def kuramotos_f(): for i in range(n): coupling_sum = sum( sin(y(j)-y(i)) for j in range(n) if A[j,i] ) yield omega[i] + c/(n-1)*coupling_sum
def f(): for i in range(N): coupling_sum = sum( y(3*j)-y(3*i) for j in range(N) if A[i,j] ) coupling_term = k * symengine.sin(t) * coupling_sum yield -ω[i] * y(3*i+1) - y(3*i+2) + coupling_term yield ω[i] * y(3*i) + a*y(3*i+1) coupling_term_2 = k * (sum_z-N*y(3*i+2)) yield b + y(3*i+2) * (y(3*i) - c) + coupling_term_2
def f():
for i in range(N):
coupling_sum = sum(
y(3 * j) - y(3 * i) for j in range(N) if A[i, j])
coupling_term = k * symengine.sin(t) * coupling_sum
yield -ω[i] * y(3 * i + 1) - y(3 * i + 2) + coupling_term
yield ω[i] * y(3 * i) + a * y(3 * i + 1)
coupling_term_2 = k * (sum_z - N * y(3 * i + 2))
yield b + y(3 * i + 2) * (y(3 * i) - c) + coupling_term_2
def getData(train_data_ratio, trans_ratio):
'''
Integrates the rossler system, records the data into
train_data, test_data based on train_data_ratio (train_data_length/total length of data)
trans_ratio = (transience length/ total length of data)
Returns: (train_data, test_data)
'''
# Lorenz equation for motion
f = [
10 * (y(1) - y(0)),
y(0) * (28 - y(2)) - y(1),
y(0) * y(1) - (8.0 / 3) * y(2)
]
inital_state = 2.0 * (1 - 2 * np.random.random(3))
ODE = jitcode(f)
ODE.set_integrator("dopri5")
ODE.set_initial_value(inital_state, 0.0)
data = []
times = np.arange(1000, 10000, 0.1)
for time in times:
data.append(ODE.integrate(time))
data_arr = np.array(data)
train_len = int(train_data_ratio * len(data_arr))
trans_len = int(trans_ratio * len(data_arr))
train_data = data_arr[0:train_len, :]
test_data = data_arr[train_len + 1:, :]
return train_data, test_data, trans_len
def tearDown(self):
if isinstance(self.ODE, jitcode) and self.ODE.f_sym():
self.ODE.check()
self.assertIsNotNone(self.ODE.f)
assert_allclose(self.ODE.f(0.0, y0), f_of_y0, rtol=1e-5)
if not self.ODE.jac is None:
assert_allclose(self.ODE.jac(0.0, y0), jac_of_y0, rtol=1e-5)
assert_allclose(self.ODE.integrate(1.0), y1, rtol=1e-4)
for i in reversed(range(n)):
assert_allclose(self.ODE.y_dict[y(i)], y1[i], rtol=1e-4)
def __init__(self, n, para):
# Put all the internal variables and instance specific constants here
# Examples of varibales include Vm, gating variables, calcium ...etc
# Constants can be variouse conductances, which can vary across
# instances.
i = n2i(n) #integration variable index
self.mem_pot = y(i) # the jitcode y
# self.m = y(i+1)
# ... and stuff like that
self.int_freq = para[0]
self.dim = NUM_DIM_NEURON # can vary across different types of neuron
def set_integration_index(self, i):
self.ii = i
self.V = y(i)
self.n = y(i + 1)
self.s = y(i + 2)
self.v = y(i + 3)
self.q = y(i + 4)
self.Ca = y(i + 5)
def set_integration_index(self, i):
self.ii = i
self.V = y(i)
self.m = y(i + 1)
self.h = y(i + 2)
self.n = y(i + 3)
self.z = y(i + 4)
self.u = y(i + 5)
def set_integration_index(self, i):
"""
Args:
i: integration variable index
"""
self.ii = i # integration index
self.v_mem = y(i) # membrane potential
self.m_gate = y(i + 1)
self.n_gate = y(i + 2)
self.h_gate = y(i + 3)
self.a_gate = y(i + 4)
self.b_gate = y(i + 5)
self.calcium = y(i + 6)
def dydt(self, pre_synapses,
pre_neurons): # a list of pre-synaptic neurons
# define how neurons are coupled here
VV = self.V
mm = self.m
hh = self.h
nn = self.n
i_inj = self.i_inj
i_syn = sum(
self.I_syn(VV, y(synapse.get_ind()),
synapse.get_params()[0],
synapse.get_params()[1], synapse.weight)
for (i, synapse) in enumerate(pre_synapses))
i_base = (self.I_Na(VV, mm, hh) + self.I_K(VV, nn) + self.I_L(VV) +
i_syn)
yield -1 / self.C_m * (i_inj + i_base)
yield self.dm_dt(VV, mm)
yield self.dh_dt(VV, hh)
yield self.dn_dt(VV, nn)
from jitcode import jitcode, y
import pdb
substances = Ca, Na, Ko = [y(i) for i in range(3)]
diffusion_rate = {Ca: 0.3, Na: 0.4, Ko: 0.5}
def diffusion_loss(substance):
return -diffusion_rate[substance] * substance
pdb.set_trace()
f = {substance: diffusion_loss(substance) for substance in substances}
ODE = jitcode(f)
def Paci2018(tDrugApplication, INaFRedMed, ICaLRedMed, IKrRedMed, IKsRedMed):
dY = [None] * 23
VmaxUp = 0.5113 # millimolar_per_second (in calcium_dynamics)
