Multiary Complex Model of GPCR Signaling Activations¶
This notebook is the Supplemental Material for ``Watabe et al. Multiary complex formations in GPCR signaling activations. arXiv:xxx.xxxxxx (2020)".
In [1]:
# Multiary Complex Model in GPCR signaling activation
import os
import sys
import numpy
%matplotlib inline
import matplotlib.pylab as plt
from ecell4.prelude import *
Parameters¶
In [2]:
class ParConfigs() :
'''
Set Parameters
'''
# Set model parameters
def __init__(self, user_configs_dict = None):
self.A = 10000. # Cell-Area: µm^2
self.T = 4.977 # Receptor concetration: receptors/µm^2
self.r0 = int(self.T*self.A)
# ligand-receptor first-order interactions
# Phi <==> M
# Phi' <==> M'
# M' <==> D'
# dissociation rates
self.dl0 = 1.00 # 1/sec
self.dl1 = 1.00 # 1/sec
self.dl2 = 1.00 # 1/sec
# equilibrium constants
self.Kl0 = 1.00 # nM
self.Kl1 = None
self.Kl2 = None
# receptor-Gprotein first-order interactions
# Phi <==> G Phi
# Phi' <==> G Phi'
# dissociation rates
self.dg0 = 1.00 # 1/sec
self.dg1 = 1.00 # 1/sec
# equilibrium constants
self.Kg0 = 1.00 # nM
self.Kg1 = None
# ligand-(receptor-Gprotein) first-order interactions
# G Phi <==> G M
# G Phi' <==> G M'
# G M' <==> G D'
# dissociation rates
self.da0 = 1.00 # 1/sec
self.da1 = 1.00 # 1/sec
self.da2 = 1.00 # 1/sec
# equilibrium constants
self.Ka0 = 1.00 # nM
self.Ka1 = None
self.Ka2 = None
# Gprotein-(ligand-receptor) first-order interactions
# M <==> G M
# M' <==> G M'
# D' <==> G D'
# dissociation rates
self.db0 = 1.00 # 1/sec
self.db1 = 1.00 # 1/sec
self.db2 = 1.00 # 1/sec
# equilibrium constants
self.Kb0 = 1.00 # nM
self.Kb1 = None
self.Kb2 = None
# receptor-receptor interactions:
# Phi + Phi <==> Phi'
# M + Phi <==> M'
# M + M <==> D'
# dissociation rates
self.dx0 = 1.00 # 1/sec
self.dx1 = 1.00 # 1/sec
self.dx2 = 1.00 # 1/sec
# equilibrium constants
self.Kx0 = None
self.Kx1 = None
self.Kx2 = None
# receptor-Gprotein coupling
# G Phi + Phi <==> G Phi'
# G M + Phi <==> G M'
# G Phi + M <==> G M'
# G M + M <==> G D'
# dissociation rates
self.dy0 = 1.00 # 1/sec
self.dy1 = 1.00 # 1/sec
self.dy2 = 1.00 # 1/sec
self.dy3 = 1.00 # 1/sec
# equilibrium constants
self.Ky0 = None
self.Ky1 = None
self.Ky2 = None
self.Ky3 = None
def get_r0(self):
r0 = self.r0
return r0
def get_dl(self):
dl0 = self.dl0
dl1 = self.dl1
dl2 = self.dl2
return dl0, dl1, dl2
def get_kl(self, sigma_l1, sigma_l2):
self.Kl1 = sigma_l1*self.Kl0
self.Kl2 = sigma_l2*self.Kl0
kl0 = self.dl0/self.Kl0 # 1/(sec nM)
kl1 = self.dl1/self.Kl1 # 1/(sec nM)
kl2 = self.dl2/self.Kl2 # 1/(sec nM)
return kl0, kl1, kl2
def get_dg(self):
dg0 = self.dg0
dg1 = self.dg1
return dg0, dg1
def get_kg(self, sigma_g1):
self.Kg1 = sigma_g1*self.Kg0
kg0 = self.dg0/self.Kg0
kg1 = self.dg1/self.Kg1
return kg0, kg1
def get_da(self):
da0 = self.da0
da1 = self.da1
da2 = self.da2
return da0, da1, da2
def get_ka(self, alpha, sigma_a1, sigma_a2):
self.Ka0 = alpha*self.Kl0
self.Ka1 = sigma_a1*self.Ka0
self.Ka2 = sigma_a2*self.Ka0
ka0 = self.da0/self.Ka0
ka1 = self.da1/self.Ka1
ka2 = self.da2/self.Ka2
return ka0, ka1, ka2
def get_db(self):
db0 = self.db0
db1 = self.db1
db2 = self.db2
return db0, db1, db2
def get_kb(self, beta, sigma_b1, sigma_b2):
self.Kb0 = beta*self.Kg0
self.Kb1 = sigma_b1*self.Kb0
self.Kb2 = sigma_b2*self.Kb0
kb0 = self.db0/self.Kb0
kb1 = self.db1/self.Kb1
kb2 = self.db2/self.Kb2
return kb0, kb1, kb2
def get_dx(self):
dx0 = self.dx0
dx1 = self.dx1
dx2 = self.dx2
return dx0, dx1, dx2
def get_kx(self, kx, N):
self.Kx0 = self.T/kx # 1/µm^2
self.Kx1 = (self.Kl1*self.Kx0)/self.Kl0 # 1/µm^2
self.Kx2 = (self.Kl2*self.Kl1*self.Kx0)/(self.Kl0**2) # 1/µm^2
kx0 = self.dx0/self.Kx0 # µm^2/sec
kx1 = self.dx1/self.Kx1 # µm^2/sec
kx2 = self.dx2/self.Kx2 # µm^2/sec
return kx0/N, kx1/N, kx2/N
def get_dy(self):
dy0 = self.dy0
dy1 = self.dy1
dy2 = self.dy2
dy3 = self.dy3
return dy0, dy1, dy2, dy3
def get_ky(self, sigma_y0, sigma_y1, sigma_y2, sigma_y3):
self.Ky0 = sigma_y0*self.Kx0
self.Ky1 = sigma_y1*self.Kx1
self.Ky2 = sigma_y2*self.Kx1
self.Ky3 = sigma_y3*self.Kx2
ky0 = self.dy0/self.Ky0 # µm^2/sec
ky1 = self.dy1/self.Ky1 # µm^2/sec
ky2 = self.dy2/self.Ky2 # µm^2/sec
ky3 = self.dy3/self.Ky3 # µm^2/sec
return ky0, ky1, ky2, ky3
In [3]:
def run_N0(m, mols, obs0):
# Create simulator (ODE)
w = ode.World()
w.bind_to(m)
sim = ode.Simulator(w)
# Initialization
print ("Initial condition")
for i in range(len(mols)) :
obs0_i = int(round(obs0[i]))
w.add_molecules(Species("%s" % (mols[i])), obs0_i)
print (mols[i], ':', obs0_i)
sim.initialize()
# Run simulator
period = 50. # sec
obs = FixedIntervalNumberObserver(1.0, mols)
