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G2_M_v1.py
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G2_M_v1.py
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"""An implementation of the model from:
Mathematical modeling and sensitivity analysis of G2/S phase in the cell cycle
involving the p53/Mdm2 oscillation system. Yoshihiko Tashima, Yu Kisaka,
Taizo Hanai, Hiroyuki Hamada, Yukihiro Eguchi, Masahiro Okamoto.
Proc. Int. Fed. Med. Biomed. Eng., 14(2006), pp.195-198
doi:10.1016/j.biosystems.2008.05.016 "Update"
http://www.researchgate.net/publication/226126852_Mathematical_modeling_of_G2M_phase_in_the_cell_cycle_with_involving_the_p53Mdm2_oscillation_system
Implemented by: Corey Hayford
"""
from pysb import *
from pysb.util import *
from pysb.macros import *
from pysb.bng import *
from pysb.integrate import odesolve
import pylab as pl
from numpy import linspace
from sympy import sympify
Model()
def set_dna_damage(damage):
model.parameters['DDS_0'].value = damage
def declare_monomers():
"""Declare the monomers in the Tashima model
'state' is the activity state between the monomers
'a' is the active conformation binding state
'i' is the inactive conformation binding state
'phos' is the phosphorylation state
'u' is the unphosphorylated monomer
'p' is the phosphorylated monomer
'b' is the binding site between p## and other proteins"""
Monomer("Signal") #State can be on or off
Monomer("SignalDamp") #Dampens signal in Deg(t) function
# **Regulatory proteins**
Monomer("p53")
Monomer("p21", ['b'])
Monomer("x14_3_3", ['b'])
Monomer("ATR", ['b'])
Monomer("Mdm2")
Monomer("I")
Monomer('Cdc25', ['b', 'state', 'phos'], {'state':['i','a'], 'phos':['u','p']})
Monomer('MPF' , ['b', 'state'], {'state':['i','a']})
#MPF should be split into Cyclin B and CDK1
Monomer('Wee1', ['phos'], {'phos':['u','p']})
Monomer('Chk1', ['phos'], {'phos':['u','p']})
# **Cyclins** """ #MPF Complex
#Monomer("CycB", [ 'c'])
# **Cyclin-dependent kinases** """ #MPF Complex
#Monomer("CDK1",['phos','b','c'], {'phos':['u','p']})
def declare_parameters():
# ***Declare Initial Conditions***
Parameter("X1_0", 1.0e-6) #Chk1p
Parameter("X1pre_0", 0.9999999) #Chk1
Parameter("X2_0", 0.2) #ATR
Parameter("X3_0", 0.0265) #p53
Parameter("X4_0", 1.0e-6) #preMPF
Parameter("X5_0", 1.0e-8) #MPF
Parameter("X6_0", 0.0) #p21
Parameter("X7_0", 0.0) #p21/MPF
Parameter("X8_0", 1.0e-6) #iCdc25
Parameter("X9_0", 2.0e-5) #iCdc25Ps216
Parameter("X10_0", 0.03) #iCdc25Ps216/14-3-3
Parameter("X11_0", 1.0e-6) #aCdc25
Parameter("X12_0", 0.0) #aCdc25Ps216
Parameter("X13_0", 2.0) #x14_3_3
Parameter("X14_0", 0.001) #Wee1
Parameter("X15_0", 0.0) #Wee1p
Parameter("X16_0", 2.35e-4) #Mdm2
Parameter("X17_0", 0.0) #I(Intermediate)
Parameter("DDS_0") #DDS
# ***Declare Kinetic Parameters***
Parameter("k1", 0.2)
Parameter("k2", 1.0)
Parameter("k3", 1.0)
Parameter("km3", 1.0)
Parameter("k4", 0.01)
Parameter("km4", 0.01)
Parameter("k5", 1.0)
Parameter("km5", 0.01)
Parameter("k6", 1.0)
Parameter("km6", 0.01)
Parameter("k7", 0.01)
Parameter("k8", 100.0)
Parameter("k9", 0.0005)
Parameter("k10", 1.0)
Parameter("km10", 1.0)
Parameter("k11", 0.1)
Parameter("km11", 1.0)
