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/testenzymerxn.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

```bash

Clone the repository

then

pip install . ```

Usage

Example:

```python 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.getkineticparameters()) pprint(er.simplifyflux()) {'KmP': (k2k4 + k2k5 + k3k5)/(k6(k2 + k3 + k4)), 'KmS': (k2k4 + k2k5 + k3k5)/(k1(k3 + k4 + k5)), 'Vmf': E0k3k5/(k3 + k4 + k5), 'Vmr': E0k2k4/(k2 + k3 + k4), 'flux': E0(-Pk2k4k6 + Sk1k3k5)/(Pk2k6 + Pk3k6 + Pk4k6 + Sk1k3 + Sk1k4 + Sk1k5 + k2k4 + k2k5 + k3k5), 'keqmicro': k1k3k5/(k2k4k6)} (Vmf*Vmr(S - P/Keq)/(Km_SVmr + S*Vmr + PVmf/Keq), {'KmP': (k2k4 + k2k5 + k3k5)/(k2k6 + k3k6 + k4k6), 'Km_S': (k2k4 + k2k5 + k3k5)/(k1k3 + k1k4 + k1k5), 'Vmr': KmPVmf/(Keq*KmS)}) `` Seetests/testenzymerxn.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.