XPP model

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

# This ODE code is a comparable implementation of the BGCT model described in the
# following paper:
#
#     Title:   Bidirectional Control of Absence Seizures by the Basal Ganglia: A
#              Computational Evidence (2014)
#     Authors: Mingming Chen, Daqing Guo*, Tiebin Wang, Wei Jing, Yang Xia, Peng Xu, 
#              Cheng Luo, Pedro A. Valdes-Sosa1, and Dezhong Yao*
#     Journal: PLoS Computational Biology
#     Emails:  twqylsf@gmail.com and dqguo@uestc.edu.cn
# You can use XPPAut (http://www.math.pitt.edu/~bard/xpp/xpp.html) for runing this code.
#

# Intergation step
dt=0.00005 

# Simulation time
time=13    

# SNr-TRN pathway, 1 open and 0 close
p open1=1 

# SNr-SRN pathway, 1 open and 0 close  
p open2=1 

# Scale factor   
p KK=1    

# Maximum firing rate (Table 1 A)
Qmax_i=250 
Qmax_d1=65 
Qmax_d2=65
Qmax_p1=250
Qmax_p2=300
Qmax_xi=500
Qmax_s=250
Qmax_r=250

# Mean firing threshold (Table 1 B)
theta_i=15e-3
theta_d1=19e-3 
theta_d2=19e-3
theta_p1=10e-3 
theta_p2=9e-3
theta_xi=1e-2 
theta_s=15e-3 
theta_r=15e-3

# Coupling strength (Table 1 C)
v_ee=1.0e-3   
v_ei=1.8e-3 
v_re=5.0e-5
v_rs=5.0e-4
v_d1e=1.0e-3
v_d1d1=2.0e-4
v_d1s=1.0e-4
v_d2e=7.0e-4
v_d2d2=3.0e-4
v_d2s=5e-5
v_p1d1=1.0e-4
v_p1p2=3.0e-5
v_p2d2=3.0e-4
v_p2p2=0.75e-4 
v_p2xi=4.5e-4 
v_xip2=4.0e-5 
v_es=1.8e-3
v_se=2.2e-3
v_xie=0.1e-3

# Other parameters (Table 1 D)
gamma_e=100 
alpha=50 
beta=200 
sigma=0.006
v_sn_phi_n=2.0e-3 

# TRN-SRN
p v_sr=8.0e-4 

# STN-SNr
p v_p1xi=3e-4
 
# delay parameter 
p tau=0.05
 
v_sp1=open2*3.5e-5 
v_rp1=KK*open1*3.5e-5

# random initial condition
init x[1]=0.5*0*ran;       x[2]=-1500+6000*ran;     x[3]=0.02*ran;        x[4]=-2*3.5*ran;   x[5]=0.04*ran 
init x[6]=-0.7+1.5*ran;    x[7]=0.001+0.025*ran;    x[8]=-0.4+ran;        x[9]=0.004+0.013*ran
init x[10]=-0.15+0.4*ran;  x[11]=0.0005+0.0035*ran; x[12]=-0.12+0.22*ran; x[13]=-0.001+0.0055*ran
init x[14]=-0.1+0.2*ran;   x[15]=-0.09+0.1*ran;     x[16]=-4+7*ran;       x[17]=0.025*ran;   x[18]=-0.6+2*ran

# sigmoid function for different neural populations

S_i=Qmax_i/(1+exp(-pi/sqrt(3)*(x3-theta_i)/sigma))

S_d1=Qmax_d1/(1+exp(-pi/sqrt(3)*(x5-theta_d1)/sigma))

S_d2=Qmax_d2/(1+exp(-pi/sqrt(3)*(x7-theta_d2)/sigma))

S_p1=Qmax_p1/(1+exp(-pi/sqrt(3)*(x9-theta_p1)/sigma))

S_p2=Qmax_p2/(1+exp(-pi/sqrt(3)*(x11-theta_p2)/sigma))

