Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 36
sizeStates = 14
sizeConstants = 39
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_constants[0] = "q_cAMP_init in component environment (fmol)"
legend_constants[1] = "q_PKI_init in component environment (fmol)"
legend_constants[2] = "q_PKACI_init in component environment (fmol)"
legend_constants[3] = "q_ARCI_init in component environment (fmol)"
legend_constants[4] = "q_A2RCI_init in component environment (fmol)"
legend_constants[5] = "q_CI_init in component environment (fmol)"
legend_constants[6] = "q_A2RI_init in component environment (fmol)"
legend_constants[7] = "q_PKACI_PKI_init in component environment (fmol)"
legend_constants[8] = "q_PKACII_init in component environment (fmol)"
legend_constants[9] = "q_ARCII_init in component environment (fmol)"
legend_constants[10] = "q_A2RCII_init in component environment (fmol)"
legend_constants[11] = "q_CII_init in component environment (fmol)"
legend_constants[12] = "q_A2RII_init in component environment (fmol)"
legend_constants[13] = "q_PKACII_PKI_init in component environment (fmol)"
legend_algebraic[0] = "q_cAMP in component environment (fmol)"
legend_algebraic[1] = "q_PKI in component environment (fmol)"
legend_algebraic[2] = "q_PKACI in component environment (fmol)"
legend_algebraic[3] = "q_ARCI in component environment (fmol)"
legend_algebraic[4] = "q_A2RCI in component environment (fmol)"
legend_algebraic[5] = "q_CI in component environment (fmol)"
legend_algebraic[6] = "q_A2RI in component environment (fmol)"
legend_algebraic[7] = "q_PKACI_PKI in component environment (fmol)"
legend_algebraic[8] = "q_PKACII in component environment (fmol)"
legend_algebraic[9] = "q_ARCII in component environment (fmol)"
legend_algebraic[10] = "q_A2RCII in component environment (fmol)"
legend_algebraic[11] = "q_CII in component environment (fmol)"
legend_algebraic[12] = "q_A2RII in component environment (fmol)"
legend_algebraic[13] = "q_PKACII_PKI in component environment (fmol)"
legend_states[0] = "q_cAMP in component PKA (fmol)"
legend_states[1] = "q_PKI in component PKA (fmol)"
legend_states[2] = "q_PKACI in component PKA (fmol)"
legend_states[3] = "q_ARCI in component PKA (fmol)"
legend_states[4] = "q_A2RCI in component PKA (fmol)"
legend_states[5] = "q_CI in component PKA (fmol)"
legend_states[6] = "q_A2RI in component PKA (fmol)"
legend_states[7] = "q_PKACI_PKI in component PKA (fmol)"
legend_states[8] = "q_PKACII in component PKA (fmol)"
legend_states[9] = "q_ARCII in component PKA (fmol)"
legend_states[10] = "q_A2RCII in component PKA (fmol)"
legend_states[11] = "q_CII in component PKA (fmol)"
legend_states[12] = "q_A2RII in component PKA (fmol)"
legend_states[13] = "q_PKACII_PKI in component PKA (fmol)"
legend_constants[14] = "kappa_aI in component PKA_parameters (fmol_per_sec)"
legend_constants[15] = "kappa_bI in component PKA_parameters (fmol_per_sec)"
legend_constants[16] = "kappa_dI in component PKA_parameters (fmol_per_sec)"
legend_constants[17] = "kappa_iI in component PKA_parameters (fmol_per_sec)"
legend_constants[18] = "kappa_aII in component PKA_parameters (fmol_per_sec)"
legend_constants[19] = "kappa_bII in component PKA_parameters (fmol_per_sec)"
legend_constants[20] = "kappa_dII in component PKA_parameters (fmol_per_sec)"
legend_constants[21] = "kappa_iII in component PKA_parameters (fmol_per_sec)"
legend_constants[22] = "K_cAMP in component PKA_parameters (per_fmol)"
legend_constants[23] = "K_PKI in component PKA_parameters (per_fmol)"
