Normalized species

Example model which calculates functions depending on the normalized values of a species which can be either in active state SA or inactive state SI.

The normalized values are SA_f and SI_f, respectively, with the total concentration of S given as

ST = SA + SI

Model definition

The model is defined using Tellurium and Antimony. The identical equations could be typed directly in COPASI.

The created model is exported as SBML which than can be used in COPASI.



In [1]:

    
from __future__ import print_function, division
import tellurium as te
te.setDefaultPlottingEngine("matplotlib")
%matplotlib inline
r = te.loada("""
    model normalized_species()
    
    # conversion between active (SA) and inactive (SI)
    J1: SA -> SI; k1*SA - k2*SI;
    k1 = 0.1; k2 = 0.02;
    
    # species
    species SA, SI, ST;
    SA = 10.0; SI = 0.0;
    const ST := SA + SI;
    
    SA is "active state S";
    SI is "inactive state S";
    ST is "total state S";
    
    # normalized species calculated via assignment rules
    species SA_f, SI_f;
    SA_f := SA/ST;
    SI_f := SI/ST;
    
    SA_f is "normalized active state S";
    SI_f is "normalized inactive state S";
    
    # parameters for your function
    P = 0.1;
    tau = 10.0;
    nA = 1.0;
    nI = 2.0;
    kA = 0.1;
    kI = 0.2;
    # now just use the normalized species in some math
    F := ( (1-(SI_f^nI)/(kI^nI+SI_f^nI)*(kI^nI+1) ) * ( (SA_f^nA)/(kA^nA+SA_f^nA)*(kA^nA+1) ) -P)*tau;

    end
""")
# print(r.getAntimony())

# Store the SBML for COPASI
import os
import tempfile
temp_dir = tempfile.mkdtemp()
file_path = os.path.join(temp_dir, 'normalizedSpecies.xml')
r.exportToSBML(file_path)

Model simulation

We perform a simple model simulation to demonstrate the main features using roadrunner:

normalized values SA_f and SI_f are normalized in [0,1]
the normalized values have same dynamics like SA and SF
the normalized values can be used to calculates some dependent function, here F



In [2]:

    
r.reset()
# select the variables of interest in output
r.selections = ['time', 'F'] + r.getBoundarySpeciesIds() \
                             + r.getFloatingSpeciesIds()
# simulate from 0 to 50 with 1001 points
s = r.simulate(0,50,1001)
# plot the results
r.plot(s);