Identification of optimal structural connectivity using functional connectivity and neural modeling.

The complex network dynamics that arise from the interaction of the brain's structural and functional architectures give rise to mental function. Theoretical models demonstrate that the structure-function relation is maximal when the global network dynamics operate at a critical point of state transition. In the present work, we used a dynamic mean-field neural model to fit empirical structural connectivity (SC) and functional connectivity (FC) data acquired in humans and macaques and developed a new iterative-fitting algorithm to optimize the SC matrix based on the FC matrix. A dramatic improvement of the fitting of the matrices was obtained with the addition of a small number of anatomical links, particularly cross-hemispheric connections, and reweighting of existing connections. We suggest that the notion of a critical working point, where the structure-function interplay is maximal, may provide a new way to link behavior and cognition, and a new perspective to understand recovery of function in clinical conditions.

Modeling the impact of lesions in the human brain.

Lesions of anatomical brain networks result in functional disturbances of brain systems and behavior which depend sensitively, often unpredictably, on the lesion site. The availability of whole-brain maps of structural connections within the human cerebrum and our increased understanding of the physiology and large-scale dynamics of cortical networks allow us to investigate the functional consequences of focal brain lesions in a computational model. We simulate the dynamic effects of lesions placed in different regions of the cerebral cortex by recording changes in the pattern of endogenous ("resting-state") neural activity. We find that lesions produce specific patterns of altered functional connectivity among distant regions of cortex, often affecting both cortical hemispheres. The magnitude of these dynamic effects depends on the lesion location and is partly predicted by structural network properties of the lesion site. In the model, lesions along the cortical midline and in the vicinity of the temporo-parietal junction result in large and widely distributed changes in functional connectivity, while lesions of primary sensory or motor regions remain more localized. The model suggests that dynamic lesion effects can be predicted on the basis of specific network measures of structural brain networks and that these effects may be related to known behavioral and cognitive consequences of brain lesions.

Molecular modeling of peptide-MHC class I complexes : applications to peptide based immunotherapy

Summary The specific CD8+ T cell immune response against tumors relies on the recognition by the T cell receptor (TCR) on cytotoxic T lymphocytes (CTL) of antigenic peptides bound to the class I major histocompatibility complex (MHC) molecule. Such tumor associated antigenic peptides are the focus of tumor immunotherapy with peptide vaccines. The strategy for obtaining an improved immune response often involves the design of modified tumor associated antigenic peptides. Such modifications aim at creating higher affinity and/or degradation resistant peptides and require precise structures of the peptide-MHC class I complex. In addition, the modified peptide must be cross-recognized by CTLs specific for the parental peptide, i.e. preserve the structure of the epitope. Detailed structural information on the modified peptide in complex with MHC is necessary for such predictions. In this thesis, the main focus is the development of theoretical in silico methods for prediction of both structure and cross-reactivity of peptide-MHC class I complexes. Applications of these methods in the context of immunotherapy are also presented. First, a theoretical method for structure prediction of peptide-MHC class I complexes is developed and validated. The approach is based on a molecular dynamics protocol to sample the conformational space of the peptide in its MHC environment. The sampled conformers are evaluated using conformational free energy calculations. The method, which is evaluated for its ability to reproduce 41 X-ray crystallographic structures of different peptide-MHC class I complexes, shows an overall prediction success of 83%. Importantly, in the clinically highly relevant subset of peptide-HLAA*0201 complexes, the prediction success is 100%. Based on these structure predictions, a theoretical approach for prediction of cross-reactivity is developed and validated. This method involves the generation of quantitative structure-activity relationships using three-dimensional molecular descriptors and a genetic neural network. The generated relationships are highly predictive as proved by high cross-validated correlation coefficients (0.78-0.79). Together, the here developed theoretical methods open the door for efficient rational design of improved peptides to be used in immunotherapy. Résumé La réponse immunitaire spécifique contre des tumeurs dépend de la reconnaissance par les récepteurs des cellules T CD8+ de peptides antigéniques présentés par les complexes majeurs d'histocompatibilité (CMH) de classe I. Ces peptides sont utilisés comme cible dans l'immunothérapie par vaccins peptidiques. Afin d'augmenter la réponse immunitaire, les peptides sont modifiés de façon à améliorer l'affinité et/ou la résistance à la dégradation. Ceci nécessite de connaître la structure tridimensionnelle des complexes peptide-CMH. De plus, les peptides modifiés doivent être reconnus par des cellules T spécifiques du peptide natif. La structure de l'épitope doit donc être préservée et des structures détaillées des complexes peptide-CMH sont nécessaires. Dans cette thèse, le thème central est le développement des méthodes computationnelles de prédiction des structures des complexes peptide-CMH classe I et de la reconnaissance croisée. Des applications de ces méthodes de prédiction à l'immunothérapie sont également présentées. Premièrement, une méthode théorique de prédiction des structures des complexes peptide-CMH classe I est développée et validée. Cette méthode est basée sur un échantillonnage de l'espace conformationnel du peptide dans le contexte du récepteur CMH classe I par dynamique moléculaire. Les conformations sont évaluées par leurs énergies libres conformationnelles. La méthode est validée par sa capacité à reproduire 41 structures des complexes peptide-CMH classe I obtenues par cristallographie aux rayons X. Le succès prédictif général est de 83%. Pour le sous-groupe HLA-A*0201 de complexes de grande importance pour l'immunothérapie, ce succès est de 100%. Deuxièmement, à partir de ces structures prédites in silico, une méthode théorique de prédiction de la reconnaissance croisée est développée et validée. Celle-ci consiste à générer des relations structure-activité quantitatives en utilisant des descripteurs moléculaires tridimensionnels et un réseau de neurones couplé à un algorithme génétique. Les relations générées montrent une capacité de prédiction remarquable avec des valeurs de coefficients de corrélation de validation croisée élevées (0.78-0.79). Les méthodes théoriques développées dans le cadre de cette thèse ouvrent la voie du design de vaccins peptidiques améliorés.