g_irel_max = 62.5434 # millimolar_per_second (in calcium_dynamics)
RyRa1 = 0.05354 # uM
RyRa2 = 0.0488 # uM
RyRahalf = 0.02427 # uM
RyRohalf = 0.01042 # uM
RyRchalf = 0.00144 # uM
kNaCa = 3917.0463 # A_per_F (in i_NaCa)
PNaK = 2.6351 # A_per_F (in i_NaK)
Kup = 3.1928e-4 # millimolar (in calcium_dynamics)
V_leak = 4.7279e-4 # per_second (in calcium_dynamics)
alpha = 2.5371 # dimensionless (in i_NaCa)
## Constants
F = 96485.3415 # coulomb_per_mole (in model_parameters)
R = 8.314472 # joule_per_mole_kelvin (in model_parameters)
T = 310.0 # kelvin (in model_parameters)
## Cell geometry
V_SR = 583.73 # micrometre_cube (in model_parameters)
Vc = 8800.0 # micrometre_cube (in model_parameters)
Cm = 9.87109e-11 # farad (in model_parameters)
## Extracellular concentrations
Nao = 151.0 # millimolar (in model_parameters)
Ko = 5.4 # millimolar (in model_parameters)
Cao = 1.8 #3#5#1.8 # millimolar (in model_parameters)
## Intracellular concentrations
# Naio = 10 mM y(17)
Ki = 150.0 # millimolar (in model_parameters)
# Cai = 0.0002 mM y(2)
# caSR = 0.3 mM y(1)
# time (second)
## Nernst potential
E_Na = R * T / F * symengine.log(Nao / y(17))
E_Ca = 0.5 * R * T / F * symengine.log(Cao / y(2))
E_K = R * T / F * log(Ko / Ki)
PkNa = 0.03 # dimensionless (in electric_potentials)
E_Ks = R * T / F * symengine.log((Ko + PkNa * Nao) / (Ki + PkNa * y(17)))
## INa
g_Na = 3671.2302 # S_per_F (in i_Na)
drug_no_drug_na = [
g_Na * y(13)**3.0 * y(11) * y(12) * (y(0) - E_Na),
INaFRedMed * g_Na * y(13)**3.0 * y(11) * y(12) * (y(0) - E_Na)
]
i_Na = drug_no_drug_na[0]
h_inf = 1.0 / symengine.sqrt(1.0 +
symengine.exp((y(0) * 1000.0 + 72.1) / 5.7))
alpha_h = 0.057 * symengine.exp(-(y(0) * 1000.0 + 80.0) / 6.8)
beta_h = 2.7 * symengine.exp(
0.079 * y(0) * 1000.0) + 3.1 * 10.0**5.0 * symengine.exp(
0.3485 * y(0) * 1000.0)
tau_h = sigmoid_generator(y(0), -0.0385, -1) * (1.5 / (
(alpha_h + beta_h) * 1000.0)) + sigmoid_generator(
y(0), -0.0385, 1) * (1.5 * 1.6947 / 1000.0)
dY[11] = (h_inf - y(11)) / tau_h
j_inf = 1.0 / symengine.sqrt(1.0 +
symengine.exp((y(0) * 1000.0 + 72.1) / 5.7))
alpha_j = sigmoid_generator(y(0), -0.04, -1) * (
-25428.0 * symengine.exp(0.2444 * y(0) * 1000.0) - 6.948 * 10.0**-6.0 *
symengine.exp(-0.04391 * y(0) * 1000.0)) * (y(0) * 1000.0 + 37.78) / (
1.0 + symengine.exp(0.311 *
(y(0) * 1000.0 + 79.23))) + sigmoid_generator(
y(0), -0.04, 1) * 0
beta_j = sigmoid_generator(y(0), -0.04, -1) * (
(0.02424 * symengine.exp(-0.01052 * y(0) * 1000) /
(1 + symengine.exp(-0.1378 *
(y(0) * 1000 + 40.14))))) + sigmoid_generator(
y(0), -0.04, 1) * (
(0.6 * symengine.exp(
(0.057) * y(0) * 1000) /
(1 + symengine.exp(-0.1 *
(y(0) * 1000 + 32)))))
tau_j = 7.0 / ((alpha_j + beta_j) * 1000.0)
dY[12] = (j_inf - y(12)) / tau_j
m_inf = 1.0 / (1.0 + symengine.exp(
(-y(0) * 1000.0 - 34.1) / 5.9))**(1.0 / 3.0)
alpha_m = 1.0 / (1.0 + symengine.exp((-y(0) * 1000.0 - 60.0) / 5.0))
beta_m = 0.1 / (1.0 + symengine.exp(
(y(0) * 1000.0 + 35.0) / 5.0)) + 0.1 / (1.0 + symengine.exp(
(y(0) * 1000.0 - 50.0) / 200.0))
tau_m = 1.0 * alpha_m * beta_m / 1000.0
dY[13] = (m_inf - y(13)) / tau_m
## INaL
myCoefTauM = 1
tauINaL = 200 #ms
GNaLmax = 2.3 * 7.5 #(S/F)
Vh_hLate = 87.61
i_NaL = GNaLmax * y(18)**(3) * y(19) * (y(0) - E_Na)
m_inf_L = 1 / (1 + symengine.exp(-(y(0) * 1000 + 42.85) / (5.264)))
alpha_m_L = 1 / (1 + symengine.exp((-60 - y(0) * 1000) / 5))
beta_m_L = 0.1 / (1 + symengine.exp(
(y(0) * 1000 + 35) / 5)) + 0.1 / (1 + symengine.exp(
(y(0) * 1000 - 50) / 200))
tau_m_L = 1 / 1000 * myCoefTauM * alpha_m_L * beta_m_L
dY[18] = (m_inf_L - y(18)) / tau_m_L
h_inf_L = 1 / (1 + symengine.exp((y(0) * 1000 + Vh_hLate) / (7.488)))
tau_h_L = 1 / 1000 * tauINaL
dY[19] = (h_inf_L - y(19)) / tau_h_L
## If
E_f = -0.017 # volt (in i_f)
g_f = 30.10312 # S_per_F (in i_f)
i_f = g_f * y(14) * (y(0) - E_f)
i_fNa = 0.42 * g_f * y(14) * (y(0) - E_Na)
Xf_infinity = 1.0 / (1.0 + symengine.exp((y(0) * 1000.0 + 77.85) / 5.0))
tau_Xf = 1900.0 / (1.0 + symengine.exp(
(y(0) * 1000.0 + 15.0) / 10.0)) / 1000.0
dY[14] = (Xf_infinity - y(14)) / tau_Xf
## ICaL
g_CaL = 8.635702e-5 # metre_cube_per_F_per_s (in i_CaL)
drug_no_drug_CaL = [
g_CaL * 4.0 * y(0) * F**2.0 / (R * T) *