legend_constants[24] = "K_PKACI in component PKA_parameters (per_fmol)"
legend_constants[25] = "K_ARCI in component PKA_parameters (per_fmol)"
legend_constants[26] = "K_A2RCI in component PKA_parameters (per_fmol)"
legend_constants[27] = "K_CI in component PKA_parameters (per_fmol)"
legend_constants[28] = "K_A2RI in component PKA_parameters (per_fmol)"
legend_constants[29] = "K_PKACI_PKI in component PKA_parameters (per_fmol)"
legend_constants[30] = "K_PKACII in component PKA_parameters (per_fmol)"
legend_constants[31] = "K_ARCII in component PKA_parameters (per_fmol)"
legend_constants[32] = "K_A2RCII in component PKA_parameters (per_fmol)"
legend_constants[33] = "K_CII in component PKA_parameters (per_fmol)"
legend_constants[34] = "K_A2RII in component PKA_parameters (per_fmol)"
legend_constants[35] = "K_PKACII_PKI in component PKA_parameters (per_fmol)"
legend_constants[36] = "R in component constants (J_per_K_per_mol)"
legend_constants[37] = "T in component constants (kelvin)"
legend_algebraic[28] = "vaI in component PKA (fmol_per_sec)"
legend_algebraic[29] = "vbI in component PKA (fmol_per_sec)"
legend_algebraic[30] = "vdI in component PKA (fmol_per_sec)"
legend_algebraic[31] = "viI in component PKA (fmol_per_sec)"
legend_algebraic[32] = "vaII in component PKA (fmol_per_sec)"
legend_algebraic[33] = "vbII in component PKA (fmol_per_sec)"
legend_algebraic[34] = "vdII in component PKA (fmol_per_sec)"
legend_algebraic[35] = "viII in component PKA (fmol_per_sec)"
legend_algebraic[14] = "mu_cAMP in component PKA (J_per_mol)"
legend_algebraic[15] = "mu_PKI in component PKA (J_per_mol)"
legend_algebraic[16] = "mu_PKACI in component PKA (J_per_mol)"
legend_algebraic[17] = "mu_ARCI in component PKA (J_per_mol)"
legend_algebraic[18] = "mu_A2RCI in component PKA (J_per_mol)"
legend_algebraic[19] = "mu_CI in component PKA (J_per_mol)"
legend_algebraic[20] = "mu_A2RI in component PKA (J_per_mol)"
legend_algebraic[21] = "mu_PKACI_PKI in component PKA (J_per_mol)"
legend_algebraic[22] = "mu_PKACII in component PKA (J_per_mol)"
legend_algebraic[23] = "mu_ARCII in component PKA (J_per_mol)"
legend_algebraic[24] = "mu_A2RCII in component PKA (J_per_mol)"
legend_algebraic[25] = "mu_CII in component PKA (J_per_mol)"
legend_algebraic[26] = "mu_A2RII in component PKA (J_per_mol)"
legend_algebraic[27] = "mu_PKACII_PKI in component PKA (J_per_mol)"
legend_constants[38] = "F in component constants (C_per_mol)"
legend_rates[0] = "d/dt q_cAMP in component PKA (fmol)"
legend_rates[1] = "d/dt q_PKI in component PKA (fmol)"
legend_rates[2] = "d/dt q_PKACI in component PKA (fmol)"
legend_rates[3] = "d/dt q_ARCI in component PKA (fmol)"
legend_rates[4] = "d/dt q_A2RCI in component PKA (fmol)"
legend_rates[5] = "d/dt q_CI in component PKA (fmol)"
legend_rates[6] = "d/dt q_A2RI in component PKA (fmol)"
legend_rates[7] = "d/dt q_PKACI_PKI in component PKA (fmol)"
legend_rates[8] = "d/dt q_PKACII in component PKA (fmol)"
legend_rates[9] = "d/dt q_ARCII in component PKA (fmol)"
legend_rates[10] = "d/dt q_A2RCII in component PKA (fmol)"
legend_rates[11] = "d/dt q_CII in component PKA (fmol)"
legend_rates[12] = "d/dt q_A2RII in component PKA (fmol)"
legend_rates[13] = "d/dt q_PKACII_PKI in component PKA (fmol)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 3.212E-02
constants[1] = 6.840E-03
constants[2] = 2.242E-02
constants[3] = 3.800E-15
constants[4] = 3.800E-15
constants[5] = 3.800E-15
constants[6] = 3.800E-15
constants[7] = 3.800E-15
constants[8] = 9.500E-04
constants[9] = 3.800E-15
constants[10] = 3.800E-15