State-of-the-art of 3D cultures (organs-on-a-chip) in safety testing and pathophysiology.

Integrated approaches using different in vitro methods in combination with bioinformatics can (i) increase the success rate and speed of drug development; (ii) improve the accuracy of toxicological risk assessment; and (iii) increase our understanding of disease. Three-dimensional (3D) cell culture models are important building blocks of this strategy which has emerged during the last years. The majority of these models are organotypic, i.e., they aim to reproduce major functions of an organ or organ system. This implies in many cases that more than one cell type forms the 3D structure, and often matrix elements play an important role. This review summarizes the state of the art concerning commonalities of the different models. For instance, the theory of mass transport/metabolite exchange in 3D systems and the special analytical requirements for test endpoints in organotypic cultures are discussed in detail. In the next part, 3D model systems for selected organs--liver, lung, skin, brain--are presented and characterized in dedicated chapters. Also, 3D approaches to the modeling of tumors are presented and discussed. All chapters give a historical background, illustrate the large variety of approaches, and highlight up- and downsides as well as specific requirements. Moreover, they refer to the application in disease modeling, drug discovery and safety assessment. Finally, consensus recommendations indicate a roadmap for the successful implementation of 3D models in routine screening. It is expected that the use of such models will accelerate progress by reducing error rates and wrong predictions from compound testing.

Prediction of Infant Drug Exposure Through Breastfeeding: Population PK Modeling and Simulation of Fluoxetine Exposure.

The likelihood of significant exposure to drugs in infants through breast milk is poorly defined, given the difficulties of conducting pharmacokinetics (PK) studies. Using fluoxetine (FX) as an example, we conducted a proof-of-principle study applying population PK (popPK) modeling and simulation to estimate drug exposure in infants through breast milk. We simulated data for 1,000 mother-infant pairs, assuming conservatively that the FX clearance in an infant is 20% of the allometrically adjusted value in adults. The model-generated estimate of the milk-to-plasma ratio for FX (mean: 0.59) was consistent with those reported in other studies. The median infant-to-mother ratio of FX steady-state plasma concentrations predicted by the simulation was 8.5%. Although the disposition of the active metabolite, norfluoxetine, could not be modeled, popPK-informed simulation may be valid for other drugs, particularly those without active metabolites, thereby providing a practical alternative to conventional PK studies for exposure risk assessment in this population.