(y(2) * symengine.exp(2.0 * y(0) * F / (R * T)) - 0.341 * Cao) /
(symengine.exp(2.0 * y(0) * F / (R * T)) - 1.0) * y(4) * y(5) * y(6) *
y(7), ICaLRedMed * g_CaL * 4.0 * y(0) * F**2.0 / (R * T) *
(y(2) * symengine.exp(2.0 * y(0) * F / (R * T)) - 0.341 * Cao) /
(symengine.exp(2.0 * y(0) * F /
(R * T)) - 1.0) * y(4) * y(5) * y(6) * y(7)
]
i_CaL = drug_no_drug_CaL[0]
d_infinity = 1.0 / (1.0 + symengine.exp(-(y(0) * 1000.0 + 9.1) / 7.0))
alpha_d = 0.25 + 1.4 / (1.0 + symengine.exp(
(-y(0) * 1000.0 - 35.0) / 13.0))
beta_d = 1.4 / (1.0 + symengine.exp((y(0) * 1000.0 + 5.0) / 5.0))
gamma_d = 1.0 / (1.0 + symengine.exp((-y(0) * 1000.0 + 50.0) / 20.0))
tau_d = (alpha_d * beta_d + gamma_d) * 1.0 / 1000.0
dY[4] = (d_infinity - y(4)) / tau_d
f1_inf = 1.0 / (1.0 + symengine.exp((y(0) * 1000.0 + 26.0) / 3.0))
constf1 = sigmoid_generator(f1_inf - y(5), 0, 1) * 1.0 + 1433.0 * (
y(2) - 50.0 * 1.0e-6) + sigmoid_generator(f1_inf - y(5), 0, -1) * 1.0
tau_f1 = (20.0 + 1102.5 * symengine.exp(-(
(y(0) * 1000.0 + 27.0)**2.0 / 15.0)**2.0) + 200.0 /
(1.0 + symengine.exp((13.0 - y(0) * 1000.0) / 10.0)) + 180.0 /
(1.0 + symengine.exp(
(30.0 + y(0) * 1000.0) / 10.0))) * constf1 / 1000.0
dY[5] = (f1_inf - y(5)) / tau_f1
f2_inf = 0.33 + 0.67 / (1.0 + symengine.exp((y(0) * 1000.0 + 32.0) / 4.0))
constf2 = 1.0
tau_f2 = (600.0 * symengine.exp(-(y(0) * 1000.0 + 25.0)**2.0 / 170.0) +
31.0 / (1.0 + symengine.exp(
(25.0 - y(0) * 1000.0) / 10.0)) + 16.0 /
(1.0 + symengine.exp(
(30.0 + y(0) * 1000.0) / 10.0))) * constf2 / 1000.0
dY[6] = (f2_inf - y(6)) / tau_f2
alpha_fCa = 1.0 / (1.0 + (y(2) / 0.0006)**8.0)
beta_fCa = 0.1 / (1.0 + symengine.exp((y(2) - 0.0009) / 0.0001))
gamma_fCa = 0.3 / (1.0 + symengine.exp((y(2) - 0.00075) / 0.0008))
fCa_inf = (alpha_fCa + beta_fCa + gamma_fCa) / 1.3156
constfCa = sigmoid_generator(y(0), -0.06, 1) * sigmoid_generator(
fCa_inf, y(7), 1) * 0 + (sigmoid_generator(y(0), -0.06, -1) +
sigmoid_generator(fCa_inf, y(7), -1)) * 1.0
tau_fCa = 0.002 # second (in i_CaL_fCa_gate)
dY[7] = constfCa * (fCa_inf - y(7)) / tau_fCa
## Ito
g_to = 29.9038 # S_per_F (in i_to)
i_to = g_to * (y(0) - E_K) * y(15) * y(16)
q_inf = 1.0 / (1.0 + symengine.exp((y(0) * 1000.0 + 53.0) / 13.0))
tau_q = (6.06 + 39.102 /
(0.57 * symengine.exp(-0.08 * (y(0) * 1000.0 + 44.0)) +
0.065 * symengine.exp(0.1 * (y(0) * 1000.0 + 45.93)))) / 1000.0
dY[15] = (q_inf - y(15)) / tau_q
r_inf = 1.0 / (1.0 + symengine.exp(-(y(0) * 1000.0 - 22.3) / 18.75))
tau_r = (2.75352 + 14.40516 /
(1.037 * symengine.exp(0.09 * (y(0) * 1000.0 + 30.61)) +
0.369 * symengine.exp(-0.12 * (y(0) * 1000.0 + 23.84)))) / 1000.0
dY[16] = (r_inf - y(16)) / tau_r
## IKs
g_Ks = 2.041 # S_per_F (in i_Ks)
drug_no_drug_Ks = [
g_Ks * (y(0) - E_Ks) * y(10)**2.0 *
(1.0 + 0.6 / (1.0 + (3.8 * 0.00001 / y(2))**1.4)),
IKsRedMed * g_Ks * (y(0) - E_Ks) * y(10)**2.0 *
(1.0 + 0.6 / (1.0 + (3.8 * 0.00001 / y(2))**1.4))
]
i_Ks = drug_no_drug_Ks[0]
Xs_infinity = 1.0 / (1.0 + symengine.exp((-y(0) * 1000.0 - 20.0) / 16.0))
alpha_Xs = 1100.0 / symengine.sqrt(1.0 + symengine.exp(
(-10.0 - y(0) * 1000.0) / 6.0))
beta_Xs = 1.0 / (1.0 + symengine.exp((-60.0 + y(0) * 1000.0) / 20.0))
tau_Xs = 1.0 * alpha_Xs * beta_Xs / 1000.0
dY[10] = (Xs_infinity - y(10)) / tau_Xs
## IKr
L0 = 0.025 # dimensionless (in i_Kr_Xr1_gate)
Q = 2.3 # dimensionless (in i_Kr_Xr1_gate)
g_Kr = 29.8667 # S_per_F (in i_Kr)
drug_no_drug_Kr = [
g_Kr * (y(0) - E_K) * y(8) * y(9) * sqrt(Ko / 5.4),
IKrRedMed * g_Kr * (y(0) - E_K) * y(8) * y(9) * sqrt(Ko / 5.4)
]
i_Kr = drug_no_drug_Kr[0]
V_half = 1000.0 * (-R * T / (F * Q) * log(
(1.0 + Cao / 2.6)**4.0 / (L0 * (1.0 + Cao / 0.58)**4.0)) - 0.019)
Xr1_inf = 1.0 / (1.0 + symengine.exp((V_half - y(0) * 1000.0) / 4.9))
alpha_Xr1 = 450.0 / (1.0 + symengine.exp((-45.0 - y(0) * 1000.0) / 10.0))
beta_Xr1 = 6.0 / (1.0 + symengine.exp((30.0 + y(0) * 1000.0) / 11.5))
tau_Xr1 = 1.0 * alpha_Xr1 * beta_Xr1 / 1000.0
dY[8] = (Xr1_inf - y(8)) / tau_Xr1
Xr2_infinity = 1.0 / (1.0 + symengine.exp((y(0) * 1000.0 + 88.0) / 50.0))
alpha_Xr2 = 3.0 / (1.0 + symengine.exp((-60.0 - y(0) * 1000.0) / 20.0))
beta_Xr2 = 1.12 / (1.0 + symengine.exp((-60.0 + y(0) * 1000.0) / 20.0))
tau_Xr2 = 1.0 * alpha_Xr2 * beta_Xr2 / 1000.0
