# Size of variable arrays:
sizeAlgebraic = 13
sizeStates = 14
sizeConstants = 18
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_states[0] = "O2 in component O2 (molar)"
legend_algebraic[0] = "v1 in component v1 (flux)"
legend_algebraic[4] = "v5 in component v5 (flux)"
legend_algebraic[6] = "v7 in component v7 (flux)"
legend_algebraic[10] = "v11 in component v11 (flux)"
legend_algebraic[12] = "v13_back in component v13_back (flux)"
legend_constants[17] = "v13 in component v13 (flux)"
legend_states[1] = "O2_radical in component O2_radical (molar)"
legend_algebraic[5] = "v6 in component v6 (flux)"
legend_states[2] = "NADH in component NADH (molar)"
legend_constants[16] = "v12 in component v12 (flux)"
legend_algebraic[11] = "v14 in component v14 (flux)"
legend_states[3] = "NAD in component NAD (molar)"
legend_algebraic[7] = "v8 in component v8 (flux)"
legend_algebraic[9] = "v10 in component v10 (flux)"
legend_states[4] = "NAD_radical in component NAD_radical (molar)"
legend_algebraic[8] = "v9 in component v9 (flux)"
legend_states[5] = "NAD2 in component NAD2 (molar)"
legend_states[6] = "H2O2 in component H2O2 (molar)"
legend_algebraic[1] = "v2 in component v2 (flux)"
legend_states[7] = "Per3 in component Per3 (molar)"
legend_algebraic[3] = "v4 in component v4 (flux)"
legend_states[8] = "Per2 in component Per2 (molar)"
legend_states[9] = "coI in component coI (molar)"
legend_algebraic[2] = "v3 in component v3 (flux)"
legend_states[10] = "coII in component coII (molar)"
legend_states[11] = "coIII in component coIII (molar)"
legend_states[12] = "Ar_radical in component Ar_radical (molar)"
legend_states[13] = "ArH in component ArH (molar)"
legend_constants[0] = "k1 in component v1 (second_order_rate_constant)"
legend_constants[1] = "k2 in component v2 (second_order_rate_constant)"
legend_constants[2] = "k3 in component v3 (second_order_rate_constant)"
legend_constants[3] = "k4 in component v4 (second_order_rate_constant)"
legend_constants[4] = "k5 in component v5 (second_order_rate_constant)"
legend_constants[5] = "k6 in component v6 (second_order_rate_constant)"
legend_constants[6] = "k7 in component v7 (second_order_rate_constant)"
legend_constants[7] = "k8 in component v8 (second_order_rate_constant)"
legend_constants[8] = "k9 in component v9 (second_order_rate_constant)"
legend_constants[9] = "k10 in component v10 (second_order_rate_constant)"
legend_constants[10] = "k11 in component v11 (second_order_rate_constant)"
legend_constants[11] = "k12 in component v12 (flux)"
legend_constants[12] = "O2eq in component v13 (molar)"
legend_constants[13] = "k13 in component v13 (first_order_rate_constant)"
legend_constants[14] = "k13_ in component v13_back (first_order_rate_constant)"
legend_constants[15] = "k14 in component v14 (second_order_rate_constant)"
legend_rates[0] = "d/dt O2 in component O2 (molar)"
legend_rates[1] = "d/dt O2_radical in component O2_radical (molar)"
legend_rates[2] = "d/dt NADH in component NADH (molar)"
legend_rates[3] = "d/dt NAD in component NAD (molar)"
legend_rates[4] = "d/dt NAD_radical in component NAD_radical (molar)"
legend_rates[5] = "d/dt NAD2 in component NAD2 (molar)"
legend_rates[6] = "d/dt H2O2 in component H2O2 (molar)"
legend_rates[7] = "d/dt Per3 in component Per3 (molar)"
