XPP model

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

# Six Subunit Model of CaMKII
#
# Graupner, M. and Brunel, N., STDP in a bistable synapse model based on CaMKII and associated signaling pathways, PLoS Comput Biol, 3(11), e221, 2299-2323 (2007). 
#
#   Please note that this file allows to compute the steady-states of the CaMKII 
#   phosphorylation level with respect to calicum. The parameter used here allow 
#   to reproduce the data shown in Fig.3C by the blue line (p.2303) in the above 
#	menioned paper. 
#   The steady-state diagram consits of two separate branches which have to be computed
#   separately. This is the case since the initial point (specified by 'init') has to 
#   be a fixed point on the respective branch. This file allows to compute the lower branch 
#   including the DOWN state. The computation starts at Ca_0 = 0.01 \mu M.
#   
#   Note however that all the dynamic simulations of the model were not done with xppaut. 
#   The dynamics of the CaMKII-system has been implemented in a C++ code. Please contact
#   the authors for further informations.
#
#  this file is set to run:
#  1. start xppaut and load file
#     $ xppaut 
#  2. lauch auto
#     click -> File -> AUTO
#  3. run auto
#     click -> Run -> Steady State 
#  and you will get the fix-points of the system with the bistability
#
# 
# auto parameters
@ NPR=400, NMAX=40000, DSMAX=0.01, DS=.01, PARMIN=0, PARMAX=2
@ AUTOXMIN=0, AUTOXMAX=2, AUTOYMIN=0, AUTOYMAX=210, AUTOVAR=Ta
#
# note that total receptor pop is conserved
# so p0+p1+...+p10 is constant
# this leads to a zero eigenvalue, so we set the total
# receptor population to be p0i=20 and eliminate p0
# this allows AUTO to do its thing without 
# choking
#
#
# inital conditions to start at Ca=0.01
# required to compuate the fix-points including the DOWN state
init B1=0,B2=0,B3=0
init PP1=0.001108,I1P=0.0359
# 
# parameters
param Ca=0.01
param b0i=33.3
param K5=0.1, CaM=0.1
param L1=0.1, L2=0.025, L3=0.32, L4=0.40
param k6=6, k7=6
param PP10=0.2
param k12=6000
param KM=0.4
param k11=500, km11=0.1
param I10=1
param Kdcan=0.053, ncan=3, kcan0=0.1, kcan=18
param Kdpka=0.11, npka=8, kpka0=0.00359, kpka=100


# occupied receptors
rr=sum(0,12)of(shift(B1,i'))
# p0 is whats left from total
B0=b0i-rr

# total activated and inactivated subunit concentrations
tact= B1 + 2*(B2 + B3 + B4) + 3*(B5 + B6 + B7 + B8) + 4*(B9 + B10 + B11) + 5*B12 + 6*B13

# kinetic equations
phossum=B1 + 2*(B2 + B3 + B4) + 3*(B5 + B6 + B7 + B8) + 4*(B9 + B10 + B11) + 5*B12 + 6*B13
#PP1=Ca^3/(KL^3 + Ca^3)
#PP1=base + kpp1*Ca^3/(KL^3 +  Ca^3)*KH^4/(KH^4 + Ca^4)
k10=k12*PP1/(KM + phossum)
#
C=CaM/(1 + L4/Ca + L3*L4/(Ca^2) + L2*L3*L4/(Ca^3) + L1*L2*L3*L4/(Ca^4))
gamma=C/(K5+C) 
vPKA=kpka0 + kpka/(1 + (Kdpka/C)^npka)
vCaN=kcan0 + kcan/(1 + (Kdcan/C)^ncan)

