Generated Code
The following is python code generated by the CellML API from this CellML file. (Back to language selection)
The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 2
sizeStates = 13
sizeConstants = 65
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 (ms)"
legend_constants[0] = "V in component membrane (V)"
legend_algebraic[1] = "i_Na in component sodium_current (dimensionless)"
legend_constants[1] = "E_Na in component sodium_current (V)"
legend_constants[2] = "g_Na in component sodium_current (per_V)"
legend_algebraic[0] = "P_open in component Markov_model (dimensionless)"
legend_states[0] = "O1 in component Markov_model (dimensionless)"
legend_states[1] = "O2 in component Markov_model (dimensionless)"
legend_states[2] = "C0 in component Markov_model (dimensionless)"
legend_states[3] = "C1 in component Markov_model (dimensionless)"
legend_states[4] = "C2 in component Markov_model (dimensionless)"
legend_states[5] = "C3 in component Markov_model (dimensionless)"
legend_states[6] = "C4 in component Markov_model (dimensionless)"
legend_states[7] = "C0I in component Markov_model (dimensionless)"
legend_states[8] = "C1I in component Markov_model (dimensionless)"
legend_states[9] = "C2I in component Markov_model (dimensionless)"
legend_states[10] = "C3I in component Markov_model (dimensionless)"
legend_states[11] = "C4I in component Markov_model (dimensionless)"
legend_states[12] = "I in component Markov_model (dimensionless)"
legend_constants[3] = "a in component Markov_model (dimensionless)"
legend_constants[51] = "alpha in component rate_constants (first_order_rate_constant)"
legend_constants[52] = "beta in component rate_constants (first_order_rate_constant)"
legend_constants[53] = "cf in component rate_constants (first_order_rate_constant)"
legend_constants[54] = "cn in component rate_constants (first_order_rate_constant)"
legend_constants[55] = "of in component rate_constants (first_order_rate_constant)"
legend_constants[56] = "on in component rate_constants (first_order_rate_constant)"
legend_constants[57] = "eta in component rate_constants (first_order_rate_constant)"
legend_constants[58] = "gamma in component rate_constants (first_order_rate_constant)"
legend_constants[59] = "delta in component rate_constants (first_order_rate_constant)"
legend_constants[60] = "epsilon in component rate_constants (first_order_rate_constant)"
legend_constants[61] = "omega in component rate_constants (first_order_rate_constant)"
legend_constants[62] = "v in component rate_constants (first_order_rate_constant)"
legend_constants[63] = "gamma_gamma in component rate_constants (first_order_rate_constant)"
legend_constants[64] = "delta_delta in component rate_constants (first_order_rate_constant)"
legend_constants[4] = "R in component rate_constants (J_mol_K)"
legend_constants[5] = "T in component rate_constants (K)"
legend_constants[6] = "F in component rate_constants (C_mol)"
legend_constants[7] = "k in component rate_constants (J_K)"
legend_constants[8] = "h in component rate_constants (J_ms)"
legend_constants[9] = "z_alpha in component rate_constants (dimensionless)"
legend_constants[10] = "z_beta in component rate_constants (dimensionless)"
legend_constants[11] = "z_gamma in component rate_constants (dimensionless)"
legend_constants[12] = "z_delta in component rate_constants (dimensionless)"
legend_constants[13] = "z_on in component rate_constants (dimensionless)"
legend_constants[14] = "z_of in component rate_constants (dimensionless)"
legend_constants[15] = "z_gamma_gamma in component rate_constants (dimensionless)"
