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 rather than the deterministic models underlying the linear inversion methods discussed in Section 6.6. 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 parametric intrinsic noise models, on the one hand, and the nonparametric inference of gene expression statistics, on the other hand, from population snapshot data. Along with modelling and inference, identifiability analysis is dedicated special attention. Other problems related with single-cell modelling, extracellular variability and inheritance of traits at cell division are considered also through external collaborations, as discussed below (Section 6.4).

Concerning identification of intrinsic noise dynamics in single cells, previous results on the contribution of stochasticity to parameter identifiability and on reconstruction of unknown gene regulatory networks have been taken further. For the case of population snapshot meaurements, where the dynamics of the population statistics are observed by simple time-lapse experiments, our earlier results showing that variance measurements may provide tremendous improvement in network reconstruction relative to sole mean measurements have been developed into a full-blown method for first-order gene network reconstruction. Additionally, parameter identifiability methods and results initially developed for gene expression models have been generalized to the whole class of first-order stochastic reaction networks. These developments have been presented and demonstrated by simulation in a paper published in the journal Processes [15].

Reconstruction of promoter activity statistics from reporter gene population snapshot data has been further investigated, leading to a full-blown spectral analysis and reconstruction method for reporter gene systems. In the context of the ANR project MEMIP (Section 7.2), we have characterized reporter systems as noisy linear systems operating on a stochastic input (promoter activity), and developed an inversion method for estimation of promoter activation statistics from reporter population snapshots that is nonparametric, in the sense that it does not assume any parametric model for the unknown promoter dynamics. This analysis rests on a more general, original generalization of moment equations that we have developed for stochastic reaction networks with state-affine rates subject to random input processes. The theoretical results, together with a demonstration of the reporter gene inversion method on simulated data, have been accepted for publication in Automatica this year [16]. In addition to utilization of the method on real gene-expression data, the results lend themselves to several additional applications, among which the study of extrinsic noise and the optimal design of reporter systems.