michaelis_menten : an enzymatic reaction

Overview

The cmepy.models.michaelis_menten module defines a model for the following simple enzymatic reaction system:

The rate coefficients are defined to be , and , while the default initial counts are 50 copies of the species and 10 copies of the species , with all other initial species counts set to zero.

This model can be used in CmePy as follows:

from cmepy.models import michaelis_menten

model = michaelis_menten.create_model_michaelis_menten()

This is roughly the same model used in the enzyme kinetics example. See Example: enzyme kinetics for a detailed example explaining how this similar model can be defined and solved.

Source

"""
Model for Michaelis-Menten type enzymatic reaction systems
"""

from cmepy import model
from cmepy.util import non_neg

def create_model_michaelis_menten(s_0 = 50, e_0 = 10):
    """
    Creates a model for a simple michaelis-menten enzymatic reaction system:
    
    E+S <-> C -> E + D
    
    The reaction propensities are
    
    E+S -> C : 0.01
    C -> E+S : 35.0
    C -> E+D : 30.0
    
    while the initial counts are s_0 copies of S, e_0 copies of E, 
    and zero copies of both C and D.
    """
    
    # first, define functions mapping states to species copy counts
    species_c = (
        lambda *x : x[0],
        lambda *x : non_neg(e_0 - x[1]),
        lambda *x : x[1],
        lambda *x : non_neg(s_0 - x[0] - x[1]),
    )
    # second, define reaction propensities via species counts
    props = (
        lambda *x : 0.01*species_c[0](*x)*species_c[1](*x),
        lambda *x : 35.0*species_c[2](*x),
        lambda *x : 30.0*species_c[2](*x),
    )
    
    # construct the model
    return model.create(
        name = 'simple Michaelis-Menten system',
        species = ('S', 'E', 'C', 'D', ),
        species_counts = species_c,
        reactions = ('E+S->C', 'C->E+S', 'C->E+D', ),
        propensities = props,
        transitions = ((-1, 1), (1, -1), (0, -1)),
        shape = (s_0 + 1, max(s_0, e_0) + 1),
        initial_state = (s_0, 0)
    )