legend_constants[16] = "z_delta_delta in component rate_constants (dimensionless)"
legend_constants[17] = "z_epsilon in component rate_constants (dimensionless)"
legend_constants[18] = "z_omega in component rate_constants (dimensionless)"
legend_constants[19] = "z_eta in component rate_constants (dimensionless)"
legend_constants[20] = "z_v in component rate_constants (dimensionless)"
legend_constants[21] = "z_cn in component rate_constants (dimensionless)"
legend_constants[22] = "z_cf in component rate_constants (dimensionless)"
legend_constants[23] = "delta_H_alpha in component rate_constants (J_mol)"
legend_constants[24] = "delta_H_beta in component rate_constants (J_mol)"
legend_constants[25] = "delta_H_cf in component rate_constants (J_mol)"
legend_constants[26] = "delta_H_cn in component rate_constants (J_mol)"
legend_constants[27] = "delta_H_of in component rate_constants (J_mol)"
legend_constants[28] = "delta_H_on in component rate_constants (J_mol)"
legend_constants[29] = "delta_H_eta in component rate_constants (J_mol)"
legend_constants[30] = "delta_H_gamma in component rate_constants (J_mol)"
legend_constants[31] = "delta_H_delta in component rate_constants (J_mol)"
legend_constants[32] = "delta_H_epsilon in component rate_constants (J_mol)"
legend_constants[33] = "delta_H_omega in component rate_constants (J_mol)"
legend_constants[34] = "delta_H_v in component rate_constants (J_mol)"
legend_constants[35] = "delta_H_gamma_gamma in component rate_constants (J_mol)"
legend_constants[36] = "delta_H_delta_delta in component rate_constants (J_mol)"
legend_constants[37] = "delta_S_alpha in component rate_constants (J_mol_K)"
legend_constants[38] = "delta_S_beta in component rate_constants (J_mol_K)"
legend_constants[39] = "delta_S_cf in component rate_constants (J_mol_K)"
legend_constants[40] = "delta_S_cn in component rate_constants (J_mol_K)"
legend_constants[41] = "delta_S_of in component rate_constants (J_mol_K)"
legend_constants[42] = "delta_S_on in component rate_constants (J_mol_K)"
legend_constants[43] = "delta_S_eta in component rate_constants (J_mol_K)"
legend_constants[44] = "delta_S_gamma in component rate_constants (J_mol_K)"
legend_constants[45] = "delta_S_delta in component rate_constants (J_mol_K)"
legend_constants[46] = "delta_S_epsilon in component rate_constants (J_mol_K)"
legend_constants[47] = "delta_S_omega in component rate_constants (J_mol_K)"
legend_constants[48] = "delta_S_v in component rate_constants (J_mol_K)"
legend_constants[49] = "delta_S_gamma_gamma in component rate_constants (J_mol_K)"
legend_constants[50] = "delta_S_delta_delta in component rate_constants (J_mol_K)"
legend_rates[2] = "d/dt C0 in component Markov_model (dimensionless)"
legend_rates[3] = "d/dt C1 in component Markov_model (dimensionless)"
legend_rates[4] = "d/dt C2 in component Markov_model (dimensionless)"
legend_rates[5] = "d/dt C3 in component Markov_model (dimensionless)"
legend_rates[6] = "d/dt C4 in component Markov_model (dimensionless)"
legend_rates[0] = "d/dt O1 in component Markov_model (dimensionless)"
legend_rates[1] = "d/dt O2 in component Markov_model (dimensionless)"
legend_rates[7] = "d/dt C0I in component Markov_model (dimensionless)"
legend_rates[8] = "d/dt C1I in component Markov_model (dimensionless)"
legend_rates[9] = "d/dt C2I in component Markov_model (dimensionless)"
legend_rates[10] = "d/dt C3I in component Markov_model (dimensionless)"
legend_rates[11] = "d/dt C4I in component Markov_model (dimensionless)"
