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. 2008 Jul 11;4(7):e1000114.
doi: 10.1371/journal.pcbi.1000114.

Probing the Extent of Randomness in Protein Interaction Networks

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Free PMC article

Probing the Extent of Randomness in Protein Interaction Networks

Joseph Ivanic et al. PLoS Comput Biol. .
Free PMC article

Abstract

Protein-protein interaction (PPI) networks are commonly explored for the identification of distinctive biological traits, such as pathways, modules, and functional motifs. In this respect, understanding the underlying network structure is vital to assess the significance of any discovered features. We recently demonstrated that PPI networks show degree-weighted behavior, whereby the probability of interaction between two proteins is generally proportional to the product of their numbers of interacting partners or degrees. It was surmised that degree-weighted behavior is a characteristic of randomness. We expand upon these findings by developing a random, degree-weighted, network model and show that eight PPI networks determined from single high-throughput (HT) experiments have global and local properties that are consistent with this model. The apparent random connectivity in HT PPI networks is counter-intuitive with respect to their observed degree distributions; however, we resolve this discrepancy by introducing a non-network-based model for the evolution of protein degrees or "binding affinities." This mechanism is based on duplication and random mutation, for which the degree distribution converges to a steady state that is identical to one obtained by averaging over the eight HT PPI networks. The results imply that the degrees and connectivities incorporated in HT PPI networks are characteristic of unbiased interactions between proteins that have varying individual binding affinities. These findings corroborate the observation that curated and high-confidence PPI networks are distinct from HT PPI networks and not consistent with a random connectivity. These results provide an avenue to discern indiscriminate organizations in biological networks and suggest caution in the analysis of curated and high-confidence networks.

Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Evidence of Degree-Weighted Connectivity in Two PPI Networks.
(A) Helicobacter pylori and (B) Campylobacter jejuni. For k 1 k 2>10, probabilities of interaction P(k 1,k 2) were ordered by k 1 k 2 and averaged in groups of 10.
Figure 2
Figure 2. Degree-Weighted Connectivity in Two PPI Networks and Their DCDW Equivalents.
(A) Plasmodium falciparum and (B) Drosophila melanogaster. Points in black correspond to the PPI networks and points in red correspond to their DCDW equivalents. For the PPI networks, probabilities of interaction P(k 1,k 2) were ordered by k 1 k 2, and values for k 1 k 2>10 were averaged in groups of 10. For the DCDW networks, probabilities of interaction were averaged over 100 realizations and all values are shown.
Figure 3
Figure 3. Example of Non-Degree-Weighted Behavior in Networks Generated from a Non-Random Model.
The DCDW model was modified to eliminate both random enumeration of nodes and degree-weighted sampling for interacting partners. The degree distribution corresponding to the protein–protein interaction network of Plasmodium falciparum was used as input for the modified model.
Figure 4
Figure 4. Dependence of Clustering Coefficient upon Node Degree for Four PPI Networks and their DCDW Equivalents.
(A) Drosophila melanogaster, (B) Campylobacter jejuni, (C) Escherichia coli (HT2), and (D) Escherichia coli (HT1). Clustering profiles for the PPI networks (black) and the corresponding tenth (blue) and fiftieth (red) realizations of the DCDW model.
Figure 5
Figure 5. Dependence of Path Length upon Node Degree for Four PPI Networks and their DCDW Equivalents.
(A) Drosophila melanogaster, (B) Campylobacter jejuni, (C) Escherichia coli (HT2), and (D) Escherichia coli (HT1). Path length profiles for the PPI networks (black) and the corresponding tenth (blue) and fiftieth (red) realizations of the DCDW model.
Figure 6
Figure 6. Degree Distributions Representative of PPI Networks and of the RM+DD1 Model.
The normal PPI degree distribution (NPPI-DD) (black) is determined by averaging over eight PPI networks. Degree distributions of the RM+DD1 model are shown at time steps 1–5 (blue) and the steady state (red).

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