Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 40
sizeStates = 6
sizeConstants = 57
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_constants[4] = "K_1 in component environment (per_fmol)"
legend_constants[5] = "K_13 in component environment (per_fmol)"
legend_constants[6] = "K_14 in component environment (per_fmol)"
legend_constants[7] = "K_3 in component environment (per_fmol)"
legend_constants[8] = "K_6 in component environment (per_fmol)"
legend_constants[9] = "K_7 in component environment (per_fmol)"
legend_constants[10] = "K_H in component environment (per_fmol)"
legend_constants[11] = "K_Ke in component environment (per_fmol)"
legend_constants[12] = "K_Ki in component environment (per_fmol)"
legend_constants[13] = "K_MgADP in component environment (per_fmol)"
legend_constants[14] = "K_MgATP in component environment (per_fmol)"
legend_constants[15] = "K_Nae in component environment (per_fmol)"
legend_constants[16] = "K_Nai in component environment (per_fmol)"
legend_constants[17] = "K_P in component environment (per_fmol)"
legend_constants[18] = "kappa_1 in component environment (fmol_per_sec)"
legend_constants[19] = "kappa_13 in component environment (fmol_per_sec)"
legend_constants[20] = "kappa_15 in component environment (fmol_per_sec)"
legend_constants[21] = "kappa_3 in component environment (fmol_per_sec)"
legend_constants[22] = "kappa_6 in component environment (fmol_per_sec)"
legend_constants[23] = "kappa_8 in component environment (fmol_per_sec)"
legend_constants[24] = "z_5 in component environment (dimensionless)"
legend_constants[25] = "z_8 in component environment (dimensionless)"
legend_constants[40] = "zF_5 in component environment (C_per_mol)"
legend_constants[41] = "zF_8 in component environment (C_per_mol)"
legend_constants[39] = "x_H in component environment (fmol)"
legend_constants[37] = "x_Ke in component environment (fmol)"
legend_constants[49] = "x_Ki in component environment (fmol)"
legend_constants[52] = "x_MgADP in component environment (fmol)"
legend_constants[38] = "x_MgATP in component environment (fmol)"
legend_constants[35] = "x_Nae in component environment (fmol)"
legend_constants[36] = "x_Nai in component environment (fmol)"
legend_states[0] = "x_P7 in component environment (fmol)"
legend_constants[55] = "x_P_i in component environment (fmol)"
legend_constants[26] = "q_mem in component environment (fC)"
legend_states[1] = "x_P14 in component environment (fmol)"
legend_states[2] = "x_P1 in component environment (fmol)"
legend_states[3] = "x_P3 in component environment (fmol)"
legend_states[4] = "x_P6 in component environment (fmol)"
legend_states[5] = "x_P13 in component environment (fmol)"
legend_algebraic[0] = "x_tot in component environment (fmol)"
legend_constants[27] = "small_C in component environment (mM)"
legend_constants[28] = "W_i in component environment (pL)"
legend_constants[29] = "W_e in component environment (pL)"
legend_constants[30] = "c_Ke in component environment (mM)"
legend_constants[48] = "c_Ki in component environment (mM)"
legend_constants[51] = "c_MgADP in component environment (mM)"
legend_constants[31] = "c_MgATP in component environment (mM)"
legend_constants[32] = "c_Nae in component environment (mM)"
legend_constants[33] = "c_Nai in component environment (mM)"
legend_constants[54] = "c_P_i in component environment (mM)"
legend_constants[34] = "pH in component environment (dimensionless)"
legend_constants[42] = "mu_H in component environment (J_per_mol)"