constants[11] = 3.800E-15
constants[12] = 3.800E-15
constants[13] = 3.800E-15
states[0] = 1e-16
states[1] = 1e-16
states[2] = 1e-16
states[3] = 1e-16
states[4] = 1e-16
states[5] = 1e-16
states[6] = 1e-16
states[7] = 1e-16
states[8] = 1e-16
states[9] = 1e-16
states[10] = 1e-16
states[11] = 1e-16
states[12] = 1e-16
states[13] = 1e-16
constants[14] = 48.0417
constants[15] = 21.1895
constants[16] = 4.84331
constants[17] = 149.139
constants[18] = 48.0417
constants[19] = 21.1895
constants[20] = 4.84331
constants[21] = 149.139
constants[22] = 0.0401879
constants[23] = 14.3814
constants[24] = 0.0478876
constants[25] = 0.605095
constants[26] = 1.3719
constants[27] = 1.96997
constants[28] = 0.0885687
constants[29] = 0.194918
constants[30] = 0.0478876
constants[31] = 0.605095
constants[32] = 1.3719
constants[33] = 1.96997
constants[34] = 0.0885687
constants[35] = 0.194918
constants[36] = 8.31
constants[37] = 310
constants[38] = 96485
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[0] = states[0]+constants[0]
algebraic[14] = constants[36]*constants[37]*log(constants[22]*algebraic[0])
algebraic[2] = states[2]+constants[2]
algebraic[16] = constants[36]*constants[37]*log(constants[24]*algebraic[2])
algebraic[3] = states[3]+constants[3]
algebraic[17] = constants[36]*constants[37]*log(constants[25]*algebraic[3])
algebraic[28] = constants[14]*(exp((algebraic[16]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[17]/(constants[36]*constants[37])))
rates[2] = -algebraic[28]
algebraic[4] = states[4]+constants[4]
algebraic[18] = constants[36]*constants[37]*log(constants[26]*algebraic[4])
algebraic[29] = constants[15]*(exp((algebraic[17]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[18]/(constants[36]*constants[37])))
rates[3] = algebraic[28]-algebraic[29]
algebraic[5] = states[5]+constants[5]
algebraic[19] = constants[36]*constants[37]*log(constants[27]*algebraic[5])
algebraic[6] = states[6]+constants[6]
algebraic[20] = constants[36]*constants[37]*log(constants[28]*algebraic[6])
algebraic[30] = constants[16]*(exp(algebraic[18]/(constants[36]*constants[37]))-exp((algebraic[20]+algebraic[19])/(constants[36]*constants[37])))
rates[4] = algebraic[29]-algebraic[30]
rates[6] = algebraic[30]
algebraic[1] = states[1]+constants[1]
algebraic[15] = constants[36]*constants[37]*log(constants[23]*algebraic[1])
algebraic[7] = states[7]+constants[7]
algebraic[21] = constants[36]*constants[37]*log(constants[29]*algebraic[7])
algebraic[31] = constants[17]*(exp((algebraic[19]+algebraic[15])/(constants[36]*constants[37]))-exp(algebraic[21]/(constants[36]*constants[37])))
rates[5] = algebraic[30]-algebraic[31]
rates[7] = algebraic[31]
algebraic[8] = states[8]+constants[8]
algebraic[22] = constants[36]*constants[37]*log(constants[30]*algebraic[8])
algebraic[9] = states[9]+constants[9]
algebraic[23] = constants[36]*constants[37]*log(constants[31]*algebraic[9])
algebraic[32] = constants[18]*(exp((algebraic[22]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[23]/(constants[36]*constants[37])))
rates[8] = -algebraic[32]
algebraic[10] = states[10]+constants[10]
algebraic[24] = constants[36]*constants[37]*log(constants[32]*algebraic[10])
algebraic[33] = constants[19]*(exp((algebraic[23]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[24]/(constants[36]*constants[37])))
rates[0] = ((-algebraic[28]-algebraic[29])-algebraic[32])-algebraic[33]
rates[9] = algebraic[32]-algebraic[33]
algebraic[11] = states[11]+constants[11]
algebraic[25] = constants[36]*constants[37]*log(constants[33]*algebraic[11])
