Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 8
sizeStates = 16
sizeConstants = 58
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] = "MPF in component MPF (dimensionless)"
legend_constants[0] = "k1 in component rate_constants (first_order_rate_constant)"
legend_algebraic[0] = "k2 in component rate_constants (first_order_rate_constant)"
legend_algebraic[2] = "kwee in component rate_constants (first_order_rate_constant)"
legend_algebraic[4] = "kc25 in component rate_constants (first_order_rate_constant)"
legend_constants[1] = "kj in component rate_constants (first_order_rate_constant)"
legend_constants[2] = "kjr in component rate_constants (first_order_rate_constant)"
legend_constants[3] = "k6_ in component rate_constants (first_order_rate_constant)"
legend_constants[4] = "k6 in component rate_constants (first_order_rate_constant)"
legend_states[1] = "mass in component mass (dimensionless)"
legend_states[2] = "preMPF in component preMPF (dimensionless)"
legend_states[3] = "Rum1 in component Rum1 (dimensionless)"
legend_states[4] = "Rum1P in component Rum1P (dimensionless)"
legend_states[5] = "CR in component CR (dimensionless)"
legend_states[6] = "CRP in component CRP (dimensionless)"
legend_states[7] = "Ste9 in component Ste9 (dimensionless)"
legend_constants[5] = "kste9r_ in component rate_constants (first_order_rate_constant)"
legend_constants[6] = "kste9r in component rate_constants (first_order_rate_constant)"
legend_constants[7] = "kste9 in component rate_constants (first_order_rate_constant)"
legend_constants[8] = "Jste9r in component Ste9 (dimensionless)"
legend_constants[9] = "Jste9 in component Ste9 (dimensionless)"
legend_algebraic[1] = "MPF_a in component MPF_a (dimensionless)"
legend_algebraic[3] = "PP in component PP (dimensionless)"
legend_constants[10] = "SK in component dimensionless_constants (dimensionless)"
legend_states[8] = "Mik1 in component Mik1 (dimensionless)"
legend_constants[11] = "ks in component rate_constants (first_order_rate_constant)"
legend_constants[12] = "kmr_ in component rate_constants (first_order_rate_constant)"
legend_constants[13] = "kmr in component rate_constants (first_order_rate_constant)"
legend_constants[14] = "km in component rate_constants (first_order_rate_constant)"
legend_constants[15] = "Jmikr in component Mik1 (dimensionless)"
legend_constants[16] = "Jmik in component Mik1 (dimensionless)"
legend_states[9] = "Wee1 in component Wee1 (dimensionless)"
legend_constants[17] = "kwr_ in component rate_constants (first_order_rate_constant)"
legend_constants[18] = "kwr in component rate_constants (first_order_rate_constant)"
legend_constants[19] = "kw in component rate_constants (first_order_rate_constant)"
legend_constants[20] = "Jweer in component Wee1 (dimensionless)"
legend_constants[21] = "Jwee in component Wee1 (dimensionless)"
legend_states[10] = "Cdc25 in component Cdc25 (dimensionless)"
legend_constants[22] = "k25 in component rate_constants (first_order_rate_constant)"
legend_constants[23] = "k5 in component rate_constants (first_order_rate_constant)"
legend_constants[24] = "k25r_ in component rate_constants (first_order_rate_constant)"
legend_constants[25] = "k25r in component rate_constants (first_order_rate_constant)"
legend_constants[26] = "J25 in component Cdc25 (dimensionless)"
legend_constants[27] = "J25r in component Cdc25 (dimensionless)"
legend_states[11] = "Slp1 in component Slp1 (dimensionless)"
legend_constants[28] = "kas in component rate_constants (first_order_rate_constant)"
legend_constants[29] = "kad in component rate_constants (first_order_rate_constant)"
legend_states[12] = "Slp1_a in component Slp1_a (dimensionless)"
legend_constants[30] = "kaa_ in component rate_constants (first_order_rate_constant)"
legend_constants[31] = "kaa in component rate_constants (first_order_rate_constant)"
legend_constants[32] = "kai in component rate_constants (first_order_rate_constant)"
legend_states[13] = "Inh in component Inh (dimensionless)"
legend_constants[33] = "k3 in component rate_constants (first_order_rate_constant)"
legend_constants[34] = "ki in component rate_constants (first_order_rate_constant)"
legend_constants[35] = "kir in component rate_constants (first_order_rate_constant)"
