Abundance in Protein Networks Table 3. Pearson correlation coefficients (r) and corresponding P-values for tests of linear association between log(degree) and log2(abundance) in high-confidence yeast PPI data sets. PPI data set Gavin [TAP] Krogan-CORE [TAP] Krogan-INT [TAP] Ho [HMS-PCI] Ito [Y2H] NPa 1286 2208 1081 1240 596 Western blot (Ghaemmaghami et al.) Flow cytometry (Newman et al.) Gene expression (Holstege et al.) r 0.31 (0.30) 0.20 (0.18) 0.15 (0.13) 0.26 (0.26) Pb , , , , NPa 1012 1461 778 874 380 r 0.38 (0.37) 0.16 (0.14) 0.16 (0.15) 0.26 (0.26) Pb , , , , NPa 1470 2578 1186 1535 r 0.39 (0.37) 0.22 (0.21) 0.20 (0.19) 0.21 (0.21) 0.02 (0.03) Pb , , , , 20.02 (20.01) 0.6514 20.06 (20.06) 0.2393 727 0.6726 Spearman rank correlation coefficients are provided in parentheses. aNumber of proteins in PPI data set having abundance measurements. bThe symbol ‘‘,’’ signifies P,0.0001 for both Pearson and Spearman correlation coefficients. doi:10.1371/journal.pone.0005815.t003 biologically significant. Alternatively, the observed correlations for the HC data sets could be the result of inferring procedures that are not completely effectual. The Y2H HC data set of Ito et al. is a subset of the raw PPI network and includes only those interactions that were experi- mentally detected at least three times. We find that this interaction set shows no correlation between degree and abundance (Table 3). This is not surprising as the raw data set also contains no relationship. The correlation coefficients are small, ranging from 20.06 to 0.03, and all P-values for Pearson correlation coefficients are larger than 0.23. The results for the HC PPI data sets are identical to those of the raw data sets. Those derived from affinity purification experiments show weak, but statistically significant correlations between degree and abundance, while all Y2H PPI data sets show no relationship between degree and abundance. These findings further exemplify the difference between interactions detected by Y2H screens and affinity purification procedures. Relation between Essentiality and Topology in Raw PPI Data Sets The correlation between degree and essentiality, in that proteins having more interactions are more likely to be essential, has been noted previously [20–23] and is generally an accepted precept known as the centrality-lethality rule. Recent analysis of curated, inferred, and HC yeast networks show that essential proteins are more likely to be involved in essential complex biological modules and, therefore, their degrees are on the average higher [23]. However, the findings presented here, that PPI networks determined using affinity purification procedures (TAP and HMS-PCI) have statistically significant correlations between degree and abundance while Y2H PPI networks do not, warrants another look at the degree/essentiality property. Table 4 gives average degrees of essential and nonessential proteins in the raw yeast PPI networks. We find that essential proteins have higher average degrees than nonessential proteins in all of the raw PPI networks. However, it is known that degree distributions of PPI networks are not normal; rather, they resemble power-law scaling [22,57]. Therefore, in order to determine the significance of the difference between degrees of essential and nonessential proteins we use the two-sample KS test to compare their degree distributions. We find that degree distributions of essential proteins in the TAP and HMS-PCI data sets are significantly different to those of nonessential proteins, with all PKS- values being less than 0.0001 (Table 4). These differences are illustrated in Figures 4A and 4B, which show degree distributions of essential and nonessential proteins in the raw Gavin and Krogan-TOF PPI data sets, respectively. In stark contrast, we find that degree distributions of essential and nonessential proteins in the raw Y2H networks are not significantly different, with PKS-values of 0.9915 and 0.1542 for the raw Ito and Uetz data sets, respectively. Degree distributions of essential and nonessential proteins in the Ito and Uetz PPI networks are shown in Figures 4C and 4D, respectively, and it is clear that for both data sets the curves are very similar. Therefore, we conclude that the raw Y2H data sets show no correlation between degree and essentiality. In fact, the raw Ito data set has a P-value very near to one. It has been previously reported that the Ito data set has a weak correlation between degree and essentiality [20]; however, we find no difference between degree distributions of essential and nonessential proteins for this data set. The degree/essentiality relationships discussed above for the raw PPI data sets are curious in that if there is a (weak) degree/ abundance correlation, there is also a degree/essentiality relation- ship. These tandem correlations are observed in all of the raw interaction data sets determined by affinity purification methods (TAP and HMS-PCI). The converse is also true, in that, if there is no degree/abundance relationship, there is also no degree/essentiality correlation (Table 4). These tandem non-correlations are observed in the Y2H interaction data sets. Insights into why these correlations are associated can be obtained by looking for a relationship between essentiality and abundance. In fact, we find that essential proteins are more abundant than nonessential proteins in all of the yeast abundance measurements utilized here. P-values, assuming normal distributions, for tests of difference between average log2(abundance) of essential and nonessential proteins for the WB [42], FC [43], and GE [44] measurements are 10219, 1027, and 10237 respectively. P- values for two-sample KS tests are very similar, 10218, 1028, and 10231 for WB, FC, and GE measurements, respectively. Therefore, the correlation between degree and essentiality in the raw TAP and HMS-PCI networks may be artificial due to essential proteins generally being more abundant. This would explain why there is no PLoS ONE | www.plosone.org 8 June 2009 | Volume 4 | Issue 6 | e5815