Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 9
sizeStates = 3
sizeConstants = 28
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] = "Cm in component membrane (femtoF)"
legend_algebraic[5] = "i_Ca in component calcium_current (picoA)"
legend_algebraic[0] = "i_K in component rapidly_activating_K_current (picoA)"
legend_algebraic[6] = "i_K_Ca in component calcium_activated_K_current (picoA)"
legend_algebraic[8] = "i_Na_Ca in component Na_Ca_exchanger_current (picoA)"
legend_constants[1] = "V_K in component rapidly_activating_K_current (millivolt)"
legend_constants[2] = "g_K in component rapidly_activating_K_current (picoS)"
legend_states[1] = "n in component rapidly_activating_K_current_n_gate (dimensionless)"
legend_algebraic[1] = "n_infinity in component rapidly_activating_K_current_n_gate (dimensionless)"
legend_constants[3] = "lamda in component rapidly_activating_K_current_n_gate (dimensionless)"
legend_algebraic[3] = "tau_n in component rapidly_activating_K_current_n_gate (millisecond)"
legend_constants[4] = "V_n in component rapidly_activating_K_current_n_gate (millivolt)"
legend_constants[5] = "S_n in component rapidly_activating_K_current_n_gate (millivolt)"
legend_constants[6] = "a in component rapidly_activating_K_current_n_gate (millivolt)"
legend_constants[7] = "b in component rapidly_activating_K_current_n_gate (millivolt)"
legend_constants[8] = "c in component rapidly_activating_K_current_n_gate (millisecond)"
legend_constants[9] = "V_ in component rapidly_activating_K_current_n_gate (millivolt)"
legend_constants[10] = "V_Ca in component calcium_current (millivolt)"
legend_constants[11] = "g_Ca in component calcium_current (picoS)"
legend_algebraic[2] = "m_infinity in component calcium_current_m_gate (dimensionless)"
legend_algebraic[4] = "h in component calcium_current_h_gate (dimensionless)"
legend_constants[12] = "V_m in component calcium_current_m_gate (millivolt)"
legend_constants[13] = "S_m in component calcium_current_m_gate (millivolt)"
legend_constants[14] = "V_h in component calcium_current_h_gate (millivolt)"
legend_constants[15] = "S_h in component calcium_current_h_gate (millivolt)"
legend_constants[16] = "g_K_Ca in component calcium_activated_K_current (picoS)"
legend_constants[17] = "K_d in component calcium_activated_K_current (micromolar)"
legend_states[2] = "Ca_i in component ionic_concentrations (micromolar)"
legend_constants[18] = "g_Na_Ca in component Na_Ca_exchanger_current (picoS)"
legend_constants[19] = "K_1_2 in component Na_Ca_exchanger_current (micromolar)"
legend_algebraic[7] = "V_Na_Ca in component Na_Ca_exchanger_current (millivolt)"
legend_constants[20] = "RT_F in component Na_Ca_exchanger_current (millivolt)"
legend_constants[21] = "nH in component Na_Ca_exchanger_current (dimensionless)"
legend_constants[22] = "Ca_o in component ionic_concentrations (micromolar)"
legend_constants[23] = "Na_i in component ionic_concentrations (millimolar)"
legend_constants[24] = "Na_o in component ionic_concentrations (millimolar)"
legend_constants[25] = "f in component ionic_concentrations (dimensionless)"
legend_constants[26] = "k_Ca in component ionic_concentrations (per_millisecond)"
legend_constants[27] = "alpha in component ionic_concentrations (mole_per_microlitre_coulomb)"
legend_rates[0] = "d/dt V in component membrane (millivolt)"
legend_rates[1] = "d/dt n in component rapidly_activating_K_current_n_gate (dimensionless)"
legend_rates[2] = "d/dt Ca_i in component ionic_concentrations (micromolar)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = -76.0
constants[0] = 5310.0
constants[1] = -75.0
constants[2] = 2500.0
states[1] = 0.1
constants[3] = 1.6
constants[4] = -15.0
constants[5] = 5.6
constants[6] = 65.0
constants[7] = 20.0
constants[8] = 6.0
constants[9] = -75.0
constants[10] = 110.0
constants[11] = 1400.0
constants[12] = 4.0
constants[13] = 14.0
constants[14] = -10.0
constants[15] = -10.0
constants[16] = 30000.0
constants[17] = 100.0
states[2] = 0.52
constants[18] = 234.0
constants[19] = 1.5
constants[20] = 26.54
constants[21] = 5.0
constants[22] = 2600.0
constants[23] = 10.0
constants[24] = 140.0
constants[25] = 0.001
constants[26] = 0.03
constants[27] = 0.0000045055
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
algebraic[1] = 1.00000/(1.00000+exp((constants[4]-states[0])/constants[5]))
algebraic[3] = constants[8]/(exp((states[0]-constants[9])/constants[6])+exp((constants[9]-states[0])/constants[7]))
rates[1] = constants[3]*((algebraic[1]-states[1])/algebraic[3])
algebraic[2] = 1.00000/(1.00000+exp((constants[12]-states[0])/constants[13]))
algebraic[4] = 1.00000/(1.00000+exp((constants[14]-states[0])/constants[15]))
algebraic[5] = constants[11]*algebraic[2]*algebraic[4]*(states[0]-constants[10])
algebraic[0] = constants[2]*states[1]*(states[0]-constants[1])
algebraic[6] = constants[16]*(states[2]/(constants[17]+states[2]))*(states[0]-constants[1])
algebraic[7] = constants[20]*(3.00000*log(constants[24]/constants[23]-log(constants[22]/states[2])))
algebraic[8] = constants[18]*((power(states[2], constants[21]))/(power(constants[19], constants[21])+power(states[2], constants[21])))*(states[0]-algebraic[7])
rates[0] = -(algebraic[0]+algebraic[5]+algebraic[6]+algebraic[8])/constants[0]
rates[2] = constants[25]*(-constants[27]*(algebraic[5]-2.00000*algebraic[8])-constants[26]*states[2])
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((constants[4]-states[0])/constants[5]))
algebraic[3] = constants[8]/(exp((states[0]-constants[9])/constants[6])+exp((constants[9]-states[0])/constants[7]))
algebraic[2] = 1.00000/(1.00000+exp((constants[12]-states[0])/constants[13]))
algebraic[4] = 1.00000/(1.00000+exp((constants[14]-states[0])/constants[15]))
algebraic[5] = constants[11]*algebraic[2]*algebraic[4]*(states[0]-constants[10])
algebraic[0] = constants[2]*states[1]*(states[0]-constants[1])
algebraic[6] = constants[16]*(states[2]/(constants[17]+states[2]))*(states[0]-constants[1])
algebraic[7] = constants[20]*(3.00000*log(constants[24]/constants[23]-log(constants[22]/states[2])))
algebraic[8] = constants[18]*((power(states[2], constants[21]))/(power(constants[19], constants[21])+power(states[2], constants[21])))*(states[0]-algebraic[7])
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)