Generated Code

# Size of variable arrays:
sizeAlgebraic = 7
sizeStates = 3
sizeConstants = 16
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] = "tau in component membrane (millisecond)"
    legend_algebraic[4] = "i_K in component potassium_current (picoA)"
    legend_algebraic[6] = "i_K_ATP in component ATP_sensitive_potassium_current (picoA)"
    legend_algebraic[3] = "i_Ca in component calcium_current (picoA)"
    legend_algebraic[5] = "i_s in component slow_current (picoA)"
    legend_constants[1] = "g_Ca in component calcium_current (nanoS)"
    legend_constants[2] = "V_Ca in component calcium_current (millivolt)"
    legend_algebraic[0] = "m_infinity in component calcium_current_m_gate (dimensionless)"
    legend_constants[3] = "V_m in component calcium_current_m_gate (millivolt)"
    legend_constants[4] = "theta_m in component calcium_current_m_gate (millivolt)"
    legend_constants[5] = "V_K in component potassium_current (millivolt)"
    legend_constants[6] = "g_K in component potassium_current (nanoS)"
    legend_states[1] = "n in component potassium_current_n_gate (dimensionless)"
    legend_algebraic[1] = "n_infinity in component potassium_current_n_gate (dimensionless)"
    legend_constants[7] = "V_n in component potassium_current_n_gate (millivolt)"
    legend_constants[8] = "theta_n in component potassium_current_n_gate (millivolt)"
    legend_constants[9] = "lambda in component potassium_current_n_gate (dimensionless)"
    legend_constants[10] = "g_s in component slow_current (nanoS)"
    legend_states[2] = "s in component slow_current_s_gate (dimensionless)"
    legend_algebraic[2] = "s_infinity in component slow_current_s_gate (dimensionless)"
    legend_constants[11] = "V_s in component slow_current_s_gate (millivolt)"
    legend_constants[12] = "theta_s in component slow_current_s_gate (millivolt)"
    legend_constants[13] = "tau_s in component slow_current_s_gate (millisecond)"
    legend_constants[14] = "g_K_ATP in component ATP_sensitive_potassium_current (nanoS)"
    legend_constants[15] = "p in component ATP_sensitive_potassium_current (dimensionless)"
    legend_rates[0] = "d/dt V in component membrane (millivolt)"
    legend_rates[1] = "d/dt n in component potassium_current_n_gate (dimensionless)"
    legend_rates[2] = "d/dt s in component slow_current_s_gate (dimensionless)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = -64.0
    constants[0] = 20.0
    constants[1] = 3.6
    constants[2] = 25.0
    constants[3] = -20.0
    constants[4] = 12.0
    constants[5] = -75.0
    constants[6] = 10.0
    states[1] = 0.01
    constants[7] = -17.0
    constants[8] = 5.6
    constants[9] = 0.9
    constants[10] = 4.0
    states[2] = 0.01
    constants[11] = -22.0
    constants[12] = 8.0
    constants[13] = 20000.0
    constants[14] = 1.2
    constants[15] = 0.5
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[1] = 1.00000/(1.00000+exp((constants[7]-states[0])/constants[8]))
    rates[1] = (constants[9]*(algebraic[1]-states[1]))/constants[0]
    algebraic[2] = 1.00000/(1.00000+exp((constants[11]-states[0])/constants[12]))
    rates[2] = (algebraic[2]-states[2])/constants[13]
    algebraic[4] = constants[6]*states[1]*(states[0]-constants[5])
    algebraic[6] = constants[14]*constants[15]*(states[0]-constants[5])
    algebraic[0] = 1.00000/(1.00000+exp((constants[3]-states[0])/constants[4]))
    algebraic[3] = constants[1]*algebraic[0]*(states[0]-constants[2])
    algebraic[5] = constants[10]*states[2]*(states[0]-constants[5])
    rates[0] = -(algebraic[3]+algebraic[4]+algebraic[6]+algebraic[5])/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((constants[7]-states[0])/constants[8]))
    algebraic[2] = 1.00000/(1.00000+exp((constants[11]-states[0])/constants[12]))
    algebraic[4] = constants[6]*states[1]*(states[0]-constants[5])
    algebraic[6] = constants[14]*constants[15]*(states[0]-constants[5])
    algebraic[0] = 1.00000/(1.00000+exp((constants[3]-states[0])/constants[4]))
    algebraic[3] = constants[1]*algebraic[0]*(states[0]-constants[2])
    algebraic[5] = constants[10]*states[2]*(states[0]-constants[5])
    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)