Synchronous Balanced Analysis

International audienc

Tropical Abstraction of Biochemical Reaction Networks with Guarantees

International audienceBiochemical molecules interact through modification and binding reactions, giving raise to a combinatorial number of possible biochemical species. The time-dependent evolution of concentrations of the species is commonly described by a system of coupled ordinary differential equations (ODEs). However, the analysis of such high-dimensional, non-linear system of equations is often computationally expensive and even prohibitive in practice. The major challenge towards reducing such models is providing the guarantees as to how the solution of the reduced model relates to that of the original model, while avoiding to solve the original model. In this paper, we have designed and tested an approximation method for ODE models of biochemical reaction systems, in which the guarantees are our major requirement. Borrowing from tropical analysis techniques, we look at the dominance relations among terms of each species' ODE. These dominance relations can be exploited to simplify the original model, by neglecting the dominated terms. As the dominant subsystems can change during the system's dynamics, depending on which species dominate the others, several possible modes exist. Thus, simpler models consisting of only the dominant subsystems can be assembled into hybrid, piecewise smooth models, which approximate the behavior of the initial system. By combining the detection of dominated terms with symbolic bounds propagation, we show how to approximate the original model by an assembly of simpler models, consisting in ordinary differential equations that provide time-dependent lower and upper bounds for the concentrations of the initial models species. The utility of our method is twofold. On the one hand, it provides a reduction heuristics that performs without any prior knowledge of the initial system's behavior (i.e., no simulation of the initial system is needed in order to reduce it). On the other hand, our method provides sound interval bounds for each species, and hence can serve to evaluate the faithfulness of tropicalization reduction heuristics for ODE models of biochemical reduction systems. The method is tested on several case studies

Abstractions des réseaux de réactions biochimiques

This thesis aims at studying two aspects related to the modelling of Biochemical Reaction Networks, in the context of Systems Biology. In the first part, we analyse how scale-separation in biological systems can be exploited for model reduction. We first argue for the use of rule-based models for prototyping genetic circuits, and then show how the inherent multi-scaleness of such systems can be used to devise a general model approximation method for rule-based models of genetic regulatory networks. The reduction proceeds via static analysis of the rule system. Our method relies on solid physical justifications, however not unlike other scale-separation reduction techniques, it lacks precise methods for quantifying the approximation error, while avoiding to solve the original model. Consequently, we next propose an approximation method for deterministic models of biochemical networks, in which reduction guarantees represent the major requirement. This second method combines abstraction and numerical approximation, and aims at providing a better understanding of model reduction methods that are based on time- and concentration- scale separation. In the second part of the thesis, we introduce a new re-parametrisation technique for differential equation models of biochemical networks, in order to study the effect of intracellular resource storage strategies on growth, in self-replicating mechanistic models. Finally, we aim towards the characterisation of cellular growth as an emergent property of a novel Petri Net model semantics of Biochemical Reaction Networks.Cette thèse vise à étudier deux aspects liés à la modélisation des Réseaux de Réactions Biochimiques. Dans un premier temps, nous montrons comment la séparation des échelles de temps et de concentration dans les systèmes biologiques peut être utilisée pour la réduction de modèles. Nous proposons l'utilisation des modèles par règles de réécriture pour le prototypage de circuits génétiques, puis nous exploitons le caractère multi-échelle de tels systèmes pour construire une méthode générale d’approximation de modèles. La réduction est effectuée via une analyse statique du système de règles. Notre heuristique de réduction repose sur des justifications physiques solides. Cependant, tout comme pour d'autres techniques de réduction de modèles exploitant la séparation des échelles, on note le manque de méthodes précises pour quantifier l'erreur d'approximation, tout en évitant de résoudre le modèle original. C'est pourquoi nous proposons ensuite une méthode d’approximation dans laquelle les garanties de réduction représentent l’exigence majeure. Cette seconde méthode combine abstraction et approximation numérique, et vise à fournir une meilleure compréhension des méthodes de réduction de modèles basées sur une séparation des échelles de temps et de concentration. Dans la deuxième partie du manuscrit, nous proposons une nouvelle technique de reparamétrisation pour les modèles d'équations différentielles des réseaux biochimiques, afin d'étudier l'effet des stratégies de stockage de ressources intracellulaires sur la croissance, dans des modèles mécanistiques d'auto-réplication cellulaire. Enfin, nous posons des bases pour la caractérisation de la croissance cellulaire en tant que propriété émergente d’une nouvelle sémantique des réseaux de Petri modélisant des réseaux de réactions biochimiques

