def ComplexIIb_to_MLKL():
"""Necrosome formation and MLKL activation"""
bind(RIP1(bDD = ANY, bRHIM = None, state = 'unmod'), 'bRHIM', RIP3(bRHIM = None, state = 'unmod'), 'bRHIM', [1e-6, 1e-3])
Rule('Rip3_PO4lation', RIP1(bRHIM=ANY, state = 'unmod')%RIP3(bRHIM=ANY, state='unmod') >> RIP1(bRHIM=ANY, state = 'unmod')%RIP3(bRHIM=ANY, state = 'po4'), Parameter('k19', 1e-2))
Rule('Rip1_PO4lation', RIP1(bRHIM=ANY, state = 'unmod')%RIP3(bRHIM=ANY, state='po4') >> RIP1(bRHIM=ANY, state = 'po4')%RIP3(bRHIM=ANY, state = 'po4'), Parameter('k20', 1e-3))
catalyze_state(RIP1(state='po4'), 'bMLKL', MLKL(), 'bRHIM', 'state', 'unmod', 'active', [1e-6,1e-3, 1e-1])
catalyze_state(MLKL(state='active'), 'bRHIM', MLKL(), 'bRHIM', 'state', 'unmod', 'active', [1e-7, 0.4, 0.01])
def Bid_Hypothesis():
"""The Zinkel lab found evidence of Bid mediated inhibition of necroptosis. Dr. Zinkel proposed that Bid has a third state (e.g. phosporylated) that can inhibit the necrosome by sequestering RIP3. We presume that Bid-po4 cannot be truncated. There are 3 phosphorylation sites on Bid and evidence that BId-po4 is resistant to truncation exists"""
#-------------Bid Interactions--------------------------
# Bid Phosphorylation and Truncation
catalyze_state(BidK(), 'bf', Bid(), 'bf', 'state', 'U', 'po4', [1e-6, 1e-3, 1e-1])
# Bid-PO4 sequestering RIP1
bind(RIP1(bDD = None, bRHIM = None, state = 'unmod'), 'bRHIM', Bid(bf = None, state = 'po4'), 'bf', [1e-6, 1e-3])
def PP2A_phosphatase():
Parameter('k_pp2f', 1)
Parameter('k_pp2r', 0.001)
Parameter('k_pp2e', 10)
alias_model_components()
catalyze_state(PP2A(), 'mek', MEK(erk=None), 's', 'state', 'p', 'up',
(k_pp2f, k_pp2r, k_pp2e))
def MEK_phosphorylates_ERK():
Parameter('k_mef', 1)
Parameter('k_mer', 0.1)
Parameter('k_mee', 10)
alias_model_components()
catalyze_state(MEK(s=None, state='p', inh=None), 'erk', ERK(), 's',
'state', 'up', 'p', (k_mef, k_mer, k_mee))
def PP2A_phosphatase():
Parameter('k_pp2f', 1)
Parameter('k_pp2r', 0.001)
Parameter('k_pp2e', 10)
alias_model_components()
catalyze_state(PP2A(), 'mek', MEK(erk=None), 's', 'state', 'p', 'up',
(k_pp2f, k_pp2r, k_pp2e))
def DUSP_phospatase():
Parameter('k_dspf', 1)
Parameter('k_dspr', 0.001)
Parameter('k_dspe', 10)
alias_model_components()
catalyze_state(DUSP(), 'erk', ERK(sos=None), 's', 'state', 'p', 'up',
(k_dspf, k_dspr, k_dspe))
def MEK_phosphorylates_ERK():
Parameter('k_mef', 1)
Parameter('k_mer', 0.1)
Parameter('k_mee', 10)
alias_model_components()
catalyze_state(MEK(s=None, state='p', inh=None), 'erk', ERK(), 's',
'state', 'up', 'p', (k_mef, k_mer, k_mee))
def ERK_feedback():
Parameter('k_epsf', 1e-4)
Parameter('k_epsr', 0.1)
Parameter('k_epse', 1)
alias_model_components()
catalyze_state(ERK(state='p', s=None), 'sos', SOS(ras=None, phos=None),
'erk', 'state', 'up', 'p', (k_epsf, k_epsr, k_epse))
def by_BRAF_mut():
Parameter('k_bmf', 1)
Parameter('k_bmr', 0.1)
Parameter('k_bme', 3)
alias_model_components()
catalyze_state(BRAF(vem=None), 'erk', MEK(), 's',
'state', 'up', 'p', (k_bmf, k_bmr, k_bme))
def by_BRAF_mut():
Parameter('k_bmf', 1)
Parameter('k_bmr', 0.1)
Parameter('k_bme', 3)
alias_model_components()
catalyze_state(BRAF(vem=None), 'erk', MEK(), 's', 'state', 'up', 'p',
(k_bmf, k_bmr, k_bme))
def ERK_feedback():
Parameter('k_epsf', 1e-4)
Parameter('k_epsr', 0.1)
Parameter('k_epse', 1)
alias_model_components()
catalyze_state(ERK(state='p', s=None), 'sos', SOS(ras=None, phos=None),
'erk', 'state', 'up', 'p', (k_epsf, k_epsr, k_epse))
def DUSP_phospatase():
Parameter('k_dspf', 1)
Parameter('k_dspr', 0.001)
Parameter('k_dspe', 10)
alias_model_components()
catalyze_state(DUSP(), 'erk', ERK(sos=None), 's', 'state', 'p', 'up',
(k_dspf, k_dspr, k_dspe))
def KRAS_activation():
# Rate constants
# -------------
Parameter('kf1', 1)
Parameter('kr1', 0.1)
Parameter('kf2', 1)
