Generated Code
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The raw code is available.
# 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)