Identifying hubs in protein interaction networks

Abstract

Background: In spite of the scale-free degree distribution that characterizes most protein interaction networks (PINs), it is common to define an ad hoc degree scale that defines "hub" proteins having special topological and functional significance. This raises the concern that some conclusions on the functional significance of proteins based on network properties may not be robust.

Methodology: In this paper we present three objective methods to define hub proteins in PINs: one is a purely topological method and two others are based on gene expression and function. By applying these methods to four distinct PINs, we examine the extent of agreement among these methods and implications of these results on network construction.

Conclusions: We find that the methods agree well for networks that contain a balance between error-free and unbiased interactions, indicating that the hub concept is meaningful for such networks.

Figure 1. A cartoon illustrating relative connectivity of subgraphs.

Successive subgraphs are generated from a ranked degree list, and the relative connectivity f is computed from them. Each node is represented by a black center with a gray ‘halo’ whose size is proportional to the degree of the node. Note that newer nodes have smaller halos (lower degrees). Interactions involving newly added nodes are shown as dotted edges, while previously established interactions are shown as dark edges. Note that all subgraphs upto G₄ are completely disconnected in this example.

Figure 2. Relative subgraph connectivity as a function of number of nodes.

The four yeast protein interaction networks studied are HC and LC (panel (a), first 100 nodes), HC^h and FYI (panel (b), first 500 nodes), showing regions of interest where the relative subgraph connectivity increases from a minimum.

Figure 3. Statistical significance of relative subgraph connectivity.

Empirical P-values (dashed lines) for significance of the relative connectivity measure (solid lines) for all the four networks were computed using 10,000 random networks corresponding to each real network. P-values that are less than 10⁻⁴ can be identified by the circles on the x-axis in each panel.

Figure 4. Expression correlation distributions.

The panels display distributions of the average Pearson correlation coefficient (PCC) between expression profiles of hubs with their interaction partners (solid line) and non-hubs with their interaction partners (dashed line) for HC ((a)–(f)), LC ((g)–(l)), HC^h ((m)–(r)) and FYI ((s)–(x)). The set of hubs for each network was determined from the relative subgraph connectivity analysis. Average PCC values were computed using normalized gene expression profiles over the full yeast compendium that includes expression data under all five conditions each of which is also analyzed individually.

Figure 5. Bimodality of PCC distribution for the HC network.

Inclusion of non-hub nodes into the list of HC hubs leads to reduction in bi-modality of the average PCC distribution. This can be seen as the number of hubs included increases from 40 to 419 in the HC dataset. The panel on the left displays smoothed probability density functions corresponding to the average PCC distribution while the panel on the right displays the cumulative distribution functions. Percentiles refer to the percentages of top high degree nodes included in the hub set, following .

Figure 6. Dip statistics as a function of number of included hubs.

Values of the dip statistic for all four networks studied as a function of the number of top degree nodes included in the hub set. The straight line marks the boundary between statistically significant and insignificant dip values (at 95% confidence).

Figure 7. Essential gene enrichment.

Enrichment for essential genes among hubs relative to non-hubs, as measured by the Jensen-Shannon divergence (upper panels) and the P-value for the Kolmogorov-Smirnov test (lower panels).

Figure 8. Robustness of relative subgraph connectivity.

Relative subgraph connectivity profiles for unperturbed versions of all four networks are shown, along with the corresponding profiles upon random addition and removal of 10% and 15% of the edges in the unperturbed networks.