Mathematical models are important tools in systems biology, since the regulatory networks in biological cells are too complicated to understand by biological experiments alone. Analytical solutions can be derived only for the simplest models and numerical simulations are necessary in most cases to evaluate the models and their properties and to compare them with measured data. This thesis focuses on the mesoscopic simulation level, which captures both, space dependent behavior by diffusion and the inherent stochasticity of cellular systems. Space is partitioned into compartments by a mesh and the number of molecules of each species in each compartment gives the state of the system. We first examine how to compute the jump coefficients for a discrete stochastic jump process on unstructured meshes from a first exit time approach guaranteeing the correct speed of diffusion. Furthermore, we analyze different methods leading to non-negative coefficients by backward analysis and derive a new method, minimizing both the error in the diffusion coefficient and in the particle distribution. The second part of this thesis investigates macromolecular crowding effects. A high percentage of the cytosol and membranes of cells are occupied by molecules. This impedes the diffusive motion and also affects the reaction rates. Most algorithms for cell simulations are either derived for a dilute medium or become computationally very expensive when applied to a crowded environment. Therefore, we develop a multiscale approach, which takes the microscopic positions of the molecules into account, while still allowing for efficient stochastic simulations on the mesoscopic level. Finally, we compare on- and off-lattice models on the microscopic level when applied to a crowded environment.

Pendant longtemps, la chromatine a été uniquement décrite comme un moyen de compacter près de deux mètres d’ADN dans un noyau de quelques micromètres de diamètre. On sait aujourd’hui que la chromatine représente en fait un élément majeur de régulation de toutes les fonctions nucléaires impliquant l’ADN. Dans le contexte de dommages de l’ADN induits par irradiations UV, la chromatine endommagée subit une décondensation rapide et transitoire qui l’amène à occuper un volume 1,5 fois plus grand que son volume initial. Cette relaxation chromatinienne est associée à une plus grande accessibilité de l’ADN. Néanmoins, le lien entre ces deux effets découlant de la présence de dommages, n’a pas été établi, ni caractérisé. En couplant l’imagerie de cellules vivantes à l’induction de dommages ciblés au sein de noyaux cellulaires par micro-irradiation laser, ces travaux ont permis de mettre en évidence le rôle majeur de PARP1 dans la réponse chromatinienne aux dommages de l’ADN. En effet, certaines conclusions contradictoires présentes dans la littérature scientifique concernant l’action de PARP1 sur la chromatine ont été réconciliées en démontrant que PARP1 seul peut se lier à la chromatine et entraîner une plus forte compaction de celle-ci, tandis que son activité catalytique de PARylation va, quant à elle, conduire à une décompaction de la structure chromatinienne. Cette étude s’est aussi intéressée à la dynamique particulière de l’histone H1 suite aux dommages de l’ADN. En effet, celui-ci est rapidement exclu des zones de dommages par un mécanisme encore inconnu, et les éléments apportés ici suggèrent que H1 pourrait jouer un rôle dans la décondensation de la chromatine suite aux dommages de l’ADN. Pour finir, des techniques de photo-perturbation et de spectroscopie de corrélation de fluorescence ont été employées pour comprendre et caractériser l’environnement moléculaire que constitue la chromatine endommagée et décondensée. Bien qu’une augmentation significative des interactions entre la chromatine et certains de ses partenaires d’interactions soit observée au sein des zones endommagées, aucun changement en termes d’encombrement moléculaire n’a pu être mis en évidence à ce niveau qui pourrait expliquer une plus grande accessibilité de l’ADN. / For a long time, chromatin was only described as a mean to fit the two-meters long DNA molecule into a nucleus of only a few microns. It is admitted today that chromatin actually represents a key element in the regulation of all nuclear functions dependent on DNA. In the context of UV-induced DNA damage, chromatin undergoes a rapid and transient relaxation which leads to an expansion of the damaged area to 1.5 times its original size. While this chromatin response to damage is associated with a higher DNA accessibility, the link between those two phenomena, as well as the mechanisms driving them, are still poorly understood. Using live-cell imaging and laser micro-irradiation to induce DNA damage on specific nuclear areas, this work allowed to gain hindsight on the predominant role played by PARP1 in the DNA damage-induced chromatin relaxation. Indeed, showing that PARP1 at DNA damage sites can both induce chromatin compaction through its recruitment at DNA breaks or chromatin decondensation through its PARylation activity helped reconcile its apparent opposite effects described in the literature. A focus was also made on the linker histone H1, as it displays a peculiar behavior upon DNA damage, being rapidly released from the site of DNA lesions. Even if the driving force behind H1 release from damaged chromatin areas has not been identified yet, its behavior suggests that H1 might play a part in chromatin relaxation or in increasing DNA accessibility upon DNA damage. Lastly, combining photo-activation techniques and fluorescence correlation spectroscopy, experiments were performed in order to understand the physical environment that damaged, relaxed chromatin constitutes. We report here that, while enhanced binding of random DNA binding factors is observed in the damaged chromatin area, no significant change is observed in the macromolecular crowding levels that could potentially explain this enhanced binding, as well as a higher DNA accessibility.

