A Stochastic Analysis of Autoregulation of Gene Expression

This paper analyzes, in the context of a prokaryotic cell, the stochastic variability of the number of proteins when there is a control of gene expression by an autoregulation scheme. The goal of this work is to estimate the efficiency of the regulation to limit the fluctuations of the number of copies of a given protein. The autoregulation considered in this paper relies mainly on a negative feedback: the proteins are repressors of their own gene expression. The efficiency of a production process without feedback control is compared to a production process with an autoregulation of the gene expression assuming that both of them produce the same average number of proteins. The main characteristic used for the comparison is the standard deviation of the number of proteins at equilibrium. With a Markovian representation and a simple model of repression, we prove that, under a scaling regime, the repression mechanism follows a Hill repression scheme with an hyperbolic control. An explicit asymptotic expression of the variance of the number of proteins under this regulation mechanism is obtained. Simulations are used to study other aspects of autoregulation such as the rate of convergence to equilibrium of the production process and the case where the control of the production process of proteins is achieved via the inhibition of mRNAs

Stochastic Gene Expression in Cells: A Point Process Approach

This paper investigates the stochastic fluctuations of the number of copies of a given protein in a cell. This problem has already been addressed in the past and closed-form expressions of the mean and variance have been obtained for a simplified stochastic model of the gene expression. These results have been obtained under the assumption that the duration of all the protein production steps are exponentially distributed. In such a case, a Markovian approach (via Fokker-Planck equations) is used to derive analytic formulas of the mean and the variance of the number of proteins at equilibrium. This assumption is however not totally satisfactory from a modeling point of view since the distribution of the duration of some steps is more likely to be Gaussian, if not almost deterministic. In such a setting, Markovian methods can no longer be used. A finer characterization of the fluctuations of the number of proteins is therefore of primary interest to understand the general economy of the cell. In this paper, we propose a new approach, based on marked Poisson point processes, which allows to remove the exponential assumption. This is applied in the framework of the classical three stages models of the literature: transcription, translation and degradation. The interest of the method is shown by recovering the classical results under the assumptions that all the durations are exponentially distributed but also by deriving new analytic formulas when some of the distributions are not anymore exponential. Our results show in particular that the exponential assumption may, surprisingly, underestimate significantly the variance of the number of proteins when some steps are in fact not exponentially distributed. This counter-intuitive result stresses the importance of the statistical assumptions in the protein production process

Models of protein production along the cell cycle: an investigation of possible sources of noise

In this article, we quantitatively study, through stochastic models, the efects of several intracellular phenomena, such as cell volume growth, cell division, gene replication as well as fuctuations of available RNA polymerases and ribosomes. These phenomena are indeed rarely considered in classic models of protein production and no relative quantitative comparison among them has been performed. The parameters for a large and representative class of proteins are determined using experimental measures. The main important and surprising conclusion of our study is to show that despite the signifcant fuctuations of free RNA polymerases and free ribosomes, they bring little variability to protein production contrary to what has been previously proposed in the literature. After verifying the robustness of this quite counter-intuitive result, we discuss its possible origin from a theoretical view, and interpret it as the result of a mean-feld efect

A RBA model for the chemostat modeling

A RBA model for the chemostat modeling. 58. Conference on Decision and Contro

Reduced Complexity Controllers for LPV Systems: Towards Incremental Synthesis

International audienceExisting synthesis methods for LPV systems often result in controllers of high complexity. So far, there is no efficient and systematic remedy to this issue as there exists no convex formulation of the problem of finding a solution of reduced complexity to the general case LPV synthesis problem. In this paper, the specific case is considered when parameter-dependent signals are measured. It is proven that these measures can be exploited so that the problem of reduced-complexity controller synthesis can be written as an LMI optimization problem. A complete procedure for the controller construction is provided. The interest of the result is discussed in relation with nonlinear methods. First, an interpretation of the controller strategy is proposed with regard to the feedback linearization method. Second, it is proven that a nonlinear controller ensuring the closed loop incremental properties can be constructed

Stability and performance analysis of classical decentralized control of irrigation canals

Irrigation canals have a series structure which is generally used to design multivariable controllers based on the aggregation of decentralized monovariable controllers. SISO controllers are designed for each canal pool, assuming that the interactions will not destabilize the overall system. It is shown that, when the canal pools are controlled using the discharge at one boundary, the multivariable decentralized control structure is stable if and only if the SISO controllers are stable. The performance of the multivariable system is also investigated, and it is shown that the interactions decrease the overall performance of the controlled system. This loss of performance can be reduced by using a feedforward controller. Experimental results show the effectiveness of the method

Etude de la réponse de Saccharomyces cerevisiae à une perturbation NADPH par une approche de biologie des systèmes