legend_rates[12] = "d/dt I in component Markov_model (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = -0.12
constants[1] = 0.044675
constants[2] = 0.0131
states[0] = 0.0
states[1] = 0.0
states[2] = 1.0
states[3] = 0.0
states[4] = 0.0
states[5] = 0.0
states[6] = 0.0
states[7] = 0.0
states[8] = 0.0
states[9] = 0.0
states[10] = 0.0
states[11] = 0.0
states[12] = 0.0
constants[3] = 2.5218
constants[4] = 8.314472
constants[5] = 286.0
constants[6] = 96500.0
constants[7] = 1.3806504E-23
constants[8] = 6.62607095E-31
constants[9] = 0
constants[10] = -0.9701
constants[11] = 1.5703
constants[12] = -1.3266
constants[13] = 0.6625
constants[14] = 0
constants[15] = 0
constants[16] = -3.5596
constants[17] = 0
constants[18] = 0
constants[19] = 1.5717
constants[20] = -1.3281
constants[21] = 0
constants[22] = 0
constants[23] = 116900
constants[24] = 263870
constants[25] = 57533
constants[26] = 293270
constants[27] = 79035
constants[28] = 62385
constants[29] = 150333
constants[30] = 200240
constants[31] = 127970
constants[32] = 79183
constants[33] = 123020
constants[34] = 121900
constants[35] = -99967
constants[36] = 62555
constants[37] = 224.114
constants[38] = 708.146
constants[39] = 0.00711
constants[40] = 786.217
constants[41] = 1.510
constants[42] = 39.295
constants[43] = 338.915
constants[44] = 529.952
constants[45] = 229.205
constants[46] = 70.078
constants[47] = 225.175
constants[48] = 193.265
constants[49] = -578.317
constants[50] = -130.639
constants[51] = ((constants[7]*constants[5])/constants[8])*exp(-constants[23]/(constants[4]*constants[5])+constants[37]/constants[4]+(constants[9]*constants[6]*constants[0])/(constants[4]*constants[5]))
constants[52] = ((constants[7]*constants[5])/constants[8])*exp(-constants[24]/(constants[4]*constants[5])+constants[38]/constants[4]+(constants[10]*constants[6]*constants[0])/(constants[4]*constants[5]))
constants[53] = ((constants[7]*constants[5])/constants[8])*exp(-constants[25]/(constants[4]*constants[5])+constants[39]/constants[4]+(constants[22]*constants[6]*constants[0])/(constants[4]*constants[5]))
constants[54] = ((constants[7]*constants[5])/constants[8])*exp(-constants[26]/(constants[4]*constants[5])+constants[40]/constants[4]+(constants[21]*constants[6]*constants[0])/(constants[4]*constants[5]))
constants[55] = ((constants[7]*constants[5])/constants[8])*exp(-constants[27]/(constants[4]*constants[5])+constants[41]/constants[4]+(constants[14]*constants[6]*constants[0])/(constants[4]*constants[5]))
constants[56] = ((constants[7]*constants[5])/constants[8])*exp(-constants[28]/(constants[4]*constants[5])+constants[42]/constants[4]+(constants[13]*constants[6]*constants[0])/(constants[4]*constants[5]))
constants[57] = ((constants[7]*constants[5])/constants[8])*exp(-constants[29]/(constants[4]*constants[5])+constants[43]/constants[4]+(constants[19]*constants[6]*constants[0])/(constants[4]*constants[5]))
constants[58] = ((constants[7]*constants[5])/constants[8])*exp(-constants[30]/(constants[4]*constants[5])+constants[44]/constants[4]+(constants[11]*constants[6]*constants[0])/(constants[4]*constants[5]))
constants[59] = ((constants[7]*constants[5])/constants[8])*exp(-constants[31]/(constants[4]*constants[5])+constants[45]/constants[4]+(constants[12]*constants[6]*constants[0])/(constants[4]*constants[5]))
constants[60] = ((constants[7]*constants[5])/constants[8])*exp(-constants[32]/(constants[4]*constants[5])+constants[46]/constants[4]+(constants[17]*constants[6]*constants[0])/(constants[4]*constants[5]))