Parameter('kr2', 0.1)
Parameter('kf3', 1)
Parameter('kr3', 0.1)
Parameter('kf4', 1)
Parameter('kr4', 0.001)
Parameter('ke4', 50)
Parameter('kf5', 0.5)
Parameter('kr5', 1e-9)
Parameter('k_dimf', 1)
Parameter('k_dimr', 0.1)
alias_model_components()
# Rules
# -----
# EGF binds EGFR
Rule('EGF_binds_EGFR',
EGF(egfr=None) + EGFR(egf=None) <>
EGF(egfr=1) % EGFR(egf=1), kf1, kr1)
# The EGF-EGFR complex binds another EGF-EGFR complex
Rule('EGFR_dimerization',
EGFR(egf=ANY, d=None) + EGFR(egf=ANY, d=None) <>
EGFR(egf=ANY, d=1) % EGFR(egf=ANY, d=1), k_dimf, k_dimr)
# EGFR, bound to EGFR, binds Grb2
Rule('EGFR_binds_Grb2',
EGFR(d=ANY, grb2=None) + Grb2(egfr=None) <>
EGFR(d=ANY, grb2=1) % Grb2(egfr=1), kf2, kr2)
# Grb2, bound to EGFR, binds SOS
Rule('Grb2_binds_SOS',
Grb2(egfr=ANY, sos=None) + SOS(grb2=None, state='up') <>
Grb2(egfr=ANY, sos=1) % SOS(grb2=1, state='up'), kf3, kr3)
# SOS activates KRAS
catalyze_state(SOS(grb2=ANY, state='up'), 'ras',
KRAS(raf=None), 'sos', 'state', 'gdp', 'gtp',
(kf4, kr4, ke4))
# KRAS deactivates itself
# Making this step reversible increased combinatorial complexity manifold
Rule('KRAS_inactivation',
KRAS(state='gtp') >>
KRAS(state='gdp'),
kf5)
def KRAS_activation():
# Rate constants
# -------------
Parameter('kf1', 1)
Parameter('kr1', 0.1)
Parameter('kf2', 1)
Parameter('kr2', 0.1)
Parameter('kf3', 1)
Parameter('kr3', 0.1)
Parameter('kf4', 1)
Parameter('kr4', 0.001)
Parameter('ke4', 50)
Parameter('kf5', 0.5)
Parameter('kr5', 1e-9)
Parameter('k_dimf', 1)
Parameter('k_dimr', 0.1)
alias_model_components()
# Rules
# -----
# EGF binds EGFR
Rule('EGF_binds_EGFR',
EGF(egfr=None) + EGFR(egf=None) <> EGF(egfr=1) % EGFR(egf=1), kf1,
kr1)
# The EGF-EGFR complex binds another EGF-EGFR complex
Rule(
'EGFR_dimerization',
EGFR(egf=ANY, d=None) + EGFR(egf=ANY, d=None) <>
EGFR(egf=ANY, d=1) % EGFR(egf=ANY, d=1), k_dimf, k_dimr)
# EGFR, bound to EGFR, binds Grb2
Rule(
'EGFR_binds_Grb2',
EGFR(d=ANY, grb2=None) + Grb2(egfr=None) <>
EGFR(d=ANY, grb2=1) % Grb2(egfr=1), kf2, kr2)
# Grb2, bound to EGFR, binds SOS
Rule(
'Grb2_binds_SOS',
Grb2(egfr=ANY, sos=None) + SOS(grb2=None, state='up') <>
Grb2(egfr=ANY, sos=1) % SOS(grb2=1, state='up'), kf3, kr3)
# SOS activates KRAS
catalyze_state(SOS(grb2=ANY, state='up'), 'ras', KRAS(raf=None), 'sos',
'state', 'gdp', 'gtp', (kf4, kr4, ke4))
# KRAS deactivates itself
# Making this step reversible increased combinatorial complexity manifold
Rule('KRAS_inactivation', KRAS(state='gtp') >> KRAS(state='gdp'), kf5)
def mapk_single(kinase, pptase, substrate, site):
"""Kinase phos/dephosphorylation."""
ppt_substrate = substrate()
if 'k' in ppt_substrate.monomer.sites:
# Ensure substrates which are themselves kinases don't get
# dephosphorylated while they are bound to *their* substrate.
ppt_substrate = ppt_substrate(k=None)
components = catalyze_state(kinase, 'k', substrate, site, site, 'u', 'p',
klist_phos)
components |= catalyze_state(pptase, 'ppt', ppt_substrate, site, site, 'p',
'u', klist_dephos)
return components
def mapk_single(kinase, pptase, substrate, site):
"""Kinase phos/dephosphorylation."""
ppt_substrate = substrate()
if 'k' in ppt_substrate.monomer.sites:
# Ensure substrates which are themselves kinases don't get
# dephosphorylated while they are bound to *their* substrate.
ppt_substrate = ppt_substrate(k=None)
components = catalyze_state(kinase, 'k',
substrate, site, site, 'u', 'p',
klist_phos)
components |= catalyze_state(pptase, 'ppt',
ppt_substrate, site, site, 'p', 'u',
klist_dephos)
return components
def NFkB_Activation_and_Signaling():
"""This model focuses on the decision between apoptotic and necroptotic cell death pathways. The NFkB pathway, roughly approximated here, does not induce cell death. But it may influence the expression of key regulators of the cell death pathways."""
