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1.  Structural controllability of unidirectional bipartite networks 
Scientific Reports  2013;3:1647.
The interactions between fundamental life molecules, people and social organisations build complex architectures that often result in undesired behaviours. Despite all of the advances made in our understanding of network structures over the past decade, similar progress has not been achieved in the controllability of real-world networks. In particular, an analytical framework to address the controllability of bipartite networks is still absent. Here, we present a dominating set (DS)-based approach to bipartite network controllability that identifies the topologies that are relatively easy to control with the minimum number of driver nodes. Our theoretical calculations, assisted by computer simulations and an evaluation of real-world networks offer a promising framework to control unidirectional bipartite networks. Our analysis should open a new approach to reverting the undesired behaviours in unidirectional bipartite networks at will.
doi:10.1038/srep01647
PMCID: PMC3622082  PMID: 23571689
2.  Modularity in Protein Complex and Drug Interactions Reveals New Polypharmacological Properties 
PLoS ONE  2012;7(1):e30028.
Recent studies have highlighted the importance of interconnectivity in a large range of molecular and human disease-related systems. Network medicine has emerged as a new paradigm to deal with complex diseases. Connections between protein complexes and key diseases have been suggested for decades. However, it was not until recently that protein complexes were identified and classified in sufficient amounts to carry out a large-scale analysis of the human protein complex system. We here present the first systematic and comprehensive set of relationships between protein complexes and associated drugs and analyzed their topological features. The network structure is characterized by a high modularity, both in the bipartite graph and in its projections, indicating that its topology is highly distinct from a random network and that it contains a rich and heterogeneous internal modular structure. To unravel the relationships between modules of protein complexes, drugs and diseases, we investigated in depth the origins of this modular structure in examples of particular diseases. This analysis unveils new associations between diseases and protein complexes and highlights the potential role of polypharmacological drugs, which target multiple cellular functions to combat complex diseases driven by gain-of-function mutations.
doi:10.1371/journal.pone.0030028
PMCID: PMC3261189  PMID: 22279562
3.  A Mathematical Model for the Detection Mechanism of DNA Double-Strand Breaks Depending on Autophosphorylation of ATM 
PLoS ONE  2009;4(4):e5131.
Background
After IR stress, DNA double-strand breaks (DSBs) occur and repair proteins (RPs) bind to them, generating DSB-RP complexes (DSBCs), which results in repaired DSBs (RDSBs). In recent experimental studies, it is suggested that the ATM proteins detect these DNA lesions depending on the autophosphorylation of ATM which exists as a dimer before phosphorylation. Interestingly, the ATM proteins can work as a sensor for a small number of DSBs (approximately 18 DSBs in a cell after exposure to IR). Thus the ATM proteins amplify the small input signals based on the phosphorylation of the ATM dimer proteins. The true DSB-detection mechanism depending on ATM autophosphorylation has yet to be clarified.
Methodology/Principal Findings
We propose a mathematical model for the detection mechanism of DSBs by ATM. Our model includes both a DSB-repair mechanism and an ATM-phosphorylation mechanism. We model the former mechanism as a stochastic process, and obtain theoretical mean values of DSBs and DSBCs. In the latter mechanism, it is known that ATM autophosphorylates itself, and we find that the autophosphorylation induces bifurcation of the phosphorylated ATM (ATM*). The bifurcation diagram depends on the total concentration of ATM, which makes three types of steady state diagrams of ATM*: monostable, reversible bistable, and irreversible bistable. Bistability exists depending on the Hill coefficient in the equation of ATM autophosphorylation, and it emerges as the total concentration of ATM increases. Combining these two mechanisms, we find that ATM* exhibits switch-like behaviour in the presence of bistability, and the detection time after DNA damage decreases when the total concentration of ATM increases.
Conclusions/Significance
This work provides a mathematical model that explains the DSB-detection mechanism depending on ATM autophosphorylation. These results indicate that positive auto-regulation works both as a sensor and amplifier of small input signals.
doi:10.1371/journal.pone.0005131
PMCID: PMC2667630  PMID: 19365581
4.  Local and global modes of drug action in biochemical networks 
Background
It is becoming increasingly accepted that a shift is needed from the traditional target-based approach of drug development towards an integrated perspective of drug action in biochemical systems. To make this change possible, the interaction networks connecting drug targets to all components of biological systems must be identified and characterized.
