Section: New Results

Stochastic modeling and identification of gene regulatory networks in bacteria

At the single-cell level, the processes that govern single-cell dynamics in general and gene expression in particular are better described by stochastic models. Modern techniques for the real-time monitoring of gene expression in single cells enable one to apply stochastic modelling to study the origins and consequences of random noise in response to various environmental stresses, and the emergence of phenotypic variability. The potential impact of single-cell stochastic analysis and modelling ranges from a better comprehension of the biochemical regulatory mechanisms underlying cellular phenotypes to the development of new strategies for the (computer assisted or genetically engineered) control of cell populations and even of single cells.

Work in IBIS on gene expression and interaction dynamics at the level of individual cells is addressed in terms of identification of intrinsic noise models from population snapshot data, on the one hand, and the inference of models focusing on cellular variability within isogenic populations from fluorescence microscopy gene expression profiles, on the other hand. Along with modelling and inference comes analysis of the inferred models in various respects, notably in terms of identifiability, single-cell state estimation and control. Other problems related with single-cell modelling and extracellular variability are considered in eukaryotic cells through external collaborations.

In the context of the response of yeast cells to osmotic shocks, in collaboration with the LIFEWARE project team and colleagues from Université Paris Descartes and University of Pavia (Italy), Eugenio Cinquemani has investigated the use of mixed effects-modelling and identification techniques to characterize individual cell dynamics in isogenic cell populations. Mixed-effects models are hierarchical models where parametric response profiles of individuals is subject to inter-individual parameter variability following a common population distribution. Starting from identification approaches in pharmacokinetics, we have developed and applied inference methods to microfluidics data, with a focus on the response of budding yeast to osmotic shocks. Results were described in a publication in PLoS Computational Biology [13]. A study of statistical validation methods for mixed-effects and alternative stochastic modelling paradigms has been presented at the IFAC Conference on Foundations of Systems Biology in Engineering (FOSBE) in Magdeburg [19]. In collaboration with the project-team BIOCORE at Inria Sophia-Antipolis - Méditerranée, the approach is now being investigated for the joint modelling of growth and gene expression in E. coli, based on single-cell microfluidics data from growth arrest-and-restart experiments. Further challenges stemming from this activity toward modelling and identification of extrinsic noise in individual cells are part of the recently started ANR project MEMIP (Section 8.2).

Work on identification and state estimation for single-cell gene network dynamics has been focused on the reconstruction of promoter activity profiles from fluorescent reporter data. In a stochastic, intrinsic noise modelling context, Eugenio Cinquemani addressed the problem of inferring promoter activity statistics over a cell population, such as mean and variance, from analogous statistics of the reporter output, as obtained from so-called population snapshot data. This nontrivial extension of the deterministic promoter activity deconvolution problem from population-average data is the first, crucial step toward reconstruction of promoter activity regulation and inference of stochastic network models. Earlier results, concerning parameter identifiability of stochastic promoter activity models and reconstruction of promoter activity distributions in the special case of single-switch systems, were further developed in a contribution to the HSB conference this year [18]. The relationship between the spectrum of the promoter process (cross-correlation function) and the mean-variance profiles of fluorescent reporter readouts was derived and demonstrated on examples, laying down the bases for a full-blown observability analysis and the development of spectrum estimation methods.

The collaboration of Eugenio Cinquemani with Marianna Rapsomaniki (IBM Zurich Research Lab, Switzerland), Zoi Lygerou (University of Patras, Greece) and John Lygeros (ETH Zurich, Switzerland) is moving on to applications of joint work published in Bioinformatics last year. Deployment of the methods developed into an efficient cluster-based software for the inference of protein kinetics in single cells from Fluorescence Recovery After Photobleaching (FRAP) experiments is under study. Exploitation of the same methods for the simulation and analysis of more general biochemical processes in single cells is part of the ongoing research efforts.