The repertoire of cellular functions mediated by Ribonucleic acid (RNA) molecules have expanded considerably during the last two decades. The role played by RNA in controlling and regulating gene expression in viruses, prokaryotes and eukaryotes has been a matter of continuous investigations. This interest has arisen primarily due to the discoveries of cisacting RNA structures like riboswitches, ribosensors and frameshift elements, which are found in either the 5’-, 3’-untranslated regions of mRNA or in the open reading frames. These structures control gene expression at the level of translation by either sequestering the Shine-Dalgarno (SD) sequence to regulate translation initiation or modulating ribosomal positions during an active translation process. Very often, these structures comprise of an RNA pseudoknot and it has been observed that these pseudoknots exist in a dynamic equilibrium with other intermediate structures. This equilibrium could be shifted by several factors including presence of ions, metabolites, temperature and external force. RNA pseudoknots represent the most versatile and ubiquitous class of RNA structures in the cell, whose unique folding topology could be exploited in a number of ways by the cellular machinery. In this thesis, a thorough study of programmed -1 ribosomal frameshifting (-1 PRF) process, which is a well known gene regulation event employed by many RNA viruses, was carried out. -1 PRF is a translation recoding process, necessary for viruses to main-tain a stoichiometric ratio of structural: enzymatic proteins. This ratio varies among different viral species. At the heart of this process, lies an RNA pseudoknot accompanied by a seven nucleotide long sequence motif, which pauses an actively translating ribosome on mRNA and causes it to shift its reading frame. The frameshift inducing efficiency of pseudoknot depends on multiple factors, for example the time scale of ribosomal pause and RNA unfolding, subsequent refolding of structure to native/intermediate states and/or environment conditions. With the aim of illustrating the fundamentals of the process, multiple factors involved in -1 PRF were studied. Chapters 2-4 represent distinct aspects of -1 PRF process, while Chapter 5 discusses a different work concerned with nucleocytoplasmic transport of tRNA carried out by nuclear export receptor Exporting. Chapter 1 gives an overview of the different regulatory activities with which RNA structures and sequences are found to be associated and the evolution of these stud-ies. It discusses the different types of structural motifs found to constitute tertiary RNA structure and secondary structure prediction and determination techniques. A brief description of ab initio RNA structure modeling and other relevant tools and methodologies used in this work has been presented. Details of techniques used in each study have been provided in relevant chapters. Chapter 2 describes how local factors like ionic conditions, hydration patterns, presence of protonated residues and single residue mutations affect the structural dynamics of an RNA pseudoknot involved in -1 PRF from a plant luteovirus. Single residue mutations in the loop regions or certain base-pair inversions in the stem regions of pseudoknot increase the frameshift inducing ability of the pseudoknot structure, while some others decrease this efficiency. However, it was not clear how the changes made to the wild-type (WT) RNA pseudoknot from Beet Western Yellow Mosaic virus were affecting the global structure in terms of its dynamics and other parameters. To study this, multiple all-atom molecular dynamics simulations (MD) were performed on WT and mutant structures created in silico. The effect of presence and absence of magnesium ions on the structural geometry was also studied. The analysis was done to identify the increase/decrease in the number of hydrogen bonds formed by Watson-Crick base-pairs in stem region or non Watson-Crick pairs between stem and loop. Ionic and water densities were analyzed and the role of potential ribosome-pseudoknot interaction was elaborated. With the aim of mimicking ribosome induced unfolding of an RNA pseudoknot, steered molecular dynamics pulling experiments were performed. This work was done primarily to understand the unfolding pathway of Hairpin(H)-type pseudoknots in general and the intermediate structures formed. Chapter 3 describes the thermodynamics and mechanics associated with the mechanical pulling of -1 PRF inducing RNA pseudoknot and its mutants described in previous chapter. Analysis of the trajectories reveal relative unfolding patterns in terms of disruption of various hydrogen bonds. This study allowed us to pinpoint the kind of intermediate structures being formed during pulling and whether these intermediate structures correspond to any known secondary structures, such as simple stem-loops. This