catalyze_state(NSC(bnfkb=None), 'bnfkb', NFkB(state = 'I'), 'bnsc', 'state', 'I', 'A', [1e-6, 1e-3, 0.1])
Rule('NFkB_cFlipL', NFkB(state = 'A') >> NFkB(state = 'A') + flip_L(bDED=None), Parameter('NFkB_FlipL', 1e-2))
Rule('NFkB_cFlipS', NFkB(state = 'A') >> NFkB(state = 'A') + flip_S(bDED=None), Parameter('NFkB_FlipS', 1e-2))
Rule('NFkB_TRAF', NFkB(state = 'A') >> NFkB(state = 'A') + TRAF(brip=None, bciap=None, zfinger=None), Parameter('NFkB_TRAF_kc', 1e-2))
Rule('NFkB_FlipL_deg', NFkB(state = 'A') >> NFkB(state = 'A') + Flip_L_degradase(bf=None), Parameter('Degradase_flipL', 1e-6))
Rule('NFkB_FlipS_deg', NFkB(state = 'A') >> NFkB(state = 'A') + Flip_S_degradase(bf=None), Parameter('Degradase_flipS', 1e-6))
Rule('NFkB_TRAF_deg', NFkB(state = 'A') >> NFkB(state = 'A') + TRAF_degradase(bf=None), Parameter('Degradase_TRAF', 1e-6))
Rule('Deg_cFlipL', Flip_L_degradase(bf=None) + flip_L(bDED=None) >> Flip_L_degradase(bf=None), Parameter('deg_FlipL', 5e-6))
Rule('Deg_cFlipS', Flip_S_degradase(bf=None) + flip_S(bDED=None) >> Flip_S_degradase(bf=None), Parameter('deg_FlipS', 5e-6))
Rule('Deg_TRAF', TRAF_degradase(bf=None) + TRAF(brip=None, bciap=None, zfinger=None) >> TRAF_degradase(bf=None), Parameter('deg_TRAF', 5e-6))
def SOS_dephosphorylation():
Monomer('SOS_phos', ['sos'])
Parameter('SOS_phos_0', 100)
Parameter('k_spf', 1)
Parameter('k_spr', 0.1)
Parameter('k_spe', 1e-4)
alias_model_components()
Initial(SOS_phos(sos=None), SOS_phos_0)
catalyze_state(SOS_phos(), 'sos', SOS(ras=None, erk=None), 'phos', 'state',
'p', 'up', (k_spf, k_spr, k_spe))
def Erk_catalysis():
"v723-v750"
" Erk~PP binds and phosphorylates Gab1~P via 2-step catalysis"
Parameter('k110', 3.33e-4) # k110
Parameter('kd110', 0.1) # kd110
Parameter('kd111', 6.57) # kd111
alias_model_components()
# Initial amount
# ==============
catalyze_state(ERK(pase3=None, mek=None, sos=None, state='pp'), 'gab1', Gab1(shp2=None, pi3k=None), 'erk', 'state', 'p', 'pp',
(k110, kd110, kd111))
def SOS_dephosphorylation():
Monomer('SOS_phos', ['sos'])
Parameter('SOS_phos_0', 100)
Parameter('k_spf', 1)
Parameter('k_spr', 0.1)
Parameter('k_spe', 1e-4)
alias_model_components()
Initial(SOS_phos(sos=None), SOS_phos_0)
catalyze_state(SOS_phos(), 'sos', SOS(ras=None, erk=None), 'phos',
'state', 'p', 'up', (k_spf, k_spr, k_spe))
def Shp2_catalysis():
"v707-v720"
" Shp2 binds phoshphoryated Gab1 and dephosphorylates it in a 2-step reaction "
# Initial amount
# ==============
Parameter('Shp2_0', 1e+6) # c463
# Rate constant
# ==============
Parameter('k107', 3.33e-5) # k107
Parameter('kd107',0.1) # kd107
Parameter('kd108', 5) # kd108
alias_model_components()
# Initial conditions
# ==============
Initial(Shp2(gab1=None), Shp2_0)
catalyze_state(Shp2(), 'gab1', Gab1(erk=None, pi3k=None), 'shp2', 'state', 'p', 'up', (k107, kd107, kd108))
def Pase_9t_catalysis():
"v770-v783"
"Pase_9t binds and dephoshhorylates Gab1~PP to Gab1~P in a 2 step catalysis"
# Initial amount
# ==============
Parameter('Pase9t_0', 0) # c521 // zero ic
# Rate constant
# ==============
Parameter('k117', 8.33e-8) # k117
Parameter('kd117', 0.1) # kd117
Parameter('kd118', 0.03) # k118
alias_model_components()
# Initial conditions
# ==============
Initial(Pase_9t(gab1=None), Pase9t_0)
# Rules
# =====
catalyze_state(Pase_9t(),'gab1', Gab1(), 'pase', 'state', 'pp', 'p', (k117, kd117, kd118))
def C8_catalyzed_truncations():
# RIP1 + C8 <-> RIP1:C8 >> RIP1[trunc] + C8
# RIP3 + C8 <-> RIP3:C8 >> RIP3[trunc] + C8
# Bid + C8 <-> Bid:C8 >> Bid[trunc] + C8
# CYLD + C8 <-> CYLD:C8 >> CYLD[trunc] + C8
catalyze_state(C8(bf = None, state = 'A'), 'bf', RIP1(bDD=None), 'bRHIM', 'state', 'unmod', 'trunc', [1e-6, 1e-3, 1e-1])
#RIP3 Truncation
catalyze_state(C8(bf = None, state = 'A'), 'bf', RIP3(), 'bRHIM', 'state', 'unmod', 'trunc', [1e-6, 1e-3, 1e-1])
#Bid Truncation
catalyze_state(C8(bf = None, state = 'A'), 'bf', Bid(), 'bf', 'state', 'U', 'T', [1.e-6, 0.001, 0.1])
#CYLD Truncation
catalyze_state(C8(bf = None, state = 'A'), 'bf', CYLD(), 'btraf', 'state', 'U', 'T', [1e-6, 1e-3, 0.1])
from pysb import *
from pysb.macros import catalyze_state
Model()
Parameter('vol', 10.) # volume (arbitrary units)
Parameter('kf', 1. / vol.value)
Parameter('kr', 1000)
Parameter('kcat', 100)
Monomer('E', ['s'])
Monomer('S', ['e', 'state'], {'state': ['_0', '_1']})