dY[9] = (Xr2_infinity - y(9)) / tau_Xr2
## IK1
alpha_K1 = 3.91 / (1.0 +
symengine.exp(0.5942 *
(y(0) * 1000.0 - E_K * 1000.0 - 200.0)))
beta_K1 = (-1.509 * symengine.exp(0.0002 *
(y(0) * 1000.0 - E_K * 1000.0 + 100.0)) +
symengine.exp(0.5886 * (y(0) * 1000.0 - E_K * 1000.0 - 10.0))
) / (1.0 + symengine.exp(0.4547 *
(y(0) * 1000.0 - E_K * 1000.0)))
XK1_inf = alpha_K1 / (alpha_K1 + beta_K1)
g_K1 = 28.1492 # S_per_F (in i_K1)
i_K1 = g_K1 * XK1_inf * (y(0) - E_K) * sqrt(Ko / 5.4)
## INaCa
KmCa = 1.38 # millimolar (in i_NaCa)
KmNai = 87.5 # millimolar (in i_NaCa)
Ksat = 0.1 # dimensionless (in i_NaCa)
gamma = 0.35 # dimensionless (in i_NaCa)
kNaCa1 = kNaCa # A_per_F (in i_NaCa)
i_NaCa = kNaCa1 * (symengine.exp(gamma * y(0) * F /
(R * T)) * y(17)**3.0 * Cao -
symengine.exp(
(gamma - 1.0) * y(0) * F /
(R * T)) * Nao**3.0 * y(2) * alpha) / (
(KmNai**3.0 + Nao**3.0) * (KmCa + Cao) *
(1.0 + Ksat * symengine.exp(
(gamma - 1.0) * y(0) * F / (R * T))))
## INaK
Km_K = 1.0 # millimolar (in i_NaK)
Km_Na = 40.0 # millimolar (in i_NaK)
PNaK1 = PNaK # A_per_F (in i_NaK)
i_NaK = PNaK1 * Ko / (Ko + Km_K) * y(17) / (y(17) + Km_Na) / (
1.0 + 0.1245 * symengine.exp(-0.1 * y(0) * F / (R * T)) +
0.0353 * symengine.exp(-y(0) * F / (R * T)))
## IpCa
KPCa = 0.0005 # millimolar (in i_PCa)
g_PCa = 0.4125 # A_per_F (in i_PCa)
i_PCa = g_PCa * y(2) / (y(2) + KPCa)
## Background currents
g_b_Na = 0.95 # S_per_F (in i_b_Na)
i_b_Na = g_b_Na * (y(0) - E_Na)
g_b_Ca = 0.727272 # S_per_F (in i_b_Ca)
i_b_Ca = g_b_Ca * (y(0) - E_Ca)
## Sarcoplasmic reticulum
i_up = VmaxUp / (1.0 + Kup**2.0 / y(2)**2.0)
i_leak = (y(1) - y(2)) * V_leak
dY[3] = 0
# RyR
RyRSRCass = (1 - 1 / (1 + symengine.exp((y(1) - 0.3) / 0.1)))
i_rel = g_irel_max * RyRSRCass * y(21) * y(22) * (y(1) - y(2))
RyRainfss = RyRa1 - RyRa2 / (1 + symengine.exp(
(1000 * y(2) - (RyRahalf)) / 0.0082))
RyRtauadapt = 1 #s
dY[20] = (RyRainfss - y(20)) / RyRtauadapt
RyRoinfss = (1 - 1 / (1 + symengine.exp(
(1000 * y(2) - (y(20) + RyRohalf)) / 0.003)))
RyRtauact = sigmoid_generator(
RyRoinfss, y(21), 1) * 18.75e-3 + 0.1 * 18.75e-3 * sigmoid_generator(
RyRoinfss, y(21), -1)
dY[21] = (RyRoinfss - y(21)) / RyRtauact
RyRcinfss = (1 / (1 + symengine.exp(
(1000 * y(2) - (y(20) + RyRchalf)) / 0.001)))
RyRtauinact = sigmoid_generator(RyRcinfss, y(22),
1) * 2 * 87.5e-3 + sigmoid_generator(
RyRcinfss, y(22), -1) * 87.5e-3
dY[22] = (RyRcinfss - y(22)) / RyRtauinact
## Ca2+ buffering
Buf_C = 0.25 # millimolar (in calcium_dynamics)
Buf_SR = 10.0 # millimolar (in calcium_dynamics)
Kbuf_C = 0.001 # millimolar (in calcium_dynamics)
Kbuf_SR = 0.3 # millimolar (in calcium_dynamics)
Cai_bufc = 1.0 / (1.0 + Buf_C * Kbuf_C / (y(2) + Kbuf_C)**2.0)
Ca_SR_bufSR = 1.0 / (1.0 + Buf_SR * Kbuf_SR / (y(1) + Kbuf_SR)**2.0)
## Ionic concentrations
#Nai
dY[17] = -Cm * (i_Na + i_NaL + i_b_Na + 3.0 * i_NaK + 3.0 * i_NaCa +
i_fNa) / (F * Vc * 1.0e-18)
#caSR
dY[2] = Cai_bufc * (i_leak - i_up + i_rel -
(i_CaL + i_b_Ca + i_PCa - 2.0 * i_NaCa) * Cm /
(2.0 * Vc * F * 1.0e-18))
#Cai
dY[1] = Ca_SR_bufSR * Vc / V_SR * (i_up - (i_rel + i_leak))
## Stimulation
i_stim_Amplitude = 7.5e-10 # ampere (in stim_mode)
i_stim_End = 1000.0 # second (in stim_mode)
i_stim_PulseDuration = 0.005 # second (in stim_mode)
i_stim_Start = 0.0 # second (in stim_mode)
i_stim_frequency = 60.0 # per_second (in stim_mode)
stim_flag = 0.0 # dimensionless (in stim_mode)
i_stim_Period = 60.0 / i_stim_frequency
i_stim = 0 #(sigmoid_generator(time, i_stim_Start, 1) * sigmoid_generator(time, i_stim_End, -1) * (sigmoid_generator(time-i_stim_Start-symengine.floor((time-i_stim_Start)/i_stim_Period)*i_stim_Period, i_stim_PulseDuration, -1) ))*stim_flag*i_stim_Amplitude/Cm+0.0
## Membrane potential
dY[0] = -(i_K1 + i_to + i_Kr + i_Ks + i_CaL + i_NaK + i_Na + i_NaL +
i_NaCa + i_PCa + i_f + i_b_Na + i_b_Ca - i_stim)
## Output variables
IK1 = i_K1
Ito = i_to
IKr = i_Kr
IKs = i_Ks
ICaL = i_CaL
INaK = i_NaK
INa = i_Na
INaCa = i_NaCa
IpCa = i_PCa
If = i_f
IbNa = i_b_Na
IbCa = i_b_Ca
Irel = i_rel
Iup = i_up
Ileak = i_leak
Istim = i_stim
INaL = i_NaL
dati = [
INa, If, ICaL, Ito, IKs, IKr, IK1, INaCa, INaK, IpCa, IbNa, IbCa, Irel,
Iup, Ileak, Istim, E_K, E_Na, INaL
]
