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73
The structure and function of complex networks
- SIAM REVIEW
, 2003
"... Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, ..."
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Cited by 2600 (7 self)
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Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Scale-free networks in cell biology
- JOURNAL OF CELL SCIENCE
"... A cell’s behavior is a consequence of the complex interactions between its numerous constituents, such as DNA, RNA, proteins and small molecules. Cells use signaling pathways and regulatory mechanisms to coordinate multiple processes, allowing them to respond to and adapt to an ever-changing environ ..."
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Cited by 203 (6 self)
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A cell’s behavior is a consequence of the complex interactions between its numerous constituents, such as DNA, RNA, proteins and small molecules. Cells use signaling pathways and regulatory mechanisms to coordinate multiple processes, allowing them to respond to and adapt to an ever-changing environment. The large number of components, the degree of interconnectivity and the complex control of cellular networks are becoming evident in the integrated genomic and proteomic analyses that are emerging. It is increasingly recognized that the understanding of properties that arise from whole-cell function require integrated, theoretical descriptions of the relationships between different cellular components. Recent
Evolving protein interaction networks through gene duplication
- J. Theor. Biol
"... The topology of the proteome map revealed by recent large-scale hybridization methods has shown that the distribution of protein-protein interactions is highly heterogeneous, with many proteins having few links while a few of them are heavily connected. This particular topology is shared by other ce ..."
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Cited by 86 (2 self)
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The topology of the proteome map revealed by recent large-scale hybridization methods has shown that the distribution of protein-protein interactions is highly heterogeneous, with many proteins having few links while a few of them are heavily connected. This particular topology is shared by other cellular networks, such as metabolic pathways, and it has been suggested to be responsible for the high mutational homeostasis displayed by the genome of some organisms. In this paper we explore a recent model of proteome evolution that has been shown to reproduce many of the features displayed by its real counterparts. The model is based on gene duplication plus re-wiring of the newly created genes. The statistical features displayed by the proteome of well-known organisms are reproduced, suggesting that the overall topology of the protein maps naturally emerges from the two leading mechanisms considered by the model. I.
T (2002) A model of large-scale proteome evolution. Adv Complex Syst 5: 43–54
- PLoS Computational Biology | www.ploscompbiol.org November 2007 | Volume 3 | Issue 11 | e2302278 Likelihood-Free Inference on PINs
"... The next step in the understanding of the genome organization, after the determination of complete sequences, involves proteomics. The proteome includes the whole set of protein-protein interactions, and two recent independent studies have shown that its topology displays a number of surprising fea ..."
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Cited by 63 (11 self)
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The next step in the understanding of the genome organization, after the determination of complete sequences, involves proteomics. The proteome includes the whole set of protein-protein interactions, and two recent independent studies have shown that its topology displays a number of surprising features shared by other complex networks, both natural and artificial. In order to understand the origins of this topology and its evolutionary implications, we present a simple model of proteome evolution that is able to reproduce many of the observed statistical regularities reported from the analysis of the yeast proteome. Our results suggest that the observed patterns can be explained by a process of gene duplication and diversification that would evolve proteome networks under a selection pressure, favoring robustness against failure of its individual components.
Pairwise alignment of protein interaction networks
- Journal of Computational Biology
, 2006
"... With an ever-increasing amount of available data on protein–protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Although available data on protein–protein interactions ..."
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Cited by 51 (4 self)
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With an ever-increasing amount of available data on protein–protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Although available data on protein–protein interactions is currently limited, recently developed algorithms have been shown to convey novel biological insights through employment of elegant mathematical models. The main challenge in aligning PPI networks is to define a graph theoretical measure of similarity between graph structures that captures underlying biological phenomena accurately. In this respect, modeling of conservation and divergence of interactions, as well as the interpretation of resulting alignments, are important design parameters. In this paper, we develop a framework for comprehensive alignment of PPI networks, which is inspired by duplication/divergence models that focus on understanding the evolution of protein interactions. We propose a mathematical model that extends the concepts of match, mismatch, and gap in sequence alignment to that of match, mismatch, and duplication in network alignment and evaluates similarity between graph structures through a scoring function that accounts for evolutionary events. By relying on evolutionary models, the proposed framework facilitates interpretation of resulting alignments in terms of not only conservation but also divergence of modularity in PPI networks. Furthermore, as in the case of sequence alignment, our model allows flexibility in adjusting parameters to quantify underlying evolutionary relationships. Based on the proposed model, we formulate PPI network alignment as an optimization problem and present fast algorithms to solve this problem. Detailed experimental results from an implementation of the proposed framework show that our algorithm is able to discover conserved interaction patterns very effectively, in terms of both accuracies and computational cost. Key words: protein–protein interactions, network alignment, evolutionary models. 1.
