# Size of variable arrays: sizeAlgebraic = 4 sizeStates = 3 sizeConstants = 26 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 (minute)" legend_states[0] = "Pha in component Pha (dimensionless)" legend_algebraic[0] = "V_1 in component V_1 (dimensionless)" legend_states[1] = "Z in component Z (dimensionless)" legend_algebraic[2] = "K_1 in component K_1 (dimensionless)" legend_constants[0] = "V_M2 in component Pha (per_minute)" legend_constants[1] = "alpha in component Pha (dimensionless)" legend_constants[2] = "Glc in component Pha (micromolar)" legend_constants[3] = "K_2 in component Pha (dimensionless)" legend_constants[4] = "K_a1 in component Pha (micromolar)" legend_constants[5] = "K_a2 in component Pha (micromolar)" legend_constants[6] = "V_M1 in component V_1 (per_minute)" legend_constants[7] = "gamma in component V_1 (dimensionless)" legend_constants[8] = "K_a5 in component V_1 (micromolar)" legend_constants[9] = "K_11 in component K_1 (dimensionless)" legend_constants[10] = "K_a6 in component K_1 (micromolar)" legend_constants[25] = "V_in in component V_in (dimensionless)" legend_algebraic[1] = "V_2i in component V_2i (dimensionless)" legend_algebraic[3] = "V_3i in component V_3i (dimensionless)" legend_constants[11] = "k_f in component Z (per_minute)" legend_states[2] = "Y in component Y (dimensionless)" legend_constants[12] = "k in component Z (per_minute)" legend_constants[13] = "k_f in component Y (per_minute)" legend_constants[14] = "v_0 in component V_in (micromolar_per_minute)" legend_constants[15] = "v_1 in component V_in (micromolar_per_minute)" legend_constants[16] = "beta in component V_in (dimensionless)" legend_constants[17] = "v_M2i in component V_2i (micromolar_per_minute)" legend_constants[18] = "n in component V_2i (dimensionless)" legend_constants[19] = "K_2i in component V_2i (micromolar)" legend_constants[20] = "v_M3i in component V_3i (micromolar_per_minute)" legend_constants[21] = "p in component V_3i (dimensionless)" legend_constants[22] = "m in component V_3i (dimensionless)" legend_constants[23] = "K_Ri in component V_3i (micromolar)" legend_constants[24] = "K_Ai in component V_3i (micromolar)" legend_rates[0] = "d/dt Pha in component Pha (dimensionless)" legend_rates[1] = "d/dt Z in component Z (dimensionless)" legend_rates[2] = "d/dt Y in component Y (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.098 states[1] = 0.000179 constants[0] = 0.6 constants[1] = 9 constants[2] = 10000 constants[3] = 0.2 constants[4] = 10000 constants[5] = 10000 constants[6] = 1.5 constants[7] = 9 constants[8] = 0.5 constants[9] = 0.1 constants[10] = 0.5 constants[11] = 0.7 states[2] = 0.00122 constants[12] = 10 constants[13] = 0.7 constants[14] = 1 constants[15] = 5.7 constants[16] = 0.3 constants[17] = 30 constants[18] = 2 constants[19] = 0.5 constants[20] = 325 constants[21] = 4 constants[22] = 4 constants[23] = 1.7 constants[24] = 0.46 constants[25] = constants[14]+constants[15]*constants[16] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = constants[6]*(1.00000+constants[7]*((power(states[1], 4.00000))/(power(constants[8], 4.00000))+power(states[1], 4.00000))) algebraic[2] = constants[9]/(1.00000+(power(states[1], 4.00000))/(power(constants[10], 4.00000))) rates[0] = algebraic[0]*states[1]*((1.00000-states[0])/((algebraic[2]*states[1]+1.00000)-states[0]))-(constants[0]*(1.00000+(constants[1]*constants[2])/(constants[4]+constants[2]))*states[0])/(constants[3]/(1.00000+constants[2]/constants[5])+states[0]) algebraic[1] = constants[17]*((power(states[1], constants[18]))/(power(constants[19], constants[18])+power(states[1], constants[18]))) algebraic[3] = constants[20]*((power(states[2], constants[22]))/(power(constants[23], constants[22]))+power(states[2], constants[18]))*((power(states[1], constants[21]))/(power(constants[24], constants[21])+power(states[1], constants[21]))) rates[1] = ((constants[25]-algebraic[1])+algebraic[3]+constants[11]*states[2])-constants[12]*states[1] rates[2] = (algebraic[1]-algebraic[3])-constants[13]*states[2] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[6]*(1.00000+constants[7]*((power(states[1], 4.00000))/(power(constants[8], 4.00000))+power(states[1], 4.00000))) algebraic[2] = constants[9]/(1.00000+(power(states[1], 4.00000))/(power(constants[10], 4.00000))) algebraic[1] = constants[17]*((power(states[1], constants[18]))/(power(constants[19], constants[18])+power(states[1], constants[18]))) algebraic[3] = constants[20]*((power(states[2], constants[22]))/(power(constants[23], constants[22]))+power(states[2], constants[18]))*((power(states[1], constants[21]))/(power(constants[24], constants[21])+power(states[1], constants[21]))) 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)