Linear conjugacy in biochemical reaction networks with rational reaction rates

Abstract

In this paper we show that the model form of a wide class of kinetic systems with rational terms in the reaction rates is invariant under a positive linear diagonal transformation. Thus, the concept of linear conjugacy defined originally for mass action systems is extended to rational biochemical models. The generalized Kirchhoff matrix and the kinetic weighting matrix of the linearly conjugate models are given as functions of the computed transformation parameters. It is shown through the illustrative examples that the dense realization of a linearly conjugate rational model may contain more reactions than that of a dynamically equivalent one due to the additional degrees of freedom introduced by the linear transformation. The proposed matrix-based representation is suitable for the computational search of preferred graph structures corresponding to linearly conjugate realizations of rational kinetic models