Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 40
sizeStates = 11
sizeConstants = 24
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 environment (second)"
legend_constants[0] = "R in component environment (J_per_K_per_mol)"
legend_constants[1] = "T in component environment (kelvin)"
legend_constants[2] = "F in component environment (C_per_mol)"
legend_constants[3] = "C_m in component environment (fF)"
legend_states[0] = "q_Ca_o in component environment (fmol)"
legend_states[1] = "q_Ca_i in component environment (fmol)"
legend_states[2] = "q_Na_o in component environment (fmol)"
legend_states[3] = "q_Na_i in component environment (fmol)"
legend_states[4] = "q_P1_NCX in component environment (fmol)"
legend_states[5] = "q_P2_NCX in component environment (fmol)"
legend_states[6] = "q_P3_NCX in component environment (fmol)"
legend_states[7] = "q_P4_NCX in component environment (fmol)"
legend_states[8] = "q_P5_NCX in component environment (fmol)"
legend_states[9] = "q_P6_NCX in component environment (fmol)"
legend_algebraic[29] = "v_Ca_o_NCX in component NCX (fmol_per_sec)"
legend_algebraic[22] = "v_Ca_i_NCX in component NCX (fmol_per_sec)"
legend_algebraic[33] = "v_Na_o_NCX in component NCX (fmol_per_sec)"
legend_algebraic[19] = "v_Na_i_NCX in component NCX (fmol_per_sec)"
legend_states[10] = "q_mem in component environment (fC)"
legend_algebraic[37] = "I_mem_NCX in component NCX (fA)"
legend_constants[4] = "kappa_1_NCX in component NCX_parameters (fmol_per_sec)"
legend_constants[5] = "kappa_2_NCX in component NCX_parameters (fmol_per_sec)"
legend_constants[6] = "kappa_3_NCX in component NCX_parameters (fmol_per_sec)"
legend_constants[7] = "kappa_4_NCX in component NCX_parameters (fmol_per_sec)"
legend_constants[8] = "kappa_5_NCX in component NCX_parameters (fmol_per_sec)"
legend_constants[9] = "kappa_6_NCX in component NCX_parameters (fmol_per_sec)"
legend_constants[10] = "K_1_NCX in component NCX_parameters (per_fmol)"
legend_constants[11] = "K_2_NCX in component NCX_parameters (per_fmol)"
legend_constants[12] = "K_3_NCX in component NCX_parameters (per_fmol)"
legend_constants[13] = "K_4_NCX in component NCX_parameters (per_fmol)"
legend_constants[14] = "K_5_NCX in component NCX_parameters (per_fmol)"
legend_constants[15] = "K_6_NCX in component NCX_parameters (per_fmol)"
legend_constants[16] = "K_Na_i in component NCX_parameters (per_fmol)"
legend_constants[17] = "K_Ca_i in component NCX_parameters (per_fmol)"
legend_constants[18] = "K_Na_o in component NCX_parameters (per_fmol)"
legend_constants[19] = "K_Ca_o in component NCX_parameters (per_fmol)"
legend_constants[20] = "nNa_o_NCX in component NCX_parameters (dimensionless)"
legend_constants[21] = "nNa_i_NCX in component NCX_parameters (dimensionless)"
legend_constants[22] = "zf_NCX in component NCX_parameters (dimensionless)"
legend_constants[23] = "zr_NCX in component NCX_parameters (dimensionless)"
legend_algebraic[1] = "mu_Ca_o in component NCX (J_per_mol)"
legend_algebraic[2] = "mu_Ca_i in component NCX (J_per_mol)"
legend_algebraic[3] = "mu_Na_o in component NCX (J_per_mol)"
legend_algebraic[4] = "mu_Na_i in component NCX (J_per_mol)"
legend_algebraic[5] = "mu_P1_NCX in component NCX (J_per_mol)"
legend_algebraic[6] = "mu_P2_NCX in component NCX (J_per_mol)"
legend_algebraic[7] = "mu_P3_NCX in component NCX (J_per_mol)"
legend_algebraic[8] = "mu_P4_NCX in component NCX (J_per_mol)"
legend_algebraic[9] = "mu_P5_NCX in component NCX (J_per_mol)"
legend_algebraic[10] = "mu_P6_NCX in component NCX (J_per_mol)"
legend_algebraic[38] = "v_P1_NCX in component NCX (fmol_per_sec)"
legend_algebraic[23] = "v_P2_NCX in component NCX (fmol_per_sec)"
legend_algebraic[26] = "v_P3_NCX in component NCX (fmol_per_sec)"
legend_algebraic[30] = "v_P4_NCX in component NCX (fmol_per_sec)"
legend_algebraic[35] = "v_P5_NCX in component NCX (fmol_per_sec)"
legend_algebraic[39] = "v_P6_NCX in component NCX (fmol_per_sec)"
legend_algebraic[11] = "Af_r1 in component NCX (J_per_mol)"
legend_algebraic[17] = "Ar_r1 in component NCX (J_per_mol)"
