Search

The rise of single-cell data highlights the need for a nondeterministic view of gene expression, while offering new opportunities regarding gene regulatory network inference. We recently introduced two strategies that specifically exploit time-course data, where single-cell profiling is performed after a stimulus: HARISSA, a mechanistic network model with a highly efficient simulation procedure, and CARDAMOM, a scalable inference method seen as model calibration. Here, we combine the two approaches and show that the same model driven by transcriptional bursting can be used simultaneously as an inference tool, to reconstruct biologically relevant networks, and as a simulation tool, to generate realistic transcriptional profiles emerging from gene interactions. We verify that CARDAMOM quantitatively reconstructs causal links when the data is simulated from HARISSA, and demonstrate its performance on experimental data collected onin vitrodifferentiating mouse embryonic stem cells. Overall, this integrated strategy largely overcomes the limitations of disconnected inference and simulation.Author summaryGene regulatory network (GRN) inference is an old problem, to which single-cell data has recently offered new challenges and breakthrough potential. Many GRN inference methods based on single-cell transcriptomic data have been developed over the last few years, while GRN simulation tools have also been proposed for generating synthetic datasets with realistic features. However, except for benchmarking purposes, these two fields remain largely disconnected. In this work, building on a combination of two methods we recently described, we show that a particular GRN model can be used simultaneously as an inference tool, to reconstruct a biologically relevant network from time-course single-cell gene expression data, and as a simulation tool, to generate realistic transcriptional profiles in a non-trivial way through gene interactions. This integrated strategy demonstrates the benefits of using the same executable model for both simulation and inference.

Early access; International audience; Stochastic gene expression plays a leading developmental role through its contribution to cell differentiation. It is also proposed to promote phenotypic diversification in malignant cells. However, it remains unclear if these two forms of cellular bet-hedging are identical or rather display distinct features. Here we argue that bet-hedging phenomena in cancer cells are more similar to those occurring in unicellular organisms than to those of normal metazoan cells. We further propose that the atavistic bet-hedging strategies in cancer originate from a hijacking of the normal developmental bet-hedging of metazoans. Finally, we discuss the constraints that may shape the atavistic bet-hedging strategies of cancer cells.

A biochemical network can be simulated by a set of ordinary differential equations (ODE) under well stirred reactor conditions, for large numbers of molecules, and frequent reactions. This is no longer a robust representation when some molecular species are in small numbers and reactions changing them are infrequent. In this case, discrete stochastic events trigger changes of the smooth deterministic dynamics of the biochemical network. Piecewise-deterministic Markov processes (PDMP) are well adapted for describing such situations. Although PDMP models are now well established in biology, these models remain computationally challenging. Previously we have introduced the push-forward method to compute how the probability measure is spread by the deterministic ODE flow of PDMPs, through the use of analytic expressions of the corresponding semigroup. In this paper we provide a more general simulation algorithm that works also for non-integrable systems. The method can be used for biochemical simulations with applications in fundamental biology, biotechnology and biocomputing.This work is an extended version of the work presented at the conference CMSB2019., Comment: arXiv admin note: text overlap with arXiv:1905.00235

Early Access; International audience; Genetic variability, epigenetic variability, and gene expression variability (noise) are generally considered independently in their relationship with phenotypic variation. However, they appear to be intrinsically interconnected and influence it in combination. The study of the interplay between genetic and epigenetic variability has the longest history. This article rather considers the introduction of gene expression variability in its relationships with the two others and reviews for the first time experimental evidences over the four relationships connected to gene expression noise. They show how introducing this third source of variability complicates the way of thinking evolvability and the emergence of biological novelty. Finally, cancer cells are proposed to be an ideal model to decipher the dynamic interplay between genetic, epigenetic, and gene expression variability when one of them is either experimentally increased or therapeutically targeted. This interplay is also discussed in an evolutionary perspective in the context of cancer cell drug resistance.

