Michel Le Borgne

Topology and static response of interaction networks in molecular biology

We introduce a mathematical framework describing static response of networks occurring in molecular biology. This formalism has many similarities with the Laplace–Kirchhoff equations for electrical networks. We introduce the concept of graph boundary and we show how the response of the biological networks to external perturbations can be related to the Dirichlet or Neumann problems for the corresponding equations on the interaction graph. Solutions to these two problems are given in terms of path moduli (measuring path rigidity with respect to the propagation of interaction along the graph). Path moduli are related to loop products in the interaction graph via generalized Mason–Coates formulae. We apply our results to two specific biological examples: the lactose operon and the genetic regulation of lipogenesis. Our applications show consistency with experimental results and in the case of lipogenesis check some hypothesis on the behaviour of hepatic fatty acids on fasting.

Inferring the role of transcription factors in regulatory networks

BackgroundExpression profiles obtained from multiple perturbation experiments are increasingly used to reconstruct transcriptional regulatory networks, from well studied, simple organisms up to higher eukaryotes. Admittedly, a key ingredient in developing a reconstruction method is its ability to integrate heterogeneous sources of information, as well as to comply with practical observability issues: measurements can be scarce or noisy. In this work, we show how to combine a network of genetic regulations with a set of expression profiles, in order to infer the functional effect of the regulations, as inducer or repressor. Our approach is based on a consistency rule between a network and the signs of variation given by expression arrays.ResultsWe evaluate our approach in several settings of increasing complexity. First, we generate artificial expression data on a transcriptional network of E. coli extracted from the literature (1529 nodes and 3802 edges), and we estimate that 30% of the regulations can be annotated with about 30 profiles. We additionally prove that at most 40.8% of the network can be inferred using our approach. Second, we use this network in order to validate the predictions obtained with a compendium of real expression profiles. We describe a filtering algorithm that generates particularly reliable predictions. Finally, we apply our inference approach to S. cerevisiae transcriptional network (2419 nodes and 4344 interactions), by combining ChIP-chip data and 15 expression profiles. We are able to detect and isolate inconsistencies between the expression profiles and a significant portion of the model (15% of all the interactions). In addition, we report predictions for 14.5% of all interactions.ConclusionOur approach does not require accurate expression levels nor times series. Nevertheless, we show on both data, real and artificial, that a relatively small number of perturbation experiments are enough to determine a significant portion of regulatory effects. This is a key practical asset compared to statistical methods for network reconstruction. We demonstrate that our approach is able to provide accurate predictions, even when the network is incomplete and the data is noisy.

Dynamic Regulation of Tgf-B Signaling by Tif1γ: A Computational Approach

TIF1γ (Transcriptional Intermediary Factor 1 γ) has been implicated in Smad-dependent signaling by Transforming Growth Factor beta (TGF-β). Paradoxically, TIF1γ functions both as a transcriptional repressor or as an alternative transcription factor that promotes TGF-β signaling. Using ordinary differential-equation models, we have investigated the effect of TIF1γ on the dynamics of TGF-β signaling. An integrative model that includes the formation of transient TIF1γ-Smad2-Smad4 ternary complexes is the only one that can account for TGF-β signaling compatible with the different observations reported for TIF1γ. In addition, our model predicts that varying TIF1γ/Smad4 ratios play a critical role in the modulation of the transcriptional signal induced by TGF-β, especially for short stimulation times that mediate higher threshold responses. Chromatin immunoprecipitation analyses and quantification of the expression of TGF-β target genes as a function TIF1γ/Smad4 ratios fully validate this hypothesis. Our integrative model, which successfully unifies the seemingly opposite roles of TIF1γ, also reveals how changing TIF1γ/Smad4 ratios affect the cellular response to stimulation by TGF-β, accounting for a highly graded determination of cell fate.

An integrative modeling framework reveals plasticity of TGF-β signaling

BackgroundThe TGF-β transforming growth factor is the most pleiotropic cytokine controlling a broad range of cellular responses that include proliferation, differentiation and apoptosis. The context-dependent multifunctional nature of TGF-β is associated with complex signaling pathways. Differential models describe the dynamics of the TGF-β canonical pathway, but modeling the non-canonical networks constitutes a major challenge. Here, we propose a qualitative approach to explore all TGF-β-dependent signaling pathways.ResultsUsing a new formalism, CADBIOM, which is based on guarded transitions and includes temporal parameters, we have built the first discrete model of TGF-β signaling networks by automatically integrating the 137 human signaling maps from the Pathway Interaction Database into a single unified dynamic model. Temporal property-checking analyses of 15934 trajectories that regulate 145 TGF-β target genes reveal the association of specific pathways with distinct biological processes. We identify 31 different combinations of TGF-β with other extracellular stimuli involved in non-canonical TGF-β pathways that regulate specific gene networks. Extensive analysis of gene expression data further demonstrates that genes sharing CADBIOM trajectories tend to be co-regulated.ConclusionsAs applied here to TGF-β signaling, CADBIOM allows, for the first time, a full integration of highly complex signaling pathways into dynamic models that permit to explore cell responses to complex microenvironment stimuli.