Making the right connections: biological networks in the light of evolution

Our understanding of how evolution acts on biological networks remains patchy, as is our knowledge of how that action is best identified, modelled and understood. Starting with network structure and the evolution of protein–protein interaction networks, we briefly survey the ways in which network evolution is being addressed in the fields of systems biology, development and ecology. The approaches highlighted demonstrate a movement away from a focus on network topology towards a more integrated view, placing biological properties centre‐stage. We argue that there remains great potential in a closer synergy between evolutionary biology and biological network analysis, although that may require the development of novel approaches and even different analogies for biological networks themselves.     

Understanding biological functions through molecular networks

The completion of genome sequences and subsequent high-throughput mapping of molecular networks have allowed us to study biology from the network perspective. Experimental, statistical and mathematical modeling approaches have been employed to study the structure, function and dynamics of molecular networks, and begin to reveal important links of various network properties to the functions of the biological systems. In agreement with these functional links, evolutionary selection of a network is apparently based on the function, rather than directly on the structure of the network. Dynamic modularity is one of the prominent features of molecular networks. Taking advantage of such a feature may simplify network-based biological studies through construction of process-specific modular networks and provide functional and mechanistic insights linking genotypic variations to complex traits or diseases, which is likely to be a key approach in the next wave of understanding complex human diseases. With the development of ready-to-use network analysis and modeling tools the networks approaches will be infused into everyday biological research in the near future.     

Reliability of regulatory networks and its evolution

The problem of reliability of the dynamics in biological regulatory networks is studied in the framework of a generalized Boolean network model with continuous timing and noise. Using well-known artificial genetic networks such as the repressilator, we discuss concepts of reliability of rhythmic attractors. In a simple evolution process we investigate how overall network structure affects the reliability of the dynamics. In the course of the evolution, networks are selected for reliable dynamics. We find that most networks can be easily evolved towards reliable functioning while preserving the original function.     

Formal Methods for Hopfield-Like Networks

Building a meaningful model of biological regulatory network is usually done by specifying the components (e.g. the genes) and their interactions, by guessing the values of parameters, by comparing the predicted behaviors to the observed ones, and by modifying in a trial-error process both architecture and parameters in order to reach an optimal fitness. We propose here a different approach to construct and analyze biological models avoiding the trial-error part, where structure and dynamics are represented as formal constraints. We apply the method to Hopfield-like networks, a formalism often used in both neural and regulatory networks modeling. The aim is to characterize automatically the set of all models consistent with all the available knowledge (about structure and behavior). The available knowledge is formalized into formal constraints. The latter are compiled into Boolean formula in conjunctive normal form and then submitted to a Boolean satisfiability solver. This approach allows to formulate a wide range of queries, expressed in a high level language, and possibly integrating formalized intuitions. In order to explore its potential, we use it to find cycles for 3-nodes networks and to determine the flower morphogenesis regulatory network of Arabidopsis thaliana. Applications of this technique are numerous and concern the building of models from data as well as the design of biological networks possessing specified behaviors.     

Dynamics and Control of Diseases in Networks with Community Structure

The dynamics of infectious diseases spread via direct person-to-person transmission (such as influenza, smallpox, HIV/AIDS, etc.) depends on the underlying host contact network. Human contact networks exhibit strong community structure. Understanding how such community structure affects epidemics may provide insights for preventing the spread of disease between communities by changing the structure of the contact network through pharmaceutical or non-pharmaceutical interventions. We use empirical and simulated networks to investigate the spread of disease in networks with community structure. We find that community structure has a major impact on disease dynamics, and we show that in networks with strong community structure, immunization interventions targeted at individuals bridging communities are more effective than those simply targeting highly connected individuals. Because the structure of relevant contact networks is generally not known, and vaccine supply is often limited, there is great need for efficient vaccination algorithms that do not require full knowledge of the network. We developed an algorithm that acts only on locally available network information and is able to quickly identify targets for successful immunization intervention. The algorithm generally outperforms existing algorithms when vaccine supply is limited, particularly in networks with strong community structure. Understanding the spread of infectious diseases and designing optimal control strategies is a major goal of public health. Social networks show marked patterns of community structure, and our results, based on empirical and simulated data, demonstrate that community structure strongly affects disease dynamics. These results have implications for the design of control strategies.     

