Reconstructing gene regulatory networks: from random to scale-free connectivity

The manipulation of organisms using combinations of gene knockout, RNAi and drug interaction experiments can be used to reveal regulatory interactions between genes. Several algorithms have been proposed that try to reconstruct the underlying regulatory networks from gene expression data sets arising from such experiments. Often these approaches assume that each gene has approximately the same number of interactions within the network, and the methods rely on prior knowledge, or the investigator's best guess, of the average network connectivity. Recent evidence points to scale-free properties in biological networks, however, where network connectivity follows a power-law distribution. For scale-free networks, the average number of regulatory interactions per gene does not satisfactorily characterise the network. With this in mind, a new reverse engineering approach is introduced that does not require prior knowledge of network connectivity and its performance is compared with other published algorithms using simulated gene expression data with biologically relevant network structures. Because this new approach does not make any assumptions about the distribution of network connections, it is suitable for application to scale-free networks.     

A scale-free structure prior for graphical models with applications in functional genomics

The problem of reconstructing large-scale, gene regulatory networks from gene expression data has garnered considerable attention in bioinformatics over the past decade with the graphical modeling paradigm having emerged as a popular framework for inference. Analysis in a full Bayesian setting is contingent upon the assignment of a so-called structure prior-a probability distribution on networks, encoding a priori biological knowledge either in the form of supplemental data or high-level topological features. A key topological consideration is that a wide range of cellular networks are approximately scale-free, meaning that the fraction, , of nodes in a network with degree is roughly described by a power-law with exponent between and . The standard practice, however, is to utilize a random structure prior, which favors networks with binomially distributed degree distributions. In this paper, we introduce a scale-free structure prior for graphical models based on the formula for the probability of a network under a simple scale-free network model. Unlike the random structure prior, its scale-free counterpart requires a node labeling as a parameter. In order to use this prior for large-scale network inference, we design a novel Metropolis-Hastings sampler for graphical models that includes a node labeling as a state space variable. In a simulation study, we demonstrate that the scale-free structure prior outperforms the random structure prior at recovering scale-free networks while at the same time retains the ability to recover random networks. We then estimate a gene association network from gene expression data taken from a breast cancer tumor study, showing that scale-free structure prior recovers hubs, including the previously unknown hub SLC39A6, which is a zinc transporter that has been implicated with the spread of breast cancer to the lymph nodes. Our analysis of the breast cancer expression data underscores the value of the scale-free structure prior as an instrument to aid in the identification of candidate hub genes with the potential to direct the hypotheses of molecular biologists, and thus drive future experiments.     

Emergence of scale-free distribution in protein–protein interaction networks based on random selection of interacting domain pairs

Recent analyses of biological and artificial networks have revealed a common network architecture, called scale-free topology. The origin of the scale-free topology has been explained by using growth and preferential attachment mechanisms. In a cell, proteins are the most important carriers of function, and are composed of domains as elemental units responsible for the physical interaction between protein pairs. Here, we propose a model for protein–protein interaction networks that reveals the emergence of two possible topologies. We show that depending on the number of randomly selected interacting domain pairs, the connectivity distribution follows either a scale-free distribution, even in the absence of the preferential attachment, or a normal distribution. This new approach only requires an evolutionary model of proteins (nodes) but not for the interactions (edges). The edges are added by means of random interaction of domain pairs. As a result, this model offers a new mechanistic explanation for understanding complex networks with a direct biological interpretation because only protein structures and their functions evolved through genetic modifications of amino acid sequences. These findings are supported by numerical simulations as well as experimental data.     

An exponential core in the heart of the yeast protein interaction network

Protein interactions in the budding yeast have been shown to form a scale-free network, a feature of other organized networks such as bacterial and archaeal metabolism and the World Wide Web. Here, we study the connections established by yeast proteins and discover a preferential attachment between essential proteins. The essential-essential connections are long ranged and form a subnetwork where the giant component includes 97% of these proteins. Unexpectedly, this subnetwork displays an exponential connectivity distribution, in sharp contrast to the scale-free topology of the complete network. Furthermore, the wide phylogenetic extent of these core proteins and interactions provides evidence that they represent the ancestral state of the yeast protein interaction network. Finally, we propose that this core exponential network may represent a generic scaffold around which organism-specific and taxon-specific proteins and interactions coalesce.     

