MALIN: Modular modelling and Analysis of Large biological Interacting Networks

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Publications

Majority rules with random tie-breaking in Boolean gene regulatory networks

Publication . Chaouiya, Claudine; Ourrad, Ouerdia; Lima, Ricardo

We consider threshold boolean gene regulatory networks, where the update function of each gene is described as a majority rule evaluated among the regulators of that gene: it is turned ON when the sum of its regulator contributions is positive (activators contribute positively whereas repressors contribute negatively) and turned OFF when this sum is negative. In case of a tie (when contributions cancel each other out), it is often assumed that the gene keeps it current state. This framework has been successfully used to model cell cycle control in yeast. Moreover, several studies consider stochastic extensions to assess the robustness of such a model. Here, we introduce a novel, natural stochastic extension of the majority rule. It consists in randomly choosing the next value of a gene only in case of a tie. Hence, the resulting model includes deterministic and probabilistic updates. We present variants of the majority rule, including alternate treatments of the tie situation. Impact of these variants on the corresponding dynamical behaviours is discussed. After a thorough study of a class of two-node networks, we illustrate the interest of our stochastic extension using a published cell cycle model. In particular, we demonstrate that steady state analysis can be rigorously performed and can lead to effective predictions; these relate for example to the identification of interactions whose addition would ensure that a specific state is absorbing.

2013-07-26Journal article

Open access

Estimating Attractor Reachability in Asynchronous Logical Models

Publication . Mendes, Nuno D.; Henriques, Rui; Remy, Elisabeth; Carneiro, Jorge; Monteiro, Pedro T.; Chaouiya, Claudine

Logical models are well-suited to capture salient dynamical properties of regulatory networks. For networks controlling cell fate decisions, cell fates are associated with model attractors (stable states or cyclic attractors) whose identification and reachability properties are particularly relevant. While synchronous updates assume unlikely instantaneous or identical rates associated with component changes, the consideration of asynchronous updates is more realistic but, for large models, may hinder the analysis of the resulting non-deterministic concurrent dynamics. This complexity hampers the study of asymptotical behaviors, and most existing approaches suffer from efficiency bottlenecks, being generally unable to handle cyclical attractors and quantify attractor reachability. Here, we propose two algorithms providing probability estimates of attractor reachability in asynchronous dynamics. The first algorithm, named Firefront, exhaustively explores the state space from an initial state, and provides quasi-exact evaluations of the reachability probabilities of model attractors. The algorithm progresses in breadth, propagating the probabilities of each encountered state to its successors. Second, Avatar is an adapted Monte Carlo approach, better suited for models with large and intertwined transient and terminal cycles. Avatar iteratively explores the state space by randomly selecting trajectories and by using these random walks to estimate the likelihood of reaching an attractor. Unlike Monte Carlo simulations, Avatar is equipped to avoid getting trapped in transient cycles and to identify cyclic attractors. Firefront and Avatar are validated and compared to related methods, using as test cases logical models of synthetic and biological networks. Both algorithms are implemented as new functionalities of GINsim 3.0, a well-established software tool for logical modeling, providing executable GUI, Java API, and scripting facilities.

2018-09-07Journal article

Open access

EpiLog: A software for the logical modelling of epithelial dynamics

Publication . Varela, Pedro L.; Ramos, Camila V.; Monteiro, Pedro T.; Chaouiya, Claudine

Cellular responses are governed by regulatory networks subject to external signals from surrounding cells and to other micro-environmental cues. The logical (Boolean or multi-valued) framework proved well suited to study such processes at the cellular level, by specifying qualitative models of involved signalling pathways and gene regulatory networks. Here, we describe and illustrate the main features of EpiLog, a computational tool that implements an extension of the logical framework to the tissue level. EpiLog defines a collection of hexagonal cells over a 2D grid, which embodies a mono-layer epithelium. Basically, it defines a cellular automaton in which cell behaviours are driven by associated logical models subject to external signals. EpiLog is freely available on the web at http://epilog-tool.org. It is implemented in Java (version ≥1.7 required) and the source code is provided at https://github.com/epilog-tool/epilog under a GNU General Public License v3.0.

2019-03-11Journal article

Open access

A Discrete Model of Drosophila Eggshell Patterning Reveals Cell-Autonomous and Juxtacrine Effects

Publication . Fauré, Adrien; Vreede, Barbara M. I.; Sucena, Élio; Chaouiya, Claudine

The Drosophila eggshell constitutes a remarkable system for the study of epithelial patterning, both experimentally and through computational modeling. Dorsal eggshell appendages arise from specific regions in the anterior follicular epithelium that covers the oocyte: two groups of cells expressing broad (roof cells) bordered by rhomboid expressing cells (floor cells). Despite the large number of genes known to participate in defining these domains and the important modeling efforts put into this developmental system, key patterning events still lack a proper mechanistic understanding and/or genetic basis, and the literature appears to conflict on some crucial points. We tackle these issues with an original, discrete framework that considers single-cell models that are integrated to construct epithelial models. We first build a phenomenological model that reproduces wild type follicular epithelial patterns, confirming EGF and BMP signaling input as sufficient to establish the major features of this patterning system within the anterior domain. Importantly, this simple model predicts an instructive juxtacrine signal linking the roof and floor domains. To explore this prediction, we define a mechanistic model that integrates the combined effects of cellular genetic networks, cell communication and network adjustment through developmental events. Moreover, we focus on the anterior competence region, and postulate that early BMP signaling participates with early EGF signaling in its specification. This model accurately simulates wild type pattern formation and is able to reproduce, with unprecedented level of precision and completeness, various published gain-of-function and loss-of-function experiments, including perturbations of the BMP pathway previously seen as conflicting results. The result is a coherent model built upon rules that may be generalized to other epithelia and developmental systems.

2014-03-27Journal article

Open access

Dynamical modeling and analysis of large cellular regulatory networks

Publication . Bérenguier, D.; Chaouiya, C.; Monteiro, P. T.; Naldi, A.; Remy, E.; Thieffry, D.; Tichit, L.

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.

2013-06-25Journal article

Open access