Generated Code
The following is python code generated by the CellML API from this CellML file. (Back to language selection)
The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 15
sizeStates = 13
sizeConstants = 71
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] = "Cln2 in component Cln2 (dimensionless)"
legend_constants[0] = "ks_n2 in component Cln2 (first_order_rate_constant)"
legend_constants[1] = "ks_n2_ in component Cln2 (first_order_rate_constant)"
legend_constants[2] = "kd_n2 in component Cln2 (first_order_rate_constant)"
legend_states[1] = "mass in component mass (dimensionless)"
legend_algebraic[12] = "SBF in component SBF (dimensionless)"
legend_states[2] = "Clb2_T in component Clb2_T (dimensionless)"
legend_constants[3] = "Hct1_T in component Clb2_T (dimensionless)"
legend_constants[4] = "ks_b2 in component Clb2_T (first_order_rate_constant)"
legend_constants[5] = "ks_b2_ in component Clb2_T (first_order_rate_constant)"
legend_constants[6] = "kd_b2 in component Clb2_T (first_order_rate_constant)"
legend_constants[7] = "kd_b2_ in component Clb2_T (first_order_rate_constant)"
legend_constants[8] = "kd_b2__ in component Clb2_T (first_order_rate_constant)"
legend_algebraic[0] = "Vd_b2 in component Clb2_T (first_order_rate_constant)"
legend_algebraic[3] = "Mcm1 in component Mcm1 (dimensionless)"
legend_states[3] = "Hct1 in component Hct1 (dimensionless)"
legend_states[4] = "Cdc20 in component Cdc20 (dimensionless)"
legend_algebraic[2] = "Clb2 in component Clb2 (dimensionless)"
legend_states[5] = "Clb2_Sic1 in component Clb2_Sic1 (dimensionless)"
legend_algebraic[4] = "Clb5 in component Clb5 (dimensionless)"
legend_states[6] = "Clb5_Sic1 in component Clb5_Sic1 (dimensionless)"
legend_states[7] = "Clb5_T in component Clb5_T (dimensionless)"
legend_algebraic[5] = "Sic1 in component Sic1 (dimensionless)"
legend_states[8] = "Sic1_T in component Sic1_T (dimensionless)"
legend_constants[9] = "ks_b5 in component Clb5_T (first_order_rate_constant)"
legend_constants[10] = "ks_b5_ in component Clb5_T (first_order_rate_constant)"
legend_constants[11] = "kd_b5 in component Clb5_T (first_order_rate_constant)"
legend_constants[12] = "kd_b5_ in component Clb5_T (first_order_rate_constant)"
legend_algebraic[6] = "Vd_b5 in component Clb5_T (first_order_rate_constant)"
legend_algebraic[14] = "MBF in component MBF (dimensionless)"
legend_algebraic[7] = "Bck2 in component Bck2 (dimensionless)"
legend_constants[13] = "Bck2_0 in component Bck2 (dimensionless)"
legend_algebraic[8] = "Cln3 in component Cln3 (dimensionless)"
legend_constants[14] = "Jn3 in component Cln3 (dimensionless)"
legend_constants[15] = "Dn3 in component Cln3 (dimensionless)"
legend_constants[16] = "Cln3_max in component Cln3 (dimensionless)"
legend_constants[17] = "ks_c1 in component Sic1_T (first_order_rate_constant)"
legend_constants[18] = "ks_c1_ in component Sic1_T (first_order_rate_constant)"
legend_constants[19] = "kd1_c1 in component parameters (first_order_rate_constant)"
legend_constants[20] = "Jd2_c1 in component parameters (dimensionless)"
legend_algebraic[10] = "Vd2_c1 in component Vd2_c1 (first_order_rate_constant)"
legend_algebraic[13] = "Swi5 in component Swi5 (dimensionless)"