MORM--a Petri net based model for assessing OH&S risks in industrial processes: modeling qualitative aspects.

Because of the increase in workplace automation and the diversification of industrial processes, workplaces have become more and more complex. The classical approaches used to address workplace hazard concerns, such as checklists or sequence models, are, therefore, of limited use in such complex systems. Moreover, because of the multifaceted nature of workplaces, the use of single-oriented methods, such as AEA (man oriented), FMEA (system oriented), or HAZOP (process oriented), is not satisfactory. The use of a dynamic modeling approach in order to allow multiple-oriented analyses may constitute an alternative to overcome this limitation. The qualitative modeling aspects of the MORM (man-machine occupational risk modeling) model are discussed in this article. The model, realized on an object-oriented Petri net tool (CO-OPN), has been developed to simulate and analyze industrial processes in an OH&S perspective. The industrial process is modeled as a set of interconnected subnets (state spaces), which describe its constitutive machines. Process-related factors are introduced, in an explicit way, through machine interconnections and flow properties. While man-machine interactions are modeled as triggering events for the state spaces of the machines, the CREAM cognitive behavior model is used in order to establish the relevant triggering events. In the CO-OPN formalism, the model is expressed as a set of interconnected CO-OPN objects defined over data types expressing the measure attached to the flow of entities transiting through the machines. Constraints on the measures assigned to these entities are used to determine the state changes in each machine. Interconnecting machines implies the composition of such flow and consequently the interconnection of the measure constraints. This is reflected by the construction of constraint enrichment hierarchies, which can be used for simulation and analysis optimization in a clear mathematical framework. The use of Petri nets to perform multiple-oriented analysis opens perspectives in the field of industrial risk management. It may significantly reduce the duration of the assessment process. But, most of all, it opens perspectives in the field of risk comparisons and integrated risk management. Moreover, because of the generic nature of the model and tool used, the same concepts and patterns may be used to model a wide range of systems and application fields.

Statistical Modeling of the Eye for Multimodal Treatment Planning for External Beam Radiation Therapy of Intraocular Tumors.

PURPOSE: Ocular anatomy and radiation-associated toxicities provide unique challenges for external beam radiation therapy. For treatment planning, precise modeling of organs at risk and tumor volume are crucial. Development of a precise eye model and automatic adaptation of this model to patients' anatomy remain problematic because of organ shape variability. This work introduces the application of a 3-dimensional (3D) statistical shape model as a novel method for precise eye modeling for external beam radiation therapy of intraocular tumors. METHODS AND MATERIALS: Manual and automatic segmentations were compared for 17 patients, based on head computed tomography (CT) volume scans. A 3D statistical shape model of the cornea, lens, and sclera as well as of the optic disc position was developed. Furthermore, an active shape model was built to enable automatic fitting of the eye model to CT slice stacks. Cross-validation was performed based on leave-one-out tests for all training shapes by measuring dice coefficients and mean segmentation errors between automatic segmentation and manual segmentation by an expert. RESULTS: Cross-validation revealed a dice similarity of 95% ± 2% for the sclera and cornea and 91% ± 2% for the lens. Overall, mean segmentation error was found to be 0.3 ± 0.1 mm. Average segmentation time was 14 ± 2 s on a standard personal computer. CONCLUSIONS: Our results show that the solution presented outperforms state-of-the-art methods in terms of accuracy, reliability, and robustness. Moreover, the eye model shape as well as its variability is learned from a training set rather than by making shape assumptions (eg, as with the spherical or elliptical model). Therefore, the model appears to be capable of modeling nonspherically and nonelliptically shaped eyes.