Parameter("k12", 0.01)
Parameter("k13", 1.0)
Parameter("k14", 0.01)
Parameter("k15", 0.1)
Parameter("k16", 2.0e-4)
Parameter("k17", 0.1)
Parameter("km17", 1.0)
Parameter("k18", 1.0)
Parameter("k19", 1.0)
Parameter("k20", 1.0)
Parameter("k21", 0.01)
Parameter("k22", 0.00094)
Parameter("k23", 0.02)
Parameter("k24", 10.0)
Parameter("k25", 0.005)
Parameter("k26", 0.004)
Parameter("k27", 6.0)
Parameter("k28", 0.0001)
Parameter("k30", 0.001)
Parameter("k31", 1.0)
Parameter("k32", 0.0001)
Parameter("k33", 1e-8)
Parameter("k34", 1.5)
Parameter("k_ex", 1.0)
Parameter("v_in", 1.0e-5)
Parameter("k_m", 9.5)
Parameter("n", 9.0)
Parameter("k_damp", 0.02)
Parameter("k_deg", 0.772)
Parameter("Deg_0", 0.0566)
# ***Initial Conditions***
def declare_initial_conditions():
Initial(Chk1(phos='p'), X1_0) #0
Initial(Chk1(phos='u'), X1pre_0) #1
Initial(ATR(b=None), X2_0) #2
Initial(p53(), X3_0) #3
Initial(MPF(state='i', b=None), X4_0) #4
Initial(MPF(state='a', b=None), X5_0) #5
Initial(p21(b=None), X6_0) #6
Initial(p21(b=1) % MPF(b=1, state='a'), X7_0) #7
Initial(Cdc25(b=None, state='i', phos= 'u'), X8_0) #8
Initial(Cdc25(b=None, state='i', phos='p'), X9_0) #9
Initial(Cdc25(b=1, state= 'i', phos= 'p') % x14_3_3(b=1), X10_0) #10
Initial(Cdc25(b=None, state= 'a', phos= 'u'), X11_0) #11
Initial(Cdc25(b=None, state= 'a', phos= 'p'), X12_0) #12
Initial(x14_3_3(b=None), X13_0) #13
Initial(Wee1(phos= 'u'), X14_0) #14
Initial(Wee1(phos= 'p'), X15_0) #15
Initial(Mdm2(), X16_0) #16
Initial(I(), X17_0) #17
Initial(Signal(), DDS_0) #18
Initial(SignalDamp(), DDS_0) #19
# ***Observables***
def declare_observables():
Observable("OBS_aCdc25", Cdc25(b=None, state= 'a', phos= 'u'))
Observable("OBS_MPF", MPF(b=None, state= 'a'))
Observable("OBS_p53", p53())
Observable("OBS_Wee1", Wee1(phos= 'u'))
#####
Observable("OBS_Int", I())
Observable("OBS_Mdm2", Mdm2())
Observable("signal", Signal())
Observable("signal_damp", SignalDamp())
# ***Functions***
# Developed by Leonard Harris - modified pysb in lharris branch to process functions
def declare_functions():
Expression("create_preMPF", sympify("k9/(1 + k31*OBS_p53)"))
Expression("Hill_Mdm2", sympify("k24*OBS_Int^n / (k_m^n + OBS_Int^n)"))
Expression("create_intermediate", sympify("k27*OBS_p53/ (1 + k26*OBS_p53*OBS_Mdm2)"))
Expression("sig_deg", sympify("Deg_0 - k_deg*(signal-signal_damp)"))
Expression("kdamp_DDS0", sympify("k_damp*DDS_0"))
# ***Rules***
def declare_rules():
## ** Functions **
Rule('Signal_Damp', SignalDamp() >> None, kdamp_DDS0)
Rule('Mdm2_Degrade_p53', p53() + Mdm2() >> Mdm2(), sig_deg)
Rule('Create_preMPF', None >> MPF(b=None, state='i'), create_preMPF)
Rule('Create_Mdm2_Hill', None >> Mdm2(), Hill_Mdm2)
Rule('Signal_Create_I', Signal() >> Signal() + I(), create_intermediate)
##
Rule('Signal_Create_ATR', Signal() >> Signal() + ATR(b=None), k1)
Rule('Signal_Create_p53', Signal() >> Signal() + p53(), k34)
Rule('Signal_Degrade', Signal() >> None, k33)
Rule('Chk1_Dephos', Chk1(phos= 'p') >> Chk1(phos= 'u'), km3)
Rule('Chk1_Phos', Chk1(phos= 'u') + ATR(b=None) >> Chk1(phos= 'p') + ATR(b=None), k3)
Rule('iCdc25_Phos', Chk1(phos= 'p') + Cdc25(b=None, state= 'i', phos='u') >> Chk1(phos= 'p') + Cdc25(b=None, state= 'i', phos= 'p'), k7)
