Generated Code
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# Size of variable arrays:
sizeAlgebraic = 3
sizeStates = 10
sizeConstants = 40
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 (hour)"
legend_constants[0] = "v_sP in component nucleus (nanomolar_hour)"
legend_constants[1] = "v_mP in component nucleus (nanomolar_hour)"
legend_constants[2] = "K_IP in component nucleus (nanomolar)"
legend_constants[3] = "K_mP in component nucleus (nanomolar)"
legend_constants[4] = "v_sT in component nucleus (nanomolar_hour)"
legend_constants[5] = "v_mT in component nucleus (nanomolar_hour)"
legend_constants[6] = "K_IT in component nucleus (nanomolar)"
legend_constants[7] = "K_mT in component nucleus (nanomolar)"
legend_constants[8] = "k_d in component cytosol (per_hour)"
legend_constants[9] = "n in component nucleus (dimensionless)"
legend_constants[10] = "k_1 in component cytosol (per_hour)"
legend_constants[11] = "k_2 in component cytosol (per_hour)"
legend_constants[12] = "k_dN in component nucleus (per_hour)"
legend_states[0] = "C in component cytosol (nanomolar)"
legend_states[1] = "M_P in component nucleus (nanomolar)"
legend_states[2] = "M_T in component nucleus (nanomolar)"
legend_states[3] = "C_N in component nucleus (nanomolar)"
legend_constants[13] = "k_3 in component cytosol (per_nanomolar_hour)"
legend_constants[14] = "k_4 in component cytosol (per_hour)"
legend_constants[15] = "k_dC in component cytosol (per_hour)"
legend_states[4] = "P_0 in component PER (nanomolar)"
legend_states[5] = "P_1 in component PER (nanomolar)"
legend_states[6] = "P_2 in component PER (nanomolar)"
legend_states[7] = "T_0 in component TIM (nanomolar)"
legend_states[8] = "T_1 in component TIM (nanomolar)"
legend_states[9] = "T_2 in component TIM (nanomolar)"
legend_constants[16] = "V_1P in component PER (nanomolar_hour)"
legend_constants[17] = "V_2P in component PER (nanomolar_hour)"
legend_constants[18] = "V_3P in component PER (nanomolar_hour)"
legend_constants[19] = "V_4P in component PER (nanomolar_hour)"
legend_constants[20] = "K_1P in component PER (nanomolar)"
legend_constants[21] = "K_2P in component PER (nanomolar)"
legend_constants[22] = "K_3P in component PER (nanomolar)"
legend_constants[23] = "K_4P in component PER (nanomolar)"
legend_constants[24] = "K_dP in component PER (nanomolar)"
legend_constants[25] = "v_dP in component PER (nanomolar_hour)"
legend_constants[26] = "k_sP in component PER (per_hour)"
legend_constants[27] = "V_1T in component TIM (nanomolar_hour)"
legend_constants[28] = "V_2T in component TIM (nanomolar_hour)"
legend_constants[29] = "V_3T in component TIM (nanomolar_hour)"
legend_constants[30] = "V_4T in component TIM (nanomolar_hour)"
legend_constants[31] = "K_1T in component TIM (nanomolar)"
legend_constants[32] = "K_2T in component TIM (nanomolar)"
legend_constants[33] = "K_3T in component TIM (nanomolar)"
legend_constants[34] = "K_4T in component TIM (nanomolar)"
legend_constants[35] = "K_dT in component TIM (nanomolar)"
legend_algebraic[0] = "v_dT in component LD_cycle (nanomolar_hour)"
legend_constants[36] = "k_sT in component TIM (per_hour)"
legend_constants[37] = "PI in component LD_cycle (dimensionless)"
legend_constants[38] = "v_dT_dark in component LD_cycle (nanomolar_hour)"
legend_constants[39] = "v_dT_light in component LD_cycle (nanomolar_hour)"
legend_algebraic[1] = "P_t in component PER_total (nanomolar)"
legend_algebraic[2] = "T_t in component TIM_total (nanomolar)"
legend_rates[1] = "d/dt M_P in component nucleus (nanomolar)"
legend_rates[2] = "d/dt M_T in component nucleus (nanomolar)"
legend_rates[3] = "d/dt C_N in component nucleus (nanomolar)"
legend_rates[0] = "d/dt C in component cytosol (nanomolar)"
