Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 10
sizeStates = 11
sizeConstants = 45
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] = "Cdc13_Cdc2 in component Cdc13_Cdc2 (dimensionless)"
legend_constants[0] = "k1 in component Cdc13_Cdc2 (first_order_rate_constant)"
legend_algebraic[3] = "kwee in component kwee (first_order_rate_constant)"
legend_constants[1] = "ki in component parameters (first_order_rate_constant)"
legend_algebraic[2] = "kcdc25 in component kcdc25 (first_order_rate_constant)"
legend_constants[2] = "kir in component parameters (first_order_rate_constant)"
legend_algebraic[0] = "k2 in component k2 (first_order_rate_constant)"
legend_algebraic[5] = "k4 in component k4 (first_order_rate_constant)"
legend_states[1] = "mass in component mass (dimensionless)"
legend_states[2] = "Cdc13_P_Cdc2 in component Cdc13_P_Cdc2 (dimensionless)"
legend_states[3] = "Rum1_Cdc13_Cdc2 in component Rum1_Cdc13_Cdc2 (dimensionless)"
legend_states[4] = "Rum1 in component Rum1 (dimensionless)"
legend_algebraic[1] = "k2c in component k2c (first_order_rate_constant)"
legend_constants[3] = "k3 in component Rum1 (first_order_rate_constant)"
legend_states[5] = "Cdc25P in component Cdc25P (dimensionless)"
legend_constants[4] = "k25 in component Cdc25P (first_order_rate_constant)"
legend_algebraic[7] = "k25r in component Cdc25P (first_order_rate_constant)"
legend_constants[5] = "k25r_ in component Cdc25P (first_order_rate_constant)"
legend_constants[6] = "J25 in component Cdc25P (dimensionless)"
legend_constants[7] = "J25r in component Cdc25P (dimensionless)"
legend_algebraic[6] = "ks in component parameters (first_order_rate_constant)"
legend_algebraic[4] = "MPF in component MPF (dimensionless)"
legend_states[6] = "Wee1 in component Wee1 (dimensionless)"
legend_constants[8] = "kw in component Wee1 (first_order_rate_constant)"
legend_algebraic[8] = "kwr in component Wee1 (first_order_rate_constant)"
legend_constants[9] = "kwr_ in component Wee1 (first_order_rate_constant)"
legend_constants[10] = "Jw in component Wee1 (dimensionless)"
legend_constants[11] = "Jwr in component Wee1 (dimensionless)"
legend_states[7] = "Mik1 in component Mik1 (dimensionless)"
legend_constants[12] = "km in component Mik1 (first_order_rate_constant)"
legend_algebraic[9] = "kmr in component Mik1 (first_order_rate_constant)"
legend_constants[13] = "kmr_ in component Mik1 (first_order_rate_constant)"
legend_constants[14] = "Jm in component Mik1 (dimensionless)"
legend_constants[15] = "Jmr in component Mik1 (dimensionless)"
legend_states[8] = "AAE_total in component AAE_total (dimensionless)"
legend_constants[16] = "kas in component AAE_total (first_order_rate_constant)"
legend_constants[17] = "kad in component parameters (first_order_rate_constant)"
legend_states[9] = "AAE in component AAE (dimensionless)"
legend_constants[18] = "kaa in component AAE (first_order_rate_constant)"
legend_constants[19] = "kaa_ in component AAE (first_order_rate_constant)"
legend_constants[44] = "kai in component AAE (first_order_rate_constant)"
legend_constants[20] = "kai_ in component AAE (first_order_rate_constant)"
legend_constants[21] = "kx in component AAE (first_order_rate_constant)"
legend_constants[22] = "Jaa in component AAE (dimensionless)"
legend_constants[23] = "Jai in component AAE (dimensionless)"
legend_states[10] = "APC in component APC (dimensionless)"
legend_constants[24] = "kapr in component APC (first_order_rate_constant)"
legend_constants[25] = "kapr_ in component APC (first_order_rate_constant)"
legend_constants[26] = "kap in component APC (first_order_rate_constant)"
legend_constants[27] = "Japr in component APC (dimensionless)"
legend_constants[28] = "Jap in component APC (dimensionless)"
legend_constants[29] = "Puc1 in component parameters (dimensionless)"
legend_constants[30] = "mu in component mass (first_order_rate_constant)"
legend_constants[31] = "V2 in component k2 (first_order_rate_constant)"
legend_constants[32] = "V2_ in component k2 (first_order_rate_constant)"
legend_constants[33] = "V2c in component k2c (first_order_rate_constant)"
legend_constants[34] = "V2c_ in component k2c (first_order_rate_constant)"
legend_constants[35] = "k4_ in component k4 (first_order_rate_constant)"
legend_constants[36] = "k4__ in component k4 (first_order_rate_constant)"
legend_constants[37] = "V25 in component kcdc25 (first_order_rate_constant)"
legend_constants[38] = "V25_ in component kcdc25 (first_order_rate_constant)"
legend_constants[39] = "Vwee in component kwee (first_order_rate_constant)"
legend_constants[40] = "Vwee_ in component kwee (first_order_rate_constant)"
legend_constants[41] = "Vmik in component kwee (first_order_rate_constant)"
legend_constants[42] = "Vmik_ in component kwee (first_order_rate_constant)"
legend_constants[43] = "alpha in component MPF (dimensionless)"
