Nambu Bracket Formulation of Nonlinear Biochemical Reactions Beyond Elementary Mass Action Kinetics

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.