Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 20
sizeStates = 4
sizeConstants = 48
from math import *
from numpy import *
def createLegends():
legend_states = [""] * sizeStates
legend_rates = [""] * sizeStates
legend_algebraic = [""] * sizeAlgebraic
legend_voi = ""
legend_constants = [""] * sizeConstants
legend_voi = "t in component BG_Hpump (second)"
legend_constants[0] = "R in component params_BG (J_per_K_mol)"
legend_constants[1] = "T in component params_BG (kelvin)"
legend_constants[2] = "F in component params_BG (C_per_mol)"
legend_constants[3] = "K_Hi in component params_BG (per_fmol)"
legend_constants[36] = "q_init_Hi in component params_BG (fmol)"
legend_constants[4] = "K_Ho in component params_BG (per_fmol)"
legend_constants[33] = "q_init_Ho in component params_BG (fmol)"
legend_constants[5] = "K_Pi in component params_BG (per_fmol)"
legend_constants[39] = "q_init_Pi in component params_BG (fmol)"
legend_constants[6] = "K_ATPi in component params_BG (per_fmol)"
legend_constants[42] = "q_init_ATPi in component params_BG (fmol)"
legend_constants[7] = "K_ADPi in component params_BG (per_fmol)"
legend_constants[45] = "q_init_ADPi in component params_BG (fmol)"
legend_constants[8] = "K_1 in component params_BG (per_fmol)"
legend_constants[9] = "q_init_1 in component params_BG (fmol)"
legend_constants[10] = "K_2 in component params_BG (per_fmol)"
legend_constants[11] = "q_init_2 in component params_BG (fmol)"
legend_constants[12] = "K_3 in component params_BG (per_fmol)"
legend_constants[13] = "q_init_3 in component params_BG (fmol)"
legend_constants[14] = "K_4 in component params_BG (per_fmol)"
legend_constants[15] = "q_init_4 in component params_BG (fmol)"
legend_constants[16] = "kappa_r1 in component params_BG (fmol_per_s)"
legend_constants[17] = "kappa_r2 in component params_BG (fmol_per_s)"
legend_constants[18] = "kappa_r3 in component params_BG (fmol_per_s)"
legend_constants[19] = "kappa_r4 in component params_BG (fmol_per_s)"
legend_constants[38] = "mu_Hi in component BG_Hpump (J_per_mol)"
legend_constants[35] = "mu_Ho in component BG_Hpump (J_per_mol)"
legend_constants[41] = "mu_Pi in component BG_Hpump (J_per_mol)"
legend_constants[44] = "mu_ATPi in component BG_Hpump (J_per_mol)"
legend_constants[47] = "mu_ADPi in component BG_Hpump (J_per_mol)"
legend_algebraic[0] = "mu_1 in component BG_Hpump (J_per_mol)"
legend_algebraic[18] = "v_1 in component BG_Hpump (fmol_per_s)"
legend_algebraic[1] = "mu_2 in component BG_Hpump (J_per_mol)"
legend_algebraic[10] = "v_2 in component BG_Hpump (fmol_per_s)"
legend_algebraic[2] = "mu_3 in component BG_Hpump (J_per_mol)"
legend_algebraic[14] = "v_3 in component BG_Hpump (fmol_per_s)"
legend_algebraic[3] = "mu_4 in component BG_Hpump (J_per_mol)"
legend_algebraic[19] = "v_4 in component BG_Hpump (fmol_per_s)"
legend_algebraic[4] = "A_f_r1 in component BG_Hpump (J_per_mol)"
legend_algebraic[6] = "v_r1 in component BG_Hpump (fmol_per_s)"
legend_algebraic[5] = "A_r_r1 in component BG_Hpump (J_per_mol)"
legend_algebraic[7] = "A_f_r2 in component BG_Hpump (J_per_mol)"
legend_algebraic[9] = "v_r2 in component BG_Hpump (fmol_per_s)"