S_xi=Qmax_xi/(1+exp(-pi/sqrt(3)*(x13-theta_xi)/sigma))

S_s=Qmax_s/(1+exp(-pi/sqrt(3)*(x15-theta_s)/sigma))

S_r=Qmax_r/(1+exp(-pi/sqrt(3)*(x17-theta_r)/sigma))

S_r_lag=Qmax_r/(1+exp(-pi/sqrt(3)*(delay(x17,tau)-theta_r)/sigma))

# --------------------------------cerebral cortex----------------------------------------

x1'=x2
x2'=gamma_e^2*(-x1+S_i)-2*gamma_e*x2

x3'=x4
x4'=alpha*beta*(-x3+v_ee*x1+v_es*S_s-v_ei*S_i)-(alpha+beta)*x4

# ---------------------------------striatum D1--------------------------------------------

x5'=x6
x6'=alpha*beta*(-x5+v_d1e*x1-v_d1d1*S_d1+v_d1s*S_s)-(alpha+beta)*x6

# ---------------------------------striatum D2--------------------------------------------

x7'=x8
x8'=alpha*beta*(-x7+v_d2e*x1-v_d2d2*S_d2+v_d2s*S_s)-(alpha+beta)*x8

# ----------------------------------SNr/GPi-----------------------------------------------

x9'=x10
x10'=alpha*beta*(-x9-v_p1d1*S_d1-v_p1p2*S_p2+v_p1xi*S_xi)-(alpha+beta)*x10

# -----------------------------------GPe--------------------------------------------------

x11'=x12
x12'=alpha*beta*(-x11-v_p2d2*S_d2-v_p2p2*S_p2+v_p2xi*S_xi)-(alpha+beta)*x12

# ------------------------------------STN-------------------------------------------------

x13'=x14
x14'=alpha*beta*(-x13+v_xie*x1-v_xip2*S_p2)-(alpha+beta)*x14

# ------------------------------------SRN--------------------------------------------------

x15'=x16
x16'=alpha*beta*(-x15-v_sp1*S_p1+v_se*x1-v_sr*S_r-v_sr*S_r_lag+v_sn_phi_n)-(alpha+beta)*x16  

# -----------------------------------TRN--------------------------------------------------

x17'=x18
x18'=alpha*beta*(-x17-v_rp1*S_p1+v_rs*S_s+v_re*x1)-(alpha+beta)*x18


@ xlo=0, ylo=-10, xhi=13, yhi=150, yp=x1

@ total=13, dt=0.00005, bounds=10e10, maxstore=10e15, delay=1

done

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Terms of use

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:

  1. Redistributions of this SBML file must retain the above copyright notice, this list of conditions and the following disclaimer.
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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 [4] 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

