Growing networks under geographical constraints

Scale-free networks embedded in fractal space

The impact of an inhomogeneous arrangement of nodes in space on a network organization cannot be neglected in most real-world scale-free networks. Here we propose a model for a geographical network with nodes embedded in a fractal space in which we can tune the network heterogeneity by varying the strength of the spatial embedding. When the nodes in such networks have power-law distributed intrinsic weights, the networks are scale-free with the degree distribution exponent decreasing with increasing fractal dimension if the spatial embedding is strong enough, while the weakly embedded networks are still scale-free but the degree exponent is equal to γ = 2 regardless of the fractal dimension. We show that this phenomenon is related to the transition from a noncompact to compact phase of the network and that this transition accompanies a drastic change of the network efficiency. We test our analytically derived predictions on the real-world example of networks describing the soil porous architecture.

Eigenvalue spectra of spatial-dependent networks

Many real-life networks exhibit a spatial dependence; i.e., the probability to form an edge between two nodes in the network depends on the distance between them. We investigate the influence of spatial dependence on the spectral density of the network. When increasing spatial dependence in Erdös-Rényi, scale-free, and small-world networks, it is found that the spectrum changes. Due to the spatial dependence the degree of clustering and the number of triangles increase. This results in a higher asymmetry (skewness). Our results show that the spectrum can be used to detect and quantify clustering and spatial dependence in a network.

Identification of candidate disease genes by integrating Gene Ontologies and protein-interaction networks: case study of primary immunodeficiencies

Disease gene identification is still a challenge despite modern high-throughput methods. Many diseases are very rare or lethal and thus cannot be investigated with traditional methods. Several in silico methods have been developed but they have some limitations. We introduce a new method that combines information about protein-interaction network properties and Gene Ontology terms. Genes with high-calculated network scores and statistically significant gene ontology terms based on known diseases are prioritized as candidate genes. The method was applied to identify novel primary immunodeficiency-related genes, 26 of which were found. The investigation uses the protein-interaction network for all essential immunome human genes available in the Immunome Knowledge Base and an analysis of their enriched gene ontology annotations. The identified disease gene candidates are mainly involved in cellular signaling including receptors, protein kinases and adaptor and binding proteins as well as enzymes. The method can be generalized for any disease group with sufficient information.

Efficiency of the immunome protein interaction network increases during evolution

Background

Details of the mechanisms and selection pressures that shape the emergence and development of complex biological systems, such as the human immune system, are poorly understood. A recent definition of a reference set of proteins essential for the human immunome, combined with information about protein interaction networks for these proteins, facilitates evolutionary study of this biological machinery.

Results

Here, we present a detailed study of the development of the immunome protein interaction network during eight evolutionary steps from Bilateria ancestors to human. New nodes show preferential attachment to high degree proteins. The efficiency of the immunome protein interaction network increases during the evolutionary steps, whereas the vulnerability of the network decreases.

Conclusion

Our results shed light on selective forces acting on the emergence of biological networks. It is likely that the high efficiency and low vulnerability are intrinsic properties of many biological networks, which arise from the effects of evolutionary processes yet to be uncovered.