# Size of variable arrays: sizeAlgebraic = 6 sizeStates = 13 sizeConstants = 23 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] = "Cdk2_CycE in component Cdk2_CycE (dimensionless)" legend_constants[0] = "kwee in component kinetic_parameters (first_order_rate_constant)" legend_constants[1] = "kon in component kinetic_parameters (first_order_rate_constant)" legend_constants[2] = "k25A in component kinetic_parameters (first_order_rate_constant)" legend_constants[3] = "koff in component kinetic_parameters (first_order_rate_constant)" legend_constants[4] = "kassoc in component kinetic_parameters (first_order_rate_constant)" legend_constants[5] = "kdissoc in component kinetic_parameters (first_order_rate_constant)" legend_algebraic[4] = "phi in component kinetic_parameters (dimensionless)" legend_states[1] = "Wee1_a in component Wee1_a (dimensionless)" legend_states[2] = "PCdk2_CycE in component PCdk2_CycE (dimensionless)" legend_states[3] = "Xic in component Xic (dimensionless)" legend_states[4] = "Cdk2_CycErem in component Cdk2_CycErem (dimensionless)" legend_states[5] = "Xic_Cdk2_CycE in component Xic_Cdk2_CycE (dimensionless)" legend_states[6] = "PCdk2_CycErem in component PCdk2_CycErem (dimensionless)" legend_states[7] = "Xic_PCdk2_CycE in component Xic_PCdk2_CycE (dimensionless)" legend_constants[6] = "Jwact in component Wee1_a (dimensionless)" legend_constants[7] = "Jwinact in component Wee1_a (dimensionless)" legend_constants[8] = "Wee1_total in component Wee1_a (dimensionless)" legend_constants[9] = "kwact in component Wee1_a (first_order_rate_constant)" legend_constants[10] = "kwinact in component Wee1_a (first_order_rate_constant)" legend_states[8] = "Kin_a in component Kin_a (dimensionless)" legend_constants[11] = "Jiact in component Kin_a (dimensionless)" legend_constants[12] = "Jiinact in component Kin_a (dimensionless)" legend_constants[13] = "kiact in component Kin_a (first_order_rate_constant)" legend_constants[14] = "kiinact in component Kin_a (first_order_rate_constant)" legend_constants[15] = "kedeg in component kinetic_parameters (first_order_rate_constant)" legend_constants[16] = "kxdeg in component kinetic_parameters (first_order_rate_constant)" legend_states[9] = "Deg_a in component Deg_a (dimensionless)" legend_states[10] = "Xic_Cdk2_CycErem in component Xic_Cdk2_CycErem (dimensionless)" legend_states[11] = "Xic_PCdk2_CycErem in component Xic_PCdk2_CycErem (dimensionless)" legend_algebraic[5] = "Heav in component Deg_a (dimensionless)" legend_constants[17] = "kdact in component Deg_a (first_order_rate_constant)" legend_constants[18] = "theta in component Deg_a (dimensionless)" legend_algebraic[1] = "x in component Deg_a (dimensionless)" legend_constants[19] = "Deg in component kinetic_parameters (dimensionless)" legend_states[12] = "Xicrem in component Xicrem (dimensionless)" legend_algebraic[2] = "Cyc_total in component Cyc_total (dimensionless)" legend_algebraic[3] = "Xic_total in component Xic_total (dimensionless)" legend_constants[20] = "epsilon in component kinetic_parameters (dimensionless)" legend_algebraic[0] = "pool in component kinetic_parameters (dimensionless)" legend_constants[21] = "n in component kinetic_parameters (dimensionless)" legend_constants[22] = "L in component kinetic_parameters (dimensionless)" legend_rates[0] = "d/dt Cdk2_CycE in component Cdk2_CycE (dimensionless)" legend_rates[2] = "d/dt PCdk2_CycE in component PCdk2_CycE (dimensionless)" legend_rates[1] = "d/dt Wee1_a in component Wee1_a (dimensionless)" legend_rates[8] = "d/dt Kin_a in component Kin_a (dimensionless)" legend_rates[4] = "d/dt Cdk2_CycErem in component Cdk2_CycErem (dimensionless)" legend_rates[6] = "d/dt PCdk2_CycErem in component PCdk2_CycErem (dimensionless)" legend_rates[9] = "d/dt Deg_a in component Deg_a (dimensionless)" legend_rates[3] = "d/dt Xic in component Xic (dimensionless)" legend_rates[5] = "d/dt Xic_Cdk2_CycE in component Xic_Cdk2_CycE (dimensionless)" legend_rates[7] = "d/dt Xic_PCdk2_CycE in component Xic_PCdk2_CycE (dimensionless)" legend_rates[10] = "d/dt Xic_Cdk2_CycErem