Tropical Abstraction of Biochemical Reaction Networks with Guarantees

Biochemical molecules interact through modification and binding reactions, giving raise to a combinatorial number of possible biochemical species. The time-dependent evolution of concentrations of the species is commonly described by a system of coupled ordinary differential equations (ODEs). However, the analysis of such high-dimensional, non-linear system of equations is often computationally expensive and even prohibitive in practice. The major challenge towards reducing such models is providing the guarantees as to how the solution of the reduced model relates to that of the original model, while avoiding to solve the original model.In this paper, we have designed and tested an approximation method for ODE models of biochemical reaction systems, in which the guarantees are our major requirement. Borrowing from tropical analysis techniques, we look at the dominance relations among terms of each species' ODE. These dominance relations can be exploited to simplify the original model, by neglecting the dominated terms. As the dominant subsystems can change during the system's dynamics, depending on which species dominate the others, several possible modes exist. Thus, simpler models consisting of only the dominant subsystems can be assembled into hybrid, piecewise smooth models, which approximate the behavior of the initial system. By combining the detection of dominated terms with symbolic bounds propagation, we show how to approximate the original model by an assembly of simpler models, consisting in ordinary differential equations that provide time-dependent lower and upper bounds for the concentrations of the initial model's species.The utility of our method is twofold. On the one hand, it provides a reduction heuristics that performs without any prior knowledge of the initial system's behavior (i.e., no simulation of the initial system is needed in order to reduce it). On the other hand, our method provides sound interval bounds for each species, and hence can serve to evaluate the faithfulness of tropicalization reduction heuristics for ODE models of biochemical reduction systems. The method is tested on several case studies.publishe

LNCS

When designing genetic circuits, the typical primitives used in major existing modelling formalisms are gene interaction graphs, where edges between genes denote either an activation or inhibition relation. However, when designing experiments, it is important to be precise about the low-level mechanistic details as to how each such relation is implemented. The rule-based modelling language Kappa allows to unambiguously specify mechanistic details such as DNA binding sites, dimerisation of transcription factors, or co-operative interactions. Such a detailed description comes with complexity and computationally costly executions. We propose a general method for automatically transforming a rule-based program, by eliminating intermediate species and adjusting the rate constants accordingly. To the best of our knowledge, we show the first automated reduction of rule-based models based on equilibrium approximations. Our algorithm is an adaptation of an existing algorithm, which was designed for reducing reaction-based programs; our version of the algorithm scans the rule-based Kappa model in search for those interaction patterns known to be amenable to equilibrium approximations (e.g. Michaelis-Menten scheme). Additional checks are then performed in order to verify if the reduction is meaningful in the context of the full model. The reduced model is efficiently obtained by static inspection over the rule-set. The tool is tested on a detailed rule-based model of a λ-phage switch, which lists 92 rules and 13 agents. The reduced model has 11 rules and 5 agents, and provides a dramatic reduction in simulation time of several orders of magnitude

Consumers’ food choices, understanding and perceptions in response to different front-of-pack nutrition labelling systems in Belgium: results from an online experimental study

International audienceFront-of-pack nutrition labels (FoPLs) are increasingly implemented by governments internationally to support consumers to make healthier food choices. Although the Nutri-Score FOPL has officially been implemented in Belgium since April 2019, no study has been conducted before its implementation to compare the effectiveness of different FOPLs. The aim of this study was to compare food choices, objective understanding and perceptions of Belgian consumers in response to five different FOPLs, currently implemented in different countries internationally, namely the Health Star Ratings (HSR), the Multiple Traffic Lights (MTL), Nutri-Score, Guideline Daily Amounts (GDA), and Warning symbols. During the summer 2019, 1007 Belgian consumers were recruited and randomized to one of the five different FOPLs. Through an online questionnaire they were asked to choose one of three different foods within each of three categories (pizzas, cakes, breakfast cereals), as well as rank those same three foods according to nutritional quality, in the condition without as well as with FOPL. In addition, various questions were asked on their perceptions in relation to the FOPL they were exposed to. Perceptions of consumers were favorable for all FOPLs with no significant differences between the different FOPLs. There were no significant differences in food choices among the different FOPLs, but Nutri-Score performed best for ranking food products according to nutritional quality. While there were no significant differences among different FOPLs for food choices and perceptions, the Nutri-Score was the most effective FOPL in informing Belgian consumers of the nutritional quality of food products