legend_algebraic[29] = "v_H in component environment (fmol_per_sec)"
legend_constants[43] = "mu_Ke in component environment (J_per_mol)"
legend_algebraic[35] = "v_Ke in component environment (fmol_per_sec)"
legend_constants[50] = "mu_Ki in component environment (J_per_mol)"
legend_algebraic[18] = "v_Ki in component environment (fmol_per_sec)"
legend_constants[53] = "mu_MgADP in component environment (J_per_mol)"
legend_algebraic[14] = "v_MgADP in component environment (fmol_per_sec)"
legend_constants[44] = "mu_MgATP in component environment (J_per_mol)"
legend_algebraic[9] = "v_MgATP in component environment (fmol_per_sec)"
legend_constants[45] = "mu_Nae in component environment (J_per_mol)"
legend_algebraic[36] = "v_Nae in component environment (fmol_per_sec)"
legend_constants[46] = "mu_Nai in component environment (J_per_mol)"
legend_algebraic[23] = "v_Nai in component environment (fmol_per_sec)"
legend_algebraic[1] = "mu_P7 in component environment (J_per_mol)"
legend_algebraic[37] = "v_P7 in component environment (fmol_per_sec)"
legend_constants[56] = "mu_P_i in component environment (J_per_mol)"
legend_algebraic[30] = "v_P_i in component environment (fmol_per_sec)"
legend_constants[47] = "V_mem in component environment (volt)"
legend_algebraic[38] = "I_mem in component environment (fA)"
legend_algebraic[27] = "Af_R13 in component environment (J_per_mol)"
legend_algebraic[4] = "Ar_R13 in component environment (J_per_mol)"
legend_algebraic[28] = "v_R13 in component environment (fmol_per_sec)"
legend_algebraic[5] = "Af_R15 in component environment (J_per_mol)"
legend_algebraic[7] = "Ar_R15 in component environment (J_per_mol)"
legend_algebraic[8] = "v_R15 in component environment (fmol_per_sec)"
legend_algebraic[12] = "Af_R6 in component environment (J_per_mol)"
legend_algebraic[2] = "Ar_R6 in component environment (J_per_mol)"
legend_algebraic[13] = "v_R6 in component environment (fmol_per_sec)"
legend_algebraic[3] = "mu_P14 in component environment (J_per_mol)"
legend_algebraic[31] = "v_P14 in component environment (fmol_per_sec)"
legend_algebraic[6] = "mu_P1 in component environment (J_per_mol)"
legend_algebraic[19] = "v_P1 in component environment (fmol_per_sec)"
legend_algebraic[10] = "mu_P3 in component environment (J_per_mol)"
legend_algebraic[24] = "v_P3 in component environment (fmol_per_sec)"
legend_algebraic[11] = "mu_P6 in component environment (J_per_mol)"
legend_algebraic[25] = "v_P6 in component environment (fmol_per_sec)"
legend_algebraic[15] = "Af_R1 in component environment (J_per_mol)"
legend_algebraic[16] = "Ar_R1 in component environment (J_per_mol)"
legend_algebraic[17] = "v_R1 in component environment (fmol_per_sec)"
legend_algebraic[20] = "Af_R3 in component environment (J_per_mol)"
legend_algebraic[21] = "Ar_R3 in component environment (J_per_mol)"
legend_algebraic[22] = "v_R3 in component environment (fmol_per_sec)"
legend_algebraic[26] = "mu_P13 in component environment (J_per_mol)"
legend_algebraic[39] = "v_P13 in component environment (fmol_per_sec)"
legend_algebraic[32] = "Af_R8 in component environment (J_per_mol)"
legend_algebraic[33] = "Ar_R8 in component environment (J_per_mol)"
legend_algebraic[34] = "v_R8 in component environment (fmol_per_sec)"
legend_rates[0] = "d/dt x_P7 in component environment (fmol)"
legend_rates[1] = "d/dt x_P14 in component environment (fmol)"
legend_rates[2] = "d/dt x_P1 in component environment (fmol)"
legend_rates[3] = "d/dt x_P3 in component environment (fmol)"
