Directed graph theory for the analysis of biological regulatory networks

The discrete modeling formalism of René Thomas is a well known approach for the modeling and analysis of Biological Regulatory Networks (BRNs). This formalism uses a set of parameters which reflect the dynamics of the BRN under study. These parameters are initially unknown but may be deduced from the appropriately chosen observed dynamics of a BRN. The discrete model can be further enriched by using the model checking tool HyTech along with delay parameters. This paves the way to accurately analyse a BRN and to make predictions about critical trajectories which lead to a normal or diseased response. In this paper, we apply the formal discrete and hybrid (discrete and continuous) modeling approaches to characterize behavior of the BRN associated with MyD88-adapter-like (MAL) – a key protein involved with innate immune response to infections. In order to demonstrate the practical effectiveness of our current work, different trajectories and corresponding conditions that may lead to the development of cerebral malaria (CM) are identified. Our results suggest that the system converges towards hyperinflammation if Bruton's tyrosine kinase (BTK) remains constitutively active along with pre-existing high cytokine levels which may play an important role in CM pathogenesis.

Applying differential dynamic logic to reconfigurable biological networks

The analysis of biological regulatory network leads to compute the set of the possible behaviors of the biological components. These behaviors are seen as trajectories, some of which are cyclic, and we are specifically interested in these cycles since they stand for stability. The set of cycles is given by the so-called invariance kernel of a biological regulatory network. This article presents a method for deriving symbolic formulae for the length, volume and diameter of a cylindrical invariance kernel. These formulae are expressed in terms of delay parameters expressions and give the existence of an invariance kernel and a hint of the number of cyclic trajectories. We use PolyLib library for the operations on the polyhedra. The method is explained by using the example of the bacterium Pseudomonas aeruginosa.

In the last two decades, formal verification has emerged as an important technique for the formal modeling and analysis of real time reactive and unpredictable systems. The main advantage of model checking over simulation based analysis is its inherent soundness and reliability of computed results. In this paper, we propose to use explicit state model checker (SPIN) for formal modeling and Linear Temporal Logic(LTL) for the exploration of the complex dynamics (cycles) of biological regulatory networks (BRNs). The main contribution of this paper also includes the generalized framework for modeling BRNs based on well known Kinetic Logic of Ren´e Thomas and state-of-the-art SPIN model checker. To demonstrate the usefulness of current work, we utilized it for the analysis of mucus production system in Pseudomonas aeruginosa and BRN involving Indoleamine 2, 3-dioxygenase (IDO).

The analysis of Biological Regulatory Network (BRN) leads to the computing of the set of the possible behaviours of the biological components. These behaviours are seen as trajectories and we are specifically interested in cyclic trajectories since they stand for stability. The set of cycles is given by the so-called invariance kernel of a BRN. This paper presents a method for deriving symbolic formulae for the length, volume and diameter of a cylindrical invariance kernel. These formulae are expressed in terms of delay parameters expressions and give the existence of an invariance kernel and a hint of the number of cyclic trajectories.

A defining feature of many large empirical networks is their intrinsic complexity. However, many networks also contain a large degree of structural repetition. An immediate question then arises: can we characterize essential network complexity while excluding structural redundancy? In this article we utilize inherent network symmetry to collapse all redundant information from a network, resulting in a coarse graining which we show to carry the essential structural information of the "parent" network. In the context of algebraic combinatorics, this coarse-graining is known as the "quotient." We systematically explore the theoretical properties of network quotients and summarize key statistics of a variety of "real-world" quotients with respect to those of their parent networks. In particular, we find that quotients can be substantially smaller than their parent networks yet typically preserve various key functional properties such as complexity (heterogeneity and hub vertices) and communication (diameter and mean geodesic distance), suggesting that quotients constitute the essential structural skeletons of their parent networks. We summarize with a discussion of potential uses of quotients in analysis of biological regulatory networks and ways in which using quotients can reduce the computational complexity of network algorithms.

Symbolic dynamics offers a powerful technique to relate the structure and dynamics of complex networks. We contrast the predictions of two methods of symbolic dynamics for the analysis of monotonic networks suggested by models of genetic control systems.

