rxnrater

This is a Python package to derive rate expressions from enzyme mechanisms based on the steady-state assumption of intermediary enzyme complexes. The rate expressions can be generated in terms of microscopic (mass action) rate constants or in terms of kinetic parameters (K_M, K_i, ...).

Currently, only sequential mechanisms are supported. For some reactions, the computation time can be prohibitively long and could certainly be reduced. For supported examples, see tests/test_enzyme_rxn.py.

For background information, see e.g.:

• R. A. Alberty, “The Relationship between Michaelis Constants, Maximum Velocities and the Equilibrium Constant for an Enzyme-catalyzed Reaction,” Journal of the American Chemical Society, vol. 75, no. 8, pp. 1928–1932, Apr. 1953, doi: 10.1021/ja01104a045.

• W. W. Cleland, “The kinetics of enzyme-catalyzed reactions with two or more substrates or products: I. Nomenclature and rate equations,” Biochimica et Biophysica Acta (BBA), vol. 67, pp. 104–137, 1963, doi: 10.1016/0926-6569(63)90211-6.

This project is in the early stages of development and is not necessarily ready for production use. Double-check the results.

If you are interested in collaborating, please contact me (https://github.com/dweindl/).

Installation

# Clone the repository
# then
pip install .

Usage

Example:

from pprint import pprint
from rxnrater import EnzymeReaction
# Define the enzyme mechanism (E + S ⇌ E:S ⇌ E + P)
mechanism = """
E + S -- E:S , k1 , k2
E:S -- E:P , k3 , k4
E:P -- E + P , k5 , k6
"""
er = EnzymeReaction(mechanism)
pprint(er.get_kinetic_parameters())
pprint(er.simplify_flux())

{'Km_P': (k2*k4 + k2*k5 + k3*k5)/(k6*(k2 + k3 + k4)),
 'Km_S': (k2*k4 + k2*k5 + k3*k5)/(k1*(k3 + k4 + k5)),
 'V_mf': E0*k3*k5/(k3 + k4 + k5),
 'V_mr': E0*k2*k4/(k2 + k3 + k4),
 'flux': E0*(-P*k2*k4*k6 + S*k1*k3*k5)/(P*k2*k6 + P*k3*k6 + P*k4*k6 + S*k1*k3 + S*k1*k4 + S*k1*k5 + k2*k4 + k2*k5 + k3*k5),
 'keq_micro': k1*k3*k5/(k2*k4*k6)}
(V_mf*V_mr*(S - P/Keq)/(Km_S*V_mr + S*V_mr + P*V_mf/Keq),
 {'Km_P': (k2*k4 + k2*k5 + k3*k5)/(k2*k6 + k3*k6 + k4*k6),
  'Km_S': (k2*k4 + k2*k5 + k3*k5)/(k1*k3 + k1*k4 + k1*k5),
  'V_mr': Km_P*V_mf/(Keq*Km_S)})

See tests/test_enzyme_rxn.py for more examples.

Reaction syntax

The syntax is still a bit awkward:

• Each line contains one micro-reaction:
• The syntax is reactants -- products , k_forward , k_reverse for reversible reactions, or reactants -> products , k_forward for irreversible reactions. the rate constants are separated by , (spaces are currently required).
• Individual reactions are assumed to follow mass action kinetics.
• Enzyme-species are denoted by E or anything starting with E: or E_.
• Reactants are separated by + (spaces are currently required).
• Species names must consist of [A-Za-z0-9_] and start with a letter.

Availability

The source code is available at https://github.com/dweindl/rxnrater.