A Nash Equilibrium Approach to Metabolic Network Analysis

  • Angelo LuciaEmail author
  • Peter A. DiMaggio
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10122)


A novel approach to metabolic network analysis using a Nash Equilibrium formulation is proposed. Enzymes are considered to be players in a multi-player game in which each player attempts to minimize the dimensionless Gibbs free energy associated with the biochemical reaction(s) it catalyzes subject to elemental mass balances. Mathematical formulation of the metabolic network as a set of nonlinear programming (NLP) sub-problems and appropriate solution methodologies are described. A small example representing part of the production cycle for acetyl-CoA is used to demonstrate the efficacy of the proposed Nash Equilibrium framework and show that it represents a paradigm shift in metabolic network analysis.


Nash Equilibrium Metabolic Network Flux Balance Analysis Acetyl Phosphate Nash Equilibrium Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



objective function coefficients in any LP formulation


number of chemical species


objective function




Gibbs free energy


enthalpy, Hessian matrix


level set value


dimension of space


number of products


number of reactants


number of sub-problems


gas constant, number of reactions

\(\mathfrak {R}^n\)

real space of dimension n


stoichiometric numbers


stoichiometric coefficients




mole fraction


unknown variables

Greek Symbols


unknown fluxes

\(\phi \)

fugacity coefficient





component index


sub-problem or node index


excluding j


reference state





lower bound


upper bound


optimal value


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of Chemical EngineeringUniversity of Rhode IslandKingstonUSA
  2. 2.Department of Chemical EngineeringImperial College LondonLondonUK

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