa+kpmca*c)
jleak=pleak*(cer-c)
jserca=kserca*c
jer=jleak-jserca

% IONIC CURRENTS
INa= (gNa_max * m**3 * h * (Vm - ENa))
IT= ((Vm - Vt) / Rs)
IKCa=gkca*o*w*(Vm-EK)
ICa= gca*d^2
IL= (gL_max * (Vm - EL))
IK= (gK_max * n * n * n * n * (Vm - EK))

% DIFFERENTIAL EQUATIONS 
dVm/dt = ((iStim - (INa + ICa + IK + IL + IT + IKCa)) / Cm)
dm/dt = ((alpha_m * (1.0 - m)) - (beta_m * m))
dh/dt = ((alpha_h * (1.0 - h)) - (beta_h * h))
dn/dt = ((alpha_n * (1.0 - n)) - (beta_n * n))
dVt/dt = ((Vm - Vt) / (Rs * Ct))
dd/dt = (1-d)*alphad - d*betad
do/dt = (ooinf(Vm)-o)/tau(Vm)
dc/dt = fcyt*(jmem+jer)
dcer/dt =-fer*(vcytver)*jer

% AUXILLARY FUNCTIONS
aux i_na=INa
aux  i_kca=IKCa

% NUMERICAL AND PLOTTING PARAMETERS FOR XPP
@ METH=Euler, DT=0.01, TOTAL=150, MAXSTOR=50000
@ YP=vm, YHI=50, YLO=-90, XLO=0, XHI=150, BOUND=5000

done
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Copyright © 2017 Matthias Koenig

Redistribution and use of any part of this model, with or without modification, are permitted provided that the following conditions are met:

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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.


Model :

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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
alp vm abar c d1 k1 abar 1 k1 2 d1 96.485 vm 8.313424 310 c
beta vm bbar c d2 k2 bbar 1 c k2 2 d2 96.485 vm 8.313424 310
tau vm abar bbar c d1 d2 k1 k2 1 alp vm d1 k1 abar c beta vm bbar k2 d2 c
ooinf vm abar bbar c d1 d2 k1 k2 alp vm d1 k1 abar c tau vm abar bbar c d1 d2 k1 k2

Parameters [81] name constant value unit derived unit sbo cvterm
vm vm = -75 -75.0 None
m m = 0.0 0.0 None
h h = 1.0 1.0 None
n n = 0.0 0.0 None
vt vt = -70 -70.0 None
c c = 0.15 0.15 None
o o = 0.15 0.15 None
cer cer = 200 200.0 None
gna_max gna_max = 0.9 0.9 None
gcabar gcabar = 0.05 0.05 None
gk_max gk_max = 0.415 0.415 None
gl_max gl_max = 0.0024 0.0024 None
gkca gkca = 0.5 0.5 None
ena ena = 50.0 50.0 None
ek ek = -70.0 -70.0 None
el el = -75.0 -75.0 None
eca eca = 50 50.0 None
en en = -40.0 -40.0 None
em em = -42.0 -42.0 None
eh eh = -41.0 -41.0 None
ct ct = 0.04 0.04 None
cm cm = 0.0090 0.009 None
rs rs = 15.0 15.0 None
am am = 200.0 200.0 None
alpha_n_max alpha_n_max = 0.0229 0.0229 None
beta_n_max beta_n_max = 0.09616 0.09616 None
v_alpha_m v_alpha_m = 10.0 10.0 None
v_alpha_n v_alpha_n = 7.0 7.0 None
v_alpha_h v_alpha_h = 14.7 14.7 None
alpha_m_max alpha_m_max = 0.208 0.208 None
beta_m_max beta_m_max = 2.081 2.081 None
v_beta_n v_beta_n = 40.0 40.0 None
v_beta_m v_beta_m = 18.0 18.0 None
v_beta_h v_beta_h = 7.6 7.6 None
alpha_h_max alpha_h_max = 0.0156 0.0156 None
beta_h_max beta_h_max = 3.382 3.382 None
kd kd = 0.18 0.18 None
alpha alpha = 4.5e-6 4.5e-06 None
kpmca kpmca = 0.2 0.2 None
pleak pleak = 0.0005 0.0005 None
kserca kserca = 0.4 0.4 None
d1 d1 = 0.84 0.84 None
d2 d2 = 1.0 1.0 None
k1 k1 = 0.18 0.18 None
k2 k2 = 0.011 0.011 None
bbar bbar = 0.28 0.28 None
abar abar = 0.48 0.48 None
fer fer = 0.01 0.01 None
vcytver vcytver = 5 5.0 None
fcyt fcyt = 0.01 0.01 None
period period = 50 50.0 None
istim_mag istim_mag = 2 2.0 None
istim_beg istim_beg = 5 5.0 None
istim_dur istim_dur = 1 1.0 None
d 0.0 dimensionless None
istim 0.0 dimensionless None
beta_n 0.0 dimensionless None
beta_m 0.0 dimensionless None
beta_h 0.0 dimensionless None
alpha_n 0.0 dimensionless None
alpha_m 0.0 dimensionless None
alpha_h 0.0 dimensionless None
dinf 0.0 dimensionless None
taud 0.0 dimensionless None
alphad 0.0 dimensionless None
betad 0.0 dimensionless None
gca 0.0 dimensionless None
w 0.0 dimensionless None
jmem 0.0 dimensionless None
jleak 0.0 dimensionless None
jserca 0.0 dimensionless None
jer 0.0 dimensionless None
ina 0.0 dimensionless None
it 0.0 dimensionless None
ikca 0.0 dimensionless None
ica 0.0 dimensionless None
il 0.0 dimensionless None
ik 0.0 dimensionless None
i_na 0.0 dimensionless None
i_kca 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [35]   assignment name derived units sbo cvterm
d vm/dt = istim ina ica ik il it ikca cm None
d m/dt = alpha_m 1 m beta_m m None
d h/dt = alpha_h 1 h beta_h h None
d n/dt = alpha_n 1 n beta_n n None
d vt/dt = vm vt rs ct None
d d/dt = 1 d alphad d betad None
d o/dt = ooinf vm abar bbar c d1 d2 k1 k2 o tau vm abar bbar c d1 d2 k1 k2 None
d c/dt = fcyt jmem jer None
d cer/dt = fer vcytver jer None
istim = istim_mag heav mod t period istim_beg heav istim_beg istim_dur mod t period None
beta_n = beta_n_max en vm v_beta_n None
beta_m = beta_m_max em vm v_beta_m None
beta_h = beta_h_max 1 eh vm v_beta_h None
alpha_n = alpha_n_max vm en 1 en vm v_alpha_n None
alpha_m = alpha_m_max vm em 1 em vm v_alpha_m None
alpha_h = alpha_h_max eh vm v_alpha_h None
dinf = 1 1 24.6 vm 11.3 None
taud = 80 1 0.031 vm 37.1 None
alphad = dinf taud None
betad = 1 dinf taud None
gca = gcabar vm 0.117 vm 1 None
w = c 5 c 5 kd 5 None
jmem = alpha ica kpmca c None
jleak = pleak cer c None
jserca = kserca c None
jer = jleak jserca None
ina = gna_max m 3 h vm ena None
it = vm vt rs None
ikca = gkca o w vm ek None
ica = gca d 2 None
il = gl_max vm el None
ik = gk_max n n n n vm ek None
i_na = ina None
i_kca = ikca None
t = time None