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 upper branch 
#   including the UP state. The computation starts at Ca_0 = 0.2 \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
#
# initial conditions to start at Ca=0.2
# required to compuate the fix-point island including the UP state
#
init B1=1.325911,B2=2.146327,B3=0.816472,B4=0.348016
init B5=3.218889,B6=1.346285,B7=1.380859
init B8=0.215422,B9=4.942081,B10=2.434134
init B11=1.284668,B12=8.591719,B13=4.727069
init PP1=0.00515738, I1P=0.00755588
init TA=132.3964
#
#
param Ca=0.2
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
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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 [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 = 1.325911 1.325911 None
b2 b2 = 2.146327 2.146327 None
b3 b3 = 0.816472 0.816472 None
b4 b4 = 0.348016 0.348016 None
b5 b5 = 3.218889 3.218889 None
b6 b6 = 1.346285 1.346285 None
b7 b7 = 1.380859 1.380859 None
b8 b8 = 0.215422 0.215422 None
b9 b9 = 4.942081 4.942081 None
b10 b10 = 2.434134 2.434134 None
b11 b11 = 1.284668 1.284668 None
b12 b12 = 8.591719 8.591719 None
b13 b13 = 4.727069 4.727069 None
pp1 pp1 = 0.00515738 0.00515738 None
i1p i1p = 0.00755588 0.00755588 None
ta ta = 132.3964 132.3964 None
ca ca = 0.2 0.2 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
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