information could be used for gaining insights into the folding pathways of these structures. An RNA pseudoknot stimulates -1 PRF in conjunction with a heptanucleotide “slippery site” and an intervening spacer sequence. A comprehensive study of analyzing the sequence signatures and composition of all overlapping gene segments harboring these frameshift elements from four different RNA virus families was carried out. Chapter 4 describes the sequence composition of all overlapping gene segments in Astroviridae, Coronaviridae, Retroviridae and Luteoviridae viral families which are known to employ -1 PRF process for maintaining their protein products. Sequence analysis revealed preference for GC bases in the structure forming sequence regions. A comparative study between multiple sequence alignment and secondary structure prediction revealed that while pseudoknots have a clear preference for specific base-pairs in their stem regions, viral families that employ a hairpin loop as -1 PRF structure, doesn’t show this preference. Information derived from secondary structure prediction was then used for RNA ab initio modeling to generate tertiary structures. Furthermore, the structural parameters were calculated for the helices of the frameshift inducing pseudoknots and were compared with the values calculated for a set of non -1 PRF inducing H-type pseudo-knots. This study highlighted the differences between -1 PRF pseudoknots and other H-type pseudoknot structures as well as specific sequence and structural preferences of the former. Chapter 5 discusses the dynamics of a tRNA transport factor Exportint (Xpot), which transports mature tRNA molecules from nucleus to cytoplasm and belongs to Importitβ family of proteins. The global conformational dynamics of other transport receptors has been reported earlier, using coarse-grained modeling and Elastic Network Models (ENMs), but a detailed description of the dynamics at an all-atomic resolution was lacking. This transport requires association of Xpot with RanGTP, a G-protein, in the nucleus and hydrolysis of RanGTP in the cytoplasm. The chain of events leading to tRNA release from Xpot after RanGTP hydrolysis was not studied previously. With these objectives, several molecular complexes containing Xpot bound to Ran or tRNA or both in the GTP and GDP ligand states as well as free Xpot structures in nuclear and cytosolic forms were studied. A combination of conventional and accelerated molecular dynamics simulations was used to study these molecular complexes. The study highlighted various aspects associated with tRNA release and conformational change which occurs in Xpot in cytosolic form. The nuclear to cytosolic state transition in Xpot could be attributed to large fluctuations in C-terminal region and dynamic hinge-points located between specific HEAT repeats. A secondary role of Xpot in controlling the quality of tRNA transport has been proposed based on multiple sequence and structure alignment with Importin-β protein. The loss of critical contacts like hydrogen bonds and salt bridges between Xpot/Ran and Xpot/tRNA interface was evaluated in order to study the initial effects of RanGTP hydrolysis and how it influences receptor-cargo binding. This study revealed various aspects of tRNA transport process by Xpot, not understood previously. The results presented in this thesis illustrate the role of RNA sequence elements and pseudoknots present in RNA viruses in modulating -1 PRF process and how multiple environmental factors affect -1 PRF inducing ability of the structure. From the studies of Xpot and its complexes, the effects of GTP hydrolysis leading to tRNA dissociation have been presented and the progression of conformational transition in Xpot after tRNA dissociation has been highlighted. Chapter 6 summarizes major conclusions of this thesis work. The refolding of single stranded RNA chains, subjected to a previous unfolding simulation is studied. Appendix A describes this work and initial results. Appendix B describes the effect of improved molecular dynamics force fields, containing corrections for χ torsion angle for RNA, on the conformation of tertiary RNA structures. Part of the work presented in this thesis has been reported in the following publications. 1.Asmita Gupta and Manju Bansal. Local Structural and Environmental Factors De-fine the Efficiency of an RNA Pseudoknot Involved in Programmed Ribosomal Frameshift Process. J. Phys. Chem. B. 118 (41), pp 11905-11920. 2014 2.Asmita Gupta, Senthilkumar Kailasam and Manju Bansal. Insights Into Nucleo-cytoplasmic Transport of tRNA by Exportin-t. Manuscript under review. List of manuscripts that are being prepared from the work reported in Chapter 3 in this thesis. 1 Asmita Gupta and Manju Bansal. The role of sequence effects on altering the un-folding pathway of an RNA pseudoknot: a steered molecular dynamics study. Manuscript in preparation. 2 Asmita Gupta and Manju Bansal. Molecular basis for nucleocytoplasmic transport of tRNA by Exportin-t. Journal of Biomolecular Structure and Dynamics, May;33 Suppl 1:59-60, 2015