Machine learning analysis and modeling of interest rate curves

The present research deals with the review of the analysis and modeling of Swiss franc interest rate curves (IRC) by using unsupervised (SOM, Gaussian Mixtures) and supervised machine (MLP) learning algorithms. IRC are considered as objects embedded into different feature spaces: maturities; maturity-date, parameters of Nelson-Siegel model (NSM). Analysis of NSM parameters and their temporal and clustering structures helps to understand the relevance of model and its potential use for the forecasting. Mapping of IRC in a maturity-date feature space is presented and analyzed for the visualization and forecasting purposes.

Niche, distribution and global change : modeling insights into biogeography and conservation biology Olivier Broennimann

RESUME Les évidences montrant que les changements globaux affectent la biodiversité s'accumulent. Les facteurs les plus influant dans ce processus sont les changements et destructions d'habitat, l'expansion des espèces envahissantes et l'impact des changements climatiques. Une évaluation pertinente de la réponse des espèces face à ces changements est essentielle pour proposer des mesures permettant de réduire le déclin actuel de la biodiversité. La modélisation de la répartition d'espèces basée sur la niche (NBM) est l'un des rares outils permettant cette évaluation. Néanmoins, leur application dans le contexte des changements globaux repose sur des hypothèses restrictives et demande une interprétation critique. Ce travail présente une série d'études de cas investiguant les possibilités et limitations de cette approche pour prédire l'impact des changements globaux. Deux études traitant des menaces sur les espèces rares et en danger d'extinction sont présentées. Les caractéristiques éco-géographiques de 118 plantes avec un haut degré de priorité de conservation sont revues. La prévalence des types de rareté sont analysées en relation avec leur risque d'extinction UICN. La revue souligne l'importance de la conservation à l'échelle régionale. Une évaluation de la rareté à échelle globale peut être trompeuse pour certaine espèces car elle ne tient pas en compte des différents degrés de rareté que présente une espèce à différentes échelles spatiales. La deuxième étude test une approche pour améliorer l'échantillonnage d'espèces rares en incluant des phases itératives de modélisation et d'échantillonnage sur le terrain. L'application de l'approche en biologie de la conservation (illustrée ici par le cas du chardon bleu, Eryngium alpinum), permettrait de réduire le temps et les coûts d'échantillonnage. Deux études sur l'impact des changements climatiques sur la faune et la flore africaine sont présentées. La première étude évalue la sensibilité de 227 mammifères africains face aux climatiques d'ici 2050. Elle montre qu'un nombre important d'espèces pourrait être bientôt en danger d'extinction et que les parcs nationaux africains (principalement ceux situé en milieux xériques) pourraient ne pas remplir leur mandat de protection de la biodiversité dans le futur. La seconde étude modélise l'aire de répartition en 2050 de 975 espèces de plantes endémiques du sud de l'Afrique. L'étude propose l'inclusion de méthodes améliorant la prédiction des risques liés aux changements climatiques. Elle propose également une méthode pour estimer a priori la sensibilité d'une espèce aux changements climatiques à partir de ses propriétés écologiques et des caractéristiques de son aire de répartition. Trois études illustrent l'utilisation des modèles dans l'étude des invasions biologiques. Une première étude relate l'expansion de la laitue sáuvage (Lactuca serriola) vers le nord de l'Europe en lien avec les changements du climat depuis 250 ans. La deuxième étude analyse le potentiel d'invasion de la centaurée tachetée (Centaures maculosa), une mauvaise herbe importée en Amérique du nord vers 1890. L'étude apporte la preuve qu'une espèce envahissante peut occuper une niche climatique différente après introduction sur un autre continent. Les modèles basés sur l'aire native prédisent de manière incorrecte l'entier de l'aire envahie mais permettent de prévoir les aires d'introductions potentielles. Une méthode alternative, incluant la calibration du modèle à partir des deux aires où l'espèce est présente, est proposée pour améliorer les prédictions de l'invasion en Amérique du nord. Je présente finalement une revue de la littérature sur la dynamique de la niche écologique dans le temps et l'espace. Elle synthétise les récents développements théoriques concernant le conservatisme de la niche et propose des solutions pour améliorer la pertinence des prédictions d'impact des changements climatiques et des invasions biologiques. SUMMARY Evidences are accumulating that biodiversity is facing the effects of global change. The most influential drivers of change in ecosystems are land-use change, alien species invasions and climate change impacts. Accurate projections of species' responses to these changes are needed to propose mitigation measures to slow down the on-going erosion of biodiversity. Niche-based models (NBM) currently represent one of the only tools for such projections. However, their application in the context of global changes relies on restrictive assumptions, calling for cautious interpretations. In this thesis I aim to assess the effectiveness and shortcomings of niche-based models for the study of global change impacts on biodiversity through the investigation of specific, unsolved limitations and suggestion of new approaches. Two studies investigating threats to rare and endangered plants are presented. I review the ecogeographic characteristic of 118 endangered plants with high conservation priority in Switzerland. The prevalence of rarity types among plant species is analyzed in relation to IUCN extinction risks. The review underlines the importance of regional vs. global conservation and shows that a global assessment of rarity might be misleading for some species because it can fail to account for different degrees of rarity at a variety of spatial scales. The second study tests a modeling framework including iterative steps of modeling and field surveys to improve the sampling of rare species. The approach is illustrated with a rare alpine plant, Eryngium alpinum and shows promise for complementing conservation practices and reducing sampling costs. Two studies illustrate the impacts of climate change on African taxa. The first one assesses the sensitivity of 277 mammals at African scale to climate change by 2050 in terms of species richness and turnover. It shows that a substantial number of species could be critically endangered in the future. National parks situated in xeric ecosystems are not expected to meet their mandate of protecting current species diversity in the future. The second study model the distribution in 2050 of 975 endemic plant species in southern Africa. The study proposes the inclusion of new methodological insights improving the accuracy and ecological realism of predictions of global changes studies. It also investigates the possibility to estimate a priori the sensitivity of a species to climate change from the geographical distribution and ecological proprieties of the species. Three studies illustrate the application of NBM in the study of biological invasions. The first one investigates the Northwards expansion of Lactuca serriola L. in Europe during the last 250 years in relation with climate changes. In the last two decades, the species could not track climate change due to non climatic influences. A second study analyses the potential invasion extent of spotted knapweed, a European weed first introduced into North America in the 1890s. The study provides one of the first empirical evidence that an invasive species can occupy climatically distinct niche spaces following its introduction into a new area. Models fail to predict the current full extent of the invasion, but correctly predict areas of introduction. An alternative approach, involving the calibration of models with pooled data from both ranges, is proposed to improve predictions of the extent of invasion on models based solely on the native range. I finally present a review on the dynamic nature of ecological niches in space and time. It synthesizes the recent theoretical developments to the niche conservatism issues and proposes solutions to improve confidence in NBM predictions of the impacts of climate change and species invasions on species distributions.

