Les méthodes formelles informatiques constituent un outil très puissant pour la modélisation des réseaux génétiques et en particulier pour l'étude de leur dynamique. La modélisation discrète de René Thomas permet à la fois de représenter judicieusement les connaissances biologiques et d'utiliser les méthodes formelles. Cependant, ces modèles présentent deux limitations principales : la combinatoire sous-jacente ne permet pas de traiter des réseaux de très grande taille et les aspects chronométriques ne sont pas pris en compte. Cette thèse offre deux contributions respectivement liées à ces questions. La modélisation des réseaux génétiques commence par la sélection des entités les plus pertinentes pour la question abordée. Les réseaux obtenus restent souvent trop grands et nous cherchons donc à les réduire sans altérer les propriétés dynamiques importantes. Ici, nous définissons un cadre entièrement formel inspiré d'une technique d'Aurélien Naldi pour la suppression de variables et de seuils. Ces réductions conservent les comportements asymptotiques et permettent de prouver formellement l'équivalence asymptotique de différents modèles publiés d'un même réseau. Pour prendre en compte les informations chronométriques cruciales dans certains systèmes (e.g. cycle circadien), nous définissons un formalisme hybride fondé sur le formalisme de Thomas où les niveaux d'expression sont discrets, mais le temps continu. Ce cadre permet de construire un modèle abstrait de l'horloge circadienne des mammifères qui explique avec très peu de variables les propriétés de robustesse face à des changements de durées des alternances jour/nuit. / Formal methods from computer science constitute a powerful tool for the modelling of gene networks, including the study of their dynamics. The discrete modelling of René Thomas allows for a proper representation of biological knowledge as well as for use of formal methods. These models have two main limitations: the underlying combinatorics does not allow one to process very large networks, and the chronometric aspects are not taken into account. This thesis offers two contributions according to these issues. The design of gene network models begins with a selectiCalibrion of the most relevant entities. The resulting networks are often too large, and we show how to reduce them without altering the important dynamic properties. Here, we define a completely formal framework, inspired by a technique from Aurélien Naldi, driving the suppression of variables or thresholds. These reductions preserve the asymptotic behaviour. We formally prove the asymptotic equivalence of different published models for the same network. In order to take into account chronometric information that are crucial in some systems (e.g. circadian cycle), we define a hybrid formalism based on the Thomas' formalism where expression levels are discrete but time is continuous. This framework allows for the construction of an abstract model of the circadian clock in mammals. The model explains with very few variables the robustness of the system when submitted to duration changes of the day/night alternation.

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Nuestro conocimiento de las interacciones moleculares nos ha conducido hoy hacia una perspectiva ingenieril, donde diseños e implementaciones de sistemas artificiales de regulación intentan proporcionar instrucciones fundamentales para la reprogramación celular. Nosotros aquí abordamos el diseño de redes de genes como una forma de profundizar en la comprensión de las regulaciones naturales. También abordamos el problema de la diseñabilidad dada una genoteca de elementos compatibles. Con este fin, aplicamos métodos heuríticos de optimización que implementan rutinas para resolver problemas inversos, así como herramientas de análisis matemático para estudiar la dinámica de la expresión genética. Debido a que la ingeniería de redes de transcripción se ha basado principalmente en el ensamblaje de unos pocos elementos regulatorios usando principios de diseño racional, desarrollamos un marco de diseño computacional para explotar este enfoque. Modelos asociados a genotecas fueron examinados para descubrir el espacio genotípico asociado a un cierto fenotipo. Además, desarrollamos un procedimiento completamente automatizado para diseñar moleculas de ARN no codificante con capacidad regulatoria, basándonos en un modelo fisicoquímico y aprovechando la regulación alostérica. Los circuitos de ARN resultantes implementaban un mecanismo de control post-transcripcional para la expresión de proteínas que podía ser combinado con elementos transcripcionales. También aplicamos los métodos heurísticos para analizar la diseñabilidad de rutas metabólicas. Ciertamente, los métodos de diseño computacional pueden al mismo tiempo aprender de los mecanismos naturales con el fin de explotar sus principios fundamentales. Así, los estudios de estos sistemas nos permiten profundizar en la ingeniería genética. De relevancia, el control integral y las regulaciones incoherentes son estrategias generales que los organismos emplean y que aquí analizamos. / Rodrigo Tarrega, G. (2011). Computational design and designability of gene regulatory networks [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/14179