legend_rates[4] = "d/dt x_P6 in component environment (fmol)"
legend_rates[5] = "d/dt x_P13 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
constants[4] = 13085378.038167767
constants[5] = 0.6020622798357556
constants[6] = 69.38568269665376
constants[7] = 46.24091666474313
constants[8] = 79.09015560598799
constants[9] = 4239.416835123694
constants[10] = 0.04565
constants[11] = 0.009236
constants[12] = 0.0012595
constants[13] = 7.976e-05
constants[14] = 2.3715
constants[15] = 0.0061242
constants[16] = 0.00083514
constants[17] = 0.04565
constants[18] = 6.973455976480863
constants[19] = 475.81557480252013
constants[20] = 0.035418056157766185
constants[21] = 861399.5138047301
constants[22] = 1.4100547742408052
constants[23] = 2.2855
constants[24] = -0.054951
constants[25] = -0.94505
states[0] = 0.8590
constants[26] = -18408
states[1] = 0.0100192141898171
states[2] = 6.50836196830909e-10
states[3] = 0.00292644413780957
states[4] = 0.0154965229998754
states[5] = 0.112426414453276
constants[27] = 1e-3
constants[28] = 38
constants[29] = 5.182
constants[30] = 5.4
constants[31] = 10
constants[32] = 150
constants[33] = 50
constants[34] = 7.4
constants[35] = constants[32]*constants[29]
constants[36] = constants[33]*constants[28]
constants[37] = constants[30]*constants[29]
constants[38] = constants[31]*constants[28]
constants[39] = (power(10.0000, -constants[34]))*1000.00*constants[28]
constants[40] = constants[24]*constants[2]
constants[41] = constants[25]*constants[2]
constants[42] = constants[0]*constants[1]*log(constants[10]*constants[39])
constants[43] = constants[0]*constants[1]*log(constants[11]*constants[37])
constants[44] = constants[0]*constants[1]*log(constants[14]*constants[38])
constants[45] = constants[0]*constants[1]*log(constants[15]*constants[35])
constants[46] = constants[0]*constants[1]*log(constants[16]*constants[36])
constants[47] = constants[26]/constants[3]
constants[48] = constants[27]
constants[49] = constants[48]*constants[28]
constants[50] = constants[0]*constants[1]*log(constants[12]*constants[49])
constants[51] = constants[27]
constants[52] = constants[51]*constants[28]
constants[53] = constants[0]*constants[1]*log(constants[13]*constants[52])
constants[54] = constants[27]
constants[55] = constants[54]*constants[28]
constants[56] = constants[0]*constants[1]*log(constants[17]*constants[55])
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[3] = constants[0]*constants[1]*log(constants[6]*states[1])
algebraic[5] = algebraic[3]+constants[44]
algebraic[6] = constants[0]*constants[1]*log(constants[4]*states[2])
algebraic[7] = algebraic[6]
algebraic[8] = constants[20]*(exp(algebraic[5]/(constants[0]*constants[1]))-exp(algebraic[7]/(constants[0]*constants[1])))
algebraic[15] = algebraic[6]
algebraic[10] = constants[0]*constants[1]*log(constants[7]*states[3])
algebraic[16] = algebraic[10]+2.00000*constants[50]
algebraic[17] = constants[18]*(exp(algebraic[15]/(constants[0]*constants[1]))-exp(algebraic[16]/(constants[0]*constants[1])))
algebraic[19] = algebraic[8]-algebraic[17]
rates[2] = algebraic[19]
algebraic[20] = algebraic[10]+3.00000*constants[46]
algebraic[11] = constants[0]*constants[1]*log(constants[8]*states[4])
algebraic[21] = constants[40]*constants[47]+algebraic[11]
algebraic[22] = constants[21]*(exp(algebraic[20]/(constants[0]*constants[1]))-exp(algebraic[21]/(constants[0]*constants[1])))
algebraic[24] = algebraic[17]-algebraic[22]
rates[3] = algebraic[24]
algebraic[12] = algebraic[11]
algebraic[1] = constants[0]*constants[1]*log(constants[9]*states[0])