Qualitative modeling identifies IL-11 as a novel regulator in maintaining self-renewal in human pluripotent stem cells.

Pluripotency in human embryonic stem cells (hESCs) and induced pluripotent stem cells (iPSCs) is regulated by three transcription factors-OCT3/4, SOX2, and NANOG. To fully exploit the therapeutic potential of these cells it is essential to have a good mechanistic understanding of the maintenance of self-renewal and pluripotency. In this study, we demonstrate a powerful systems biology approach in which we first expand literature-based network encompassing the core regulators of pluripotency by assessing the behavior of genes targeted by perturbation experiments. We focused our attention on highly regulated genes encoding cell surface and secreted proteins as these can be more easily manipulated by the use of inhibitors or recombinant proteins. Qualitative modeling based on combining boolean networks and in silico perturbation experiments were employed to identify novel pluripotency-regulating genes. We validated Interleukin-11 (IL-11) and demonstrate that this cytokine is a novel pluripotency-associated factor capable of supporting self-renewal in the absence of exogenously added bFGF in culture. To date, the various protocols for hESCs maintenance require supplementation with bFGF to activate the Activin/Nodal branch of the TGFβ signaling pathway. Additional evidence supporting our findings is that IL-11 belongs to the same protein family as LIF, which is known to be necessary for maintaining pluripotency in mouse but not in human ESCs. These cytokines operate through the same gp130 receptor which interacts with Janus kinases. Our finding might explain why mESCs are in a more naïve cell state compared to hESCs and how to convert primed hESCs back to the naïve state. Taken together, our integrative modeling approach has identified novel genes as putative candidates to be incorporated into the expansion of the current gene regulatory network responsible for inducing and maintaining pluripotency.

