# Size of variable arrays:
sizeAlgebraic = 5
sizeStates = 2
sizeConstants = 12
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 (second)"
legend_algebraic[0] = "H_int in component concentrations (mM)"
legend_algebraic[1] = "H_ext in component concentrations (mM)"
legend_constants[0] = "psi_int in component concentrations (volt)"
legend_constants[1] = "psi_ext in component concentrations (volt)"
legend_constants[9] = "psi in component concentrations (volt)"
legend_states[0] = "pH_int in component concentrations (dimensionless)"
legend_states[1] = "pH_ext in component concentrations (dimensionless)"
legend_constants[2] = "J_Vtype_H_Max in component H_ATPase (mM_per_s)"
legend_algebraic[3] = "J_Vtype_H in component H_ATPase (mM_per_s)"
legend_algebraic[4] = "plot in component fluxes (dimensionless)"
legend_algebraic[2] = "mu_H in component H_ATPase (joule_per_mmole)"
legend_constants[3] = "mu_0 in component H_ATPase (joule_per_mmole)"
legend_constants[4] = "xi in component H_ATPase (mmole_per_joule)"
legend_constants[5] = "F in component H_ATPase (coulomb_per_mmole)"
legend_constants[6] = "R in component H_ATPase (joule_per_mmole_kelvin)"
legend_constants[7] = "T in component H_ATPase (kelvin)"
legend_constants[8] = "z in component H_ATPase (dimensionless)"
legend_rates[0] = "d/dt pH_int in component concentrations (dimensionless)"
legend_rates[1] = "d/dt pH_ext in component concentrations (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
constants[0] = -0.03
constants[1] = 0.0
states[0] = 7.5
states[1] = 4.0
constants[2] = 1.8
constants[3] = 4.0
constants[4] = 0.4
constants[5] = 96.5
constants[6] = 0.008315
constants[7] = 300
constants[8] = -1.57
constants[9] = constants[1]-constants[0]
constants[10] = 0.00000
constants[11] = 0.100000
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[0] = constants[10]
rates[1] = constants[11]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = 1000.00*(power(10.0000, -states[0]))
algebraic[1] = 1000.00*(power(10.0000, -states[1]))
algebraic[2] = constants[6]*constants[7]*log(algebraic[1]/algebraic[0])+constants[8]*constants[5]*constants[9]
algebraic[3] = constants[2]/(1.00000+exp(constants[4]*(algebraic[2]-constants[3])))
algebraic[4] = algebraic[3]/constants[2]
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)