Generated Code

# Size of variable arrays:
sizeAlgebraic = 10
sizeStates = 7
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 = "time in component environment (second)"
    legend_states[0] = "q_L in component environment (fmol)"
    legend_states[1] = "q_K1 in component environment (fmol)"
    legend_states[2] = "q_K2 in component environment (fmol)"
    legend_states[3] = "q_LK1 in component environment (fmol)"
    legend_states[4] = "q_K2P in component environment (fmol)"
    legend_states[5] = "q_P in component environment (fmol)"
    legend_states[6] = "q_LK1K2 in component environment (fmol)"
    legend_algebraic[7] = "v_Re1 in component RTK (fmol_per_sec)"
    legend_algebraic[8] = "v_Re2 in component RTK (fmol_per_sec)"
    legend_algebraic[9] = "v_Re3 in component RTK (fmol_per_sec)"
    legend_constants[0] = "kappa_Re1 in component RTK_parameters (fmol_per_sec)"
    legend_constants[1] = "kappa_Re2 in component RTK_parameters (fmol_per_sec)"
    legend_constants[2] = "kappa_Re3 in component RTK_parameters (fmol_per_sec)"
    legend_constants[3] = "K_L in component RTK_parameters (per_fmol)"
    legend_constants[4] = "K_K1 in component RTK_parameters (per_fmol)"
    legend_constants[5] = "K_K2 in component RTK_parameters (per_fmol)"
    legend_constants[6] = "K_LK1 in component RTK_parameters (per_fmol)"
    legend_constants[7] = "K_K2P in component RTK_parameters (per_fmol)"
    legend_constants[8] = "K_P in component RTK_parameters (per_fmol)"
    legend_constants[9] = "K_LK1K2 in component RTK_parameters (per_fmol)"
    legend_constants[10] = "R in component constants (J_per_K_per_mol)"
    legend_constants[11] = "T in component constants (kelvin)"
    legend_algebraic[0] = "mu_L in component RTK (J_per_mol)"
    legend_algebraic[1] = "mu_K1 in component RTK (J_per_mol)"
    legend_algebraic[2] = "mu_K2 in component RTK (J_per_mol)"
    legend_algebraic[3] = "mu_LK1 in component RTK (J_per_mol)"
    legend_algebraic[4] = "mu_K2P in component RTK (J_per_mol)"
    legend_algebraic[5] = "mu_P in component RTK (J_per_mol)"
    legend_algebraic[6] = "mu_LK1K2 in component RTK (J_per_mol)"
    legend_constants[12] = "F in component constants (C_per_mol)"
    legend_rates[0] = "d/dt q_L in component environment (fmol)"
    legend_rates[1] = "d/dt q_K1 in component environment (fmol)"
    legend_rates[2] = "d/dt q_K2 in component environment (fmol)"
    legend_rates[3] = "d/dt q_LK1 in component environment (fmol)"
    legend_rates[4] = "d/dt q_K2P in component environment (fmol)"
    legend_rates[5] = "d/dt q_P in component environment (fmol)"
    legend_rates[6] = "d/dt q_LK1K2 in component environment (fmol)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 1
    states[1] = 1e-3
    states[2] = 1e-3
    states[3] = 1e-6
    states[4] = 1e-9
    states[5] = 1
    states[6] = 1e-9
    constants[0] = 0.000186898
    constants[1] = 0.0125535
    constants[2] = 132.879
    constants[3] = 197.162
    constants[4] = 197.162
    constants[5] = 4.01297e+09
    constants[6] = 0.00144219
    constants[7] = 3.79118e-07
    constants[8] = 2.54645e+07
    constants[9] = 2.14714e-05
    constants[10] = 8.31
    constants[11] = 310
    constants[12] = 96485
    return (states, constants)

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