Dynamic properties of network motifs contribute to biological network organization

Biological networks, such as those describing gene regulation, signal transduction, and neural synapses, are representations of large-scale dynamic systems. Discovery of organizing principles of biological networks can be enhanced by embracing the notion that there is a deep interplay between network structure and system dynamics. Recently, many structural characteristics of these non-random networks have been identified, but dynamical implications of the features have not been explored comprehensively. We demonstrate by exhaustive computational analysis that a dynamical property—stability or robustness to small perturbations—is highly correlated with the relative abundance of small subnetworks (network motifs) in several previously determined biological networks. We propose that robust dynamical stability is an influential property that can determine the non-random structure of biological networks.     

H-CORE: enabling genome-scale Bayesian analysis of biological systems without prior knowledge

The Bayesian network is a popular tool for describing relationships between data entities by representing probabilistic (in)dependencies with a directed acyclic graph (DAG) structure. Relationships have been inferred between biological entities using the Bayesian network model with high-throughput data from biological systems in diverse fields. However, the scalability of those approaches is seriously restricted because of the huge search space for finding an optimal DAG structure in the process of Bayesian network learning. For this reason, most previous approaches limit the number of target entities or use additional knowledge to restrict the search space. In this paper, we use the hierarchical clustering and order restriction (H-CORE) method for the learning of large Bayesian networks by clustering entities and restricting edge directions between those clusters, with the aim of overcoming the scalability problem and thus making it possible to perform genome-scale Bayesian network analysis without additional biological knowledge. We use simulations to show that H-CORE is much faster than the widely used sparse candidate method, whilst being of comparable quality. We have also applied H-CORE to retrieving gene-to-gene relationships in a biological system (The 'Rosetta compendium'). By evaluating learned information through literature mining, we demonstrate that H-CORE enables the genome-scale Bayesian analysis of biological systems without any prior knowledge.     

Finding gene regulatory network candidates using the gene expression knowledge base

Background

Network-based approaches for the analysis of large-scale genomics data have become well established. Biological networks provide a knowledge scaffold against which the patterns and dynamics of ‘omics’ data can be interpreted. The background information required for the construction of such networks is often dispersed across a multitude of knowledge bases in a variety of formats. The seamless integration of this information is one of the main challenges in bioinformatics. The Semantic Web offers powerful technologies for the assembly of integrated knowledge bases that are computationally comprehensible, thereby providing a potentially powerful resource for constructing biological networks and network-based analysis.

Results

We have developed the Gene eXpression Knowledge Base (GeXKB), a semantic web technology based resource that contains integrated knowledge about gene expression regulation. To affirm the utility of GeXKB we demonstrate how this resource can be exploited for the identification of candidate regulatory network proteins. We present four use cases that were designed from a biological perspective in order to find candidate members relevant for the gastrin hormone signaling network model. We show how a combination of specific query definitions and additional selection criteria derived from gene expression data and prior knowledge concerning candidate proteins can be used to retrieve a set of proteins that constitute valid candidates for regulatory network extensions.

Conclusions

Semantic web technologies provide the means for processing and integrating various heterogeneous information sources. The GeXKB offers biologists such an integrated knowledge resource, allowing them to address complex biological questions pertaining to gene expression. This work illustrates how GeXKB can be used in combination with gene expression results and literature information to identify new potential candidates that may be considered for extending a gene regulatory network.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0386-y) contains supplementary material, which is available to authorized users.     

A declarative constraint-based method for analyzing discrete genetic regulatory networks

Dynamical modeling has proven useful for understanding how complex biological processes emerge from the many components and interactions composing genetic regulatory networks (GRNs). However, the development of models is hampered by large uncertainties in both the network structure and parameter values. To remedy this problem, the models are usually developed through an iterative process based on numerous simulations, confronting model predictions with experimental data and refining the model structure and/or parameter values to repair the inconsistencies. In this paper, we propose an alternative to this generate-and-test approach. We present a four-step method for the systematic construction and analysis of discrete models of GRNs by means of a declarative approach. Instead of instantiating the models as in classical modeling approaches, the biological knowledge on the network structure and its dynamics is formulated in the form of constraints. The compatibility of the network structure with the constraints is queried and in case of inconsistencies, some constraints are relaxed. Common properties of the consistent models are then analyzed by means of dedicated languages. Two such languages are introduced in the paper. Removing questionable constraints or adding interesting ones allows to further analyze the models. This approach allows to identify the best experiments to be carried out, in order to discriminate sets of consistent models and refine our knowledge on the system functioning. We test the feasibility of our approach, by applying it to the re-examination of a model describing the nutritional stress response in the bacterium Escherichia coli.     

