Graph Theory and Networks in Biology

In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape

Characterization of complex networks: A survey of measurements

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the proper application and interpretation of measurements.Comment: A working manuscript with 78 pages, 32 figures. Suggestions of measurements for inclusion are welcomed by the author

Mathematical model of a telomerase transcriptional regulatory network developed by cell-based screening: analysis of inhibitor effects and telomerase expression mechanisms

Cancer cells depend on transcription of telomerase reverse transcriptase (TERT). Many transcription factors affect TERT, though regulation occurs in context of a broader network. Network effects on telomerase regulation have not been investigated, though deeper understanding of TERT transcription requires a systems view. However, control over individual interactions in complex networks is not easily achievable. Mathematical modelling provides an attractive approach for analysis of complex systems and some models may prove useful in systems pharmacology approaches to drug discovery. In this report, we used transfection screening to test interactions among 14 TERT regulatory transcription factors and their respective promoters in ovarian cancer cells. The results were used to generate a network model of TERT transcription and to implement a dynamic Boolean model whose steady states were analysed. Modelled effects of signal transduction inhibitors successfully predicted TERT repression by Src-family inhibitor SU6656 and lack of repression by ERK inhibitor FR180204, results confirmed by RT-QPCR analysis of endogenous TERT expression in treated cells. Modelled effects of GSK3 inhibitor 6-bromoindirubin-3′-oxime (BIO) predicted unstable TERT repression dependent on noise and expression of JUN, corresponding with observations from a previous study. MYC expression is critical in TERT activation in the model, consistent with its well known function in endogenous TERT regulation. Loss of MYC caused complete TERT suppression in our model, substantially rescued only by co-suppression of AR. Interestingly expression was easily rescued under modelled Ets-factor gain of function, as occurs in TERT promoter mutation. RNAi targeting AR, JUN, MXD1, SP3, or TP53, showed that AR suppression does rescue endogenous TERT expression following MYC knockdown in these cells and SP3 or TP53 siRNA also cause partial recovery. The model therefore successfully predicted several aspects of TERT regulation including previously unknown mechanisms. An extrapolation suggests that a dominant stimulatory system may programme TERT for transcriptional stability

Network centrality: an introduction

Centrality is a key property of complex networks that influences the behavior of dynamical processes, like synchronization and epidemic spreading, and can bring important information about the organization of complex systems, like our brain and society. There are many metrics to quantify the node centrality in networks. Here, we review the main centrality measures and discuss their main features and limitations. The influence of network centrality on epidemic spreading and synchronization is also pointed out in this chapter. Moreover, we present the application of centrality measures to understand the function of complex systems, including biological and cortical networks. Finally, we discuss some perspectives and challenges to generalize centrality measures for multilayer and temporal networks.Comment: Book Chapter in "From nonlinear dynamics to complex systems: A Mathematical modeling approach" by Springe

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 on (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

Hierarchical characterization of complex networks

While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be obtained by considering further neighborhoods. The current work discusses on how the concepts of hierarchical node degree and hierarchical clustering coefficient (introduced in cond-mat/0408076), complemented by new hierarchical measurements, can be used in order to obtain a powerful set of topological features of complex networks. The interpretation of such measurements is discussed, including an analytical study of the hierarchical node degree for random networks, and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random, scale-free and regular network models as well as real data (airports, proteins and word associations). The enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network, a possibility which is also illustrated in the current article.Comment: 19 pages, 23 figure