legend_algebraic[8] = "A_r_r2 in component BG_Hpump (J_per_mol)"
legend_algebraic[11] = "A_f_r3 in component BG_Hpump (J_per_mol)"
legend_algebraic[13] = "v_r3 in component BG_Hpump (fmol_per_s)"
legend_algebraic[12] = "A_r_r3 in component BG_Hpump (J_per_mol)"
legend_algebraic[15] = "A_f_r4 in component BG_Hpump (J_per_mol)"
legend_algebraic[17] = "v_r4 in component BG_Hpump (fmol_per_s)"
legend_algebraic[16] = "A_r_r4 in component BG_Hpump (J_per_mol)"
legend_constants[37] = "q_Hi in component BG_Hpump (fmol)"
legend_constants[34] = "q_Ho in component BG_Hpump (fmol)"
legend_constants[40] = "q_Pi in component BG_Hpump (fmol)"
legend_constants[43] = "q_ATPi in component BG_Hpump (fmol)"
legend_constants[46] = "q_ADPi in component BG_Hpump (fmol)"
legend_states[0] = "q_1 in component BG_Hpump (fmol)"
legend_states[1] = "q_2 in component BG_Hpump (fmol)"
legend_states[2] = "q_3 in component BG_Hpump (fmol)"
legend_states[3] = "q_4 in component BG_Hpump (fmol)"
legend_constants[20] = "z_zr1 in component params_BG (dimensionless)"
legend_constants[21] = "z_zr2 in component params_BG (dimensionless)"
legend_constants[31] = "mu_zr1 in component BG_Hpump (J_per_mol)"
legend_constants[32] = "mu_zr2 in component BG_Hpump (J_per_mol)"
legend_constants[30] = "V_Vm in component BG_Hpump (volt)"
legend_constants[22] = "V_E in component params_BG (volt)"
legend_constants[23] = "V_i in component params_BG (pL)"
legend_constants[24] = "H_i in component params_BG (mM)"
legend_constants[25] = "H_o in component params_BG (mM)"
legend_constants[26] = "Pi_i in component params_BG (mM)"
legend_constants[27] = "ATP_i in component params_BG (mM)"
legend_constants[28] = "ADP_i in component params_BG (mM)"
legend_constants[29] = "V_o in component params_BG (pL)"
legend_rates[0] = "d/dt q_1 in component BG_Hpump (fmol)"
legend_rates[1] = "d/dt q_2 in component BG_Hpump (fmol)"
legend_rates[2] = "d/dt q_3 in component BG_Hpump (fmol)"
legend_rates[3] = "d/dt q_4 in component BG_Hpump (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] = 96485
constants[3] = 1
constants[4] = 1
constants[5] = 1
constants[6] = 1
constants[7] = 1
constants[8] = 1
constants[9] = 1
constants[10] = 1
constants[11] = 1
constants[12] = 1
constants[13] = 1
constants[14] = 1
constants[15] = 1
constants[16] = 1
constants[17] = 1
constants[18] = 1
constants[19] = 1
constants[20] = 1
constants[21] = 1
constants[22] = -0.05
constants[23] = 0.09
constants[24] = 1
constants[25] = 1e-5
constants[26] = 1e-5
constants[27] = 1e-5
constants[28] = 1e-5
constants[29] = 0.09
constants[30] = constants[22]
constants[31] = constants[20]*constants[2]*constants[30]
constants[32] = constants[21]*constants[2]*constants[30]
constants[33] = constants[25]*constants[29]
constants[34] = constants[33]
constants[35] = constants[0]*constants[1]*log(constants[4]*constants[34])
constants[36] = constants[24]*constants[23]
constants[37] = constants[36]
constants[38] = constants[0]*constants[1]*log(constants[3]*constants[37])
constants[39] = constants[26]*constants[23]
constants[40] = constants[39]
constants[41] = constants[0]*constants[1]*log(constants[5]*constants[40])
constants[42] = constants[27]*constants[23]