Nous étudions les propriétés des états stationnaires et de dynamiques hors-équilibre, d’un point de vue théorique et numérique. Ces dynamiques sont obtenues en perturbant la dynamique d’équilibre par forçage mécanique et/ou thermique. Dans l’approche théorique, le système considéré évolue selon une dynamique de Langevin à laquelle on ajoute une force extérieure. Nous étudions la convergence de la loi de la dynamique vers la mesure stationnaire, en donnant des estimations quantitatives du taux, dans les régimes Hamiltonien et sur amorties. Dans l’approche numérique, nous considérons une chaîne de rotateurs soumise aux deux forçages et une chaîne d’oscillateurs de Toda soumise à un forçage thermique et à une perturbation stochastique. Nous étudions les caractéristiques de l’état stationnaire et les propriétés de transport. Dans le cas de la chaîne de rotateurs nous observons en particulier que le courant d’énergie moyen est dans certains cas accru par un gradient de température opposé. / We study the properties of stationary states associated with nonequilibrium dynamics from a theoretical and a numerical point of view. These dynamics are obtained by perturbing equilibrium dynamics with mechanical and / or thermal forcings. In the theoretical approach, the system considered evolves according to a Langevin dynamics perturbed by a torque. In this framework, we study the convergence of the law of dynamics to the stationary measure, giving quantitative estimates of the exponential rate, both in the Hamiltonian and `` overdamped '' regimes.By a numerical approach, we consider a chain of rotors subjected to both forcings and a chain of Toda oscillators subject to a thermal forcing and a stochastic perturbation. We study the features of the stationary state and analyze its transport properties. In particular, in the case of the rotor chain, contrary to what is naively expected, we observe that the average energy current is in some cases increased by an opposite temperature gradient.

Cette thèse est consacrée à l’étude de deux problèmes différents : l’asymptotique suramortie de la dynamique de Langevin d’une part, et l’étude d’une technique de réduction de variance dans une méthode de Monte Carlo par une repondération optimale des échantillons, d’autre part. Dans le premier problème, on montre la convergence en distribution de processus de Langevin dans l’asymptotique sur-amortie. La preuve repose sur la méthode classique des “fonctions test perturbées”, qui est utilisée pour montrer la tension dans l’espace des chemins, puis pour identifier la limite comme solution d’un problème de martingale. L’originalité du résultat tient aux hypothèses très faibles faites sur la régularité de l’énergie potentielle. Dans le deuxième problème, nous concevons des méthodes de réduction de la variance pour l’estimation de Monte Carlo d’une espérance de type E[φ(X, Y )], lorsque la distribution de X est exactement connue. L’idée générale est de donner à chaque échantillon un poids, de sorte que la distribution empirique pondérée qui en résulterait une marginale par rapport à la variable X aussi proche que possible de sa cible. Nous prouvons plusieurs résultats théoriques sur la méthode, en identifiant des régimes où la réduction de la variance est garantie. Nous montrons l’efficacité de la méthode en pratique, par des tests numériques qui comparent diverses variantes de notre méthode avec la méthode naïve et des techniques de variable de contrôle. La méthode est également illustrée pour une simulation d’équation différentielle stochastique de Langevin / This dissertation is devoted to studying two different problems: the over-damped asymp- totics of Langevin dynamics and a new variance reduction technique based on an optimal reweighting of samples.In the first problem, the convergence in distribution of Langevin processes in the over- damped asymptotic is proven. The proof relies on the classical perturbed test function (or corrector) method, which is used (i) to show tightness in path space, and (ii) to identify the extracted limit with a martingale problem. The result holds assuming the continuity of the gradient of the potential energy, and a mild control of the initial kinetic energy. In the second problem, we devise methods of variance reduction for the Monte Carlo estimation of an expectation of the type E [φ(X, Y )], when the distribution of X is exactly known. The key general idea is to give each individual sample a weight, so that the resulting weighted empirical distribution has a marginal with respect to the variable X as close as possible to its target. We prove several theoretical results on the method, identifying settings where the variance reduction is guaranteed, and also illustrate the use of the weighting method in Langevin stochastic differential equation. We perform numerical tests comparing the methods and demonstrating their efficiency