legend_algebraic[5] = "k4 in component rate_constants (first_order_rate_constant)"
legend_states[14] = "PI in component PI (dimensionless)"
legend_constants[36] = "kp in component rate_constants (first_order_rate_constant)"
legend_constants[37] = "kpp_ in component rate_constants (first_order_rate_constant)"
legend_constants[38] = "kpp in component rate_constants (first_order_rate_constant)"
legend_algebraic[6] = "k2c in component rate_constants (first_order_rate_constant)"
legend_constants[39] = "epsilon_p in component dimensionless_constants (dimensionless)"
legend_constants[40] = "mu in component mass (first_order_rate_constant)"
legend_states[15] = "R_dna in component R_dna (dimensionless)"
legend_constants[41] = "K in component R_dna (dimensionless)"
legend_constants[42] = "Y in component R_dna (dimensionless)"
legend_constants[43] = "epsilon in component dimensionless_constants (dimensionless)"
legend_algebraic[7] = "ratio in component ratio (dimensionless)"
legend_constants[44] = "V2_ in component rate_constants (first_order_rate_constant)"
legend_constants[45] = "V2 in component rate_constants (first_order_rate_constant)"
legend_constants[46] = "V2c in component rate_constants (first_order_rate_constant)"
legend_constants[47] = "V2c_ in component rate_constants (first_order_rate_constant)"
legend_constants[48] = "Vwee in component rate_constants (first_order_rate_constant)"
legend_constants[49] = "Vwee_ in component rate_constants (first_order_rate_constant)"
legend_constants[50] = "Vmik in component rate_constants (first_order_rate_constant)"
legend_constants[51] = "Vmik_ in component rate_constants (first_order_rate_constant)"
legend_constants[52] = "V25 in component rate_constants (first_order_rate_constant)"
legend_constants[53] = "V25_ in component rate_constants (first_order_rate_constant)"
legend_constants[54] = "Vpyp in component rate_constants (first_order_rate_constant)"
legend_constants[55] = "V4 in component rate_constants (first_order_rate_constant)"
legend_constants[56] = "V4_ in component rate_constants (first_order_rate_constant)"
legend_constants[57] = "Pyp3 in component rate_constants (dimensionless)"
legend_rates[0] = "d/dt MPF in component MPF (dimensionless)"
legend_rates[2] = "d/dt preMPF in component preMPF (dimensionless)"
legend_rates[7] = "d/dt Ste9 in component Ste9 (dimensionless)"
legend_rates[8] = "d/dt Mik1 in component Mik1 (dimensionless)"
legend_rates[9] = "d/dt Wee1 in component Wee1 (dimensionless)"
legend_rates[10] = "d/dt Cdc25 in component Cdc25 (dimensionless)"
legend_rates[11] = "d/dt Slp1 in component Slp1 (dimensionless)"
legend_rates[12] = "d/dt Slp1_a in component Slp1_a (dimensionless)"
legend_rates[13] = "d/dt Inh in component Inh (dimensionless)"
legend_rates[14] = "d/dt PI in component PI (dimensionless)"
legend_rates[6] = "d/dt CRP in component CRP (dimensionless)"
legend_rates[5] = "d/dt CR in component CR (dimensionless)"
legend_rates[3] = "d/dt Rum1 in component Rum1 (dimensionless)"
legend_rates[4] = "d/dt Rum1P in component Rum1P (dimensionless)"
legend_rates[1] = "d/dt mass in component mass (dimensionless)"
legend_rates[15] = "d/dt R_dna in component R_dna (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 0
constants[0] = 0.02
constants[1] = 400
constants[2] = 1
constants[3] = 0.1
constants[4] = 5
states[1] = 1
states[2] = 1
states[3] = 0
states[4] = 0
states[5] = 0
states[6] = 0
states[7] = 0
constants[5] = 0.03
constants[6] = 8
constants[7] = 5
constants[8] = 0.01
constants[9] = 0.01
constants[10] = 0.018
states[8] = 0
constants[11] = 0.1
constants[12] = 0.01
constants[13] = 5
constants[14] = 1
constants[15] = 0.15
constants[16] = 0.15
states[9] = 0
constants[17] = 0.4
constants[18] = 1
constants[19] = 2
constants[20] = 0.2
constants[21] = 0.2
states[10] = 0
constants[22] = 1
constants[23] = 0.1
constants[24] = 0.4
constants[25] = 2
constants[26] = 0.05
constants[27] = 0.05
states[11] = 0
constants[28] = 0.1
constants[29] = 0.1
states[12] = 0
constants[30] = 0.01
constants[31] = 0.1
constants[32] = 0.1
states[13] = 0
constants[33] = 0.1
constants[34] = 50
constants[35] = 0.5
states[14] = 0.2
constants[36] = 100
constants[37] = 1