The role of log-normal dynamics in the evolution of biochemical pathways

The study of the scale-free topology in non-biological and biological networks and the dynamics that can explain this fascinating property of complex systems have captured the attention of the scientific community in the last years. Here, we analyze the biochemical pathways of three organisms (Methanococcus jannaschii, Escherichia coli, Saccharomyces cerevisiae) which are representatives of the main kingdoms Archaea, Bacteria and Eukaryotes during the course of the biological evolution. We can consider two complementary representations of the biochemical pathways: the enzymes network and the chemical compounds network. In this article, we propose a stochastic model that explains that the scale-free topology with exponent in the vicinity of gamma approximately 3/2 found across these three organisms is governed by the log-normal dynamics in the evolution of the enzymes network. Precisely, the fluctuations of the connectivity degree of enzymes in the biochemical pathways between evolutionary distant organisms follow the same conserved dynamical principle, which in the end is the origin of the stationary scale-free distribution observed among species, from Archaea to Eukaryotes. In particular, the log-normal dynamics guarantees the conservation of the scale-free distribution in evolving networks. Furthermore, the log-normal dynamics also gives a possible explanation for the restricted range of observed exponents gamma in the scale-free networks (i.e., gamma > or = 3/2). Finally, our model is also applied to the chemical compounds network of biochemical pathways and the Internet network.     

The community structure of human cellular signaling network

Living cell is highly responsive to specific chemicals in its environment, such as hormones and molecules in food or aromas. The reason is ascribed to the existence of widespread and diverse signal transduction pathways, between which crosstalks usually exist, thus constitute a complex signaling network. Evidently, knowledge of topology characteristic of this network could contribute a lot to the understanding of diverse cellular behaviors and life phenomena thus come into being. In this presentation, signal transduction data is extracted from KEGG to construct a cellular signaling network of Homo sapiens, which has 931 nodes and 6798 links in total. Computing the degree distribution, we find it is not a random network, but a scale-free network following a power-law of P(K) approximately K(-gamma), with gamma approximately equal to 2.2. Among three graph partition algorithms, the Guimera's simulated annealing method is chosen to study the details of topology structure and other properties of this cellular signaling network, as it shows the best performance. To reveal the underlying biological implications, further investigation is conducted on ad hoc community and sketch map of individual community is drawn accordingly. The involved experiment data can be found in the supplementary material.     

Analysis of feedback loops and robustness in network evolution based on Boolean models

Background  

Many biological networks such as protein-protein interaction networks, signaling networks, and metabolic networks have topological characteristics of a scale-free degree distribution. Preferential attachment has been considered as the most plausible evolutionary growth model to explain this topological property. Although various studies have been undertaken to investigate the structural characteristics of a network obtained using this growth model, its dynamical characteristics have received relatively less attention.     

Some protein interaction data do not exhibit power law statistics

It has been claimed that protein-protein interaction (PPI) networks are scale-free, and that identifying high-degree "hub" proteins reveals important features of PPI networks. In this paper, we evaluate the claims that PPI node degree sequences follow a power law, a necessary condition for networks to be scale-free. We provide two PPI network examples which clearly do not have power laws when analyzed correctly, and thus at least these PPI networks are not scale-free. We also show that these PPI networks do appear to have power laws according to methods that have become standard in the existing literature. We explain the source of this error using numerically generated data from analytic formulas, where there are no sampling or noise ambiguities.     