Variation in gene expression among genetically identical individual cells (called gene expression noise) directly contributes to phenotypic diversity. Whether such variation can impact genome stability and lead to variation in genotype remains poorly explored. We addressed this question by investigating whether noise in the expression of genes affecting homologous recombination (HR) activity either directly (RAD52) or indirectly (RAD27) confers cell-to-cell heterogeneity in HR rate inSaccharomyces cerevisiae. Using cell sorting to isolate subpopulations with various expression levels, we show that spontaneous HR rate is highly heterogeneous from cell-to-cell in clonal populations depending on the cellular amount of proteins affecting HR activity. Phleomycin-induced HR is even more heterogeneous, showing thatRAD27expression noise strongly affects the rate of recombination from cell-to-cell. Strong variations in HR rate between subpopulations are not correlated to strong changes in cell cycle stage. Moreover, this heterogeneity occurs even when simultaneously sorting cells at equal expression level of another gene involved in DNA damage response (BMH1) that is upregulated by DNA damage, showing that the initiating DNA damage is not responsible for the observed heterogeneity in HR rate. Thus gene expression noise seems mainly responsible for this phenomenon. Finally, HR rate non-linearly scales with Rad27 levels showing that total amount of HR cannot be explained solely by the time- or population-averaged Rad27 expression. Altogether, our data reveal interplay between heterogeneity at the gene expression and genetic levels in the production of phenotypic diversity with evolutionary consequences from microbial to cancer cell populations.

A population of genetically identical individuals sharing the same environment exhibits some residual phenotypic variability. Such heterogeneity arises from the stochastic, or random, nature of gene expression also referred as noise. This stochasticity results on the one hand from the random encounter of chemical species during both transcription and translation (intrinsic noise), and on the other hand from the fluctuations in the concentration of these chemicals (extrinsic noise). A stochastic model involving only intrinsic noise predicts that phenotypic noise strength varies linearly with translational efficiency but does not depend on transcriptional one. This prediction was shown to be compatible with data on a limited number of strains and conditions but has never been fully tested on a large collection of strains with different transcription and translation efficiencies. We aim to go further in the test of this prediction by using a collection of ~40 strains of the bacterium Bacillus subtilis where GFP is expressed under the control of different Promoters, TSS and RBS. For each strain, cell-to-cell heterogeneity is investigated by quantifying fluorescence signal at the single cell level, based on flow cytometry techniques and epifluorescence microscopy. Our results show that, contrary to expectations, phenotypic noise strength shows a strong positive correlation with transcriptional efficiency. We demonstrated that over a wide range of expression covering most of the proteome of B. subtilis, the expression noise is dominated by external noise sources. Therefore, stochastic models of gene expression are not suitable for quantifying the effects of translation and transcription on gene expression noise.; Une population d'individus génétiquement identiques partageant le même environnement présente une certaine variabilité phénotypique résiduelle. Cette hétérogénéité découle de la nature stochastique, ou aléatoire, de l'expression des gènes, également appelée bruit. Cette stochasticité résulte d'une part de la rencontre aléatoire d'espèces chimiques pendant la transcription et la traduction (bruit intrinsèque), et d'autre part des fluctuations dans la concentration de ces substances chimiques (bruit extrinsèque). Un modèle stochastique ne faisant intervenir que le bruit intrinsèque prédit que la force du bruit phénotypique varie linéairement avec l'efficacité de la traduction, mais qu'il ne dépend pas du taux de transcription. Cette prédiction s'est révélée compatible avec des données portant sur un nombre limité de souches et de conditions, mais n'a jamais été entièrement testée sur un grand nombre de souches ayant différentes efficacités de transcription et de traduction. Notre objectif est d'aller plus loin dans le test de cette prédiction en utilisant une collection d'une quarantaine de souches de la bactérie Bacillus subtilis où la protéine GFP est exprimée sous le contrôle de différents promoteurs, TSS et RBS. Pour chaque souche, l'hétérogénéité entre cellules est étudiée en quantifiant le signal de fluorescence au niveau de la cellule unique, à l'aide de techniques de cytométrie en flux et de microscopie en épifluorescence. Nos résultats montrent que, contrairement aux attentes, la force du bruit phénotypique montre une forte corrélation positive avec l'efficacité transcriptionnelle. Nous avons démontré que sur une large gamme d'expression couvrant la majeure partie du protéome de B. subtilis, le bruit d'expression est dominé par les sources de bruit extrinsèques. Par conséquent, les modèles stochastiques d'expression génique ne conviennent pas pour quantifier les effets de la traduction et de la transcription sur le bruit d'expression génétique.