Rule('aCdc25_Phos', Chk1(phos= 'p') + Cdc25(b=None, state= 'a', phos='u') >> Chk1(phos= 'p') + Cdc25(b=None, state= 'a', phos= 'p'), k4)
Rule('ATR_Degrade', ATR(b=None) >> None, k2)
Rule('p53_Create', None >> p53(), k28)
Rule('p53_Degrade', p53() >> None, k30)
Rule('p53_Create_p21', p53() >> p53() + p21(b=None), k15)
Rule('p53_Create_x14_3_3', p53() >> p53() + x14_3_3(b=None), k21)
Rule('Activate_MPF', MPF(b=None, state='i') + Cdc25(b=None, state='a') >> MPF(b=None, state='a') + Cdc25(b=None, state='a'), k10) #Removed 'phos' from Activate_MPF1/2
# Rule('Activate_MPF1', MPF(b=None, state='i') + Cdc25(b=None, state='a', phos='u') >> MPF(b=None, state='a') + Cdc25(b=None, state='a', phos='u'), k10) #With unphosphorylated aCdc25
# Rule('Activate_MPF2', MPF(b=None, state='i') + Cdc25(b=None, state='a', phos='p') >> MPF(b=None, state='a') + Cdc25(b=None, state='a', phos='p'), k10) #With phosphorylated aCdc25
Rule('Inactivate_MPF', MPF(b=None, state='a') + Wee1(phos='u') >> MPF(b=None, state='i') + Wee1(phos='u'), km10)
Rule('Degrade_MPF', MPF(b=None, state='a') + MPF(b=None, state='a') >> None, k12)
Rule('Complex_MPF_p21', MPF(b=None, state='a') + p21(b=None) <> MPF(b=1, state= 'a') % p21(b=1), k11, km11)
# Rule('Complex_MPF_p21', MPF(b=None, state='a') + p21(b=None) >> MPF(b=1, state= 'a') % p21(b=1), k11)
# Rule('Decomplex_MPF_p21', MPF(b=1, state= 'a') % p21(b=1) >> MPF(b=None, state='a') + p21(b=None), km11)
Rule('Activate_Cdc25', MPF(b=None, state='a') + Cdc25(b=None, state= 'i', phos= 'u') >> MPF(b=None, state= 'a') + Cdc25(b=None, state= 'a', phos= 'u'), k5)
Rule('Acitvate_Cdc25Ps216', MPF(b=None, state='a') + Cdc25(b=None, state= 'i', phos= 'p') >> MPF(b=None, state= 'a') + Cdc25(b=None, state= 'a', phos= 'p'), k6)
Rule('Create_p21', None >> p21(b=None), k14)
Rule('Degrade_p21', p21(b=None) >> None, k13)
Rule('Create_iCdc25', None >> Cdc25(b=None, state= 'i', phos= 'u'), v_in)
Rule('Deactivate_aCdc25', Cdc25(b=None, state= 'a', phos= 'u') >> Cdc25(b=None, state= 'i', phos= 'u'), km5)
Rule('Complex_iCdc25Ps216_x14_3_3', Cdc25(b=None, state= 'i', phos= 'p') + x14_3_3(b=None) >> Cdc25(b=1, state= 'i', phos= 'p') % x14_3_3(b=1), k8)
Rule('Deactivate_Cdc25Ps216', Cdc25(b=None, state= 'a', phos= 'p') >> Cdc25(b=None, state= 'i', phos= 'p'), km6)
Rule('Degrade_Complex_iCdc25Ps216_x14_3_3', Cdc25(b=1, state= 'i', phos= 'p') % x14_3_3(b=1) >> None, k_ex)
Rule('Degrade_aCdc25', Cdc25(b=None, state= 'a', phos= 'u') >> None, k32)
Rule('aCdc25Ps216_Dephos', Cdc25(b=None, state= 'a', phos= 'p') >> Cdc25(b=None, state= 'a', phos= 'u'), km4)
Rule('Create_x14_3_3', None >> x14_3_3(b=None), k20)
Rule('Degrade_x14_3_3', x14_3_3(b=None) >> None, k19)
Rule('Create_Wee1u', None >> Wee1(phos='u'), k16)
Rule('Wee1_Phos', MPF(b=None, state= 'a') + Wee1(phos= 'u') >> MPF(b=None, state= 'a') + Wee1(phos= 'p'), k17)
Rule('Wee1_Dephos', Wee1(phos= 'p') >> Wee1(phos= 'u'), km17)
Rule('Degrade_Wee1p', Wee1(phos= 'p') >> None, k18)
Rule('Create_Mdm2', None >> Mdm2(), k22)
Rule('Degrade_Mdm2', Mdm2() >> None, k23)
Rule('Degrade_Intermediate', I() >> None, k25)