legend_rates[4] = "d/dt P_0 in component PER (nanomolar)"
legend_rates[5] = "d/dt P_1 in component PER (nanomolar)"
legend_rates[6] = "d/dt P_2 in component PER (nanomolar)"
legend_rates[7] = "d/dt T_0 in component TIM (nanomolar)"
legend_rates[8] = "d/dt T_1 in component TIM (nanomolar)"
legend_rates[9] = "d/dt T_2 in component TIM (nanomolar)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = 0.8
constants[1] = 0.8
constants[2] = 1
constants[3] = 0.2
constants[4] = 1
constants[5] = 0.7
constants[6] = 1
constants[7] = 0.2
constants[8] = 0.01
constants[9] = 4
constants[10] = 1.2
constants[11] = 0.2
constants[12] = 0.01
states[0] = 0.1790
states[1] = 0.09107
states[2] = 1.427
states[3] = 1.203
constants[13] = 1.2
constants[14] = 0.6
constants[15] = 0.01
states[4] = 0.02324
states[5] = 0.02210
states[6] = 0.01251
states[7] = 0.5420
states[8] = 0.8000
states[9] = 4.733
constants[16] = 8
constants[17] = 1
constants[18] = 8
constants[19] = 1
constants[20] = 2
constants[21] = 2
constants[22] = 2
constants[23] = 2
constants[24] = 0.2
constants[25] = 2
constants[26] = 0.9
constants[27] = 8
constants[28] = 1
constants[29] = 8
constants[30] = 1
constants[31] = 2
constants[32] = 2
constants[33] = 2
constants[34] = 2
constants[35] = 0.2
constants[36] = 0.9
constants[37] = 3.141592653589793
constants[38] = 2
constants[39] = 4
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[1] = constants[0]*constants[2]**constants[9]/(constants[2]**constants[9]+states[3]**constants[9])-constants[1]*states[1]/(constants[3]+states[1])-constants[8]*states[1]
rates[2] = constants[4]*constants[6]**constants[9]/(constants[6]**constants[9]+states[3]**constants[9])-constants[5]*states[2]/(constants[7]+states[2])-constants[8]*states[2]
rates[3] = constants[10]*states[0]-constants[11]*states[3]-constants[12]*states[3]
rates[0] = constants[13]*states[6]*states[9]-constants[14]*states[0]-constants[10]*states[0]+constants[11]*states[3]-constants[15]*states[0]
rates[4] = constants[26]*states[1]-constants[16]*states[4]/(constants[20]+states[4])+constants[17]*states[5]/(constants[21]+states[5])-constants[8]*states[4]
rates[5] = constants[16]*states[4]/(constants[20]+states[4])-constants[17]*states[5]/(constants[21]+states[5])-constants[18]*states[5]/(constants[22]+states[5])+constants[19]*states[6]/(constants[23]+states[6])-constants[8]*states[5]
rates[6] = constants[18]*states[5]/(constants[22]+states[5])-constants[19]*states[6]/(constants[23]+states[6])-constants[13]*states[6]*states[9]+constants[14]*states[0]-constants[25]*states[6]/(constants[24]+states[6])-constants[8]*states[6]
rates[7] = constants[36]*states[2]-constants[27]*states[7]/(constants[31]+states[7])+constants[28]*states[8]/(constants[32]+states[8])-constants[8]*states[7]
rates[8] = constants[27]*states[7]/(constants[31]+states[7])-constants[28]*states[8]/(constants[32]+states[8])-constants[29]*states[8]/(constants[33]+states[8])+constants[30]*states[9]/(constants[34]+states[9])-constants[8]*states[8]
algebraic[0] = custom_piecewise([less_equal(sin(constants[37]*voi/12.0000) , 0.00000), constants[38] , True, constants[39]])
rates[9] = constants[29]*states[8]/(constants[33]+states[8])-constants[30]*states[9]/(constants[34]+states[9])-constants[13]*states[6]*states[9]+constants[14]*states[0]-algebraic[0]*states[9]/(constants[35]+states[9])-constants[8]*states[9]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = custom_piecewise([less_equal(sin(constants[37]*voi/12.0000) , 0.00000), constants[38] , True, constants[39]])
algebraic[1] = states[4]+states[5]+states[6]+states[0]+states[3]
algebraic[2] = states[7]+states[8]+states[9]+states[0]+states[3]
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)