legend_constants[21] = "kas_b2 in component Clb2_Sic1 (first_order_rate_constant)"
legend_constants[22] = "kdi_b2 in component Clb2_Sic1 (first_order_rate_constant)"
legend_constants[23] = "kas_b5 in component Clb5_Sic1 (first_order_rate_constant)"
legend_constants[24] = "kdi_b5 in component Clb5_Sic1 (first_order_rate_constant)"
legend_constants[25] = "kd2_c1 in component Vd2_c1 (first_order_rate_constant)"
legend_constants[26] = "epsilonc1_n3 in component Vd2_c1 (dimensionless)"
legend_constants[27] = "epsilonc1_k2 in component Vd2_c1 (dimensionless)"
legend_constants[28] = "epsilonc1_b5 in component Vd2_c1 (dimensionless)"
legend_constants[29] = "epsilonc1_b2 in component Vd2_c1 (dimensionless)"
legend_states[9] = "Cdc20_T in component Cdc20_T (dimensionless)"
legend_constants[30] = "ks_20 in component Cdc20_T (first_order_rate_constant)"
legend_constants[31] = "ks_20_ in component Cdc20_T (first_order_rate_constant)"
legend_constants[32] = "kd_20 in component parameters (first_order_rate_constant)"
legend_constants[33] = "ka_20 in component Cdc20 (first_order_rate_constant)"
legend_constants[34] = "ki_20 in component Cdc20 (first_order_rate_constant)"
legend_constants[35] = "ki_20_ in component Cdc20 (first_order_rate_constant)"
legend_algebraic[1] = "Vi_20 in component Cdc20 (first_order_rate_constant)"
legend_states[10] = "ORI in component ORI (dimensionless)"
legend_states[11] = "SPN in component SPN (dimensionless)"
legend_constants[36] = "ka_t1 in component Hct1 (first_order_rate_constant)"
legend_constants[37] = "ka_t1_ in component Hct1 (first_order_rate_constant)"
legend_constants[38] = "ki_t1 in component Hct1 (first_order_rate_constant)"
legend_constants[39] = "ki_t1_ in component Hct1 (first_order_rate_constant)"
legend_algebraic[11] = "Vi_t1 in component Hct1 (first_order_rate_constant)"
legend_constants[40] = "Ji_t1 in component Hct1 (dimensionless)"
legend_constants[41] = "Ja_t1 in component Hct1 (dimensionless)"
legend_constants[42] = "epsiloni_t1_n2 in component Hct1 (dimensionless)"
legend_constants[43] = "epsiloni_t1_b5 in component Hct1 (dimensionless)"
legend_constants[44] = "epsiloni_t1_b2 in component Hct1 (dimensionless)"
legend_constants[45] = "mu in component mass (first_order_rate_constant)"
legend_constants[46] = "ks_ori in component ORI (first_order_rate_constant)"
legend_constants[47] = "kd_ori in component ORI (first_order_rate_constant)"
legend_constants[48] = "epsilonori_b2 in component ORI (dimensionless)"
legend_states[12] = "BUD in component BUD (dimensionless)"
legend_constants[49] = "ks_bud in component BUD (first_order_rate_constant)"
legend_constants[50] = "kd_bud in component BUD (first_order_rate_constant)"
legend_constants[51] = "epsilonbud_b5 in component BUD (dimensionless)"
legend_constants[52] = "ks_spn in component SPN (first_order_rate_constant)"
legend_constants[53] = "kd_spn in component SPN (first_order_rate_constant)"
legend_constants[54] = "J_spn in component SPN (dimensionless)"
legend_constants[55] = "ka_sbf in component SBF (first_order_rate_constant)"
legend_constants[56] = "ki_sbf in component SBF (first_order_rate_constant)"
legend_constants[57] = "ki_sbf_ in component SBF (first_order_rate_constant)"
legend_algebraic[9] = "Va_sbf in component SBF (first_order_rate_constant)"