Parameters [114] name constant value unit derived unit sbo cvterm
open1 open1 = 1 1.0 None
open2 open2 = 1 1.0 None
kk kk = 1 1.0 None
v_sr v_sr = 8.0e-4 0.0008 None
v_p1xi v_p1xi = 3e-4 0.0003 None
tau tau = 0.05 0.05 None
x[1] 0.0 None
x[2] 0.0 None
x[3] 0.0 None
x[4] 0.0 None
x[5] 0.0 None
x[6] 0.0 None
x[7] 0.0 None
x[8] 0.0 None
x[9] 0.0 None
x[10] 0.0 None
x[11] 0.0 None
x[12] 0.0 None
x[13] 0.0 None
x[14] 0.0 None
x[15] 0.0 None
x[16] 0.0 None
x[17] 0.0 None
x[18] 0.0 None
x[1] = 0.5*0*ran; 0.0 dimensionless None
x[2] = -1500+6000*ran; 0.0 dimensionless None
x[3] = 0.02*ran; 0.0 dimensionless None
x[4] = -2*3.5*ran; 0.0 dimensionless None
x[5] = 0.04*ran 0.0 dimensionless None
x[6] = -0.7+1.5*ran; 0.0 dimensionless None
x[7] = 0.001+0.025*ran; 0.0 dimensionless None
x[8] = -0.4+ran; 0.0 dimensionless None
x[9] = 0.004+0.013*ran 0.0 dimensionless None
x[10] = -0.15+0.4*ran; 0.0 dimensionless None
x[11] = 0.0005+0.0035*ran; 0.0 dimensionless None
x[12] = -0.12+0.22*ran; 0.0 dimensionless None
x[13] = -0.001+0.0055*ran 0.0 dimensionless None
x[14] = -0.1+0.2*ran; 0.0 dimensionless None
x[15] = -0.09+0.1*ran; 0.0 dimensionless None
x[16] = -4+7*ran; 0.0 dimensionless None
x[17] = 0.025*ran; 0.0 dimensionless None
x[18] = -0.6+2*ran 0.0 dimensionless None
x1 0.0 dimensionless None
x2 0.0 dimensionless None
x3 0.0 dimensionless None
x4 0.0 dimensionless None
x5 0.0 dimensionless None
x6 0.0 dimensionless None
x7 0.0 dimensionless None
x8 0.0 dimensionless None
x9 0.0 dimensionless None
x10 0.0 dimensionless None
x11 0.0 dimensionless None
x12 0.0 dimensionless None
x13 0.0 dimensionless None
x14 0.0 dimensionless None
x15 0.0 dimensionless None
x16 0.0 dimensionless None
x17 0.0 dimensionless None
x18 0.0 dimensionless None
dt 0.0 dimensionless None
time 0.0 dimensionless None
qmax_i 0.0 dimensionless None
qmax_d1 0.0 dimensionless None
qmax_d2 0.0 dimensionless None
qmax_p1 0.0 dimensionless None
qmax_p2 0.0 dimensionless None
qmax_xi 0.0 dimensionless None
qmax_s 0.0 dimensionless None
qmax_r 0.0 dimensionless None
theta_i 0.0 dimensionless None
theta_d1 0.0 dimensionless None
theta_d2 0.0 dimensionless None
theta_p1 0.0 dimensionless None
theta_p2 0.0 dimensionless None
theta_xi 0.0 dimensionless None
theta_s 0.0 dimensionless None
theta_r 0.0 dimensionless None
v_ee 0.0 dimensionless None
v_ei 0.0 dimensionless None
v_re 0.0 dimensionless None
v_rs 0.0 dimensionless None
v_d1e 0.0 dimensionless None
v_d1d1 0.0 dimensionless None
v_d1s 0.0 dimensionless None
v_d2e 0.0 dimensionless None
v_d2d2 0.0 dimensionless None
v_d2s 0.0 dimensionless None
v_p1d1 0.0 dimensionless None
v_p1p2 0.0 dimensionless None
v_p2d2 0.0 dimensionless None
v_p2p2 0.0 dimensionless None
v_p2xi 0.0 dimensionless None
v_xip2 0.0 dimensionless None
v_es 0.0 dimensionless None
v_se 0.0 dimensionless None
v_xie 0.0 dimensionless None
gamma_e 0.0 dimensionless None
alpha 0.0 dimensionless None
beta 0.0 dimensionless None
sigma 0.0 dimensionless None
v_sn_phi_n 0.0 dimensionless None
v_sp1 0.0 dimensionless None
v_rp1 0.0 dimensionless None
s_i 0.0 dimensionless None
s_d1 0.0 dimensionless None
s_d2 0.0 dimensionless None
s_p1 0.0 dimensionless None
s_p2 0.0 dimensionless None
s_xi 0.0 dimensionless None
s_s 0.0 dimensionless None
s_r 0.0 dimensionless None
s_r_lag 0.0 dimensionless None
t model time 0.0 dimensionless None