A population of genetically identical individuals sharing the same environment exhibits some residual phenotypic variability. Such heterogeneity arises from the stochastic, or random, nature of gene expression also referred as noise. This stochasticity results on the one hand from the random encounter of chemical species during both transcription and translation (intrinsic noise), and on the other hand from the fluctuations in the concentration of these chemicals (extrinsic noise). A stochastic model involving only intrinsic noise predicts that phenotypic noise strength varies linearly with translational efficiency but does not depend on transcriptional one. This prediction was shown to be compatible with data on a limited number of strains and conditions but has never been fully tested on a large collection of strains with different transcription and translation efficiencies. We aim to go further in the test of this prediction by using a collection of ~40 strains of the bacterium Bacillus subtilis where GFP is expressed under the control of different Promoters, TSS and RBS. For each strain, cell-to-cell heterogeneity is investigated by quantifying fluorescence signal at the single cell level, based on flow cytometry techniques and epifluorescence microscopy. Our results show that, contrary to expectations, phenotypic noise strength shows a strong positive correlation with transcriptional efficiency. We demonstrated that over a wide range of expression covering most of the proteome of B. subtilis, the expression noise is dominated by external noise sources. Therefore, stochastic models of gene expression are not suitable for quantifying the effects of translation and transcription on gene expression noise., Une population d'individus génétiquement identiques partageant le même environnement présente une certaine variabilité phénotypique résiduelle. Cette hétérogénéité découle de la nature stochastique, ou aléatoire, de l'expression des gènes, également appelée bruit. Cette stochasticité résulte d'une part de la rencontre aléatoire d'espèces chimiques pendant la transcription et la traduction (bruit intrinsèque), et d'autre part des fluctuations dans la concentration de ces substances chimiques (bruit extrinsèque). Un modèle stochastique ne faisant intervenir que le bruit intrinsèque prédit que la force du bruit phénotypique varie linéairement avec l'efficacité de la traduction, mais qu'il ne dépend pas du taux de transcription. Cette prédiction s'est révélée compatible avec des données portant sur un nombre limité de souches et de conditions, mais n'a jamais été entièrement testée sur un grand nombre de souches ayant différentes efficacités de transcription et de traduction. Notre objectif est d'aller plus loin dans le test de cette prédiction en utilisant une collection d'une quarantaine de souches de la bactérie Bacillus subtilis où la protéine GFP est exprimée sous le contrôle de différents promoteurs, TSS et RBS. Pour chaque souche, l'hétérogénéité entre cellules est étudiée en quantifiant le signal de fluorescence au niveau de la cellule unique, à l'aide de techniques de cytométrie en flux et de microscopie en épifluorescence. Nos résultats montrent que, contrairement aux attentes, la force du bruit phénotypique montre une forte corrélation positive avec l'efficacité transcriptionnelle. Nous avons démontré que sur une large gamme d'expression couvrant la majeure partie du protéome de B. subtilis, le bruit d'expression est dominé par les sources de bruit extrinsèques. Par conséquent, les modèles stochastiques d'expression génique ne conviennent pas pour quantifier les effets de la traduction et de la transcription sur le bruit d'expression génétique.

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.; L'expression des gènes dans les cellules a longtemps été observable uniquement à travers des quantités moyennes mesurées sur des populations. L'arrivée des techniques « single-cell » permet aujourd'hui de mesurer des niveaux d'ARN et de protéines dans des cellules individuelles : il s'avère que même dans une population de génome identique, la variabilité entre les cellules est parfois très forte. En particulier, une description moyenne est insuffisante pour étudier la différenciation cellulaire, c'est-à-dire la façon dont les cellules souches effectuent des choix de spécialisation. Dans cette thèse, on s'intéresse à l'émergence de tels choix à partir de réseaux de régulation sous-jacents entre les gènes, que l'on souhaiterait pouvoir inférer à partir de données. Le point de départ est la construction d'un modèle stochastique de réseau de gènes capable de reproduire les observations à partir d'arguments physiques. Les gènes sont alors décrits comme un système de particules en interaction qui se trouve être un processus de Markov déterministe par morceaux, et l'on cherche à obtenir un modèle statistique à partir de sa loi invariante. Nous présentons deux approches : la première correspond à une approximation de champ auto-cohérent assez populaire en physique, pour laquelle nous obtenons un résultat de concentration, et la deuxième se base sur un cas particulier que l'on sait résoudre explicitement, ce qui aboutit à un champ de Markov caché aux propriétés intéressantes.

International audience; The increase in phenotypic variability through gene expression noise is proposed to be an evolutionary strategy in selective environments. Differences in promoter-mediated noise between Saccharomyces cerevisiae strains could have been selected for thanks to the benefit conferred by gene expression heterogeneity in the stressful conditions, for instance, those experienced by industrial strains. Here, we used a genome-wide approach to identify promoters conferring high noise levels in the industrial wine strain EC1118. Many promoters of genes related to environmental factors were identified, some of them containing genetic variations compared with their counterpart in the laboratory strain S288c. Each variant of eight promoters has been fused to yeast-Enhanced Green Fluorescent Protein and integrated in the genome of both strains. Some industrial variants conferred higher expression associated, as expected, with lower noise, but other variants either increased or decreased expression without modifying variability, so that they might exhibit different levels of transcriptional-mediated noise at equal mean. At different induction conditions giving similar expression for both variants of the CUP1 promoter, we indeed observed higher noise with the industrial variant. Nevertheless, this difference was only observed in the industrial strain, revealing epistasis in the generation of promoter-mediated noise. Moreover, the increased expression variability conferred by this natural yeast promoter variant provided a clear benefit in the face of an environmental stress. Thus, modulation of gene expression noise by a combination of promoter modifications and trans-influences might be a possible adaptation mechanism in yeast.

