Table 4. Tests of difference beween degree distributions of essential and nonessential proteins in raw and high-confidence yeast PPI data sets. Abundance in Protein Networks Correlation between degree/ abundance yes yes yes yes no no yes yes yes yes no PPI data set Raw Gavin [TAP] Krogan-TOF [TAP] Krogan-LCMS [TAP] Ho [HMS-PCI] Ito [Y2H] Uetz [Y2H] High-confidence Gavin [TAP] Krogan-CORE [TAP] Krogan-INT [TAP] Ho [HMS-PCI] Ito [Y2H] Essentiala Nonessentialb 20.79 18.02 28.49 12.24 3.04 2.59 5.88 7.82 5.21 6.04 2.13 11.02 10.63 14.36 8.18 2.60 1.96 5.90 4.20 2.95 3.89 1.84 PKSc , , , , , , , 0.9915 0.1542 0.5160 0.9994 aAverage degree of essential proteins. bAverage degree of nonessential proteins. cP-value for two-sample Kolmogorov-Smirnov test for difference between degree distributions of essential and nonessential proteins. The symbol ‘‘,’’ signifies P,0.0001. doi:10.1371/journal.pone.0005815.t004 correlation between degree and essentiality in the Y2H data sets as they also contain no correlations between degree and abundance. Therefore, the common notion that essential proteins generally have higher degrees than nonessential proteins may be misleading. In an effort to identify deterministic, or nonrandom, signatures in the raw yeast PPI networks, we quantified the enrichment of essential-essential interactions in the data sets by comparing the observed numbers with those from strict randomized simulations. For a given PPI network, proteins to be considered as essential were selected at random with the constraint that the degree distribution of the selected proteins matched those of the actual essential proteins. This ensures that the results are not perturbed by varying degree distributions of the ‘essential’ proteins whilst simultaneously conserving the network structures. Data were deduced from 1000 realizations and the results are given in Table 5. We consistently find that the numbers of actual essential-essential interactions are larger than those from the randomized simulations and that standard deviations are relatively small. Accordingly, all P-values, being less than 0.0001, indicated significant nonrandom enrichments. There- fore, biological signatures seem evident in all raw yeast PPI data sets, including Y2H despite that these networks show no correlation between degree and essentiality. Relation between Essentiality and Topology in HC Data Sets Table 4 also shows the average degrees of essential and nonessential proteins in the HC yeast PPI networks together with P-values from two-sample KS tests. The Y2H HC Ito data set, with a P-value of essentially one, has no correlation between degree and essentiality. This result is almost identical to that of the raw Ito PPI network, indicating that the Y2H method does not bias essential proteins to have more interacting partners. The HC Krogan data sets, like their raw counterparts, show significant correlations (all P- values are less than 0.0001) between degree and essentiality. This result is unsurprising as these data sets also show a relationship between degree and abundance. Similar findings are obtained for the HC Ho data set (HMS-PCI). Up to this point, the findings for HC data sets lend support to the notion that any identified correlation between degree and essentiality in a PPI network may be artificially induced, as essential proteins are generally more abundant than nonessential. In stark contrast, however, the HC Gavin data set, with a P-value of 0.52, shows no correlation between degree and essentiality although it does contain a degree/abundance associa- tion. Of the PPI networks investigated in this work, the HC Gavin data set is the only one that contains a degree/abundance correlation but not a degree/essentiality relationship. The reasons for this are not immediately clear but are presumably related to the steps in the HC interaction inferring procedure. We find that all of the HC yeast PPI networks show enriched interactions between essential proteins (Table 5). All P-values are less than 0.0001, indicating that the observed numbers of essential- essential interactions are significantly larger than from the strict randomized simulations. Our test for enrichment is very strict in that we freeze the network structure and degree distributions of essential (actual and randomly chosen) proteins and, therefore, it is difficult to form any extensive topological insights. However, our tests indicate, without question, that all raw and HC yeast PPI networks show a propensity for essential proteins to prefer to interact with each other. We deduce that a biological signature in a PPI network does not appear in the commonly acknowledged form of a degree/essentiality correlation; rather it manifests itself by enhancing interactions between essential proteins. While a recent study concludes that in HC PPI networks essential proteins are more likely to be involved in essential complex biological modules [23], here we find the more general case that essential proteins prefer to interact with each other. Discussion It is shown that raw and HC TAP and HMS-PCI PPI networks contain statistically significant correlations between protein degree and abundance. The previously noted trend between protein PLoS ONE | www.plosone.org 9 June 2009 | Volume 4 | Issue 6 | e5815