Duplication models for biological networks.

Are biological networks different from other large complex networks? Both large biological and nonbiological networks exhibit power-law graphs (number of nodes with degree k, N(k) approximately k(-beta)), yet the exponents, beta, fall into different ranges. This may be because duplication of the information in the genome is a dominant evolutionary force in shaping biological networks (like gene regulatory networks and protein-protein interaction networks) and is fundamentally different from the mechanisms thought to dominate the growth of most nonbiological networks (such as the Internet). The preferential choice models used for nonbiological networks like web graphs can only produce power-law graphs with exponents greater than 2. We use combinatorial probabilistic methods to examine the evolution of graphs by node duplication processes and derive exact analytical relationships between the exponent of the power law and the parameters of the model. Both full duplication of nodes (with all their connections) as well as partial duplication (with only some connections) are analyzed. We demonstrate that partial duplication can produce power-law graphs with exponents less than 2, consistent with current data on biological networks. The power-law exponent for large graphs depends only on the growth process, not on the starting graph.     

Supervised inference of gene-regulatory networks

Background  

Inference of protein interaction networks from various sources of data has become an important topic of both systems and computational biology. Here we present a supervised approach to identification of gene expression regulatory networks.     

A biological approach to computational models of proteomic networks

Computational modeling is useful as a means to assemble and test what we know about proteins and networks. Models can help address key questions about the measurement, definition and function of proteomic networks. Here, we place these biological questions at the forefront in reviewing the computational strategies that are available to analyze proteomic networks. Recent examples illustrate how models can extract more information from proteomic data, test possible interactions between network proteins and link networks to cellular behavior. No single model can achieve all these goals, however, which is why it is critical to prioritize biological questions before specifying a particular modeling approach.     

Evolution of biological interaction networks: from models to real data

We are beginning to uncover common mechanisms leading to the evolution of biological networks. The driving force behind these advances is the increasing availability of comparative data in several species.     

Dominating biological networks

Proteins are essential macromolecules of life that carry out most cellular processes. Since proteins aggregate to perform function, and since protein-protein interaction (PPI) networks model these aggregations, one would expect to uncover new biology from PPI network topology. Hence, using PPI networks to predict protein function and role of protein pathways in disease has received attention. A debate remains open about whether network properties of "biologically central (BC)" genes (i.e., their protein products), such as those involved in aging, cancer, infectious diseases, or signaling and drug-targeted pathways, exhibit some topological centrality compared to the rest of the proteins in the human PPI network.To help resolve this debate, we design new network-based approaches and apply them to get new insight into biological function and disease. We hypothesize that BC genes have a topologically central (TC) role in the human PPI network. We propose two different concepts of topological centrality. We design a new centrality measure to capture complex wirings of proteins in the network that identifies as TC those proteins that reside in dense extended network neighborhoods. Also, we use the notion of domination and find dominating sets (DSs) in the PPI network, i.e., sets of proteins such that every protein is either in the DS or is a neighbor of the DS. Clearly, a DS has a TC role, as it enables efficient communication between different network parts. We find statistically significant enrichment in BC genes of TC nodes and outperform the existing methods indicating that genes involved in key biological processes occupy topologically complex and dense regions of the network and correspond to its "spine" that connects all other network parts and can thus pass cellular signals efficiently throughout the network. To our knowledge, this is the first study that explores domination in the context of PPI networks.     

Elementary network reconstruction: A framework for the analysis of regulatory networks in biological systems

Complexity of regulatory networks arises from the high degree of interaction between network components such as DNA, RNA, proteins, and metabolites. We have developed a modeling tool, elementary network reconstruction (ENR), to characterize these networks. ENR is a knowledge-driven, steady state, deterministic, quantitative modeling approach based on linear perturbation theory. In ENR we demonstrate a novel means of expressing control mechanisms by way of dimensionless steady state gains relating input and output variables, which are purely in terms of species abundances (extensive variables). As a result of systematic enumeration of network species in n×n matrix, the two properties of linear perturbation are manifested in graphical representations: transitive property is evident in a special L-shape structure, and additive property is evident in multiple L-shape structures arriving at the same matrix cell. Upon imposing mechanistic (lowest-level) gains, network self-assembly through transitive and additive properties results in elucidation of inherent topology and explicit cataloging of higher level gains, which in turn can be used to predict perturbation results. Application of ENR to the regulatory network behind carbon catabolite repression in Escherichia coli is presented. Through incorporation of known molecular mechanisms governing transient and permanent repressions, the ENR model correctly predicts several key features of this regulatory network, including a 50% downshift in intracellular cAMP level upon exposure to glucose. Since functional genomics studies are mainly concerned with redistribution of species abundances in perturbed systems, ENR could be exploited in the system-level analysis of biological systems.     