in component Xic_Cdk2_CycErem (dimensionless)" legend_rates[11] = "d/dt Xic_PCdk2_CycErem in component Xic_PCdk2_CycErem (dimensionless)" legend_rates[12] = "d/dt Xicrem in component Xicrem (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.06 constants[0] = 1.5 constants[1] = 0.02 constants[2] = 0.1 constants[3] = 0.0001 constants[4] = 0.1 constants[5] = 0.001 states[1] = 1.02 states[2] = 0.94 states[3] = 3 states[4] = 0 states[5] = 0 states[6] = 0 states[7] = 0 constants[6] = 0.01 constants[7] = 0.01 constants[8] = 8 constants[9] = 0.75 constants[10] = 1.5 states[8] = 0.6 constants[11] = 0.01 constants[12] = 0.01 constants[13] = 0.15 constants[14] = 0.6 constants[15] = 0.017 constants[16] = 0.01 states[9] = 0 states[10] = 0 states[11] = 0 constants[17] = 0.023 constants[18] = 0.3 constants[19] = 0 states[12] = 0 constants[20] = 0.001 constants[21] = 4 constants[22] = 0.4 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[1] = (constants[9]*(constants[8]-states[1]))/((constants[6]+constants[8])-states[1])-(constants[10]*states[8]*states[1])/(constants[7]+states[1]) rates[8] = (constants[13]*(1.00000-states[8]))/((constants[11]+1.00000)-states[8])-(constants[14]*states[0]*states[8])/(constants[12]+states[8]) rates[3] = constants[5]*(states[5]+states[7]+states[10]+states[11])-constants[4]*states[3]*(states[0]+states[2]+states[4]+states[6]) rates[12] = (constants[15]*states[9]*states[10]+constants[15]*states[9]*states[11])-constants[16]*states[12] algebraic[0] = states[4]+states[6]+states[10]+states[11] algebraic[4] = (constants[20]+power(algebraic[0], constants[21]))/(power(constants[22], constants[21])+power(algebraic[0], constants[21])) rates[0] = (constants[2]*states[2]+constants[3]*states[4]+constants[5]*states[5])-(constants[0]*states[1]*states[0]+constants[1]*algebraic[4]*states[0]+constants[4]*states[3]*states[0]) rates[2] = (constants[0]*states[1]*states[0]+constants[3]*states[6]+constants[5]*states[7])-(constants[2]*states[2]+constants[1]*algebraic[4]*states[2]+constants[4]*states[3]*states[2]) rates[4] = (constants[1]*algebraic[4]*states[0]+constants[16]*states[10]+constants[5]*states[10])-(constants[3]*states[4]+constants[15]*states[9]*states[4]+constants[4]*states[3]*states[4]) rates[6] = (constants[1]*algebraic[4]*states[2]+constants[16]*states[11]+constants[5]*states[11])-(constants[3]*states[6]+constants[15]*states[9]*states[6]+constants[4]*states[3]*states[6]) algebraic[1] = states[4]-constants[18] algebraic[5] = custom_piecewise([less(algebraic[1] , 0.00000), 0.00000 , True, 1.00000]) rates[9] = constants[17]*algebraic[5] rates[5] = (constants[4]*states[3]*states[0]+constants[3]*states[10]+constants[2]*states[7])-(constants[5]*states[5]+constants[1]*algebraic[4]*states[5]+constants[0]*states[1]*states[5]) rates[7] = (constants[4]*states[3]*states[2]+constants[3]*states[11]+constants[0]*states[1]*states[5])-(constants[5]*states[7]+constants[1]*algebraic[4]*states[7]+constants[2]*states[7]) rates[10] = (constants[4]*states[3]*states[4]+constants[1]*algebraic[4]*states[5])-(constants[5]*states[10]+constants[3]*states[10]+constants[15]*states[9]*states[10]+constants[16]*states[10]) rates[11] = (constants[4]*states[3]*states[6]+constants[1]*algebraic[4]*states[7])-(constants[5]*states[11]+constants[3]*states[11]+constants[15]*constants[19]*states[11]+constants[16]*states[11]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = states[4]+states[6]+states[10]+states[11] algebraic[4] = (constants[20]+power(algebraic[0], constants[21]))/(power(constants[22], constants[21])+power(algebraic[0], constants[21])) algebraic[1] = states[4]-constants[18] algebraic[5] = custom_piecewise([less(algebraic[1] , 0.00000), 0.00000 , True, 1.00000]) algebraic[2] = states[7]+states[5]+states[11]+states[10]+states[6]+states[4]+states[0]+states[2] algebraic[3] = (states[3]+states[7]+states[5]+states[11]+states[10]+states[12])/3.00000 return algebraic def custom_piecewise(cases): """Compute result of a piecewise function""" return select(cases[0::2],cases[1::2]) 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)