# at last the equations

B1' = 6*k6*gamma^2*B0 - 4*k6*gamma^2*B1 - k7*gamma*B1 - k10*B1 + 2*k10*(B2 + B3 + B4)
#
B2' = k7*gamma*B1 + k6*gamma^2*B1 - 3*k6*gamma^2*B2 - k7*gamma*B2 - 2*k10*B2 + k10*(2*B5 + B6 + B7)
B3' = 2*k6*gamma^2*B1 - 2*k7*gamma*B3 - 2*k6*gamma^2*B3 - 2*k10*B3 + k10*(B5 + B6 + B7 + 3*B8) 
B4' = k6*gamma^2*B1 - 2*k7*gamma*B4 - 2*k6*gamma^2*B4 - 2*k10*B4 + k10*(B6 + B7)
#
B5' = k7*gamma*B2 + k7*gamma*B3 + k6*gamma^2*B2 - k7*gamma*B5 - 2*k6*gamma^2*B5 - 3*k10*B5 + k10*(2*B9 + B10)
B6' = k6*gamma^2*B2 + k6*gamma^2*B3  + 2*k7*gamma*B4 - k6*gamma^2*B6 - 2*k7*gamma*B6 - 3*k10*B6 + k10*(B9 + B10 + 2*B11)
B7' = k6*gamma^2*B2 + k7*gamma*B3 + 2*k6*gamma^2*B4 - k6*gamma^2*B7 - 2*k7*gamma*B7 - 3*k10*B7 + k10*(B9 + B10 + 2*B11)
B8' = k6*gamma^2*B3 - 3*k7*gamma*B8 - 3*k10*B8 + k10*B10
#
B9' = k7*gamma*B5 + k6*gamma^2*B5 + k7*gamma*B6 + k7*gamma*B7 - k6*gamma^2*B9 - k7*gamma*B9 - 4*k10*B9 + 2*k10*B12
B10'= k6*gamma^2*B5 + k6*gamma^2*B6 + k7*gamma*B7 + 3*k7*gamma*B8 - 2*k7*gamma*B10 - 4*k10*B10 + 2*k10*B12
B11'= k7*gamma*B6 +  k6*gamma^2*B7 - 2*k7*gamma*B11 - 4*k10*B11 + k10*B12
#
B12'= k7*gamma*B9 + k6*gamma^2*B9 + 2*k7*gamma*B10 + 2*k7*gamma*B11 - k7*gamma*B12 - 5*k10*B12 + 6*k10*B13
#
B13'= k7*gamma*B12 - 6*k10*B13
#
PP1'= -k11*I1P*PP1 + km11*(PP10 - PP1)
I1P'= -k11*I1P*PP1 + km11*(PP10 - PP1) + vPKA*I10 - vCaN*I1P


# dummy to get steady-state value of total phosphate - this can be plotted now
# in AUTO!
ta'=-ta+tact
aux act=tact
#@ total=2000,dt=5,meth=cvode
#@ total=100,dt=0.001
@ total=1000,dt=0.001
@ bound=100000
@ maxstor=100000
@ njmp=10

done
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.


Model :