constants[38] = 100
constants[39] = 0.025
constants[40] = 0.00462
states[15] = 1
constants[41] = 0.06
constants[42] = 0
constants[43] = 0.05
constants[44] = 0.02
constants[45] = 1
constants[46] = 0.5
constants[47] = 0.02
constants[48] = 10
constants[49] = 0.08
constants[50] = 2
constants[51] = 0.04
constants[52] = 10
constants[53] = 0.05
constants[54] = 0.07
constants[55] = 1
constants[56] = 0.01
constants[57] = 1
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[1] = constants[40]*states[1]
algebraic[1] = states[0]+constants[43]*states[2]
rates[11] = constants[28]*algebraic[1]-constants[29]*states[11]
rates[12] = (constants[30]+constants[31]*algebraic[1])*(states[11]-states[12])-(constants[32]+constants[29])*states[12]
rates[15] = (constants[41]*1.00000)/(1.00000+constants[42]*algebraic[1])
algebraic[3] = 1.00000-states[14]
rates[7] = ((constants[5]+constants[6]*algebraic[3])*(1.00000-states[7]))/((constants[8]+1.00000)-states[7])-(constants[7]*(algebraic[1]+constants[10]*states[1])*states[7])/(constants[9]+states[7])
rates[8] = ((constants[11]+constants[12]+constants[13]*algebraic[3])*(1.00000-states[8]))/((constants[15]+1.00000)-states[8])-(constants[14]*algebraic[1]*states[8])/(constants[16]+states[8])
rates[9] = ((constants[17]+constants[18]*algebraic[3])*(1.00000-states[9]))/((constants[20]+1.00000)-states[9])-(constants[19]*algebraic[1]*states[9])/(constants[21]+states[9])
rates[10] = (constants[22]*algebraic[1]*(1.00000-states[10]))/((constants[26]+1.00000)-states[10])-((constants[23]+constants[24]+constants[25]*algebraic[3])*states[10])/(constants[27]+states[10])
algebraic[0] = constants[44]+constants[45]*states[7]
algebraic[2] = constants[48]*states[9]+constants[49]*(1.00000-states[9])+constants[50]*states[8]+constants[51]*(1.00000-states[8])
algebraic[4] = constants[52]*states[10]+constants[53]*(1.00000-states[10])+constants[54]*constants[57]
rates[0] = ((((constants[0]*states[1]-algebraic[0]*states[0])-algebraic[2]*states[0])+algebraic[4]*states[2])-constants[1]*states[0]*(states[3]+states[4]))+constants[2]*(states[5]+states[6])+constants[3]*states[5]+(constants[3]+constants[4])*states[6]
rates[2] = (algebraic[2]*states[0]-algebraic[4]*states[2])-algebraic[0]*states[2]
algebraic[5] = constants[56]+constants[55]*states[12]
rates[13] = ((constants[33]-constants[34]*states[13]*algebraic[3])+constants[35]*states[14])-algebraic[5]*states[13]
rates[14] = (constants[34]*states[13]*algebraic[3]-constants[35]*states[14])-algebraic[5]*states[14]
algebraic[6] = constants[47]+constants[46]*states[7]
rates[6] = ((((constants[36]*(algebraic[1]+constants[39]*constants[10]*states[1])*states[5]-(constants[37]+constants[38]*algebraic[3])*states[6])+constants[1]*states[0]*states[4])-constants[2]*states[6])-algebraic[6]*states[6])-(constants[3]+constants[4])*states[6]
rates[5] = ((((constants[1]*states[0]*states[3]-constants[2]*states[5])-algebraic[6]*states[5])-constants[3]*states[5])-constants[36]*(algebraic[1]+constants[39]*constants[10]*states[1])*states[5])+(constants[37]+constants[38]*algebraic[3])*states[6]
rates[3] = ((((constants[23]-constants[3]*states[3])-constants[36]*(algebraic[1]+constants[39]*constants[10]*states[1])*states[3])+(constants[37]+constants[38]*algebraic[3])*states[4])-constants[1]*states[0]*states[3])+constants[2]*states[5]+algebraic[6]*states[5]
rates[4] = (((constants[36]*(algebraic[1]+constants[39]*constants[10]*states[1])*states[3]-(constants[37]+constants[38]*algebraic[3])*states[4])-(constants[3]+constants[4])*states[4])-constants[1]*states[0]*states[4])+constants[2]*states[6]+algebraic[6]*states[6]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[1] = states[0]+constants[43]*states[2]
algebraic[3] = 1.00000-states[14]
algebraic[0] = constants[44]+constants[45]*states[7]
algebraic[2] = constants[48]*states[9]+constants[49]*(1.00000-states[9])+constants[50]*states[8]+constants[51]*(1.00000-states[8])
algebraic[4] = constants[52]*states[10]+constants[53]*(1.00000-states[10])+constants[54]*constants[57]
algebraic[5] = constants[56]+constants[55]*states[12]
algebraic[6] = constants[47]+constants[46]*states[7]
algebraic[7] = algebraic[1]/algebraic[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)