def run_fermentor():
system = {
'dS': 'Q_in/V*(S_in-S)-1/Ys*mu_max*S/(S+K_S)*X',
'dX': '-Q_in/V*X+mu_max*S/(S+K_S)*X'
}
parameters = {
'mu_max': 0.4,
'K_S': 0.015,
'Q_in': 2,
'Ys': 0.67,
'S_in': 0.02,
'V': 20
}
M_fermentor = Model('fermentor', system, parameters)
M_fermentor.independent = {'t': np.linspace(0, 100, 5000)}
M_fermentor.initial_conditions = {'S': 0.02, 'X': 5e-5}
sens_numeric = NumericalLocalSensitivity(M_fermentor,
parameters=['mu_max', 'K_S'])
sens_analytic = DirectLocalSensitivity(M_fermentor,
parameters=['mu_max', 'K_S'])
#sens_out = sens.get_sensitivity()
pert_factors = 10.**np.arange(-14, 0, 1)
out_fig = sens.calc_quality_num_lsa(pert_factors)
return out_fig, sens_numeric, sens_analytic
def michaelis_menten():
system = {'v': 'Vmax*S/(Ks + S)', 'dS': '-v', 'dP': 'v'}
parameters = {'Vmax': 1e-1, 'Ks': 0.5}
MMmodel = Model('MichaelisMenten', system, parameters)
MMmodel.initial_conditions = {'S': 0.5, 'P': 0.0}
MMmodel.independent = {'t': np.linspace(0, 72, 1000)}
MMmodel.initialize_model()
return MMmodel
def run_second_order():
'''
y'' + 2*tau*omega*y' + omega**2*y = omega**2*K*u
x1 = y
x1' = y' = x2
x2' = y''= -2*tau*omega*x2 - omega**2*x1 + K*omega**2
'''
parameters = {'K': 0.01, 'tau': 0.3, 'omega': 0.6} # mM
system = {
'dx1': 'x2',
'dx2': '-2*tau*omega*x2 - (omega**2)*x1 + K*omega**2'
}
M1 = Model('second_order', system, parameters)
M1.initial_conditions = {'x1': 0, 'x2': 0}
M1.independent = {'t': np.linspace(0, 20, 10000)}
M1.initialize_model()
return M1.run()['x1'].values
def test_alg_state():
system = {'dP': 'k1 * P', 'dS': 'k2 * S', 'A': 'P + S'}
parameters = {'k1': -0.2, 'k2': 1.0}
model = Model('simple_test', system, parameters)
x = np.linspace(0, 10, 11)
model.initial_conditions = {'P': 50, 'S': 10}
model.independent = {'t': x}
result = model.run()
# expected output (analytical solution)
S = 10 * np.exp(1.0 * x)
P = 50 * np.exp(-0.2 * x)
expected = pd.DataFrame({'P': P, 'S': S}, index=x)
expected['A'] = expected['S'] + expected['P']
expected.index.names = ['t']
assert_frame_equal(result, expected.reindex(columns=result.columns))
def test_alg_substitution():
system = {'dP': 'k1 * P + A', 'dS': 'k2 * S', 'A': 'S + P'}
parameters = {'k1': -0.5, 'k2': 1.0}
model = Model('simple_test', system, parameters)
x = np.linspace(0, 10, 11)
model.initial_conditions = {'P': 50, 'S': 10}
model.independent = {'t': x}
result = model.run()
# expected output (analytical solution)
k1, k2 = -0.5, 1.0
S = 10 * np.exp(k2 * x)
P = 10 * (np.exp((k1 + 1)*x) - np.exp((k2)*x)) / (k1 - k2 + 1) \
+ 50 * np.exp((k1 + 1)*x)
expected = pd.DataFrame({'S': S, 'P': P}, index=x)
expected['A'] = expected['S'] + expected['P']
expected.index.names = ['t']
assert_frame_equal(result, expected.reindex(columns=result.columns))
system = {
'dS': 'Q_in/V*(S_in-S)-1/Ys*mu_max*S/(S+K_S)*X',
'dX': '-Q_in/V*X+mu_max*S/(S+K_S)*X'
}
parameters = {
'mu_max': 0.4,
'K_S': 0.015,
'Q_in': 2,
'Ys': 0.67,
'S_in': 0.02,
'V': 20
}
M1 = Model('ode', system, parameters)
M1.independent = {'t': np.linspace(0, 100, 5000)}
M1.initial_conditions = {'S': 0.02, 'X': 5e-5}
result = M1._run()
def test_model():
assert_almost_equal(result[-1, 0], 0.0049996401543859316, decimal=5)
assert_almost_equal(result[-1, 1], 0.010050542322437175, decimal=5)
if __name__ == "__main__":
test_model()
def LSA_comparison():
# Plain ping-pong bi-bi kinetics
ping_pong = ('(Vf*Vr*(MBA*Pyr-Ace*Ala/Keq))/(Vr*Km*Pyr + Vr*Kp*MBA +'