return dY
# 1 - evaluate function at Y...
# 2 - loop over Y, perturb each element by a small percent of its total
# 3 - during each loop, find dY/dt, given the perturbation
# 4 - find the change in Y as a function of the change in the perturbation
# Conditionals
# tau_h = 1.5*1.6947/1000.0
# alpha_j = 0.0
# beta_j = ((0.6*exp((0.057)*Y[0]*1000)/(1+exp(-0.1*(Y[0]*1000+32)))))
# constf1 = 1.0
# constfCa = 1.0
# RyRtauact = 0.1*18.75e-3 #s
# RyRtauinact = 87.5e-3 #s
# i_stim = 0.0
'''
def set_integration_index(self, i):
self.ii = i
self.r = y(i)
self.s = y(i + 1)
self.G = y(i + 2)
def set_integration_index(self, i):
self.ii = i # integration index
#self.syn_weight = y(i)
self.reduced_weight = y(i)
self.rho_gate = y(i + 1)
self.ca = y(i + 2) ###
def test_check_index_negative(self):
ODE = jitcode([y(-1)])
with self.assertRaises(ValueError):
ODE.check()
current_time = time state = I.y yield state result = np.vstack(solutions()) # Using compiled functions to make things faster def get_compiled_function(f): dummy = jitcode(f,verbose=False) dummy.compile_C() return dummy.f # The actual scenarios test_scenario( name = "two coupled FitzHugh–Nagumo oscillators", fun = get_compiled_function([ y(0)*(-0.025794-y(0))*(y(0)-1.0)-y(1)+0.128*(y(2)-y(0)), 0.0065*y(0)-0.02*y(1), y(2)*(-0.025794-y(2))*(y(2)-1.0)-y(3)+0.128*(y(0)-y(2)), 0.0135*y(2)-0.02*y(3) ]), initial = np.array([1.,2.,3.,4.]), times = 2000+np.arange(0,100000,10), rtol = 1e-5, atol = 1e-8, ) n, c, q = 100, 3.0, 0.2 A = choice( [1,0], size=(n,n), p=[q,1-q] ) omega = uniform(-0.5,0.5,n) def kuramotos_f():
result = np.vstack(list(solutions()))
# Using compiled functions to make things faster
def get_compiled_function(f):
dummy = jitcode(f, verbose=False)
dummy.compile_C()
return dummy.f
# The actual scenarios
test_scenario(
name="two coupled FitzHugh–Nagumo oscillators",
fun=get_compiled_function([
y(0) * (-0.025794 - y(0)) * (y(0) - 1.0) - y(1) + 0.128 *
(y(2) - y(0)), 0.0065 * y(0) - 0.02 * y(1),
y(2) * (-0.025794 - y(2)) * (y(2) - 1.0) - y(3) + 0.128 *
(y(0) - y(2)), 0.0135 * y(2) - 0.02 * y(3)
]),
initial=np.array([1., 2., 3., 4.]),
times=2000 + np.arange(0, 100000, 10),
rtol=1e-5,
atol=1e-8,
)
n, c, q = 100, 3.0, 0.2
A = choice([1, 0], size=(n, n), p=[q, 1 - q])
omega = uniform(-0.5, 0.5, n)
0.0195744683782066,
-0.0057801623466600,
])
lyaps = [0.00710, 0, -0.0513, -0.187]
# vanilla
a = -0.025794
b1 = 0.0065
b2 = 0.0135
c = 0.02
k = 0.128
f = [
y(0) * (a - y(0)) * (y(0) - 1.0) - y(1) + k * (y(2) - y(0)),
b1 * y(0) - c * y(1),
y(2) * (a - y(2)) * (y(2) - 1.0) - y(3) + k * (y(0) - y(2)),
b2 * y(2) - c * y(3)
]
vanilla = {"f_sym": f}
# as dictionary
f_dict = {y(i): entry for i, entry in reversed(list(enumerate(f)))}
with_dictionary = {"f_sym": f_dict}
# with generator
def f_generator():
Note that the initial state (line 17) is reduced in dimensionality and there is only one component for each synchronisation group.
"""
if __name__ == "__main__":
# example-start
from jitcode import jitcode_transversal_lyap, y
from scipy.stats import sem
import numpy as np
a = -0.025794
b = 0.01
c = 0.02
k = 0.128
f = [
y(0) * ( a-y(0) ) * ( y(0)-1.0 ) - y(1) + k * (y(2) - y(0)),
b*y(0) - c*y(1),
y(2) * ( a-y(2) ) * ( y(2)-1.0 ) - y(3) + k * (y(0) - y(2)),
b*y(2) - c*y(3)
]
initial_state = np.array([1.,2.])
groups = [ [0,2], [1,3] ]
ODE = jitcode_transversal_lyap(f, groups=groups)
ODE.set_integrator("lsoda")
ODE.set_initial_value(initial_state,0.0)
times = range(10,100000,10)
lyaps = []
for time in times:
:start-after: example-st\u0061rt
:dedent: 1
:linenos:
"""
if __name__ == "__main__":
# example-start
from jitcode import y, jitcode
import numpy as np
γ = 0.6
φ = 1.0
ω = 0.5
ν = 0.5
R,B = [ y(i) for i in range(2) ]
lotka_volterra_diff = {
B: γ*B - φ*R*B,
R: -ω*R + ν*R*B,
}
ODE = jitcode(lotka_volterra_diff)
ODE.set_integrator("dopri5")
initial_state = np.array(np.random.random(2))
ODE.set_initial_value(initial_state,0.0)
times = np.arange(0.0,100,0.1)
data = []
for time in times:
state = ODE.integrate(time)
0.0195744683782066,
-0.0057801623466600,
])
lyaps = [0.00710, 0, -0.0513, -0.187]
# vanilla
a = -0.025794
b1 = 0.0065
b2 = 0.0135
c = 0.02
k = 0.128
f = [
y(0) * ( a-y(0) ) * ( y(0)-1.0 ) - y(1) + k * (y(2) - y(0)),
b1*y(0) - c*y(1),
y(2) * ( a-y(2) ) * ( y(2)-1.0 ) - y(3) + k * (y(0) - y(2)),
b2*y(2) - c*y(3)
]
vanilla = {"f_sym": f}
# as dictionary
f_dict = { y(i):entry for i,entry in reversed(list(enumerate(f))) }
with_dictionary = {"f_sym": f_dict}
# with generator
def f_generator():
for entry in f:
from itertools import combinations
from jitcode import jitcode_restricted_lyap, y, jitcode_transversal_lyap
import numpy as np
from scipy.stats import sem
from symengine import Symbol
a = -0.025794
b = 0.01
c = 0.02
k = Symbol("k")
scenarios = [
{
"f": [
y(0) * (a - y(0)) * (y(0) - 1.0) - y(3) + k * (y(1) - y(0)),
y(1) * (a - y(1)) * (y(1) - 1.0) - y(4) + k * (y(2) - y(1)),
y(2) * (a - y(2)) * (y(2) - 1.0) - y(5) + k * (y(0) - y(2)),
b * y(0) - c * y(3),
b * y(1) - c * y(4),
b * y(2) - c * y(5),
],
"vectors": [[1., 1., 1., 0., 0., 0.], [0., 0., 0., 1., 1., 1.]],
"groups": ([0, 1, 2], [3, 4, 5])
},
{
"f": [
y(0) * (a - y(0)) * (y(0) - 1.0) - y(1) + k * (y(2) - y(0)),
b * y(0) - c * y(1),
y(2) * (a - y(2)) * (y(2) - 1.0) - y(3) + k * (y(4) - y(2)),
b * y(2) - c * y(3),
def set_integration_index(self, i):
self.ii = i
self.r = y(i)
def set_integration_index(self, i):
self.ii = i # integration index
self.syn_weight = y(i)
self.rho_gate = y(i + 1)
from itertools import combinations
from jitcode import jitcode_restricted_lyap, y, jitcode_transversal_lyap
import numpy as np
from scipy.stats import sem
from symengine import Symbol
a = -0.025794
b = 0.01
c = 0.02
k = Symbol("k")
scenarios = [
{
"f":
[
y(0)*(a-y(0))*(y(0)-1.0) - y(3) + k*(y(1)-y(0)),
y(1)*(a-y(1))*(y(1)-1.0) - y(4) + k*(y(2)-y(1)),
y(2)*(a-y(2))*(y(2)-1.0) - y(5) + k*(y(0)-y(2)),
b*y(0) - c*y(3),
b*y(1) - c*y(4),
b*y(2) - c*y(5),
],
"vectors":
[
[1.,1.,1.,0.,0.,0.],
[0.,0.,0.,1.,1.,1.]