sim.run(period, [obs])
obs_data = numpy.array(obs.data())
time = obs_data[:,0]
R0 = obs_data[:,1]
RM = numpy.zeros(shape=(len(time)))
RD = obs_data[:,2]
G0 = obs_data[:,3]
GM = obs_data[:,4]
GD = numpy.zeros(shape=(len(time)))
data = obs_data.T
plt.plot(data[0], RM+RD+GM+GD, "b-", label="Bound states")
plt.plot(data[0], RM, "-", label="M")
plt.plot(data[0], RD, "-", label="D")
plt.plot(data[0], GM, "-", label="G•M")
plt.plot(data[0], GM, "-", label="G•D")
plt.xlabel("Time [sec]")
plt.ylabel("Bounds")
plt.xlim(data[0][0], data[0][-1])
plt.legend(loc="best", shadow=True)
plt.show()
In [4]:
def run_N1(m, mols, obs0):
# Create simulator (ODE)
w = ode.World()
w.bind_to(m)
sim = ode.Simulator(w)
# Initialization
print ("Initial condition")
for i in range(len(mols)) :
obs0_i = int(round(obs0[i]))
w.add_molecules(Species("%s" % (mols[i])), obs0_i)
print (mols[i], ':', obs0_i)
sim.initialize()
# Run simulator
period = 50. # sec
obs = FixedIntervalNumberObserver(1.0, mols)
sim.run(period, [obs])
obs_data = numpy.array(obs.data())
time = obs_data[:,0]
R0 = obs_data[:,1] + obs_data[:,2]
RM = obs_data[:,3] + obs_data[:,4]
RD = obs_data[:,5]
G0 = obs_data[:,6] + obs_data[:,7]
GM = obs_data[:,8] + obs_data[:,9]
GD = obs_data[:,10]
data = obs_data.T
plt.plot(data[0], RM+RD+GM+GD, "b-", label="Bound states")
plt.plot(data[0], RM, "-", label="M")
plt.plot(data[0], RD, "-", label="D")
plt.plot(data[0], GM, "-", label="G•M")
plt.plot(data[0], GM, "-", label="G•D")
plt.xlabel("Time [sec]")
plt.ylabel("Bounds")
plt.xlim(data[0][0], data[0][-1])
plt.legend(loc="best", shadow=True)
plt.show()
In [5]:
def run_N2(m, mols, obs0):
# Create simulator (ODE)
w = ode.World()
w.bind_to(m)
sim = ode.Simulator(w)
# Initialization
print ("Initial condition")
for i in range(len(mols)) :
obs0_i = int(round(obs0[i]))
w.add_molecules(Species("%s" % (mols[i])), obs0_i)
print (mols[i], ':', obs0_i)
sim.initialize()
# Run simulator
period = 50. # sec
obs = FixedIntervalNumberObserver(1.0, mols)
sim.run(period, [obs])
obs_data = numpy.array(obs.data())
time = obs_data[:,0]
R0 = obs_data[:,1] + obs_data[:,2] + obs_data[:,3] + obs_data[:,4]
RM = obs_data[:,5] + obs_data[:,6] + obs_data[:,7] + obs_data[:,8]
RD = obs_data[:,9] + obs_data[:,10] + obs_data[:,11]
G0 = obs_data[:,12] + obs_data[:,13] + obs_data[:,14] + obs_data[:,15]
GM = obs_data[:,16] + obs_data[:,17] + obs_data[:,18] + obs_data[:,19]
GD = obs_data[:,20] + obs_data[:,21] + obs_data[:,22]
data = obs_data.T
plt.plot(data[0], RM+RD+GM+GD, "b-", label="Bound states")
plt.plot(data[0], RM, "-", label="M")
plt.plot(data[0], RD, "-", label="D")
plt.plot(data[0], GM, "-", label="G•M")
plt.plot(data[0], GM, "-", label="G•D")
plt.xlabel("Time [sec]")
plt.ylabel("Bounds")
plt.xlim(data[0][0], data[0][-1])
plt.legend(loc="best", shadow=True)
plt.show()
In [6]:
def run_N3(m, mols, obs0):
# Create simulator (ODE)
w = ode.World()
w.bind_to(m)
sim = ode.Simulator(w)
# Initialization
print ("Initial condition")
for i in range(len(mols)) :
obs0_i = int(round(obs0[i]))
w.add_molecules(Species("%s" % (mols[i])), obs0_i)
print (mols[i], ':', obs0_i)
sim.initialize()
# Run simulator
period = 50. # sec
obs = FixedIntervalNumberObserver(1.0, mols)
sim.run(period, [obs])
obs_data = numpy.array(obs.data())
time = obs_data[:,0]
R0 = obs_data[:,1] + obs_data[:,2] + obs_data[:,3] + obs_data[:,4] + obs_data[:,5] + obs_data[:,6]
RM = obs_data[:,7] + obs_data[:,8] + obs_data[:,9] + obs_data[:,10] + obs_data[:,11] + obs_data[:,12]
RD = obs_data[:,13] + obs_data[:,14] + obs_data[:,15] + obs_data[:,16] + obs_data[:,17]
G0 = obs_data[:,18] + obs_data[:,19] + obs_data[:,20] + obs_data[:,21] + obs_data[:,22] + obs_data[:,23]
GM = obs_data[:,24] + obs_data[:,25] + obs_data[:,26] + obs_data[:,27] + obs_data[:,28] + obs_data[:,29]
GD = obs_data[:,30] + obs_data[:,31] + obs_data[:,32] + obs_data[:,33] + obs_data[:,34]
data = obs_data.T
plt.plot(data[0], RM+RD+GM+GD, "b-", label="Bound states")
plt.plot(data[0], RM, "-", label="M")
plt.plot(data[0], RD, "-", label="D")
plt.plot(data[0], GM, "-", label="G•M")
plt.plot(data[0], GM, "-", label="G•D")
plt.xlabel("Time [sec]")
plt.ylabel("Bounds")
plt.xlim(data[0][0], data[0][-1])
plt.legend(loc="best", shadow=True)
plt.show()
In [7]:
def run_N4(m, mols, obs0):
# Create simulator (ODE)
w = ode.World()
w.bind_to(m)
sim = ode.Simulator(w)
# Initialization
print ("Initial condition")
for i in range(len(mols)) :
obs0_i = int(round(obs0[i]))
w.add_molecules(Species("%s" % (mols[i])), obs0_i)
print (mols[i], ':', obs0_i)
sim.initialize()
