A Computational Approach to Steady State Correspondence of Regular and Generalized Mass Action Systems
For researchers studying biochemical reaction networks, this work provides a computational tool to simplify steady-state analysis via network translation, though it is an incremental extension of existing theory.
The authors develop theory for network translation in mass action systems, focusing on improper translations, and derive topological conditions ensuring steady-state correspondence. They present a MILP algorithm to determine if a mass action system can be translated to a generalized system.
It has been recently observed that the dynamical properties of mass action systems arising from many models of biochemical reaction networks can be derived by considering the corresponding properties of a related generalized mass action system. The correspondence process known as network translation in particular has been shown to be useful in characterizing a system's steady states. In this paper, we further develop the theory of network translation with particular focus on a subclass of translations known as improper translations. For these translations, we derive conditions on the network topology of the translated network which are sufficient to guarantee the original and translated systems share the same steady states. We then present a mixed-integer linear programming (MILP) algorithm capable of determining whether a mass action system can be corresponded to a generalized system through the process of network translation.