Information Theory of Complex Networks: on evolution and architectural constraints
- In
, 2004
"... Complex networks are characterized by highly heterogeneous distributions of links, often pervading the presence of key properties such as robustness under node removal. Several correlation measures have been defined in order to characterize the structure of these nets. Here we show that mutual infor ..."
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Cited by 42 (1 self)
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Complex networks are characterized by highly heterogeneous distributions of links, often pervading the presence of key properties such as robustness under node removal. Several correlation measures have been defined in order to characterize the structure of these nets. Here we show that mutual information, noise and joint entropies can be properly defined on a static graph. These measures are computed for a number of real networks and analytically estimated for some simple standard models. It is shown that real networks are clustered in a well-defined domain of the entropy/noise space. By using simulated annealing optimization, it is shown that optimally heterogeneous nets actually cluster around the same narrow domain, suggesting that strong constraints actually operate on the possible universe of complex networks. The evolutionary implications are discussed.
Fitting a geometric graph to a protein–protein interaction network
- BIOINFORMATICS
, 2008
"... Motivation: Finding a good network null model for protein–protein interaction (PPI) networks is a fundamental issue. Such a model would provide insights into the interplay between network structure and biological function as well as into evolution. Also, network (graph) models are used to guide biol ..."
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Cited by 24 (1 self)
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Motivation: Finding a good network null model for protein–protein interaction (PPI) networks is a fundamental issue. Such a model would provide insights into the interplay between network structure and biological function as well as into evolution. Also, network (graph) models are used to guide biological experiments and discover new biological features. It has been proposed that geometric random graphs are a good model for PPI networks. In a geometric random graph, nodes correspond to uniformly randomly distributed points in a metric space and edges (links) exist between pairs of nodes for which the corresponding points in the metric space are close enough according to some distance norm. Computational experiments have revealed close matches between key topological properties of PPI networks and geometric random graph models. In this work, we push the comparison further by
Selection, Tinkering, and Emergence in Complex Networks - Crossing the Land of Tinkering
- Complexity
, 2003
"... In this article the different features exhibited by four types of natural and artificial networks are reviewed, after a brief account of the basic quantitative characterizations that allow to measure network complexity. Some key questions that will be explored are: 1. What mechanisms have originated ..."
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Cited by 23 (4 self)
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In this article the different features exhibited by four types of natural and artificial networks are reviewed, after a brief account of the basic quantitative characterizations that allow to measure network complexity. Some key questions that will be explored are: 1. What mechanisms have originated observed topological regularities in complex networks? 2. To what extent does optimization shape network topology ? 3. What is the origin of homeostasis in complex networks? 4. Is homeostasis a driving force or a side effect in network topology? 5. Is tinkering an inevitable component of network evolution ? 6. Are engineered systems free of tinkering? Comparison between the mechanisms that drive the building process of different graphs reveals that optimization might be a driving force, canalized in biological systems by both tinkering and the presence of conflicting constraints common to any hard multidimensional optimization process. Conversely, the presence of global features in technology graphs that closely resemble those observed in biological webs indicates that, in spite of the engineered design that should lead to hierarchical structures (such as the one shown in Figure 1) the tinkerer seems to be at work. 2. MEASURING NETWORK COMPLEXITY Since we are interested in comparing the global features of both biological and artificial (engineered) networks, we need to consider a number of quantitative measures in order to characterize them properly. In order to do so, the network structure is represented by a graph #, as before. Some of these measures (minimal distance, clustering coefficient) are usually applied to topological (i.e., static) descriptors of the graph structure, but others (entropy, redundancy, degeneracy) also apply to states that average dynamic variables
Spontaneous emergence of modularity in cellular networks
"... Modularity is known to be one of the most relevant characteristics of biological systems and appears to be present at multiple scales. Given its adaptive potential, it is often assumed to be the target of selective pressures. Under such interpretation, selection would be actively favouring the forma ..."
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Cited by 21 (1 self)
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Modularity is known to be one of the most relevant characteristics of biological systems and appears to be present at multiple scales. Given its adaptive potential, it is often assumed to be the target of selective pressures. Under such interpretation, selection would be actively favouring the formation of modular structures, which would specialize in different functions. Here we show that, within the context of cellular networks, no such a selection pressure is needed to obtain modularity. Instead, the intrinsic dynamics of network growth by duplication and diversification is able to generate it for free and explain the statistical features exhibited by small subgraphs. The implications for the evolution and evolvability of both biological and technological systems are discussed.
