Table 1.
Structural properties of the tested protein interaction networks.
Table 2.
Amount of overlap between tested networks.
Figure 1.
Relationship between degree and essentiality in the tested networks.
(A) For each tested network the fraction of essential nodes among nodes with highest degree (hubs) is shown. The horizontal axis shows the fraction of the total network nodes that were designated as hubs. (B) Correlation between degree and essentiality is assessed by Kendall's tau and Spearman's rho rank correlation coefficients.
Figure 2.
Centrality measures demonstrated on a toy network.
Here we demonstrate the difference in the five centrality measures on a toy network. (A) The toy network consists of two cliques: K50 with nodes A1–A50 and K10 with nodes B1–B10. The two cliques are interconnected by an edge (A1, B1) and through an additional vertex D. Additional node C attaches to the network through A2. (B) As the measures assign centrality values based on different network properties they will rank nodes differently. Briefly, the eigenvector centrality measure (EC) will assign high-centrality values to nodes that are close to many other central nodes in the network. The subgraph centrality measure (SC) assigns centrality values to a node based on the number of closed walks that originate at the node. The shortest path betweenness centrality measure (SPBC) assigns the node centrality value based on the fraction of shortest paths that pass through the node averaged over all pairs of nodes in the network. The current-flow betweenness centrality measure (CFC) generalizes the SPBC measure by including additional paths, not just the shortest paths, in the computation. Here, the difference between the measures is exemplified by the rankings that they produce for the toy network nodes.
Figure 3.
Vulnerability to attack against most central proteins.
(A–F) The impact of node removal is quantified by the fraction of nodes in the largest connected component. There is one curve for each centrality measure that shows the fraction of nodes in the largest connected component as a function of the fraction of the most central nodes removed. We also show the impact of node removal in a random order and the size of the largest connected component when all essential proteins are removed.
Table 3.
Impact of the removal of essential proteins as compared to the removal of an equivalent number of random nonessential proteins with the same degree distribution.
Figure 4.
Enrichment of hubs and an equivalent number of most central nodes according to other centrality measures in essential proteins.
Fraction of essential proteins among hubs and an equivalent number of most central nodes according to four other centrality measures. The fraction of essential proteins among the nodes of the network is shown as ntwk.avg.
Table 4.
Correlation between centrality indices and essentiality.
Table 5.
Difference between the observed and expected number of pairs where both proteins are either essential or nonessential.
Figure 5.
The automatic method for extraction of ECOBIMs.
Here we demonstrate the major steps of the method on the HC network. The input to the method is a protein interaction network, GO annotation, and the set of essential nodes, which are shown in red. The method considers subnetworks induced by proteins annotated with the same GO biological process term, one subnetwork at a time, to identify densely connected regions or COBIMs. The COBIMs are shown by a COBIM intersection graph, where nodes correspond to COBIMs (the size of the node is proportional to the number of genes in the corresponding COBIM) and there is an edge between a pair of COBIMs if they have at least two proteins in common. The COBIMs that are enriched in essential proteins are selected as ECOBIMs, shown in green.
Figure 6.
Enrichment of ECOBIM and non-ECOBIM hubs in essential proteins.
Fraction of essential proteins among various types of hubs: all hubs, hubs that are members of ECOBIMs (ECOBIM hubs), and hubs that are not members of ECOBIMs (non-ECOBIM hubs). The fraction of essential proteins among all proteins in the network is also shown (ntwk.avg.). The numbers above the bars show the number of essential hubs out of the total number of hubs of this type for ECOBIM and non-ECOBIM hubs.
Table 6.
Membership in ECOBIMs and the centrality-lethality rule.
Table 7.
Largest ECOBIMs extracted from the tested networks.
Table 8.
ECOBIMs contain a large fraction of essential COBIM proteins.
Figure 7.
GO terms that are overrepresented among ECOBIM nodes.
For every network the GO terms that are overrepresented among ECOBIM nodes are shown. The overrepresentation of a GO term is quantified by the natural logarithm of a p-value, where the p-value is the probability that at least this number of ECOBIM genes would belong to the GO term had the ECOBIM genes been selected uniformly at random from the network genes.
Table 9.
Enrichment of ECOBIM and non-ECOBIM COBIM nodes for GO subnetworks in the DIP CORE network.