International audience; Despite the stochastic noise that characterizes all cellular processes the cells are able to maintain and transmit to their daughter cells the stable level of gene expression. In order to better understand this phenomenon, we investigated the temporal dynamics of gene expression variation using a double reporter gene model. We compared cell clones with transgenes coding for highly stable mRNA and fluorescent proteins with clones expressing destabilized mRNA-s and proteins. Both types of clones displayed strong heterogeneity of reporter gene expression levels. However, cells expressing stable gene products produced daughter cells with similar level of reporter proteins, while in cell clones with short mRNA and protein half-lives the epigenetic memory of the gene expression level was completely suppressed. Computer simulations also confirmed the role of mRNA and protein stability in the conservation of constant gene expression levels over several cell generations. These data indicate that the conservation of a stable phenotype in a cellular lineage may largely depend on the slow turnover of mRNA-s and proteins.

Stochastic gene expression (SGE) is now considered to be an established fact and has become an important subject of research (Viñuelas et al. 2012). During the last decade, the availability of new techniques has made possible the production of more precise and more spectacular data showing the extensive variability in gene expression occurring between individual cells. However, evidence supporting probabilistic models of cell behaviour and gene expression has been available for quite a long time – for example, see the reviews in Laforge et al. (2005) and Golubev (2010). It should be noted that the first model of stochastic cell differentiation was proposed in 1964 (Till et al. 1964), which is almost at the same time as the genetic programming theory (Jacob and Monod 1961), which is deterministic in nature. One can thus wonder why the determinist view of biology has remained dominant for such a long time, and what makes a probabilistic view more acceptable nowadays? In this short paper, I will briefly argue that there is a strong epistemological obstacle to the acceptance of probabilism in biology, and that even today SGE is not integrated into a fully probabilistic approach of cellular processes, but rather into a concept that I call ‘determinism with noise’. I will argue that a new fully probabilistic theoretical framework is needed to truly integrate the stochastic aspects of cell physiology.

Biochemical reactions underlying the functioning of cells are inherently stochastic processes. As a consequence, the whole system is noisy and undergoes fluctuations in its fundamental components. Proteins are major players in the life of a cell; their stochastic character manifests itself through striking differences in phenotypes, even in the case of cloned cells exposed to identical environmental conditions. Given the context, it is crucial that models embrace realistic assumptions. In this thesis we have introduced a new mathematical framework based on Marked Poisson Point Processes (MPPP) to describe the main steps of the production of a specific protein. We were able to overcome the restrictive assumption, crucial in the classical framework, of an exponentially distributed duration of all steps. The non-Markovian description of gene expression obtained through this new framework has allowed us to propose a more realistic model of gene expression, which includes protein elongation step and protein dilution due to volume growth. We also made the first steps towards a modeling of the production of many proteins, considering interactions as the result of the competition for common resources. The system of production is studied via a mean-field approach. The multi-protein model brings a completely new approach in the domain and marks a new direction in the investigation of protein fluctuations at the cellular level. In conclusion, the thesis has focused on the study of the stochastic nature of gene expression, by developing different models in order to progress towards a more realistic description of the phenomena.; Les réactions biochimiques sous-jacentes au fonctionnement des cellules sont des processus intrinsèquement stochastiques. En conséquence, le fonctionnement de la cellule, considérée comme un système, est aléatoire en raison des fluctuations de ses composantes fondamentales. Parmi ces dernières se trouvent les protéines, qui jouent un rôle majeur dans les cellules. Le caractère stochastique des protéines est tel qu'il est même responsable des différences observées dans le phénotype et ce même dans le cas de cellules clonées exposées à des conditions environnementales identiques. Dans ce travail de thèse nous avons mis en place un nouveau cadre mathématique basé sur les Processus Ponctuels de Poisson Marqués (MPPP) pour décrire les principales étapes de la production d'une protéine spécifique. Avec ce cadre, nous avons réussi à surmonter l'hypothèse fondamentale et restrictive des modèles classiques, ce qui exige une durée exponentielle de toutes les étapes. La description non-markovienne de l'expression génétique obtenue a permis de proposer un modèle plus réaliste comprenant l'étape d'élongation de la protéine et de la dilution des protéines en raison de la croissance du volume. Nous avons également proposé une première modélisation de la production de plusieurs protéines en considérant les interactions comme le résultat de la compétition pour des ressources communes. Le système de production est étudié par une approche de champ moyen. En conclusion, la thèse a porté sur l'étude de la nature stochastique de l'expression génétique, en développant différents modèles afin de progresser vers une description plus réaliste des phénomènes.