Results
We here present an integrative analysis of the interactions between drugs and metabolism by introducing the concept of metabolic drug scope. The metabolic drug scope represents the full set of metabolic compounds and reactions that are potentially affected by a drug. We constructed and analyzed the scopes of all US approved drugs having metabolic targets. Our analysis shows that the distribution of metabolic drug scopes is highly uneven, and that drugs can be classified into several categories based on their scopes. Some of them have small scopes corresponding to localized action, while others have large scopes corresponding to potential large-scale systemic action. These groups are well conserved throughout different topologies of the underlying metabolic network. They can furthermore be associated to specific drug therapeutic properties.
Conclusion
These findings demonstrate the relevance of metabolic drug scopes to the characterization of drug-metabolism interactions and to understanding the mechanisms of drug action in a system-wide context.
doi:10.1186/1472-6769-9-4
PMCID: PMC2670818  PMID: 19351397
5.  A global view of drug-therapy interactions 
BMC Pharmacology  2008;8:5.
Background
Network science is already making an impact on the study of complex systems and offers a promising variety of tools to understand their formation and evolution in many disparate fields from technological networks to biological systems. Even though new high-throughput technologies have rapidly been generating large amounts of genomic data, drug design has not followed the same development, and it is still complicated and expensive to develop new single-target drugs. Nevertheless, recent approaches suggest that multi-target drug design combined with a network-dependent approach and large-scale systems-oriented strategies create a promising framework to combat complex multi-genetic disorders like cancer or diabetes.
Results
We here investigate the human network corresponding to the interactions between all US approved drugs and human therapies, defined by known relationships between drugs and their therapeutic applications. Our results show that the average paths in this drug-therapy network are shorter than three steps, indicating that distant therapies are separated by a surprisingly low number of chemical compounds. We also identify a sub-network composed by drugs with high centrality measures in the drug-therapy network, which represent the structural backbone of this system and act as hubs routing information between distant parts of the network.
Conclusion
These findings provide for the first time a global map of the large-scale organization of all known drugs and associated therapies, bringing new insights on possible strategies for future drug development. Special attention should be given to drugs which combine the two properties of (a) having a high centrality value in the drug-therapy network and (b) acting on multiple molecular targets in the human system.
doi:10.1186/1471-2210-8-5
PMCID: PMC2294115  PMID: 18318892
6.  Correlation between structure and temperature in prokaryotic metabolic networks 
BMC Bioinformatics  2007;8:303.
Background
In recent years, an extensive characterization of network structures has been made in an effort to elucidate design principles of metabolic networks, providing valuable insights into the functional organization and the evolutionary history of organisms. However, previous analyses have not discussed the effects of environmental factors (i.e., exogenous forces) in shaping network structures. In this work, we investigate the effect of temperature, which is one of the environmental factors that may have contributed to shaping structures of metabolic networks.
Results
For this, we investigate the correlations between several structural properties characterized by graph metrics like the edge density, the degree exponent, the clustering coefficient, and the subgraph concentration in the metabolic networks of 113 prokaryotes and optimal growth temperature. As a result, we find that these structural properties are correlated with the optimal growth temperature. With increasing temperature, the edge density, the clustering coefficient and the subgraph concentration decrease and the degree exponent becomes large.
Conclusion
This result implies that the metabolic networks transit with temperature as follows. The density of chemical reactions becomes low, the connectivity of the networks becomes homogeneous such as random networks and both the network modularity, based on the graph-theoretic clustering coefficient, and the frequency of recurring subgraphs decay. In short, metabolic networks undergo a change from heterogeneous and high-modular structures to homogeneous and low-modular structures, such as random networks, with temperature. This finding may suggest that the temperature plays an important role in the design principles of metabolic networks.
doi:10.1186/1471-2105-8-303
PMCID: PMC2045116  PMID: 17711568
7.  Evolutionary history and functional implications of protein domains and their combinations in eukaryotes 
Genome Biology  2007;8(6):R121.
A rapid emergence of animal-specific domains was observed in animals, contributing to specific domain combinations and functional diversification, but no similar trends were observed in other clades of eukaryotes.