legend_constants[58] = "Ji_sbf in component SBF (dimensionless)"
legend_constants[59] = "Ja_sbf in component SBF (dimensionless)"
legend_constants[60] = "epsilonsbf_n3 in component SBF (dimensionless)"
legend_constants[61] = "epsilonsbf_b5 in component SBF (dimensionless)"
legend_constants[62] = "ka_mcm in component Mcm1 (first_order_rate_constant)"
legend_constants[63] = "ki_mcm in component Mcm1 (first_order_rate_constant)"
legend_constants[64] = "Ji_mcm in component Mcm1 (dimensionless)"
legend_constants[65] = "Ja_mcm in component Mcm1 (dimensionless)"
legend_constants[66] = "ka_swi in component Swi5 (first_order_rate_constant)"
legend_constants[67] = "ki_swi in component Swi5 (first_order_rate_constant)"
legend_constants[68] = "ki_swi_ in component Swi5 (first_order_rate_constant)"
legend_constants[69] = "Ji_swi in component Swi5 (dimensionless)"
legend_constants[70] = "Ja_swi in component Swi5 (dimensionless)"
legend_rates[0] = "d/dt Cln2 in component Cln2 (dimensionless)"
legend_rates[2] = "d/dt Clb2_T in component Clb2_T (dimensionless)"
legend_rates[7] = "d/dt Clb5_T in component Clb5_T (dimensionless)"
legend_rates[8] = "d/dt Sic1_T in component Sic1_T (dimensionless)"
legend_rates[5] = "d/dt Clb2_Sic1 in component Clb2_Sic1 (dimensionless)"
legend_rates[6] = "d/dt Clb5_Sic1 in component Clb5_Sic1 (dimensionless)"
legend_rates[9] = "d/dt Cdc20_T in component Cdc20_T (dimensionless)"
legend_rates[4] = "d/dt Cdc20 in component Cdc20 (dimensionless)"
legend_rates[3] = "d/dt Hct1 in component Hct1 (dimensionless)"
legend_rates[1] = "d/dt mass in component mass (dimensionless)"
legend_rates[10] = "d/dt ORI in component ORI (dimensionless)"
legend_rates[12] = "d/dt BUD in component BUD (dimensionless)"
legend_rates[11] = "d/dt SPN in component SPN (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 0.0078
constants[0] = 0
constants[1] = 0.05
constants[2] = 0.1
states[1] = 0.6608
states[2] = 0.2342
constants[3] = 1
constants[4] = 0.002
constants[5] = 0.05
constants[6] = 0.01
constants[7] = 2
constants[8] = 0.05
states[3] = 0.9946
states[4] = 0.6848
states[5] = 0.079
states[6] = 0.0207
states[7] = 0.0614
states[8] = 0.1231
constants[9] = 0.006
constants[10] = 0.02
constants[11] = 0.1
constants[12] = 0.25
constants[13] = 0.0027
constants[14] = 6
constants[15] = 1
constants[16] = 0.02
constants[17] = 0.02
constants[18] = 0.1
constants[19] = 0.01
constants[20] = 0.05
constants[21] = 50
constants[22] = 0.05
constants[23] = 50
constants[24] = 0.05
constants[25] = 0.3
constants[26] = 20
constants[27] = 2
constants[28] = 1
constants[29] = 0.067
states[9] = 0.8332
constants[30] = 0.005
constants[31] = 0.06
constants[32] = 0.08
constants[33] = 1
constants[34] = 0.1
constants[35] = 10
states[10] = 0
states[11] = 0
constants[36] = 0.04
constants[37] = 2
constants[38] = 0
constants[39] = 0.64
constants[40] = 0.05
constants[41] = 0.05
constants[42] = 1
constants[43] = 0.5
constants[44] = 1
constants[45] = 0.005776
constants[46] = 2
constants[47] = 0.06
constants[48] = 0.4
states[12] = 0
constants[49] = 0.3
constants[50] = 0.06
constants[51] = 1
constants[52] = 0.08
constants[53] = 0.06
constants[54] = 0.2
constants[55] = 1
constants[56] = 0.5
constants[57] = 6
constants[58] = 0.01
