Aurélien Naldi

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.

Diversity and Plasticity of Th Cell Types Predicted from Regulatory Network Modelling

Alternative cell differentiation pathways are believed to arise from the concerted action of signalling pathways and transcriptional regulatory networks. However, the prediction of mammalian cell differentiation from the knowledge of the presence of specific signals and transcriptional factors is still a daunting challenge. In this respect, the vertebrate hematopoietic system, with its many branching differentiation pathways and cell types, is a compelling case study. In this paper, we propose an integrated, comprehensive model of the regulatory network and signalling pathways controlling Th cell differentiation. As most available data are qualitative, we rely on a logical formalism to perform extensive dynamical analyses. To cope with the size and complexity of the resulting network, we use an original model reduction approach together with a stable state identification algorithm. To assess the effects of heterogeneous environments on Th cell differentiation, we have performed a systematic series of simulations considering various prototypic environments. Consequently, we have identified stable states corresponding to canonical Th1, Th2, Th17 and Treg subtypes, but these were found to coexist with other transient hybrid cell types that co-express combinations of Th1, Th2, Treg and Th17 markers in an environment-dependent fashion. In the process, our logical analysis highlights the nature of these cell types and their relationships with canonical Th subtypes. Finally, our logical model can be used to explore novel differentiation pathways in silico.

Decision diagrams for the representation and analysis of logical models of genetic networks

The complexity of biological regulatory networks calls for the development of proper mathematical methods to model their structures and to obtain insight in their dynamical behaviours. One qualitative approach consists in modelling regulatory networks in terms of logical equations (using either Boolean or multi-valued discretisation). In this paper, we propose a novel implementation of the generalised logical formalism by means of Multi-valued Decision Diagrams. We show that the use of this representation enables the development of efficient algorithms for the analysis of specific dynamical properties of the regulatory graphs. In particular, we address the question of determining conditions insuring the functionality of feedback circuits, as well as the identification of stable states. Finally, we apply these algorithms to logical models of T cell activation and differentiation.

SBML qualitative models: a model representation format and infrastructure to foster interactions between qualitative modelling formalisms and tools

BackgroundQualitative frameworks, especially those based on the logical discrete formalism, are increasingly used to model regulatory and signalling networks. A major advantage of these frameworks is that they do not require precise quantitative data, and that they are well-suited for studies of large networks. While numerous groups have developed specific computational tools that provide original methods to analyse qualitative models, a standard format to exchange qualitative models has been missing.ResultsWe present the Systems Biology Markup Language (SBML) Qualitative Models Package (“qual”), an extension of the SBML Level 3 standard designed for computer representation of qualitative models of biological networks. We demonstrate the interoperability of models via SBML qual through the analysis of a specific signalling network by three independent software tools. Furthermore, the collective effort to define the SBML qual format paved the way for the development of LogicalModel, an open-source model library, which will facilitate the adoption of the format as well as the collaborative development of algorithms to analyse qualitative models.ConclusionsSBML qual allows the exchange of qualitative models among a number of complementary software tools. SBML qual has the potential to promote collaborative work on the development of novel computational approaches, as well as on the specification and the analysis of comprehensive qualitative models of regulatory and signalling networks.

Logical Modelling of Gene Regulatory Networks with GINsim

Discrete mathematical formalisms are well adapted to model large biological networks, for which detailed kinetic data are scarce. This chapter introduces the reader to a well-established qualitative (logical) framework for the modelling of regulatory networks. Relying on GINsim, a software implementing this logical formalism, we guide the reader step by step towards the definition and the analysis of a simple model of the lysis-lysogeny decision in the bacteriophage λ.

A multiplicity of factors contributes to selective RNA polymerase III occupancy of a subset of RNA polymerase III genes in mouse liver

The genomic loci occupied by RNA polymerase (RNAP) III have been characterized in human culture cells by genome-wide chromatin immunoprecipitations, followed by deep sequencing (ChIP-seq). These studies have shown that only ∼40% of the annotated 622 human tRNA genes and pseudogenes are occupied by RNAP-III, and that these genes are often in open chromatin regions rich in active RNAP-II transcription units. We have used ChIP-seq to characterize RNAP-III-occupied loci in a differentiated tissue, the mouse liver. Our studies define the mouse liver RNAP-III-occupied loci including a conserved mammalian interspersed repeat (MIR) as a potential regulator of an RNAP-III subunit-encoding gene. They reveal that synteny relationships can be established between a number of human and mouse RNAP-III genes, and that the expression levels of these genes are significantly linked. They establish that variations within the A and B promoter boxes, as well as the strength of the terminator sequence, can strongly affect RNAP-III occupancy of tRNA genes. They reveal correlations with various genomic features that explain the observed variation of 81% of tRNA scores. In mouse liver, loci represented in the NCBI37/mm9 genome assembly that are clearly occupied by RNAP-III comprise 50 Rn5s (5S RNA) genes, 14 known non-tRNA RNAP-III genes, nine Rn4.5s (4.5S RNA) genes, and 29 SINEs. Moreover, out of the 433 annotated tRNA genes, half are occupied by RNAP-III. Transfer RNA gene expression levels reflect both an underlying genomic organization conserved in dividing human culture cells and resting mouse liver cells, and the particular promoter and terminator strengths of individual genes.

