Interpretation of complex reaction networks in Boolean network framework

Abstract

Real world chemical systems are modeled as Complex Reaction Networks (CRNs) in attempt to study their behavior in mathematical framework. Structures and reactive properties of small reactions can be computed efficiently and accurately using mass action kinetics. However, the CRNs with large number of nodes, requirements on amount and accuracy of data and computational complexity increases rapidly with number of nodes, rendering the conventional methods unfeasible when accuracy of data available and/or availability of computational power is not sufficient. The CRN dynamics are given by the deterministic differential equations which can demonstrate to different behaviors such as Oscillations, fixed points (unique or multiple, stable or unstable). This paper focuses on the results related to the fixed points, the attractor hypothesis. The paper proposes an approach to analyze the mass action kinetics of a CRN with the help of it's linear state-space formulation. The CRN is represented by a Boolean network. Formulating it's dynamics in the form of Boolean functions, the state transition matrix of the CRN is obtained using semi tensor product (STP) approach. This state transition matrix is analyzed for finding out possible equilibria and cycles of CRN. The method makes use of mass action dynamics without any quantitative knowledge of reaction rates to give qualitative behavior of system evolution.