],
"groups":
( [0,1,2], [3,4,5] )
},
{
def test_check_index_negative(self): ODE = jitcode([y(-1)]) with self.assertRaises(ValueError): ODE.check()
def kuramotos_f():
for i in range(n):
coupling_sum = sum(
sin(y(j) - y(i)) for j in range(n) if networkMatrix[j, i])
yield omegas[i] + couplingConstant * coupling_sum
def test_check_index_too_high(self): ODE = jitcode([y(1)]) with self.assertRaises(ValueError): ODE.check()
def kuramotos_f():
for i in range(n):
coupling_sum = sum(sin(y(j) - y(i)) for j in range(n) if A[j, i])
yield omega[i] + c / (n - 1) * coupling_sum
b = 0.2
c = 10.0
k = 0.01
# get adjacency matrix of a small-world network
A = small_world_network(
number_of_nodes = N,
nearest_neighbours = 20,
rewiring_probability = 0.1
)
# generate differential equations
# -------------------------------
sum_z = symengine.Symbol("sum_z")
helpers = [( sum_z, sum( y(3*j+2) for j in range(N) ) )]
def f():
for i in range(N):
coupling_sum = sum( y(3*j)-y(3*i) for j in range(N) if A[i,j] )
coupling_term = k * symengine.sin(t) * coupling_sum
yield -ω[i] * y(3*i+1) - y(3*i+2) + coupling_term
yield ω[i] * y(3*i) + a*y(3*i+1)
coupling_term_2 = k * (sum_z-N*y(3*i+2))
yield b + y(3*i+2) * (y(3*i) - c) + coupling_term_2
# integrate
# ---------
initial_state = np.random.random(3*N)
ω = np.random.uniform(0.8, 1.0, N)
a = 0.165
b = 0.2
c = 10.0
k = 0.01
# get adjacency matrix of a small-world network
A = small_world_network(number_of_nodes=N,
nearest_neighbours=20,
rewiring_probability=0.1)
# generate differential equations
# -------------------------------
sum_z = symengine.Symbol("sum_z")
helpers = [(sum_z, sum(y(3 * j + 2) for j in range(N)))]
def f():
for i in range(N):
coupling_sum = sum(
y(3 * j) - y(3 * i) for j in range(N) if A[i, j])
coupling_term = k * symengine.sin(t) * coupling_sum
yield -ω[i] * y(3 * i + 1) - y(3 * i + 2) + coupling_term
yield ω[i] * y(3 * i) + a * y(3 * i + 1)
coupling_term_2 = k * (sum_z - N * y(3 * i + 2))
yield b + y(3 * i + 2) * (y(3 * i) - c) + coupling_term_2
# integrate
# ---------
initial_state = np.random.random(3 * N)
def test_initalise_with_dict(self):
self.ODE = jitcode(**vanilla)
initial_value = {y(i): y0[i] for i in range(n)}
self.ODE.set_initial_value(initial_value)
self.ODE.set_integrator("dop853")
self.assertTrue(_is_C(self.ODE.f))
#!/usr/bin/python3
# -*- coding: utf-8 -*-
from jitcode import jitcode_restricted_lyap, y
import numpy as np
from scipy.stats import sem
a = -0.025794
b1 = 0.01
b2 = 0.01
c = 0.02
k = 0.128
f = [
y(0) * (a - y(0)) * (y(0) - 1.0) - y(1) + k * (y(2) - y(0)),
b1 * y(0) - c * y(1),
y(2) * (a - y(2)) * (y(2) - 1.0) - y(3) + k * (y(0) - y(2)),
b2 * y(2) - c * y(3)
]
initial_state = np.random.random(4)
vectors = [np.array([1., 0., 1., 0.]), np.array([0., 1., 0., 1.])]
ODE = jitcode_restricted_lyap(f, vectors=vectors)
ODE.set_integrator("dopri5")
ODE.set_initial_value(initial_state, 0.0)
data = np.hstack(ODE.integrate(T)[1] for T in range(10, 100000, 10))
print(np.average(data[500:]), sem(data[500:]))
:start-after: example-st\u0061rt
:dedent: 1
:linenos:
"""
if __name__ == "__main__":
# example-start
from jitcode import y, jitcode
import numpy as np
γ = 0.6
φ = 1.0
ω = 0.5
ν = 0.5
R, B = dynvars = [y(i) for i in range(2)]
lotka_volterra_diff = {
B: γ * B - φ * R * B,
R: -ω * R + ν * R * B,
}
ODE = jitcode(lotka_volterra_diff)
ODE.set_integrator("dopri5")
initial_state = {R: 0.2, B: 0.5}
ODE.set_initial_value(initial_state, 0.0)
times = np.arange(0.0, 100, 0.1)
values = {R: [], B: []}
for time in times:
ODE.integrate(time)
def test_check_index_too_high(self):
ODE = jitcode([y(1)])
with self.assertRaises(ValueError):
ODE.check()
def Paci2018(tDrugApplication, INaFRedMed,ICaLRedMed, IKrRedMed, IKsRedMed):
dY = [None]*23
'''
Parameters from optimizer
VmaxUp = param(1)
g_irel_max = param(2)
RyRa1 = param(3)
RyRa2 = param(4)
RyRahalf = param(5)
RyRohalf = param(6)
RyRchalf = param(7)
kNaCa = param(8)
PNaK = param(9)
Kup = param(10)
V_leak = param(11)
alpha = param(12)
'''
VmaxUp = 0.5113 # millimolar_per_second (in calcium_dynamics)
g_irel_max = 62.5434 # millimolar_per_second (in calcium_dynamics)
RyRa1 = 0.05354 # uM
RyRa2 = 0.0488 # uM
RyRahalf = 0.02427 # uM
RyRohalf = 0.01042 # uM
RyRchalf = 0.00144 # uM
kNaCa = 3917.0463 # A_per_F (in i_NaCa)
PNaK = 2.6351 # A_per_F (in i_NaK)
Kup = 3.1928e-4 # millimolar (in calcium_dynamics)
