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. First results presented at conference in 2013 and the identification and validation work performed with Andres Gonzales, who visited IBIS for a few months in 2014 during his PhD at the University of Pavia, have been finalized into a journal article recently accepted for publication in PLoS Computational Biology [20] .

Started with a study of the arabinose uptake dynamics in E. coli, work on identification and state estimation for single-cell intrinsic noise models of gene networks has focused on the reconstruction of promoter activity profiles from fluorescent reporter data. In the single-cell stochastic context, given population snapshots of fluorescence levels at subsequent experimental instants, the problem becomes that of inferring promoter activity statistics over a cell population such as mean, variance or even higher-order moments from analogous statistics of the reporter output. This nontrivial extension of the deterministic deconvolution of promoter activity from population-average data requires knowledge of the stochastic reporter dynamics and of the relation between promoter and fluorescence statistical moments. In two conference papers, Eugenio Cinquemani investigated identifiability and identification of the kinetic parameters of the stochastic reporter dynamics [28] and proposed parametric and nonparametric methods for the reconstruction of the desired promoter activity statistics [27] , [28] , demonstrating their effectiveness in silico. Further developments of these methods and application to experimental data for addressing relevant biological questions will be the subject of future journal publications.

In parallel, collaboration of Eugenio Cinquemani with Marianna Rapsomaniki, post-doctoral researcher at at IBM Zurich Research Lab (Switzerland), Zoi Lygerou at the University of Patras (Greece) and John Lygeros at ETH Zurich (Switzerland) has been devoted to the analysis of data from Fluorescence Recovery After Photobleaching (FRAP) experiments and the inference of kinetic parameters of protein dynamics in single eukaryotic cells. As an alternative to current approximate analytical methods, we have explored inference methods based on simulation of biological processes in realistic environments at a particle level. We introduced and demonstrated a new method for the inference of kinetic parameters of protein dynamics, where a limited number of in-silico FRAP experiments is used to construct a mapping from FRAP recovery curves to the parameters sought. Parameter estimates from experimental data are then computed by applying the mapping to the observed recovery curves, at virtually no additional price for any number of experiments, along with the application of a bootstrap procedure for determining identifiability of the parameters and confidence intervals for their estimates. After validation on synthetic data, the method was successfully applied to the analysis of the nuclear proteins Cdt1, PCNA and GFPnls in mammalian cells, also sheding light on cell-to-cell variability of the protein kinetics. Method and results have been published in Bioinformatics this year [22] .