Class Of Biological Networks Research Articles

Michaelis–Menten networks are structurally stable

We consider a class of biological networks where the nodes are associated with first-order linear dynamics and their interactions, which can be either activating or inhibitory, are modelled by nonlinear Michaelis–Menten functions (i.e., Hill functions with unitary Hill coefficient), possibly in the presence of external constant inputs. We show that all the systems belonging to this class admit at most one strictly positive equilibrium, which is stable; this property is structural, i.e., it holds for any possible choice of the parameter values, and topology-independent, i.e., it holds for any possible topology of the interaction network. When the network is strongly connected, the strictly positive equilibrium is the only equilibrium of the system if and only if the network includes either at least one inhibiting function, or a strictly positive external input (otherwise, the zero vector is an equilibrium). The proposed stability results hold also for more general classes of interaction functions, and even in the presence of arbitrary delays in the interactions.

Searching and inferring colorful topological motifs in vertex-colored graphs

The analysis of biological networks allows the understanding of many biological processes, including the structure, function, interaction and evolutionary relationships of their components. One of the most important concepts in biological network analysis is that of network motifs, which are patterns of interconnections that occur in a given network at a frequency higher than expected in a random network. In this work we are interested in searching and inferring network motifs in a class of biological networks that can be represented by vertex-colored graphs. We show the computational complexity for many problems related to colorful topological motifs and present efficient algorithms for special cases. A colorful motif can be represented by a graph in which each vertex has a different color. We also present a probabilistic strategy to detect highly frequent motifs in vertex-colored graphs. Experiments on real data sets show that our algorithms are very competitive both in efficiency and in quality of the solutions.

EndNote: Feature-based classification of networks.

Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural features. These features tend to be shared by networks belonging to the same broad class, such as the class of social networks or the class of biological networks. Within each such class, networks describing similar systems tend to have similar features. This occurs presumably because networks representing similar systems would be expected to be generated by a shared set of domain specific mechanisms, and it should therefore be possible to classify networks based on their features at various structural levels. Here we describe and demonstrate a new hybrid approach that combines manual selection of network features of potential interest with existing automated classification methods. In particular, selecting well-known network features that have been studied extensively in social network analysis and network science literature, and then classifying networks on the basis of these features using methods such as random forest, which is known to handle the type of feature collinearity that arises in this setting, we find that our approach is able to achieve both higher accuracy and greater interpretability in shorter computation time than other methods.

Information theoretic approaches for inference of biological networks from continuous-valued data.

BackgroundCharacterising programs of gene regulation by studying individual protein-DNA and protein-protein interactions would require a large volume of high-resolution proteomics data, and such data are not yet available. Instead, many gene regulatory network (GRN) techniques have been developed, which leverage the wealth of transcriptomic data generated by recent consortia to study indirect, gene-level relationships between transcriptional regulators. Despite the popularity of such methods, previous methods of GRN inference exhibit limitations that we highlight and address through the lens of information theory.ResultsWe introduce new model-free and non-linear information theoretic measures for the inference of GRNs and other biological networks from continuous-valued data. Although previous tools have implemented mutual information as a means of inferring pairwise associations, they either introduce statistical bias through discretisation or are limited to modelling undirected relationships. Our approach overcomes both of these limitations, as demonstrated by a substantial improvement in empirical performance for a set of 160 GRNs of varying size and topology.ConclusionsThe information theoretic measures described in this study yield substantial improvements over previous approaches (e.g. ARACNE) and have been implemented in the latest release of NAIL (Network Analysis and Inference Library). However, despite the theoretical and empirical advantages of these new measures, they do not circumvent the fundamental limitation of indeterminacy exhibited across this class of biological networks. These methods have presently found value in computational neurobiology, and will likely gain traction for GRN analysis as the volume and quality of temporal transcriptomics data continues to improve.

Mining Functional Modules in Heterogeneous Biological Networks Using Multiplex PageRank Approach.