catalyze_state(E(), 's', S(), 'e', 'state', '_0', '_1', [kf, kr, kcat])
Observable("E_free", E(s=None))
Observable("S_free", S(e=None, state='_0'))
Observable("ES_complex", E(s=1) % S(e=1))
Observable("Product", S(e=None, state='_1'))
Parameter("Etot", 1. * vol.value)
Initial(E(s=None), Etot)
Parameter('S0', 10. * vol.value)
Initial(S(e=None, state='_0'), S0)
def AKT_rxns():
"v639-v649, v765-768"
# Initial amount
# ==============
Parameter('AKT_0', 905000) # c107
Parameter('PDK1_0', 3.00416e8) # c109
Parameter('Pase4_0', 4.5e+5) # c113
Parameter('PTEN_0', 56100.9) # c279
Parameter('Shp_0', 2213.59) # c461
Parameter('RAF_0', 71131.2) # c41
# Rate constants
# ==============
Parameter('k69',3.33e-5) # k69
Parameter('kd69',0.1) # kd69
Parameter('k70',6.67e-7) # k70
Parameter('kd70',0.1) # kd70
Parameter('kd71', 25.2)
Parameter('kd72', 5.01187)
Parameter('kd76', 142.262) # kd76
Parameter('k74',6.36184e-7) #k74
Parameter('kd74',0.355656) # kd74
Parameter('k73',0.00374845) # k73
Parameter('kd73',0.5) # kd73
Parameter('kd75',0.00633957) # kd75
Parameter('k109', 5e-6) # k109
Parameter('kd109',0.1) # kd109
Parameter('kd104', 0.2) # kd104
Parameter('k114', 4.98816e-6) # k114
Parameter('kd114',0.1) # kd114
Parameter('kd115', 1.0) # kd115
alias_model_components()
# Initial conditions
# ==================
Initial(AKT(pip=None, pase=None,raf=None, state='up'), AKT_0)
Initial(PDK1(pip=None), PDK1_0)
Initial(Pase4(akt=None), Pase4_0)
Initial(PTEN(pip=None), PTEN_0)
Initial(Shp(pip=None), Shp_0)
Initial(RAF(akt=None, pase1=None, mek=None, ras=None, state='up'), RAF_0)
# Rules
# =====
pstates = ['up', 'p', 'pp']
for ps in pstates[:2]:
# PIP3 + AKT (up/p) <-> PIP3:AKT (up/p)
Rule('Pip3_binds_AKT_'+ps, PIP3(akt=None, pdk=None, bnd=None) + AKT(pip=None, pase=None,raf=None, state=ps) <>
PIP3(akt=1, pdk=None, bnd=None) % AKT(pip=1, pase=None,raf=None, state=ps), k69, kd69)
# PIp3:AKT + PDK1
Rule('Pip3AKT_bind_PDK_'+ps, PIP3(akt=1, pdk=None, bnd=None) % AKT(pip=1, pase=None,raf=None, state=ps) +PDK1(pip=None) <>
PIP3(akt=1, pdk=2, bnd=None) % AKT(pip=1, pase=None,raf=None, state=ps) % PDK1(pip=2), k70, kd70)
# PIp3:AKT:PDK1 -> PIp3:PDK1 + AKT~P
Rule('AKT_first_phosphoryl', PIP3(akt=1, pdk=2, bnd=None) % AKT(pip=1, pase=None,raf=None, state='up') % PDK1(pip=2) >>
PIP3(akt=None, pdk=2, bnd=None) % PDK1(pip=2) + AKT(pip=None,raf=None, pase=None, state='p'), kd71)
# PIp3:AKT~P:PDK1 -> PIp3:PDK1 + AKT~PP
Rule('AKT_second_phosphoryl', PIP3(akt=1, pdk=2, bnd=None) % AKT(pip=1,raf=None, pase=None, state='p') % PDK1(pip=2) >>
PIP3(akt=None, pdk=2, bnd=None) % PDK1(pip=2) + AKT(pip=None,raf=None, pase=None, state='pp') , kd72)
# Dissoc pip3:PDk1
Rule('dissoc_pip3_pdk1', PIP3(akt=None, pdk=1, bnd=None) % PDK1(pip=1) >> PIP3(akt=None, pdk=None, bnd=None) + PDK1(pip=None), kd76)
# Catalyse dephoshporylation of ATK by Pase4
catalyze_state(Pase4(),'akt', AKT(pip=None,raf=None), 'pase', 'state', 'pp', 'p', (k74, kd74, kd75))
catalyze_state(Pase4(),'akt', AKT(pip=None,raf=None), 'pase', 'state', 'p', 'up', (k73, kd73, kd75))
# Pip3 binds SHP/PTEN to give Pip2
for binder in Shp, PTEN:
Rule('bind_Pip3_'+binder.name, binder(pip=None) + PIP3(akt=None, pdk=None, bnd=None) <>
binder(pip=1) % PIP3(akt=None, pdk=None, bnd=1), k109, kd109)
Rule('Pip3_2_'+binder.name, binder(pip=1) % PIP3(akt=None, pdk=None,bnd=1) >> binder(pip=None) + PIP2(pi3k=None), kd104)
# Akt convers Raf#p to Raf#p:Ser
catalyze_state(AKT(pip=None, pase=None,state='pp'),'raf', RAF(pase1=None, mek=None), 'akt', 'state', 'p', 'p_ser',
(k114, kd114, kd115))
from pysb import *
from pysb.macros import catalyze_state
Model()
Parameter('vol', 10.) # volume (arbitrary units)
Parameter('kf', 1./vol.value)
Parameter('kr', 1000)
Parameter('kcat', 100)
Monomer('E', ['s'])
Monomer('S', ['e', 'state'], {'state': ['_0', '_1']})
catalyze_state(E(), 's', S(), 'e', 'state', '_0', '_1', [kf, kr, kcat])
Observable("E_free", E(s=None))
Observable("S_free", S(e=None, state='_0'))
Observable("ES_complex", E(s=1) % S(e=1))
Observable("Product", S(e=None, state='_1'))
Parameter("Etot", 1.*vol.value)
Initial(E(s=None), Etot)
Parameter('S0', 10.*vol.value)
Initial(S(e=None, state='_0'), S0)
def pore_to_parp():
"""Defines what happens after the pore is activated and Cytochrome C and
Smac are released.
