Volume 19, Issue 1, March 2012, Pages 81 - 97
Nambu Bracket Formulation of Nonlinear Biochemical Reactions Beyond Elementary Mass Action Kinetics
Authors
T. D. Frank
UCD School of Physics, University College Dublin, Belfield, Dublin 4, Ireland
Systems Biology Ireland, University College Dublin, Belfield, Dublin 4, Ireland,till.frank@ucd.ie
Received 31 August 2011, Accepted 25 November 2011, Available Online 6 January 2021.
- DOI
- 10.1142/S1402925112500076How to use a DOI?
- Keywords
- Nambu brackets; biochemical reactions; stoichiometric matrix
- Abstract
We develop a Nambu bracket formulation for a wide class of nonlinear biochemical reactions by exploiting previous work that focused on elementary biochemical mass action reactions. To this end, we consider general reaction mechanisms including for example enzyme kinetics. Furthermore, we go beyond elementary reactions and account for reactions involving stoichiometric coefficients different from unity. In particular, we show that the stoichiometric matrix of biochemical reactions can be expressed in terms of Nambu brackets. Finally, we solve the sign problem that arises in the context of coupled biochemical reactions.
- Copyright
- © 2012 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - T. D. Frank PY - 2021 DA - 2021/01/06 TI - Nambu Bracket Formulation of Nonlinear Biochemical Reactions Beyond Elementary Mass Action Kinetics JO - Journal of Nonlinear Mathematical Physics SP - 81 EP - 97 VL - 19 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925112500076 DO - 10.1142/S1402925112500076 ID - Frank2021 ER -