Technological advances in sequencing and computation have allowed deep exploration of the molecular basis of diseases. Biological networks have proven to be a valuable framework for analyzing omics data and modeling regulatory interactions between genes and proteins. Large collaborative projects, such as The Cancer Genome Atlas (TCGA), have provided a rich resource for building and validating new computational methods, resulting in a plethora of open-source software for downloading, pre-processing, and analyzing those data. However, for an end-to-end analysis of regulatory networks, a coherent and reusable workflow is essential to integrate all relevant packages into a robust pipeline. We developed tcga-data-nf, a Nextflow workflow that allows users to reproducibly infer regulatory networks from the thousands of samples in TCGA using a single command. The workflow can be divided into three main steps: multi-omic data, such as RNA-seq and methylation, are (i) downloaded, (ii) pre-processed, and (iii) analyzed to infer regulatory network models with the Network Zoo. The workflow is powered by the NetworkDataCompanion R package, a standalone collection of functions for managing, mapping, and filtering TCGA data. Here, we demonstrate how the pipeline can be used to investigate the differences between colon cancer subtypes attributed to epigenetic mechanisms. Lastly, we provide a database of pre-generated networks for the 10 most common cancer types that can be readily accessed by the public. tcga-data-nf is a complete, yet flexible and extensible, framework that enables the reproducible inference and analysis of cancer regulatory networks, bridging a gap in the current universe of software tools for analyzing TCGA data.

Attaining a detailed understanding of the various biological networks in an organism lies at the core of the emerging discipline of systems biology. A precise description of the relationships formed between genes, mRNA molecules, and proteins is a necessary step toward a complete description of the dynamic behavior of an organism at the cellular level, and toward intelligent, efficient, and directed modification of an organism. The importance of understanding such regulatory, signaling, and interaction networks has fueled the development of numerous in silico inference algorithms, as well as new experimental techniques and a growing collection of public databases. The Software Environment for BIological Network Inference (SEBINI) has been created to provide an interactive environment for the deployment, evaluation, and improvement of algorithms used to reconstruct the structure of biological regulatory and interaction networks. SEBINI can be used to analyze high-throughput gene expression, protein abundance, or protein activation data via a suite of state-of-the-art network inference algorithms. It also allows algorithm developers to compare and train network inference methods on artificial networks and simulated gene expression perturbation data. SEBINI can therefore be used by software developers wishing to evaluate, refine, or combine inference techniques, as well as by bioinformaticians analyzing experimental data. Networks inferred from the SEBINI software platform can be further analyzed using the Collective Analysis of Biological Interaction Networks (CABIN) tool, which is an exploratory data analysis software that enables integration and analysis of protein-protein interaction and gene-to-gene regulatory evidence obtained from multiple sources. The collection of edges in a public database, along with the confidence held in each edge (if available), can be fed into CABIN as one "evidence network," using the Cytoscape SIF file format. Using CABIN, one may increase the confidence in individual edges in a network inferred by an algorithm in SEBINI, as well as extend such a network by combining it with species-specific or generic information, e.g., known protein-protein interactions or target genes identified for known transcription factors. Thus, the combined SEBINI-CABIN toolkit aids in the more accurate reconstruction of biological networks, with less effort, in less time.A demonstration web site for SEBINI can be accessed from https://www.emsl.pnl.gov/SEBINI/RootServlet . Source code and PostgreSQL database schema are available under open source license. ronald.taylor@pnl.gov. For commercial use, some algorithms included in SEBINI require licensing from the original developers. CABIN can be downloaded from http://www.sysbio.org/dataresources/cabin.stm . mudita.singhal@pnl.gov.

Together with computational analysis and modeling, the development of whole-genome measurement technologies holds the potential to fundamentally change research on complex disorders such as coronary artery disease. With these tools, the stage has been set to reveal the full repertoire of biological components (genes, proteins, and metabolites) in complex diseases and their interplay in modules and networks. Here we review how network identification based on reverse engineering, as applied to whole-genome datasets from simpler organisms, is now being adapted to more complex settings such as datasets from human cell lines and organs in relation to physiological and pathological states. Our focus is on the use of a systems biological approach to identify gene networks in coronary atherosclerosis. We also address how gene networks will probably play a key role in the development of early diagnostics and treatments for complex disorders in the coming era of individualized medicine.