Application of network theory to potential mycorrhizal networks

The concept of a common mycorrhizal network implies that the arrangement of plants and mycorrhizal fungi in a community shares properties with other networks. A network is a system of nodes connected by links. Here we apply network theory to mycorrhizas to determine whether the architecture of a potential common mycorrhizal network is random or scale-free. We analyzed mycorrhizal data from an oak woodland from two perspectives: the phytocentric view using trees as nodes and fungi as links and the mycocentric view using fungi as nodes and trees as links. From the phytocentric perspective, the distribution of potential mycorrhizal links, as measured by the number of ectomycorrhizal morphotypes on trees of Quercus garryana, was random with a short tail, implying that all the individuals of this species are more or less equal in linking to fungi in a potential network. From the mycocentric perspective, however, the distribution of plant links to fungi was scale-free, suggesting that certain fungus species may act as hubs with frequent connections to the network. Parallels exist between social networks and mycorrhizas that suggest future lines of study on mycorrhizal networks.     

Asymptotic states and topological structure of an activation-deactivation chemical network

The influence of the topology on the asymptotic states of a network of interacting chemical species has been studied by simulating its time evolution. Random and scale-free networks have been designed to support relevant features of activation-deactivation reactions networks (mapping signal transduction networks) and the system of ordinary differential equations associated to the dynamics has been numerically solved. We analysed stationary states of the dynamics as a function of the network's connectivity and of the distribution of the chemical species on the network; we found important differences between the two topologies in the regime of low connectivity. In particular, only for low connected scale-free networks it is possible to find zero activity patterns as stationary states of the dynamics which work as signal off-states. Asymptotic features of random and scale-free networks become similar as the connectivity increases.     

Effect of sampling on topology predictions of protein-protein interaction networks

Currently available protein-protein interaction (PPI) network or 'interactome' maps, obtained with the yeast two-hybrid (Y2H) assay or by co-affinity purification followed by mass spectrometry (co-AP/MS), only cover a fraction of the complete PPI networks. These partial networks display scale-free topologies--most proteins participate in only a few interactions whereas a few proteins have many interaction partners. Here we analyze whether the scale-free topologies of the partial networks obtained from Y2H assays can be used to accurately infer the topology of complete interactomes. We generated four theoretical interaction networks of different topologies (random, exponential, power law, truncated normal). Partial sampling of these networks resulted in sub-networks with topological characteristics that were virtually indistinguishable from those of currently available Y2H-derived partial interactome maps. We conclude that given the current limited coverage levels, the observed scale-free topology of existing interactome maps cannot be confidently extrapolated to complete interactomes.     

What do we learn from high-throughput protein interaction data?

The biological significance of protein interactions, their method of generation and reliability is briefly reviewed. Protein interaction networks adopt a scale-free topology that explains their error tolerance or vulnerability, depending on whether hubs or peripheral proteins are attacked. Networks also allow the prediction of protein function from their interaction partners and therefore, the formulation of analytical hypotheses. Comparative network analysis predicts interactions for distantly related species based on conserved interactions, even if sequences are only weakly conserved. Finally, the medical relevance of protein interaction analysis is discussed and the necessity for data integration is emphasized.     

Protein chips for high-throughput doping screening in athletes

The biological significance of protein interactions, their method of generation and reliability is briefly reviewed. Protein interaction networks adopt a scale-free topology that explains their error tolerance or vulnerability, depending on whether hubs or peripheral proteins are attacked. Networks also allow the prediction of protein function from their interaction partners and therefore, the formulation of analytical hypotheses. Comparative network analysis predicts interactions for distantly related species based on conserved interactions, even if sequences are only weakly conserved. Finally, the medical relevance of protein interaction analysis is discussed and the necessity for data integration is emphasized.     

From large networks to small molecules

Large-scale analysis of genetic and physical interaction networks has begun to reveal the global organization of the cell. Cellular phenotypes observed at the macroscopic level depend on the collective characteristics of protein and genetic interaction networks, which exhibit scale-free properties and are highly resistant to perturbation of a single node. The nascent field of chemical genetics promises a host of small-molecule probes to explore these emerging networks. Although the robust nature of cellular networks usually resists the action of single agents, they may be susceptible to rationally designed combinations of small molecules able to collectively shift network behavior.     