Uses CytoC, Smac, Apaf, Apop, C3, C6, C8, C9, PARP, XIAP monomers and their
associated parameters to generate the rules that describe apoptosome
formation, XIAP inhibition, activation of caspases (including
caspase-6-mediated feedback), and cleavage of effector caspase substrates
as specified in EARM 1.0.
Declares initial conditions for CytoC, Smac, Apaf-1, Apoptosome, caspases
3, 6, and 9, XIAP, and PARP.
"""
# Declare initial conditions:
Parameter('Apaf_0' , 48176) # Apaf-1 (J Immunol 2005)
Parameter('C3_0' , 96352) # procaspase-3 (pro-C3) (J Immunol 2005)
Parameter('C6_0' , 1.0e4) # procaspase-6 (pro-C6)
Parameter('C9_0' , 9635) # procaspase-9 (pro-C9) (J Immunol 2005)
Parameter('XIAP_0' , 14452) # X-linked inhibitor of apoptosis protein (J Immunol 2005)
Parameter('PARP_0' , 1.0e6) # C3* substrate
alias_model_components()
Initial(Apaf(bf=None, state='I'), Apaf_0)
Initial(C3(bf=None, state='pro'), C3_0)
Initial(C6(bf1=None, bf2=None, state='pro'), C6_0)
#Initial(C6(bf=None, state='pro'), C6_0)
Initial(C9(bf=None), C9_0)
Initial(PARP(bf=None, state='U'), PARP_0)
Initial(XIAP(bf=None), XIAP_0)
# CytoC and Smac activation after release
# --------------------------------------
equilibrate(Smac(bf=None, state='C'), Smac(bf=None, state='A'),
transloc_rates)
equilibrate(CytoC(bf=None, state='C'), CytoC(bf=None, state='A'),
transloc_rates)
# Apoptosome formation
# --------------------
# Apaf + cCytoC <--> Apaf:cCytoC --> aApaf + cCytoC
# aApaf + pC9 <--> Apop
# Apop + pC3 <--> Apop:pC3 --> Apop + C3
catalyze(CytoC(state='A'), Apaf(state='I'), Apaf(state='A'), [5.77e-10, 5.7e-3, KC])#(J Immunol 2005)
one_step_conv(Apaf(state='A'), C9(), Apop(bf=None), [5.90e-7, 0.07493])
catalyze(Apop(), C3(state='pro'), C3(bf=None, state='A'), [9.15e-7, 0.1, 0.7])
# Apoptosome-related inhibitors
# -----------------------------
# Apop + XIAP <--> Apop:XIAP
# cSmac + XIAP <--> cSmac:XIAP
bind(Apop(), XIAP(), [2e-6, KR])
bind(Smac(state='A'), XIAP(), [1.45e-5, 2.21e-3])
# Caspase reactions
# -----------------
# Includes effectors, inhibitors, and feedback initiators:
#
# pC3 + C8 <--> pC3:C8 --> C3 + C8 CSPS
# pC6 + C3 <--> pC6:C3 --> C6 + C3 CSPS
# XIAP + C3 <--> XIAP:C3 --> XIAP + C3_U CSPS
# PARP + C3 <--> PARP:C3 --> CPARP + C3 CSPS
# pC8 + C6 <--> pC8:C6 --> C8 + C6 CSPS
from pysb.macros import catalyze_state
catalyze(C8(state='A'), C3(state= 'pro'),C3(state = 'A'), [1e-7, KR, KC])
catalyze(XIAP(), C3(state='A'), C3(state = 'ub'), [KF, KR, 1e-1]) #[5.13e-6, 2.40e-3, 1e-1]
catalyze(C3(state='A'), PARP(state='U'), PARP(state='C'), [KF, 1e-2, KC])
#catalyze_state(C3(state='A'), 'bf', C6(), 'bf', 'state', 'pro', 'A', [KF, KR, KC])
#catalyze(C6(state='A'), C8(state='pro'), C8(state='A'), [3e-8, KR, KC])
Parameter('kf51', 1e-6) # Generic association rate constant
Parameter('kr51', 1e-3) # Generic dessociation rate constant
Parameter('kf52', 1e-6) # Generic association rate constant
Parameter('kr52', 1e-3) # Generic dessociation rate constant
Parameter('kc52', 1) # Generic catalytic rate constant
alias_model_components()
catalyze_state(C3(state='A'), 'bf', C6(), 'bf1', 'state', 'pro', 'A', [KF, KR, KC])
from pysb.macros import bind as bind2
bind2(C6(bf1 = None, bf2 = None, state = 'A'), 'bf1', proC8(bDED = None), 'bDED', [kf51, kr51])
bind2(C6(bf1 = ANY, bf2 = None, state = 'A'), 'bf2', proC8(bDED = None), 'bDED', [kf52, kr52])
