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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)

Abstract

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.

Keywords

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.

Nomenclature

c

objective function coefficients in any LP formulation

C

number of chemical species

f

objective function

g

gradient

G

Gibbs free energy

H

enthalpy, Hessian matrix

L

level set value

n

dimension of space

\(n_p\)

number of products

\(n_r\)

number of reactants

N

number of sub-problems

R

gas constant, number of reactions

\(\mathfrak {R}^n\)

real space of dimension n

s

stoichiometric numbers

S

stoichiometric coefficients

T

temperature

x

mole fraction

Z

unknown variables

Greek Symbols

v

unknown fluxes

\(\phi \)

fugacity coefficient

Subscripts

f

formation

i

component index

j

sub-problem or node index

\(-j\)

excluding j

0

reference state

Superscripts

R

reaction

L

lower bound

U

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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