Dynamical modeling and analysis of large cellular regulatory networks.

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.

Logical modelling of regulatory networks with GINsim 2.3.

Many important problems in cell biology require the consideration of dense nonlinear interactions between functional modules. The requirement of computer simulation for the understanding of cellular processes is now widely accepted, and a variety of modelling frameworks have been designed to meet this need. Here, we present a novel public release of the Gene Interaction Network simulation suite (GINsim), a software designed for the qualitative modelling and analysis of regulatory networks. The main functionalities of GINsim are illustrated through the analysis of a logical model for the core network controlling the fission yeast cell cycle. The last public release of GINsim (version 2.3), as well as development versions, can be downloaded from the dedicated website (http://gin.univ-mrs.fr/GINsim/), which further includes a model library, along with detailed tutorial and user manual.

GINsim: a software suite for the qualitative modelling, simulation and analysis of regulatory networks.

This paper presents GINsim, a Java software suite devoted to the qualitative modelling, analysis and simulation of genetic regulatory networks. Formally, our approach leans on discrete mathematical and graph-theoretical concepts. GINsim encompasses an intuitive graph editor, enabling the definition and the parameterisation of a regulatory graph, as well as a simulation engine to compute the corresponding qualitative dynamical behaviour. Our computational approach is illustrated by a preliminary model analysis of the inter-cellular regulatory network activating Notch at the dorsal-ventral boundary in the wing imaginal disc of Drosophila. We focus on the cross-regulations between five genes (within and between two cells), which implements the dorsal-ventral border in the developing imaginal disc. Our simulations qualitatively reproduce the wild-type developmental pathway, as well as the outcome of various types of experimental perturbations, such as loss-of-function mutations or ectopically induced gene expression.

Qualitative modelling of regulated metabolic pathways: application to the tryptophan biosynthesis in E.coli.

MOTIVATION: The integrated dynamical modelling of mixed metabolic/genetic networks constitutes one of the challenges of systems biology. Furthermore, as most of available data about genetic and metabolic regulations are qualitative, there is a pressing need for rigorous qualitative mathematical approaches. RESULTS: On the basis of two established formalisms, the logical modelling of genetic regulatory networks and the Petri net modelling of metabolic networks, we propose a systematic approach for the modelling of regulated metabolic networks. This approach leans on previous work defining a systematic procedure to translate logical regulatory graphs into standard (discrete) Petri nets (PNs). This approach is illustrated by the qualitative modelling of the biosynthesis of tryptophan (Trp) in Escherichia coli, taking into account two types of regulatory feedbacks: the direct inhibition of the first enzyme of the pathway by the final product of the pathway, and the transcriptional inhibition of the Trp operon by the Trp-repressor complex. On the basis of this integrated PN model, we further indicate how available dynamical analysis tools can be applied to obtain significant insights in the behaviour of the system. AVAILABILITY: The software GINsim for the logical modelling of genetic regulatory networks together with the PN model of the regulated Trp biosynthesis pathway are available at: http://gin.univ-mrs.fr/GINsim.

A description of dynamical graphs associated to elementary regulatory circuits.

The biological and dynamical importance of feedback circuits in regulatory graphs has often been emphasized. The work presented here aims at completely describing the dynamics of isolated elementary regulatory circuits. Our analytical approach is based on a discrete formal framework, built upon the logical approach of R. Thomas. Given a regulatory circuit, we show that the structure of synchronous and asynchronous dynamical graphs depends only on the length of the circuit (number of genes) and on its sign (which depends on the parity of the number of negative interactions). This work constitutes a first step towards the analytical characterisation of discrete dynamical graphs for more complex regulatory networks in terms of contributions corresponding to their embedded elementary circuits.