In each individual cell, there are many signaling pathways that may interact or cross talk with each other. Especially, some can sense the same signal and go through different pathways but eventually converge at some points. Therefore repetitive signal stimulations may result in intricate cell responses, among which the priming effect has been extensively studied in monocytes and macrophages as it plays an unambiguously crucial role in immunological protection against pathogen infection. Priming basically describes the phenomena that host cells can launch a dramatically enhanced response to the second higher dose of stimulus if cells have been previously treated with a lower dose of identical stimulus. It was reported to be associated with many human immune diseases (such as rheumatoid arthritis and hepatitis) that are attracting more and more researches on the priming effect. It is undoubtable that many genes are involved in this complicated biological process. Microarray is one of the standard techniques that are applied to do the transcriptome profiling of cells under repetitive stimuli and reveal gene regulatory networks. Therefore a well-established pipeline to analyze microarray data is of special help to investigate the underlying mechanism of priming effect. In this research, we aimed to design a strategy that can be used to interpret microarray data and to propose gene candidates that potentially participate in priming effect. To confirm our analysis results, we used a detailed mathematical model to further demonstrate the mechanism of a specific case of priming effect in a computational perspective. / Master of Science

MicroRNAs represent a special class of small (~21–25 nucleotides) non-coding RNA molecules which exert powerful post-transcriptional control over gene expression in eukaryotes. Indeed microRNAs likely represent the most abundant class of regulators in animal gene regulatory networks. This study describes the recovery and network analyses of a suite of homologous microRNA targets recovered through two different prediction methods for whole gene regions across twelve Drosophila species. Phylogenetic criteria under an accepted tree topology were used as a reference frame to 1) make inference into microRNA-target predictions, 2) study mathematical properties of microRNA-gene regulatory networks, 3) and conduct novel phylogenetic analyses using character data derived from weighted edges of the microRNA-target networks. This study investigates the evidences of natural selection and phylogenetic signatures inherent within the microRNA regulatory networks and quantifies time and mutation necessary to rewire a microRNA regulatory network. Selective factors that appear to operate upon seed aptamers include cooperativity (redundancy) of interactions and transcript length. Topological analyses of microRNA regulatory networks recovered significant enrichment for a motif possessing a redundant link in all twelve species sampled. This would suggest that optimization of the whole interactome topology itself has been historically subject to natural selection where resilience to attack have offered selective advantage. It seems that only a modest number of microRNA–mRNA interactions exhibit conservation over Drosophila cladogenesis. The decrease in conserved microRNA-target interactions with increasing phylogenetic distance exhibited a cure typical of a saturation phenomena. Scale free properties of a network intersection of microRNA target predictions methods were found to transect taxonomic hierarchy.

Genetic regulatory networks can model dynamics of cells. They also allow for studying the effect of internal or external interventions. Selectively applying interventions towards a certain objective is known as controlling network dynamics. In this thesis work, the issue of how the external interventions af fect the network is studied. The effects are determined using differential gene expression analysis. The differential gene expression problem is further studied to improve the power of the given method. Control problem for dynamic discrete regulatory networks is formulated. This also addresses the needs for various control strategies, e.g., finite horizon, infinite horizon, and various accounting of state and intervention costs. Control schemes for small to large networks are proposed and experimented. A case study is provided to show how the proposals are exploited / also given is the need for and effectiveness of various control schemes.

