Growing biological networks: beyond the gene-duplication model

In this paper we propose a generalized growth model for biological interaction networks, including a set of biological features which have been inspired by a long tradition of simulations of immune system and chemical reaction networks. In our models we include characteristics such as the heterogeneity of biological nodes, the existence of natural hubs, the nodes binding by mutual affinity and the significance of type-based networks as compared with instance-based networks. Under these assumptions, we analyse the importance of the nodes concentration with respect to the selection of incoming nodes. We show that networks with fat-tailed degree distribution and highly clustered structure naturally emerge in systems possessing certain properties: new instances need to be produced through an endogenous source and this source needs to provide a positive feedback favouring nodes with high concentration to receive new connections. Furthermore, we show that understanding the concentration dynamics of each node and the consequent correlation between connectivity and concentration is a more adequate way to capture the global properties of type-based biological networks.     

An evolving model of undirected networks based on microscopic biological interaction systems

With protein or gene interaction systems as the background, this paper proposes an evolving model of biological undirected networks, which are consistent with some plausible mechanisms in biology. Through introducing a rule of preferential duplication of a node inversely proportional to the degree of existing nodes and an attribute of the age of the node (the older, the more influence), by which the probability of a node receiving re-wiring links is chosen, the model networks generated in certain parameter conditions could reproduce series of statistic topological characteristics of real biological graphs, including the scale-free feature, small world effect, hierarchical modularity, limited structural robustness, and disassortativity of degree–degree correlation.     

Designing connected nature reserve networks using a graph theory approach

Habitat fragmentation has been cited as one of the critical reasons for biodiversity loss. Establishing connected nature reserve networks is an effective way to reduce habit fragmentation. However, the resources devoted to nature reserves have always been scarce. Therefore it is important to allocate our scarce resources in an optimal way. The optimal design of a reserve network which is effective both ecologically and economically has become an important research topic in the reserve design literature. The problem of optimal selection of a subset from a larger group of potential habitat sites is solved using either heuristic or formal optimization methods. The heuristic methods, although flexible and computationally fast, can not guarantee the solution is optimal therefore may lead to scarce resources being used in an ineffective way. The formal optimization methods, on the other hand, guarantees the solution is optimal, but it has been argued that it would be difficult to model site selection process using optimization models, especially when spatial attributes of the reserve have to be taken into account. This paper presents a linear integer programming model for the design of a minimal connected reserve network using a graph theory approach. A connected tree is determined corresponding to a connected reserve. Computational performance of the model is tested using datasets randomly generated by the software GAMS. Results show that the model can solve a connected reserve design problem which includes 100 potential sites and 30 species in a reasonable period of time. As an empirical application, the model is applied to the protection of endangered and threatened bird species in the Cache River basin area in Illinois, US. Two connected reserve networks are determined for 13 bird species.     

Protein flexibility predictions using graph theory

Techniques from graph theory are applied to analyze the bond networks in proteins and identify the flexible and rigid regions. The bond network consists of distance constraints defined by the covalent and hydrogen bonds and salt bridges in the protein, identified by geometric and energetic criteria. We use an algorithm that counts the degrees of freedom within this constraint network and that identifies all the rigid and flexible substructures in the protein, including overconstrained regions (with more crosslinking bonds than are needed to rigidify the region) and underconstrained or flexible regions, in which dihedral bond rotations can occur. The number of extra constraints or remaining degrees of bond-rotational freedom within a substructure quantifies its relative rigidity/flexibility and provides a flexibility index for each bond in the structure. This novel computational procedure, first used in the analysis of glassy materials, is approximately a million times faster than molecular dynamics simulations and captures the essential conformational flexibility of the protein main and side-chains from analysis of a single, static three-dimensional structure. This approach is demonstrated by comparison with experimental measures of flexibility for three proteins in which hinge and loop motion are essential for biological function: HIV protease, adenylate kinase, and dihydrofolate reductase.     

Designing connected nature reserve networks using a graph theory approach

Habitat fragmentation has been cited as one of the critical reasons for biodiversity loss. Establishing connected nature reserve networks is an effective way to reduce habit fragmentation. However, the resources devoted to nature reserves have always been scarce. Therefore it is important to allocate our scarce resources in an optimal way. The optimal design of a reserve network which is effective both ecologically and economically has become an important research topic in the reserve design literature. The problem of optimal selection of a subset from a larger group of potential habitat sites is solved using either heuristic or formal optimization methods. The heuristic methods, although flexible and computationally fast, can not guarantee the solution is optimal therefore may lead to scarce resources being used in an ineffective way. The formal optimization methods, on the other hand, guarantees the solution is optimal, but it has been argued that it would be difficult to model site selection process using optimization models, especially when spatial attributes of the reserve have to be taken into account. This paper presents a linear integer programming model for the design of a minimal connected reserve network using a graph theory approach. A connected tree is determined corresponding to a connected reserve. Computational performance of the model is tested using datasets randomly generated by the software GAMS. Results show that the model can solve a connected reserve design problem which includes 100 potential sites and 30 species in a reasonable period of time. As an empirical application, the model is applied to the protection of endangered and threatened bird species in the Cache River basin area in Illinois, US. Two connected reserve networks are determined for 13 bird species.     

