Generated Code

# Size of variable arrays:
sizeAlgebraic = 16
sizeStates = 6
sizeConstants = 19
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_constants[0] = "q_PKACI_init in component environment (fmol)"
    legend_constants[1] = "q_Ip_init in component environment (fmol)"
    legend_constants[2] = "q_Ip_PKACI_init in component environment (fmol)"
    legend_constants[3] = "q_PP2a_init in component environment (fmol)"
    legend_constants[4] = "q_Ip_PP2a_init in component environment (fmol)"
    legend_constants[5] = "q_I_init in component environment (fmol)"
    legend_algebraic[0] = "q_PKACI in component environment (fmol)"
    legend_algebraic[1] = "q_Ip in component environment (fmol)"
    legend_algebraic[2] = "q_Ip_PKACI in component environment (fmol)"
    legend_algebraic[3] = "q_PP2a in component environment (fmol)"
    legend_algebraic[4] = "q_Ip_PP2a in component environment (fmol)"
    legend_algebraic[5] = "q_I in component environment (fmol)"
    legend_states[0] = "q_PKACI in component Inhib1 (fmol)"
    legend_states[1] = "q_Ip in component Inhib1 (fmol)"
    legend_states[2] = "q_Ip_PKACI in component Inhib1 (fmol)"
    legend_states[3] = "q_PP2a in component Inhib1 (fmol)"
    legend_states[4] = "q_Ip_PP2a in component Inhib1 (fmol)"
    legend_states[5] = "q_I in component Inhib1 (fmol)"
    legend_constants[6] = "kappa_PKAi1 in component Inhib1_parameters (fmol_per_sec)"
    legend_constants[7] = "kappa_PKAi2 in component Inhib1_parameters (fmol_per_sec)"
    legend_constants[8] = "kappa_PP2ai1 in component Inhib1_parameters (fmol_per_sec)"
    legend_constants[9] = "kappa_PP2ai2 in component Inhib1_parameters (fmol_per_sec)"
    legend_constants[10] = "K_PKACI in component Inhib1_parameters (per_fmol)"
    legend_constants[11] = "K_Ip in component Inhib1_parameters (per_fmol)"
    legend_constants[12] = "K_Ip_PKACI in component Inhib1_parameters (per_fmol)"
    legend_constants[13] = "K_PP2a in component Inhib1_parameters (per_fmol)"
    legend_constants[14] = "K_Ip_PP2a in component Inhib1_parameters (per_fmol)"
    legend_constants[15] = "K_I in component Inhib1_parameters (per_fmol)"
    legend_constants[16] = "R in component constants (J_per_K_per_mol)"
    legend_constants[17] = "T in component constants (kelvin)"
    legend_algebraic[12] = "vPKAi1 in component Inhib1 (fmol_per_sec)"
    legend_algebraic[13] = "vPKAi2 in component Inhib1 (fmol_per_sec)"
    legend_algebraic[14] = "vPP2ai1 in component Inhib1 (fmol_per_sec)"
    legend_algebraic[15] = "vPP2ai2 in component Inhib1 (fmol_per_sec)"
    legend_algebraic[6] = "mu_PKACI in component Inhib1 (J_per_mol)"
    legend_algebraic[7] = "mu_Ip in component Inhib1 (J_per_mol)"
    legend_algebraic[8] = "mu_Ip_PKACI in component Inhib1 (J_per_mol)"
    legend_algebraic[9] = "mu_PP2a in component Inhib1 (J_per_mol)"
    legend_algebraic[10] = "mu_Ip_PP2a in component Inhib1 (J_per_mol)"
    legend_algebraic[11] = "mu_I in component Inhib1 (J_per_mol)"
    legend_constants[18] = "F in component constants (C_per_mol)"
    legend_rates[0] = "d/dt q_PKACI in component Inhib1 (fmol)"
    legend_rates[1] = "d/dt q_Ip in component Inhib1 (fmol)"
    legend_rates[2] = "d/dt q_Ip_PKACI in component Inhib1 (fmol)"
    legend_rates[3] = "d/dt q_PP2a in component Inhib1 (fmol)"
    legend_rates[4] = "d/dt q_Ip_PP2a in component Inhib1 (fmol)"
    legend_rates[5] = "d/dt q_I in component Inhib1 (fmol)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 1.117E-03
    constants[1] = 9.994E-04
    constants[2] = 1e-13
    constants[3] = 8.512E-03
