Modélisation stochastique de l’expression des gènes et inférence de réseaux de régulation

Ulysse Herbach 1, 2, 3, 4
3 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
ICJ - Institut Camille Jordan [Villeurbanne], Inria Grenoble - Rhône-Alpes, CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire
4 PSPM - Probabilités, statistique, physique mathématique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : Gene expression in cells has long been only observable through averaged quantities over cell populations. The recent development of single-cell transcriptomics has enabled gene expression to be measured in individual cells: it turns out that even in an isogenic population, the molecular variability can be very important. In particular, an average description is not sufficient to account for cell differentiation. In this thesis, we are interested in the emergence of such cell decision-making from underlying gene regulatory networks, which we would like to infer from data. The starting point is the construction of a stochastic gene network model that is able to explain the data using physical arguments. Genes are then seen as an interacting particle system that happens to be a piecewise-deterministic Markov process, and our aim is to derive a tractable statistical model from its invariant distribution. We present two approaches: the first one is a popular self-consistent field approximation, for which we obtain a concentration result, and the second one is based on an analytically tractable particular case, which provides a hidden Markov random field with interesting properties.
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Submitted on : Wednesday, November 21, 2018 - 9:24:44 PM
Last modification on : Monday, May 13, 2019 - 11:19:37 AM
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  • HAL Id : tel-01930398, version 1


Ulysse Herbach. Modélisation stochastique de l’expression des gènes et inférence de réseaux de régulation. Mathématiques [math]. Université de Lyon, 2018. Français. ⟨NNT : 2018LYSE1155⟩. ⟨tel-01930398⟩



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