Comparing brain networks of different size and connectivity density using graph theory

Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring) non-significant (significant) connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others.     

Insights into the organization of biochemical regulatory networks using graph theory analyses

Graph theory has been a valuable mathematical modeling tool to gain insights into the topological organization of biochemical networks. There are two types of insights that may be obtained by graph theory analyses. The first provides an overview of the global organization of biochemical networks; the second uses prior knowledge to place results from multivariate experiments, such as microarray data sets, in the context of known pathways and networks to infer regulation. Using graph analyses, biochemical networks are found to be scale-free and small-world, indicating that these networks contain hubs, which are proteins that interact with many other molecules. These hubs may interact with many different types of proteins at the same time and location or at different times and locations, resulting in diverse biological responses. Groups of components in networks are organized in recurring patterns termed network motifs such as feedback and feed-forward loops. Graph analysis revealed that negative feedback loops are less common and are present mostly in proximity to the membrane, whereas positive feedback loops are highly nested in an architecture that promotes dynamical stability. Cell signaling networks have multiple pathways from some input receptors and few from others. Such topology is reminiscent of a classification system. Signaling networks display a bow-tie structure indicative of funneling information from extracellular signals and then dispatching information from a few specific central intracellular signaling nexuses. These insights show that graph theory is a valuable tool for gaining an understanding of global regulatory features of biochemical networks.     

Modeling for evolving biological networks with scale-free connectivity, hierarchical modularity, and disassortativity

We propose a growing network model that consists of two tunable mechanisms: growth by merging modules which are represented as complete graphs and a fitness-driven preferential attachment. Our model exhibits the three prominent statistical properties are widely shared in real biological networks, for example gene regulatory, protein-protein interaction, and metabolic networks. They retain three power law relationships, such as the power laws of degree distribution, clustering spectrum, and degree-degree correlation corresponding to scale-free connectivity, hierarchical modularity, and disassortativity, respectively. After making comparisons of these properties between model networks and biological networks, we confirmed that our model has inference potential for evolutionary processes of biological networks.     

Application of formal methods to biological regulatory networks: extending Thomas' asynchronous logical approach with temporal logic

Based on the discrete definition of biological regulatory networks developed by René Thomas, we provide a computer science formal approach to treat temporal properties of biological regulatory networks, expressed in computational tree logic. It is then possible to build all the models satisfying a set of given temporal properties. Our approach is illustrated with the mucus production in Pseudomonas aeruginosa. This application of formal methods from computer science to biological regulatory networks should open the way to many other fruitful applications.     

A conceptual review on systems biology in health and diseases: from biological networks to modern therapeutics

Human physiology is an ensemble of various biological processes spanning from intracellular molecular interactions to the whole body phenotypic response. Systems biology endures to decipher these multi-scale biological networks and bridge the link between genotype to phenotype. The structure and dynamic properties of these networks are responsible for controlling and deciding the phenotypic state of a cell. Several cells and various tissues coordinate together to generate an organ level response which further regulates the ultimate physiological state. The overall network embeds a hierarchical regulatory structure, which when unusually perturbed can lead to undesirable physiological state termed as disease. Here, we treat a disease diagnosis problem analogous to a fault diagnosis problem in engineering systems. Accordingly we review the application of engineering methodologies to address human diseases from systems biological perspective. The review highlights potential networks and modeling approaches used for analyzing human diseases. The application of such analysis is illustrated in the case of cancer and diabetes. We put forth a concept of cell-to-human framework comprising of five modules (data mining, networking, modeling, experimental and validation) for addressing human physiology and diseases based on a paradigm of system level analysis. The review overtly emphasizes on the importance of multi-scale biological networks and subsequent modeling and analysis for drug target identification and designing efficient therapies.     

New species in evolving networks--stochastic theory of sensitive networks and applications on the metaphorical level

In this paper we develop a theory to describe stochastic influences on the fate of new species with non-linear growth rates in evolutionary processes. We develop a theoretical framework based on notions of species, network, innovation, competition, survival and fitness. We introduce a stochastic picture describing the role of fluctuations in the survival of new species in non-linear systems. In particular we consider the fate of new species with non-linear growth. As an application of the general model framework we consider the fate of 'rare species' in early biological evolution. We show that hypercycle systems do not represent the end of the evolutionary process as they may evolve further in small niches. This has implications for different types of applications ranging from biological systems on one level to socio-technological systems on a more metaphoric level.     

