Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 3
sizeStates = 13
sizeConstants = 30
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 (minute)"
legend_states[0] = "cAMP in component cAMP (nmol_g)"
legend_constants[0] = "Ko in component cAMP (dimensionless)"
legend_constants[1] = "Ka in component cAMP (per_nanomolar)"
legend_constants[2] = "Kb in component cAMP (per_nanomolar)"
legend_constants[3] = "Kdsm in component cAMP (nmol_g)"
legend_constants[4] = "Vmsm in component cAMP (flux)"
legend_constants[5] = "Vdsm in component cAMP (flux)"
legend_algebraic[0] = "ACTH in component cAMP (picomolar)"
legend_algebraic[1] = "IS in component IS (nmol_g)"
legend_constants[6] = "Crpt in component IS (nmol_g)"
legend_constants[7] = "K in component IS (dimensionless)"
legend_constants[8] = "Kd in component IS (nmol_g)"
legend_constants[9] = "n in component IS (dimensionless)"
legend_states[1] = "V in component V (flux)"
legend_constants[10] = "P in component V (minute_2)"
legend_constants[11] = "Q in component V (first_order_rate_constant)"
legend_states[2] = "W in component W (flux)"
legend_constants[12] = "T in component W (nmol2_min2_g2)"
legend_constants[13] = "U in component W (first_order_rate_constant)"
legend_states[3] = "CHOC in component CHOC (nmol_g)"
legend_constants[14] = "Lmtr in component model_parameters (first_order_rate_constant)"
legend_states[4] = "Kmtr in component Kmtr (first_order_rate_constant)"
legend_states[5] = "CHOM in component CHOM (nmol_g)"
legend_constants[15] = "Kbac in component model_parameters (first_order_rate_constant)"
legend_states[6] = "Kfor in component Kfor (first_order_rate_constant)"
legend_constants[16] = "Kcb in component model_parameters (first_order_rate_constant)"
legend_constants[17] = "Kcf in component model_parameters (first_order_rate_constant)"
legend_states[7] = "CHON in component CHON (nmol_g)"
legend_states[8] = "CHOL in component CHOL (nmol_g)"
legend_constants[18] = "C in component Kmtr (g_nmol_min2)"
legend_constants[19] = "D in component Kmtr (first_order_rate_constant)"
legend_constants[20] = "R in component Kfor (g_nmol_min2)"
legend_constants[21] = "S in component Kfor (first_order_rate_constant)"
legend_constants[22] = "Vm in component model_parameters (flux)"
legend_constants[23] = "Km in component model_parameters (nmol_g)"
legend_states[9] = "PREG in component PREG (nmol_g)"
legend_constants[24] = "Vmptr in component model_parameters (flux)"
legend_constants[25] = "Kmptr in component model_parameters (nmol_g)"
legend_states[10] = "PRO in component PRO (nmol_g)"
legend_constants[26] = "HA in component PRO (dimensionless)"
legend_constants[27] = "AH in component model_parameters (first_order_rate_constant)"
legend_states[11] = "HYPR in component HYPR (nmol_g)"
legend_constants[28] = "HY in component model_parameters (first_order_rate_constant)"
legend_states[12] = "CORT in component CORT (nmol_g)"
legend_constants[29] = "LH in component CORT (first_order_rate_constant)"
legend_algebraic[2] = "LH_CORT in component CORT (flux)"
legend_rates[0] = "d/dt cAMP in component cAMP (nmol_g)"
legend_rates[1] = "d/dt V in component V (flux)"
legend_rates[2] = "d/dt W in component W (flux)"
legend_rates[3] = "d/dt CHOC in component CHOC (nmol_g)"
legend_rates[5] = "d/dt CHOM in component CHOM (nmol_g)"
legend_rates[8] = "d/dt CHOL in component CHOL (nmol_g)"
legend_rates[4] = "d/dt Kmtr in component Kmtr (first_order_rate_constant)"
legend_rates[6] = "d/dt Kfor in component Kfor (first_order_rate_constant)"
legend_rates[7] = "d/dt CHON in component CHON (nmol_g)"