Background
In higher multicellular eukaryotes, complex protein domain combinations contribute to various cellular functions such as regulation of intercellular or intracellular signaling and interactions. To elucidate the characteristics and evolutionary mechanisms that underlie such domain combinations, it is essential to examine the different types of domains and their combinations among different groups of eukaryotes.
Results
We observed a large number of group-specific domain combinations in animals, especially in vertebrates. Examples include animal-specific combinations in tyrosine phosphorylation systems and vertebrate-specific combinations in complement and coagulation cascades. These systems apparently underwent extensive evolution in the ancestors of these groups. In extant animals, especially in vertebrates, animal-specific domains have greater connectivity than do other domains on average, and contribute to the varying number of combinations in each animal subgroup. In other groups, the connectivities of older domains were greater on average. To observe the global behavior of domain combinations during evolution, we traced the changes in domain combinations among animals and fungi in a network analysis. Our results indicate that there is a correlation between the differences in domain combinations among different phylogenetic groups and different global behaviors.
Conclusion
Rapid emergence of animal-specific domains was observed in animals, contributing to specific domain combinations and functional diversification, but no such trends were observed in other clades of eukaryotes. We therefore suggest that the strategy for achieving complex multicellular systems in animals differs from that of other eukaryotes.
doi:10.1186/gb-2007-8-6-r121
PMCID: PMC2394772  PMID: 17588271
8.  Observing metabolic functions at the genome scale 
Genome Biology  2007;8(6):R123.
A modular approach is presented that allows the observation of the transcriptional activity of metabolic functions at the genome scale.
Background
High-throughput techniques have multiplied the amount and the types of available biological data, and for the first time achieving a global comprehension of the physiology of biological cells has become an achievable goal. This aim requires the integration of large amounts of heterogeneous data at different scales. It is notably necessary to extend the traditional focus on genomic data towards a truly functional focus, where the activity of cells is described in terms of actual metabolic processes performing the functions necessary for cells to live.
Results
In this work, we present a new approach for metabolic analysis that allows us to observe the transcriptional activity of metabolic functions at the genome scale. These functions are described in terms of elementary modes, which can be computed in a genome-scale model thanks to a modular approach. We exemplify this new perspective by presenting a detailed analysis of the transcriptional metabolic response of yeast cells to stress. The integration of elementary mode analysis with gene expression data allows us to identify a number of functionally induced or repressed metabolic processes in different stress conditions. The assembly of these elementary modes leads to the identification of specific metabolic backbones.
Conclusion
This study opens a new framework for the cell-scale analysis of metabolism, where transcriptional activity can be analyzed in terms of whole processes instead of individual genes. We furthermore show that the set of active elementary modes exhibits a highly uneven organization, where most of them conduct specialized tasks while a smaller proportion performs multi-task functions and dominates the general stress response.
doi:10.1186/gb-2007-8-6-r123
PMCID: PMC2394767  PMID: 17594483
9.  Clustering under the line graph transformation: application to reaction network 
BMC Bioinformatics  2004;5:207.
Background
Many real networks can be understood as two complementary networks with two kind of nodes. This is the case of metabolic networks where the first network has chemical compounds as nodes and the second one has nodes as reactions. In general, the second network may be related to the first one by a technique called line graph transformation (i.e., edges in an initial network are transformed into nodes). Recently, the main topological properties of the metabolic networks have been properly described by means of a hierarchical model. While the chemical compound network has been classified as hierarchical network, a detailed study of the chemical reaction network had not been carried out.
Results
We have applied the line graph transformation to a hierarchical network and the degree-dependent clustering coefficient C(k) is calculated for the transformed network. C(k) indicates the probability that two nearest neighbours of a vertex of degree k are connected to each other. While C(k) follows the scaling law C(k) ~ k-1.1 for the initial hierarchical network, C(k) scales weakly as k0.08 for the transformed network. This theoretical prediction was compared with the experimental data of chemical reactions from the KEGG database finding a good agreement.
Conclusions
The weak scaling found for the transformed network indicates that the reaction network can be identified as a degree-independent clustering network. By using this result, the hierarchical classification of the reaction network is discussed.
doi:10.1186/1471-2105-5-207
PMCID: PMC545960  PMID: 15617578

Results 1-9 (9)