constants[43] = constants[42]
constants[44] = constants[0]*constants[1]*log(constants[6]*constants[43])
constants[45] = constants[28]*constants[23]
constants[46] = constants[45]
constants[47] = constants[0]*constants[1]*log(constants[7]*constants[46])
states[0] = constants[9]
states[1] = constants[11]
states[2] = constants[13]
states[3] = constants[15]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[0] = constants[0]*constants[1]*log(constants[8]*states[0])
algebraic[4] = algebraic[0]
algebraic[1] = constants[0]*constants[1]*log(constants[10]*states[1])
algebraic[5] = algebraic[1]+constants[41]
algebraic[6] = constants[16]*(exp(algebraic[4]/(constants[0]*constants[1]))-exp(algebraic[5]/(constants[0]*constants[1])))
algebraic[7] = algebraic[1]+constants[44]
algebraic[2] = constants[0]*constants[1]*log(constants[12]*states[2])
algebraic[8] = algebraic[2]
algebraic[9] = constants[17]*(exp(algebraic[7]/(constants[0]*constants[1]))-exp(algebraic[8]/(constants[0]*constants[1])))
algebraic[10] = algebraic[6]-algebraic[9]
rates[1] = algebraic[10]
algebraic[11] = algebraic[2]+constants[38]
algebraic[3] = constants[0]*constants[1]*log(constants[14]*states[3])
algebraic[12] = algebraic[3]+constants[47]+constants[31]
algebraic[13] = constants[18]*(exp(algebraic[11]/(constants[0]*constants[1]))-exp(algebraic[12]/(constants[0]*constants[1])))
algebraic[14] = algebraic[9]-algebraic[13]
rates[2] = algebraic[14]
algebraic[15] = algebraic[3]
algebraic[16] = algebraic[0]+constants[35]+constants[32]
algebraic[17] = constants[19]*(exp(algebraic[15]/(constants[0]*constants[1]))-exp(algebraic[16]/(constants[0]*constants[1])))
algebraic[18] = algebraic[17]-algebraic[6]
rates[0] = algebraic[18]
algebraic[19] = algebraic[13]-algebraic[17]
rates[3] = algebraic[19]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = constants[0]*constants[1]*log(constants[8]*states[0])
algebraic[4] = algebraic[0]
algebraic[1] = constants[0]*constants[1]*log(constants[10]*states[1])
algebraic[5] = algebraic[1]+constants[41]
algebraic[6] = constants[16]*(exp(algebraic[4]/(constants[0]*constants[1]))-exp(algebraic[5]/(constants[0]*constants[1])))
algebraic[7] = algebraic[1]+constants[44]
algebraic[2] = constants[0]*constants[1]*log(constants[12]*states[2])
algebraic[8] = algebraic[2]
algebraic[9] = constants[17]*(exp(algebraic[7]/(constants[0]*constants[1]))-exp(algebraic[8]/(constants[0]*constants[1])))
algebraic[10] = algebraic[6]-algebraic[9]
algebraic[11] = algebraic[2]+constants[38]
algebraic[3] = constants[0]*constants[1]*log(constants[14]*states[3])
algebraic[12] = algebraic[3]+constants[47]+constants[31]
algebraic[13] = constants[18]*(exp(algebraic[11]/(constants[0]*constants[1]))-exp(algebraic[12]/(constants[0]*constants[1])))
algebraic[14] = algebraic[9]-algebraic[13]
algebraic[15] = algebraic[3]
algebraic[16] = algebraic[0]+constants[35]+constants[32]
algebraic[17] = constants[19]*(exp(algebraic[15]/(constants[0]*constants[1]))-exp(algebraic[16]/(constants[0]*constants[1])))
algebraic[18] = algebraic[17]-algebraic[6]
algebraic[19] = algebraic[13]-algebraic[17]
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)