XPP model

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

# XPP has its own rule of naming parameters, so the parameter names in this code might be different from those in the paper.

# Equations of PKA and ERK dynamics are same as the ones in Nature Neuroscience paper
 
pRaf'=(K_fRaf*(delay(5HT, 25)))*Raf-K_bRaf*pRaf
Raf=Raf_total-pRaf

MAPKK'=-K_fMAPKK*pRaf*(MAPKK/(MAPKK+K_1mkk))+K_bMAPKK*(pMAPKK/(pMAPKK+K_2mkk))

ppMAPKK'=K_fMAPKK*pRaf*(pMAPKK/(pMAPKK+K_1mkk))-K_bMAPKK*(ppMAPKK/(ppMAPKK+K_2mkk))

pMAPKK=MAPKK_tt-MAPKK-ppMAPKK


MAPK'=-K_fMAPK*ppMAPKK*(MAPK/(MAPK+K_1mk))+K_bMAPK*(pMAPK/(pMAPK+K_2mk))
ppMAPK'=K_fMAPK*ppMAPKK*(pMAPK/(pMAPK+K_1mk))-K_bMAPK*(ppMAPK/(ppMAPK+K_2mk))
pMAPK=MAPK_tt-ppMAPK-MAPK


cAMP'=lamda*(5HT/(5HT+K_5HT))-K_bcamp*cAMP

PKAR'=K_fpka*PKARC*cAMP^2-K_bpka*PKAR*PKAC

PKARC'=-K_fpka*PKARC*cAMP^2+K_bpka*PKAR*PKAC

PKAC'=K_fpka*PKARC*cAMP^2-K_bpka*PKAR*PKAC



p K_fRaf=0.004
p K_bRaf=0.1
p Raf_total=0.5

p K_fMAPKK=0.41
p K_bMAPKK=0.04
p K_1mkk=0.20
p K_2mkk=0.19
p MAPKK_tt=0.5


p K_fMAPK=0.41
p K_bMAPK=0.12
p K_1mk=0.19
p K_2mk=0.21
p MAPK_tt=0.5

p lamda=3.64
p K_bcamp=1
p K_5HT=85


p K_fpka=20
p K_bpka=12




# PKACA is the activity of PKA, calculated in the way as described in Muller and Carew 1998.
# 3.8 is the maximal PKAC.

PKACA=PKAC/3.8
inducer=PKACA*ppMAPK


init pRaf=0
init MAPKK=0.5
init ppMAPKK=0
init MAPK=0.5
init PPMAPK=0

init PKAC=0
init cAMP=0
init PKAR=0
init PKARC=4



# the following are the equations of CREB1, CREB2, and CEBP

#phosphorylated CREB1 protein
pCREB1'=K_phosC1*PKACA*CREB1-K_dephC1*pCREB1


#phosphorylated CREB2 protein
pCREB2'=K_phosC2*ppMAPK*CREB2-K_dephC2*pCREB2

CREB1=0.05-pCREB1
CREB2=0.05-pCREB2


p K_phosC1=0.15
p K_dephC1=0.05

p K_phosC2=3.5
p K_dephC2=0.5


#synthesis OF CEBP protein
CEBP'=((V_xCBP*((f5^2/K_xCBP)/(1+f5^2/K_xCBP+f6^2/K_yCBP)))-K_dxCBP*CEBP)-(K_phosC3*ppMAPK*CEBP-K_dephC3*pCEBP)

#phosphorylated CEBP protein
pCEBP'=(K_phosC3*ppMAPK*CEBP-K_dephC3*pCEBP-K_dZ2*pCEBP)

f5=pCREB1
f6=CREB2

# CBP would be reduced to 0.65 when CBP knockdown was simulated. 
CBP=1

# we do not know the binding affinity of CBP, so we actually tried different Kcbp, ranging from 1 to 20. 
# We found that varying Kcbp did not change the rank of the Rescue Protocol in 10000 protocols, which always ended up as the one with highest peak pCEBP. 
# Varying Kcbp, we got different numbers of potential rescue protocols. The maximum number of potential rescue protocols we got was 421.    