De nos jours, il n'existe encore aucune théorie capable de proposer une description précise et quantitative du transfert de proton en solution. En effet, ce problème est complexe du fait de la grande diversité des interactions existant dans l'eau liquide, à savoir: des interactions non liantes de type Van der Waals, des liaisons faiblement covalentes et des liaisons hydrogènes remarquablement fortes. Ces dernières sont d'ailleurs à l'origine des nombreuses propriétés fascinantes de l'eau à l'échelle macroscopique. À cela s'ajoutent les effets quantiques nucléaires dus à la faible masse de l'hydrogène, qui modifient profondément la nature de la surface d'énergie potentielle décrivant le transfert de proton le long de sa coordonnée de réaction. Nous proposons dans cette thèse une approche tout quantique basée sur une description quasi exacte de la fonction d'onde du système par l'utilisation de méthodes stochastiques de type Monte Carlo Quantique. Cette technique, combinée avec le formalisme des équations de Langevin et des intégrales de chemin de Feynman, permet de simuler à un niveau de précision inédit, n'importe quel système chimique en phase gaz ou en solution. Nous appliquons cette méthodologie à des agrégats d'eau neutres ou protonés pour apporter de nouveaux éclaircissements sur les phénomènes microscopiques régissant la diffusion du proton hydraté dans de tels systèmes. Il est mis en évidence que la mobilité du proton est optimale pour des températures proches des conditions ambiantes, du fait de la compétition subtile entre les effets thermiques et quantiques nucléaires. / There is no theory up to now able to provide an accurate and quantitative description of the proton transfer (PT) yet. Indeed, the complexity of the problem stems from the large diversity of the existing interactions in liquid water, namely: non bonding Van der Waals interactions, weakly covalent bonds and remarkably strong H-bonds. The latter ones are at the origin of the numerous fascinating properties of water at the macroscopic scale. In addition to such interactions, the nuclear quantum effects arising from the hydrogen light mass deeply modify the potential energy surface, and must be taken into account. In this thesis, we propose a fully quantum approach based on an almost exact description of the electronic wave function by means of Quantum Monte Carlo (QMC) methods. Our novel technique combines QMC with a Langevin-based Molecular Dynamics and the Feynman's path integral formalism. This allows one to perform fully quantum simulations of systems in gas or condensed phase, at an unprecedented level of accuracy,. We apply our approach to neutral or charged protonated water clusters to shed light on the microscopic phenomena driving the proton diffusion in such systems. We discovered that the proton hopping is optimal for temperatures close to ambient conditions, due to the subtle competition between thermal and nuclear quantum effects. This is highly suggestive of the importance of quantum nuclear effects to make PT processes - relevant for life - most efficient at room temperature.

This thesis describes an experimental study on fluctuations of a Brownian particle immersed in a fluid, confined by optical tweezers and subject to two different kinds of non-equilibrium conditions. We aim to gain a rather general understanding of the relation between spontaneous fluctuations, linear response and total entropy production for processes away from thermal equilibrium. The first part addresses the motion of a colloidal particle driven into a periodic non-equilibrium steady state by a nonconservative force and its response to an external perturbation. The dynamics of the system is analyzed in the context of several generalized fluctuation-dissipation relations derived from different theoretical approaches. We show that, when taking into account the role of currents due to the broken detailed balance, the theoretical relations are verified by the experimental data. The second part deals with fluctuations and response of a Brownian particle in two different aging baths relaxing towards thermal equilibrium: a Laponite colloidal glass and an aqueous gelatin solution. The experimental results show that heat fluxes from the particle to the bath during the relaxation process play the same role of steady state currents as a non-equilibrium correction of the fluctuation-dissipation theorem. Then, the present thesis provides evidence that the total entropy production constitutes a unifying concept which links the statistical properties of fluctuations and the linear response function for non-equilibrium systems either in stationary or non stationary states.

