Network controllability analysis of intracellular signalling reveals viruses are actively controlling molecular systems.

In recent years control theory has been applied to biological systems with the aim of identifying the minimum set of molecular interactions that can drive the network to a required state. However, in an intra-cellular network it is unclear how control can be achieved in practice. To address this limitation we use viral infection, specifically human immunodeficiency virus type 1 (HIV-1) and hepatitis C virus (HCV), as a paradigm to model control of an infected cell. Using a large human signalling network comprised of over 6000 human proteins and more than 34000 directed interactions, we compared two states: normal/uninfected and infected. Our network controllability analysis demonstrates how a virus efficiently brings the dynamically organised host system into its control by mostly targeting existing critical control nodes, requiring fewer nodes than in the uninfected network. The lower number of control nodes is presumably to optimise exploitation of specific sub-systems needed for virus replication and/or involved in the host response to infection. Viral infection of the human system also permits discrimination between available network-control models, which demonstrates that the minimum dominating set (MDS) method better accounts for how the biological information and signals are organised during infection by identifying most viral proteins as critical driver nodes compared to the maximum matching (MM) method. Furthermore, the host driver nodes identified by MDS are distributed throughout the pathways enabling effective control of the cell via the high 'control centrality' of the viral and targeted host nodes. Our results demonstrate that control theory gives a more complete and dynamic understanding of virus exploitation of the host system when compared with previous analyses limited to static single-state networks.

Finding and analysing the minimum set of driver nodes required to control multilayer networks.

It is difficult to control multilayer networks in situations with real-world complexity. Here, we first define the multilayer control problem in terms of the minimum dominating set (MDS) controllability framework and mathematically demonstrate that simple formulas can be used to estimate the size of the minimum dominating set in multilayer (MDSM) complex networks. Second, we develop a new algorithm that efficiently identifies the MDSM in up to 6 layers, with several thousand nodes in each layer network. Interestingly, the findings reveal that the MDSM size for similar networks does not significantly differ from that required to control a single network. This result opens future directions for controlling, for example, multiple species by identifying a common set of enzymes or proteins for drug targeting. We apply our methods to 70 genome-wide metabolic networks across major plant lineages, unveiling some relationships between controllability in multilayer networks and metabolic functions at the genome scale.

Analysis of Critical and Redundant Vertices in Controlling Directed Complex Networks Using Feedback Vertex Sets.

Controlling complex networks through a small number of controller vertices is of great importance in wide-ranging research fields. Recently, a new approach based on the minimum feedback vertex set (MFVS) has been proposed to find such vertices in directed networks in which the target states are restricted to steady states. However, multiple MFVS configurations may exist and thus the selection of vertices may depend on algorithms and input data representations. Our attempts to address this ambiguity led us to adopt an existing approach that classifies vertices into three categories. This approach has been successfully applied to maximum matching-based and minimum dominating set-based controllability analysis frameworks. In this article, we present an algorithm as well as its implementation to compute and evaluate the critical, intermittent, and redundant vertices under the MFVS-based framework, where these three categories include vertices belonging to all MFVSs, some (but not all) MFVSs, and none of the MFVSs, respectively. The results of computational experiments using artificially generated networks and real-world biological networks suggest that the proposed algorithm is useful for identifying these three kinds of vertices for relatively large-scale networks, and that the fraction of critical and intermittent vertices is considerably small. Moreover, an analysis of the signal pathways indicates that critical and intermittent MFVSs tend to be enriched by essential genes.

Critical controllability analysis of directed biological networks using efficient graph reduction.

Network science has recently integrated key concepts from control theory and has applied them to the analysis of the controllability of complex networks. One of the proposed frameworks uses the Minimum Dominating Set (MDS) approach, which has been successfully applied to the identification of cancer-related proteins and in analyses of large-scale undirected networks, such as proteome-wide protein interaction networks. However, many real systems are better represented by directed networks. Therefore, fast algorithms are required for the application of MDS to directed networks. Here, we propose an algorithm that utilises efficient graph reduction to identify critical control nodes in large-scale directed complex networks. The algorithm is 176-fold faster than existing methods and increases the computable network size to 65,000 nodes. We then applied the developed algorithm to metabolic pathways consisting of 70 plant species encompassing major plant lineages ranging from algae to angiosperms and to signalling pathways from C. elegans, D. melanogaster and H. sapiens. The analysis not only identified functional pathways enriched with critical control molecules but also showed that most control categories are largely conserved across evolutionary time, from green algae and early basal plants to modern angiosperm plant lineages.

Identification of genes and critical control proteins associated with inflammatory breast cancer using network controllability.

One of the most aggressive forms of breast cancer is inflammatory breast cancer (IBC), whose lack of tumour mass also makes a prompt diagnosis difficult. Moreover, genomic differences between common breast cancers and IBC have not been completely assessed, thus substantially limiting the identification of biomarkers unique to IBC. Here, we developed a novel statistical analysis of gene expression profiles corresponding to microdissected IBC, non-IBC (nIBC) and normal samples that enabled us to identify a set of genes significantly associated with a specific disease state. Second, by using advanced methods based on controllability network theory, we identified a set of critical control proteins that uniquely and structurally control the entire proteome. By mapping high change variance genes in protein interaction networks, we found that a large statistically significant fraction of genes whose variance changed significantly between normal and IBC and nIBC disease states were among the set of critical control proteins. Moreover, this analysis identified the overlapping genes with the highest statistical significance; these genes may assist in developing future biomarkers and determining drug targets to disrupt the molecular pathways driving carcinogenesis in IBC.

Critical controllability in proteome-wide protein interaction network integrating transcriptome.

Recently, the number of essential gene entries has considerably increased. However, little is known about the relationships between essential genes and their functional roles in critical network control at both the structural (protein interaction network) and dynamic (transcriptional) levels, in part because the large size of the network prevents extensive computational analysis. Here, we present an algorithm that identifies the critical control set of nodes by reducing the computational time by 180 times and by expanding the computable network size up to 25 times, from 1,000 to 25,000 nodes. The developed algorithm allows a critical controllability analysis of large integrated systems composed of a transcriptome- and proteome-wide protein interaction network for the first time. The data-driven analysis captures a direct triad association of the structural controllability of genes, lethality and dynamic synchronization of co-expression. We believe that the identified optimized critical network control subsets may be of interest as drug targets; thus, they may be useful for drug design and development.

The electric properties of low-magnetic-loss magnetic composites containing Zn-Ni-Fe particles.

Recently, magnetic composites consisting of magnetic particles dispersed in a polymer matrix have been widely discussed for miniaturizing high-frequency electronic components such as antennae. Previously, we investigated the influence of the manufacturing process on the homogeneous dispersion of magnetic particles in the polymer and on the magnetic properties of the magnetic composites. In order to miniaturize electronic components, it is crucial to be able to independently control the permeability and permittivity in magnetic composites. This paper investigates the anisotropy and frequency dependence of the dielectric properties of magnetic composites fabricated from 20 vol% Zn(5)Ni(75)Fe(20) flaked particles. The permittivity of magnetic composites fabricated from Zn(5)Ni(75)Fe(20) flaked particles is anisotropic: at 1 GHz, the relative permittivities parallel and perpendicular to the plane of the specimens are 27.2 and 16.9, respectively. The permittivity varied little between frequencies of 50 MHz and 10 GHz.