Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 20
sizeStates = 17
sizeConstants = 33
from math import *
from numpy import *
def createLegends():
legend_states = [""] * sizeStates
legend_rates = [""] * sizeStates
legend_algebraic = [""] * sizeAlgebraic
legend_voi = ""
legend_constants = [""] * sizeConstants
legend_voi = "time in component environment (second)"
legend_algebraic[0] = "v1 in component v1 (flux)"
legend_states[0] = "pM9 in component pM9 (molar)"
legend_states[1] = "M3 in component M3 (molar)"
legend_states[2] = "M3_pM9 in component M3_pM9 (molar)"
legend_constants[0] = "kon_M3pM9 in component kinetic_parameters (second_order_rate_constant)"
legend_constants[1] = "koff_M3pM9 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[1] = "v2 in component v2 (flux)"
legend_constants[2] = "kact_M3pM9 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[2] = "v3 in component v3 (flux)"
legend_states[3] = "M3_T1 in component M3_T1 (molar)"
legend_states[4] = "T1 in component T1 (molar)"
legend_constants[3] = "kon_M3T1 in component kinetic_parameters (second_order_rate_constant)"
legend_constants[4] = "koff_M3T1 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[3] = "v4 in component v4 (flux)"
legend_states[5] = "pM9_T1 in component pM9_T1 (molar)"
legend_constants[5] = "kon_pM9T1 in component kinetic_parameters (second_order_rate_constant)"
legend_constants[6] = "koff_pM9T1 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[4] = "v5 in component v5 (flux)"
legend_states[6] = "M3_pM9_T1 in component M3_pM9_T1 (molar)"
legend_constants[7] = "kon_M3pM9T1 in component kinetic_parameters (second_order_rate_constant)"
legend_constants[8] = "koff_M3pM9T1 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[5] = "v6 in component v6 (flux)"
legend_constants[9] = "kact_M3pM9T1 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[6] = "v7 in component v7 (flux)"
legend_states[7] = "M9_T1_star in component M9_T1_star (molar)"
legend_states[8] = "M9 in component M9 (molar)"
legend_constants[10] = "kon_M9T1_star in component kinetic_parameters (second_order_rate_constant)"
legend_constants[11] = "koff_M9T1_star in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[7] = "v8 in component v8 (flux)"
legend_states[9] = "M9_T1 in component M9_T1 (molar)"
legend_constants[12] = "kon_M9T1 in component kinetic_parameters (first_order_rate_constant)"
legend_constants[13] = "koff_M9T1 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[8] = "v9 in component v9 (flux)"
legend_states[10] = "M9_T1_M3 in component M9_T1_M3 (molar)"
legend_constants[14] = "kon_M9_M3T1 in component kinetic_parameters (first_order_rate_constant)"
legend_constants[15] = "koff_M9_M3T1 in component kinetic_parameters (second_order_rate_constant)"
legend_algebraic[9] = "v10 in component v10 (flux)"
legend_states[11] = "pM9_T1_M3 in component pM9_T1_M3 (molar)"
legend_constants[16] = "kon_M3_pM9T1 in component kinetic_parameters (second_order_rate_constant)"
legend_constants[17] = "koff_M3_pM9T1 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[10] = "v11 in component v11 (flux)"
legend_constants[18] = "kon_pM9T1M3 in component kinetic_parameters (second_order_rate_constant)"
legend_constants[19] = "koff_pM9T1M3 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[11] = "v12 in component v12 (flux)"
legend_states[12] = "M3_pM9_T1_M3 in component M3_pM9_T1_M3 (molar)"
legend_constants[20] = "kon_M3pM9T1M3 in component kinetic_parameters (second_order_rate_constant)"
legend_constants[21] = "koff_M3pM9T1M3 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[12] = "v13 in component v13 (flux)"
legend_constants[22] = "kact_M3pM9T1M3 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[13] = "v14 in component v14 (flux)"
legend_constants[23] = "kact_M9T1M3 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[14] = "v15 in component v15 (flux)"
legend_states[13] = "Tr in component Tr (molar)"
legend_states[14] = "Tr_pM9 in component Tr_pM9 (molar)"
