An Algebraic Approach to Reverse Engineering Finite Dynamical Systems Arising from Biology

Finite dynamical systems have been used successfully in modeling biological processes. When certain regulatory mechanisms of a biological system or a model are unknown it is important to be able to identify the best model with the available data. In this context, reverse engineering of finite dynamical systems from partial information is an important problem. While this problem has been studied in the past, there are currently no algorithms that can predict the signs of the interactions. In this paper we propose a framework and algorithms to reverse engineer the possible signed wiring diagrams of a finite dynamical system from data. The algorithm consists of encoding all possible wiring diagrams using ideals and algebraic sets and choosing those that are minimal using the primary decomposition and the irreducible components.