Analyzing large biological datasets with association networks

Due to advances in high-throughput biotechnologies biological information is being collected in databases at an amazing rate, requiring novel computational approaches that process collected data into new knowledge in a timely manner. In this study, we propose a computational framework for discovering modular structure, relationships and regularities in complex data. The framework utilizes a semantic-preserving vocabulary to convert records of biological annotations of an object, such as an organism, gene, chemical or sequence, into networks (Anets) of the associated annotations. An association between a pair of annotations in an Anet is determined by the similarity of their co-occurrence pattern with all other annotations in the data. This feature captures associations between annotations that do not necessarily co-occur with each other and facilitates discovery of the most significant relationships in the collected data through clustering and visualization of the Anet. To demonstrate this approach, we applied the framework to the analysis of metadata from the Genomes OnLine Database and produced a biological map of sequenced prokaryotic organisms with three major clusters of metadata that represent pathogens, environmental isolates and plant symbionts.     

Extracting protein regulatory networks with graphical models

During the last decade the development of high-throughput biotechnologies has resulted in the production of exponentially expanding quantities of biological data, such as genomic and proteomic expression data. One fundamental problem in systems biology is to learn the architecture of biochemical pathways and regulatory networks in an inferential way from such postgenomic data. Along with the increasing amount of available data, a lot of novel statistical methods have been developed and proposed in the literature. This article gives a non-mathematical overview of three widely used reverse engineering methods, namely relevance networks, graphical Gaussian models, and Bayesian networks, whereby the focus is on their relative merits and shortcomings. In addition the reverse engineering results of these graphical methods on cytometric protein data from the RAF-signalling network are cross-compared via AUROC scatter plots.     

Scale-freeness and biological networks

The notion of scale-freeness and its prevalence in both natural and artificial networks have recently attracted much attention. The concept of scale-freeness is enthusiastically applied to almost any conceivable network, usually with affirmative conclusions. Well-known scale-free examples include the internet, electric lines among power plants, the co-starring of movie actors, the co-authorship of researchers, food webs, and neural, protein-protein interactional, genetic, and metabolic networks. The purpose of this review is to clarify the relationship between scale-freeness and power-law distribution, and to assess critically the previous related works, especially on biological networks. In addition, I will focus on the close relationship between power-law distribution and lognormal distribution to show that power-law distribution is not a special characteristic of natural selection.     

Exploring biological network structure with clustered random networks

Background  

Complex biological systems are often modeled as networks of interacting units. Networks of biochemical interactions among proteins, epidemiological contacts among hosts, and trophic interactions in ecosystems, to name a few, have provided useful insights into the dynamical processes that shape and traverse these systems. The degrees of nodes (numbers of interactions) and the extent of clustering (the tendency for a set of three nodes to be interconnected) are two of many well-studied network properties that can fundamentally shape a system. Disentangling the interdependent effects of the various network properties, however, can be difficult. Simple network models can help us quantify the structure of empirical networked systems and understand the impact of various topological properties on dynamics.     

microRNA调控的生物网络

生物网络是生物体内各种分子通过相互作用来完成各种复杂的生物功能的一个体系。网络水平的研究,有助于我们从整体上理解生物体内各种复杂事件发生的内在机制。microRNA（miRNA）是一类在转录后水平调控基因表达的小RNA分子。研究结果表明,miRNA调控的靶基因分布范围很广,因此必然与目前所研究的生物网络有着各种各样的联系。对这种关系的揭示,将对阐明miRNA的调控规律起到重要的作用。本文重点讨论了miRNA调控的基因调控网络、蛋白质相互作用网络以及细胞信号传导网络的特征。此外,还总结了miRNA调控的网络模体（motif）和miRNA协同作用网络的特征。     

Assessing the reconstruction of macromolecular assemblies with toleranced models

We introduce toleranced models (TOMs), a generic and versatile framework meant to handle models of macromolecular assemblies featuring uncertainties on the shapes and the positions of proteins. A TOM being a continuum of nested shapes, the inner (resp. outer) ones representing high (low) confidence regions, we present topological and geometric statistics assessing features of this continuum at multiple scales. While the topological statistics qualify contacts between instances of protein types and complexes involving prescribed protein types, the geometric statistics scale the geometric accuracy of these complexes. We validate the TOM framework on recent average models of the entire nuclear pore complex (NPC) obtained from reconstruction by data integration, and confront our quantitative analysis against experimental findings related to complexes of the NPC, namely the Y-complex, the T-complex, and the Nsp1-Nup82-Nup159 complex. In the three cases, our analysis bridges the gap between global qualitative models of the entire NPC, and atomic resolution models or putative models of the aforementioned complexes. In a broader perspective, the quantitative assessments provided by the TOM framework should prove instrumental to implement a virtuous loop "model reconstruction-model selection", in the context of reconstruction by data integration.     