constants[59] = 0.01
constants[60] = 75
constants[61] = 0.5
constants[62] = 1
constants[63] = 0.15
constants[64] = 1
constants[65] = 1
constants[66] = 1
constants[67] = 0.3
constants[68] = 0.2
constants[69] = 0.1
constants[70] = 0.1
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[1] = constants[45]*states[1]
algebraic[1] = custom_piecewise([greater_equal(states[10] , 1.00000), constants[35] , greater_equal(states[11] , 1.00000), constants[34] , True, 0.100000])
rates[4] = constants[33]*(states[9]-states[4])-states[4]*(algebraic[1]+constants[32])
algebraic[2] = states[2]-states[5]
rates[9] = (constants[30]+constants[31]*algebraic[2])-constants[32]*states[9]
rates[11] = (constants[52]*algebraic[2])/(constants[54]+algebraic[2])-constants[53]*states[11]
algebraic[0] = constants[6]*(constants[3]-states[3])+constants[7]*states[3]+constants[8]*states[4]
algebraic[3] = (2.00000*constants[62]*algebraic[2]*constants[64])/(((constants[63]+constants[62]*algebraic[2]*constants[64]+constants[63]*constants[65])-constants[62]*algebraic[2])+power(power((constants[63]+constants[62]*algebraic[2]*constants[64]+constants[63]*constants[65])-constants[62]*algebraic[2], 2.00000)-4.00000*(constants[63]-constants[62]*algebraic[2])*constants[62]*algebraic[2]*constants[64], 1.0/2))
rates[2] = states[1]*(constants[4]+constants[5]*algebraic[3])-algebraic[0]*states[2]
algebraic[4] = states[7]-states[6]
rates[10] = constants[46]*(algebraic[4]+constants[48]*algebraic[2])-constants[47]*states[10]
algebraic[8] = (constants[16]*constants[15]*states[1])/(constants[14]+constants[15]*states[1])
rates[12] = constants[49]*(states[0]+algebraic[8]+constants[51]*algebraic[4])-constants[50]*states[12]
algebraic[5] = states[8]-(states[5]+states[6])
algebraic[7] = constants[13]*states[1]
algebraic[10] = constants[25]*(constants[26]*algebraic[8]+constants[27]*algebraic[7]+states[0]+constants[28]*algebraic[4]+constants[29]*algebraic[2])
rates[5] = constants[21]*algebraic[2]*algebraic[5]-states[5]*(constants[22]+algebraic[0]+constants[19]+algebraic[10]/(constants[20]+states[8]))
algebraic[6] = constants[11]+constants[12]*states[4]
rates[6] = constants[23]*algebraic[4]*algebraic[5]-states[6]*(constants[24]+algebraic[6]+constants[19]+algebraic[10]/(constants[20]+states[8]))
algebraic[11] = constants[38]+constants[39]*(algebraic[8]+constants[42]*states[0]+constants[43]*algebraic[4]+constants[44]*algebraic[2])
rates[3] = ((constants[36]+constants[37]*states[4])*(constants[3]-states[3]))/((constants[41]+constants[3])-states[3])-(algebraic[11]*states[3])/(constants[40]+states[3])
algebraic[9] = constants[55]*(states[0]+constants[60]*(algebraic[8]+algebraic[7])+constants[61]*algebraic[4])
algebraic[12] = (2.00000*algebraic[9]*constants[58])/(((constants[56]+constants[57]*algebraic[2]+algebraic[9]*constants[58]+(constants[56]+constants[57]*algebraic[2])*constants[59])-algebraic[9])+power(power((constants[56]+constants[57]*algebraic[2]+algebraic[9]*constants[58]+(constants[56]+constants[57]*algebraic[2])*constants[59])-algebraic[9], 2.00000)-4.00000*algebraic[9]*constants[58]*((constants[56]+constants[57]*algebraic[2])-algebraic[9]), 1.0/2))
rates[0] = states[1]*(constants[0]+constants[1]*algebraic[12])-constants[2]*states[0]