Kcbp=20


v_xCBP=20*(CBP/(Kcbp+CBP))

# parameters K5 and K6 in J Neurosci. paper are the square root of K_xCBP and K_yCBP.
p K_xCBP=0.00009
p K_yCBP=0.00001

p K_dxCBP=0.075
p K_dZ2=0.0015

p K_phosC3=0.25
p K_dephC3=0.5


#init pCREB1, pCREB2, CEBP
init pCREB1=0
init pCREB2=0
init CEBP=0

# 5 pulses of 5-HT
5HT'=50*(on0*heav(t-t2)*heav(t2+5-t)+on1*heav(t-t2-inter1)*heav(inter1+5+t2-t)+on2*heav(t-t2-inter1-inter2)*heav(inter1+inter2+5+t2-t)+on3*heav(t-t2-inter1-inter2-inter3)*heav(inter1+inter2+inter3+5+t2-t)+on4*heav(t-t2-inter1-inter2-inter3-inter4)*heav(inter1+inter2+inter3+inter4+5+t2-t))*turnon-5HT

# calculation of ISIs
inter1=5*(1+a1)

inter2=5*(1+a2)

inter3=5*(1+a3)

inter4=5*(1+a4)

# on0 - on4 control how many pulses of 5-HT we will use
p on0=1
p on1=1
p on2=1
p on3=1
p on4=1


p turnon=1
p t1=2995
p t2=2910


aux 1=(t-t2)
aux 4=5HT
aux 7=a1
aux 8=a2
aux 9=a3
aux 10=a4
aux 13=inducer
aux 14=PKACA
aux 15=ppMAPK
auX 17=CEBP+pCEBP
aux 18=pCEBP




p step=1131


# This is how we code 10,000 protocols
a4=(step-10*flr(step/10))
a3=flr((step-100*flr(step/100))/10)
a2=flr((step-1000*flr(step/1000))/100)
a1=flr(step/1000)

@ total=4000, xlo=0, xhi=5000, ylo=0, yhi=10, bounds=10e30, MAXSTOR=1300000,xp=vs, yp=mk,nout=250, dt=0.01,
@ delay=6000
#@ output=test.txt

# This is how we run 10,000 simulations. 
@ RANGE=1, RANGEOVER=step, RANGESTEP=10000, RANGELOW=0, RANGEHIGH=10000, RANGERESET=yes, RANGEOLDIC=yes, output=test
This file has been produced by sbmlutils.