We aim to investigate the management of the stochastic noise in gene expression and more precisely the study of noise in dynamical cellular responses. How the noise varies following a perturbation? What mechanisms are at play? How important is noise in the cellular function? To answer these questions, we are interested in the genetic regulatory network that handles the nutritional stress response in E. Coli. The noise of gene expression is quantified in a key node of the network control. For that bacteria are followed individually by fluorescence and phase contrast microscopy over several generations. This variability between cells is quantified throughout the response to the nutritional perturbation: at every moment, we know the density distribution of cellular fluorescence in the cell population. And monitoring of individual lines allows us to take into account only the population of healthy cells: individuals that do not divide neither grow, are discarded. Thereby reducing other sources of variability (e.g. cellular phenomena) we reduce the number of parameters. Noise sources are less numerous, and it is easier to understand the mechanisms at play. Also the information on cell lineage allow to study the variability introduced by the phase of the cell cycle: the events of cell division can be artificially synchronized. This study shows that the noise sounded is not dominated by differences in the phase of the cell cycle. We can therefore model our cells regardless of the differences introduced by the cell cycle. The tested model is simplified to the steps of transcription-translation-maturation. The model parameters are inferred from our experimental data and the model is tested through simulations., Nous nous proposons d'étudier la gestion du bruit stochastique d'expression génique. On s'intéresse plus particulièrement à la dynamique du bruit lors de la réponse cellulaire. Comment évolue le bruit? Quels sont les mécanismes en jeux? Quelle est l'importance du bruit dans le fonctionnement cellulaire? Pour répondre à ces questions, nous nous appuyons sur le réseau de régulation génétique qui gère la réponse au stress nutritionnel chez E. Coli. L'étude du comportement dynamique de ce réseau, au niveau d'une population de bactéries, a été initiée et est portée par la forte collaboration de deux équipes de la région : une de bio-informaticiens (l'équipe de Hidde de Jong de l'INRIA Rhône-Alpes) et la deuxième de biologistes (l'équipe de Hans Geiselmann, Laboratoire d'Adaptation et Pathogénie des Micro-organismes). En profitant donc de l'expérience et de la compréhension acquise par ces équipes, nous étudions les réponses individuelles de chaque bactérie lors de la transition entre état de stress nutritionnel, et état de croissance exponentielle. Le bruit d'expression génique est quantifié dans des nœuds clés du réseau de régulation. Pour ce faire, les bactéries sont suivies individuellement par microscopie de fluorescence sur plusieurs générations. Les données de fluorescence collectées sur cellules uniques permettent d'étudier la variabilité inter-cellulaire. Cette variabilité est quantifiée tout le long de la réponse: à chaque instant, on connaît la distribution des densités de fluorescence cellulaire dans la population de cellules. Et le suivi des lignées individuelles permet de travailler sur une population de cellules saines: les individus malades ou morts qui ne se divisent pas, sont écartés. En réduisant ainsi les phénomènes cellulaires en jeux, on réduit le nombre de paramètres. Les sources de bruit sont moins nombreuses, et il est plus facile de comprendre les mécanismes en jeux. Les informations de lignage cellulaire permettent aussi d'étudier la variabilité introduite par la phase du cycle cellulaire: les événements de division cellulaire peut être artificiellement synchronisés. Le bruit est alors étudié sur une population en phase lors de la division. Cette étude montre que le bruit sondé n'est pas dominé par les différences dans la phase du cycle cellulaire. On peut donc modéliser nos cellules sans tenir compte des différences introduites par le cycle cellulaire. Le modèle testé est simplifié aux étapes de transcription-traduction-maturation. Les paramètres du modèle sont inférés de nos données expérimentales, et le modèle est testé à travers des simulations.

Current differentiation therapies for cancer may not be effective because it might not be enough to only use molecules targeting chromatin remodelers. It may also be necessary to stabilize the re-expressed genes to convert malignant cells into benign ones.