id
name
time
substance
extent
volume
area
length
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 [51] name constant value unit derived unit sbo cvterm
b1 b1 = 0 0.0 None
b2 b2 = 0 0.0 None
b3 b3 = 0 0.0 None
pp1 pp1 = 0.001108 0.001108 None
i1p i1p = 0.0359 0.0359 None
ca ca = 0.01 0.01 None
b0i b0i = 33.3 33.3 None
k5 k5 = 0.1 0.1 None
cam cam = 0.1 0.1 None
l1 l1 = 0.1 0.1 None
l2 l2 = 0.025 0.025 None
l3 l3 = 0.32 0.32 None
l4 l4 = 0.40 0.4 None
k6 k6 = 6 6.0 None
k7 k7 = 6 6.0 None
pp10 pp10 = 0.2 0.2 None
k12 k12 = 6000 6000.0 None
km km = 0.4 0.4 None
k11 k11 = 500 500.0 None
km11 km11 = 0.1 0.1 None
i10 i10 = 1 1.0 None
kdcan kdcan = 0.053 0.053 None
ncan ncan = 3 3.0 None
kcan0 kcan0 = 0.1 0.1 None
kcan kcan = 18 18.0 None
kdpka kdpka = 0.11 0.11 None
npka npka = 8 8.0 None
kpka0 kpka0 = 0.00359 0.00359 None
kpka kpka = 100 100.0 None
b4 0.0 dimensionless None
b5 0.0 dimensionless None
b6 0.0 dimensionless None
b7 0.0 dimensionless None
b8 0.0 dimensionless None
b9 0.0 dimensionless None
b10 0.0 dimensionless None
b11 0.0 dimensionless None
b12 0.0 dimensionless None
b13 0.0 dimensionless None
ta 0.0 dimensionless None
rr 0.0 dimensionless None
b0 0.0 dimensionless None
tact 0.0 dimensionless None
phossum 0.0 dimensionless None
k10 0.0 dimensionless None
c 0.0 dimensionless None
gamma 0.0 dimensionless None
vpka 0.0 dimensionless None
vcan 0.0 dimensionless None
act 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [27]   assignment name derived units sbo cvterm
d b1/dt = 6 k6 gamma 2 b0 4 k6 gamma 2 b1 k7 gamma b1 k10 b1 2 k10 b2 b3 b4 None
d b2/dt = k7 gamma b1 k6 gamma 2 b1 3 k6 gamma 2 b2 k7 gamma b2 2 k10 b2 k10 2 b5 b6 b7 None
d b3/dt = 2 k6 gamma 2 b1 2 k7 gamma b3 2 k6 gamma 2 b3 2 k10 b3 k10 b5 b6 b7 3 b8 None
d b4/dt = k6 gamma 2 b1 2 k7 gamma b4 2 k6 gamma 2 b4 2 k10 b4 k10 b6 b7 None
d b5/dt = k7 gamma b2 k7 gamma b3 k6 gamma 2 b2 k7 gamma b5 2 k6 gamma 2 b5 3 k10 b5 k10 2 b9 b10 None
d b6/dt = k6 gamma 2 b2 k6 gamma 2 b3 2 k7 gamma b4 k6 gamma 2 b6 2 k7 gamma b6 3 k10 b6 k10 b9 b10 2 b11 None
d b7/dt = k6 gamma 2 b2 k7 gamma b3 2 k6 gamma 2 b4 k6 gamma 2 b7 2 k7 gamma b7 3 k10 b7 k10 b9 b10 2 b11 None
d b8/dt = k6 gamma 2 b3 3 k7 gamma b8 3 k10 b8 k10 b10 None
d b9/dt = k7 gamma b5 k6 gamma 2 b5 k7 gamma b6 k7 gamma b7 k6 gamma 2 b9 k7 gamma b9 4 k10 b9 2 k10 b12 None
d b10/dt = k6 gamma 2 b5 k6 gamma 2 b6 k7 gamma b7 3 k7 gamma b8 2 k7 gamma b10 4 k10 b10 2 k10 b12 None
d b11/dt = k7 gamma b6 k6 gamma 2 b7 2 k7 gamma b11 4 k10 b11 k10 b12 None
d b12/dt = k7 gamma b9 k6 gamma 2 b9 2 k7 gamma b10 2 k7 gamma b11 k7 gamma b12 5 k10 b12 6 k10 b13 None
d b13/dt = k7 gamma b12 6 k10 b13 None
d pp1/dt = k11 i1p pp1 km11 pp10 pp1 None
d i1p/dt = k11 i1p pp1 km11 pp10 pp1 vpka i10 vcan i1p None
d ta/dt = ta tact None
rr = None None
b0 = b0i rr None
tact = b1 2 b2 b3 b4 3 b5 b6 b7 b8 4 b9 b10 b11 5 b12 6 b13 None
phossum = b1 2 b2 b3 b4 3 b5 b6 b7 b8 4 b9 b10 b11 5 b12 6 b13 None
k10 = k12 pp1 km phossum None
c = cam 1 l4 ca l3 l4 ca 2 l2 l3 l4 ca 3 l1 l2 l3 l4 ca 4 None
gamma = c k5 c None
vpka = kpka0 kpka 1 kdpka c npka None
vcan = kcan0 kcan 1 kdcan c ncan None
act = tact None
t = time None