Evolution of cooperation on dynamical graphs

There are two key characteristic of animal and human societies: (1) degree heterogeneity, meaning that not all individual have the same number of associates; and (2) the interaction topology is not static, i.e. either individuals interact with different set of individuals at different times of their life, or at least they have different associations than their parents. Earlier works have shown that population structure is one of the mechanisms promoting cooperation. However, most studies had assumed that the interaction network can be described by a regular graph (homogeneous degree distribution). Recently there are an increasing number of studies employing degree heterogeneous graphs to model interaction topology. But mostly the interaction topology was assumed to be static. Here we investigate the fixation probability of the cooperator strategy in the prisoner's dilemma, when interaction network is a random regular graph, a random graph or a scale-free graph and the interaction network is allowed to change.     

A thermodynamic view of networks

Networks can be described by the frequency distribution of the number of links associated with each node (the degree of the node). Of particular interest are the power law distributions, which give rise to the so-called scale-free networks, and the distributions of the form of the simplified canonical law (SCL) introduced by Mandelbrot, which give what we shall call the Mandelbrot networks. Many dynamical methods have been obtained for the construction of scale-free networks, but no dynamical construction of Mandelbrot networks has been demonstrated. Here we develop a systematic technique to obtain networks with any given distribution of the degrees of the nodes. This is done using a thermodynamic approach in which we maximise the entropy associated with degree distribution of the nodes of the network subject to certain constraints. These constraints can be chosen systematically to produce the desired network architecture. For large networks we therefore replace a dynamical approach to the stationary state by a thermodynamical viewpoint. We use the method to generate scale-free and Mandelbrot networks with arbitrarily chosen parameters. We emphasise that this approach opens the possibility of insights into a thermodynamics of networks by suggesting thermodynamic relations between macroscopic variables for networks.     

Data mining and predictive modeling of biomolecular network from biomedical literature databases

In this paper, we present a novel approach Bio-IEDM (biomedical information extraction and data mining) to integrate text mining and predictive modeling to analyze biomolecular network from biomedical literature databases. Our method consists of two phases. In phase 1, we discuss a semisupervised efficient learning approach to automatically extract biological relationships such as protein-protein interaction, protein-gene interaction from the biomedical literature databases to construct the biomolecular network. Our method automatically learns the patterns based on a few user seed tuples and then extracts new tuples from the biomedical literature based on the discovered patterns. The derived biomolecular network forms a large scale-free network graph. In phase 2, we present a novel clustering algorithm to analyze the biomolecular network graph to identify biologically meaningful subnetworks (communities). The clustering algorithm considers the characteristics of the scale-free network graphs and is based on the local density of the vertex and its neighborhood functions that can be used to find more meaningful clusters with different density level. The experimental results indicate our approach is very effective in extracting biological knowledge from a huge collection of biomedical literature. The integration of data mining and information extraction provides a promising direction for analyzing the biomolecular network     

金黄色葡萄球菌蛋白质相互作用网络及功能

【目的】金黄色葡萄球菌是一种革兰氏阳性菌,是目前最难以对付的病菌之一。它能引起多种感染,特别是在医院环境中。近年来,抗药性金黄色葡萄球菌传染更加严重,已成为公共卫生威胁。由于以前对于金黄色葡萄球菌的实验性研究大都是基于单个基因或者蛋白进行的,为了更好的研究这个物种,有必要从整体上把握金黄色葡萄球菌的蛋白作用机理。【方法】采用系统发生谱、操纵子法、基因融合法、基因邻近法、同源映射法等五种计算方法预测金黄色葡萄球菌蛋白质相互作用网络。【结果】从蛋白组的角度构建了金黄色葡萄球菌蛋白相互作用网络,并对网络进行功能分析。【结论】网络的分析表明金黄色葡萄球菌的蛋白质相互作用网络也服从scale-free属性,发现了SA0939、SA0868、rplD等重要的蛋白。通过对金黄色葡萄球菌的重要的细胞壁合成和信号转导调控蛋白局部网络分析,发现了一些对这两个系统十分重要的蛋白分子,这些信息将为更好的了解金黄色葡萄球菌的致病机理和开发新的药物靶点提供指导。