V_leak = 4.7279e-4 # per_second (in calcium_dynamics)
alpha = 2.5371 # dimensionless (in i_NaCa)
## Constants
F = 96485.3415 # coulomb_per_mole (in model_parameters)
R = 8.314472 # joule_per_mole_kelvin (in model_parameters)
T = 310 # kelvin (in model_parameters)
## Cell geometry
V_SR = 583.73 # micrometre_cube (in model_parameters)
Vc = 8800 # micrometre_cube (in model_parameters)
Cm = 9.87109e-11 # farad (in model_parameters)
## Extracellular concentrations
Nao = 151 # millimolar (in model_parameters)
Ko = 5.4 # millimolar (in model_parameters)
Cao = 1.8 #3#5#1.8 # millimolar (in model_parameters)
## Intracellular concentrations
# Naio = 10 mM y(17)
Ki = 150 # millimolar (in model_parameters)
# Cai = 0.0002 mM y(2)
# caSR = 0.3 mM y(1)
## Nernst potential
E_Na = R*T/F*log(Nao/y(17))
E_Ca = 0.5*R*T/F*log(Cao/y(2))
E_K = R*T/F*log(Ko/Ki)
PkNa = 0.03 # dimensionless (in electric_potentials)
E_Ks = R*T/F*log((Ko+PkNa*Nao)/(Ki+PkNa*y(17)))
## INa
g_Na = 3671.2302 # S_per_F (in i_Na)
i_Na = g_Na*y(13)**3*y(11)*y(12)*(y(0)-E_Na)
h_inf = 1/sqrt(1+exp((y(0)*1000+72.1)/5.7))
alpha_h = 0.057*exp(-(y(0)*1000+80)/6.8)
beta_h = 2.7*exp(0.079*y(0)*1000)+3.1*10**5*exp(0.3485*y(0)*1000)
tau_h = conditional(y(0),-0.0385,1.5/((alpha_h+beta_h)*1000),1.5*1.6947/1000)
dY[11] = (h_inf-y(11))/tau_h
j_inf = 1/sqrt(1+exp((y(0)*1000+72.1)/5.7))
alpha_j = conditional(y(0),-0.04,(-25428*exp(0.2444*y(0)*1000)-6.948*10**-6*exp(-0.04391*y(0)*1000))*(y(0)*1000+37.78)/(1+exp(0.311*(y(0)*1000+79.23))),0)
beta_j = conditional(
y(0),-0.04,
0.02424*exp(-0.01052*y(0)*1000)/(1+exp(-0.1378*(y(0)*1000+40.14))),
0.6*exp((0.057)*y(0)*1000)/(1+exp(-0.1*(y(0)*1000+32))),
)
tau_j = 7/((alpha_j+beta_j)*1000)
dY[12] = (j_inf-y(12))/tau_j
m_inf = 1/(1+exp((-y(0)*1000-34.1)/5.9))**(1/3)
alpha_m = 1/(1+exp((-y(0)*1000-60)/5))
beta_m = 0.1/(1+exp((y(0)*1000+35)/5))+0.1/(1+exp((y(0)*1000-50)/200))
tau_m = 1*alpha_m*beta_m/1000
dY[13] = (m_inf-y(13))/tau_m
## INaL
myCoefTauM = 1
tauINaL = 200 #ms
GNaLmax = 2.3*7.5 #(S/F)
Vh_hLate = 87.61
i_NaL = GNaLmax* y(18)**(3)*y(19)*(y(0)-E_Na)
m_inf_L = 1/(1+exp(-(y(0)*1000+42.85)/(5.264)))
alpha_m_L = 1/(1+exp((-60-y(0)*1000)/5))
beta_m_L = 0.1/(1+exp((y(0)*1000+35)/5))+0.1/(1+exp((y(0)*1000-50)/200))
tau_m_L = 1/1000 * myCoefTauM*alpha_m_L*beta_m_L
dY[18] = (m_inf_L-y(18))/tau_m_L
h_inf_L = 1/(1+exp((y(0)*1000+Vh_hLate)/(7.488)))
tau_h_L = 1/1000 * tauINaL
dY[19] = (h_inf_L-y(19))/tau_h_L
## If
E_f = -0.017 # volt (in i_f)
g_f = 30.10312 # S_per_F (in i_f)
i_f = g_f*y(14)*(y(0)-E_f)
i_fNa = 0.42*g_f*y(14)*(y(0)-E_Na)
Xf_infinity = 1/(1+exp((y(0)*1000+77.85)/5))
tau_Xf = 1900/(1+exp((y(0)*1000+15)/10))/1000
dY[14] = (Xf_infinity-y(14))/tau_Xf
## ICaL
g_CaL = 8.635702e-5 # metre_cube_per_F_per_s (in i_CaL)
i_CaL = g_CaL*4*y(0)*F**2/(R*T)*(y(2)*exp(2*y(0)*F/(R*T))-0.341*Cao)/(exp(2*y(0)*F/(R*T))-1)*y(4)*y(5)*y(6)*y(7)
d_infinity = 1/(1+exp(-(y(0)*1000+9.1)/7))
alpha_d = 0.25+1.4/(1+exp((-y(0)*1000-35)/13))
beta_d = 1.4/(1+exp((y(0)*1000+5)/5))
gamma_d = 1/(1+exp((-y(0)*1000+50)/20))
tau_d = (alpha_d*beta_d+gamma_d)*1/1000
dY[4] = (d_infinity-y(4))/tau_d
f1_inf = 1/(1+exp((y(0)*1000+26)/3))
constf1 = 1 + 1433*(y(2)-50*1e-6)
tau_f1 = (20+1102.5*exp(-((y(0)*1000+27)**2/15)**2)+200/(1+exp((13-y(0)*1000)/10))+180/(1+exp((30+y(0)*1000)/10)))*constf1/1000
dY[5] = (f1_inf-y(5))/tau_f1
f2_inf = 0.33+0.67/(1+exp((y(0)*1000+32)/4))
constf2 = 1
tau_f2 = (600*exp(-(y(0)*1000+25)**2/170)+31/(1+exp((25-y(0)*1000)/10))+16/(1+exp((30+y(0)*1000)/10)))*constf2/1000
dY[6] = (f2_inf-y(6))/tau_f2
alpha_fCa = 1/(1+(y(2)/0.0006)**8)
beta_fCa = 0.1/(1+exp((y(2)-0.0009)/0.0001))
gamma_fCa = 0.3/(1+exp((y(2)-0.00075)/0.0008))
fCa_inf = (alpha_fCa+beta_fCa+gamma_fCa)/1.3156
constfCa = conditional( y(0), -0.06, 1, conditional(fCa_inf,y(7),1,0) )
tau_fCa = 0.002 # second (in i_CaL_fCa_gate)
dY[7] = constfCa*(fCa_inf-y(7))/tau_fCa
## Ito
g_to = 29.9038 # S_per_F (in i_to)
i_to = g_to*(y(0)-E_K)*y(15)*y(16)
q_inf = 1/(1+exp((y(0)*1000+53)/13))
tau_q = (6.06+39.102/(0.57*exp(-0.08*(y(0)*1000+44))+0.065*exp(0.1*(y(0)*1000+45.93))))/1000
dY[15] = (q_inf-y(15))/tau_q
r_inf = 1/(1+exp(-(y(0)*1000-22.3)/18.75))
tau_r = (2.75352+14.40516/(1.037*exp(0.09*(y(0)*1000+30.61))+0.369*exp(-0.12*(y(0)*1000+23.84))))/1000
dY[16] = (r_inf-y(16))/tau_r
## IKs
g_Ks = 2.041 # S_per_F (in i_Ks)