legend_algebraic[18] = "v_r1 in component NCX (fmol_per_sec)"
legend_algebraic[12] = "Af_r2 in component NCX (J_per_mol)"
legend_algebraic[20] = "Ar_r2 in component NCX (J_per_mol)"
legend_algebraic[21] = "v_r2 in component NCX (fmol_per_sec)"
legend_algebraic[13] = "Af_r3 in component NCX (J_per_mol)"
legend_algebraic[24] = "Ar_r3 in component NCX (J_per_mol)"
legend_algebraic[25] = "v_r3 in component NCX (fmol_per_sec)"
legend_algebraic[14] = "Af_r4 in component NCX (J_per_mol)"
legend_algebraic[27] = "Ar_r4 in component NCX (J_per_mol)"
legend_algebraic[28] = "v_r4 in component NCX (fmol_per_sec)"
legend_algebraic[15] = "Af_r5 in component NCX (J_per_mol)"
legend_algebraic[31] = "Ar_r5 in component NCX (J_per_mol)"
legend_algebraic[32] = "v_r5 in component NCX (fmol_per_sec)"
legend_algebraic[16] = "Af_r6 in component NCX (J_per_mol)"
legend_algebraic[34] = "Ar_r6 in component NCX (J_per_mol)"
legend_algebraic[36] = "v_r6 in component NCX (fmol_per_sec)"
legend_algebraic[0] = "V_mem in component NCX (volt)"
legend_rates[0] = "d/dt q_Ca_o in component environment (fmol)"
legend_rates[1] = "d/dt q_Ca_i in component environment (fmol)"
legend_rates[2] = "d/dt q_Na_o in component environment (fmol)"
legend_rates[3] = "d/dt q_Na_i in component environment (fmol)"
legend_rates[10] = "d/dt q_mem in component environment (fC)"
legend_rates[4] = "d/dt q_P1_NCX in component environment (fmol)"
legend_rates[5] = "d/dt q_P2_NCX in component environment (fmol)"
legend_rates[6] = "d/dt q_P3_NCX in component environment (fmol)"
legend_rates[7] = "d/dt q_P4_NCX in component environment (fmol)"
legend_rates[8] = "d/dt q_P5_NCX in component environment (fmol)"
legend_rates[9] = "d/dt q_P6_NCX in component environment (fmol)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 8.314
constants[1] = 310
constants[2] = 96485
constants[3] = 153400
states[0] = 9.3276
states[1] = 0.00456
states[2] = 725.48
states[3] = 380
states[4] = 0.000103509
states[5] = 0.000103509
states[6] = 0.000103509
states[7] = 0.000103509
states[8] = 0.000103509
states[9] = 0.000103509
states[10] = -13039
constants[4] = 417309
constants[5] = 1.39522e+07
constants[6] = 472.755
constants[7] = 1.39522e+07
constants[8] = 417309
constants[9] = 0.370405
constants[10] = 2.93394e+08
constants[11] = 14.1045
constants[12] = 263471
constants[13] = 2.39875e+06
constants[14] = 2373.73
constants[15] = 956.214
constants[16] = 0.0137751
constants[17] = 10.2446
constants[18] = 0.470129
constants[19] = 7572.91
constants[20] = 3
constants[21] = 3
constants[22] = -0.55679
constants[23] = 0.44321
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[5] = constants[0]*constants[1]*log(constants[10]*states[4])
algebraic[11] = algebraic[5]
algebraic[4] = constants[0]*constants[1]*log(constants[16]*states[3])
algebraic[6] = constants[0]*constants[1]*log(constants[11]*states[5])
algebraic[17] = constants[21]*algebraic[4]+algebraic[6]
algebraic[18] = constants[4]*(exp(algebraic[11]/(constants[0]*constants[1]))-exp(algebraic[17]/(constants[0]*constants[1])))
algebraic[19] = constants[21]*algebraic[18]
rates[3] = algebraic[19]
algebraic[2] = constants[0]*constants[1]*log(constants[17]*states[1])
algebraic[12] = algebraic[6]+algebraic[2]
algebraic[7] = constants[0]*constants[1]*log(constants[12]*states[6])
algebraic[20] = algebraic[7]
algebraic[21] = constants[5]*(exp(algebraic[12]/(constants[0]*constants[1]))-exp(algebraic[20]/(constants[0]*constants[1])))
algebraic[22] = -algebraic[21]
rates[1] = algebraic[22]
algebraic[23] = algebraic[18]-algebraic[21]
rates[5] = algebraic[23]
algebraic[13] = algebraic[7]
algebraic[8] = constants[0]*constants[1]*log(constants[13]*states[7])
algebraic[24] = algebraic[8]
algebraic[25] = constants[6]*(exp(algebraic[13]/(constants[0]*constants[1]))-exp(algebraic[24]/(constants[0]*constants[1])))
algebraic[26] = algebraic[21]-algebraic[25]
rates[6] = algebraic[26]
algebraic[14] = algebraic[8]
algebraic[1] = constants[0]*constants[1]*log(constants[19]*states[0])
algebraic[9] = constants[0]*constants[1]*log(constants[14]*states[8])
algebraic[27] = algebraic[9]+algebraic[1]
