Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 14
sizeStates = 4
sizeConstants = 25
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 (millisecond)"
legend_states[0] = "V in component membrane (millivolt)"
legend_constants[0] = "C in component membrane (picoF)"
legend_constants[1] = "i_app in component membrane (picoA)"
legend_algebraic[11] = "i_NaP in component persistent_sodium_current (picoA)"
legend_algebraic[4] = "i_Na in component fast_sodium_current (picoA)"
legend_algebraic[8] = "i_K in component potassium_current (picoA)"
legend_algebraic[9] = "i_KS in component slow_potassium_current (picoA)"
legend_algebraic[12] = "i_L in component leakage_current (picoA)"
legend_algebraic[13] = "i_tonic_e in component tonic_current (picoA)"
legend_constants[2] = "E_Na in component fast_sodium_current (millivolt)"
legend_constants[3] = "g_Na in component fast_sodium_current (nanoS)"
legend_algebraic[0] = "m_infinity in component fast_sodium_current_m_gate (dimensionless)"
legend_states[1] = "n in component fast_sodium_current_n_gate (dimensionless)"
legend_constants[4] = "theta_m in component fast_sodium_current_m_gate (millivolt)"
legend_constants[5] = "sigma_m in component fast_sodium_current_m_gate (millivolt)"
legend_algebraic[1] = "n_infinity in component fast_sodium_current_n_gate (dimensionless)"
legend_algebraic[5] = "tau_n in component fast_sodium_current_n_gate (millisecond)"
legend_constants[6] = "tau_n_max in component fast_sodium_current_n_gate (millisecond)"
legend_constants[7] = "theta_n in component fast_sodium_current_n_gate (millivolt)"
legend_constants[8] = "sigma_n in component fast_sodium_current_n_gate (millivolt)"
legend_constants[9] = "E_K in component potassium_current (millivolt)"
legend_constants[10] = "g_K in component potassium_current (nanoS)"
legend_states[2] = "n in component potassium_current_n_gate (dimensionless)"
legend_algebraic[2] = "n_infinity in component potassium_current_n_gate (dimensionless)"
legend_algebraic[6] = "tau_n in component potassium_current_n_gate (millisecond)"
legend_constants[11] = "tau_n_max in component potassium_current_n_gate (millisecond)"
legend_constants[12] = "theta_n in component potassium_current_n_gate (millivolt)"
legend_constants[13] = "sigma_n in component potassium_current_n_gate (millivolt)"
legend_constants[14] = "g_KS in component slow_potassium_current (nanoS)"
legend_states[3] = "k in component slow_potassium_current_k_gate (dimensionless)"
legend_algebraic[3] = "k_infinity in component slow_potassium_current_k_gate (dimensionless)"
legend_algebraic[7] = "tau_k in component slow_potassium_current_k_gate (millisecond)"
legend_constants[15] = "tau_k_max in component slow_potassium_current_k_gate (millisecond)"
legend_constants[16] = "theta_k in component slow_potassium_current_k_gate (millivolt)"
legend_constants[17] = "sigma_k in component slow_potassium_current_k_gate (millivolt)"
legend_constants[18] = "g_NaP in component persistent_sodium_current (nanoS)"
legend_algebraic[10] = "m_infinity in component persistent_sodium_current_m_gate (dimensionless)"
legend_constants[19] = "theta_m in component persistent_sodium_current_m_gate (millivolt)"
legend_constants[20] = "sigma_m in component persistent_sodium_current_m_gate (millivolt)"
legend_constants[21] = "g_L in component leakage_current (nanoS)"
legend_constants[22] = "E_L in component leakage_current (millivolt)"
legend_constants[23] = "g_tonic_e in component tonic_current (nanoS)"