i_Ks = g_Ks*(y(0)-E_Ks)*y(10)**2*(1+0.6/(1+(3.8*0.00001/y(2))**1.4))
Xs_infinity = 1/(1+exp((-y(0)*1000-20)/16))
alpha_Xs = 1100/sqrt(1+exp((-10-y(0)*1000)/6))
beta_Xs = 1/(1+exp((-60+y(0)*1000)/20))
tau_Xs = 1*alpha_Xs*beta_Xs/1000
dY[10] = (Xs_infinity-y(10))/tau_Xs
## IKr
L0 = 0.025 # dimensionless (in i_Kr_Xr1_gate)
Q = 2.3 # dimensionless (in i_Kr_Xr1_gate)
g_Kr = 29.8667 # S_per_F (in i_Kr)
i_Kr = g_Kr*(y(0)-E_K)*y(8)*y(9)*sqrt(Ko/5.4)
V_half = 1000*(-R*T/(F*Q)*log((1+Cao/2.6)**4/(L0*(1+Cao/0.58)**4))-0.019)
Xr1_inf = 1/(1+exp((V_half-y(0)*1000)/4.9))
alpha_Xr1 = 450/(1+exp((-45-y(0)*1000)/10))
beta_Xr1 = 6/(1+exp((30+y(0)*1000)/11.5))
tau_Xr1 = 1*alpha_Xr1*beta_Xr1/1000
dY[8] = (Xr1_inf-y(8))/tau_Xr1
Xr2_infinity = 1/(1+exp((y(0)*1000+88)/50))
alpha_Xr2 = 3/(1+exp((-60-y(0)*1000)/20))
beta_Xr2 = 1.12/(1+exp((-60+y(0)*1000)/20))
tau_Xr2 = 1*alpha_Xr2*beta_Xr2/1000
dY[9] = (Xr2_infinity-y(9))/tau_Xr2
## IK1
alpha_K1 = 3.91/(1+exp(0.5942*(y(0)*1000-E_K*1000-200)))
beta_K1 = (-1.509*exp(0.0002*(y(0)*1000-E_K*1000+100))+exp(0.5886*(y(0)*1000-E_K*1000-10)))/(1+exp(0.4547*(y(0)*1000-E_K*1000)))
XK1_inf = alpha_K1/(alpha_K1+beta_K1)
g_K1 = 28.1492 # S_per_F (in i_K1)
i_K1 = g_K1*XK1_inf*(y(0)-E_K)*sqrt(Ko/5.4)
## INaCa
KmCa = 1.38 # millimolar (in i_NaCa)
KmNai = 87.5 # millimolar (in i_NaCa)
Ksat = 0.1 # dimensionless (in i_NaCa)
gamma = 0.35 # dimensionless (in i_NaCa)
kNaCa1 = kNaCa # A_per_F (in i_NaCa)
i_NaCa = kNaCa1*(exp(gamma*y(0)*F/(R*T))*y(17)**3*Cao-exp((gamma-1)*y(0)*F/(R*T))*Nao**3*y(2)*alpha)/((KmNai**3+Nao**3)*(KmCa+Cao)*(1+Ksat*exp((gamma-1)*y(0)*F/(R*T))))
## INaK
Km_K = 1 # millimolar (in i_NaK)
Km_Na = 40 # millimolar (in i_NaK)
PNaK1 = PNaK # A_per_F (in i_NaK)
i_NaK = PNaK1*Ko/(Ko+Km_K)*y(17)/(y(17)+Km_Na)/(1+0.1245*exp(-0.1*y(0)*F/(R*T))+0.0353*exp(-y(0)*F/(R*T)))
## IpCa
KPCa = 0.0005 # millimolar (in i_PCa)
g_PCa = 0.4125 # A_per_F (in i_PCa)
i_PCa = g_PCa*y(2)/(y(2)+KPCa)
## Background currents
g_b_Na = 0.95 # S_per_F (in i_b_Na)
i_b_Na = g_b_Na*(y(0)-E_Na)
g_b_Ca = 0.727272 # S_per_F (in i_b_Ca)
i_b_Ca = g_b_Ca*(y(0)-E_Ca)
## Sarcoplasmic reticulum
i_up = VmaxUp/(1+Kup**2/y(2)**2)
i_leak = (y(1)-y(2))*V_leak
dY[3] = 0
# RyR
RyRSRCass = (1 - 1/(1 + exp((y(1)-0.3)/0.1)))
i_rel = g_irel_max*RyRSRCass*y(21)*y(22)*(y(1)-y(2))
RyRainfss = RyRa1-RyRa2/(1 + exp((1000*y(2)-(RyRahalf))/0.0082))
RyRtauadapt = 1 #s
dY[20] = (RyRainfss- y(20))/RyRtauadapt
RyRoinfss = (1 - 1/(1 + exp((1000*y(2)-(y(20)+ RyRohalf))/0.003)))
RyRtauact = conditional(RyRoinfss,y(21),0.1,1)*18.75e-3
dY[21] = (RyRoinfss- y(21))/RyRtauact
RyRcinfss = (1/(1 + exp((1000*y(2)-(y(20)+RyRchalf))/0.001)))
RyRtauinact = conditional(RyRcinfss,y(22),1,2)*87.5e-3
dY[22] = (RyRcinfss- y(22))/RyRtauinact
## Ca2+ buffering
Buf_C = 0.25 # millimolar (in calcium_dynamics)
Buf_SR = 10 # millimolar (in calcium_dynamics)
Kbuf_C = 0.001 # millimolar (in calcium_dynamics)
Kbuf_SR = 0.3 # millimolar (in calcium_dynamics)
Cai_bufc = 1/(1+Buf_C*Kbuf_C/(y(2)+Kbuf_C)**2)
Ca_SR_bufSR = 1/(1+Buf_SR*Kbuf_SR/(y(1)+Kbuf_SR)**2)
## Ionic concentrations
#Nai
dY[17] = -Cm*(i_Na+i_NaL+i_b_Na+3*i_NaK+3*i_NaCa+i_fNa)/(F*Vc*1e-18)
#caSR
dY[2] = Cai_bufc*(i_leak-i_up+i_rel-(i_CaL+i_b_Ca+i_PCa-2*i_NaCa)*Cm/(2*Vc*F*1e-18))
#Cai
dY[1] = Ca_SR_bufSR*Vc/V_SR*(i_up-(i_rel+i_leak))
i_stim = 0
## Membrane potential
dY[0] = -(i_K1+i_to+i_Kr+i_Ks+i_CaL+i_NaK+i_Na+i_NaL+i_NaCa+i_PCa+i_f+i_b_Na+i_b_Ca-i_stim)
return dY
#cdc25 and wee1 activity depend on cdk1, but also on their total
def cdc25(cdk, cdc25T=1):
return cdc25T * (p['acdc25'] + p['bcdc25'] * cdk**p['ncdc25'] /
(p['Kcdc25']**p['ncdc25'] + cdk**p['ncdc25']))
def wee1(cdk, wee1T=1):
return wee1T * (p['awee1'] + p['bwee1'] * p['Kwee1']**p['nwee1'] /
(p['Kwee1']**p['nwee1'] + cdk**p['nwee1']))
#solve
#order: cyc, cdk, cdc
#nucleus cytoplasm
cycn = y(0)
cycc = y(1)
cdkn = y(2)
cdkc = y(3)
cdcn = y(4)
cdcc = y(5)
#import rates depend on Cdk1 levels
impcdc = .1 + cdkc / 30 #import factor for cdc25
impcyc = 1 + cdkn / 60 #import factor for cyclin
# derivatives
dcycn = pr['kncyc'] * impcyc * cycc - pr['kccyc'] * cycn
dcycc = -pr['kncyc'] * impcyc * cycc + pr['kccyc'] * cycn + p['ks']
def f(): for n in range(NUM_NEURON): coupling_sum = sum(symengine.sin(y(m)-y(n)) for m in A_list[n]) # nonlinearity! coupling_term = couple_const * coupling_sum yield int_freqs[n] + coupling_term