legend_constants[24] = "kon_TrpM9 in component kinetic_parameters (second_order_rate_constant)"
legend_constants[25] = "koff_TrpM9 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[15] = "v16 in component v16 (flux)"
legend_constants[26] = "kact_TrpM9 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[16] = "v17 in component v17 (flux)"
legend_states[15] = "Tr_pM9_T1 in component Tr_pM9_T1 (molar)"
legend_constants[27] = "kon_TrpM9T1 in component kinetic_parameters (second_order_rate_constant)"
legend_constants[28] = "koff_TrpM9T1 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[17] = "v18 in component v18 (flux)"
legend_constants[29] = "kact_TrpM9T1 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[18] = "v19 in component v19 (flux)"
legend_states[16] = "Tr_pM9_T1_M3 in component Tr_pM9_T1_M3 (molar)"
legend_constants[30] = "kon_TrpM9T1M3 in component kinetic_parameters (second_order_rate_constant)"
legend_constants[31] = "koff_TrpM9T1M3 in component kinetic_parameters (first_order_rate_constant)"
legend_algebraic[19] = "v20 in component v20 (flux)"
legend_constants[32] = "kact_TrpM9T1M3 in component kinetic_parameters (first_order_rate_constant)"
legend_rates[0] = "d/dt pM9 in component pM9 (molar)"
legend_rates[1] = "d/dt M3 in component M3 (molar)"
legend_rates[2] = "d/dt M3_pM9 in component M3_pM9 (molar)"
legend_rates[4] = "d/dt T1 in component T1 (molar)"
legend_rates[3] = "d/dt M3_T1 in component M3_T1 (molar)"
legend_rates[5] = "d/dt pM9_T1 in component pM9_T1 (molar)"
legend_rates[6] = "d/dt M3_pM9_T1 in component M3_pM9_T1 (molar)"
legend_rates[7] = "d/dt M9_T1_star in component M9_T1_star (molar)"
legend_rates[8] = "d/dt M9 in component M9 (molar)"
legend_rates[9] = "d/dt M9_T1 in component M9_T1 (molar)"
legend_rates[11] = "d/dt pM9_T1_M3 in component pM9_T1_M3 (molar)"
legend_rates[12] = "d/dt M3_pM9_T1_M3 in component M3_pM9_T1_M3 (molar)"
legend_rates[10] = "d/dt M9_T1_M3 in component M9_T1_M3 (molar)"
legend_rates[13] = "d/dt Tr in component Tr (molar)"
legend_rates[14] = "d/dt Tr_pM9 in component Tr_pM9 (molar)"
legend_rates[15] = "d/dt Tr_pM9_T1 in component Tr_pM9_T1 (molar)"
legend_rates[16] = "d/dt Tr_pM9_T1_M3 in component Tr_pM9_T1_M3 (molar)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 3e-7
states[1] = 5e-8
states[2] = 0
constants[0] = 1e4
constants[1] = 0.001
constants[2] = 0.0019
states[3] = 0
states[4] = 3e-7
constants[3] = 1.9e6
constants[4] = 1.26e-4
states[5] = 0
constants[5] = 3.4e4
constants[6] = 7.48e-5
states[6] = 0
constants[7] = 1e4
constants[8] = 0.001
constants[9] = 0.00057
states[7] = 0
states[8] = 0
constants[10] = 5.6e6
constants[11] = 1.6e-5
states[9] = 0
constants[12] = 6.3e-4
constants[13] = 2.5e-4
states[10] = 0
constants[14] = 7.48e-5
constants[15] = 3.4e4
states[11] = 0
constants[16] = 1.9e6
constants[17] = 1.26e-4
constants[18] = 3.4e4
constants[19] = 7.48e-5
states[12] = 0
constants[20] = 1e4
constants[21] = 0.001
constants[22] = 0.00057
constants[23] = 1.26e-4
states[13] = 1e-7
states[14] = 0
constants[24] = 1e4
constants[25] = 0.007
constants[26] = 0.002
states[15] = 0
constants[27] = 1e4
constants[28] = 0.007
constants[29] = 0.0006
states[16] = 0
constants[30] = 1e4
constants[31] = 0.007
constants[32] = 0.0006
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[0] = constants[0]*states[1]*states[0]-constants[1]*states[2]
algebraic[1] = constants[2]*states[2]
rates[2] = algebraic[0]-algebraic[1]
algebraic[4] = constants[7]*states[5]*states[1]-constants[8]*states[6]
algebraic[5] = constants[9]*states[6]
rates[6] = algebraic[4]-algebraic[5]
algebraic[2] = constants[3]*states[1]*states[4]-constants[4]*states[3]
algebraic[3] = constants[5]*states[0]*states[4]-constants[6]*states[5]
algebraic[6] = constants[10]*states[4]*states[8]-constants[11]*states[7]
rates[4] = -(algebraic[2]+algebraic[3]+algebraic[6])
algebraic[8] = constants[14]*states[10]-constants[15]*states[8]*states[3]
algebraic[10] = constants[18]*states[0]*states[3]-constants[19]*states[11]