Cell cycle (CC) and TP53 regulatory networks are frequently deregulated in cancer. While numerous genome-wide studies of TP53 and CC-regulated genes have been performed, significant variation between studies has made it difficult to assess regulation of any given gene of interest. To overcome the limitation of individual studies, we developed a meta-analysis approach to identify high confidence target genes that reflect their frequency of identification in independent datasets. Gene regulatory networks were generated by comparing differential expression of TP53 and CC-regulated genes with chromatin immunoprecipitation studies for TP53, RB1, E2F, DREAM, B-MYB, FOXM1 and MuvB. RNA-seq data from p21-null cells revealed that gene downregulation by TP53 generally requires p21 (CDKN1A). Genes downregulated by TP53 were also identified as CC genes bound by the DREAM complex. The transcription factors RB, E2F1 and E2F7 bind to a subset of DREAM target genes that function in G1/S of the CC while B-MYB, FOXM1 and MuvB control G2/M gene expression. Our approach yields high confidence ranked target gene maps for TP53, DREAM, MMB-FOXM1 and RB-E2F and enables prediction and distinction of CC regulation. A web-based atlas at www.targetgenereg.org enables assessing the regulation of any human gene of interest.

Understanding the underlying architecture of gene regulatory networks (GRNs) has been one of the major goals in systems biology and bioinformatics as it can provide insights in disease dynamics and drug development. Such GRNs are characterized by their scale-free degree distributions and existence of network motifs, which are small subgraphs of specific types and appear more abundantly in GRNs than in other randomized networks. In fact, such motifs are considered to be the building blocks of GRNs (and other complex networks) and they help achieve the underlying robustness demonstrated by most biological networks. The goal of this thesis is to design biological network (specifically, GRN) growing models. As the motif distribution in networks grown using preferential attachment based algorithms do not match that of the GRNs seen in model organisms like E. coli and yeast, we hypothesize that such models at a single node level may not properly reproduce the observed degree and motif distributions of biological networks. Hence, we propose a new network growing algorithm wherein the central idea is to grow the network one motif (specifically, we consider one downlink motif) at a time. The accuracy of our proposed algorithm was evaluated extensively and show much better performance than existing network growing models both in terms of degree and motif distributions. We also propose a complex network growing game that can identify important strategies behind motif interactions by exploiting human (i.e., gamer) intelligence. Our proposed gaming software can also help in educational purposes specifically designed for complex network studies.

Em sistemas biológicos, o estudo da estabilidade das redes de regulação gênica é visto como uma contribuição importante que a Matemática pode proporcionar a pesquisas sobre câncer e outras doenças genéticas. Neste trabalho, utilizamos o conceito de ``canalização\'\' como sinônimo de estabilidade em uma rede biológica. Como as características de uma rede de regulação canalizada ainda são superficialmente compreendidas, estudamos esse conceito sob o ponto de vista computacional: propomos um modelo matemático simplificado para descrever o fenômeno e realizamos algumas análises sobre o mesmo. Mais especificamente, a estabilidade da maior bacia de atração das redes Booleanas - um clássico paradigma para a modelagem de redes de regulação - é analisada. Os resultados indicam que a estabilidade da maior bacia de atração está relacionada com dados biológicos sobre o crescimento de colônias de leveduras e que considerações sobre a interação entre as funções Booleanas e a topologia da rede devem ser realizadas conjuntamente na análise de redes estáveis. / In biological systems, the study of gene regulatory networks stability is seen as an important contribution that Mathematics can make to cancer research and that of other genetic diseases. In this work, we consider the concept of ``canalization\'\' as a consequence of stability in gene regulatory networks. The characteristics of canalized regulatory networks are superficially understood. Hence, we study the canalization concept under a computational framework: a simplified model is proposed to describe the phenomenon using Boolean Networks - a classical paradigm to modeling regulatory networks. Specifically, the stability of the largest basin of attraction in gene regulatory networks is analyzed. Our results indicate that the stability of the largest basin of attraction is related to biological data on growth of yeast colonies, and that thoughts about the interaction between Boolean functions and network topologies must be given in the analysis of stable networks.