Generated Code
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# Size of variable arrays:
sizeAlgebraic = 23
sizeStates = 4
sizeConstants = 26
from math import *
from numpy import *
def createLegends():
legend_states = [""] * sizeStates
legend_rates = [""] * sizeStates
legend_algebraic = [""] * sizeAlgebraic
legend_voi = ""
legend_constants = [""] * sizeConstants
legend_constants[0] = "R in component params_BG (J_per_K_mol)"
legend_constants[1] = "T in component params_BG (kelvin)"
legend_constants[2] = "K_Ai in component params_BG (per_fmol)"
legend_constants[21] = "q_init_Ai in component params_BG (fmol)"
legend_constants[3] = "K_Ao in component params_BG (per_fmol)"
legend_constants[20] = "q_init_Ao in component params_BG (fmol)"
legend_constants[4] = "K_1 in component params_BG (per_fmol)"
legend_constants[5] = "q_init_1 in component params_BG (fmol)"
legend_constants[6] = "K_2 in component params_BG (per_fmol)"
legend_constants[7] = "q_init_2 in component params_BG (fmol)"
legend_constants[8] = "K_3 in component params_BG (per_fmol)"
legend_constants[9] = "q_init_3 in component params_BG (fmol)"
legend_constants[10] = "K_4 in component params_BG (per_fmol)"
legend_constants[11] = "q_init_4 in component params_BG (fmol)"
legend_constants[12] = "kappa_r1 in component params_BG (fmol_per_s)"
legend_constants[13] = "kappa_r2 in component params_BG (fmol_per_s)"
legend_constants[14] = "kappa_r3 in component params_BG (fmol_per_s)"
legend_constants[15] = "kappa_r4 in component params_BG (fmol_per_s)"
legend_constants[16] = "V_i in component params_BG (pL)"
legend_constants[17] = "g_i in component params_BG (mM)"
legend_constants[18] = "g_o in component params_BG (mM)"
legend_constants[19] = "V_o in component params_BG (pL)"
legend_voi = "t in component GLUT2_BG (second)"
legend_constants[23] = "mu_Ai in component GLUT2_BG (J_per_mol)"
legend_algebraic[17] = "v_Ai in component GLUT2_BG (fmol_per_s)"
legend_constants[25] = "mu_Ao in component GLUT2_BG (J_per_mol)"
legend_algebraic[18] = "v_Ao in component GLUT2_BG (fmol_per_s)"
legend_algebraic[0] = "mu_1 in component GLUT2_BG (J_per_mol)"
legend_algebraic[19] = "v_1 in component GLUT2_BG (fmol_per_s)"
legend_algebraic[2] = "mu_2 in component GLUT2_BG (J_per_mol)"
legend_algebraic[20] = "v_2 in component GLUT2_BG (fmol_per_s)"
legend_algebraic[3] = "mu_3 in component GLUT2_BG (J_per_mol)"
legend_algebraic[21] = "v_3 in component GLUT2_BG (fmol_per_s)"
legend_algebraic[4] = "mu_4 in component GLUT2_BG (J_per_mol)"
legend_algebraic[22] = "v_4 in component GLUT2_BG (fmol_per_s)"
legend_algebraic[5] = "A_f_r1 in component GLUT2_BG (J_per_mol)"
legend_algebraic[7] = "v_r1 in component GLUT2_BG (fmol_per_s)"
legend_algebraic[6] = "A_r_r1 in component GLUT2_BG (J_per_mol)"
legend_algebraic[8] = "A_f_r2 in component GLUT2_BG (J_per_mol)"
legend_algebraic[10] = "v_r2 in component GLUT2_BG (fmol_per_s)"
legend_algebraic[9] = "A_r_r2 in component GLUT2_BG (J_per_mol)"
legend_algebraic[11] = "A_f_r3 in component GLUT2_BG (J_per_mol)"
legend_algebraic[15] = "v_r3 in component GLUT2_BG (fmol_per_s)"
legend_algebraic[13] = "A_r_r3 in component GLUT2_BG (J_per_mol)"
legend_algebraic[12] = "A_f_r4 in component GLUT2_BG (J_per_mol)"
legend_algebraic[16] = "v_r4 in component GLUT2_BG (fmol_per_s)"
legend_algebraic[14] = "A_r_r4 in component GLUT2_BG (J_per_mol)"
legend_constants[22] = "q_Ai in component GLUT2_BG (fmol)"
legend_constants[24] = "q_Ao in component GLUT2_BG (fmol)"
legend_states[0] = "q_1 in component GLUT2_BG (fmol)"
legend_states[1] = "q_2 in component GLUT2_BG (fmol)"
legend_states[2] = "q_3 in component GLUT2_BG (fmol)"
legend_states[3] = "q_4 in component GLUT2_BG (fmol)"
legend_algebraic[1] = "q_all in component GLUT2_BG (fmol)"
legend_rates[0] = "d/dt q_1 in component GLUT2_BG (fmol)"