    constants[4] = 1e-13
    constants[5] = 1.140E-02
    states[0] = 1e-16
    states[1] = 1e-16
    states[2] = 1e-16
    states[3] = 1e-16
    states[4] = 1e-16
    states[5] = 1e-16
    constants[6] = 20.9606
    constants[7] = 22.2706
    constants[8] = 5.39341
    constants[9] = 5.30013
    constants[10] = 0.284433
    constants[11] = 0.133405
    constants[12] = 1.38688
    constants[13] = 0.0704691
    constants[14] = 0.342795
    constants[15] = 0.150247
    constants[16] = 8.31
    constants[17] = 310
    constants[18] = 96485
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = states[0]+constants[0]
    algebraic[6] = constants[16]*constants[17]*log(constants[10]*algebraic[0])
    algebraic[2] = states[2]+constants[2]
    algebraic[8] = constants[16]*constants[17]*log(constants[12]*algebraic[2])
    algebraic[5] = states[5]+constants[5]
    algebraic[11] = constants[16]*constants[17]*log(constants[15]*algebraic[5])
    algebraic[12] = constants[6]*(exp((algebraic[6]+algebraic[11])/(constants[16]*constants[17]))-exp(algebraic[8]/(constants[16]*constants[17])))
    algebraic[1] = states[1]+constants[1]
    algebraic[7] = constants[16]*constants[17]*log(constants[11]*algebraic[1])
    algebraic[13] = constants[7]*(exp(algebraic[8]/(constants[16]*constants[17]))-exp((algebraic[6]+algebraic[7])/(constants[16]*constants[17])))
    rates[0] = algebraic[13]-algebraic[12]
    rates[2] = algebraic[12]-algebraic[13]
    algebraic[3] = states[3]+constants[3]
    algebraic[9] = constants[16]*constants[17]*log(constants[13]*algebraic[3])
    algebraic[4] = states[4]+constants[4]
    algebraic[10] = constants[16]*constants[17]*log(constants[14]*algebraic[4])
    algebraic[14] = constants[8]*(exp((algebraic[9]+algebraic[7])/(constants[16]*constants[17]))-exp(algebraic[10]/(constants[16]*constants[17])))
    rates[1] = algebraic[13]-algebraic[14]
    algebraic[15] = constants[9]*(exp(algebraic[10]/(constants[16]*constants[17]))-exp((algebraic[9]+algebraic[11])/(constants[16]*constants[17])))
    rates[3] = algebraic[15]-algebraic[14]
    rates[4] = algebraic[14]-algebraic[15]
    rates[5] = algebraic[15]-algebraic[12]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = states[0]+constants[0]
    algebraic[6] = constants[16]*constants[17]*log(constants[10]*algebraic[0])
    algebraic[2] = states[2]+constants[2]
    algebraic[8] = constants[16]*constants[17]*log(constants[12]*algebraic[2])
    algebraic[5] = states[5]+constants[5]
    algebraic[11] = constants[16]*constants[17]*log(constants[15]*algebraic[5])
    algebraic[12] = constants[6]*(exp((algebraic[6]+algebraic[11])/(constants[16]*constants[17]))-exp(algebraic[8]/(constants[16]*constants[17])))
    algebraic[1] = states[1]+constants[1]
    algebraic[7] = constants[16]*constants[17]*log(constants[11]*algebraic[1])
    algebraic[13] = constants[7]*(exp(algebraic[8]/(constants[16]*constants[17]))-exp((algebraic[6]+algebraic[7])/(constants[16]*constants[17])))
    algebraic[3] = states[3]+constants[3]
    algebraic[9] = constants[16]*constants[17]*log(constants[13]*algebraic[3])
    algebraic[4] = states[4]+constants[4]
    algebraic[10] = constants[16]*constants[17]*log(constants[14]*algebraic[4])
    algebraic[14] = constants[8]*(exp((algebraic[9]+algebraic[7])/(constants[16]*constants[17]))-exp(algebraic[10]/(constants[16]*constants[17])))
    algebraic[15] = constants[9]*(exp(algebraic[10]/(constants[16]*constants[17]))-exp((algebraic[9]+algebraic[11])/(constants[16]*constants[17])))
    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)