Many novel graph neural network models have reported an impressive performance on benchmark dataset, but the theory behind these networks is still being developed. In this thesis, we study the trajectory of Gradient descent (GD) and Stochastic gradient descent (SGD) in the loss landscape of Graph neural networks by replicating Xing et al. [1] study for feed-forward networks. Furthermore, we empirically examine if the training process could be accelerated by an optimization algorithm inspired from Stochastic gradient Langevin dynamics and what effect the topology of the graph has on the convergence of GD by perturbing its structure. We find that the loss landscape is relatively flat and that SGD does not encounter any significant obstacles during its propagation. The noise-induced gradient appears to aid SGD in finding a stationary point with desirable generalisation capabilities when the learning rate is poorly optimized. Additionally, we observe that the topological structure of the graph plays a part in the convergence of GD but further research is required to understand how. / Många nya grafneurala nätverk har visat imponerande resultat på existerande dataset, dock är teorin bakom dessa nätverk fortfarande under utveckling. I denna uppsats studerar vi banor av gradientmetoden (GD) och den stokastiska gradientmetoden (SGD) i lösningslandskapet till grafiska faltningsnätverk genom att replikera studien av feed-forward nätverk av Xing et al. [1]. Dessutom undersöker vi empiriskt om träningsprocessen kan accelereras genom en optimeringsalgoritm inspirerad av Stokastisk gradient Langevin dynamik, samt om grafens topologi har en inverkan på konvergensen av GD genom att ändra strukturen. Vi ser att lösningslandskapet är relativt plant och att bruset inducerat i gradienten verkar hjälpa SGD att finna stabila stationära punkter med önskvärda generaliseringsegenskaper när inlärningsparametern har blivit olämpligt optimerad. Dessutom observerar vi att den topologiska grafstrukturen påverkar konvergensen av GD, men det behövs mer forskning för att förstå hur.

<div>The rise of artificial intelligence (AI) hinges on the efficient training of modern deep neural networks (DNNs) for non-convex optimization and uncertainty quantification, which boils down to a non-convex Bayesian learning problem. A standard tool to handle the problem is Langevin Monte Carlo, which proposes to approximate the posterior distribution with theoretical guarantees. However, non-convex Bayesian learning in real big data applications can be arbitrarily slow and often fails to capture the uncertainty or informative modes given a limited time. As a result, advanced techniques are still required.</div><div><br></div><div>In this thesis, we start with the replica exchange Langevin Monte Carlo (also known as parallel tempering), which is a Markov jump process that proposes appropriate swaps between exploration and exploitation to achieve accelerations. However, the na\"ive extension of swaps to big data problems leads to a large bias, and the bias-corrected swaps are required. Such a mechanism leads to few effective swaps and insignificant accelerations. To alleviate this issue, we first propose a control variates method to reduce the variance of noisy energy estimators and show a potential to accelerate the exponential convergence. We also present the population-chain replica exchange and propose a generalized deterministic even-odd scheme to track the non-reversibility and obtain an optimal round trip rate. Further approximations are conducted based on stochastic gradient descents, which yield a user-friendly nature for large-scale uncertainty approximation tasks without much tuning costs. </div><div><br></div><div>In the second part of the thesis, we study scalable dynamic importance sampling algorithms based on stochastic approximation. Traditional dynamic importance sampling algorithms have achieved successes in bioinformatics and statistical physics, however, the lack of scalability has greatly limited their extensions to big data applications. To handle this scalability issue, we resolve the vanishing gradient problem and propose two dynamic importance sampling algorithms based on stochastic gradient Langevin dynamics. Theoretically, we establish the stability condition for the underlying ordinary differential equation (ODE) system and guarantee the asymptotic convergence of the latent variable to the desired fixed point. Interestingly, such a result still holds given non-convex energy landscapes. In addition, we also propose a pleasingly parallel version of such algorithms with interacting latent variables. We show that the interacting algorithm can be theoretically more efficient than the single-chain alternative with an equivalent computational budget.</div>