algebraic[28] = constants[7]*(exp(algebraic[14]/(constants[0]*constants[1]))-exp(algebraic[27]/(constants[0]*constants[1])))
algebraic[29] = algebraic[28]
rates[0] = algebraic[29]
algebraic[30] = -algebraic[28]+algebraic[25]
rates[7] = algebraic[30]
algebraic[3] = constants[0]*constants[1]*log(constants[18]*states[2])
algebraic[15] = algebraic[9]+constants[20]*algebraic[3]
algebraic[10] = constants[0]*constants[1]*log(constants[15]*states[9])
algebraic[31] = algebraic[10]
algebraic[32] = constants[8]*(exp(algebraic[15]/(constants[0]*constants[1]))-exp(algebraic[31]/(constants[0]*constants[1])))
algebraic[33] = -constants[20]*algebraic[32]
rates[2] = algebraic[33]
algebraic[35] = -algebraic[32]+algebraic[28]
rates[8] = algebraic[35]
algebraic[0] = states[10]/constants[3]
algebraic[16] = constants[0]*constants[1]*log(constants[15]*states[9])+constants[22]*constants[2]*algebraic[0]
algebraic[34] = constants[0]*constants[1]*log(constants[10]*states[4])+constants[23]*constants[2]*algebraic[0]
algebraic[36] = constants[9]*(exp(algebraic[16]/(constants[0]*constants[1]))-exp(algebraic[34]/(constants[0]*constants[1])))
algebraic[37] = constants[2]*(-constants[22]*algebraic[36]+constants[23]*algebraic[36])
rates[10] = algebraic[37]
algebraic[38] = algebraic[36]-algebraic[18]
rates[4] = algebraic[38]
algebraic[39] = -algebraic[36]+algebraic[32]
rates[9] = algebraic[39]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[5] = constants[0]*constants[1]*log(constants[10]*states[4])
algebraic[11] = algebraic[5]
algebraic[4] = constants[0]*constants[1]*log(constants[16]*states[3])
algebraic[6] = constants[0]*constants[1]*log(constants[11]*states[5])
algebraic[17] = constants[21]*algebraic[4]+algebraic[6]
algebraic[18] = constants[4]*(exp(algebraic[11]/(constants[0]*constants[1]))-exp(algebraic[17]/(constants[0]*constants[1])))
algebraic[19] = constants[21]*algebraic[18]
algebraic[2] = constants[0]*constants[1]*log(constants[17]*states[1])
algebraic[12] = algebraic[6]+algebraic[2]
algebraic[7] = constants[0]*constants[1]*log(constants[12]*states[6])
algebraic[20] = algebraic[7]
algebraic[21] = constants[5]*(exp(algebraic[12]/(constants[0]*constants[1]))-exp(algebraic[20]/(constants[0]*constants[1])))
algebraic[22] = -algebraic[21]
algebraic[23] = algebraic[18]-algebraic[21]
algebraic[13] = algebraic[7]
algebraic[8] = constants[0]*constants[1]*log(constants[13]*states[7])
algebraic[24] = algebraic[8]
algebraic[25] = constants[6]*(exp(algebraic[13]/(constants[0]*constants[1]))-exp(algebraic[24]/(constants[0]*constants[1])))
algebraic[26] = algebraic[21]-algebraic[25]
algebraic[14] = algebraic[8]
algebraic[1] = constants[0]*constants[1]*log(constants[19]*states[0])
algebraic[9] = constants[0]*constants[1]*log(constants[14]*states[8])
algebraic[27] = algebraic[9]+algebraic[1]
algebraic[28] = constants[7]*(exp(algebraic[14]/(constants[0]*constants[1]))-exp(algebraic[27]/(constants[0]*constants[1])))
algebraic[29] = algebraic[28]
algebraic[30] = -algebraic[28]+algebraic[25]
algebraic[3] = constants[0]*constants[1]*log(constants[18]*states[2])
algebraic[15] = algebraic[9]+constants[20]*algebraic[3]
algebraic[10] = constants[0]*constants[1]*log(constants[15]*states[9])
algebraic[31] = algebraic[10]
algebraic[32] = constants[8]*(exp(algebraic[15]/(constants[0]*constants[1]))-exp(algebraic[31]/(constants[0]*constants[1])))
algebraic[33] = -constants[20]*algebraic[32]
algebraic[35] = -algebraic[32]+algebraic[28]
algebraic[0] = states[10]/constants[3]
algebraic[16] = constants[0]*constants[1]*log(constants[15]*states[9])+constants[22]*constants[2]*algebraic[0]
algebraic[34] = constants[0]*constants[1]*log(constants[10]*states[4])+constants[23]*constants[2]*algebraic[0]
algebraic[36] = constants[9]*(exp(algebraic[16]/(constants[0]*constants[1]))-exp(algebraic[34]/(constants[0]*constants[1])))
algebraic[37] = constants[2]*(-constants[22]*algebraic[36]+constants[23]*algebraic[36])
algebraic[38] = algebraic[36]-algebraic[18]
algebraic[39] = -algebraic[36]+algebraic[32]
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)