Influence of degree correlations on network structure and stability in protein-protein interaction networks

Background: The existence of negative correlations between degrees
of interacting proteins is being discussed since such negative
degree correlations were found for the large-scale yeast
protein-protein interaction (PPI) network of Ito et al. More recent
studies observed no such negative correlations for high-confidence
interaction sets. In this article, we analyzed a range of
experimentally derived interaction networks to understand the role
and prevalence of degree correlations in PPI networks. We
investigated how degree correlations influence the structure of
networks and their tolerance against perturbations such as the
targeted deletion of hubs. Results: For each PPI network, we
simulated uncorrelated, positively and negatively correlated
reference networks. Here, a simple model was developed which can
create different types of degree correlations in a network without
changing the degree distribution. Differences in static properties
associated with degree correlations were compared by analyzing the
network characteristics of the original PPI and reference networks.
Dynamics were compared by simulating the effect of a selective
deletion of hubs in all networks. Conclusion: Considerable
differences between the network types were found for the number of
components in the original networks. Negatively correlated networks
are fragmented into significantly less components than observed for
positively correlated networks. On the other hand, the selective
deletion of hubs showed an increased structural tolerance to these
deletions for the positively correlated networks. This results in a
lower rate of interaction loss in these networks compared to the
negatively correlated networks and a decreased disintegration rate.
Interestingly, real PPI networks are most similar to the randomly
correlated references with respect to all properties analyzed.
Thus, although structural properties of networks can be modified
considerably by degree correlations, biological PPI networks do not
actually seem to make use of this possibility.