algebraic[2] = algebraic[1]+constants[53]
algebraic[13] = constants[22]*(exp(algebraic[12]/(constants[0]*constants[1]))-exp(algebraic[2]/(constants[0]*constants[1])))
algebraic[25] = algebraic[22]-algebraic[13]
rates[4] = algebraic[25]
algebraic[26] = constants[0]*constants[1]*log(constants[5]*states[5])
algebraic[27] = algebraic[26]
algebraic[4] = algebraic[3]+constants[56]+constants[42]
algebraic[28] = constants[19]*(exp(algebraic[27]/(constants[0]*constants[1]))-exp(algebraic[4]/(constants[0]*constants[1])))
algebraic[31] = algebraic[28]-algebraic[8]
rates[1] = algebraic[31]
algebraic[32] = algebraic[1]+2.00000*constants[43]
algebraic[33] = algebraic[26]+3.00000*constants[45]+constants[41]*constants[47]
algebraic[34] = constants[23]*(exp(algebraic[32]/(constants[0]*constants[1]))-exp(algebraic[33]/(constants[0]*constants[1])))
algebraic[37] = algebraic[13]-algebraic[34]
rates[0] = algebraic[37]
algebraic[39] = algebraic[34]-algebraic[28]
rates[5] = algebraic[39]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[3] = constants[0]*constants[1]*log(constants[6]*states[1])
algebraic[5] = algebraic[3]+constants[44]
algebraic[6] = constants[0]*constants[1]*log(constants[4]*states[2])
algebraic[7] = algebraic[6]
algebraic[8] = constants[20]*(exp(algebraic[5]/(constants[0]*constants[1]))-exp(algebraic[7]/(constants[0]*constants[1])))
algebraic[15] = algebraic[6]
algebraic[10] = constants[0]*constants[1]*log(constants[7]*states[3])
algebraic[16] = algebraic[10]+2.00000*constants[50]
algebraic[17] = constants[18]*(exp(algebraic[15]/(constants[0]*constants[1]))-exp(algebraic[16]/(constants[0]*constants[1])))
algebraic[19] = algebraic[8]-algebraic[17]
algebraic[20] = algebraic[10]+3.00000*constants[46]
algebraic[11] = constants[0]*constants[1]*log(constants[8]*states[4])
algebraic[21] = constants[40]*constants[47]+algebraic[11]
algebraic[22] = constants[21]*(exp(algebraic[20]/(constants[0]*constants[1]))-exp(algebraic[21]/(constants[0]*constants[1])))
algebraic[24] = algebraic[17]-algebraic[22]
algebraic[12] = algebraic[11]
algebraic[1] = constants[0]*constants[1]*log(constants[9]*states[0])
algebraic[2] = algebraic[1]+constants[53]
algebraic[13] = constants[22]*(exp(algebraic[12]/(constants[0]*constants[1]))-exp(algebraic[2]/(constants[0]*constants[1])))
algebraic[25] = algebraic[22]-algebraic[13]
algebraic[26] = constants[0]*constants[1]*log(constants[5]*states[5])
algebraic[27] = algebraic[26]
algebraic[4] = algebraic[3]+constants[56]+constants[42]
algebraic[28] = constants[19]*(exp(algebraic[27]/(constants[0]*constants[1]))-exp(algebraic[4]/(constants[0]*constants[1])))
algebraic[31] = algebraic[28]-algebraic[8]
algebraic[32] = algebraic[1]+2.00000*constants[43]
algebraic[33] = algebraic[26]+3.00000*constants[45]+constants[41]*constants[47]
algebraic[34] = constants[23]*(exp(algebraic[32]/(constants[0]*constants[1]))-exp(algebraic[33]/(constants[0]*constants[1])))
algebraic[37] = algebraic[13]-algebraic[34]
algebraic[39] = algebraic[34]-algebraic[28]
algebraic[0] = states[2]+states[3]+states[4]+states[5]+states[0]+states[1]
algebraic[9] = -algebraic[8]
algebraic[14] = algebraic[13]
algebraic[18] = 2.00000*algebraic[17]
algebraic[23] = -3.00000*algebraic[22]
algebraic[29] = algebraic[28]
algebraic[30] = algebraic[28]
algebraic[35] = -2.00000*algebraic[34]
algebraic[36] = 3.00000*algebraic[34]
algebraic[38] = constants[40]*algebraic[22]+constants[41]*algebraic[34]
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)