Generated Code

# Size of variable arrays:
sizeAlgebraic = 9
sizeStates = 4
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 (second)"
    legend_states[0] = "Ca_m in component Ca_m (micromolar)"
    legend_algebraic[0] = "J_min in component J_min (micromolar)"
    legend_algebraic[1] = "J_mout in component J_mout (micromolar)"
    legend_constants[0] = "k_min in component J_min (micromolar)"
    legend_states[1] = "Ca_cyt in component Ca_cyt (micromolar)"
    legend_constants[1] = "K_m in component J_min (micromolar)"
    legend_constants[2] = "n in component J_min (micromolar)"
    legend_constants[3] = "k_mout in component J_mout (micromolar)"
    legend_algebraic[2] = "J_ERch in component J_ERch (micromolar)"
    legend_algebraic[3] = "J_ERpump in component J_ERpump (micromolar)"
    legend_algebraic[4] = "J_ERleak in component J_ERleak (micromolar)"
    legend_algebraic[6] = "J_CaPr in component J_CaPr (micromolar)"
    legend_algebraic[8] = "J_Pr in component J_Pr (micromolar)"
    legend_constants[4] = "rho_m in component Ca_cyt (dimensionless)"
    legend_constants[5] = "beta_m in component Ca_cyt (dimensionless)"
    legend_states[2] = "Ca_tot in component Ca_tot (micromolar)"
    legend_states[3] = "Ca_ER in component Ca_ER (micromolar)"
    legend_constants[6] = "rho_ER in component Ca_ER (dimensionless)"
    legend_constants[7] = "beta_ER in component Ca_ER (dimensionless)"
    legend_algebraic[5] = "CaPr in component CaPr (micromolar)"
    legend_constants[8] = "k_ERch in component J_ERch (micromolar)"
    legend_constants[9] = "K_ch in component J_ERch (micromolar)"
    legend_constants[10] = "k_ERpump in component J_ERpump (per_second)"
    legend_constants[11] = "k_ERleak in component J_ERleak (per_second)"
    legend_constants[12] = "k_min in component J_CaPr (per_second)"
    legend_constants[13] = "k_plus in component J_Pr (per_micromolar_per_second)"
    legend_algebraic[7] = "Pr in component Pr (micromolar)"
    legend_constants[14] = "Ca_tot in component CaPr (micromolar)"
    legend_constants[15] = "Pr_tot in component Pr (micromolar)"
    legend_rates[0] = "d/dt Ca_m in component Ca_m (micromolar)"
    legend_rates[1] = "d/dt Ca_cyt in component Ca_cyt (micromolar)"
    legend_rates[2] = "d/dt Ca_tot in component Ca_tot (micromolar)"
    legend_rates[3] = "d/dt Ca_ER in component Ca_ER (micromolar)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 0.1
    constants[0] = 330
    states[1] = 0.01
    constants[1] = 1.6
    constants[2] = 8
    constants[3] = 0.5
    constants[4] = 0.01
    constants[5] = 0.025
    states[2] = 0.01
    states[3] = 20
    constants[6] = 0.01
    constants[7] = 0.0025
    constants[8] = 0.001
    constants[9] = 5
    constants[10] = 20
    constants[11] = 0.05
    constants[12] = 0.01
    constants[13] = 0.1
    constants[14] = 90
    constants[15] = 120
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = (constants[0]*(power(states[1], constants[2])))/(power(constants[1], constants[2])+power(states[1], constants[2]))
    algebraic[1] = (constants[3]*states[0])/1.00000
    rates[0] = algebraic[0]-algebraic[1]
    algebraic[2] = ((constants[8]*(power(states[1], 2.00000)))/(power(constants[9], 2.00000)+power(states[1], 2.00000)))*(states[3]-states[1])
    algebraic[3] = constants[10]*states[1]
    algebraic[4] = constants[11]*(states[3]-states[1])
    rates[3] = (constants[7]/constants[6])*((algebraic[3]-algebraic[4])-algebraic[2])*1.00000
    algebraic[5] = constants[14]-(states[1]+(constants[6]/constants[7])*states[3])
    rates[2] = states[1]+(constants[6]/constants[7])*states[3]+(constants[4]/constants[5])*states[0]+algebraic[5]
    algebraic[6] = constants[12]*algebraic[5]
    algebraic[7] = constants[15]-algebraic[5]
    algebraic[8] = constants[13]*states[1]*algebraic[7]
    rates[1] = ((((algebraic[2]-algebraic[3])+algebraic[4]+algebraic[6])-algebraic[8])+(constants[4]/constants[5])*(algebraic[1]-algebraic[0]))*1.00000
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = (constants[0]*(power(states[1], constants[2])))/(power(constants[1], constants[2])+power(states[1], constants[2]))
    algebraic[1] = (constants[3]*states[0])/1.00000
    algebraic[2] = ((constants[8]*(power(states[1], 2.00000)))/(power(constants[9], 2.00000)+power(states[1], 2.00000)))*(states[3]-states[1])
    algebraic[3] = constants[10]*states[1]
    algebraic[4] = constants[11]*(states[3]-states[1])
    algebraic[5] = constants[14]-(states[1]+(constants[6]/constants[7])*states[3])
    algebraic[6] = constants[12]*algebraic[5]
    algebraic[7] = constants[15]-algebraic[5]
    algebraic[8] = constants[13]*states[1]*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)