# Run simulator
period = 50. # sec
obs = FixedIntervalNumberObserver(1.0, mols)
sim.run(period, [obs])
obs_data = numpy.array(obs.data())
time = obs_data[:,0]
R0 = obs_data[:,1] + obs_data[:,2] + obs_data[:,3] + obs_data[:,4] + obs_data[:,5] + obs_data[:,6] + obs_data[:,7] + obs_data[:,8]
RM = obs_data[:,9] + obs_data[:,10] + obs_data[:,11] + obs_data[:,12] + obs_data[:,13] + obs_data[:,14] + obs_data[:,15] + obs_data[:,16]
RD = obs_data[:,17] + obs_data[:,18] + obs_data[:,19] + obs_data[:,20] + obs_data[:,21] + obs_data[:,22] + obs_data[:,23]
G0 = obs_data[:,24] + obs_data[:,25] + obs_data[:,26] + obs_data[:,27] + obs_data[:,28] + obs_data[:,29] + obs_data[:,30] + obs_data[:,31]
GM = obs_data[:,32] + obs_data[:,33] + obs_data[:,34] + obs_data[:,35] + obs_data[:,36] + obs_data[:,37] + obs_data[:,38] + obs_data[:,39]
GD = obs_data[:,40] + obs_data[:,41] + obs_data[:,42] + obs_data[:,43] + obs_data[:,44] + obs_data[:,45] + obs_data[:,46]
data = obs_data.T
plt.plot(data[0], RM+RD+GM+GD, "b-", label="Bound states")
plt.plot(data[0], RM, "-", label="M")
plt.plot(data[0], RD, "-", label="D")
plt.plot(data[0], GM, "-", label="G•M")
plt.plot(data[0], GM, "-", label="G•D")
plt.xlabel("Time [sec]")
plt.ylabel("Bounds")
plt.xlim(data[0][0], data[0][-1])
plt.legend(loc="best", shadow=True)
plt.show()
In [8]:
def run_N5(m, mols, obs0):
# Create simulator (ODE)
w = ode.World()
w.bind_to(m)
sim = ode.Simulator(w)
# Initialization
print ("Initial condition")
for i in range(len(mols)) :
obs0_i = int(round(obs0[i]))
w.add_molecules(Species("%s" % (mols[i])), obs0_i)
print (mols[i], ':', obs0_i)
sim.initialize()
# Run simulator
period = 50. # sec
obs = FixedIntervalNumberObserver(1.0, mols)
sim.run(period, [obs])
obs_data = numpy.array(obs.data())
time = obs_data[:,0]
R0 = obs_data[:,1] + obs_data[:,2] + obs_data[:,3] + obs_data[:,4] + obs_data[:,5] + obs_data[:,6] + obs_data[:,7] + obs_data[:,8] + obs_data[:,9] + obs_data[:,10]
RM = obs_data[:,11] + obs_data[:,12] + obs_data[:,13] + obs_data[:,14] + obs_data[:,15] + obs_data[:,16] + obs_data[:,17] + obs_data[:,18] + obs_data[:,19] + obs_data[:,20]
RD = obs_data[:,21] + obs_data[:,22] + obs_data[:,23] + obs_data[:,24] + obs_data[:,25] + obs_data[:,26] + obs_data[:,27] + obs_data[:,28] + obs_data[:,29]
G0 = obs_data[:,30] + obs_data[:,31] + obs_data[:,32] + obs_data[:,33] + obs_data[:,34] + obs_data[:,35] + obs_data[:,36] + obs_data[:,37] + obs_data[:,38] + obs_data[:,39]
GM = obs_data[:,40] + obs_data[:,41] + obs_data[:,42] + obs_data[:,43] + obs_data[:,44] + obs_data[:,45] + obs_data[:,46] + obs_data[:,47] + obs_data[:,48] + obs_data[:,49]
GD = obs_data[:,50] + obs_data[:,51] + obs_data[:,52] + obs_data[:,53] + obs_data[:,54] + obs_data[:,55] + obs_data[:,56] + obs_data[:,57] + obs_data[:,58]
data = obs_data.T
plt.plot(data[0], RM+RD+GM+GD, "b-", label="Bound states")
plt.plot(data[0], RM, "-", label="M")
plt.plot(data[0], RD, "-", label="D")
plt.plot(data[0], GM, "-", label="G•M")
plt.plot(data[0], GM, "-", label="G•D")
plt.xlabel("Time [sec]")
plt.ylabel("Bounds")
plt.xlim(data[0][0], data[0][-1])
plt.legend(loc="best", shadow=True)
plt.show()
The simplest ternary complex model (kx = 0)¶
In [9]:
# this is the ternary complex model (TCM): N=0
N = 0.00
# Inputs :
# Ligand and G-protein concentrations
L = 1.00
G = 1.00
# scaling factor
alpha = 1.00
# The lumped dimensionless parameter
kx = 0.00
mols = ["r", "R", "Gr", "GR"]
par = ParConfigs()
obs0 = numpy.zeros(shape=(len(mols)))
obs0[0] = par.get_r0()
###############################################################
print ('Model-order: N =', N)
print ('Ligand: L =', L)
print ('G-protein: G =', G)
print ('alpha-factor: a =', alpha)
print ('Initial condition:')
for i in range(len(mols)) :
print (' ', mols[i], ': ', obs0[i])
###############################################################
# ligands-receptors first-order coupling
dl0, dl1, dl2 = par.get_dl()
kl0, kl1, kl2 = par.get_kl(100, 100)
# Gproteins-receptors first-order coupling
dg0, dg1 = par.get_dg()
kg0, kg1 = par.get_kg(100)
# ligand-(Gproteins-receptors) first-order coupling
da0, da1, da2 = par.get_da()
ka0, ka1, ka2 = par.get_ka(alpha, 100, 100)
# Gproteins-(ligand-receptors) first-order coupling
db0, db1, db2 = par.get_db()
kb0, kb1, kb2 = par.get_kb(alpha, 100, 100)
## receptor-receptor second-order coupling
#dx0, dx1, dx2 = par.get_dx()
#kx0, kx1, kx2 = par.get_kx(kx, N)
#
## receptor-Gprotein second-order coupling
#dy0, dy1, dy2, dy3 = par.get_dy()
#ky0, ky1, ky2, ky3 = par.get_ky(1, 1, 1, 1)
In [10]:
with reaction_rules():
