Generated Code

# Size of variable arrays:
sizeAlgebraic = 1
sizeStates = 5
sizeConstants = 18
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 (hour)"
    legend_states[0] = "M in component M (micromolar)"
    legend_constants[0] = "Km in component M (micromolar)"
    legend_constants[1] = "vs in component M (flux)"
    legend_constants[2] = "vm in component M (flux)"
    legend_constants[3] = "n in component M (dimensionless)"
    legend_constants[4] = "KI in component M (micromolar)"
    legend_states[1] = "PN in component PN (micromolar)"
    legend_states[2] = "P0 in component P0 (micromolar)"
    legend_constants[5] = "ks in component P0 (first_order_rate_constant)"
    legend_states[3] = "P1 in component P1 (micromolar)"
    legend_constants[6] = "K1 in component parameters (micromolar)"
    legend_constants[7] = "V1 in component parameters (flux)"
    legend_constants[8] = "K2 in component parameters (micromolar)"
    legend_constants[9] = "V2 in component parameters (flux)"
    legend_states[4] = "P2 in component P2 (micromolar)"
    legend_constants[10] = "K3 in component parameters (micromolar)"
    legend_constants[11] = "V3 in component parameters (flux)"
    legend_constants[12] = "K4 in component parameters (micromolar)"
    legend_constants[13] = "V4 in component parameters (flux)"
    legend_constants[14] = "Kd in component P2 (micromolar)"
    legend_constants[15] = "vd in component P2 (flux)"
    legend_constants[16] = "k1 in component parameters (first_order_rate_constant)"
    legend_constants[17] = "k2 in component parameters (first_order_rate_constant)"
    legend_algebraic[0] = "Pt in component Pt (micromolar)"
    legend_rates[0] = "d/dt M in component M (micromolar)"
    legend_rates[2] = "d/dt P0 in component P0 (micromolar)"
    legend_rates[3] = "d/dt P1 in component P1 (micromolar)"
    legend_rates[4] = "d/dt P2 in component P2 (micromolar)"
    legend_rates[1] = "d/dt PN in component PN (micromolar)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    states[0] = 0.6
    constants[0] = 0.5
    constants[1] = 0.76
    constants[2] = 0.65
    constants[3] = 4.0
    constants[4] = 1.0
    states[1] = 1.1
    states[2] = 0.5
    constants[5] = 0.38
    states[3] = 0.6
    constants[6] = 2.0
    constants[7] = 3.2
    constants[8] = 2.0
    constants[9] = 1.58
    states[4] = 0.6
    constants[10] = 2.0
    constants[11] = 5.0
    constants[12] = 2.0
    constants[13] = 2.5
    constants[14] = 0.2
    constants[15] = 0.95
    constants[16] = 1.9
    constants[17] = 1.3
    return (states, constants)

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

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = states[2]+states[3]+states[4]+states[1]
    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)