# Size of variable arrays: sizeAlgebraic = 9 sizeStates = 13 sizeConstants = 43 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_constants[0] = "k1 in component rate_constants (first_order_rate_constant)" legend_algebraic[1] = "k2 in component rate_constants (first_order_rate_constant)" legend_constants[1] = "k2_ in component rate_constants (first_order_rate_constant)" legend_constants[2] = "k3 in component rate_constants (first_order_rate_constant)" legend_constants[3] = "k4 in component rate_constants (first_order_rate_constant)" legend_constants[4] = "k5 in component rate_constants (first_order_rate_constant)" legend_algebraic[0] = "k6 in component rate_constants (first_order_rate_constant)" legend_constants[5] = "k6_ in component rate_constants (first_order_rate_constant)" legend_constants[6] = "k7 in component rate_constants (first_order_rate_constant)" legend_constants[7] = "k7r in component rate_constants (first_order_rate_constant)" legend_constants[8] = "k8 in component rate_constants (first_order_rate_constant)" legend_constants[9] = "k8r in component rate_constants (first_order_rate_constant)" legend_algebraic[5] = "kwee in component rate_constants (first_order_rate_constant)" legend_algebraic[7] = "k25 in component rate_constants (first_order_rate_constant)" legend_constants[10] = "ku in component rate_constants (first_order_rate_constant)" legend_constants[11] = "kp in component rate_constants (first_order_rate_constant)" legend_constants[12] = "kur in component rate_constants (first_order_rate_constant)" legend_constants[13] = "ku2 in component rate_constants (first_order_rate_constant)" legend_constants[14] = "kur2 in component rate_constants (first_order_rate_constant)" legend_constants[15] = "kc in component rate_constants (first_order_rate_constant)" legend_constants[16] = "kcr in component rate_constants (first_order_rate_constant)" legend_constants[17] = "kw in component rate_constants (first_order_rate_constant)" legend_constants[18] = "kwr in component rate_constants (first_order_rate_constant)" legend_constants[19] = "ki in component rate_constants (first_order_rate_constant)" legend_constants[20] = "kir in component rate_constants (first_order_rate_constant)" legend_constants[21] = "mu in component rate_constants (first_order_rate_constant)" legend_constants[22] = "Kmu2 in component rate_constants (dimensionless)" legend_constants[23] = "Kmur2 in component rate_constants (dimensionless)" legend_constants[24] = "Kmi in component rate_constants (dimensionless)" legend_constants[25] = "Kmir in component rate_constants (dimensionless)" legend_constants[26] = "Kmw in component rate_constants (dimensionless)" legend_constants[27] = "Kmwr in component rate_constants (dimensionless)" legend_constants[28] = "Kmu in component rate_constants (dimensionless)" legend_constants[29] = "Kmur in component rate_constants (dimensionless)" legend_constants[30] = "Kmc in component rate_constants (dimensionless)" legend_constants[31] = "Kmcr in component rate_constants (dimensionless)" legend_constants[32] = "Kmp in component rate_constants (dimensionless)" legend_constants[33] = "V2 in component rate_constants (first_order_rate_constant)" legend_constants[34] = "V2_ in component rate_constants (first_order_rate_constant)" legend_constants[35] = "V6 in component rate_constants (first_order_rate_constant)" legend_constants[36] = "V6_ in component rate_constants (first_order_rate_constant)" legend_constants[37] = "V25 in component rate_constants (first_order_rate_constant)" legend_constants[38] = "V25_ in component rate_constants (first_order_rate_constant)" legend_constants[39] = "Vw in component rate_constants (first_order_rate_constant)" legend_constants[40] = "Vw_ in component rate_constants (first_order_rate_constant)" legend_states[0] = "Cdc25 in component Cdc25 (dimensionless)" legend_states[1] = "UbE in component UbE (dimensionless)" legend_states[2] = "UbE2 in component UbE2 (dimensionless)" legend_states[3] = "Wee1 in component Wee1 (dimensionless)" legend_algebraic[8] = "SPF in component concentration_variables (dimensionless)" legend_algebraic[6] = "MPF in component concentration_variables (dimensionless)" legend_constants[41] = "alpha in component concentration_variables (dimensionless)" legend_constants[42] = "beta in component concentration_variables (dimensionless)" legend_states[4] = "G1K in component G1K (dimensionless)" legend_states[5] = "G2K in component G2K (dimensionless)" legend_states[6] = "PG2 in component PG2 (dimensionless)" legend_states[7] = "G2R in component G2R (dimensionless)" legend_states[8] = "R in component R (dimensionless)" legend_states[9] = "G1R in component G1R (dimensionless)" legend_states[10] = "PG2R in component PG2R (dimensionless)" legend_states[11] = "mass in component mass (dimensionless)" legend_states[12] = "IE in component IE (dimensionless)" legend_algebraic[2] = "Cig2_total in component Cig2_total (dimensionless)" legend_algebraic[3] = "Rum1_total in component Rum1_total (dimensionless)" legend_algebraic[4] = "Cdc13_total in component Cdc13_total (dimensionless)" legend_rates[5] = "d/dt G2K in component G2K (dimensionless)" legend_rates[8] = "d/dt R in component R (dimensionless)" legend_rates[4] = "d/dt G1K in component G1K (dimensionless)" legend_rates[7] = "d/dt G2R in component G2R (dimensionless)" legend_rates[12] = "d/dt IE in component IE (dimensionless)" legend_rates[2] = "d/dt UbE2 in component UbE2 (dimensionless)" legend_rates[3] = "d/dt Wee1 in component Wee1 (dimensionless)" legend_rates[6] = "d/dt PG2 in component PG2 (dimensionless)" legend_rates[9] = "d/dt G1R in component G1R (dimensionless)" legend_rates[10] = "d/dt PG2R in component PG2R (dimensionless)" legend_rates[1] = "d/dt UbE in component UbE (dimensionless)" legend_rates[11] = "d/dt mass in component mass (dimensionless)" legend_rates[0] = "d/dt Cdc25 in component Cdc25 (dimensionless)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; constants[0] = 0.015 constants[1] = 0.05 constants[2] = 0.09375 constants[3] = 0.1875 constants[4] = 0.00175 constants[5] = 0 constants[6] = 100 constants[7] = 0.1 constants[8] = 10 constants[9] = 0.1 constants[10] = 0.2 constants[11] = 3.25 constants[12] = 0.1 constants[13] = 1 constants[14] = 0.3 constants[15] = 1 constants[16] = 0.25 constants[17] = 1 constants[18] = 0.25 constants[19] = 0.4 constants[20] = 0.1 constants[21] = 0.00495 constants[22] = 0.05 constants[23] = 0.05 constants[24] = 0.01 constants[25] = 0.01 constants[26] = 0.1 constants[27] = 0.1 constants[28] = 0.01 constants[29] = 0.01 constants[30] = 0.1 constants[31] = 0.1 constants[32] = 0.001 constants[33] = 0.25 constants[34] = 0.0075 constants[35] = 7.5 constants[36] = 0.0375 constants[37] = 0.5 constants[38] = 0.025 constants[39] = 0.35 constants[40] = 0.035 states[0] = 0 states[1] = 1 states[2] = 0 states[3] = 0 constants[41] = 0.25 constants[42] = 0.05 states[4] = 0 states[5] = 0 states[6] = 0 states[7] = 0 states[8] = 0.4 states[9] = 0 states[10] = 0 states[11] = 0.5 states[12] = 0 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic rates[9] = constants[8]*states[8]*states[4]-(constants[9]+constants[3]+constants[5])*states[9] rates[1] = (constants[10]*states[12]*(1.00000-states[1]))/((constants[28]+1.00000)-states[1])-(constants[12]*states[1])/(constants[29]+states[1]) rates[11] = constants[21]*states[11] algebraic[0] = constants[36]*(1.00000-states[2])+constants[35]*states[2] rates[4] = (constants[4]+(constants[9]+constants[3])*states[9])-(algebraic[0]+constants[8]*states[8])*states[4] algebraic[1] = constants[34]*(1.00000-states[1])+constants[33]*states[1] rates[7] = constants[6]*states[8]*states[5]-(constants[7]+constants[3]+algebraic[1]+constants[1])*states[7] rates[10] = constants[6]*states[8]*states[6]-(constants[7]+constants[3]+algebraic[1]+constants[1])*states[10] algebraic[6] = states[5]+constants[42]*states[6] rates[12] = (constants[19]*algebraic[6]*(1.00000-states[12]))/((constants[24]+1.00000)-states[12])-(constants[20]*states[12])/(constants[25]+states[12]) rates[2] = (constants[13]*algebraic[6]*(1.00000-states[2]))/((constants[22]+1.00000)-states[2])-(constants[14]*states[2])/(constants[23]+states[2]) rates[3] = (constants[18]*(1.00000-states[3]))/((constants[27]+1.00000)-states[3])-(constants[17]*algebraic[6]*states[3])/(constants[26]+states[3]) rates[0] = (constants[15]*algebraic[6]*(1.00000-states[0]))/((constants[30]+1.00000)-states[0])-(constants[16]*states[0])/(constants[31]+states[0]) algebraic[5] = constants[40]*(1.00000-states[3])+constants[39]*states[3] algebraic[7] = constants[38]*(1.00000-states[0])+constants[37]*states[0] rates[5] = (constants[0]+algebraic[7]*states[6]+(constants[7]+constants[3])*states[7])-(algebraic[1]+algebraic[5]+constants[6]*states[8])*states[5] algebraic[8] = algebraic[6]+constants[41]*states[4] rates[8] = (constants[2]+(constants[7]+algebraic[1]+constants[1])*(states[7]+states[10])+(constants[9]+constants[5])*states[9])-(constants[3]*states[8]+constants[6]*states[8]*(states[5]+states[6])+constants[8]*states[8]*states[4]+(constants[11]*states[8]*algebraic[8]*states[11])/(constants[32]+states[8])) rates[6] = (algebraic[5]*states[5]+(constants[7]+constants[3])*states[10])-(algebraic[7]+algebraic[1]+constants[6]*states[8])*states[6] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[36]*(1.00000-states[2])+constants[35]*states[2] algebraic[1] = constants[34]*(1.00000-states[1])+constants[33]*states[1] algebraic[6] = states[5]+constants[42]*states[6] algebraic[5] = constants[40]*(1.00000-states[3])+constants[39]*states[3] algebraic[7] = constants[38]*(1.00000-states[0])+constants[37]*states[0] algebraic[8] = algebraic[6]+constants[41]*states[4] algebraic[2] = states[4]+states[9] algebraic[3] = states[8]+states[9]+states[7]+states[10] algebraic[4] = states[5]+states[7]+states[6]+states[10] 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)