legend_rates[0] = "d/dt Cdc13_Cdc2 in component Cdc13_Cdc2 (dimensionless)"
legend_rates[2] = "d/dt Cdc13_P_Cdc2 in component Cdc13_P_Cdc2 (dimensionless)"
legend_rates[3] = "d/dt Rum1_Cdc13_Cdc2 in component Rum1_Cdc13_Cdc2 (dimensionless)"
legend_rates[4] = "d/dt Rum1 in component Rum1 (dimensionless)"
legend_rates[5] = "d/dt Cdc25P in component Cdc25P (dimensionless)"
legend_rates[6] = "d/dt Wee1 in component Wee1 (dimensionless)"
legend_rates[7] = "d/dt Mik1 in component Mik1 (dimensionless)"
legend_rates[8] = "d/dt AAE_total in component AAE_total (dimensionless)"
legend_rates[9] = "d/dt AAE in component AAE (dimensionless)"
legend_rates[10] = "d/dt APC in component APC (dimensionless)"
legend_rates[1] = "d/dt mass in component mass (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 1
constants[0] = 0.03
constants[1] = 200
constants[2] = 1
states[1] = 1
states[2] = 0
states[3] = 0
states[4] = 0
constants[3] = 0.15
states[5] = 0
constants[4] = 0.5
constants[5] = 0.2
constants[6] = 0.2
constants[7] = 0.2
states[6] = 0
constants[8] = 0.5
constants[9] = 0.2
constants[10] = 0.2
constants[11] = 0.2
states[7] = 0
constants[12] = 0.1
constants[13] = 0
constants[14] = 0.2
constants[15] = 0.2
states[8] = 2
constants[16] = 0.25
constants[17] = 0.1
states[9] = 2
constants[18] = 0.001
constants[19] = 1
constants[20] = 0.25
constants[21] = 0
constants[22] = 0.1
constants[23] = 0.1
states[10] = 0
constants[24] = 0.04
constants[25] = 3
constants[26] = 4
constants[27] = 0.01
constants[28] = 0.01
constants[29] = 0.013
constants[30] = 0.005776
constants[31] = 0.03
constants[32] = 1
constants[33] = 0.03
constants[34] = 0.16
constants[35] = 0.15
constants[36] = 20
constants[37] = 0.01
constants[38] = 0.4
constants[39] = 0.01
constants[40] = 0.93
constants[41] = 0.002
constants[42] = 0.2
constants[43] = 0.1
constants[44] = constants[20]+constants[21]
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[1] = constants[30]*states[1]
algebraic[3] = constants[39]*((1.00000-states[6])*1.00000+constants[40]*states[6]+constants[41]*(1.00000-states[7]))*1.00000+constants[42]*states[7]
algebraic[2] = constants[37]*(1.00000-states[5])+constants[38]*states[5]
algebraic[0] = constants[31]*(1.00000-states[10])+constants[32]*states[10]
rates[2] = algebraic[3]*states[0]-(algebraic[2]*states[2]+algebraic[0]*states[2])
algebraic[4] = states[0]+constants[43]*states[2]
rates[8] = constants[16]*algebraic[4]-constants[17]*states[8]
rates[9] = ((constants[18]+constants[19]*algebraic[4])*(states[8]-states[9]))/((constants[22]+states[8])-states[9])-((constants[44]*states[9])/(constants[23]+states[9])+constants[17]*states[9])
rates[10] = ((constants[24]+constants[25]*states[9])*(1.00000-states[10]))/((constants[27]+1.00000)-states[10])-(constants[26]*(constants[29]*states[1]+algebraic[4])*states[10])/(constants[28]+states[10])
algebraic[5] = constants[35]+constants[36]*(constants[29]*states[1]+algebraic[4])
rates[0] = (constants[0]*states[1]+algebraic[2]*states[2]+states[3]*(constants[2]+algebraic[5]))-(algebraic[3]*states[0]+constants[1]*states[0]*states[4]+algebraic[0]*states[0])
algebraic[1] = constants[33]*(1.00000-states[10])+constants[34]*states[10]
rates[3] = constants[1]*states[4]*states[0]-states[3]*(algebraic[5]+algebraic[1]+constants[2])
rates[4] = (constants[3]+states[3]*(constants[2]+algebraic[1]))-(algebraic[5]*states[4]+constants[1]*states[0]*states[4])
algebraic[6] = custom_piecewise([less_equal(states[10] , 0.200000), 0.500000 , True, 0.00000])
algebraic[7] = constants[5]+algebraic[6]
rates[5] = (constants[4]*algebraic[4]*(1.00000-states[5]))/((constants[6]+1.00000)-states[5])-(algebraic[7]*states[5])/(constants[7]+states[5])
algebraic[8] = constants[9]+algebraic[6]
rates[6] = (algebraic[8]*(1.00000-states[6]))/((constants[11]+1.00000)-states[6])-(constants[8]*algebraic[4]*states[6])/(constants[10]+states[6])
algebraic[9] = constants[13]+algebraic[6]
rates[7] = (algebraic[9]*(1.00000-states[7]))/((constants[15]+1.00000)-states[7])-(constants[12]*states[7])/(constants[14]+states[7])
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[3] = constants[39]*((1.00000-states[6])*1.00000+constants[40]*states[6]+constants[41]*(1.00000-states[7]))*1.00000+constants[42]*states[7]
algebraic[2] = constants[37]*(1.00000-states[5])+constants[38]*states[5]
algebraic[0] = constants[31]*(1.00000-states[10])+constants[32]*states[10]
algebraic[4] = states[0]+constants[43]*states[2]
algebraic[5] = constants[35]+constants[36]*(constants[29]*states[1]+algebraic[4])
algebraic[1] = constants[33]*(1.00000-states[10])+constants[34]*states[10]
algebraic[6] = custom_piecewise([less_equal(states[10] , 0.200000), 0.500000 , True, 0.00000])
algebraic[7] = constants[5]+algebraic[6]
algebraic[8] = constants[9]+algebraic[6]
algebraic[9] = constants[13]+algebraic[6]
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)