Rule('C8_activation_byC6', C6(bf1 = ANY, bf2 = ANY, state = 'A')%proC8(bDED = ANY)%proC8(bDED = ANY) >> C8(bf = None, state = 'A') + C6(bf1=None, bf2=None, state = 'A'), kc52)
def MAPK_pathway():
" v409-412, v487-512 "
# Initial amount
# ==============
Parameter('MEK_0', 3020000) # c47
Parameter('ERK_0', 695000) # c55
Parameter('Pase1_0', 5e+4) # c44
Parameter('Pase2_0', 124480) # c53
Parameter('Pase3_0', 16870.2) # c60
# Rate constants
# ==============
Parameter('k28', 5e-06) #k28
Parameter('kd28', 0.0053) #kd28
Parameter('kd29', 3.1) # kd29
Parameter('k29', 1.17e-06) # k29
Parameter('k42', 6e-5) # k42
Parameter('kd42', 0.0141589) # kd42
Parameter('kd43', 31.6228) # kd43
Parameter('k44', 1.07e-5) # k44
Parameter('kd52', 0.033) # kd52
Parameter('kd45', 1.9) # kd45
Parameter('kd47', 0.8) # kd45
Parameter('k48', 2.37e-5) # k48
Parameter('kd48', 0.79) # kd48
Parameter('k50', 4.74801e-8) # k48
Parameter('kd50', 0.252982) # kd48
Parameter('kd49', 0.112387) # kd49
Parameter('k52', 8.85125e-6) # k48
Parameter('kd44', 0.01833) # kd48
Parameter('kd53', 0.28) # kd49
Parameter('kd55', 70.1662) # kd49
Parameter('k56', 3.97392e-4) # k56
Parameter('kd56', 5.0) # kd56
Parameter('kd57', 0.0076) # kd57
Parameter('k58', 8.33e-7) # k56
Parameter('kd58', 56.7862) # kd56
Parameter('k64', 1.67e-05)
Parameter('kd64', 0.3)
Parameter('kd65', 0.2)
alias_model_components()
# Initial conditions
# ==================
Initial(MEK(raf=None, pase2=None, erk=None, state='up'), MEK_0)
Initial(ERK(mek=None, pase3=None, sos=None, state='up', gab1=None), ERK_0)
Initial(Pase1(raf=None), Pase1_0)
Initial(Pase2(mek=None), Pase2_0)
Initial(Pase3(erk=None), Pase3_0)
# Rules
# =====
" v409-412, v487-512 "
alias_model_components()
# RAS:GTP + RAF -> RasGTP:RAF
# RAS:active_GTP + RAF~P -> RasGTP:RAF
Rule(
'RAS_binds_RAF',
RAS(sos=None, pi3k=None, raf=None, state='gtp') +
RAF(akt=None, mek=None, pase1=None, ras=None, state='up') <>
RAS(sos=None, pi3k=None, raf=1, state='gtp') %
RAF(akt=None, mek=None, pase1=None, ras=1, state='up'), k28, kd28)
Rule(
'RAS_RAF_cat',
RAS(sos=None, pi3k=None, raf=1, state='gtp') %
RAF(akt=None, mek=None, pase1=None, ras=1, state='up') <>
RAS(sos=None, pi3k=None, raf=None, state='active_gtp') +
RAF(akt=None, mek=None, pase1=None, ras=None, state='p'), kd29, k29)
# RAF1~P dephoshporylated by Pase1
catalyze_state(Pase1(), 'raf', RAF(ras=None, akt=None, mek=None), 'pase1',
'state', 'p', 'up', (k42, kd42, kd43))
# RAF~P phoshprylates MEK
catalyze_state(RAF(akt=None, ras=None, pase1=None, state='p'), 'mek',
MEK(pase2=None, erk=None), 'raf', 'state', 'up', 'p',
(k44, kd52, kd45))
catalyze_state(RAF(akt=None, ras=None, pase1=None, state='p'), 'mek',
MEK(pase2=None, erk=None), 'raf', 'state', 'p', 'pp',
(k44, kd52, kd47))
# MEK~P dephosphorylated by Pase2
catalyze_state(Pase2(), 'mek', MEK(raf=None, erk=None), 'pase2', 'state',
'p', 'up', (k50, kd50, kd49))
catalyze_state(Pase2(), 'mek', MEK(raf=None, erk=None), 'pase2', 'state',
'pp', 'p', (k48, kd48, kd49))
# MEK~P phosphorylates ERk
catalyze_state(MEK(raf=None, pase2=None, state='pp'), 'erk',
ERK(pase3=None, sos=None, gab1=None), 'mek', 'state', 'up',
'p', (k52, kd44, kd53))
catalyze_state(MEK(raf=None, pase2=None, state='pp'), 'erk',
ERK(pase3=None, sos=None, gab1=None), 'mek', 'state', 'p',