legend_rates[1] = "d/dt q_2 in component GLUT2_BG (fmol)"
legend_rates[2] = "d/dt q_3 in component GLUT2_BG (fmol)"
legend_rates[3] = "d/dt q_4 in component GLUT2_BG (fmol)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 8.31
constants[1] = 273.15
constants[2] = 149.65
constants[3] = 149.65
constants[4] = 33.2
constants[5] = 0.00522328462838574
constants[6] = 4250
constants[7] = 5.63952537547441e-09
constants[8] = 344.59
constants[9] = 0.000689813123835594
constants[10] = 1.99
constants[11] = 0.000886896608254689
constants[12] = 0.36
constants[13] = 0.26
constants[14] = 101000
constants[15] = 10100
constants[16] = 0.09
constants[17] = 5
constants[18] = 5
constants[19] = 0.09
constants[20] = constants[18]*constants[19]
constants[21] = constants[17]*constants[16]
constants[22] = constants[21]
constants[23] = constants[0]*constants[1]*log(constants[2]*constants[22])
constants[24] = constants[20]
constants[25] = constants[0]*constants[1]*log(constants[3]*constants[24])
states[0] = constants[5]
states[1] = constants[7]
states[2] = constants[9]
states[3] = constants[11]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[4] = constants[0]*constants[1]*log(constants[10]*states[3])
algebraic[5] = algebraic[4]
algebraic[0] = constants[0]*constants[1]*log(constants[4]*states[0])
algebraic[6] = algebraic[0]
algebraic[7] = constants[12]*(exp(algebraic[5]/(constants[0]*constants[1]))-exp(algebraic[6]/(constants[0]*constants[1])))
algebraic[11] = constants[25]+algebraic[0]
algebraic[2] = constants[0]*constants[1]*log(constants[6]*states[1])
algebraic[13] = algebraic[2]
algebraic[15] = constants[14]*(exp(algebraic[11]/(constants[0]*constants[1]))-exp(algebraic[13]/(constants[0]*constants[1])))
algebraic[19] = algebraic[7]-algebraic[15]
rates[0] = algebraic[19]
algebraic[8] = algebraic[2]
algebraic[3] = constants[0]*constants[1]*log(constants[8]*states[2])
algebraic[9] = algebraic[3]
algebraic[10] = constants[13]*(exp(algebraic[8]/(constants[0]*constants[1]))-exp(algebraic[9]/(constants[0]*constants[1])))
algebraic[20] = algebraic[15]-algebraic[10]
rates[1] = algebraic[20]
algebraic[12] = algebraic[3]
algebraic[14] = constants[23]+algebraic[4]
algebraic[16] = constants[15]*(exp(algebraic[12]/(constants[0]*constants[1]))-exp(algebraic[14]/(constants[0]*constants[1])))
algebraic[21] = algebraic[10]-algebraic[16]
rates[2] = algebraic[21]
algebraic[22] = algebraic[16]-algebraic[7]
rates[3] = algebraic[22]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[4] = constants[0]*constants[1]*log(constants[10]*states[3])
algebraic[5] = algebraic[4]
algebraic[0] = constants[0]*constants[1]*log(constants[4]*states[0])
algebraic[6] = algebraic[0]
algebraic[7] = constants[12]*(exp(algebraic[5]/(constants[0]*constants[1]))-exp(algebraic[6]/(constants[0]*constants[1])))
algebraic[11] = constants[25]+algebraic[0]
algebraic[2] = constants[0]*constants[1]*log(constants[6]*states[1])
algebraic[13] = algebraic[2]
algebraic[15] = constants[14]*(exp(algebraic[11]/(constants[0]*constants[1]))-exp(algebraic[13]/(constants[0]*constants[1])))
algebraic[19] = algebraic[7]-algebraic[15]
algebraic[8] = algebraic[2]
algebraic[3] = constants[0]*constants[1]*log(constants[8]*states[2])
algebraic[9] = algebraic[3]
algebraic[10] = constants[13]*(exp(algebraic[8]/(constants[0]*constants[1]))-exp(algebraic[9]/(constants[0]*constants[1])))
algebraic[20] = algebraic[15]-algebraic[10]
algebraic[12] = algebraic[3]
algebraic[14] = constants[23]+algebraic[4]
algebraic[16] = constants[15]*(exp(algebraic[12]/(constants[0]*constants[1]))-exp(algebraic[14]/(constants[0]*constants[1])))
algebraic[21] = algebraic[10]-algebraic[16]
algebraic[22] = algebraic[16]-algebraic[7]
algebraic[1] = states[0]+states[1]+states[2]+states[3]
algebraic[17] = algebraic[16]
algebraic[18] = -algebraic[15]
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)