  The inference of gene-regulatory processes from gene-expression data belongs
to the major challenges of computational systems biology. Here we address the
problem from a statistical-physics perspective and develop a message-passing
algorithm which is able to infer sparse, directed and combinatorial regulatory
mechanisms. Using the replica technique, the algorithmic performance can be
characterized analytically for artificially generated data. The algorithm is
applied to genome-wide expression data of baker's yeast under various
environmental conditions. We find clear cases of combinatorial control, and
enrichment in common functional annotations of regulated genes and their
regulators.