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.
  2. Redistributions in a different form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
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 [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 [83] name constant value unit derived unit sbo cvterm
k_fraf k_fraf = 0.004 0.004 None
k_braf k_braf = 0.1 0.1 None
raf_total raf_total = 0.5 0.5 None
k_fmapkk k_fmapkk = 0.41 0.41 None
k_bmapkk k_bmapkk = 0.04 0.04 None
k_1mkk k_1mkk = 0.20 0.2 None
k_2mkk k_2mkk = 0.19 0.19 None
mapkk_tt mapkk_tt = 0.5 0.5 None
k_fmapk k_fmapk = 0.41 0.41 None
k_bmapk k_bmapk = 0.12 0.12 None
k_1mk k_1mk = 0.19 0.19 None
k_2mk k_2mk = 0.21 0.21 None
mapk_tt mapk_tt = 0.5 0.5 None
lamda lamda = 3.64 3.64 None
k_bcamp k_bcamp = 1 1.0 None
k_5ht k_5ht = 85 85.0 None
k_fpka k_fpka = 20 20.0 None
k_bpka k_bpka = 12 12.0 None
praf praf = 0 0.0 None
mapkk mapkk = 0.5 0.5 None
ppmapkk ppmapkk = 0 0.0 None
mapk mapk = 0.5 0.5 None
ppmapk ppmapk = 0 0.0 None
pkac pkac = 0 0.0 None
camp camp = 0 0.0 None
pkar pkar = 0 0.0 None
pkarc pkarc = 4 4.0 None
k_phosc1 k_phosc1 = 0.15 0.15 None
k_dephc1 k_dephc1 = 0.05 0.05 None
k_phosc2 k_phosc2 = 3.5 3.5 None
k_dephc2 k_dephc2 = 0.5 0.5 None
k_xcbp k_xcbp = 0.00009 9e-05 None
k_ycbp k_ycbp = 0.00001 1e-05 None
k_dxcbp k_dxcbp = 0.075 0.075 None
k_dz2 k_dz2 = 0.0015 0.0015 None
k_phosc3 k_phosc3 = 0.25 0.25 None
k_dephc3 k_dephc3 = 0.5 0.5 None
pcreb1 pcreb1 = 0 0.0 None
pcreb2 pcreb2 = 0 0.0 None
cebp cebp = 0 0.0 None
on0 on0 = 1 1.0 None
on1 on1 = 1 1.0 None
on2 on2 = 1 1.0 None
on3 on3 = 1 1.0 None
on4 on4 = 1 1.0 None
turnon turnon = 1 1.0 None
t1 t1 = 2995 2995.0 None
t2 t2 = 2910 2910.0 None
step step = 1131 1131.0 None
pcebp 0.0 dimensionless None
0.0 dimensionless None
raf 0.0 dimensionless None
pmapkk 0.0 dimensionless None
pmapk 0.0 dimensionless None
pkaca 0.0 dimensionless None
inducer 0.0 dimensionless None
creb1 0.0 dimensionless None
creb2 0.0 dimensionless None
f5 0.0 dimensionless None
f6 0.0 dimensionless None
cbp 0.0 dimensionless None
kcbp 0.0 dimensionless None
v_xcbp 0.0 dimensionless None
inter1 0.0 dimensionless None
inter2 0.0 dimensionless None
inter3 0.0 dimensionless None
inter4 0.0 dimensionless None
0.0 dimensionless None
0.0 dimensionless None
0.0 dimensionless None
0.0 dimensionless None
0.0 dimensionless None
0.0 dimensionless None
0.0 dimensionless None
0.0 dimensionless None
0.0 dimensionless None
0.0 dimensionless None
0.0 dimensionless None
a4 0.0 dimensionless None
a3 0.0 dimensionless None
a2 0.0 dimensionless None
a1 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [46]   assignment name derived units sbo cvterm
d praf/dt = k_fraf delay 5 25 raf k_braf praf None
d mapkk/dt = k_fmapkk praf mapkk mapkk k_1mkk k_bmapkk pmapkk pmapkk k_2mkk None
d ppmapkk/dt = k_fmapkk praf pmapkk pmapkk k_1mkk k_bmapkk ppmapkk ppmapkk k_2mkk None
d mapk/dt = k_fmapk ppmapkk mapk mapk k_1mk k_bmapk pmapk pmapk k_2mk None
d ppmapk/dt = k_fmapk ppmapkk pmapk pmapk k_1mk k_bmapk ppmapk ppmapk k_2mk None
d camp/dt = lamda 5 5 k_5ht k_bcamp camp None
d pkar/dt = k_fpka pkarc camp 2 k_bpka pkar pkac None
d pkarc/dt = k_fpka pkarc camp 2 k_bpka pkar pkac None
d pkac/dt = k_fpka pkarc camp 2 k_bpka pkar pkac None
d pcreb1/dt = k_phosc1 pkaca creb1 k_dephc1 pcreb1 None
d pcreb2/dt = k_phosc2 ppmapk creb2 k_dephc2 pcreb2 None
d cebp/dt = v_xcbp f5 2 k_xcbp 1 f5 2 k_xcbp f6 2 k_ycbp k_dxcbp cebp k_phosc3 ppmapk cebp k_dephc3 pcebp None
d pcebp/dt = k_phosc3 ppmapk cebp k_dephc3 pcebp k_dz2 pcebp None
= 50 on0 heav t t2 heav t2 5 t on1 heav t t2 inter1 heav inter1 5 t2 t on2 heav t t2 inter1 inter2 heav inter1 inter2 5 t2 t on3 heav t t2 inter1 inter2 inter3 heav inter1 inter2 inter3 5 t2 t on4 heav t t2 inter1 inter2 inter3 inter4 heav inter1 inter2 inter3 inter4 5 t2 t turnon 5 None
raf = raf_total praf None
pmapkk = mapkk_tt mapkk ppmapkk None
pmapk = mapk_tt ppmapk mapk None
pkaca = pkac 3.8 None
inducer = pkaca ppmapk None
creb1 = 0.05 pcreb1 None
creb2 = 0.05 pcreb2 None
f5 = pcreb1 None
f6 = creb2 None
cbp = 1 None
kcbp = 20 None
v_xcbp = 20 cbp kcbp cbp None
inter1 = 5 1 a1 None
inter2 = 5 1 a2 None
inter3 = 5 1 a3 None
inter4 = 5 1 a4 None
= t t2 None
= 5 None
= a1 None
= a2 None
= a3 None
= a4 None
= inducer None
= pkaca None
= ppmapk None
= cebp pcebp None
= pcebp None
a4 = step 10 flr step 10 None
a3 = flr step 100 flr step 100 10 None
a2 = flr step 1000 flr step 1000 100 None
a1 = flr step 1000 None
t = time None