Predicting the physicochemical profile of diastereoisomeric histidine-containing dipeptides by property space analysis.

OBJECTIVES: This study aimed at measuring the lipophilicity and ionization constants of diastereoisomeric dipeptides, interpreting them in terms of conformational behavior, and developing statistical models to predict them. METHODS: A series of 20 dipeptides of general structure NH(2) -L-X-(L or D)-His-OMe was designed and synthetized. Their experimental ionization constants (pK(1) , pK(2) and pK(3) ) and lipophilicity parameters (log P(N) and log D(7.4) ) were measured by potentiometry. Molecular modeling in three media (vacuum, water, and chloroform) was used to explore and sample their conformational space, and for each stored conformer to calculate their radius of gyration, virtual log P (preferably written as log P(MLP) , meaning obtained by the molecular lipophilicity potential (MLP) method) and polar surface area (PSA). Means and ranges were calculated for these properties, as was their sensitivity (i.e., the ratio between property range and number of rotatable bonds). RESULTS: Marked differences between diastereoisomers were seen in their experimental ionization constants and lipophilicity parameters. These differences are explained by molecular flexibility, configuration-dependent differences in intramolecular interactions, and accessibility of functional groups. Multiple linear equations correlated experimental lipophilicity parameters and ionization constants with PSA range and other calculated parameters. CONCLUSION: This study documents the differences in lipophilicity and ionization constants between diastereoisomeric dipeptides. Such configuration-dependent differences are shown to depend markedly on differences in conformational behavior and to be amenable to multiple linear regression. Chirality 24:566-576, 2012. © 2012 Wiley Periodicals, Inc.