legend_constants[24] = "E_syn_e in component tonic_current (millivolt)"
legend_rates[0] = "d/dt V in component membrane (millivolt)"
legend_rates[1] = "d/dt n in component fast_sodium_current_n_gate (dimensionless)"
legend_rates[2] = "d/dt n in component potassium_current_n_gate (dimensionless)"
legend_rates[3] = "d/dt k in component slow_potassium_current_k_gate (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = -55.0
constants[0] = 21.0
constants[1] = 0.0
constants[2] = 50.0
constants[3] = 28.0
states[1] = 0.01
constants[4] = -34.0
constants[5] = -5.0
constants[6] = 10.0
constants[7] = -29.0
constants[8] = -4.0
constants[9] = -85.0
constants[10] = 11.2
states[2] = 0.01
constants[11] = 10.0
constants[12] = -29.0
constants[13] = -4.0
constants[14] = 5.6
states[3] = 0.22
constants[15] = 10000.0
constants[16] = -38.0
constants[17] = -6.0
constants[18] = 2.8
constants[19] = -40.0
constants[20] = -6.0
constants[21] = 2.8
constants[22] = -50.0
constants[23] = 0.0
constants[24] = 0.0
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[1] = 1.00000/(1.00000+exp((states[0]-constants[7])/constants[8]))
algebraic[5] = constants[6]/cosh((states[0]-constants[7])/(2.00000*constants[8]))
rates[1] = (algebraic[1]-states[1])/algebraic[5]
algebraic[2] = 1.00000/(1.00000+exp((states[0]-constants[12])/constants[13]))
algebraic[6] = constants[11]/cosh((states[0]-constants[12])/(2.00000*constants[13]))
rates[2] = (algebraic[2]-states[2])/algebraic[6]
algebraic[3] = 1.00000/(1.00000+exp((states[0]-constants[16])/constants[17]))
algebraic[7] = constants[15]/cosh((states[0]-constants[16])/(2.00000*constants[17]))
rates[3] = (algebraic[3]-states[3])/algebraic[7]
algebraic[10] = 1.00000/(1.00000+exp((states[0]-constants[19])/constants[20]))
algebraic[11] = constants[18]*algebraic[10]*(states[0]-constants[2])
algebraic[0] = 1.00000/(1.00000+exp((states[0]-constants[4])/constants[5]))
algebraic[4] = constants[3]*(power(algebraic[0], 3.00000))*(1.00000-states[1])*(states[0]-constants[2])
algebraic[8] = constants[10]*(power(states[2], 4.00000))*(states[0]-constants[9])
algebraic[9] = constants[14]*states[3]*(states[0]-constants[9])
algebraic[12] = constants[21]*(states[0]-constants[22])
algebraic[13] = constants[23]*(states[0]-constants[24])
rates[0] = (-(algebraic[11]+algebraic[9]+algebraic[4]+algebraic[8]+algebraic[12]+algebraic[13])+constants[1])/constants[0]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[1] = 1.00000/(1.00000+exp((states[0]-constants[7])/constants[8]))
algebraic[5] = constants[6]/cosh((states[0]-constants[7])/(2.00000*constants[8]))
algebraic[2] = 1.00000/(1.00000+exp((states[0]-constants[12])/constants[13]))
algebraic[6] = constants[11]/cosh((states[0]-constants[12])/(2.00000*constants[13]))
algebraic[3] = 1.00000/(1.00000+exp((states[0]-constants[16])/constants[17]))
algebraic[7] = constants[15]/cosh((states[0]-constants[16])/(2.00000*constants[17]))
algebraic[10] = 1.00000/(1.00000+exp((states[0]-constants[19])/constants[20]))
algebraic[11] = constants[18]*algebraic[10]*(states[0]-constants[2])
algebraic[0] = 1.00000/(1.00000+exp((states[0]-constants[4])/constants[5]))
algebraic[4] = constants[3]*(power(algebraic[0], 3.00000))*(1.00000-states[1])*(states[0]-constants[2])
algebraic[8] = constants[10]*(power(states[2], 4.00000))*(states[0]-constants[9])
algebraic[9] = constants[14]*states[3]*(states[0]-constants[9])
algebraic[12] = constants[21]*(states[0]-constants[22])
algebraic[13] = constants[23]*(states[0]-constants[24])
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)