constants[61] = ((constants[7]*constants[5])/constants[8])*exp(-constants[33]/(constants[4]*constants[5])+constants[47]/constants[4]+(constants[18]*constants[6]*constants[0])/(constants[4]*constants[5]))
constants[62] = ((constants[7]*constants[5])/constants[8])*exp(-constants[34]/(constants[4]*constants[5])+constants[48]/constants[4]+(constants[20]*constants[6]*constants[0])/(constants[4]*constants[5]))
constants[63] = ((constants[7]*constants[5])/constants[8])*exp(-constants[35]/(constants[4]*constants[5])+constants[49]/constants[4]+(constants[15]*constants[6]*constants[0])/(constants[4]*constants[5]))
constants[64] = ((constants[7]*constants[5])/constants[8])*exp(-constants[36]/(constants[4]*constants[5])+constants[50]/constants[4]+(constants[16]*constants[6]*constants[0])/(constants[4]*constants[5]))
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[2] = (constants[52]*states[3]+constants[53]*states[7])-(constants[54]+4.00000*constants[51])*states[2]
rates[3] = (2.00000*constants[52]*states[4]+4.00000*constants[51]*states[2]+(constants[53]/constants[3])*states[8])-(constants[52]+3.00000*constants[51]+constants[54]*constants[3])*states[3]
rates[4] = (3.00000*constants[52]*states[5]+3.00000*constants[51]*states[3]+(constants[53]/(power(constants[3], 2.00000)))*states[9])-(2.00000*constants[52]+2.00000*constants[51]+constants[54]*(power(constants[3], 2.00000)))*states[4]
rates[5] = (4.00000*constants[52]*states[6]+2.00000*constants[51]*states[4]+(constants[53]/(power(constants[3], 3.00000)))*states[10])-(3.00000*constants[52]+constants[51]+constants[54]*(power(constants[3], 3.00000)))*states[5]
rates[6] = (constants[59]*states[0]+constants[62]*states[1]+constants[51]*states[5]+(constants[53]/(power(constants[3], 4.00000)))*states[11])-(4.00000*constants[52]+constants[58]+constants[57]+constants[54]*(power(constants[3], 4.00000)))*states[6]
rates[0] = (constants[58]*states[6]+constants[61]*states[1]+constants[55]*states[12])-(constants[59]+constants[60]+constants[56])*states[0]
rates[1] = (constants[60]*states[0]+constants[57]*states[6])-(constants[62]+constants[61])*states[1]
rates[7] = ((constants[52]/constants[3])*states[8]+constants[54]*states[2])-(constants[53]+4.00000*constants[51]*constants[3])*states[7]
rates[8] = (((2.00000*constants[52])/constants[3])*states[9]+4.00000*constants[51]*constants[3]*states[7]+constants[54]*constants[3]*states[3])-(constants[52]/constants[3]+3.00000*constants[51]*constants[3]+constants[53]/constants[3])*states[8]
rates[9] = (((3.00000*constants[52])/constants[3])*states[10]+3.00000*constants[51]*constants[3]*states[8]+constants[54]*(power(constants[3], 2.00000))*states[4])-((2.00000*constants[52])/constants[3]+2.00000*constants[51]*constants[3]+constants[53]/(power(constants[3], 2.00000)))*states[9]
rates[10] = (((4.00000*constants[52])/constants[3])*states[11]+2.00000*constants[51]*constants[3]*states[9]+constants[54]*(power(constants[3], 3.00000))*states[5])-((3.00000*constants[52])/constants[3]+constants[51]*constants[3]+constants[53]/(power(constants[3], 3.00000)))*states[10]
rates[11] = (constants[64]*states[12]+constants[51]*constants[3]*states[10]+constants[54]*(power(constants[3], 4.00000))*states[6])-((4.00000*constants[52])/constants[3]+constants[63]+constants[53]/(power(constants[3], 4.00000)))*states[11]
rates[12] = (constants[63]*states[11]+constants[56]*states[0])-(constants[64]+constants[55])*states[12]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = states[0]+states[1]
algebraic[1] = constants[2]*algebraic[0]*(constants[0]-constants[1])
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)