Motivation: To understand the behaviour of complex biological regulatory networks, a proper integration of molecular data into a full-fledge formal dynamical model is ultimately required. As most available data on regulatory interactions are qualitative, logical modelling offers an interesting framework to delineate the main dynamical properties of the underlying networks. Results: Transposing a generic model of the core network controlling the mammalian cell cycle into the logical framework, we compare different strategies to explore its dynamical properties. In particular, we assess the respective advantages and limits of synchronous versus asynchronous updating assumptions to delineate the asymptotical behaviour of regulatory networks. Furthermore, we propose several intermediate strategies to optimize the computation of asymptotical properties depending on available knowledge. Availability: The mammalian cell cycle model is available in a dedicated XML format (GINML) on our website, along with our logical simulation software GINsim ( ). Higher resolution state transitions graphs are also found on this web site (Model Repository page). Contact: thieffry@ibdm.univ-mrs.fr

Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle

A new matrix product, called semi-tensor product of matrices, is reviewed Using it, a matrix expression of logic is proposed, where a logical variable is expressed as a vector, a logical function is expressed as a multiple linear mapping Under this framework, a Boolean network equation is converted into an equivalent algebraic form as a conventional discrete-time linear system Analyzing the transition matrix of the linear system, formulas are obtained to show a) the number of fixed points; b) the numbers of cycles of different lengths; c) transient period, for all points to enter the set of attractors; and d) basin of each attractor The corresponding algorithms are developed and used to some examples

/pdf/a-linear-representation-of-dynamics-of-boolean-networks-3437k0s8yx.pdf

A Linear Representation of Dynamics of Boolean Networks

Structural analysis of cellular interaction networks contributes to a deeper understanding of network-wide interdependencies, causal relationships, and basic functional capabilities. While the structural analysis of metabolic networks is a well-established field, similar methodologies have been scarcely developed and applied to signaling and regulatory networks. We propose formalisms and methods, relying on adapted and partially newly introduced approaches, which facilitate a structural analysis of signaling and regulatory networks with focus on functional aspects. We use two different formalisms to represent and analyze interaction networks: interaction graphs and (logical) interaction hypergraphs. We show that, in interaction graphs, the determination of feedback cycles and of all the signaling paths between any pair of species is equivalent to the computation of elementary modes known from metabolic networks. Knowledge on the set of signaling paths and feedback loops facilitates the computation of intervention strategies and the classification of compounds into activators, inhibitors, ambivalent factors, and non-affecting factors with respect to a certain species. In some cases, qualitative effects induced by perturbations can be unambiguously predicted from the network scheme. Interaction graphs however, are not able to capture AND relationships which do frequently occur in interaction networks. The consequent logical concatenation of all the arcs pointing into a species leads to Boolean networks. For a Boolean representation of cellular interaction networks we propose a formalism based on logical (or signed) interaction hypergraphs, which facilitates in particular a logical steady state analysis (LSSA). LSSA enables studies on the logical processing of signals and the identification of optimal intervention points (targets) in cellular networks. LSSA also reveals network regions whose parametrization and initial states are crucial for the dynamic behavior. We have implemented these methods in our software tool CellNetAnalyzer (successor of FluxAnalyzer) and illustrate their applicability using a logical model of T-Cell receptor signaling providing non-intuitive results regarding feedback loops, essential elements, and (logical) signal processing upon different stimuli. The methods and formalisms we propose herein are another step towards the comprehensive functional analysis of cellular interaction networks. Their potential, shown on a realistic T-cell signaling model, makes them a promising tool.

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A methodology for the structural and functional analysis of signaling and regulatory networks

Motivation:In silico modeling of gene regulatory networks has gained some momentum recently due to increased interest in analyzing the dynamics of biological systems. This has been further facilitated by the increasing availability of experimental data on gene–gene, protein–protein and gene–protein interactions. The two dynamical properties that are often experimentally testable are perturbations and stable steady states. Although a lot of work has been done on the identification of steady states, not much work has been reported on in silico modeling of cellular differentiation processes.

Results: In this manuscript, we provide algorithms based on reduced ordered binary decision diagrams (ROBDDs) for Boolean modeling of gene regulatory networks. Algorithms for synchronous and asynchronous transition models have been proposed and their corresponding computational properties have been analyzed. These algorithms allow users to compute cyclic attractors of large networks that are currently not feasible using existing software.

Hereby we provide a framework to analyze the effect of multiple gene perturbation protocols, and their effect on cell differentiation processes. These algorithms were validated on the T-helper model showing the correct steady state identification and Th1–Th2 cellular differentiation process.

Availability: The software binaries for Windows and Linux platforms can be downloaded from http://si2.epfl.ch/~garg/genysis.html.

Contact: abhishek.garg@epfl.ch

Synchronous versus asynchronous modeling of gene regulatory networks

https://www.i3s.unice.fr/~bernot/Biomodels/2004-JTB-BernotComet.pdf

Vincent Devloo

Papers

Identification of all steady states in large networks by logical analysis