legend_rates[8] = "d/dt Per2 in component Per2 (molar)"
legend_rates[9] = "d/dt coI in component coI (molar)"
legend_rates[10] = "d/dt coII in component coII (molar)"
legend_rates[11] = "d/dt coIII in component coIII (molar)"
legend_rates[12] = "d/dt Ar_radical in component Ar_radical (molar)"
legend_rates[13] = "d/dt ArH in component ArH (molar)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 5.33e-6
states[1] = 0.026e-6
states[2] = 0.95e-6
states[3] = 558e-6
states[4] = 5e-10
states[5] = 0.12e-6
states[6] = 0.013e-6
states[7] = 0.059e-6
states[8] = 1e-10
states[9] = 8.9e-10
states[10] = 0.026e-6
states[11] = 1.31e-6
states[12] = 0.12e-6
states[13] = 299.88e-6
constants[0] = 3
constants[1] = 1.8e7
constants[2] = 1.5e5
constants[3] = 5.2e3
constants[4] = 2e7
constants[5] = 1.7e7
constants[6] = 2e7
constants[7] = 4e7
constants[8] = 6e7
constants[9] = 1.8e6
constants[10] = 1e5
constants[11] = 0.08e-6
constants[12] = 1.2e-5
constants[13] = 6e-3
constants[14] = 6e-3
constants[15] = 7e5
constants[16] = constants[11]
constants[17] = constants[13]*constants[12]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[3] = constants[3]*states[10]*states[13]
algebraic[2] = constants[2]*states[9]*states[13]
rates[10] = algebraic[2]-algebraic[3]
algebraic[4] = constants[4]*states[4]*states[0]
algebraic[6] = constants[6]*(power(states[1], 2.00000))
algebraic[5] = constants[5]*states[1]*states[7]
rates[1] = (algebraic[4]-algebraic[5])-2.00000*algebraic[6]
algebraic[0] = constants[0]*states[2]*states[0]
algebraic[1] = constants[1]*states[6]*states[7]
rates[6] = (algebraic[0]-algebraic[1])-algebraic[6]
algebraic[7] = constants[7]*states[11]*states[4]
rates[9] = (algebraic[1]-algebraic[2])+algebraic[7]
algebraic[8] = constants[8]*(power(states[4], 2.00000))
rates[5] = algebraic[8]
algebraic[9] = constants[9]*states[7]*states[4]
rates[3] = algebraic[0]+algebraic[4]+algebraic[7]+algebraic[9]
rates[7] = ((-algebraic[1]+algebraic[3])-algebraic[5])-algebraic[9]
algebraic[11] = constants[15]*states[12]*states[2]
rates[2] = (-algebraic[0]+constants[16])-algebraic[11]
rates[4] = (((-2.00000*algebraic[8]-algebraic[4])-algebraic[7])-algebraic[9])+algebraic[11]
algebraic[10] = constants[10]*states[8]*states[0]
rates[8] = -algebraic[10]+algebraic[9]
rates[11] = (algebraic[5]-algebraic[7])+algebraic[10]
rates[12] = (algebraic[2]+algebraic[3])-algebraic[11]
rates[13] = (-algebraic[2]-algebraic[3])+algebraic[11]
algebraic[12] = constants[14]*states[0]
rates[0] = ((((-algebraic[0]-algebraic[4])+algebraic[6])-algebraic[10])+constants[17])-algebraic[12]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[3] = constants[3]*states[10]*states[13]
algebraic[2] = constants[2]*states[9]*states[13]
algebraic[4] = constants[4]*states[4]*states[0]
algebraic[6] = constants[6]*(power(states[1], 2.00000))
algebraic[5] = constants[5]*states[1]*states[7]
algebraic[0] = constants[0]*states[2]*states[0]
algebraic[1] = constants[1]*states[6]*states[7]
algebraic[7] = constants[7]*states[11]*states[4]
algebraic[8] = constants[8]*(power(states[4], 2.00000))
algebraic[9] = constants[9]*states[7]*states[4]
algebraic[11] = constants[15]*states[12]*states[2]
algebraic[10] = constants[10]*states[8]*states[0]
algebraic[12] = constants[14]*states[0]
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)