Figure 1.
Schematic Showing a Bottleneck and the Four Categories of Nodes in a Network
Four nodes with different colors represent examples of the four categories defined by degree and betweenness. Please note that every node in the network belongs to one of the four categories. However, in this schematic, we only point out the categories of the four example nodes.
Figure 2.
Comparison of Essentiality among Various Categories of Proteins within Interaction and Regulatory Networks
(A) Bottlenecks tend to be essential genes in both interaction and regulatory networks. p-Values measure the statistical significance of the different essentialities between bottlenecks and nonbottlenecks.
(B) Essentiality of different categories of proteins. NH-NB, nonhub–nonbottlenecks; H-NB, hub–nonbottlenecks; B-NH, nonhub–bottlenecks; BH, hub–bottlenecks. p-Values measure the statistical significance of the different essentialities between different categories of proteins against nonhub–nonbottlenecks using cumulative binomial distributions (see Methods).
Figure 3.
Essentialities of Different Categories of Nonhub–Bottlenecks in the Interaction Network
To find all proteins participating in signaling transduction pathways (i.e., the bar “Signal”), we manually went through all available pathways in KEGG and collected all proteins in them. Since this is a very small dataset, we further included all proteins, more than half of whose interacting partners are involved in signaling transduction pathways in KEGG. This inclusion is reasonable because the general belief is that interacting proteins share the same function. The fraction of essential genes among nonhub–nonbottlenecks is used as the random expectation, which is also indicated by the horizontal line. p-Values measure the statistical significance of the different essentialities of different categories of nonhub–bottlenecks relative to the random expectation. The bar “MIPS” refers to nonhub–bottlenecks involved in the complexes defined by the MIPS complex catalog. The bar “Permanent” refers to nonhub–bottlenecks involved in permanent interactions. The bar “Transient” refers to nonhub–bottlenecks only involved in transient interactions. The bar “All” refers to all nonhub–bottlenecks. *p-Value above the bar “Transient” measures the statistical significance of transient nonhub–bottlenecks being less essential than random.
Figure 4.
Expression Dynamics of Hub–Nonbottlenecks and Hub–Bottlenecks
Histograms of the average correlation coefficient of the expression profile of any given gene with its direct interaction partners. Expression dynamics for all four categories of nodes are shown in Figure S7.
Figure 5.
A Biological Example of a Nonhub–Bottleneck in the Interaction Network
Cak1p is a cyclin-dependent kinase-activating kinase involved in two key signaling-transduction pathways: cell cycle and sporulation.