L'élucidation des propriétés du réseau métabolique est fondamentale pour la compréhension du fonctionnement cellulaire et pour l'élaboration de stratégies d'ingénierie métabolique. L'objectif de cette thèse était de mieux comprendre la régulation du métabolisme du NADPH, un métabolite "hub" qui joue un rôle central dans de nombreux processus cellulaires, chez Saccharomyces cerevisiae en fermentation. Nous avons utilisé une démarche systématique couplant modélisation et approches multi- omics pour étudier de façon quantitative la réponse à une perturbation de la demande en NADPH. Un système expérimental original, basé sur l'expression d'une butanediol déshydrogénase modifiée NADPH-dépendante a été utilisé pour augmenter de façon contrôlée la demande en NADPH. L'utilisation de ce dispositif, le développement et l'utilisation d'un modèle stœchiométrique de la levure dédié à la fermentation ont permis de prédire la répartition des flux pour différents niveaux de perturbation. Ces analyses ont montré, en premier lieu, la très grande capacité de la levure à faire face à des demandes très importantes de NADPH représentant jusqu'à 40 fois la demande anabolique. Pour des demandes modérées (allant jusqu'à 20 fois la demande anabolique), la perturbation est principalement compensée par une augmentation du flux à travers la voie des pentoses phosphate (VPP) et à moindre titre à travers la voie acétate (Ald6p). Pour une forte demande en NADPH, correspondant à 40 fois la demande anabolique, le modèle prédit la saturation de la VPP ainsi que la mise en place du cycle glycérol-DHA, qui permet l'échange du NADH en NADPH. Des analyses fluxomique (13C), métabolomique et transcriptomique, ont permis de valider ces hypothèses et de les compléter. Nous avons mis en évidence différents niveaux de régulation selon l'intensité de la perturbation : pour les demandes modérées, les flux sont réajustés par un contrôle au niveau enzymatique ; pour de fortes demandes, un contrôle transcriptionnel de plusieurs gènes de la VPP ainsi que de certains gènes des voies de biosynthèse des acides aminés est observé, cet effet résultant probablement de la moindre disponibilité en NADPH. Dans l'ensemble, ce travail a apporté un nouvel éclairage sur les mécanismes impliqués dans l'homéostasie du NADPH et plus généralement dans l'équilibre redox intracellulaire.The elucidation of the properties of metabolic network is essential to increase our understanding of cellular function and to design metabolic engineering strategies. The objective of this thesis was to better understand the regulation of the metabolism of NADPH, a hub metabolite which plays a central role in many cellular processes in Saccharomyces cerevisiae during fermentation. We used a systematic approach combining modeling and multi- omics analyses to study quantitatively the response to a perturbation of the NADPH demand. An original experimental system, based on the expression of a modified NADPH-dependent butanediol dehydrogenase was used to increase the demand for NADPH in a controlled manner. Through the use of this device and the development and use of a stoichiometric model of yeast dedicated to the fermentation, we predicted the flux distribution for different levels of perturbation. These experiments showed, first, the overwhelming ability of yeast to cope with very high NADPH demand, up to 40 times the anabolic demand. For a moderate level (up to 20 times the anabolic demand), the perturbation is mainly compensated by increased flux through the pentose phosphate pathway (PPP) and to a lesser extent through the acetate pathway (Ald6p). For a high NADPH demand, corresponding to 40 times the anabolic demand, the model predicts the saturation of the PPP as well as the operation of the glycerol-DHA cycle, which allows the exchange of NADH to NADPH. Fluxomics (13C), metabolomics and transcriptomics data were used to validate and to complement these hypotheses. We showed different levels of control depending on the intensity of the perturbation: for moderate demands, flux remodeling is mainly achieved by enzymatic control; for a high demand, a transcriptional control is observed for several genes of the PPP as well as some genes of the amino acids biosynthetic pathways, this latter effect being likely due to the low NADPH availability. Overall, this work has shed new light on the mechanisms governing NADPH homeostasis and more generally the intracellular redox balance.MONTPELLIER-SupAgro La Gaillarde (341722306) / SudocSudocFranceF

Reconstruction and analysis of the genetic and metabolic regulatory networks of the central metabolism of Bacillus subtilis

International audienceBACKGROUND: Few genome-scale models of organisms focus on the regulatory networks and none of them integrates all known levels of regulation. In particular, the regulations involving metabolite pools are often neglected. However, metabolite pools link the metabolic to the genetic network through genetic regulations, including those involving effectors of transcription factors or riboswitches. Consequently, they play pivotal roles in the global organization of the genetic and metabolic regulatory networks. RESULTS: We report the manually curated reconstruction of the genetic and metabolic regulatory networks of the central metabolism of Bacillus subtilis (transcriptional, translational and post-translational regulations and modulation of enzymatic activities). We provide a systematic graphic representation of regulations of each metabolic pathway based on the central role of metabolites in regulation. We show that the complex regulatory network of B. subtilis can be decomposed as sets of locally regulated modules, which are coordinated by global regulators. CONCLUSION: This work reveals the strong involvement of metabolite pools in the general regulation of the metabolic network. Breaking the metabolic network down into modules based on the control of metabolite pools reveals the functional organization of the genetic and metabolic regulatory networks of B. subtilis

Reconciling gene expression data with regulatory network models

The reconstruction of genome-scale metabolic models from genome annotations has become a routine practice in Systems Biology research. The potential of metabolic models for predictive biology is widely accepted by the scientific community, but these same models still lack the capability to account for the effect of gene regulation on metabolic activity. Our focus organism, Bacillus subtilis is most commonly found in soil, being subject to a wide variety of external environmental conditions. This reinforces the importance of the regulatory mechanisms that allow the bacteria to survive and adapt to such conditions. We introduce a manually curated regulatory network for Bacillus subtilis, tapping into the notable resources for B. subtilis regulation. We propose the concept of Atomic Regulon, as a set of genes that share the same ON and OFF gene expression profile across multiple samples of experimental data. Atomic regulon inference uses prior knowledge from curated SEED subsystems, in addition to expression data to infer regulatory interactions. We show how atomic regulons for B. subtilis are able to capture many sets of genes corresponding to regulated operons in our manually curated network. Additionally, we demonstrate how atomic regulons can be used to help expand/ validate the knowledge of the regulatory networks and gain insights into novel biology