Ces travaux de thèse présentent une étude expérimentale des fluctuations d'une particule Brownienne soumise à deux différentes conditions hors-équilibre dans un fluide . Le but est de comprendre d'une manière générale la relation entre les fluctuations spontanées, la fonction de réponse linéaire et la production totale d'entropie des processus loin de l'équilibre thermique. La première partie est consacrée à l'étude du mouvement d'une particule colloïdale dans un état stationnaire périodique hors-équilibre induit par une force non-conservative et à sa réponse à une perturbation externe. Nous analysons la dynamique du système dans le contexte des différentes approches généralisées de fluctuation-dissipation. Nous montrons que ces relations théoriques sont satisfaites par les données expérimentales quand on prend en compte le rôle du courant du à la rupture du bilan détaillé. Dans une deuxième partie nous étudions les fluctuations et la réponse d'une particule Brownienne dans deux types de bains vieillissants qui relaxent vers l'équilibre thermique: un verre colloïdal de Laponite et une solution aqueuse de gélatine. Dans ce cas-là nous montrons que le flux de chaleur de la particule vers le bain pendant sa relaxation représente une correction hors-équilibre du théorème de fluctuation-dissipation. Donc, le flux de chaleur joue le même rôle que le courant dans un état stationnaire. En conséquence, les résultats de la thèse mettent en évidence l'importance générale de la production totale d'entropie pour quantifier les relations de fluctuation-dissipation généralisées dans les systèmes hors-équilibre. / This thesis describes an experimental study on fluctuations of a Brownian particle immersed in a fluid, confined by optical tweezers and subject to two different kinds of non-equilibrium conditions. We aim to gain a rather general understanding of the relation between spontaneous fluctuations, linear response and total entropy production for processes away from thermal equilibrium. The first part addresses the motion of a colloidal particle driven into a periodic non-equilibrium steady state by a nonconservative force and its response to an external perturbation. The dynamics of the system is analyzed in the context of several generalized fluctuation-dissipation relations derived from different theoretical approaches. We show that, when taking into account the role of currents due to the broken detailed balance, the theoretical relations are verified by the experimental data. The second part deals with fluctuations and response of a Brownian particle in two different aging baths relaxing towards thermal equilibrium: a Laponite colloidal glass and an aqueous gelatin solution. The experimental results show that heat fluxes from the particle to the bath during the relaxation process play the same role of steady state currents as a non-equilibrium correction of the fluctuation-dissipation theorem. Then, the present thesis provides evidence that the total entropy production constitutes a unifying concept which links the statistical properties of fluctuations and the linear response function for non-equilibrium systems either in stationary or non stationary states.

Proteinadsorption ist in vielen biotechnologischen Anwendungen ubiquitär und ein zentrales Forschungsfeld in der Physik der weichen Materie. Das Verstehen der treibenden Kräfte hinter der Proteinadsorption würde zu einer besseren Kontrolle des Adsorptionsprozesses führen und die Entwicklung von Biosystemen mit beispielloser Funktionalität ermöglichen. In der vorliegenden Arbeit wird die Proteinadsorption an weichen polymerartigen Biomaterialien sowie deren physikalische Wechselwirkungen unter Verwendung von zwei unterschiedlichen neu entwickelten Ansätzen theoretisch untersucht. Im ersten Teil wird ein neues mehrkomponentiges kooperatives Bindungsmodell entwickelt, um die Gleichgewichts-Adsorption von Proteinen auf Mikrogelen zu beschreiben. Es war somit möglich, die wahre treibende Kraft der Proteinadsorption zu identifizieren, die hauptsächlich elektrostatischen Ursprungs ist. Eine Errungenschaft des kooperativen Bindungsmodells ist die Vorhersage der kompetitiven Proteinadsorption und -desorption auf das Mikrogel, die auf thermodynamischen Parametern der Adsorption von Proteinen einzelner Sorten basiert. Vergleiche zwischen Experimenten mit binären Proteinmischungen und theoretischen Berechnungen zeigten sehr gute Übereinstimmungen. Der zweite Teil fokussiert auf Protein-Wechselwirkungen mit Polyelektrolyten, um Adsorptionsprozesse auf mikroskopischer Ebene zu erklären. Dafür wurden geladene fleckige Partikel konstruiert und als Proteinmodelle verwendet, während ein einfaches Kugel-Feder-Modell für das Polyelektrolyt und Polyelektrolytbürste benutzt wurde. Ein zentraler Aspekt war die Bestimmung der freien Energie, das Potential der mittleren Kraft (PMF), für die Komplexbildung der beiden Bestandteile mit Vergleichen zur Modellentwicklungen. Die Simulationsergebnisse legen ein komplexes Wechselspiel von elektrostatischen Kräften und Ionenfreisetzungsmechanismen dar, die für die starken attraktiven Wechselwirkungen in den PMFs