Generalized mass action systems: Complex balancing equilibria and sign vectors of the stoichiometric and kineticorder subspaces
Abstract
Mass action systems capture chemical reaction networks in homogeneous and dilute solutions. We suggest a notion of generalized mass action systems that admits arbitrary nonnegative powerlaw rate functions and serves as a more realistic model for reaction networks in intracellular environments. In addition to the chemical complexes and the related stoichiometric subspace, we introduce corresponding kinetic complexes, which represent the nonnegative exponents in the rate functions and determine the kineticorder subspace. We show that several results of Chemical Reaction Network Theory carry over to the case of generalized mass action kinetics. Our main result essentially states that, if the sign vectors of the stoichiometric and the kineticorder subspace coincide, there exists a unique positive complex balancing equilibrium in every stoichiometric compatibility class. However, in contrast to classical mass action systems, multiple complex balancing equilibria in one stoichiometric compatibility class are possible in general.
 Publication:

arXiv eprints
 Pub Date:
 September 2012
 arXiv:
 arXiv:1209.6488
 Bibcode:
 2012arXiv1209.6488M
 Keywords:

 Mathematics  Dynamical Systems;
 Quantitative Biology  Molecular Networks;
 92C42;
 37C25;
 52C40
 EPrint:
 SIAM Journal on Applied Mathematics 72 (2012) 19261947