Generated Code
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The raw code is available.
# Size of variable arrays:
sizeAlgebraic = 6
sizeStates = 9
sizeConstants = 51
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 (day)"
legend_algebraic[0] = "A_B in component A_B (mm2)"
legend_states[0] = "r_B in component r_B (mm)"
legend_constants[0] = "X_c in component r_B (pM)"
legend_constants[1] = "X_b in component r_B (pM)"
legend_constants[2] = "X_y in component r_B (pM)"
legend_constants[3] = "k_rB in component r_B (first_order_rate_constant)"
legend_constants[4] = "k_for in component r_B (mm_per_day)"
legend_constants[5] = "k_res in component r_B (mm_per_day)"
legend_states[1] = "xc in component xc (pM)"
legend_states[2] = "xb in component xb (pM)"
legend_states[3] = "xy in component xy (pM)"
legend_constants[6] = "X_bss in component xy (pM)"
legend_constants[7] = "X_yss in component xy (pM)"
legend_constants[8] = "k_byp in component xy (first_order_rate_constant)"
legend_constants[9] = "k_yd in component xy (first_order_rate_constant)"
legend_algebraic[5] = "F_sti in component F_sti (pM_N_per_mm2)"
legend_constants[10] = "k_Fs in component F_sti (mm2_per_N)"
legend_constants[11] = "k_y in component F_sti (per_pM)"
legend_algebraic[4] = "F_s in component F_s (N_per_mm2)"
legend_algebraic[2] = "F_a in component F_s (newton)"
legend_states[4] = "x_no in component x_no (pM)"
legend_constants[12] = "X_noe in component x_no (flux)"
legend_constants[13] = "k_yno in component x_no (mm2_day_per_dyn)"
legend_constants[14] = "k_nod in component x_no (first_order_rate_constant)"
legend_states[5] = "x_pge in component x_pge (pM)"
legend_constants[15] = "X_pgex in component x_pge (flux)"
legend_constants[16] = "k_pged in component x_pge (first_order_rate_constant)"
legend_constants[17] = "k_nopge in component x_pge (first_order_rate_constant)"
legend_constants[18] = "k_ypge in component x_pge (mm2_day_per_dyn)"
legend_states[6] = "x_opg in component x_opg (pM)"
legend_constants[19] = "k_opgd in component x_opg (first_order_rate_constant)"
legend_constants[20] = "k_nopg in component x_opg (first_order_rate_constant)"
legend_constants[21] = "Io in component model_parameters (flux)"
legend_constants[22] = "K_o_p in component model_parameters (picomole_per_day_picomole_cells)"
legend_states[7] = "xr in component xr (pM)"
legend_algebraic[3] = "pi_c in component model_parameters (dimensionless)"
legend_states[8] = "x_kl in component x_kl (pM)"
legend_algebraic[1] = "pi_L in component x_kl (dimensionless)"
legend_constants[23] = "K_l_p in component x_kl (dimensionless)"
legend_constants[24] = "K in component x_kl (pM)"
legend_constants[25] = "k_nokl in component x_kl (first_order_rate_constant)"
legend_constants[26] = "Il in component x_kl (flux)"
legend_constants[27] = "rl in component x_kl (flux)"
legend_constants[28] = "k1 in component x_kl (second_order_rate_constant)"
legend_constants[29] = "k2 in component x_kl (first_order_rate_constant)"
legend_constants[30] = "k3 in component x_kl (second_order_rate_constant)"
legend_constants[31] = "k4 in component x_kl (first_order_rate_constant)"
legend_constants[32] = "ko in component x_kl (first_order_rate_constant)"
legend_constants[50] = "pi_p in component model_parameters (dimensionless)"
legend_constants[33] = "D_R in component xr (flux)"
legend_constants[34] = "k_pger in component xr (first_order_rate_constant)"
legend_constants[46] = "D_B in component model_parameters (first_order_rate_constant)"
legend_constants[35] = "k_B in component xb (first_order_rate_constant)"
legend_constants[36] = "D_C in component xc (flux)"
legend_constants[37] = "D_A in component xc (first_order_rate_constant)"
legend_constants[38] = "f0 in component model_parameters (dimensionless)"
legend_constants[39] = "dB in component model_parameters (first_order_rate_constant)"
legend_constants[40] = "C_s in component model_parameters (pM)"
legend_constants[47] = "P in component model_parameters (pM)"
legend_constants[48] = "P_0 in component model_parameters (pM)"
legend_constants[49] = "P_s in component model_parameters (pM)"
legend_constants[41] = "SP in component model_parameters (flux)"
legend_constants[42] = "k5 in component model_parameters (second_order_rate_constant)"
legend_constants[43] = "k6 in component model_parameters (first_order_rate_constant)"
legend_constants[44] = "IP in component model_parameters (flux)"