legend_rates[9] = "d/dt PREG in component PREG (nmol_g)"
legend_rates[10] = "d/dt PRO in component PRO (nmol_g)"
legend_rates[11] = "d/dt HYPR in component HYPR (nmol_g)"
legend_rates[12] = "d/dt CORT in component CORT (nmol_g)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 0.95
constants[0] = 0.013
constants[1] = 0.01
constants[2] = 1000.0
constants[3] = 10.0
constants[4] = 6.0
constants[5] = 10.0
constants[6] = 3.0
constants[7] = 80.0
constants[8] = 2.11
constants[9] = 4.0
states[1] = 11.3
constants[10] = 0.052
constants[11] = 0.042
states[2] = 10.0
constants[12] = 8.0
constants[13] = 0.0015
states[3] = 532.0
constants[14] = 1.65
states[4] = 0.446
states[5] = 11.3
constants[15] = 10.0
states[6] = 0.370
constants[16] = 0.01
constants[17] = 0.00033
states[7] = 3.03
states[8] = 3000.0
constants[18] = 6.25
constants[19] = 125.0
constants[20] = 3.0
constants[21] = 76.0
constants[22] = 1890.0
constants[23] = 270.0
states[9] = 6.56
constants[24] = 500.0
constants[25] = 150.0
states[10] = 0.64
constants[26] = 0.5
constants[27] = 16.4
states[11] = 0.64
constants[28] = 16.4
states[12] = 5.2
constants[29] = 0.724
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[2] = constants[12]*(power(states[3], -1.00000))-constants[13]*states[2]
rates[3] = (states[1]+states[2]+constants[14]*states[5])-states[4]*states[3]
rates[5] = (states[4]*states[3]+constants[15]*states[7]+constants[17]*states[8])-(constants[14]*states[5]+constants[16]*states[5]+states[6]*states[5])
rates[8] = constants[16]*states[5]-constants[17]*states[8]
rates[7] = states[6]*states[5]-(constants[15]*states[7]+(constants[22]*states[7])/(constants[23]+states[7]))
rates[9] = (constants[22]*states[7])/(constants[23]+states[7])-(constants[24]*states[9])/(constants[25]+states[9])
rates[10] = constants[26]*((constants[24]*states[9])/(constants[25]+states[9]))-constants[27]*states[10]
rates[11] = constants[27]*states[10]-constants[28]*states[11]
rates[12] = constants[28]*states[11]-constants[29]*states[12]
algebraic[0] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , 10.0000), 12.0000 , greater_equal(voi , 10.0000) & less(voi , 20.0000), 16.0000 , greater_equal(voi , 20.0000) & less(voi , 35.0000), 12.0000 , greater_equal(voi , 35.0000) & less(voi , 45.0000), 16.0000 , True, 12.0000])
rates[0] = (constants[4]*constants[0]*(1.00000+constants[2]*algebraic[0]))/((1.00000+constants[1]*algebraic[0])+constants[0]*(1.00000+constants[2]*algebraic[0]))-(constants[5]*states[0])/(constants[3]+states[0])
algebraic[1] = (constants[7]*constants[6]*(power(states[0], constants[9])))/(power(constants[8], constants[9])+power(states[0], constants[9]))
rates[1] = constants[10]*algebraic[1]-constants[11]*states[1]
rates[4] = constants[18]*algebraic[1]-constants[19]*states[4]
rates[6] = constants[20]*algebraic[1]-constants[21]*states[6]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = custom_piecewise([greater_equal(voi , 0.00000) & less(voi , 10.0000), 12.0000 , greater_equal(voi , 10.0000) & less(voi , 20.0000), 16.0000 , greater_equal(voi , 20.0000) & less(voi , 35.0000), 12.0000 , greater_equal(voi , 35.0000) & less(voi , 45.0000), 16.0000 , True, 12.0000])
algebraic[1] = (constants[7]*constants[6]*(power(states[0], constants[9])))/(power(constants[8], constants[9])+power(states[0], constants[9]))
algebraic[2] = constants[29]*states[12]
return algebraic
def custom_piecewise(cases):
"""Compute result of a piecewise function"""
return select(cases[0::2],cases[1::2])
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)