Model checking to assess T-helper cell plasticity.

Computational modeling constitutes a crucial step toward the functional understanding of complex cellular networks. In particular, logical modeling has proven suitable for the dynamical analysis of large signaling and transcriptional regulatory networks. In this context, signaling input components are generally meant to convey external stimuli, or environmental cues. In response to such external signals, cells acquire specific gene expression patterns modeled in terms of attractors (e.g., stable states). The capacity for cells to alter or reprogram their differentiated states upon changes in environmental conditions is referred to as cell plasticity. In this article, we present a multivalued logical framework along with computational methods recently developed to efficiently analyze large models. We mainly focus on a symbolic model checking approach to investigate switches between attractors subsequent to changes of input conditions. As a case study, we consider the cellular network regulating the differentiation of T-helper (Th) cells, which orchestrate many physiological and pathological immune responses. To account for novel cellular subtypes, we present an extended version of a published model of Th cell differentiation. We then use symbolic model checking to analyze reachability properties between Th subtypes upon changes of environmental cues. This allows for the construction of a synthetic view of Th cell plasticity in terms of a graph connecting subtypes with arcs labeled by input conditions. Finally, we explore novel strategies enabling specific Th cell polarizing or reprograming events.

Genome-wide analysis of SREBP1 activity around the clock reveals its combined dependency on nutrient and circadian signals.

In mammals, the circadian clock allows them to anticipate and adapt physiology around the 24 hours. Conversely, metabolism and food consumption regulate the internal clock, pointing the existence of an intricate relationship between nutrient state and circadian homeostasis that is far from being understood. The Sterol Regulatory Element Binding Protein 1 (SREBP1) is a key regulator of lipid homeostasis. Hepatic SREBP1 function is influenced by the nutrient-response cycle, but also by the circadian machinery. To systematically understand how the interplay of circadian clock and nutrient-driven rhythm regulates SREBP1 activity, we evaluated the genome-wide binding of SREBP1 to its targets throughout the day in C57BL/6 mice. The recruitment of SREBP1 to the DNA showed a highly circadian behaviour, with a maximum during the fed status. However, the temporal expression of SREBP1 targets was not always synchronized with its binding pattern. In particular, different expression phases were observed for SREBP1 target genes depending on their function, suggesting the involvement of other transcription factors in their regulation. Binding sites for Hepatocyte Nuclear Factor 4 (HNF4) were specifically enriched in the close proximity of SREBP1 peaks of genes, whose expression was shifted by about 8 hours with respect to SREBP1 binding. Thus, the cross-talk between hepatic HNF4 and SREBP1 may underlie the expression timing of this subgroup of SREBP1 targets. Interestingly, the proper temporal expression profile of these genes was dramatically changed in Bmal1 −/− mice upon time-restricted feeding, for which a rhythmic, but slightly delayed, binding of SREBP1 was maintained. Collectively, our results show that besides the nutrient-driven regulation of SREBP1 nuclear translocation, a second layer of modulation of SREBP1 transcriptional activity, strongly dependent from the circadian clock, exists. This system allows us to fine tune the expression timing of SREBP1 target genes, thus helping to temporally separate the different physiological processes in which these genes are involved.

Petri net representation of multi-valued logical regulatory graphs

Relying on a convenient logical representation of regulatory networks, we propose a generic method to qualitatively model regulatory interactions in the standard elementary and coloured Petri net frameworks. Logical functions governing the behaviours of the components of logical regulatory graphs are efficiently represented by Multivalued Decision Diagrams, which are also at the basis of the translation of logical models in terms of Petri nets. We further delineate a simple strategy to sort trajectories through the introduction of priority classes (in the logical framework) or priority functions (in the Petri net framework). We also focus on qualitative behaviours such as multistationarity or sustained oscillations, identified as specific structures in state transition graphs (for logical models) or in marking graphs (in Petri nets). Regulatory circuits are known to be at the origin of such properties. In this respect, we present a method that allows to determine the functionality contexts of regulatory circuits, i.e. constraints on external regulator states enabling the corresponding dynamical properties. Finally, this approach is illustrated through an application to the modelling of a regulatory network controlling T lymphocyte activation and differentiation.

On circuit functionality in boolean networks.

It has been proved, for several classes of continuous and discrete dynamical systems, that the presence of a positive (resp. negative) circuit in the interaction graph of a system is a necessary condition for the presence of multiple stable states (resp. a cyclic attractor). A positive (resp. negative) circuit is said to be functional when it “generates” several stable states (resp. a cyclic attractor). However, there are no definite mathematical frameworks translating the underlying meaning of “generates.” Focusing on Boolean networks, we recall and propose some definitions concerning the notion of functionality along with associated mathematical results.