Generated Code
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# Size of variable arrays:
sizeAlgebraic = 11
sizeStates = 10
sizeConstants = 31
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] = "ATP in component ATP (micromolar)"
legend_constants[0] = "V_hyd in component V_hyd (flux)"
legend_algebraic[1] = "V_MMCK in component V_MMCK (flux)"
legend_algebraic[8] = "J_ATP in component J_ATP (flux)"
legend_constants[1] = "V_cyt in component fractional_volumes (dimensionless)"
legend_states[1] = "ADP in component ADP (micromolar)"
legend_algebraic[9] = "J_ADP in component J_ADP (flux)"
legend_states[2] = "PCr in component PCr (micromolar)"
legend_algebraic[5] = "J_PCr in component J_PCr (flux)"
legend_states[3] = "Cr in component Cr (micromolar)"
legend_algebraic[6] = "J_Cr in component J_Cr (flux)"
legend_states[4] = "Pi in component Pi (micromolar)"
legend_algebraic[10] = "J_Pi in component J_Pi (flux)"
legend_states[5] = "ATP_i in component ATP_i (micromolar)"
legend_algebraic[3] = "V_MiCK in component V_MiCK (flux)"
legend_algebraic[7] = "V_syn in component V_syn (flux)"
legend_constants[2] = "V_ims in component fractional_volumes (dimensionless)"
legend_states[6] = "ADP_i in component ADP_i (micromolar)"
legend_states[7] = "PCr_i in component PCr_i (micromolar)"
legend_states[8] = "Cr_i in component Cr_i (micromolar)"
legend_states[9] = "Pi_i in component Pi_i (micromolar)"
legend_algebraic[0] = "Den_MMCK in component V_MMCK (dimensionless)"
legend_constants[3] = "Kia in component V_MMCK (micromolar)"
legend_constants[4] = "Kb in component V_MMCK (micromolar)"
legend_constants[5] = "Kib in component V_MMCK (micromolar)"
legend_constants[27] = "KIb in component V_MMCK (micromolar)"
legend_constants[28] = "Kc in component V_MMCK (micromolar)"
legend_constants[6] = "Kic in component V_MMCK (micromolar)"
legend_constants[7] = "Kd in component V_MMCK (micromolar)"
legend_constants[8] = "Kid in component V_MMCK (micromolar)"
legend_constants[9] = "Vf in component V_MMCK (flux)"
legend_constants[10] = "Vb in component V_MMCK (flux)"
legend_algebraic[2] = "Den_MiCK in component V_MiCK (dimensionless)"
legend_constants[11] = "Kia in component V_MiCK (micromolar)"
legend_constants[12] = "Kb in component V_MiCK (micromolar)"
legend_constants[13] = "Kib in component V_MiCK (micromolar)"
legend_constants[29] = "KIb in component V_MiCK (micromolar)"
legend_constants[30] = "Kc in component V_MiCK (micromolar)"
legend_constants[14] = "Kic in component V_MiCK (micromolar)"
legend_constants[15] = "Kd in component V_MiCK (micromolar)"
legend_constants[16] = "Kid in component V_MiCK (micromolar)"
legend_constants[17] = "Vf in component V_MiCK (flux)"
legend_constants[18] = "Vb in component V_MiCK (flux)"
legend_algebraic[4] = "Den_syn in component V_syn (dimensionless)"
legend_constants[19] = "KPi in component V_syn (micromolar)"
legend_constants[20] = "KADP in component V_syn (micromolar)"
legend_constants[21] = "V_syn_max in component V_syn (flux)"
legend_constants[22] = "R_ATP in component J_ATP (first_order_rate_constant)"
legend_constants[23] = "R_ADP in component J_ADP (first_order_rate_constant)"
legend_constants[24] = "R_PCr in component J_PCr (first_order_rate_constant)"
legend_constants[25] = "R_Cr in component J_Cr (first_order_rate_constant)"
legend_constants[26] = "R_Pi in component J_Pi (first_order_rate_constant)"
legend_rates[0] = "d/dt ATP in component ATP (micromolar)"
legend_rates[1] = "d/dt ADP in component ADP (micromolar)"
legend_rates[2] = "d/dt PCr in component PCr (micromolar)"
legend_rates[3] = "d/dt Cr in component Cr (micromolar)"
legend_rates[4] = "d/dt Pi in component Pi (micromolar)"
legend_rates[5] = "d/dt ATP_i in component ATP_i (micromolar)"
legend_rates[6] = "d/dt ADP_i in component ADP_i (micromolar)"
legend_rates[7] = "d/dt PCr_i in component PCr_i (micromolar)"
legend_rates[8] = "d/dt Cr_i in component Cr_i (micromolar)"
legend_rates[9] = "d/dt Pi_i in component Pi_i (micromolar)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 9644.425
constants[0] = 4.6E3
constants[1] = 0.75
states[1] = 60.0
states[2] = 12500.0
states[3] = 13500.0
states[4] = 8000.0
