Inferring Networks with Gene Knockouts and Computational Algebra

The network inference problem is a significant problem in systems biology. In this paper, we will describe an approach to this problem involving computational algebra. Specifically, given an unknown Boolean function, we can create a square-free monomial or pseudomonomial ideal whose primary decomposition encodes the possible sets of variables that the function can depend on, and whether those interactions are activations or inhibitions. We apply this problem to time series data generated from a non-linear ODE, built over unknown feed-forward loops, and subject to gene knockouts.