Identification of functional modules/sub-networks in large-scale biological networks is one of the important research challenges in current bioinformatics and systems biology. Approaches have been developed to identify functional modules in single-class biological networks; however, methods for systematically and interactively mining multiple classes of heterogeneous biological networks are lacking. In this paper, we present a novel algorithm (called mPageRank) that utilizes the Multiplex PageRank approach to mine functional modules from two classes of biological networks. We demonstrate the capabilities of our approach by successfully mining functional biological modules through integrating expression-based gene-gene association networks and protein-protein interaction networks. We first compared the performance of our method with that of other methods using simulated data. We then applied our method to identify the cell division cycle related functional module and plant signaling defense-related functional module in the model plant Arabidopsis thaliana. Our results demonstrated that the mPageRank method is effective for mining sub-networks in both expression-based gene-gene association networks and protein-protein interaction networks, and has the potential to be adapted for the discovery of functional modules/sub-networks in other heterogeneous biological networks. The mPageRank executable program, source code, the datasets and results of the presented two case studies are publicly and freely available at http://plantgrn.noble.org/MPageRank/.

Directionality Theory and the Entropic Principle of Natural Selection

Darwinian fitness describes the capacity of an organism to appropriate resources from the environment and to convert these resources into net-offspring production. Studies of competition between related types indicate that fitness is analytically described by entropy, a statistical measure which is positively correlated with population stability, and describes the number of accessible pathways of energy flow between the individuals in the population. Directionality theory is a mathematical model of the evolutionary process based on the concept evolutionary entropy as the measure of fitness. The theory predicts that the changes which occur as a population evolves from one non-equilibrium steady state to another are described by the following directionality principle–fundamental theorem of evolution: (a) an increase in evolutionary entropy when resource composition is diverse, and resource abundance constant; (b) a decrease in evolutionary entropy when resource composition is singular, and resource abundance variable. Evolutionary entropy characterizes the dynamics of energy flow between the individual elements in various classes of biological networks: (a) where the units are individuals parameterized by age, and their age-specific fecundity and mortality; where the units are metabolites, and the transitions are the biochemical reactions that convert substrates to products; (c) where the units are social groups, and the forces are the cooperative and competitive interactions between the individual groups. % This article reviews the analytical basis of the evolutionary entropic principle, and describes applications of directionality theory to the study of evolutionary dynamics in two biological systems; (i) social networks–the evolution of cooperation; (ii) metabolic networks–the evolution of body size. Statistical thermodynamics is a mathematical model of macroscopic behavior in inanimate matter based on entropy, a statistical measure which describes the number of ways the molecules that compose the a material aggregate can be arranged to attain the same total energy. This theory predicts an increase in thermodynamic entropy as the system evolves towards its equilibrium state. We will delineate the relation between directionality theory and statistical thermodynamics, and review the claim that the entropic principle for thermodynamic systems is the limit, as the resource production rate tends to zero, and population size tends to infinity, of the entropic principle for evolutionary systems.

Discriminating Different Classes of Biological Networks by Analyzing the Graphs Spectra Distribution

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e.g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a “fingerprint”. Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the “uncertainty” of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them to (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed.

Natural selection governs local, but not global, evolutionary gene coexpression networks in Caenorhabditis elegans

BackgroundLarge-scale evaluation of gene expression variation among Caenorhabditis elegans lines that have diverged from a common ancestor allows for the analysis of a novel class of biological networks – evolutionary gene coexpression networks. Comparative analysis of these evolutionary networks has the potential to uncover the effects of natural selection in shaping coexpression network topologies since C. elegans mutation accumulation (MA) lines evolve essentially free from the effects of natural selection, whereas natural isolate (NI) populations are subject to selective constraints.ResultsWe compared evolutionary gene coexpression networks for C. elegans MA lines versus NI populations to evaluate the role that natural selection plays in shaping the evolution of network topologies. MA and NI evolutionary gene coexpression networks were found to have very similar global topological properties as measured by a number of network topological parameters. Observed MA and NI networks show node degree distributions and average values for node degree, clustering coefficient, path length, eccentricity and betweeness that are statistically indistinguishable from one another yet highly distinct from randomly simulated networks. On the other hand, at the local level the MA and NI coexpression networks are highly divergent; pairs of genes coexpressed in the MA versus NI lines are almost entirely different as are the connectivity and clustering properties of individual genes.ConclusionIt appears that selective forces shape how local patterns of coexpression change over time but do not control the global topology of C. elegans evolutionary gene coexpression networks. These results have implications for the evolutionary significance of global network topologies, which are known to be conserved across disparate complex systems.