Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 5
sizeStates = 9
sizeConstants = 31
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] = "k1AA in component rate_constants (first_order_rate_constant)"
legend_constants[1] = "k3 in component rate_constants (first_order_rate_constant)"
legend_constants[2] = "kinh in component rate_constants (first_order_rate_constant)"
legend_constants[3] = "kcak in component rate_constants (first_order_rate_constant)"
legend_constants[4] = "kbPPase in component rate_constants (first_order_rate_constant)"
legend_constants[5] = "kfPPase in component rate_constants (first_order_rate_constant)"
legend_constants[6] = "khPPase in component rate_constants (first_order_rate_constant)"
legend_constants[7] = "kd_antiIE in component rate_constants (first_order_rate_constant)"
legend_constants[8] = "ka in component rate_constants (first_order_rate_constant)"
legend_constants[9] = "kc in component rate_constants (first_order_rate_constant)"
legend_constants[10] = "ke in component rate_constants (first_order_rate_constant)"
legend_constants[11] = "kg in component rate_constants (first_order_rate_constant)"
legend_constants[12] = "V2_ in component rate_constants (first_order_rate_constant)"
legend_constants[13] = "V2__ in component rate_constants (first_order_rate_constant)"
legend_constants[14] = "V25_ in component rate_constants (first_order_rate_constant)"
legend_constants[15] = "V25__ in component rate_constants (first_order_rate_constant)"
legend_constants[16] = "Vwee_ in component rate_constants (first_order_rate_constant)"
legend_constants[17] = "Vwee__ in component rate_constants (first_order_rate_constant)"
legend_constants[18] = "K_a in component rate_constants (dimensionless)"
legend_constants[19] = "K_b in component rate_constants (dimensionless)"
legend_constants[20] = "K_c in component rate_constants (dimensionless)"
legend_constants[21] = "K_d in component rate_constants (dimensionless)"
legend_constants[22] = "K_e in component rate_constants (dimensionless)"
legend_constants[23] = "K_f in component rate_constants (dimensionless)"
legend_constants[24] = "K_g in component rate_constants (dimensionless)"
legend_constants[25] = "K_h in component rate_constants (dimensionless)"
legend_constants[26] = "Cdc25_T in component concentration_variables (dimensionless)"
legend_states[0] = "Cdc25_P in component Cdc25_P (dimensionless)"
legend_states[1] = "Wee1_P in component Wee1_P (dimensionless)"
legend_constants[27] = "Wee1_T in component concentration_variables (dimensionless)"
legend_constants[28] = "UbE_T in component concentration_variables (dimensionless)"
legend_states[2] = "UbE in component UbE (dimensionless)"
legend_algebraic[0] = "k25 in component rate_constants (first_order_rate_constant)"
legend_algebraic[2] = "kwee in component rate_constants (first_order_rate_constant)"
legend_algebraic[3] = "k2 in component rate_constants (first_order_rate_constant)"
legend_constants[29] = "Cdc2_T in component concentration_variables (dimensionless)"
legend_constants[30] = "IE_T in component concentration_variables (dimensionless)"
legend_states[3] = "cyclin in component cyclin (dimensionless)"
legend_algebraic[4] = "Cdc2 in component Cdc2 (dimensionless)"
legend_states[4] = "cyclin_Cdc2 in component cyclin_Cdc2 (dimensionless)"
legend_states[5] = "MPF_active in component MPF_active (dimensionless)"
legend_states[6] = "Tyr15P_dimer in component Tyr15P_dimer (dimensionless)"
legend_states[7] = "MPF_pre in component MPF_pre (dimensionless)"
