# Size of variable arrays: sizeAlgebraic = 8 sizeStates = 7 sizeConstants = 35 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] = "Y in component Y (dimensionless)" legend_constants[0] = "k1 in component Y (first_order_rate_constant)" legend_algebraic[6] = "k2 in component kinetic_parameters (first_order_rate_constant)" legend_constants[1] = "k3 in component kinetic_parameters (first_order_rate_constant)" legend_algebraic[0] = "C in component C (dimensionless)" legend_states[1] = "M in component M (dimensionless)" legend_algebraic[7] = "kwee in component kinetic_parameters (first_order_rate_constant)" legend_algebraic[5] = "kcdc25 in component kinetic_parameters (first_order_rate_constant)" legend_states[2] = "preMPF in component preMPF (dimensionless)" legend_states[3] = "Cdc25P in component Cdc25P (dimensionless)" legend_constants[2] = "k25 in component Cdc25P (first_order_rate_constant)" legend_constants[3] = "Km25 in component Cdc25P (dimensionless)" legend_constants[4] = "k25r in component Cdc25P (first_order_rate_constant)" legend_constants[33] = "k25ro in component Cdc25P (first_order_rate_constant)" legend_constants[5] = "Km25r in component Cdc25P (dimensionless)" legend_constants[32] = "p in component p (dimensionless)" legend_algebraic[2] = "Cdc25 in component Cdc25 (dimensionless)" legend_states[4] = "Wee1 in component Wee1 (dimensionless)" legend_constants[6] = "kw in component Wee1 (first_order_rate_constant)" legend_constants[7] = "Kmw in component Wee1 (dimensionless)" legend_constants[8] = "kwr in component Wee1 (first_order_rate_constant)" legend_constants[34] = "kwro in component Wee1 (first_order_rate_constant)" legend_constants[9] = "Kmwr in component Wee1 (dimensionless)" legend_algebraic[3] = "Wee1P in component Wee1P (dimensionless)" legend_states[5] = "IEP in component IEP (dimensionless)" legend_constants[10] = "kie in component IEP (first_order_rate_constant)" legend_constants[11] = "Kmie in component IEP (dimensionless)" legend_constants[12] = "kier in component IEP (first_order_rate_constant)" legend_constants[13] = "Kmier in component IEP (dimensionless)" legend_algebraic[1] = "IE in component IE (dimensionless)" legend_states[6] = "APC_ in component APC_ (dimensionless)" legend_constants[14] = "kap in component APC_ (first_order_rate_constant)" legend_constants[15] = "Kmap in component APC_ (dimensionless)" legend_constants[16] = "kapr in component APC_ (first_order_rate_constant)" legend_constants[17] = "Kmapr in component APC_ (dimensionless)" legend_algebraic[4] = "APC in component APC (dimensionless)" legend_constants[18] = "Cdc2tot in component C (dimensionless)" legend_constants[19] = "Cdc25tot in component Cdc25 (dimensionless)" legend_constants[20] = "Wee1tot in component Wee1P (dimensionless)" legend_constants[21] = "IEtot in component IE (dimensionless)" legend_constants[22] = "APCtot in component APC (dimensionless)" legend_constants[23] = "R in component p (dimensionless)" legend_constants[24] = "s in component p (dimensionless)" legend_constants[25] = "q in component p (dimensionless)" legend_constants[26] = "V2 in component kinetic_parameters (first_order_rate_constant)" legend_constants[27] = "V2_ in component kinetic_parameters (first_order_rate_constant)" legend_constants[28] = "V25 in component kinetic_parameters (first_order_rate_constant)" legend_constants[29] = "V25_ in component kinetic_parameters (first_order_rate_constant)" legend_constants[30] = "Vwee in component kinetic_parameters (first_order_rate_constant)" legend_constants[31] = "Vwee_ in component kinetic_parameters (first_order_rate_constant)" legend_rates[0] = "d/dt Y in component Y (dimensionless)" legend_rates[1] = "d/dt M in component M (dimensionless)" legend_rates[2] = "d/dt preMPF in component preMPF (dimensionless)" legend_rates[3] = "d/dt Cdc25P in component Cdc25P (dimensionless)" legend_rates[4] = "d/dt Wee1 in component Wee1 (dimensionless)" legend_rates[5] = "d/dt IEP in component IEP (dimensionless)" legend_rates[6] = "d/dt APC_ in component APC_ (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 0.01577552 constants[0] = 0.024 constants[1] = 1.15 states[1] = 0.0142077 states[2] = 0.02541723 states[3] = 0.4844362 constants[2] = 18 constants[3] = 0.1 constants[4] = 0.8 constants[5] = 1 states[4] = 0.5155638 constants[6] = 18 constants[7] = 0.1 constants[8] = 0.8 constants[9] = 1 states[5] = 0.002287817 constants[10] = 4.5 constants[11] = 0.01 constants[12] = 0.34 constants[13] = 0.01 states[6] = 0.5051103 constants[14] = 0.3 constants[15] = 0.01 constants[16] = 0.3 constants[17] = 1 constants[18] = 1 constants[19] = 1 constants[20] = 1 constants[21] = 1 constants[22] = 1 constants[23] = 1 constants[24] = 0.021 constants[25] = 1 constants[26] = 0.01 constants[27] = 0.6 constants[28] = 0.04 constants[29] = 0.4 constants[30] = 0.025 constants[31] = 2.5 constants[32] = constants[24]*constants[23]+constants[25] constants[33] = constants[4]/constants[32] constants[34] = constants[8]/constants[32] return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[1] = constants[21]-states[5] rates[5] = (constants[10]*states[1]*algebraic[1])/(constants[11]+algebraic[1])-(constants[12]*states[5])/(constants[13]+states[5]) algebraic[2] = constants[19]-states[3] rates[3] = (constants[2]*states[1]*algebraic[2])/(constants[3]+algebraic[2])-(constants[4]*states[3])/(constants[5]+states[3]) algebraic[3] = constants[20]-states[4] rates[4] = (-constants[6]*states[1]*states[4])/(constants[7]+states[4])+(constants[8]*algebraic[3])/(constants[9]+algebraic[3]) algebraic[4] = constants[22]-states[6] rates[6] = (constants[14]*states[5]*algebraic[4])/(constants[15]+algebraic[4])-(constants[16]*states[6])/(constants[17]+states[6]) algebraic[6] = constants[26]*algebraic[4]+constants[27]*states[6] algebraic[0] = constants[18]-(states[1]+states[2]) rates[0] = constants[0]-(algebraic[6]*states[0]+constants[1]*states[0]*algebraic[0]) algebraic[7] = constants[30]*algebraic[3]+constants[31]*states[4] algebraic[5] = constants[28]*algebraic[2]+constants[29]*states[3] rates[1] = (algebraic[5]*states[2]+constants[1]*states[0]*algebraic[0])-(algebraic[6]*states[1]+algebraic[7]*states[1]) rates[2] = algebraic[7]*states[1]-(algebraic[6]*states[2]+algebraic[5]*states[2]) return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[1] = constants[21]-states[5] algebraic[2] = constants[19]-states[3] algebraic[3] = constants[20]-states[4] algebraic[4] = constants[22]-states[6] algebraic[6] = constants[26]*algebraic[4]+constants[27]*states[6] algebraic[0] = constants[18]-(states[1]+states[2]) algebraic[7] = constants[30]*algebraic[3]+constants[31]*states[4] algebraic[5] = constants[28]*algebraic[2]+constants[29]*states[3] 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)