Pore-scale modeling of two-phase flow instabilities in porous media

Les problèmes d'écoulements multiphasiques en média poreux sont d'un grand intérêt pour de nombreuses applications scientifiques et techniques ; comme la séquestration de C02, l'extraction de pétrole et la dépollution des aquifères. La complexité intrinsèque des systèmes multiphasiques et l'hétérogénéité des formations géologiques sur des échelles multiples représentent un challenge majeur pour comprendre et modéliser les déplacements immiscibles dans les milieux poreux. Les descriptions à l'échelle supérieure basées sur la généralisation de l'équation de Darcy sont largement utilisées, mais ces méthodes sont sujettes à limitations pour les écoulements présentant de l'hystérèse. Les avancées récentes en terme de performances computationnelles et le développement de méthodes précises pour caractériser l'espace interstitiel ainsi que la distribution des phases ont favorisé l'utilisation de modèles qui permettent une résolution fine à l'échelle du pore. Ces modèles offrent un aperçu des caractéristiques de l'écoulement qui ne peuvent pas être facilement observées en laboratoire et peuvent être utilisé pour expliquer la différence entre les processus physiques et les modèles à l'échelle macroscopique existants. L'objet premier de la thèse se porte sur la simulation numérique directe : les équations de Navier-Stokes sont résolues dans l'espace interstitiel et la méthode du volume de fluide (VOF) est employée pour suivre l'évolution de l'interface. Dans VOF, la distribution des phases est décrite par une fonction fluide pour l'ensemble du domaine et des conditions aux bords particulières permettent la prise en compte des propriétés de mouillage du milieu poreux. Dans la première partie de la thèse, nous simulons le drainage dans une cellule Hele-Shaw 2D avec des obstacles cylindriques. Nous montrons que l'approche proposée est applicable même pour des ratios de densité et de viscosité très importants et permet de modéliser la transition entre déplacement stable et digitation visqueuse. Nous intéressons ensuite à l'interprétation de la pression capillaire à l'échelle macroscopique. Nous montrons que les techniques basées sur la moyenne spatiale de la pression présentent plusieurs limitations et sont imprécises en présence d'effets visqueux et de piégeage. Au contraire, une définition basée sur l'énergie permet de séparer les contributions capillaires des effets visqueux. La seconde partie de la thèse est consacrée à l'investigation des effets d'inertie associés aux reconfigurations irréversibles du ménisque causé par l'interface des instabilités. Comme prototype pour ces phénomènes, nous étudions d'abord la dynamique d'un ménisque dans un pore angulaire. Nous montrons que, dans un réseau de pores cubiques, les sauts et reconfigurations sont si fréquents que les effets d'inertie mènent à différentes configurations des fluides. A cause de la non-linéarité du problème, la distribution des fluides influence le travail des forces de pression, qui, à son tour, provoque une chute de pression dans la loi de Darcy. Cela suggère que ces phénomènes devraient être pris en compte lorsque que l'on décrit l'écoulement multiphasique en média poreux à l'échelle macroscopique. La dernière partie de la thèse s'attache à démontrer la validité de notre approche par une comparaison avec des expériences en laboratoire : un drainage instable dans un milieu poreux quasi 2D (une cellule Hele-Shaw avec des obstacles cylindriques). Plusieurs simulations sont tournées sous différentes conditions aux bords et en utilisant différents modèles (modèle intégré 2D et modèle 3D) afin de comparer certaines quantités macroscopiques avec les observations au laboratoire correspondantes. Malgré le challenge de modéliser des déplacements instables, où, par définition, de petites perturbations peuvent grandir sans fin, notre approche numérique apporte de résultats satisfaisants pour tous les cas étudiés. - Problems involving multiphase flow in porous media are of great interest in many scientific and engineering applications including Carbon Capture and Storage, oil recovery and groundwater remediation. The intrinsic complexity of multiphase systems and the multi scale heterogeneity of geological formations represent the major challenges to understand and model immiscible displacement in porous media. Upscaled descriptions based on generalization of Darcy's law are widely used, but they are subject to several limitations for flow that exhibit hysteric and history- dependent behaviors. Recent advances in high performance computing and the development of accurate methods to characterize pore space and phase distribution have fostered the use of models that allow sub-pore resolution. These models provide an insight on flow characteristics that cannot be easily achieved by laboratory experiments and can be used to explain the gap between physical processes and existing macro-scale models. We focus on direct numerical simulations: we solve the Navier-Stokes equations for mass and momentum conservation in the pore space and employ the Volume Of Fluid (VOF) method to track the evolution of the interface. In the VOF the distribution of the phases is described by a fluid function (whole-domain formulation) and special boundary conditions account for the wetting properties of the porous medium. In the first part of this thesis we simulate drainage in a 2-D Hele-Shaw cell filled with cylindrical obstacles. We show that the proposed approach can handle very large density and viscosity ratios and it is able to model the transition from stable displacement to viscous fingering. We then focus on the interpretation of the macroscopic capillary pressure showing that pressure average techniques are subject to several limitations and they are not accurate in presence of viscous effects and trapping. On the contrary an energy-based definition allows separating viscous and capillary contributions. In the second part of the thesis we investigate inertia effects associated with abrupt and irreversible reconfigurations of the menisci caused by interface instabilities. As a prototype of these phenomena we first consider the dynamics of a meniscus in an angular pore. We show that in a network of cubic pores, jumps and reconfigurations are so frequent that inertia effects lead to different fluid configurations. Due to the non-linearity of the problem, the distribution of the fluids influences the work done by pressure forces, which is in turn related to the pressure drop in Darcy's law. This suggests that these phenomena should be taken into account when upscaling multiphase flow in porous media. The last part of the thesis is devoted to proving the accuracy of the numerical approach by validation with experiments of unstable primary drainage in a quasi-2D porous medium (i.e., Hele-Shaw cell filled with cylindrical obstacles). We perform simulations under different boundary conditions and using different models (2-D integrated and full 3-D) and we compare several macroscopic quantities with the corresponding experiment. Despite the intrinsic challenges of modeling unstable displacement, where by definition small perturbations can grow without bounds, the numerical method gives satisfactory results for all the cases studied.

