  We develop a matrix-based approach to predict and verify indirect
interactions in gene and protein regulatory networks. It is based on the
approximate transitivity of indirect regulations (e.g. A regulates B and B
regulates C often implies that A regulates C) and optimally takes into account
the length of a cascade and signs of intermediate interactions. Our method is
at its most powerful when applied to large and densely interconnected networks.
It successfully predicts both the yet unknown indirect regulations, as well as
the sign (activation or repression) of already known ones. The reliability of
sign predictions was calibrated using the gold-standard sets of positive and
negative interactions. We fine-tuned the parameters of our algorithm by
maximizing the area under the Receiver Operating Characteristic (ROC) curve. We
then applied the optimized algorithm to large literature-derived networks of
all direct and indirect regulatory interactions in several model organisms
(Homo sapiens, Saccharomyces cerevisiae, Arabidopsis thaliana and Drosophila
melanogaster).