'pp', (k52, kd44, kd55))
# ERK~P dephosphorylated by Pase3
catalyze_state(Pase3(), 'erk', ERK(mek=None, sos=None, gab1=None), 'pase3',
'state', 'p', 'up', (k58, kd58, kd57))
catalyze_state(Pase3(), 'erk', ERK(mek=None, sos=None, gab1=None), 'pase3',
'state', 'pp', 'p', (k56, kd56, kd57))
# ERK#PP phosphorylates SOS in ErbB1 homodimers "only
Rule(
'sos_binds_erk',
ERK(mek=None, gab1=None, pase3=None, state='pp', sos=None) +
ErbB1(cpp=None, rtk=None, comp='pm') %
ErbB1(cpp=None, rtk=None, comp='pm') %
SOS(ras=None, erk=None, state='up') <>
ERK(mek=None, gab1=None, pase3=None, state='pp', sos=1) %
ErbB1(cpp=None, rtk=None, comp='pm') % ErbB1(
cpp=None, rtk=None, comp='pm') % SOS(ras=None, erk=1, state='up'),
k64, kd64)
# ERK#PP phosphorylaes free SOS
Rule(
'freeSos_binds_erk',
ERK(mek=None, gab1=None, pase3=None, state='pp', sos=None) +
SOS(ras=None, erk=None, grb=None, state='up') <>
ERK(mek=None, gab1=None, pase3=None, state='pp', sos=1) %
SOS(ras=None, erk=1, grb=None, state='up'), k64, kd64)
Rule(
'free_Sos_p_catalysis',
ERK(sos=1, state='pp') % SOS(erk=1, state='up', grb=None) >>
ERK(sos=None, state='pp') + SOS(grb=None, erk=None, state='p'), kd65)
Rule(
'Sos_p_catalysis',
ERK(sos=1, state='pp') % SOS(erk=1, state='up') %
ErbB1(cpp=None, rtk=None, comp='pm') %
ErbB1(cpp=None, rtk=None, comp='pm') >> ERK(sos=None, state='pp') +
SOS(erk=None, state='p') % ErbB1(cpp=None, rtk=None, comp='pm') %
ErbB1(cpp=None, rtk=None, comp='pm'), kd65)
# Degrade Pase3 (V769)
Rule('degrade_Pase3', Pase3(erk=None) >> None, k116)
Initial(USM3(b=None, state='inactive'), USM3_0)
# 1. Receptor ligation: TRAIL + Receptor <-> TRAIL:Receptor kf0, kr0
Parameter('kf0', 1.0e-06)
Parameter('kr0', 1.0e-03)
Rule('Receptor_ligation', L(b=None) + R(b=None) | L(b=1) % R(b=1), kf0, kr0)
# 2. Death inducing signaling complex: TRAIL:Receptor --> DISC kc0
Parameter('kc0', 1.0e-04)
Rule('DISC_formation', L(b=1) % R(b=1) >> DISC(b=None), kc0)
# 3. Initiator Caspase Activation: DISC-> iCaspases --> *iCaspases kf1, kr1, kc1
Parameter('kf1', 1.0e-06)
Parameter('kr1', 1.0e-03)
Parameter('kc1', 1.0e-00)
catalyze_state(DISC(), 'b', IC(), 'b', 'state', 'inactive', 'active',
[kf1, kr1, kc1])
# 4. Effector Caspase Activation: *iCaspases-> eCaspases --> *eCaspases kf2, kr2, kc2
Parameter('kf2', 1.0e-06)
Parameter('kr2', 1.0e-03)
Parameter('kc2', 1.0e-00)
catalyze_state(IC(state='active'), 'b', EC(), 'b', 'state', 'inactive',
'active', [kf2, kr2, kc2])
# 5. Feedback Capsase Activation: *eCaspases-> iCaspases --> *iCaspases kf3, kr3, kc3
Parameter('kf3', 1.0e-06)
Parameter('kr3', 1.0e-03)
Parameter('kc3', 1.0e-00)
catalyze_state(EC(state='active'), 'b', IC(), 'b', 'state', 'inactive',
'active', [kf3, kr3, kc3])
def Bid_proC8_cleaves_substrates():
#--------------Phospho-Bid Interactions------------------
catalyze_state(Bid_po4(bf1 = ANY, bf2 =ANY), 'bf3', RIP1(), 'bRHIM', 'state', 'unmod', 'trunc', [1e-6, 1e-3, 1e-1])
catalyze_state(Bid_po4(bf1 = ANY, bf2 =ANY), 'bf3', CYLD(), 'btraf', 'state', 'U', 'T', [1e-6, 1e-3, 1e-1])
def C3_inhibits_MLKL():
"""it has not been established whether MLKL is de-activated in apoptosis. But inorder to make a cellular decision you have to have one choice, once selected, inhibit all of the alternative pathways. This is a hypothetical apoptosis mediated inhibition of necrosis effector, MLKL."""
