  In this paper we present the first mathematical analysis of the protein
interaction network found in the yeast, S. cerevisiae. We show that, (a) the
identified protein network display a characteristic scale-free topology that
demonstrate striking similarity to the inherent organization of metabolic
networks in particular, and to that of robust and error-tolerant networks in
general. (b) the likelihood that deletion of an individual gene product will
prove lethal for the yeast cell clearly correlates with the number of
interactions the protein has, meaning that highly-connected proteins are more
likely to prove essential than proteins with low number of links to other
proteins. These results suggest that a scale-free architecture is a generic
property of cellular networks attributable to universal self-organizing
principles of robust and error-tolerant networks and that will likely to
represent a generic topology for protein-protein interactions.