# TCM (Ternary complex model)
r == R | (kl0*L, dl0)
R == GR | (ka0*G, da0)
r == Gr | (kg0*G, dg0)
Gr == GR | (kb0*L, db0)
m = get_model()
show(m)
In [11]:
run_N0(m, mols, obs0)
The multiary complex model¶
Monovalent model (N = 1 and kx > 0)¶
In [12]:
# this is the monovalent model : N=1
N = 1.00
# Inputs :
# Ligand and G-protein concentrations
L = 1.00
G = 1.00
# scaling factor
alpha = 1.00
# The lumped dimensionless parameter (kx > 0)
kx = 0.001
# get model-parameters
par = ParConfigs()
mols = ["r", "rr", "R", "rR", "RR", "Gr", "Grr", "GR", "GrR", "GRR"]
obs0 = numpy.zeros(shape=(len(mols)))
obs0[0] = par.get_r0()
###############################################################
print ('Model-order: N =', N)
print ('Ligand: L =', L)
print ('G-protein: G =', G)
print ('alpha-factor: a =', alpha)
print ('Initial condition:')
for i in range(len(mols)) :
print (' ', mols[i], ': ', obs0[i])
###############################################################
# ligands-receptors first-order coupling
dl0, dl1, dl2 = par.get_dl()
kl0, kl1, kl2 = par.get_kl(100, 100)
# Gproteins-receptors first-order coupling
dg0, dg1 = par.get_dg()
kg0, kg1 = par.get_kg(100)
# ligand-(Gproteins-receptors) first-order coupling
da0, da1, da2 = par.get_da()
ka0, ka1, ka2 = par.get_ka(alpha, 100, 100)
# Gproteins-(ligand-receptors) first-order coupling
db0, db1, db2 = par.get_db()
kb0, kb1, kb2 = par.get_kb(alpha, 100, 100)
# receptor-receptor second-order coupling
dx0, dx1, dx2 = par.get_dx()
kx0, kx1, kx2 = par.get_kx(kx, N)
# receptor-Gprotein second-order coupling
dy0, dy1, dy2, dy3 = par.get_dy()
ky0, ky1, ky2, ky3 = par.get_ky(1, 1, 1, 1)
In [13]:
with reaction_rules():
# TCM (Ternary complex model)
r == R | (kl0*L, dl0)
R == GR | (ka0*G, da0)
r == Gr | (kg0*G, dg0)
Gr == GR | (kb0*L, db0)
# receptor dimerization
r + r == rr | (kx0, dx0)
R + r == rR | (kx1, dx1)
R + R == RR | (kx2, dx2)
rr == rR | (kl1*L, dl1)
rR == RR | (kl2*L, dl2)
# dimers coupled with G-proteins
rr == Grr | (kg1*G, dg1)
rR == GrR | (kb1*G, db1)
RR == GRR | (kb2*G, db2)
Gr + r == Grr | (ky0, dy0)
GR + r == GrR | (ky1, dy1)
Gr + R == GrR | (ky2, dy2)
GR + R == GrR | (ky3, dy3)
Grr == GrR | (ka1*L, da1)
GrR == GRR | (ka2*L, da2)
m = get_model()
show(m)
In [14]:
run_N1(m, mols, obs0)
Bivalent model (N = 2 and kx > 0)¶
In [15]:
# this is the bivalent model : N=2
N = 2.00
mols = ["r", "rr", "rrr", "rrrr",
"R", "rR", "rrR", "rrrR",
"RR", "rRR", "rrRR",
"Gr", "Grr", "Grrr", "Grrrr",
"GR", "GrR", "GrrR", "GrrrR",
"GRR", "GrRR", "GrrRR"]
In [16]:
with reaction_rules():
# TCM (Ternary complex model)
r == R | (kl0*L, dl0)
R == GR | (ka0*G, da0)
r == Gr | (kg0*G, dg0)
Gr == GR | (kb0*L, db0)
# receptor dimerization
r + r == rr | (kx0, dx0)
r + rr == rrr | (kx0, dx0)
rr + r == rrr | (kx0, dx0)
rr + rr == rrrr | (kx0, dx0)
R + r == rR | (kx1, dx1)
R + rr == rrR | (kx1, dx1)
rR + r == rrR | (kx1, dx1)
rR + rr == rrrR | (kx1, dx1)
R + R == RR | (kx2, dx2)
R + rR == rRR | (kx2, dx2)
rR + R == rRR | (kx2, dx2)
rR + rR == rrRR | (kx2, dx2)
rr == rR | (kl1*L, dl1)
rrr == rrR | (kl1*L, dl1)
rrrr == rrrR | (kl1*L, dl1)
rR == RR | (kl2*L, dl2)
rrR == rRR | (kl2*L, dl2)
rrrR == rrRR | (kl2*L, dl2)
# dimers coupled with G-proteins
rr == Grr | (kg1*G, dg1)
rrr == Grrr | (kg1*G, dg1)
rrrr == Grrrr | (kg1*G, dg1)
rR == GrR | (kb1*G, db1)
rrR == GrrR | (kb1*G, db1)
rrrR == GrrrR | (kb1*G, db1)
RR == GRR | (kb2*G, db2)
rRR == GrRR | (kb2*G, db2)
rrRR == GrrRR | (kb2*G, db2)
Gr + r == Grr | (ky0, dy0)
Gr + rr == Grrr | (ky0, dy0)
Grr + r == Grrr | (ky0, dy0)
Grr + rr == Grrrr | (ky0, dy0)
GR + r == GrR | (ky1, dy1)
GR + rr == GrrR | (ky1, dy1)
GrR + r == GrrR | (ky1, dy1)
GrR + rr == GrrrR | (ky1, dy1)
R + Gr == GrR | (ky2, dy2)
R + Grr == GrrR | (ky2, dy2)
rR + Gr == GrrR | (ky2, dy2)
rR + Grr == GrrrR | (ky2, dy2)
GR + R == GRR | (ky3, dy3)
GR + rR == GrRR | (ky3, dy3)
GrR + R == GrRR | (ky3, dy3)
GrR + rR == GrrRR | (ky3, dy3)
Grr == GrR | (ka1*L, da1)
Grrr == GrrR | (ka1*L, da1)
Grrrr == GrrrR | (ka1*L, da1)
GrR == GRR | (ka2*L, da2)
GrrR == GrRR | (ka2*L, da2)
GrrrR == GrrRR | (ka2*L, da2)
m = get_model()
show(m)
In [17]:
obs0 = numpy.zeros(shape=(len(mols)))
obs0[0] = par.get_r0()
run_N2(m, mols, obs0)
Trivalent model (N = 3 and kx > 0)¶
In [18]:
# this is the trivalent model : N=3
N = 3.00
mols = ["r", "rr", "rrr", "rrrr", "rrrrr", "rrrrrr",
"R", "rR", "rrR", "rrrR", "rrrrR", "rrrrrR",
"RR", "rRR", "rrRR", "rrrRR", "rrrrRR",
"Gr", "Grr", "Grrr", "Grrrr", "Grrrrr", "Grrrrrr",
"GR", "GrR", "GrrR", "GrrrR", "GrrrrR", "GrrrrrR",
"GRR", "GrRR", "GrrRR", "GrrrRR", "GrrrrRR"]
In [19]:
with reaction_rules():
# TCM (Ternary complex model)
r == R | (kl0*L, dl0)
R == GR | (ka0*G, da0)
r == Gr | (kg0*G, dg0)
Gr == GR | (kb0*L, db0)
# receptor dimerization
r + r == rr | (kx0, dx0)
r + rr == rrr | (kx0, dx0)
r + rrr == rrrr | (kx0, dx0)
rr + r == rrr | (kx0, dx0)
rr + rr == rrrr | (kx0, dx0)
rr + rrr == rrrrr | (kx0, dx0)
rrr + r == rrrr | (kx0, dx0)
rrr + rr == rrrrr | (kx0, dx0)
rrr + rrr == rrrrrr | (kx0, dx0)
R + r == rR | (kx1, dx1)
R + rr == rrR | (kx1, dx1)
R + rrr == rrrR | (kx1, dx1)
rR + r == rrR | (kx1, dx1)
rR + rr == rrrR | (kx1, dx1)
rR + rrr == rrrrR | (kx1, dx1)
rrR + r == rrrR | (kx1, dx1)
rrR + rr == rrrrR | (kx1, dx1)
rrR + rrr == rrrrrR | (kx1, dx1)
R + R == RR | (kx2, dx2)
R + rR == rRR | (kx2, dx2)
R + rrR == rrRR | (kx2, dx2)
rR + R == rRR | (kx2, dx2)
rR + rR == rrRR | (kx2, dx2)
rR + rrR == rrrRR | (kx2, dx2)
rrR + R == rrRR | (kx2, dx2)
rrR + rR == rrrRR | (kx2, dx2)
rrR + rrR == rrrrRR | (kx2, dx2)
rr == rR | (kl1*L, dl1)
rrr == rrR | (kl1*L, dl1)
rrrr == rrrR | (kl1*L, dl1)
rrrrr == rrrrR | (kl1*L, dl1)
rrrrrr == rrrrrR | (kl1*L, dl1)
rR == RR | (kl2*L, dl2)
rrR == rRR | (kl2*L, dl2)
rrrR == rrRR | (kl2*L, dl2)
rrrrR == rrrRR | (kl2*L, dl2)
rrrrrR == rrrrRR | (kl2*L, dl2)
# dimers coupled with G-proteins
rr == Grr | (kg1*G, dg1)
rrr == Grrr | (kg1*G, dg1)
rrrr == Grrrr | (kg1*G, dg1)
rrrrr == Grrrrr | (kg1*G, dg1)
rrrrrr == Grrrrrr | (kg1*G, dg1)
rR == GrR | (kb1*G, db1)
rrR == GrrR | (kb1*G, db1)
rrrR == GrrrR | (kb1*G, db1)
rrrrR == GrrrrR | (kb1*G, db1)
rrrrrR == GrrrrrR | (kb1*G, db1)
RR == GRR | (kb2*G, db2)
rRR == GrRR | (kb2*G, db2)
rrRR == GrrRR | (kb2*G, db2)
rrrRR == GrrrRR | (kb2*G, db2)
rrrrRR == GrrrrRR | (kb2*G, db2)
Gr + r == Grr | (ky0, dy0)
Gr + rr == Grrr | (ky0, dy0)
Gr + rrr == Grrrr | (ky0, dy0)
Grr + r == Grrr | (ky0, dy0)
Grr + rr == Grrrr | (ky0, dy0)
Grr + rrr == Grrrrr | (ky0, dy0)
Grrr + r == Grrrr | (ky0, dy0)
Grrr + rr == Grrrrr | (ky0, dy0)
Grrr + rrr == Grrrrrr | (ky0, dy0)
GR + r == GrR | (ky1, dy1)
GR + rr == GrrR | (ky1, dy1)
GR + rrr == GrrrR | (ky1, dy1)
GrR + r == GrrR | (ky1, dy1)
GrR + rr == GrrrR | (ky1, dy1)
GrR + rrr == GrrrrR | (ky1, dy1)
GrrR + r == GrrrR | (ky1, dy1)
GrrR + rr == GrrrrR | (ky1, dy1)
GrrR + rrr == GrrrrrR | (ky1, dy1)
R + Gr == GrR | (ky2, dy2)
R + Grr == GrrR | (ky2, dy2)
R + Grrr == GrrrR | (ky2, dy2)
rR + Gr == GrrR | (ky2, dy2)
rR + Grr == GrrrR | (ky2, dy2)
rR + Grrr == GrrrrR | (ky2, dy2)
rrR + Gr == GrrrR | (ky2, dy2)
rrR + Grr == GrrrrR | (ky2, dy2)
rrR + Grrr == GrrrrrR | (ky2, dy2)
GR + R == GRR | (ky3, dy3)
GR + rR == GrRR | (ky3, dy3)
GR + rrR == GrrRR | (ky3, dy3)
GrR + R == GrRR | (ky3, dy3)
GrR + rR == GrrRR | (ky3, dy3)
GrR + rrR == GrrrRR | (ky3, dy3)
GrrR + R == GrrRR | (ky3, dy3)
GrrR + rR == GrrrRR | (ky3, dy3)
GrrR + rrR == GrrrrRR | (ky3, dy3)
Grr == GrR | (ka1*L, da1)
Grrr == GrrR | (ka1*L, da1)
Grrrr == GrrrR | (ka1*L, da1)
Grrrrr == GrrrrR | (ka1*L, da1)
Grrrrrr == GrrrrrR | (ka1*L, da1)
GrR == GRR | (ka2*L, da2)
GrrR == GrRR | (ka2*L, da2)
GrrrR == GrrRR | (ka2*L, da2)
GrrrrR == GrrrRR | (ka2*L, da2)
GrrrrrR == GrrrrRR | (ka2*L, da2)
m = get_model()
show(m)
In [20]:
obs0 = numpy.zeros(shape=(len(mols)))
obs0[0] = par.get_r0()
run_N3(m, mols, obs0)
Tetravalent model (N = 4 and kx > 0)¶
In [21]:
# this is the tetravalent model : N=4
N = 4.00
mols = ["r", "rr", "rrr", "rrrr", "rrrrr", "rrrrrr", "rrrrrrr", "rrrrrrrr",
"R", "rR", "rrR", "rrrR", "rrrrR", "rrrrrR", "rrrrrrR", "rrrrrrrR",
"RR", "rRR", "rrRR", "rrrRR", "rrrrRR", "rrrrrRR", "rrrrrrRR",
"Gr", "Grr", "Grrr", "Grrrr", "Grrrrr", "Grrrrrr", "Grrrrrrr", "Grrrrrrrr",
"GR", "GrR", "GrrR", "GrrrR", "GrrrrR", "GrrrrrR", "GrrrrrrR", "GrrrrrrrR",
"GRR", "GrRR", "GrrRR", "GrrrRR", "GrrrrRR", "GrrrrrRR", "GrrrrrrRR"]
In [22]:
with reaction_rules():
# TCM (Ternary complex model)
r == R | (kl0*L, dl0)
R == GR | (ka0*G, da0)
r == Gr | (kg0*G, dg0)
Gr == GR | (kb0*L, db0)
# receptor dimerization
r + r == rr | (kx0, dx0)
r + rr == rrr | (kx0, dx0)
r + rrr == rrrr | (kx0, dx0)
r + rrrr == rrrrr | (kx0, dx0)
rr + r == rrr | (kx0, dx0)
rr + rr == rrrr | (kx0, dx0)
rr + rrr == rrrrr | (kx0, dx0)
rr + rrrr == rrrrrr | (kx0, dx0)
rrr + r == rrrr | (kx0, dx0)
rrr + rr == rrrrr | (kx0, dx0)
rrr + rrr == rrrrrr | (kx0, dx0)
rrr + rrrr == rrrrrrr | (kx0, dx0)
rrrr + r == rrrrr | (kx0, dx0)
rrrr + rr == rrrrrr | (kx0, dx0)
rrrr + rrr == rrrrrrr | (kx0, dx0)
rrrr + rrrr == rrrrrrrr | (kx0, dx0)
R + r == rR | (kx1, dx1)
R + rr == rrR | (kx1, dx1)
R + rrr == rrrR | (kx1, dx1)
R + rrrr == rrrrR | (kx1, dx1)
rR + r == rrR | (kx1, dx1)