Predicting biological networks from genomic data

Continuing improvements in DNA sequencing technologies are providing us with vast amounts of genomic data from an ever-widening range of organisms. The resulting challenge for bioinformatics is to interpret this deluge of data and place it back into its biological context. Biological networks provide a conceptual framework with which we can describe part of this context, namely the different interactions that occur between the molecular components of a cell. Here, we review the computational methods available to predict biological networks from genomic sequence data and discuss how they relate to high-throughput experimental methods.     

Forecasting the effect of feast and famine conditions on biological sulphate reduction in an anaerobic inverse fluidized bed reactor using artificial neural networks

The longevity and robustness of bioreactors used for wastewater treatment is determined by the activity of the microorganisms under steady and transient loading conditions. Two identical continuously operated inverse fluidized bed bioreactors (IFB), IFB R1 and IFB R2, were tested for sulphate removal under the same operating conditions for 140 d (Periods I–IV). Later, IFB R1 was used as the control reactor (Period V), while IFB R2 was operated under feast (Period V-A) and famine (Period V-B) feeding conditions for 66 d. The sulphate removal efficiency was comparable in both IFB, <20% in Period I and ∼70% during Periods II, III and IV. The robustness of the IFB was evident when the sulphate removal efficiency remained comparable during the feast Period (67 ± 15%) applied to IFB R2 compared to continuous feeding Periods (Period IV (71 ± 4%) for IFB R2 and Period V (61 ± 15%) for IFB R1). The IFB performance was modelled using a three-layered artificial neural networks (ANN) model (5-11-3) and a sensitivity analysis, the sulphate removal was found to be dependent on the COD:sulphate ratio. Besides, the robustness, resilience and adaptation time of the IFB were affected by the degree of mixing and the hydraulic retention time.     

Self-similarity analysis of eubacteria genome based on weighted graph

We introduce a weighted graph model to investigate the self-similarity characteristics of eubacteria genomes. The regular treating in similarity comparison about genome is to discover the evolution distance among different genomes. Few people focus their attention on the overall statistical characteristics of each gene compared with other genes in the same genome. In our model, each genome is attributed to a weighted graph, whose topology describes the similarity relationship among genes in the same genome. Based on the related weighted graph theory, we extract some quantified statistical variables from the topology, and give the distribution of some variables derived from the largest social structure in the topology. The 23 eubacteria recently studied by Sorimachi and Okayasu are markedly classified into two different groups by their double logarithmic point-plots describing the similarity relationship among genes of the largest social structure in genome. The results show that the proposed model may provide us with some new sights to understand the structures and evolution patterns determined from the complete genomes.     

Geometric robustness theory and biological networks

We provide a geometric framework for investigating the robustness of information flows over biological networks. We use information measures to quantify the impact of knockout perturbations on simple networks. Robustness has two components, a measure of the causal contribution of a node or nodes, and a measure of the change or exclusion dependence, of the network following node removal. Causality is measured as statistical contribution of a node to network function, wheras exclusion dependence measures a distance between unperturbed network and reconfigured network function. We explore the role that redundancy plays in increasing robustness, and how redundacy can be exploited through error-correcting codes implemented by networks. We provide examples of the robustness measure when applied to familiar boolean functions such as the AND, OR and XOR functions. We discuss the relationship between robustness measures and related measures of complexity and how robustness always implies a minimal level of complexity.     

Petri net modelling of biological networks

Mathematical modelling is increasingly used to get insights into the functioning of complex biological networks. In this context, Petri nets (PNs) have recently emerged as a promising tool among the various methods employed for the modelling and analysis of molecular networks. PNs come with a series of extensions, which allow different abstraction levels, from purely qualitative to more complex quantitative models. Noteworthily, each of these models preserves the underlying graph, which depicts the interactions between the biological components. This article intends to present the basics of the approach and to foster the potential role PNs could play in the development of the computational systems biology.     

Molecular analysis of genes encoding phenazine biosynthesis in the biological control bacterium Pseudomonas aureofaciens 30–84

Abstract The DNA sequence of five contiguous open reading frames encoding enzymes for phenazine biosynthesis in the biological control bacterium Pseudomonas aureofaciens 30–84 was determined. These open reading frames were named phzF, phzA, phzB, phzC and phzD . Protein PhzF is similar to 3-deoxy-D-arabino-heptulosonate-7-phosphate synthases of solanaceous plants. PhzA is similar to 2,3-dihydro-2,3-dihydroxybenzoate synthase (EntB) of Escherichia coli . PhzB shares similarity with both subunits of anthranilate synthase and the phzB open reading frame complemented an E. coli trpE mutant deficient in anthranilate synthase activity. Although phzC shares little similarity to known genes, its product is responsible for the conversion of phenazine-1-carboxylic acid to 2-hydroxy-phenazine-1-carboxylic acid. PhzD is similar to pyridoxamine phosphate oxidases. These results indicate that phenazine biosynthesis in P. aureofaciens shares similarities with the shikimic acid, enterochelin, and tryptophan biosynthetic pathways.