Section: New Results
Models: Development and reduction of models of bacterial regulatory networks
The new results in 2009 concern (i) the development or the extension of models of the E. coli carbon starvation response and their experimental validation and (ii) the reduction of previously-developed models to simplified nonlinear models.
Development and validation of models of the carbon starvation response in E. coli
In the bacterium E. coli , the adaptation to the carbon-source availability is controlled by a complex network involving signaling cascades, metabolic reactions, and gene expression (Section 3.1 ). The different modes of regulation are interwoven to such an extent that it is difficult to understand how they coordinate the response of E. coli cells to changes in nutrient conditions. To address this question we previously developed kinetic models that focus on the role played by global regulators in the adaptation to the carbon-source availability. The initial confrontation of model predictions with experimental data obtained in the laboratory of Hans Geiselmann was inconclusive and has brought to the fore phenomena that are interesting, but difficult to explain by means of our models. We have therefore focused on the development of new hypotheses and new models based on them.
In particular, the data suggest that the interactions between global regulators of transcription are not sufficient to account for the control of gene expression during the growth transitions of E. coli . The analysis of the patterns of expression of global regulators duringthe growth transitions of E. coli suggests an effect of the cellular gene expression machinery, which controls the global regulators at the transcriptional, translational, and stability levels. To verify this hypothesis, Cao Yan, Vaibhhav Sinha, and Delphine Ropers have been developing kinetic models of the global control of gene expression by the cellular machinery, using standard approaches in biochemistry. These models, taking the form of systems of nonlinear differential-algebraic equations, describe the rate of change of the concentrations of the network components. They allow to analyze the effect of the regulation of the concentration and activity of the RNA polymerase and the ribosomes in the global control of gene expression during growth recovery following a carbon upshift. These models are also used for the development of growth control strategies in the ColAge project (Section 8.1 ).
In parallel, we have continued the investigation of the role of metabolic and genetic interactions in the control of gene expression during the growth transitions of E. coli . Global regulators of transcription control the synthesis of enzymes as well as their own synthesis, while the products of the metabolism control the activity of transcription factors. In order to work with models that can be easily manipulated and calibrated with experimental data, Guillaume Baptist, Mohammed El Amine Youcef, and Delphine Ropers have developed simplified kinetic models. These ODE models focus on components which have been experimentally identified as key players in the adaptation to carbon-source availability. They are tailored to a specific biological question, such as the regulation of the expression of the gene acs , coding for an enzyme in acetate metabolism, under different growth conditions, e.g. , glucose exhaustion. These ODE models have proven useful in the explanation of experimental observations on acs expression and the generation of new hypothesis on the regulation of this gene. A paper on the latter study is in preparation.
Reduction of models of the carbon starvation response
We previously developed a model of the control of glycolysis and neoglucogenesis in E. coli , composed of 39 nonlinear differential equations with 159 parameters. Most of the parameters are unknown and the time constants of the system span several orders of magnitudes. In order to reduce the model to a more manageable form, Valentina Baldazzi and Hidde de Jong, in collaboration with other IBIS members and Daniel Kahn (BAMBOO), have used an approach based on the systematic derivation of direct and indirect interactions in a genetic regulatory network from the underlying biochemical reaction network. They have shown that model reduction based on quasi-steady-state approximations in combination with sensitivity criteria are able to uncover such interactions. A paper describing this method and its application to the analysis of the network controlling glycolysis and neoglucogenesis in E. coli has been submitted for publication. As an extension of this work, Valentina Baldazzi has developed in the context of the EC-MOAN project a PL model describing the adaptation of the expression levels of the genes encoding global regulators and enzymes following a shift from glycolytic to neoglucogenetic growth.
A basic module in all of the above models, are equations describing the process of gene expression, that is, the synthesis of a protein from a DNA template. Classically, gene expression is modeled as a single step or assumed to be composed of two steps, transcription and translation. Especially when studying high-dimensional models it may be worthwhile to lump the entire gene expression step into a single step. Chris Barot, Hidde de Jong, Jean-Luc Gouzé (COMORE), and Eric Benoît (Université de la Rochelle) have studied the conditions under which it is justified to make these simplifications, using the mathematical framework of singular perturbations, and verified if these conditions are satisfied in actual time-series data sets. An article on this study is in preparation.