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 synthesized) control of cell populations and even of single cells.

Work in IBIS on the probabilistic 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 individual cell 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 single-cell state estimation and control. Other problems related with single-cell modelling and extracellular variability are considered in high-eukariotic cells through external collaborations.

In the context of yeast cell response to osmotic shocks, in collaboration with the CONTRAINTES 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 the context of microfluidics data, with focus on the budding yeast response to osmotic shocks. First results presented at conference in 2013 have been taken further, both in terms of mathematical analysis of the models developed and in terms of biological interpretation. Model identification and validation were performed together with Andres Gonzales, PhD student at the University of Pavia, who has visited IBIS for six months in 2014. A journal publication is currently being prepared for publication.

In a second line of work, starting from the models inferred in the above collaboration, the problem of real-time state estimation and control of single yeast cells has been considered. Together with the BIOCORE project-team, we have put in place algorithms for state estimation in presence of hybrid random switching and continuous dynamics, and integrated them with a feedback control approach developed by collaborators at TU Delft (the Netherlands). The whole monitoring, estimation and control chain has been deployed and applied in silico to the stochastic control of osmosensitive genes in single yeast cells. Methods and results have been presented at the 12th international conference on Computational Methods for Systems Biology (CMSB 2014), whose proceedings have been published as a volume of the LNCS series [14] . It is shown in particular that stochastic model-based estimation and control outperforms existing methods of single-cell control based on deterministic approximations.

Additional work on identification and estimation of hidden states for intrinsic noise models of gene expression/regulation in single bacterial cells, started with reference to arabinose uptake dynamics but also applicable to other regulatory networks in E. coli, is being developed. In parallel, collaboration of Eugenio Cinquemani with Marianna Rapsomaniki, PhD student affiliated with the University of Patras (Greece) and ETH Zürich (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 high-eukariotic 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 shedding light on cell-to-cell variability of the protein kinetics. Method and results have recently been published in Bioinformatics [6] .