InitialAssignments [18] name assignment derived units sbo cvterm
= None None
= None None
= None None
= None None
= 0.04 ran None
= None None
= None None
= None None
= 0.004 0.013 ran None
= None None
= None None
= None None
= 0.001 0.0055 ran None
= None None
= None None
= None None
= None None
= 0.6 2 ran None

Rules [72]   assignment name derived units sbo cvterm
d x1/dt = x2 None
d x2/dt = gamma_e 2 x1 s_i 2 gamma_e x2 None
d x3/dt = x4 None
d x4/dt = alpha beta x3 v_ee x1 v_es s_s v_ei s_i alpha beta x4 None
d x5/dt = x6 None
d x6/dt = alpha beta x5 v_d1e x1 v_d1d1 s_d1 v_d1s s_s alpha beta x6 None
d x7/dt = x8 None
d x8/dt = alpha beta x7 v_d2e x1 v_d2d2 s_d2 v_d2s s_s alpha beta x8 None
d x9/dt = x10 None
d x10/dt = alpha beta x9 v_p1d1 s_d1 v_p1p2 s_p2 v_p1xi s_xi alpha beta x10 None
d x11/dt = x12 None
d x12/dt = alpha beta x11 v_p2d2 s_d2 v_p2p2 s_p2 v_p2xi s_xi alpha beta x12 None
d x13/dt = x14 None
d x14/dt = alpha beta x13 v_xie x1 v_xip2 s_p2 alpha beta x14 None
d x15/dt = x16 None
d x16/dt = alpha beta x15 v_sp1 s_p1 v_se x1 v_sr s_r v_sr s_r_lag v_sn_phi_n alpha beta x16 None
d x17/dt = x18 None
d x18/dt = alpha beta x17 v_rp1 s_p1 v_rs s_s v_re x1 alpha beta x18 None
dt = 5 -5 None
time = 13 None
qmax_i = 250 None
qmax_d1 = 65 None
qmax_d2 = 65 None
qmax_p1 = 250 None
qmax_p2 = 300 None
qmax_xi = 500 None
qmax_s = 250 None
qmax_r = 250 None
theta_i = 15 -3 None
theta_d1 = 19 -3 None
theta_d2 = 19 -3 None
theta_p1 = 10 -3 None
theta_p2 = 9 -3 None
theta_xi = 1 -2 None
theta_s = 15 -3 None
theta_r = 15 -3 None
v_ee = 1 -3 None
v_ei = 1.8 -3 None
v_re = 5 -5 None
v_rs = 5 -4 None
v_d1e = 1 -3 None
v_d1d1 = 2 -4 None
v_d1s = 1 -4 None
v_d2e = 7 -4 None
v_d2d2 = 3 -4 None
v_d2s = 5 -5 None
v_p1d1 = 1 -4 None
v_p1p2 = 3 -5 None
v_p2d2 = 3 -4 None
v_p2p2 = 0.75 -4 None
v_p2xi = 4.5 -4 None
v_xip2 = 4 -5 None
v_es = 1.8 -3 None
v_se = 2.2 -3 None
v_xie = 0.1 -3 None
gamma_e = 100 None
alpha = 50 None
beta = 200 None
sigma = 0.006 None
v_sn_phi_n = 2 -3 None
v_sp1 = open2 3.5 -5 None
v_rp1 = kk open1 3.5 -5 None
s_i = qmax_i 1 2 3 x3 theta_i sigma None
s_d1 = qmax_d1 1 2 3 x5 theta_d1 sigma None
s_d2 = qmax_d2 1 2 3 x7 theta_d2 sigma None
s_p1 = qmax_p1 1 2 3 x9 theta_p1 sigma None
s_p2 = qmax_p2 1 2 3 x11 theta_p2 sigma None
s_xi = qmax_xi 1 2 3 x13 theta_xi sigma None
s_s = qmax_s 1 2 3 x15 theta_s sigma None
s_r = qmax_r 1 2 3 x17 theta_r sigma None
s_r_lag = qmax_r 1 2 3 delay x17 tau theta_r sigma None
t = time None