Synthesizing Boolean networks with a given attractor structure

The long-run characteristics of a dynamical system are critical and their determination is a primary aspect of system analysis. In the other direction, system synthesis involves constructing a network possessing a given set of properties. This constitutes the inverse problem. This paper addresses the long-run inverse problem pertaining to Boolean networks (BNs). The long-run behavior of a BN is characterized by its attractors. We derive two algorithms for the attractor inverse problem where the attractors are specified, and the sizes of the predictor sets and the number of levels are constrained. Under the assumption that sampling is from the steady state, a basic criterion for checking the validity of a designed network is that there should be concordance between the attractor states of the model and the data states. This criterion has been used to test a designed probabilistic Boolean network (PBN) constructed from melanoma gene-expression data.