legend_constants[45] = "kP in component model_parameters (first_order_rate_constant)"
legend_rates[0] = "d/dt r_B in component r_B (mm)"
legend_rates[3] = "d/dt xy in component xy (pM)"
legend_rates[4] = "d/dt x_no in component x_no (pM)"
legend_rates[5] = "d/dt x_pge in component x_pge (pM)"
legend_rates[6] = "d/dt x_opg in component x_opg (pM)"
legend_rates[8] = "d/dt x_kl in component x_kl (pM)"
legend_rates[7] = "d/dt xr in component xr (pM)"
legend_rates[2] = "d/dt xb in component xb (pM)"
legend_rates[1] = "d/dt xc in component xc (pM)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 0.9912
constants[0] = 9.127e-4
constants[1] = 7.282e-4
constants[2] = 7.300e-3
constants[3] = 1.0e0
constants[4] = 1.0e-3
constants[5] = 10.0e-3
states[1] = 9.127e-4
states[2] = 7.282e-4
states[3] = 7.300e-3
constants[6] = 7.282e-4
constants[7] = 7.300e-3
constants[8] = 1.00e-1
constants[9] = 1.00e0
constants[10] = 1.00e0
constants[11] = 1.00e0
states[4] = 0.02
constants[12] = 0e0
constants[13] = 2e4
constants[14] = 1e3
states[5] = 0.01
constants[15] = 0e0
constants[16] = 1e2
constants[17] = 1e0
constants[18] = 1e2
states[6] = 0.01
constants[19] = 3.5e-1
constants[20] = 1e1
constants[21] = 0.0
constants[22] = 2e5
states[7] = 7.734e-4
states[8] = 0.01
constants[23] = 3e6
constants[24] = 10
constants[25] = 1e2
constants[26] = 0
constants[27] = 1e3
constants[28] = 1e-2
constants[29] = 10
constants[30] = 5.8e-4
constants[31] = 1.7e-2
constants[32] = 0.35
constants[33] = 7e-4
constants[34] = 1e-4
constants[35] = 0.189
constants[36] = 0.189
constants[37] = 0.7
constants[38] = 0.05
constants[39] = 0.7
constants[40] = 5e-3
constants[41] = 250
constants[42] = 0.02
constants[43] = 3
constants[44] = 0
constants[45] = 86
constants[46] = constants[38]*constants[39]
constants[47] = constants[44]/constants[45]
constants[48] = constants[41]/constants[45]
constants[49] = constants[43]/constants[42]
constants[50] = (constants[47]+constants[48])/(constants[47]+constants[49])
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[0] = ((constants[4]/constants[1])*states[2]+(1.00000/constants[2])*states[3])-((constants[5]/constants[0])*states[1]+constants[3]*states[0])
rates[3] = constants[8]*(states[2]-constants[6])-constants[9]*(states[3]-constants[7])
rates[8] = (constants[27]+constants[26])-(constants[25]*states[4]+constants[27]*((1.00000+(constants[28]/constants[29])*states[6]+(constants[30]/constants[31])*constants[24])/(constants[23]*constants[50]*states[2]))*states[8])
algebraic[3] = (states[1]+constants[38]*constants[40])/(states[1]+constants[40])
rates[6] = ((constants[22]/1.00000)*algebraic[3]*states[7]+constants[21]+constants[20]*states[4])-constants[19]*states[6]
rates[7] = (constants[33]*algebraic[3]+constants[34]*states[5])-(constants[46]/algebraic[3])*states[7]
rates[2] = (constants[46]/algebraic[3])*states[7]-constants[35]*states[2]
algebraic[1] = ((((constants[30]/constants[31])*constants[23])*constants[50]*states[2])/(1.00000+(constants[30]*constants[24])/constants[31]+(constants[28]/(constants[29]*constants[32]))*(((constants[22]/1.00000)/constants[50])*states[7]+constants[21])))*(1.00000+constants[26]/constants[27])
rates[1] = constants[36]*algebraic[1]-constants[37]*algebraic[3]*states[1]
algebraic[0] = (power(states[0], 2.00000))* pi
algebraic[2] = custom_piecewise([greater_equal(voi , 100.000) & less(voi , 130.000), 10000.0 , True, 100.000])
algebraic[4] = algebraic[2]/algebraic[0]
algebraic[5] = (algebraic[4]*states[3])/(1.00000+exp(-(constants[10]*algebraic[4]+constants[11]*states[3])))
rates[4] = (constants[13]*algebraic[5]+constants[12])-constants[14]*states[4]
rates[5] = (constants[18]*algebraic[5]+constants[17]*states[4]+constants[15])-constants[16]*states[5]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[3] = (states[1]+constants[38]*constants[40])/(states[1]+constants[40])
algebraic[1] = ((((constants[30]/constants[31])*constants[23])*constants[50]*states[2])/(1.00000+(constants[30]*constants[24])/constants[31]+(constants[28]/(constants[29]*constants[32]))*(((constants[22]/1.00000)/constants[50])*states[7]+constants[21])))*(1.00000+constants[26]/constants[27])
algebraic[0] = (power(states[0], 2.00000))* pi
algebraic[2] = custom_piecewise([greater_equal(voi , 100.000) & less(voi , 130.000), 10000.0 , True, 100.000])
algebraic[4] = algebraic[2]/algebraic[0]
algebraic[5] = (algebraic[4]*states[3])/(1.00000+exp(-(constants[10]*algebraic[4]+constants[11]*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)