algebraic[13] = (2.00000*constants[66]*states[4]*constants[69])/(((constants[67]+constants[68]*algebraic[2]+constants[66]*states[4]*constants[69]+(constants[67]+constants[68]*algebraic[2])*constants[70])-constants[66]*states[4])+power(power((constants[67]+constants[68]*algebraic[2]+constants[66]*states[4]*constants[69]+(constants[67]+constants[68]*algebraic[2])*constants[70])-constants[66]*states[4], 2.00000)-4.00000*((constants[67]+constants[68]*algebraic[2])-constants[66]*states[4])*constants[66]*states[4]*constants[69], 1.0/2))
rates[8] = (constants[17]+constants[18]*algebraic[13])-states[8]*(constants[19]+algebraic[10]/(constants[20]+states[8]))
algebraic[14] = algebraic[12]
rates[7] = states[1]*(constants[9]+constants[10]*algebraic[14])-algebraic[6]*states[7]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[1] = custom_piecewise([greater_equal(states[10] , 1.00000), constants[35] , greater_equal(states[11] , 1.00000), constants[34] , True, 0.100000])
algebraic[2] = states[2]-states[5]
algebraic[0] = constants[6]*(constants[3]-states[3])+constants[7]*states[3]+constants[8]*states[4]
algebraic[3] = (2.00000*constants[62]*algebraic[2]*constants[64])/(((constants[63]+constants[62]*algebraic[2]*constants[64]+constants[63]*constants[65])-constants[62]*algebraic[2])+power(power((constants[63]+constants[62]*algebraic[2]*constants[64]+constants[63]*constants[65])-constants[62]*algebraic[2], 2.00000)-4.00000*(constants[63]-constants[62]*algebraic[2])*constants[62]*algebraic[2]*constants[64], 1.0/2))
algebraic[4] = states[7]-states[6]
algebraic[8] = (constants[16]*constants[15]*states[1])/(constants[14]+constants[15]*states[1])
algebraic[5] = states[8]-(states[5]+states[6])
algebraic[7] = constants[13]*states[1]
algebraic[10] = constants[25]*(constants[26]*algebraic[8]+constants[27]*algebraic[7]+states[0]+constants[28]*algebraic[4]+constants[29]*algebraic[2])
algebraic[6] = constants[11]+constants[12]*states[4]
algebraic[11] = constants[38]+constants[39]*(algebraic[8]+constants[42]*states[0]+constants[43]*algebraic[4]+constants[44]*algebraic[2])
algebraic[9] = constants[55]*(states[0]+constants[60]*(algebraic[8]+algebraic[7])+constants[61]*algebraic[4])
algebraic[12] = (2.00000*algebraic[9]*constants[58])/(((constants[56]+constants[57]*algebraic[2]+algebraic[9]*constants[58]+(constants[56]+constants[57]*algebraic[2])*constants[59])-algebraic[9])+power(power((constants[56]+constants[57]*algebraic[2]+algebraic[9]*constants[58]+(constants[56]+constants[57]*algebraic[2])*constants[59])-algebraic[9], 2.00000)-4.00000*algebraic[9]*constants[58]*((constants[56]+constants[57]*algebraic[2])-algebraic[9]), 1.0/2))
algebraic[13] = (2.00000*constants[66]*states[4]*constants[69])/(((constants[67]+constants[68]*algebraic[2]+constants[66]*states[4]*constants[69]+(constants[67]+constants[68]*algebraic[2])*constants[70])-constants[66]*states[4])+power(power((constants[67]+constants[68]*algebraic[2]+constants[66]*states[4]*constants[69]+(constants[67]+constants[68]*algebraic[2])*constants[70])-constants[66]*states[4], 2.00000)-4.00000*((constants[67]+constants[68]*algebraic[2])-constants[66]*states[4])*constants[66]*states[4]*constants[69], 1.0/2))
algebraic[14] = algebraic[12]
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)