legend_algebraic[1] = "cyclin_T in component cyclin_T (dimensionless)"
legend_states[8] = "IE_P in component IE_P (dimensionless)"
legend_rates[3] = "d/dt cyclin in component cyclin (dimensionless)"
legend_rates[4] = "d/dt cyclin_Cdc2 in component cyclin_Cdc2 (dimensionless)"
legend_rates[6] = "d/dt Tyr15P_dimer in component Tyr15P_dimer (dimensionless)"
legend_rates[7] = "d/dt MPF_pre in component MPF_pre (dimensionless)"
legend_rates[5] = "d/dt MPF_active in component MPF_active (dimensionless)"
legend_rates[0] = "d/dt Cdc25_P in component Cdc25_P (dimensionless)"
legend_rates[1] = "d/dt Wee1_P in component Wee1_P (dimensionless)"
legend_rates[8] = "d/dt IE_P in component IE_P (dimensionless)"
legend_rates[2] = "d/dt UbE in component UbE (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 0
constants[1] = 0.01
constants[2] = 0.025
constants[3] = 0.25
constants[4] = 0.125
constants[5] = 0.1
constants[6] = 0.087
constants[7] = 0.095
constants[8] = 0.01
constants[9] = 0.1
constants[10] = 0.0133
constants[11] = 0.0065
constants[12] = 0
constants[13] = 0
constants[14] = 0.1
constants[15] = 2
constants[16] = 0.1
constants[17] = 1
constants[18] = 0.1
constants[19] = 0.1
constants[20] = 0.01
constants[21] = 0.01
constants[22] = 0.3
constants[23] = 0.3
constants[24] = 0.01
constants[25] = 0.01
constants[26] = 1
states[0] = 0
states[1] = 0
constants[27] = 1
constants[28] = 1
states[2] = 0
constants[29] = 100
constants[30] = 1
states[3] = 1
states[4] = 0
states[5] = 0
states[6] = 0
states[7] = 0
states[8] = 0
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[0] = (constants[8]*states[5]*(constants[26]-states[0]))/((constants[18]+constants[26])-states[0])-(constants[4]*states[0])/(constants[19]+states[0])
rates[1] = (constants[10]*states[5]*(constants[27]-states[1]))/((constants[22]+constants[27])-states[1])-(constants[5]*states[1])/(constants[23]+states[1])
rates[8] = (constants[11]*states[5]*(constants[30]-states[8]))/((constants[24]+constants[30])-states[8])-(constants[6]*states[8])/(constants[25]+states[8])
rates[2] = (constants[9]*states[8]*(constants[28]-states[2]))/((constants[20]+constants[28])-states[2])-(constants[7]*states[2])/(constants[21]+states[2])
algebraic[0] = constants[14]*(constants[26]-states[0])+constants[15]*states[0]
algebraic[2] = constants[16]*states[1]+constants[17]*(constants[27]-states[1])
algebraic[3] = constants[12]*(constants[28]-states[2])+constants[13]*states[2]
rates[6] = (algebraic[2]*states[4]-(algebraic[0]+constants[3]+algebraic[3])*states[6])+constants[2]*states[7]
rates[7] = (algebraic[2]*states[5]-(constants[2]+algebraic[0]+algebraic[3])*states[7])+constants[3]*states[6]
rates[5] = (constants[3]*states[4]-(constants[2]+algebraic[2]+algebraic[3])*states[5])+algebraic[0]*states[7]
algebraic[4] = constants[29]-(states[4]+states[5]+states[7]+states[6])
rates[3] = (constants[0]-algebraic[3]*states[3])-constants[1]*states[3]*algebraic[4]
rates[4] = (constants[2]*states[5]-(algebraic[2]+constants[3]+algebraic[3])*states[4])+algebraic[0]*states[6]+constants[1]*states[3]*algebraic[4]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = constants[14]*(constants[26]-states[0])+constants[15]*states[0]
algebraic[2] = constants[16]*states[1]+constants[17]*(constants[27]-states[1])
algebraic[3] = constants[12]*(constants[28]-states[2])+constants[13]*states[2]
algebraic[4] = constants[29]-(states[4]+states[5]+states[7]+states[6])
algebraic[1] = states[3]+states[4]+states[5]+states[7]+states[6]
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)