The dynamical analysis of large biological regulatory networks requires the development of scalable methods for mathematical modeling. Following the approach initially introduced by Thomas, we formalize the interactions between the components of a network in terms of discrete variables, functions, and parameters. Model simulations result in directed graphs, called state transition graphs. We are particularly interested in reachability properties and asymptotic behaviors, which correspond to terminal strongly connected components (or "attractors") in the state transition graph. A well-known problem is the exponential increase of the size of state transition graphs with the number of network components, in particular when using the biologically realistic asynchronous updating assumption. To address this problem, we have developed several complementary methods enabling the analysis of the behavior of large and complex logical models: (i) the definition of transition priority classes to simplify the dynamics; (ii) a model reduction method preserving essential dynamical properties, (iii) a novel algorithm to compact state transition graphs and directly generate compressed representations, emphasizing relevant transient and asymptotic dynamical properties. The power of an approach combining these different methods is demonstrated by applying them to a recent multilevel logical model for the network controlling CD4+ T helper cell response to antigen presentation and to a dozen cytokines. This model accounts for the differentiation of canonical Th1 and Th2 lymphocytes, as well as of inflammatory Th17 and regulatory T cells, along with many hybrid subtypes. All these methods have been implemented into the software GINsim, which enables the definition, the analysis, and the simulation of logical regulatory graphs.

Networks of interacting cellular components carry out the essential functions in living cells. Therefore, understanding the evolution and design principles of such complex networks is a central issue of systems biology. In recent years, structural analysis methods based on graph theory have revealed several intriguing features of such networks. In this chapter, we describe some of these structural analysis methods and show their application in analysis of biological networks, specifically metabolic and transcriptional regulatory networks (TRNs). We first explain the methods used for reconstruction of biological networks, and then compare the pros and cons of the different methods. It will be shown how graph theory-based methods can help to find the organization principle(s) of the networks, such as the power law degree distribution, the bow-tie connectivity structure, etc. Furthermore, we present an integrated network that includes the metabolite-protein (transcription factor) interaction to link the regulatory network with the metabolic network. This integrated network can provide more insights into the interaction patterns of cellular regulation.Key WordsMetabolic networkregulatory networknetwork reconstructionScale-free networkbow tienetwork centralitysystems biologygraph theory

Biological processes, including cell differentiation, organism development, and disease progression, can be interpreted as attractors (fixed points or limit cycles) of an underlying networked dynamical system. In this paper, we study the problem of computing a minimum-size subset of control nodes that can be used to steer a given biological network toward a desired attractor, when the networked system has Boolean dynamics. We first prove that this problem cannot be approximated to any nontrivial factor unless P = NP. We then formulate a sufficient condition and prove that the sufficient condition is equivalent to a target set selection problem, which can be solved using integer linear programming. Furthermore, we show that structural properties of biological networks can be exploited to reduce computational complexity. We prove that when the network nodes have threshold dynamics and certain topological structures, such as block cactus topology and hierarchical organization, the input selection problem can be solved or approximated in polynomial time. For networks with nested canalyzing dynamics, we propose polynomial-time algorithms that are within a polylogarithmic bound of the global optimum. We validate our approach through numerical study on real-world gene regulatory networks.

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.

BackgroundExpression of cell phenotypes highly depends on metabolism that supplies matter and energy. To achieve proper utilisation of the different metabolic pathways, metabolism is tightly regulated by a complex regulatory network composed of diverse biological entities (genes, transcripts, proteins, signalling molecules…). The integrated analysis of both regulatory and metabolic networks appears very insightful but is not straightforward because of the distinct characteristics of both networks. The classical method used for metabolic flux analysis is Flux Balance Analysis (FBA), which is constraint-based and relies on the assumption of steady-state metabolite concentrations throughout the network. Regarding regulatory networks, a broad spectrum of methods are dedicated to their analysis although logical modelling remains the major method to take charge of large-scale networks.ResultsWe present FlexFlux, an application implementing a new way to combine the analysis of both metabolic and regulatory networks, based on simulations that do not require kinetic parameters and can be applied to genome-scale networks. FlexFlux is based on seeking regulatory network steady-states by performing synchronous updates of multi-state qualitative initial values. FlexFlux is then able to use the calculated steady-state values as constraints for metabolic flux analyses using FBA. As input, FlexFlux uses the standards Systems Biology Markup Language (SBML) and SBML Qualitative Models Package (“qual”) extension (SBML-qual) file formats and provides a set of FBA based functions.ConclusionsFlexFlux is an open-source java software with executables and full documentation available online at http://lipm-bioinfo.toulouse.inra.fr/flexflux/. It can be defined as a research tool that enables a better understanding of both regulatory and metabolic networks based on steady-state simulations. FlexFlux integrates well in the flux analysis ecosystem thanks to the support of standard file formats and can thus be used as a complementary tool to existing software featuring other types of analyses.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-015-0238-z) contains supplementary material, which is available to authorized users.