states[5] = 9644.425
constants[2] = 0.0625
states[6] = 2.5
states[7] = 12500.0
states[8] = 13500.0
states[9] = 8000.0
constants[3] = 9.0E2
constants[4] = 1.55E4
constants[5] = 3.49E4
constants[6] = 2.224E2
constants[7] = 1.67E3
constants[8] = 4.73E3
constants[9] = 6.966E3
constants[10] = 2.925E4
constants[11] = 7.5E2
constants[12] = 5.2E3
constants[13] = 2.88E4
constants[14] = 2.048E2
constants[15] = 5.0E2
constants[16] = 1.6E3
constants[17] = 2.658E3
constants[18] = 1.116E4
constants[19] = 20.0
constants[20] = 8.0E2
constants[21] = 4.6E3
constants[22] = 8.16
constants[23] = 8.16
constants[24] = 14.6
constants[25] = 14.6
constants[26] = 18.4
constants[27] = constants[5]
constants[28] = (constants[6]*constants[7])/constants[8]
constants[29] = constants[13]
constants[30] = (constants[14]*constants[15])/constants[16]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[0] = 1.00000+states[3]/constants[5]+states[2]/constants[8]+states[0]*(1.00000/constants[3]+states[3]/(constants[3]*constants[4]))+states[1]*(1.00000/constants[6]+states[2]/(constants[8]*constants[28])+states[3]/(constants[6]*constants[27]))
algebraic[1] = (constants[9]*((states[0]*states[3])/(constants[3]*constants[4]))-constants[10]*((states[1]*states[2])/(constants[6]*constants[7])))/algebraic[0]
algebraic[5] = constants[24]*(states[7]-states[2])
rates[2] = (algebraic[5]+algebraic[1])/constants[1]
algebraic[6] = constants[25]*(states[8]-states[3])
rates[3] = (algebraic[6]-algebraic[1])/constants[1]
algebraic[2] = 1.00000+states[8]/constants[13]+states[7]/constants[16]+states[5]*(1.00000/constants[11]+states[8]/(constants[11]*constants[12]))+states[6]*(1.00000/constants[14]+states[7]/(constants[16]*constants[30])+states[8]/(constants[14]*constants[29]))
algebraic[3] = (constants[17]*((states[5]*states[8])/(constants[11]*constants[12]))-constants[18]*((states[6]*states[7])/(constants[14]*constants[15])))/algebraic[2]
rates[7] = (algebraic[3]-algebraic[5])/constants[2]
rates[8] = -(algebraic[3]+algebraic[6])/constants[2]
algebraic[8] = constants[22]*(states[5]-states[0])
rates[0] = (algebraic[8]-(constants[0]+algebraic[1]))/constants[1]
algebraic[9] = constants[23]*(states[6]-states[1])
rates[1] = (algebraic[9]+constants[0]+algebraic[1])/constants[1]
algebraic[10] = constants[26]*(states[9]-states[4])
rates[4] = (algebraic[10]+constants[0])/constants[1]
algebraic[4] = 1.00000+states[6]/constants[20]+states[9]/constants[19]+(states[6]*states[9])/(constants[20]*constants[19])
algebraic[7] = constants[21]*((states[6]*states[9])/(constants[19]*constants[20]*algebraic[4]))
rates[5] = -(algebraic[8]+algebraic[7]+algebraic[3])/constants[2]
rates[6] = ((algebraic[7]+algebraic[3])-algebraic[9])/constants[2]
rates[9] = (algebraic[7]-algebraic[10])/constants[2]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = 1.00000+states[3]/constants[5]+states[2]/constants[8]+states[0]*(1.00000/constants[3]+states[3]/(constants[3]*constants[4]))+states[1]*(1.00000/constants[6]+states[2]/(constants[8]*constants[28])+states[3]/(constants[6]*constants[27]))
algebraic[1] = (constants[9]*((states[0]*states[3])/(constants[3]*constants[4]))-constants[10]*((states[1]*states[2])/(constants[6]*constants[7])))/algebraic[0]
algebraic[5] = constants[24]*(states[7]-states[2])
algebraic[6] = constants[25]*(states[8]-states[3])
algebraic[2] = 1.00000+states[8]/constants[13]+states[7]/constants[16]+states[5]*(1.00000/constants[11]+states[8]/(constants[11]*constants[12]))+states[6]*(1.00000/constants[14]+states[7]/(constants[16]*constants[30])+states[8]/(constants[14]*constants[29]))
algebraic[3] = (constants[17]*((states[5]*states[8])/(constants[11]*constants[12]))-constants[18]*((states[6]*states[7])/(constants[14]*constants[15])))/algebraic[2]
algebraic[8] = constants[22]*(states[5]-states[0])
algebraic[9] = constants[23]*(states[6]-states[1])
algebraic[10] = constants[26]*(states[9]-states[4])
algebraic[4] = 1.00000+states[6]/constants[20]+states[9]/constants[19]+(states[6]*states[9])/(constants[20]*constants[19])
algebraic[7] = constants[21]*((states[6]*states[9])/(constants[19]*constants[20]*algebraic[4]))
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)