Proteins are traditionally identified on the basis of their individual actions as catalysts, signalling molecules, or building blocks in cells and microorganisms. But our post-genomic view is expanding the protein's role into an element in a network of protein–protein interactions as well, in which it has a contextual or cellular function within functional modules^1,2. Here we provide quantitative support for this idea by demonstrating that the phenotypic consequence of a single gene deletion in the yeast Saccharomyces cerevisiae is affected to a large extent by the topological position of its protein product in the complex hierarchical web of molecular interactions.

The S. cerevisiae protein–protein interaction network we investigate has 1,870 proteins as nodes, connected by 2,240 identified direct physical interactions, and is derived from combined, non-overlapping data^3,4, obtained mostly by systematic two-hybrid analyses³. Owing to its size, a complete map of the network (Fig. 1a), although informative, in itself offers little insight into its large-scale characteristics. Our first goal was therefore to identify the architecture of this network, determining whether it is best described by an inherently uniform exponential topology, with proteins on average possessing the same number of links, or by a highly heterogeneous scale-free topology, in which proteins have widely different connectivities⁵.

a, Map of protein–protein interactions. The largest cluster, which contains ∼78% of all proteins, is shown. The colour of a node signifies the phenotypic effect of removing the corresponding protein (red, lethal; green, non-lethal; orange, slow growth; yellow, unknown). b, Connectivity distribution p(k) of interacting yeast proteins, giving the probability that a given protein interacts with k other proteins. The exponential cut-off⁶ indicates that the number of proteins with more than 20 interactions is slightly less than expected for pure scale-free networks. In the absence of data on the link directions, all interactions have been considered as bidirectional. The parameter controlling the short-length scale correction has value k₀ ≈ 1. c, The fraction of essential proteins with exactly k links versus their connectivity, k, in the yeast proteome. The list of 1,572 mutants with known phenotypic profile was obtained from the Proteome database¹³. Detailed statistical analysis, including r = 0.75 for Pearson's linear correlation coefficient, demonstrates a positive correlation between lethality and connectivity. For additional details, see http://www.nd.edu/~networks/cell.

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As we show in Fig. 1b, the probability that a given yeast protein interacts with k other yeast proteins follows a power law⁵ with an exponential cut-off⁶ at k_c ≈ 20, a topology that is also shared by the protein–protein interaction network of the bacterium Helicobacter pylori⁷. This indicates that the network of protein interactions in two separate organisms forms a highly inhomogeneous scale-free network in which a few highly connected proteins play a central role in mediating interactions among numerous, less connected proteins.

An important known consequence of the inhomogeneous structure is the network's simultaneous tolerance to random errors, coupled with fragility against the removal of the most connected nodes⁸. We find that random mutations in the genome of S. cerevisiae, modelled by the removal of randomly selected yeast proteins, do not affect the overall topology of the network. By contrast, when the most connected proteins are computationally eliminated, the network diameter increases rapidly. This simulated tolerance against random mutation is in agreement with results from systematic mutagenesis experiments, which identified a striking capacity of yeast to tolerate the deletion of a substantial number of individual proteins from its proteome^9,10. However, if this is indeed due to a topological component to error tolerance, then, on average, less connected proteins should prove to be less essential than highly connected ones.

To test this, we rank-ordered all interacting proteins based on the number of links they have, and correlated this with the phenotypic effect of their individual removal from the yeast proteome. As shown in Fig. 1c, the likelihood that removal of a protein will prove lethal correlates with the number of interactions the protein has. For example, although proteins with five or fewer links constitute about 93% of the total number of proteins, we find that only about 21% of them are essential. By contrast, only some 0.7% of the yeast proteins with known phenotypic profiles have more than 15 links, but single deletion of 62% or so of these proves lethal. This implies that highly connected proteins with a central role in the network's architecture are three times more likely to be essential than proteins with only a small number of links to other proteins.

The simultaneous emergence of an inhomogeneous structure in both metabolic^5,11 and protein interaction networks suggests that there has been evolutionary selection of a common large-scale structure of biological networks and indicates that future systematic protein–protein interaction studies in other organisms will uncover an essentially identical protein-network topology. The correlation between the connectivity and indispensability of a given protein confirms that, despite the importance of individual biochemical function and genetic redundancy, the robustness against mutations in yeast is also derived from the organization of interactions and the topological positions of individual proteins¹². A better understanding of cell dynamics and robustness will be obtained from an integrated approach that simultaneously incorporates the individual and contextual properties of all constituents in complex cellular networks.

Affiliations

1. Department of Physics, University of Notre Dame, Notre Dame, 46556, Indiana, USA
   • H. Jeong
   •  & A.-L. Barabási
2. Department of Pathology, Northwestern University Medical School, Chicago, 60611, Illinois, USA
   • S. P. Mason
   •  & Z. N. Oltvai

Corresponding authors

Correspondence to A.-L. Barabási or Z. N. Oltvai.

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