Exploring biological network structure using exponential random graph models

MOTIVATION: The functioning of biological networks depends in large part on their complex underlying structure. When studying their systemic nature many modeling approaches focus on identifying simple, but prominent, structural components, as such components are easier to understand, and, once identified, can be used as building blocks to succinctly describe the network. RESULTS: In recent social network studies, exponential random graph models have been used extensively to model global social network structure as a function of their 'local features'. Starting from those studies, we describe the exponential random graph models and demonstrate their utility in modeling the architecture of biological networks as a function of the prominence of local features. We argue that the flexibility, in terms of the number of available local feature choices, and scalability, in terms of the network sizes, make this approach ideal for statistical modeling of biological networks. We illustrate the modeling on both genetic and metabolic networks and provide a novel way of classifying biological networks based on the prevalence of their local features.     

Analysis of Discrete Bioregulatory Networks Using Symbolic Steady States

A discrete model of a biological regulatory network can be represented by a discrete function that contains all available information on interactions between network components and the rules governing the evolution of the network in a finite state space. Since the state space size grows exponentially with the number of network components, analysis of large networks is a complex problem. In this paper, we introduce the notion of symbolic steady state that allows us to identify subnetworks that govern the dynamics of the original network in some region of state space. We state rules to explicitly construct attractors of the system from subnetwork attractors. Using the results, we formulate sufficient conditions for the existence of multiple attractors resp. a cyclic attractor based on the existence of positive resp. negative feedback circuits in the graph representing the structure of the system. In addition, we discuss approaches to finding symbolic steady states. We focus both on dynamics derived via synchronous as well as asynchronous update rules. Lastly, we illustrate the results by analyzing a model of T helper cell differentiation.     

The dichotomy in degree correlation of biological networks

Most complex networks from different areas such as biology, sociology or technology, show a correlation on node degree where the possibility of a link between two nodes depends on their connectivity. It is widely believed that complex networks are either disassortative (links between hubs are systematically suppressed) or assortative (links between hubs are enhanced). In this paper, we analyze a variety of biological networks and find that they generally show a dichotomous degree correlation. We find that many properties of biological networks can be explained by this dichotomy in degree correlation, including the neighborhood connectivity, the sickle-shaped clustering coefficient distribution and the modularity structure. This dichotomy distinguishes biological networks from real disassortative networks or assortative networks such as the Internet and social networks. We suggest that the modular structure of networks accounts for the dichotomy in degree correlation and vice versa, shedding light on the source of modularity in biological networks. We further show that a robust and well connected network necessitates the dichotomy of degree correlation, suggestive of an evolutionary motivation for its existence. Finally, we suggest that a dichotomous degree correlation favors a centrally connected modular network, by which the integrity of network and specificity of modules might be reconciled.     

Species traits and abundances predict metrics of plant–pollinator network structure,but not pairwise interactions

Plant–pollinator mutualistic networks represent the ecological context of foraging (for pollinators) and reproduction (for plants and some pollinators). Plant–pollinator visitation networks exhibit highly conserved structural properties across diverse habitats and species assemblages. The most successful hypotheses to explain these network properties are the neutrality and biological constraints hypotheses, which posit that species interaction frequencies can be explained by species relative abundances, and trait mismatches between potential mutualists respectively. However, previous network analyses emphasize the prediction of metrics of qualitative network structure, which may not represent stringent tests of these hypotheses. Using a newly documented temporally explicit alpine plant–pollinator visitation network, we show that metrics of both qualitative and quantitative network structure are easy to predict, even by models that predict the identity or frequency of species interactions poorly. A variety of phenological and morphological constraints as well as neutral interactions successfully predicted all network metrics tested, without accurately predicting species observed interactions. Species phenology alone was the best predictor of observed interaction frequencies. However, all models were poor predictors of species pairwise interaction frequencies, suggesting that other aspects of species biology not generally considered in network studies, such as reproduction for dipterans, play an important role in shaping plant–pollinator visitation network structure at this site. Future progress in explaining the structure and dynamics of mutualistic networks will require new approaches that emphasize accurate prediction of species pairwise interactions rather than network metrics, and better reflect the biology underlying species interactions.     

