Explore Biological Pathways from Noisy Array Data by Directed Acyclic Boolean Networks

Abstract

We consider the structure of directed acyclic Boolean (DAB) networks as a tool of exploring biological pathways. In a DAB network, the basic objects are binary elements and their Boolean duals. It is characterized by two kinds of pairwise relations: similarity and prerequisite. The former represents a pair of elements with identical on-off states. The latter is a partial order relation, namely, the on-state of one element is necessary for the on-state of another element. A DAB network is uniquely determined by the state space of its elements. We arrange samples from the state space of a DAB network in a binary array, and then introduce a random mechanism of measurement error. This results in a noisy array. Our inference strategy consists of two stages. First, we consider each pair of elements, and try to identify the most likely relation between them. In the meantime, we assign a score, s-p-score, to this relation. Second, we rank the s-p-scores obtained from the first stage. We expect that those relations with smaller s-p-scores are more likely to be true, and those with larger s-p-scores are more likely to be false. The key idea is the definition of s-scores (referring to similarity), p-scores (referring to prerequisite), and s-p-scores. Like classical statistical tests, control of false negatives and positives are our primary concerns. We test the s-p-scoring method by a simulated example and show some exploratory results on a published microarray expression dataset of yeast Saccharomyces cerevisiae obtained from experiments with activation and genetic perturbation of the pheromone response MAPK pathway. This is a joint work with Dr. Lei Li at University of Southern California.