catalyze_state(C3(state='A'), 'bf', MLKL(), 'bRHIM', 'state','unmod','inactive', [1e-6, 1e-3, 1])
def MAPK_pathway():
" v409-412, v487-512 "
# Initial amount
# ==============
Parameter('MEK_0', 3020000) # c47
Parameter('ERK_0', 695000) # c55
Parameter('Pase1_0', 5e+4) # c44
Parameter('Pase2_0', 124480) # c53
Parameter('Pase3_0', 16870.2) # c60
# Rate constants
# ==============
Parameter('k28', 5e-06 ) #k28
Parameter('kd28', 0.0053) #kd28
Parameter('kd29', 3.1) # kd29
Parameter('k29', 1.17e-06) # k29
Parameter('k42', 6e-5) # k42
Parameter('kd42', 0.0141589) # kd42
Parameter('kd43', 31.6228) # kd43
Parameter('k44', 1.07e-5) # k44
Parameter('kd52', 0.033) # kd52
Parameter('kd45', 1.9) # kd45
Parameter('kd47', 0.8) # kd45
Parameter('k48', 2.37e-5) # k48
Parameter('kd48', 0.79) # kd48
Parameter('k50', 4.74801e-8) # k48
Parameter('kd50', 0.252982) # kd48
Parameter('kd49', 0.112387) # kd49
Parameter('k52', 8.85125e-6) # k48
Parameter('kd44', 0.01833) # kd48
Parameter('kd53', 0.28) # kd49
Parameter('kd55', 70.1662) # kd49
Parameter('k56', 3.97392e-4) # k56
Parameter('kd56', 5.0) # kd56
Parameter('kd57', 0.0076) # kd57
Parameter('k58', 8.33e-7) # k56
Parameter('kd58', 56.7862) # kd56
Parameter('k64',1.67e-05)
Parameter('kd64', 0.3)
Parameter('kd65', 0.2)
alias_model_components()
# Initial conditions
# ==================
Initial(MEK(raf=None, pase2=None, erk=None,state='up'), MEK_0)
Initial(ERK(mek=None, pase3=None, sos=None, state='up', gab1=None), ERK_0)
Initial(Pase1(raf=None), Pase1_0)
Initial(Pase2(mek=None), Pase2_0)
Initial(Pase3(erk=None), Pase3_0)
# Rules
# =====
" v409-412, v487-512 "
alias_model_components()
# RAS:GTP + RAF -> RasGTP:RAF
# RAS:active_GTP + RAF~P -> RasGTP:RAF
Rule('RAS_binds_RAF', RAS(sos=None, pi3k=None, raf=None, state='gtp') +
RAF(akt=None, mek=None, pase1=None, ras=None,state='up') <>
RAS(sos=None, pi3k=None, raf=1, state='gtp') %
RAF(akt=None, mek=None, pase1=None, ras=1,state='up'), k28, kd28)
Rule('RAS_RAF_cat', RAS(sos=None, pi3k=None, raf=1, state='gtp')
% RAF(akt=None, mek=None, pase1=None, ras=1,state='up') <>
RAS(sos=None, pi3k=None, raf=None, state='active_gtp') +
RAF(akt=None, mek=None, pase1=None, ras=None,state='p'),kd29, k29)
# RAF1~P dephoshporylated by Pase1
catalyze_state(Pase1(), 'raf', RAF(ras=None, akt=None, mek=None), 'pase1', 'state', 'p', 'up', (k42, kd42, kd43))
# RAF~P phoshprylates MEK
catalyze_state(RAF(akt=None, ras=None, pase1=None, state='p'), 'mek', MEK(pase2=None, erk=None), 'raf', 'state', 'up', 'p', (k44, kd52, kd45))
catalyze_state(RAF(akt=None, ras=None, pase1=None, state='p'), 'mek', MEK(pase2=None,erk=None), 'raf', 'state', 'p', 'pp', (k44, kd52, kd47))
# MEK~P dephosphorylated by Pase2
catalyze_state(Pase2(), 'mek', MEK(raf=None,erk=None), 'pase2', 'state', 'p', 'up', (k50, kd50, kd49))
catalyze_state(Pase2(), 'mek', MEK(raf=None,erk=None), 'pase2', 'state', 'pp', 'p', (k48, kd48, kd49))
# MEK~P phosphorylates ERk
catalyze_state(MEK(raf=None, pase2=None, state='pp'), 'erk', ERK(pase3=None, sos=None, gab1=None), 'mek', 'state', 'up', 'p', (k52, kd44, kd53))
catalyze_state(MEK(raf=None, pase2=None, state='pp'), 'erk', ERK(pase3=None, sos=None, gab1=None), 'mek', 'state', 'p', 'pp', (k52, kd44, kd55))
# ERK~P dephosphorylated by Pase3
catalyze_state(Pase3(), 'erk', ERK(mek=None, sos=None, gab1=None), 'pase3', 'state', 'p', 'up', (k58, kd58, kd57))
catalyze_state(Pase3(), 'erk', ERK(mek=None,sos=None, gab1=None), 'pase3', 'state', 'pp', 'p', (k56, kd56, kd57))
# ERK#PP phosphorylates SOS in ErbB1 homodimers "only
Rule('sos_binds_erk', ERK(mek=None, gab1=None, pase3=None, state='pp', sos=None) + ErbB1(cpp=None, rtk=None, comp='pm') % ErbB1(cpp=None, rtk=None, comp='pm') % SOS(ras=None, erk=None, state='up') <>
ERK(mek=None, gab1=None, pase3=None, state='pp', sos=1) % ErbB1(cpp=None, rtk=None, comp='pm') % ErbB1(cpp=None,rtk=None, comp='pm') % SOS(ras=None, erk=1, state='up'), k64, kd64)
# ERK#PP phosphorylaes free SOS
Rule('freeSos_binds_erk', ERK(mek=None, gab1=None, pase3=None, state='pp', sos=None) + SOS(ras=None, erk=None, grb=None, state='up') <>
ERK(mek=None, gab1=None, pase3=None, state='pp', sos=1) % SOS(ras=None, erk=1, grb=None, state='up'), k64, kd64)
Rule('free_Sos_p_catalysis', ERK(sos=1, state='pp') % SOS(erk=1,state='up',grb=None) >> ERK(sos=None, state='pp') + SOS(grb=None, erk=None,state='p'), kd65)
Rule('Sos_p_catalysis', ERK(sos=1, state='pp') % SOS(erk=1,state='up') % ErbB1(cpp=None, rtk=None, comp='pm') % ErbB1(cpp=None, rtk=None, comp='pm') >> ERK(sos=None, state='pp') + SOS(erk=None,state='p') % ErbB1(cpp=None, rtk=None, comp='pm') % ErbB1(cpp=None, rtk=None, comp='pm'), kd65)
# Degrade Pase3 (V769)
Rule('degrade_Pase3', Pase3(erk=None) >> None, k116)
