# Size of variable arrays: sizeAlgebraic = 6 sizeStates = 3 sizeConstants = 28 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[27] = "v_GK in component v_GK (flux)" legend_constants[0] = "V_GK_min in component v_GK (enzyme_activity)" legend_constants[24] = "V_GK in component v_GK (enzyme_activity)" legend_constants[1] = "Sgk in component v_GK (millimolar)" legend_constants[2] = "h_GK in component v_GK (dimensionless)" legend_constants[26] = "Glc in component Glc (millimolar)" legend_constants[3] = "min_to_sec in component model_parameters (dimensionless)" legend_constants[4] = "dw_per_ml in component model_parameters (dimensionless)" legend_algebraic[1] = "v_PFK in component v_PFK (flux)" legend_constants[5] = "V_PFK_min in component v_PFK (enzyme_activity)" legend_constants[22] = "V_PFK in component v_PFK (enzyme_activity)" legend_constants[6] = "Spfk in component v_PFK (millimolar)" legend_constants[7] = "Sfba in component v_PFK (millimolar)" legend_constants[8] = "Xpfk in component v_PFK (millimolar)" legend_constants[9] = "hx in component v_PFK (dimensionless)" legend_constants[10] = "alpha in component v_PFK (dimensionless)" legend_constants[11] = "h_PFK in component v_PFK (dimensionless)" legend_constants[12] = "h_act in component v_PFK (dimensionless)" legend_states[0] = "FBP in component FBP (millimolar)" legend_algebraic[0] = "F6P in component F6P (millimolar)" legend_algebraic[5] = "v_FBA in component v_FBA (flux)" legend_constants[13] = "V_FBA_min in component v_FBA (enzyme_activity)" legend_constants[23] = "V_FBA in component v_FBA (enzyme_activity)" legend_constants[14] = "Qfba in component v_FBA (millimolar)" legend_constants[15] = "Sfba in component v_FBA (millimolar)" legend_constants[16] = "Pfba in component v_FBA (millimolar)" legend_constants[17] = "Keq_FBA in component v_FBA (millimolar)" legend_algebraic[2] = "G3P in component G3P (millimolar)" legend_algebraic[4] = "DHAP in component DHAP (millimolar)" legend_algebraic[3] = "v_GAPDH in component v_GAPDH (flux)" legend_constants[18] = "V_GAPDH_min in component v_GAPDH (enzyme_activity)" legend_constants[25] = "V_GAPDH in component v_GAPDH (enzyme_activity)" legend_constants[19] = "Sgapdh in component v_GAPDH (millimolar)" legend_states[1] = "G6P_F6P in component G6P_F6P (millimolar)" legend_constants[20] = "Keq_GPI in component F6P (dimensionless)" legend_states[2] = "DHAP_G3P in component DHAP_G3P (millimolar)" legend_constants[21] = "Keq_TPI in component G3P (dimensionless)" legend_rates[1] = "d/dt G6P_F6P in component G6P_F6P (millimolar)" legend_rates[0] = "d/dt FBP in component FBP (millimolar)" legend_rates[2] = "d/dt DHAP_G3P in component DHAP_G3P (millimolar)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 10.0 constants[1] = 8.0 constants[2] = 1.7 constants[3] = 60.0 constants[4] = 0.3333 constants[5] = 100.0 constants[6] = 4.0 constants[7] = 0.005 constants[8] = 0.01 constants[9] = 2.5 constants[10] = 5.0 constants[11] = 2.5 constants[12] = 1.0 states[0] = 0.00063612 constants[13] = 25.0 constants[14] = 0.275 constants[15] = 0.005 constants[16] = 0.5 constants[17] = 0.1 constants[18] = 250.0 constants[19] = 0.005 states[1] = 3.71728 constants[20] = 0.3 states[2] = 0.00262966 constants[21] = 0.045455 constants[22] = (constants[5]*constants[4])/constants[3] constants[23] = (constants[13]*constants[4])/constants[3] constants[24] = (constants[0]*constants[4])/constants[3] constants[25] = (constants[18]*constants[4])/constants[3] constants[26] = 10.0000 constants[27] = (constants[24]*(power(constants[26]/constants[1], constants[2])))/(1.00000+power(constants[26]/constants[1], constants[2])) return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = (states[1]*constants[20])/(1.00000+constants[20]) algebraic[1] = (constants[22]*(power(algebraic[0]/constants[6], constants[11]-(constants[11]-constants[12])*((states[0]/constants[7])/(1.00000+states[0]/constants[7])))))/(power(algebraic[0]/constants[6], constants[11]-(constants[11]-constants[12])*((states[0]/constants[7])/(1.00000+states[0]/constants[7])))+(1.00000+power(states[0]/constants[8], constants[9]))/(1.00000+(power(constants[10], constants[11]-(constants[11]-constants[12])*((states[0]/constants[7])/(1.00000+states[0]/constants[7]))))*(power(states[0]/constants[8], constants[9])))) rates[1] = constants[27]-algebraic[1] algebraic[2] = (states[2]*constants[21])/(1.00000+constants[21]) algebraic[4] = states[2]-algebraic[2] algebraic[5] = (constants[23]*(states[0]/constants[15]-(algebraic[2]*algebraic[4])/(constants[16]*constants[14]*constants[17])))/(1.00000+states[0]/constants[15]+algebraic[4]/constants[14]+(algebraic[2]*algebraic[4])/(constants[16]*constants[14])) rates[0] = algebraic[1]-algebraic[5] algebraic[3] = (constants[25]*algebraic[2])/(constants[19]+algebraic[2]) rates[2] = 2.00000*algebraic[5]-algebraic[3] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = (states[1]*constants[20])/(1.00000+constants[20]) algebraic[1] = (constants[22]*(power(algebraic[0]/constants[6], constants[11]-(constants[11]-constants[12])*((states[0]/constants[7])/(1.00000+states[0]/constants[7])))))/(power(algebraic[0]/constants[6], constants[11]-(constants[11]-constants[12])*((states[0]/constants[7])/(1.00000+states[0]/constants[7])))+(1.00000+power(states[0]/constants[8], constants[9]))/(1.00000+(power(constants[10], constants[11]-(constants[11]-constants[12])*((states[0]/constants[7])/(1.00000+states[0]/constants[7]))))*(power(states[0]/constants[8], constants[9])))) algebraic[2] = (states[2]*constants[21])/(1.00000+constants[21]) algebraic[4] = states[2]-algebraic[2] algebraic[5] = (constants[23]*(states[0]/constants[15]-(algebraic[2]*algebraic[4])/(constants[16]*constants[14]*constants[17])))/(1.00000+states[0]/constants[15]+algebraic[4]/constants[14]+(algebraic[2]*algebraic[4])/(constants[16]*constants[14])) algebraic[3] = (constants[25]*algebraic[2])/(constants[19]+algebraic[2]) 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)