verantwortlich sind. / Protein adsorption is ubiquitous in many biotechnological applications and has become a central research field in soft matter. Understanding the driving forces behind protein adsorption would allow a better control of the adsorption process and the development of biosystems with unprecedented functionality. In this thesis, protein adsorption onto soft polymeric biomaterials and their physical interactions is studied theoretically by using two different and newly developed approaches. In the first part, a novel multi-component cooperative binding model is developed to describe the equilibrium adsorption of proteins onto microgels. It was thus possible to correctly identify the true driving force behind the protein adsorption which was found to be mainly of electrostatic origin. A key achievement by the cooperative binding model is the prediction of competitive protein adsorption and desorption onto the microgel that is based on thermodynamic parameters related to single-type protein adsorption without any variable parameters. Comparisons between experimental data of binary protein mixtures and theoretical calculations have shown excellent agreements. The second part is focused on protein interactions with polyelectrolyte materials to elucidate adsorption processes on a microscopic level. For this purpose, charged patchy particles are constructed and used as protein models while a simple bead-spring model is employed for the polyelectrolyte and polyelectrolyte brush. A central aspect was the determination of the associated free energy, the potential of mean force (PMF), on the complex formation between the two constituents with comparisons to theoretical model developments. The simulation results evidenced a complex interplay of electrostatic forces and ion release mechanisms to be responsible for the strong attractive interactions observed in the PMFs.

Avant-propos: Cet ouvrage se base en partie sur le travail réalisé en collaboration avec Alexia Jolicoeur-Martineau, Ioannis Mitliagkas et Rémi Tachet des Combes, réalisé en 2020 et publié à la conférence internationale d'apprentissage de représentations (ICLR 2021). Les analyses présentées dans les prochaines pages approfondissent, corrigent et ajoutent à cet ouvrage de manière substantive, sans toutefois reposer sur cet ouvrage ou quelconque connaissance couverte par ce texte. / Ce mémoire a pour but de présenter des analyses pertinentes au sujet des méthodes génératives dites Denoising Score Matching dans le but de mieux comprendre leur fonctionnement et d'améliorer les techniques existantes. Ces méthodes consistent à graduellement réduire le bruit dans une image en usant de réseaux neuraux profonds à des fins de synthèse. Tandis que les premiers chapitres contextualisent le problème du Denoising Score Matching, les chapitres suivants s’affairent à reformuler l’objectif d’entraînement du réseau neuronal, puis à analyser le processus itératif générateur. J’introduis par la suite les concepts fondateurs des méthodes de Monte Carlo par chaînes de Markov (MCMC) pour dynamiques Hamiltoniennes, que j’adapte ensuite à la synthèse d’image par réduction graduelle de bruit. Tandis que les dynamiques de Langevin ont jusqu’alors eut monopole des processus génératifs dans la littérature de synthèse par le score, les dynamiques Hamiltoniennes font l'objet d’un engouement quant à leur vitesse de convergence supérieure. Je démontre leur efficacité dans les sections suivantes et précise, dans le cas de la génération d'images complexes, les contextes dans lesquels leur usage est avantageux. Lors d’une étude d’ablation complète, je présente les gains indépendants et jumelés des améliorations proposées, et par le fait même, je contribue à notre compréhension des modèles basés sur le score. / This thesis presents pertinent analysis around generative modeling of the Denoising Score Matching family with the goals of better understanding how they work and improving existing methods. These methods work by gradually reducing noise in images using deep neural networks. While the first chapters contextualize the problem of Denoising Score Matching, the following chapters focus on reformulating the training objective of the neural network and analysing the iterative generative process. I introduce the founding concepts of Markov Chain Monte Carlo (MCMC) for Hamiltonian Dynamics and adapt them to our framework of image synthesis by annealing of Gaussian noise. While Langevin Dynamics have thus far dominated generative processes in the Denoising Score Matching literature, Hamiltonian Dynamics sustained interest from their superior convergence rate. I demonstrate their efficiency in the next chapters and elaborate on the contexts in which their use is advantageous to complex image generation. In a complete ablation study, I present the independent and coupled gains from every proposed improvements and thereby elevate our comprehension of Denoising Score Matching methods.