Generated Code

# Size of variable arrays:
sizeAlgebraic = 10
sizeStates = 5
sizeConstants = 13
from math import *
from numpy import *

def createLegends():
    legend_states = [""] * sizeStates
    legend_rates = [""] * sizeStates
    legend_algebraic = [""] * sizeAlgebraic
    legend_voi = ""
    legend_constants = [""] * sizeConstants
    legend_voi = "t in component environment (second)"
    legend_constants[0] = "C_m in component environment (fF)"
    legend_constants[1] = "w_i in component environment (pL)"
    legend_constants[2] = "w_o in component environment (pL)"
    legend_states[0] = "q_mem in component environment (fC)"
    legend_constants[3] = "R in component environment (J_per_K_per_mol)"
    legend_constants[4] = "T in component environment (kelvin)"
    legend_constants[5] = "F in component environment (C_per_mol)"
    legend_algebraic[7] = "v_pCa_R1 in component pCa (fmol_per_sec)"
    legend_algebraic[8] = "v_pCa_R2 in component pCa (fmol_per_sec)"
    legend_states[1] = "q_Ca_o in component environment (fmol)"
    legend_states[2] = "q_Ca_i in component environment (fmol)"
    legend_states[3] = "q_pCa in component environment (fmol)"
    legend_states[4] = "q_pCa_Ca in component environment (fmol)"
    legend_algebraic[1] = "V_mem in component environment (J_per_C)"
    legend_algebraic[9] = "I_mem_pCa in component pCa (fA)"
    legend_algebraic[2] = "Ca_T in component environment (fmol)"
    legend_algebraic[3] = "channel_T in component environment (fmol)"
    legend_constants[6] = "kappa_pCa_R1 in component pCa_parameters (fmol_per_sec)"
    legend_constants[7] = "kappa_pCa_R2 in component pCa_parameters (fmol_per_sec)"
    legend_constants[8] = "K_Ca_i in component pCa_parameters (per_fmol)"
    legend_constants[9] = "K_Ca_o in component pCa_parameters (per_fmol)"
    legend_constants[10] = "K_pCa in component pCa_parameters (per_fmol)"
    legend_constants[11] = "K_pCa_Ca in component pCa_parameters (per_fmol)"
    legend_constants[12] = "zCa in component pCa_parameters (dimensionless)"
    legend_algebraic[0] = "mu_Ca_i in component pCa (J_per_mol)"
    legend_algebraic[4] = "mu_Ca_o in component pCa (J_per_mol)"
    legend_algebraic[5] = "mu_pCa in component pCa (J_per_mol)"
    legend_algebraic[6] = "mu_pCa_Ca in component pCa (J_per_mol)"
    legend_rates[2] = "d/dt q_Ca_i in component environment (fmol)"
    legend_rates[1] = "d/dt q_Ca_o in component environment (fmol)"
    legend_rates[3] = "d/dt q_pCa in component environment (fmol)"
    legend_rates[4] = "d/dt q_pCa_Ca in component environment (fmol)"
    legend_rates[0] = "d/dt q_mem in component environment (fC)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 153400
    constants[1] = 25.8
    constants[2] = 3.52
    states[0] = -8.5e4
    constants[3] = 8.31
    constants[4] = 310
    constants[5] = 96500
    states[1] = 9.3276
    states[2] = 0.00456
    states[3] = 0.0032
    states[4] = 1e-9
    constants[6] = 1451.43
    constants[7] = 0.00014695
    constants[8] = 32.3484
    constants[9] = 0.00010737
    constants[10] = 0.0179984
    constants[11] = 0.0100142
    constants[12] = 2
    return (states, constants)

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

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