Modeling morphogen gradient formation from arbitrary realistically shaped sources.

Much of the analytical modeling of morphogen profiles is based on simplistic scenarios, where the source is abstracted to be point-like and fixed in time, and where only the steady state solution of the morphogen gradient in one dimension is considered. Here we develop a general formalism allowing to model diffusive gradient formation from an arbitrary source. This mathematical framework, based on the Green's function method, applies to various diffusion problems. In this paper, we illustrate our theory with the explicit example of the Bicoid gradient establishment in Drosophila embryos. The gradient formation arises by protein translation from a mRNA distribution followed by morphogen diffusion with linear degradation. We investigate quantitatively the influence of spatial extension and time evolution of the source on the morphogen profile. For different biologically meaningful cases, we obtain explicit analytical expressions for both the steady state and time-dependent 1D problems. We show that extended sources, whether of finite size or normally distributed, give rise to more realistic gradients compared to a single point-source at the origin. Furthermore, the steady state solutions are fully compatible with a decreasing exponential behavior of the profile. We also consider the case of a dynamic source (e.g. bicoid mRNA diffusion) for which a protein profile similar to the ones obtained from static sources can be achieved.

Implicit methods for qualitative modeling of gene regulatory networks.

Advancements in high-throughput technologies to measure increasingly complex biological phenomena at the genomic level are rapidly changing the face of biological research from the single-gene single-protein experimental approach to studying the behavior of a gene in the context of the entire genome (and proteome). This shift in research methodologies has resulted in a new field of network biology that deals with modeling cellular behavior in terms of network structures such as signaling pathways and gene regulatory networks. In these networks, different biological entities such as genes, proteins, and metabolites interact with each other, giving rise to a dynamical system. Even though there exists a mature field of dynamical systems theory to model such network structures, some technical challenges are unique to biology such as the inability to measure precise kinetic information on gene-gene or gene-protein interactions and the need to model increasingly large networks comprising thousands of nodes. These challenges have renewed interest in developing new computational techniques for modeling complex biological systems. This chapter presents a modeling framework based on Boolean algebra and finite-state machines that are reminiscent of the approach used for digital circuit synthesis and simulation in the field of very-large-scale integration (VLSI). The proposed formalism enables a common mathematical framework to develop computational techniques for modeling different aspects of the regulatory networks such as steady-state behavior, stochasticity, and gene perturbation experiments.

Predicting human resting-state functional connectivity from structural connectivity

In the cerebral cortex, the activity levels of neuronal populations are continuously fluctuating. When neuronal activity, as measured using functional MRI (fMRI), is temporally coherent across 2 populations, those populations are said to be functionally connected. Functional connectivity has previously been shown to correlate with structural (anatomical) connectivity patterns at an aggregate level. In the present study we investigate, with the aid of computational modeling, whether systems-level properties of functional networks-including their spatial statistics and their persistence across time-can be accounted for by properties of the underlying anatomical network. We measured resting state functional connectivity (using fMRI) and structural connectivity (using diffusion spectrum imaging tractography) in the same individuals at high resolution. Structural connectivity then provided the couplings for a model of macroscopic cortical dynamics. In both model and data, we observed (i) that strong functional connections commonly exist between regions with no direct structural connection, rendering the inference of structural connectivity from functional connectivity impractical; (ii) that indirect connections and interregional distance accounted for some of the variance in functional connectivity that was unexplained by direct structural connectivity; and (iii) that resting-state functional connectivity exhibits variability within and across both scanning sessions and model runs. These empirical and modeling results demonstrate that although resting state functional connectivity is variable and is frequently present between regions without direct structural linkage, its strength, persistence, and spatial statistics are nevertheless constrained by the large-scale anatomical structure of the human cerebral cortex.