algebraic[12] = states[12]+constants[12]
algebraic[26] = constants[36]*constants[37]*log(constants[34]*algebraic[12])
algebraic[34] = constants[20]*(exp(algebraic[24]/(constants[36]*constants[37]))-exp((algebraic[26]+algebraic[25])/(constants[36]*constants[37])))
rates[10] = algebraic[33]-algebraic[34]
rates[12] = algebraic[34]
algebraic[13] = states[13]+constants[13]
algebraic[27] = constants[36]*constants[37]*log(constants[35]*algebraic[13])
algebraic[35] = constants[21]*(exp((algebraic[25]+algebraic[15])/(constants[36]*constants[37]))-exp(algebraic[27]/(constants[36]*constants[37])))
rates[1] = -algebraic[31]-algebraic[35]
rates[11] = algebraic[34]-algebraic[35]
rates[13] = algebraic[35]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = states[0]+constants[0]
algebraic[14] = constants[36]*constants[37]*log(constants[22]*algebraic[0])
algebraic[2] = states[2]+constants[2]
algebraic[16] = constants[36]*constants[37]*log(constants[24]*algebraic[2])
algebraic[3] = states[3]+constants[3]
algebraic[17] = constants[36]*constants[37]*log(constants[25]*algebraic[3])
algebraic[28] = constants[14]*(exp((algebraic[16]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[17]/(constants[36]*constants[37])))
algebraic[4] = states[4]+constants[4]
algebraic[18] = constants[36]*constants[37]*log(constants[26]*algebraic[4])
algebraic[29] = constants[15]*(exp((algebraic[17]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[18]/(constants[36]*constants[37])))
algebraic[5] = states[5]+constants[5]
algebraic[19] = constants[36]*constants[37]*log(constants[27]*algebraic[5])
algebraic[6] = states[6]+constants[6]
algebraic[20] = constants[36]*constants[37]*log(constants[28]*algebraic[6])
algebraic[30] = constants[16]*(exp(algebraic[18]/(constants[36]*constants[37]))-exp((algebraic[20]+algebraic[19])/(constants[36]*constants[37])))
algebraic[1] = states[1]+constants[1]
algebraic[15] = constants[36]*constants[37]*log(constants[23]*algebraic[1])
algebraic[7] = states[7]+constants[7]
algebraic[21] = constants[36]*constants[37]*log(constants[29]*algebraic[7])
algebraic[31] = constants[17]*(exp((algebraic[19]+algebraic[15])/(constants[36]*constants[37]))-exp(algebraic[21]/(constants[36]*constants[37])))
algebraic[8] = states[8]+constants[8]
algebraic[22] = constants[36]*constants[37]*log(constants[30]*algebraic[8])
algebraic[9] = states[9]+constants[9]
algebraic[23] = constants[36]*constants[37]*log(constants[31]*algebraic[9])
algebraic[32] = constants[18]*(exp((algebraic[22]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[23]/(constants[36]*constants[37])))
algebraic[10] = states[10]+constants[10]
algebraic[24] = constants[36]*constants[37]*log(constants[32]*algebraic[10])
algebraic[33] = constants[19]*(exp((algebraic[23]+algebraic[14])/(constants[36]*constants[37]))-exp(algebraic[24]/(constants[36]*constants[37])))
algebraic[11] = states[11]+constants[11]
algebraic[25] = constants[36]*constants[37]*log(constants[33]*algebraic[11])
algebraic[12] = states[12]+constants[12]
algebraic[26] = constants[36]*constants[37]*log(constants[34]*algebraic[12])
algebraic[34] = constants[20]*(exp(algebraic[24]/(constants[36]*constants[37]))-exp((algebraic[26]+algebraic[25])/(constants[36]*constants[37])))
algebraic[13] = states[13]+constants[13]
algebraic[27] = constants[36]*constants[37]*log(constants[35]*algebraic[13])
algebraic[35] = constants[21]*(exp((algebraic[25]+algebraic[15])/(constants[36]*constants[37]))-exp(algebraic[27]/(constants[36]*constants[37])))
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)