rR + rr == rrrR | (kx1, dx1)
rR + rrr == rrrrR | (kx1, dx1)
rR + rrrr == rrrrrR | (kx1, dx1)
rrR + r == rrrR | (kx1, dx1)
rrR + rr == rrrrR | (kx1, dx1)
rrR + rrr == rrrrrR | (kx1, dx1)
rrR + rrrr == rrrrrrR | (kx1, dx1)
rrrR + r == rrrrR | (kx1, dx1)
rrrR + rr == rrrrrR | (kx1, dx1)
rrrR + rrr == rrrrrrR | (kx1, dx1)
rrrR + rrrr == rrrrrrrR | (kx1, dx1)
R + R == RR | (kx2, dx2)
R + rR == rRR | (kx2, dx2)
R + rrR == rrRR | (kx2, dx2)
R + rrrR == rrrRR | (kx2, dx2)
rR + R == rRR | (kx2, dx2)
rR + rR == rrRR | (kx2, dx2)
rR + rrR == rrrRR | (kx2, dx2)
rR + rrrR == rrrrRR | (kx2, dx2)
rrR + R == rrRR | (kx2, dx2)
rrR + rR == rrrRR | (kx2, dx2)
rrR + rrR == rrrrRR | (kx2, dx2)
rrR + rrrR == rrrrrRR | (kx2, dx2)
rrrR + R == rrrRR | (kx2, dx2)
rrrR + rR == rrrrRR | (kx2, dx2)
rrrR + rrR == rrrrrRR | (kx2, dx2)
rrrR + rrrR == rrrrrrRR | (kx2, dx2)
rr == rR | (kl1*L, dl1)
rrr == rrR | (kl1*L, dl1)
rrrr == rrrR | (kl1*L, dl1)
rrrrr == rrrrR | (kl1*L, dl1)
rrrrrr == rrrrrR | (kl1*L, dl1)
rrrrrrr == rrrrrrR | (kl1*L, dl1)
rrrrrrrr == rrrrrrrR | (kl1*L, dl1)
rR == RR | (kl2*L, dl2)
rrR == rRR | (kl2*L, dl2)
rrrR == rrRR | (kl2*L, dl2)
rrrrR == rrrRR | (kl2*L, dl2)
rrrrrR == rrrrRR | (kl2*L, dl2)
rrrrrrR == rrrrrRR | (kl2*L, dl2)
rrrrrrrR == rrrrrrRR | (kl2*L, dl2)
# dimers coupled with G-proteins
rr == Grr | (kg1*G, dg1)
rrr == Grrr | (kg1*G, dg1)
rrrr == Grrrr | (kg1*G, dg1)
rrrrr == Grrrrr | (kg1*G, dg1)
rrrrrr == Grrrrrr | (kg1*G, dg1)
rrrrrrr == Grrrrrrr | (kg1*G, dg1)
rrrrrrrr == Grrrrrrrr | (kg1*G, dg1)
rR == GrR | (kb1*G, db1)
rrR == GrrR | (kb1*G, db1)
rrrR == GrrrR | (kb1*G, db1)
rrrrR == GrrrrR | (kb1*G, db1)
rrrrrR == GrrrrrR | (kb1*G, db1)
rrrrrrR == GrrrrrrR | (kb1*G, db1)
rrrrrrrR == GrrrrrrrR | (kb1*G, db1)
RR == GRR | (kb2*G, db2)
rRR == GrRR | (kb2*G, db2)
rrRR == GrrRR | (kb2*G, db2)
rrrRR == GrrrRR | (kb2*G, db2)
rrrrRR == GrrrrRR | (kb2*G, db2)
rrrrrRR == GrrrrrRR | (kb2*G, db2)
rrrrrrRR == GrrrrrrRR | (kb2*G, db2)
Gr + r == Grr | (ky0, dy0)
Gr + rr == Grrr | (ky0, dy0)
Gr + rrr == Grrrr | (ky0, dy0)
Gr + rrrr == Grrrrr | (ky0, dy0)
Grr + r == Grrr | (ky0, dy0)
Grr + rr == Grrrr | (ky0, dy0)
Grr + rrr == Grrrrr | (ky0, dy0)
Grr + rrrr == Grrrrrr | (ky0, dy0)
Grrr + r == Grrrr | (ky0, dy0)
Grrr + rr == Grrrrr | (ky0, dy0)
Grrr + rrr == Grrrrrr | (ky0, dy0)
Grrr + rrrr == Grrrrrrr | (ky0, dy0)
Grrrr + r == Grrrrr | (ky0, dy0)
Grrrr + rr == Grrrrrr | (ky0, dy0)
Grrrr + rrr == Grrrrrrr | (ky0, dy0)
Grrrr + rrrr == Grrrrrrrr | (ky0, dy0)
GR + r == GrR | (ky1, dy1)
GR + rr == GrrR | (ky1, dy1)
GR + rrr == GrrrR | (ky1, dy1)
GR + rrrr == GrrrrR | (ky1, dy1)
GrR + r == GrrR | (ky1, dy1)
GrR + rr == GrrrR | (ky1, dy1)
GrR + rrr == GrrrrR | (ky1, dy1)
GrR + rrrr == GrrrrrR | (ky1, dy1)
GrrR + r == GrrrR | (ky1, dy1)
GrrR + rr == GrrrrR | (ky1, dy1)
GrrR + rrr == GrrrrrR | (ky1, dy1)
GrrR + rrrr == GrrrrrrR | (ky1, dy1)
GrrrR + r == GrrrrR | (ky1, dy1)
GrrrR + rr == GrrrrrR | (ky1, dy1)
GrrrR + rrr == GrrrrrrR | (ky1, dy1)
GrrrR + rrrr == GrrrrrrrR | (ky1, dy1)
R + Gr == GrR | (ky2, dy2)
R + Grr == GrrR | (ky2, dy2)
R + Grrr == GrrrR | (ky2, dy2)
R + Grrrr == GrrrrR | (ky2, dy2)
rR + Gr == GrrR | (ky2, dy2)
rR + Grr == GrrrR | (ky2, dy2)
rR + Grrr == GrrrrR | (ky2, dy2)
rR + Grrrr == GrrrrrR | (ky2, dy2)
rrR + Gr == GrrrR | (ky2, dy2)
rrR + Grr == GrrrrR | (ky2, dy2)
rrR + Grrr == GrrrrrR | (ky2, dy2)
rrR + Grrrr == GrrrrrrR | (ky2, dy2)
rrrR + Gr == GrrrrR | (ky2, dy2)
rrrR + Grr == GrrrrrR | (ky2, dy2)
rrrR + Grrr == GrrrrrrR | (ky2, dy2)
rrrR + Grrrr == GrrrrrrrR | (ky2, dy2)
GR + R == GRR | (ky3, dy3)
GR + rR == GrRR | (ky3, dy3)
GR + rrR == GrrRR | (ky3, dy3)
GR + rrrR == GrrrRR | (ky3, dy3)
GrR + R == GrRR | (ky3, dy3)
GrR + rR == GrrRR | (ky3, dy3)
GrR + rrR == GrrrRR | (ky3, dy3)
GrR + rrrR == GrrrrRR | (ky3, dy3)
GrrR + R == GrrRR | (ky3, dy3)
GrrR + rR == GrrrRR | (ky3, dy3)
GrrR + rrR == GrrrrRR | (ky3, dy3)
GrrR + rrrR == GrrrrrRR | (ky3, dy3)
GrrrR + R == GrrrRR | (ky3, dy3)
GrrrR + rR == GrrrrRR | (ky3, dy3)
GrrrR + rrR == GrrrrrRR | (ky3, dy3)
GrrrR + rrrR == GrrrrrrRR | (ky3, dy3)
Grr == GrR | (ka1*L, da1)
Grrr == GrrR | (ka1*L, da1)
Grrrr == GrrrR | (ka1*L, da1)
Grrrrr == GrrrrR | (ka1*L, da1)
Grrrrrr == GrrrrrR | (ka1*L, da1)
Grrrrrrr == GrrrrrrR | (ka1*L, da1)
Grrrrrrrr == GrrrrrrrR | (ka1*L, da1)
GrR == GRR | (ka2*L, da2)
GrrR == GrRR | (ka2*L, da2)
GrrrR == GrrRR | (ka2*L, da2)
GrrrrR == GrrrRR | (ka2*L, da2)
GrrrrrR == GrrrrRR | (ka2*L, da2)
GrrrrrrR == GrrrrrRR | (ka2*L, da2)
GrrrrrrrR == GrrrrrrRR | (ka2*L, da2)
m = get_model()
show(m)
In [23]:
obs0 = numpy.zeros(shape=(len(mols)))
obs0[0] = par.get_r0()
run_N4(m, mols, obs0)
Pentavalent model (N = 5 and kx > 0)¶
In [24]:
# this is the pentavalent model : N=5
N = 5.00
mols = ["r", "rr", "rrr", "rrrr", "rrrrr", "rrrrrr", "rrrrrrr", "rrrrrrrr", "rrrrrrrr", "rrrrrrrrrr",
"R", "rR", "rrR", "rrrR", "rrrrR", "rrrrrR", "rrrrrrR", "rrrrrrrR", "rrrrrrrR", "rrrrrrrrrR",
"RR", "rRR", "rrRR", "rrrRR", "rrrrRR", "rrrrrRR", "rrrrrrRR", "rrrrrrRR", "rrrrrrrrRR",
"Gr", "Grr", "Grrr", "Grrrr", "Grrrrr", "Grrrrrr", "Grrrrrrr", "Grrrrrrrr", "Grrrrrrrr", "Grrrrrrrrrr",
"GR", "GrR", "GrrR", "GrrrR", "GrrrrR", "GrrrrrR", "GrrrrrrR", "GrrrrrrrR", "GrrrrrrrR", "GrrrrrrrrrR",
"GRR", "GrRR", "GrrRR", "GrrrRR", "GrrrrRR", "GrrrrrRR", "GrrrrrrRR", "GrrrrrrRR", "GrrrrrrrrRR"]
In [25]:
with reaction_rules():
# TCM (Ternary complex model)
r == R | (kl0*L, dl0)
R == GR | (ka0*G, da0)
r == Gr | (kg0*G, dg0)
Gr == GR | (kb0*L, db0)
# receptor dimerization
r + r == rr | (kx0, dx0)
r + rr == rrr | (kx0, dx0)
r + rrr == rrrr | (kx0, dx0)
r + rrrr == rrrrr | (kx0, dx0)
r + rrrrr == rrrrrr | (kx0, dx0)
rr + r == rrr | (kx0, dx0)
rr + rr == rrrr | (kx0, dx0)
rr + rrr == rrrrr | (kx0, dx0)
rr + rrrr == rrrrrr | (kx0, dx0)
rr + rrrrr == rrrrrrr | (kx0, dx0)
rrr + r == rrrr | (kx0, dx0)
rrr + rr == rrrrr | (kx0, dx0)
rrr + rrr == rrrrrr | (kx0, dx0)
rrr + rrrr == rrrrrrr | (kx0, dx0)
rrr + rrrrr == rrrrrrrr | (kx0, dx0)
rrrr + r == rrrrr | (kx0, dx0)
rrrr + rr == rrrrrr | (kx0, dx0)
rrrr + rrr == rrrrrrr | (kx0, dx0)
rrrr + rrrr == rrrrrrrr | (kx0, dx0)
rrrr + rrrrr == rrrrrrrrr | (kx0, dx0)
rrrrr + r == rrrrrr | (kx0, dx0)
rrrrr + rr == rrrrrrr | (kx0, dx0)
rrrrr + rrr == rrrrrrrr | (kx0, dx0)
rrrrr + rrrr == rrrrrrrrr | (kx0, dx0)
rrrrr + rrrrr == rrrrrrrrrr | (kx0, dx0)
R + r == rR | (kx1, dx1)
R + rr == rrR | (kx1, dx1)
R + rrr == rrrR | (kx1, dx1)
R + rrrr == rrrrR | (kx1, dx1)
R + rrrrr == rrrrrR | (kx1, dx1)
rR + r == rrR | (kx1, dx1)
rR + rr == rrrR | (kx1, dx1)
rR + rrr == rrrrR | (kx1, dx1)
rR + rrrr == rrrrrR | (kx1, dx1)
rR + rrrrr == rrrrrrR | (kx1, dx1)
rrR + r == rrrR | (kx1, dx1)
rrR + rr == rrrrR | (kx1, dx1)
rrR + rrr == rrrrrR | (kx1, dx1)
rrR + rrrr == rrrrrrR | (kx1, dx1)
rrR + rrrrr == rrrrrrrR | (kx1, dx1)
rrrR + r == rrrrR | (kx1, dx1)
rrrR + rr == rrrrrR | (kx1, dx1)
rrrR + rrr == rrrrrrR | (kx1, dx1)
rrrR + rrrr == rrrrrrrR | (kx1, dx1)
rrrR + rrrrr == rrrrrrrrR | (kx1, dx1)
rrrrR + r == rrrrrR | (kx1, dx1)
rrrrR + rr == rrrrrrR | (kx1, dx1)
rrrrR + rrr == rrrrrrrR | (kx1, dx1)
rrrrR + rrrr == rrrrrrrrR | (kx1, dx1)
rrrrR + rrrrr == rrrrrrrrrR | (kx1, dx1)
R + R == RR | (kx2, dx2)
R + rR == rRR | (kx2, dx2)
R + rrR == rrRR | (kx2, dx2)
R + rrrR == rrrRR | (kx2, dx2)
R + rrrrR == rrrrRR | (kx2, dx2)
rR + R == rRR | (kx2, dx2)
rR + rR == rrRR | (kx2, dx2)
rR + rrR == rrrRR | (kx2, dx2)
rR + rrrR == rrrrRR | (kx2, dx2)
rR + rrrrR == rrrrrRR | (kx2, dx2)
rrR + R == rrRR | (kx2, dx2)
rrR + rR == rrrRR | (kx2, dx2)
rrR + rrR == rrrrRR | (kx2, dx2)
rrR + rrrR == rrrrrRR | (kx2, dx2)
rrR + rrrrR == rrrrrrRR | (kx2, dx2)
rrrR + R == rrrRR | (kx2, dx2)
rrrR + rR == rrrrRR | (kx2, dx2)
rrrR + rrR == rrrrrRR | (kx2, dx2)
rrrR + rrrR == rrrrrrRR | (kx2, dx2)
rrrR + rrrrR == rrrrrrrRR | (kx2, dx2)
rrrrR + R == rrrrRR | (kx2, dx2)
rrrrR + rR == rrrrrRR | (kx2, dx2)
rrrrR + rrR == rrrrrrRR | (kx2, dx2)
rrrrR + rrrR == rrrrrrrRR | (kx2, dx2)
rrrrR + rrrrR == rrrrrrrrRR | (kx2, dx2)
rr == rR | (kl1*L, dl1)
rrr == rrR | (kl1*L, dl1)
rrrr == rrrR | (kl1*L, dl1)
rrrrr == rrrrR | (kl1*L, dl1)
rrrrrr == rrrrrR | (kl1*L, dl1)
rrrrrrr == rrrrrrR | (kl1*L, dl1)
rrrrrrrr == rrrrrrrR | (kl1*L, dl1)
rrrrrrrrr == rrrrrrrrR | (kl1*L, dl1)
rrrrrrrrrr == rrrrrrrrrR | (kl1*L, dl1)
rR == RR | (kl2*L, dl2)
rrR == rRR | (kl2*L, dl2)
rrrR == rrRR | (kl2*L, dl2)
rrrrR == rrrRR | (kl2*L, dl2)
rrrrrR == rrrrRR | (kl2*L, dl2)
rrrrrrR == rrrrrRR | (kl2*L, dl2)
rrrrrrrR == rrrrrrRR | (kl2*L, dl2)
rrrrrrrrR == rrrrrrrRR | (kl2*L, dl2)
rrrrrrrrrR == rrrrrrrrRR | (kl2*L, dl2)
# dimers coupled with G-proteins
rr == Grr | (kg1*G, dg1)
rrr == Grrr | (kg1*G, dg1)
rrrr == Grrrr | (kg1*G, dg1)
rrrrr == Grrrrr | (kg1*G, dg1)
rrrrrr == Grrrrrr | (kg1*G, dg1)
rrrrrrr == Grrrrrrr | (kg1*G, dg1)
rrrrrrrr == Grrrrrrrr | (kg1*G, dg1)
rrrrrrrrr == Grrrrrrrrr | (kg1*G, dg1)
rrrrrrrrrr == Grrrrrrrrrr | (kg1*G, dg1)
rR == GrR | (kb1*G, db1)
rrR == GrrR | (kb1*G, db1)
rrrR == GrrrR | (kb1*G, db1)
rrrrR == GrrrrR | (kb1*G, db1)
rrrrrR == GrrrrrR | (kb1*G, db1)
rrrrrrR == GrrrrrrR | (kb1*G, db1)
rrrrrrrR == GrrrrrrrR | (kb1*G, db1)
rrrrrrrrR == GrrrrrrrrR | (kb1*G, db1)
