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.     

Topological properties of protein-protein and metabolic interaction networks of Drosophila melanogaster

Introduction The concept of networking and its omnipresent na- ture has been an issue of considerable curiosity, cap- tivating scientists worldwide over the past few years. Simple networking can be witnessed in the physical connectivity of computer terminals or routers. On broader perspective, many networks, such as social ties—familial and professional, World Wide Web, net- work of scientific papers connected by citations, elec- trical power grids, transportation systems, and biolog- ical n…     

复杂疾病靶基因识别与网络重建的计算系统生物研究

复杂疾病相关靶基因的识别、构建疾病驱使相关基因网络及进行疾病机制研究,是功能基因组学研究中非常重要的科学问题。文章以计算系统生物学的观点和三维的角度,综述了基于生物谱（SNP遗传谱、芯片表达谱和2D-PAGE蛋白质谱等）的复杂疾病靶基因识别、多水平（SNPs虚拟网络、基因调控网络、蛋白质互作网络等）遗传网络逆向重构方法,及不同水平的网络之间在生物学和拓扑学上的纵向映射关系,并给出复杂疾病靶基因识别与网络关系的计算系统生物方法研究的未来展望。     

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.     

Inference of scale-free networks from gene expression time series

Quantitative time-series observation of gene expression is becoming possible, for example by cell array technology. However, there are no practical methods with which to infer network structures using only observed time-series data. As most computational models of biological networks for continuous time-series data have a high degree of freedom, it is almost impossible to infer the correct structures. On the other hand, it has been reported that some kinds of biological networks, such as gene networks and metabolic pathways, may have scale-free properties. We hypothesize that the architecture of inferred biological network models can be restricted to scale-free networks. We developed an inference algorithm for biological networks using only time-series data by introducing such a restriction. We adopt the S-system as the network model, and a distributed genetic algorithm to optimize models to fit its simulated results to observed time series data. We have tested our algorithm on a case study (simulated data). We compared optimization under no restriction, which allows for a fully connected network, and under the restriction that the total number of links must equal that expected from a scale free network. The restriction reduced both false positive and false negative estimation of the links and also the differences between model simulation and the given time-series data.     

基于分子生态学网络探究西藏草地放牧对土壤微生物群落的影响

【目的】揭示西藏地区放牧对在功能基因层面上的微生物相互作用的影响。【方法】利用最近发明的网络工具(基于随机矩阵理论的分子生态学网络)分别在对照和放牧条件下分析基因芯片中碳循环和氮循环基因。【结果】碳和氮循环基因网络在对照和放牧条件下都具有无标度、小世界、模块性和层次性的拓扑学特征。放牧条件下的网络关键基因(模块枢纽和连通者)与对照显著不同。放牧导致网络变得小而紧密,暗示环境压力的存在。地上植物生物量与微生物基因网络显著相关(P=0.001),证实了研究样地地上植物与地下微生物紧密相连。【结论】放牧显著改变了西藏草地在功能基因层面上的微生物相互作用关系。     

Predicting aging/longevity-related genes in the nematode Caenorhabditis elegans

We present a novel mathematical/computational strategy for predicting genes/proteins associated with aging/longevity. The novelty of our method arises from the topological analysis of an organismal longevity gene/protein network (LGPN), which extends the existing cellular networks. The LGPN nodes represent both genes and corresponding proteins. Links stand for all known interactions between the nodes. The LGPN of C. elegans incorporated 362 genes/proteins, 160 connecting and 202 age-related ones, from a list of 321 with known impact on aging/longevity. A 'longevity core' of 129 directly interacting genes or proteins was identified. This core may shed light on the large-scale mechanisms of aging. Predictions were made, based upon the finding that LGPN hubs and centrally located nodes have higher likelihoods of being associated with aging/longevity than do randomly selected nodes. Analysis singled-out 15 potential aging/longevity-related genes for further examination: mpk-1, gei-4, csp-1, pal-1, mkk-4, 4O210, sem-5, gei-16, 1O814, 5M722, ife-3, ced-10, cdc-42, 1O776Co, and 1O690.     

Particle Swarm Optimization with Scale-Free Interactions

The particle swarm optimization (PSO) algorithm, in which individuals collaborate with their interacted neighbors like bird flocking to search for the optima, has been successfully applied in a wide range of fields pertaining to searching and convergence. Here we employ the scale-free network to represent the inter-individual interactions in the population, named SF-PSO. In contrast to the traditional PSO with fully-connected topology or regular topology, the scale-free topology used in SF-PSO incorporates the diversity of individuals in searching and information dissemination ability, leading to a quite different optimization process. Systematic results with respect to several standard test functions demonstrate that SF-PSO gives rise to a better balance between the convergence speed and the optimum quality, accounting for its much better performance than that of the traditional PSO algorithms. We further explore the dynamical searching process microscopically, finding that the cooperation of hub nodes and non-hub nodes play a crucial role in optimizing the convergence process. Our work may have implications in computational intelligence and complex 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.     

Conservation and coevolution in the scale-free human gene coexpression network

The role of natural selection in biology is well appreciated. Recently, however, a critical role for physical principles of network self-organization in biological systems has been revealed. Here, we employ a systems level view of genome-scale sequence and expression data to examine the interplay between these two sources of order, natural selection and physical self-organization, in the evolution of human gene regulation. The topology of a human gene coexpression network, derived from tissue-specific expression profiles, shows scale-free properties that imply evolutionary self-organization via preferential node attachment. Genes with numerous coexpressed partners (the hubs of the coexpression network) evolve more slowly on average than genes with fewer coexpressed partners, and genes that are coexpressed show similar rates of evolution. Thus, the strength of selective constraints on gene sequences is affected by the topology of the gene coexpression network. This connection is strong for the coding regions and 3' untranslated regions (UTRs), but the 5' UTRs appear to evolve under a different regime. Surprisingly, we found no connection between the rate of gene sequence divergence and the extent of gene expression profile divergence between human and mouse. This suggests that distinct modes of natural selection might govern sequence versus expression divergence, and we propose a model, based on rapid, adaptation-driven divergence and convergent evolution of gene expression patterns, for how natural selection could influence gene expression divergence.     

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.     

Are scale-free networks robust to measurement errors?

Background  

Many complex random networks have been found to be scale-free. Existing literature on scale-free networks has rarely considered potential false positive and false negative links in the observed networks, especially in biological networks inferred from high-throughput experiments. Therefore, it is important to study the impact of these measurement errors on the topology of the observed networks.