Calibration of dynamic models of biological systems with KInfer

Methods for parameter estimation that are robust to experimental uncertainties and to stochastic and biological noise and that require a minimum of a priori input knowledge are of key importance in computational systems biology. The new method presented in this paper aims to ensure an inference model that deduces the rate constants of a system of biochemical reactions from experimentally measured time courses of reactants. This new method was applied to some challenging parameter estimation problems of nonlinear dynamic biological systems and was tested both on synthetic and real data. The synthetic case studies are the 12-state model of the SERCA pump and a model of a genetic network containing feedback loops of interaction between regulator and effector genes. The real case studies consist of a model of the reaction between the inhibitor κB kinase enzyme and its substrate in the signal transduction pathway of NF-κB, and a stiff model of the fermentation pathway of Lactococcus lactis.     

DREAM4: Combining genetic and dynamic information to identify biological networks and dynamical models

Background

Current technologies have lead to the availability of multiple genomic data types in sufficient quantity and quality to serve as a basis for automatic global network inference. Accordingly, there are currently a large variety of network inference methods that learn regulatory networks to varying degrees of detail. These methods have different strengths and weaknesses and thus can be complementary. However, combining different methods in a mutually reinforcing manner remains a challenge.

Methodology

We investigate how three scalable methods can be combined into a useful network inference pipeline. The first is a novel t-test–based method that relies on a comprehensive steady-state knock-out dataset to rank regulatory interactions. The remaining two are previously published mutual information and ordinary differential equation based methods (tlCLR and Inferelator 1.0, respectively) that use both time-series and steady-state data to rank regulatory interactions; the latter has the added advantage of also inferring dynamic models of gene regulation which can be used to predict the system''s response to new perturbations.

Conclusion/Significance

Our t-test based method proved powerful at ranking regulatory interactions, tying for first out of methods in the DREAM4 100-gene in-silico network inference challenge. We demonstrate complementarity between this method and the two methods that take advantage of time-series data by combining the three into a pipeline whose ability to rank regulatory interactions is markedly improved compared to either method alone. Moreover, the pipeline is able to accurately predict the response of the system to new conditions (in this case new double knock-out genetic perturbations). Our evaluation of the performance of multiple methods for network inference suggests avenues for future methods development and provides simple considerations for genomic experimental design. Our code is publicly available at http://err.bio.nyu.edu/inferelator/.     

Optimal, efficient reconstruction of phylogenetic networks with constrained recombination

A phylogenetic network is a generalization of a phylogenetic tree, allowing structural properties that are not tree-like. In a seminal paper, Wang et al.(1) studied the problem of constructing a phylogenetic network, allowing recombination between sequences, with the constraint that the resulting cycles must be disjoint. We call such a phylogenetic network a "galled-tree". They gave a polynomial-time algorithm that was intended to determine whether or not a set of sequences could be generated on galled-tree. Unfortunately, the algorithm by Wang et al.(1) is incomplete and does not constitute a necessary test for the existence of a galled-tree for the data. In this paper, we completely solve the problem. Moreover, we prove that if there is a galled-tree, then the one produced by our algorithm minimizes the number of recombinations over all phylogenetic networks for the data, even allowing multiple-crossover recombinations. We also prove that when there is a galled-tree for the data, the galled-tree minimizing the number of recombinations is "essentially unique". We also note two additional results: first, any set of sequences that can be derived on a galled tree can be derived on a true tree (without recombination cycles), where at most one back mutation per site is allowed; second, the site compatibility problem (which is NP-hard in general) can be solved in polynomial time for any set of sequences that can be derived on a galled tree. Perhaps more important than the specific results about galled-trees, we introduce an approach that can be used to study recombination in general phylogenetic networks. This paper greatly extends the conference version that appears in an earlier work.(8) PowerPoint slides of the conference talk can be found at our website.(7).