rrrrrrrrrR == GrrrrrrrrrR | (kb1*G, db1)
RR == GRR | (kb2*G, db2)
rRR == GrRR | (kb2*G, db2)
rrRR == GrrRR | (kb2*G, db2)
rrrRR == GrrrRR | (kb2*G, db2)
rrrrRR == GrrrrRR | (kb2*G, db2)
rrrrrRR == GrrrrrRR | (kb2*G, db2)
rrrrrrRR == GrrrrrrRR | (kb2*G, db2)
rrrrrrrRR == GrrrrrrrRR | (kb2*G, db2)
rrrrrrrrRR == GrrrrrrrrRR | (kb2*G, db2)
Gr + r == Grr | (ky0, dy0)
Gr + rr == Grrr | (ky0, dy0)
Gr + rrr == Grrrr | (ky0, dy0)
Gr + rrrr == Grrrrr | (ky0, dy0)
Gr + rrrrr == Grrrrrr | (ky0, dy0)
Grr + r == Grrr | (ky0, dy0)
Grr + rr == Grrrr | (ky0, dy0)
Grr + rrr == Grrrrr | (ky0, dy0)
Grr + rrrr == Grrrrrr | (ky0, dy0)
Grr + rrrrr == Grrrrrrr | (ky0, dy0)
Grrr + r == Grrrr | (ky0, dy0)
Grrr + rr == Grrrrr | (ky0, dy0)
Grrr + rrr == Grrrrrr | (ky0, dy0)
Grrr + rrrr == Grrrrrrr | (ky0, dy0)
Grrr + rrrrr == Grrrrrrrr | (ky0, dy0)
Grrrr + r == Grrrrr | (ky0, dy0)
Grrrr + rr == Grrrrrr | (ky0, dy0)
Grrrr + rrr == Grrrrrrr | (ky0, dy0)
Grrrr + rrrr == Grrrrrrrr | (ky0, dy0)
Grrrr + rrrrr == Grrrrrrrrr | (ky0, dy0)
Grrrrr + r == Grrrrrr | (ky0, dy0)
Grrrrr + rr == Grrrrrrr | (ky0, dy0)
Grrrrr + rrr == Grrrrrrrr | (ky0, dy0)
Grrrrr + rrrr == Grrrrrrrrr | (ky0, dy0)
Grrrrr + rrrrr == Grrrrrrrrrr | (ky0, dy0)
GR + r == GrR | (ky1, dy1)
GR + rr == GrrR | (ky1, dy1)
GR + rrr == GrrrR | (ky1, dy1)
GR + rrrr == GrrrrR | (ky1, dy1)
GR + rrrrr == GrrrrrR | (ky1, dy1)
GrR + r == GrrR | (ky1, dy1)
GrR + rr == GrrrR | (ky1, dy1)
GrR + rrr == GrrrrR | (ky1, dy1)
GrR + rrrr == GrrrrrR | (ky1, dy1)
GrR + rrrrr == GrrrrrrR | (ky1, dy1)
GrrR + r == GrrrR | (ky1, dy1)
GrrR + rr == GrrrrR | (ky1, dy1)
GrrR + rrr == GrrrrrR | (ky1, dy1)
GrrR + rrrr == GrrrrrrR | (ky1, dy1)
GrrR + rrrrr == GrrrrrrrR | (ky1, dy1)
GrrrR + r == GrrrrR | (ky1, dy1)
GrrrR + rr == GrrrrrR | (ky1, dy1)
GrrrR + rrr == GrrrrrrR | (ky1, dy1)
GrrrR + rrrr == GrrrrrrrR | (ky1, dy1)
GrrrR + rrrrr == GrrrrrrrrR | (ky1, dy1)
GrrrrR + r == GrrrrrR | (ky1, dy1)
GrrrrR + rr == GrrrrrrR | (ky1, dy1)
GrrrrR + rrr == GrrrrrrrR | (ky1, dy1)
GrrrrR + rrrr == GrrrrrrrrR | (ky1, dy1)
GrrrrR + rrrrr == GrrrrrrrrrR | (ky1, dy1)
R + Gr == GrR | (ky2, dy2)
R + Grr == GrrR | (ky2, dy2)
R + Grrr == GrrrR | (ky2, dy2)
R + Grrrr == GrrrrR | (ky2, dy2)
R + Grrrrr == GrrrrrR | (ky2, dy2)
rR + Gr == GrrR | (ky2, dy2)
rR + Grr == GrrrR | (ky2, dy2)
rR + Grrr == GrrrrR | (ky2, dy2)
rR + Grrrr == GrrrrrR | (ky2, dy2)
rR + Grrrrr == GrrrrrrR | (ky2, dy2)
rrR + Gr == GrrrR | (ky2, dy2)
rrR + Grr == GrrrrR | (ky2, dy2)
rrR + Grrr == GrrrrrR | (ky2, dy2)
rrR + Grrrr == GrrrrrrR | (ky2, dy2)
rrR + Grrrrr == GrrrrrrrR | (ky2, dy2)
rrrR + Gr == GrrrrR | (ky2, dy2)
rrrR + Grr == GrrrrrR | (ky2, dy2)
rrrR + Grrr == GrrrrrrR | (ky2, dy2)
rrrR + Grrrr == GrrrrrrrR | (ky2, dy2)
rrrR + Grrrrr == GrrrrrrrrR | (ky2, dy2)
rrrrR + Gr == GrrrrrR | (ky2, dy2)
rrrrR + Grr == GrrrrrrR | (ky2, dy2)
rrrrR + Grrr == GrrrrrrrR | (ky2, dy2)
rrrrR + Grrrr == GrrrrrrrrR | (ky2, dy2)
rrrrR + Grrrrr == GrrrrrrrrrR | (ky2, dy2)
GR + R == GRR | (ky3, dy3)
GR + rR == GrRR | (ky3, dy3)
GR + rrR == GrrRR | (ky3, dy3)
GR + rrrR == GrrrRR | (ky3, dy3)
GR + rrrrR == GrrrrRR | (ky3, dy3)
GrR + R == GrRR | (ky3, dy3)
GrR + rR == GrrRR | (ky3, dy3)
GrR + rrR == GrrrRR | (ky3, dy3)
GrR + rrrR == GrrrrRR | (ky3, dy3)
GrR + rrrrR == GrrrrrRR | (ky3, dy3)
GrrR + R == GrrRR | (ky3, dy3)
GrrR + rR == GrrrRR | (ky3, dy3)
GrrR + rrR == GrrrrRR | (ky3, dy3)
GrrR + rrrR == GrrrrrRR | (ky3, dy3)
GrrR + rrrrR == GrrrrrrRR | (ky3, dy3)
GrrrR + R == GrrrRR | (ky3, dy3)
GrrrR + rR == GrrrrRR | (ky3, dy3)
GrrrR + rrR == GrrrrrRR | (ky3, dy3)
GrrrR + rrrR == GrrrrrrRR | (ky3, dy3)
GrrrR + rrrrR == GrrrrrrrRR | (ky3, dy3)
GrrrrR + R == GrrrrRR | (ky3, dy3)
GrrrrR + rR == GrrrrrRR | (ky3, dy3)
GrrrrR + rrR == GrrrrrrRR | (ky3, dy3)
GrrrrR + rrrR == GrrrrrrrRR | (ky3, dy3)
GrrrrR + rrrrR == GrrrrrrrrRR | (ky3, dy3)
Grr == GrR | (ka1*L, da1)
Grrr == GrrR | (ka1*L, da1)
Grrrr == GrrrR | (ka1*L, da1)
Grrrrr == GrrrrR | (ka1*L, da1)
Grrrrrr == GrrrrrR | (ka1*L, da1)
Grrrrrrr == GrrrrrrR | (ka1*L, da1)
Grrrrrrrr == GrrrrrrrR | (ka1*L, da1)
Grrrrrrrrr == GrrrrrrrrR | (ka1*L, da1)
Grrrrrrrrrr == GrrrrrrrrrR | (ka1*L, da1)
GrR == GRR | (ka2*L, da2)
GrrR == GrRR | (ka2*L, da2)
GrrrR == GrrRR | (ka2*L, da2)
GrrrrR == GrrrRR | (ka2*L, da2)
GrrrrrR == GrrrrRR | (ka2*L, da2)
GrrrrrrR == GrrrrrRR | (ka2*L, da2)
GrrrrrrrR == GrrrrrrRR | (ka2*L, da2)
GrrrrrrrrR == GrrrrrrrRR | (ka2*L, da2)
GrrrrrrrrrR == GrrrrrrrrRR | (ka2*L, da2)
m = get_model()
show(m)
In [26]:
obs0 = numpy.zeros(shape=(len(mols)))
obs0[0] = par.get_r0()
run_N5(m, mols, obs0)