Novel insights through the integration of structural and functional genomics data with protein networks

In recent years, major advances in genomics, proteomics, macromolecular structure determination, and the computational resources capable of processing and disseminating the large volumes of data generated by each have played major roles in advancing a more systems-oriented appreciation of biological organization. One product of systems biology has been the delineation of graph models for describing genome-wide protein-protein interaction networks. The network organization and topology which emerges in such models may be used to address fundamental questions in an array of cellular processes, as well as biological features intrinsic to the constituent proteins (or "nodes") themselves. However, graph models alone constitute an abstraction which neglects the underlying biological and physical reality that the network's nodes and edges are highly heterogeneous entities. Here, we explore some of the advantages of introducing a protein structural dimension to such models, as the marriage of conventional network representations with macromolecular structural data helps to place static node and edge constructs in a biologically more meaningful context. We emphasize that 3D protein structures constitute a valuable conceptual and predictive framework by discussing examples of the insights provided, such as enabling in silico predictions of protein-protein interactions, providing rational and compelling classification schemes for network elements, as well as revealing interesting intrinsic differences between distinct node types, such as disorder and evolutionary features, which may then be rationalized in light of their respective functions within networks.     

The Evolutionary Dynamics of Protein-Protein Interaction Networks Inferred from the Reconstruction of Ancient Networks

Cellular functions are based on the complex interplay of proteins, therefore the structure and dynamics of these protein-protein interaction (PPI) networks are the key to the functional understanding of cells. In the last years, large-scale PPI networks of several model organisms were investigated. A number of theoretical models have been developed to explain both the network formation and the current structure. Favored are models based on duplication and divergence of genes, as they most closely represent the biological foundation of network evolution. However, studies are often based on simulated instead of empirical data or they cover only single organisms. Methodological improvements now allow the analysis of PPI networks of multiple organisms simultaneously as well as the direct modeling of ancestral networks. This provides the opportunity to challenge existing assumptions on network evolution. We utilized present-day PPI networks from integrated datasets of seven model organisms and developed a theoretical and bioinformatic framework for studying the evolutionary dynamics of PPI networks. A novel filtering approach using percolation analysis was developed to remove low confidence interactions based on topological constraints. We then reconstructed the ancient PPI networks of different ancestors, for which the ancestral proteomes, as well as the ancestral interactions, were inferred. Ancestral proteins were reconstructed using orthologous groups on different evolutionary levels. A stochastic approach, using the duplication-divergence model, was developed for estimating the probabilities of ancient interactions from today''s PPI networks. The growth rates for nodes, edges, sizes and modularities of the networks indicate multiplicative growth and are consistent with the results from independent static analysis. Our results support the duplication-divergence model of evolution and indicate fractality and multiplicative growth as general properties of the PPI network structure and dynamics.     

A Scalable Computational Framework for Establishing Long-Term Behavior of Stochastic Reaction Networks

Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, well-known for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a non-ergodic biological network are also discussed.     

Failure tolerance of motif structure in biological networks

Complex networks serve as generic models for many biological systems that have been shown to share a number of common structural properties such as power-law degree distribution and small-worldness. Real-world networks are composed of building blocks called motifs that are indeed specific subgraphs of (usually) small number of nodes. Network motifs are important in the functionality of complex networks, and the role of some motifs such as feed-forward loop in many biological networks has been heavily studied. On the other hand, many biological networks have shown some degrees of robustness in terms of their efficiency and connectedness against failures in their components. In this paper we investigated how random and systematic failures in the edges of biological networks influenced their motif structure. We considered two biological networks, namely, protein structure network and human brain functional network. Furthermore, we considered random failures as well as systematic failures based on different strategies for choosing candidate edges for removal. Failure in the edges tipping to high degree nodes had the most destructive role in the motif structure of the networks by decreasing their significance level, while removing edges that were connected to nodes with high values of betweenness centrality had the least effect on the significance profiles. In some cases, the latter caused increase in the significance levels of the motifs.