'Vr*Pyr*MBA + Vf*Kac*Ala/Keq + Vf*Kal*Ace/Keq +'
'Vf*Ace*Ala/Keq + Vr*Km*Pyr*Ala/Kialp +'
'Vf*Kal*MBA*Ace/(Keq*Kimp))')
# Replace reactants of Shin & Kim by current reactants
ping_pong = ping_pong.replace('MBA', 'IPA') # IPA = isopropylamine
ping_pong = ping_pong.replace('Pyr', 'BA') # BA = benzylacetone
ping_pong = ping_pong.replace('Ace', 'ACE') # ACE = acetone
ping_pong = ping_pong.replace('Ala', 'MPPA') # MPPA =
# Define system of interest
system = {
'v': ping_pong,
'Keq': '((Vf/Vr)**2)*(Kac*Kal)/(Km*Kp)',
'dE': '-decay*E',
'dIPA': '-v*E',
'dBA': '-v*E',
'dACE': 'v*E',
'dMPPA': 'v*E'
}
# Define all model parameters
parameters = { # Forward reaction parameters calibrated with data ULUND
'Vf': 2.47e-2, # umol/U/min
'Km': 143.18, # mM
'Kp': 3.52, # mM
# Backward reaction parameters calibrated with data UGENT
'Vr': 1.996e-2, # umol/U/min
'Kac': 207.64, # mM
'Kal': 2.301, # mM
# Remaining parameters to calibrate (first guess)
'Kialp': 1.39889, # mM
'Kimp': 2.9295, # mM
'decay': 0.00302837
} # 1/min
# Make model instance
M1 = Model('PPBB', system, parameters)
res_time = 0.01 / 1.66e-4 / 2.
# Set independent (time) range
M1.independent = {'t': np.linspace(0, res_time, 1000)}
# Set initial conditions
M1.initial_conditions = {
'IPA': 65.,
'BA': 5.,
'ACE': 0.,
'MPPA': 0.,
'E': 0.68
}
# Initialize model => Generate underlying functions
M1.initialize_model()
# DirectLocalSensitivity instance
M1sens_dir = DirectLocalSensitivity(M1,
parameters=['Kp', 'Vf', 'Km', 'Kal'])
# NumericalLocalSensitivity instance
M1sens_num = NumericalLocalSensitivity(
M1, parameters=['Kp', 'Vf', 'Km', 'Kal'])
M1sens_num.perturbation = 1e-5
# Calculate direct sensitivity
dir_sens = M1sens_dir.get_sensitivity(method='PRS')
# Calculate numerical sensivity
num_sens = M1sens_num.get_sensitivity(method='PRS')
return dir_sens, num_sens
def run_modsim_models():
# Data
file_path = os.path.join(pyideas.BASE_DIR, '..', 'examples', 'data',
'grasdata.csv')
data = pd.read_csv(file_path, header=0, names=['t', 'W'])
data = data.set_index('t')
measurements = Measurements(data)
measurements.add_measured_errors({'W': 1.0}, method='absolute')
# Logistic
parameters = {'W0': 2.0805, 'Wf': 9.7523, 'mu': 0.0659}
system = {'W': 'W0*Wf/(W0+(Wf-W0)*exp(-mu*t))'}
M1 = Model('Modsim1', system, parameters)
M1.independent = {'t': np.linspace(0, 72, 1000)}
M1.initialize_model()
# Perform parameter estimation
M1optim = ParameterOptimisation(M1, measurements)
M1optim.local_optimize()
# Calc parameter uncertainty
M1conf = CalibratedConfidence(M1optim)
FIM1 = M1conf.get_FIM()
# Exponential
parameters = {'Wf': 10.7189, 'mu': 0.0310}
system = {'W': 'Wf*(1-exp(-mu*t))'}
M2 = Model('Modsim2', system, parameters)
M2.independent = {'t': np.linspace(0, 72, 1000)}
# Perform parameter estimation
M2optim = ParameterOptimisation(M2, measurements)
M2optim.local_optimize()
# Calc parameter uncertainty
M2conf = CalibratedConfidence(M2optim)
FIM2 = M2conf.get_FIM()
# Gompertz
parameters = {'W0': 2.0424, 'D': 0.0411, 'mu': 0.0669}
system = {'W': 'W0*exp((mu*(1-exp(-D*t)))/(D))'}
M3 = Model('Modsim3', system, parameters)
M3.independent = {'t': np.linspace(0, 72, 1000)}
# Perform parameter estimation
M3optim = ParameterOptimisation(M3, measurements)
M3optim.local_optimize()
# Calc parameter uncertainty
M3conf = CalibratedConfidence(M3optim)
FIM3 = M3conf.get_FIM()
return M1, M2, M3, M1conf, M2conf, M3conf