rates[3] = (algebraic[2]+algebraic[8])-algebraic[10]
algebraic[11] = constants[20]*states[1]*states[11]-constants[21]*states[12]
algebraic[12] = constants[22]*states[12]
rates[12] = algebraic[11]-algebraic[12]
algebraic[9] = constants[16]*states[5]*states[1]-constants[17]*states[11]
algebraic[13] = constants[23]*states[10]
rates[1] = (algebraic[1]+algebraic[5]+algebraic[12]+algebraic[13])-(algebraic[0]+algebraic[2]+algebraic[4]+algebraic[9]+algebraic[11])
algebraic[7] = constants[12]*states[7]-constants[13]*states[9]
rates[7] = (algebraic[6]+algebraic[13])-algebraic[7]
algebraic[14] = constants[24]*states[13]*states[0]-constants[25]*states[14]
rates[0] = -(algebraic[0]+algebraic[3]+algebraic[14]+algebraic[10])
algebraic[15] = constants[26]*states[14]
rates[8] = (algebraic[1]+algebraic[8]+algebraic[15])-algebraic[6]
rates[14] = algebraic[14]-algebraic[15]
algebraic[16] = constants[27]*states[5]*states[13]-constants[28]*states[15]
rates[5] = algebraic[3]-(algebraic[4]+algebraic[9]+algebraic[16])
algebraic[17] = constants[29]*states[15]
rates[9] = algebraic[7]+algebraic[17]
rates[15] = algebraic[16]-algebraic[17]
algebraic[18] = constants[30]*states[13]*states[11]-constants[31]*states[16]
rates[11] = (algebraic[9]+algebraic[10])-(algebraic[11]+algebraic[18])
algebraic[19] = constants[32]*states[16]
rates[10] = (algebraic[12]+algebraic[19])-(algebraic[13]+algebraic[8])
rates[13] = (algebraic[15]+algebraic[17]+algebraic[19])-(algebraic[14]+algebraic[16]+algebraic[18])
rates[16] = algebraic[18]-algebraic[19]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = constants[0]*states[1]*states[0]-constants[1]*states[2]
algebraic[1] = constants[2]*states[2]
algebraic[4] = constants[7]*states[5]*states[1]-constants[8]*states[6]
algebraic[5] = constants[9]*states[6]
algebraic[2] = constants[3]*states[1]*states[4]-constants[4]*states[3]
algebraic[3] = constants[5]*states[0]*states[4]-constants[6]*states[5]
algebraic[6] = constants[10]*states[4]*states[8]-constants[11]*states[7]
algebraic[8] = constants[14]*states[10]-constants[15]*states[8]*states[3]
algebraic[10] = constants[18]*states[0]*states[3]-constants[19]*states[11]
algebraic[11] = constants[20]*states[1]*states[11]-constants[21]*states[12]
algebraic[12] = constants[22]*states[12]
algebraic[9] = constants[16]*states[5]*states[1]-constants[17]*states[11]
algebraic[13] = constants[23]*states[10]
algebraic[7] = constants[12]*states[7]-constants[13]*states[9]
algebraic[14] = constants[24]*states[13]*states[0]-constants[25]*states[14]
algebraic[15] = constants[26]*states[14]
algebraic[16] = constants[27]*states[5]*states[13]-constants[28]*states[15]
algebraic[17] = constants[29]*states[15]
algebraic[18] = constants[30]*states[13]*states[11]-constants[31]*states[16]
algebraic[19] = constants[32]*states[16]
return algebraic
def solve_model():
"""Solve model with ODE solver"""
from scipy.integrate import ode
# Initialise constants and state variables
(init_states, constants) = initConsts()
# Set timespan to solve over
voi = linspace(0, 10, 500)
# Construct ODE object to solve
r = ode(computeRates)
r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1)
r.set_initial_value(init_states, voi[0])
r.set_f_params(constants)
# Solve model
states = array([[0.0] * len(voi)] * sizeStates)
states[:,0] = init_states
for (i,t) in enumerate(voi[1:]):
if r.successful():
r.integrate(t)
states[:,i+1] = r.y
else:
break
# Compute algebraic variables
algebraic = computeAlgebraic(constants, states, voi)
return (voi, states, algebraic)
def plot_model(voi, states, algebraic):
"""Plot variables against variable of integration"""
import pylab
(legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends()
pylab.figure(1)
pylab.plot(voi,vstack((states,algebraic)).T)
pylab.xlabel(legend_voi)
pylab.legend(legend_states + legend_algebraic, loc='best')
pylab.show()
if __name__ == "__main__":
(voi, states, algebraic) = solve_model()
plot_model(voi, states, algebraic)