La drépanocytose, ou anémie falciforme, présente une variabilité interindividuelle considérable, conditionnée par de multiples facteurs, dynamiques et interactifs, depuis le niveau moléculaire jusqu’au niveau du patient. L’hémoglobine drépanocytaire, ou hémoglobine S (HbS, tétramère a2bS 2), est un mutant de l’hémoglobine A (a2b2) : elle possède à sa surface une valine (hydrophobe) substituant un acide glutamique natif (négativement chargé). Cette mutation entraîne l’agrégation de l’HbS désoxygénée en polymères, ainsi que l’altération des propriétés de l’érythrocyte -dont sa rhéologie et ses interactions avec les différentes cellules vasculaires. C’est pourquoi la polymérisation de l’HbS constitue un facteur étiologique clef, sinon le primum movens, de la drépanocytose, et une hypothèse thérapeutique (étayée par l’observation) postule que la réduction des fibres intra-érythrocytaires de HbS pourrait améliorer le statut clinique des patients en abaissant la fréquence et la sévérité des crises vasoocclusives. Dans l’optique de mieux comprendre et de mieux gérer la variabilité individuelle drépanocytaire, il apparaît donc indispensable de disposer, en premier lieu, d’une description réaliste de la polymérisation de l’HbS. L’objectif de ce travail de thèse est la mise en place et la validation d’un modèle mathématique de la polymérisation de l’HbS désoxygénée, en tant que processus cinétiquethermodynamique, sous l’influence de la concentration et de la température –les deux facteurs modulateurs les plus importants. A partir d’un modèle existant, mais linéaire et incomplet (Ferrone et al., 1985), nous avons procédé à son implémentation, à sa correction et à sa mise à jour, ainsi qu’à l’évaluation quantitative de ses performances dynamiques, par intégration complète et simulation numérique (Simulink©). Ceci nous a permis de réaliser un diagnostic et d’effectuer un certain nombre de raffinements, concernant en particulier (i) la voie de nucléation hétérogène (formation de néo-fibres sur les fibres préexistantes), (ii) la non-idéalité de la solution protéique de HbS, induite par le volume exclus des fibres polymères (coefficients d’activité calculé à partir de la « théorie des particules convexes »), ainsi que (iii) la structuration spatiale des polymères en domaines. Le modèle développé dans ce travail servira de base pour une description (i) de l’influence dynamique de l’oxygénation et des hémoglobines non-polymérisantes sur la polymérisation de HbS, puis (ii) des polymères de HbS sur les propriétés membranaires et rhéologiques de l’érythrocyte drépanocytaire. / Sickle cell disease pathology exhibits a strong interindividual variability, which depends upon multiple, dynamic and interacting factors, from the molecular to the patient level. Sickle hemoglobin, hemoglobin S (HbS, a2bS 2 tetramer), is a mutant of HbA (a2b2), with a surface valine (hydrophobic) substituting a native glutamic acid (negatively charged). Such a mutation endows deoxygenated HbS with the propensity to agregate into polymers, altering erythrocyte properties –including its rheology and its interactions with vascular and circulatory cells. Thus HbS polymerization is a key etiological factor of sickle cell disease, if not the primum movens. Indeed, one therapeutical hypothesis (supported by observation) postulates that the reduction of intra-erythrocytic HbS fibers could improve patients clinical status by lowering the frequency and the severity of vasooclusive crisis. In order to better understand and manage sickle cell disease variability, it is essential to have a realistic description of HbS polymerization. This work aims at developing and validating a mathematical model of deoxygenated HbS polymerization, as a kinetic and thermodynamic process under the influence of concentration and temperature –the two most important modulators. Building on an existing, but linearized and uncomplete (Ferrone et al., 1985) model, we have implemented, corrected and updated, and quantitatively evaluated its dynamical performances: this was done by full numerical integration using Simulink©. This allowed us to make several improvements, related in particular to : (i) the heterogeneous nucleation pathway (seeding and formation of new fibers from pre-existing ones), (ii) the non-ideality of the HbS protein solution, caused by polymer fibers excluded volume (activity coefficients were calculated with the CPT, Convex Particle Theory), and (iii) the spatial organization of polymers into domains. The model developped in this work will ground the description of the dynamic influence (i) oxygenation and non-polymerizing hemoglobins, (ii) HbS polymers interactions with membrane and consequences upon rheological properties of sickle cell erythrocyte.

During the past decade the effects of macromolecular crowding on reaction pathways is gaining in prominence. The stress is to move out of the realms of ideal solution studies and make conceptual modifications that consider non-ideality as a variable in our calculations. In recent years it has been shown that molecular crowding exerts significant effects on all in vivo processes, from DNA conformational changes, protein folding to DNA-protein interactions, enzyme pathways and signalling pathways. Both thermodynamic as well as kinetic parameters vary by orders of magnitude in uncrowded buffer system as compared to those in the crowded cellular milieu. Ignoring these differences will restrict our knowledge of biology to a “model system” with few practical understandings. The recent expansion of the genome database has stimulated a study on numerous previously unknown proteins. This has whetted our thirst to model the cellular determinants in a more comprehensive manner. Intracellular extract would have been the ideal solution to re-create the cellular environment. However, studies conducted in this solution will be contaminated by interference with other biologically active molecule and relevant statistical data cannot be extracted out from it. Recent advances in methodologies to mimic the cellular crowding include use of inert macromolecules to reduce the volume occupancy of target molecules and the use of immobilization techniques to increase the surface density of molecules in a small volumetric region. The use of crowding agents often results in non-specific interaction and side-reactions like aggregation of the target molecules with the crowding agents themselves. Immobilization of one of the interacting partners reduces the probability of aggregation and precipitation of bio-macromolecules by restricting their degrees of freedom. Covalent linkage of molecules on solid support is used extensively in research for creating a homogeneous surface of bound molecules which can be interrogated for their reactivity. However, when it comes to biomolecules, direct immobilization on solid support or use of organic linkers often results in denaturation. The use of bio-affinity immobilization techniques can help us overcome this problem. Since mild conditions are needed to regenerate such a surface, it finds universal applicability as bio-memory chips. This thesis focuses on our attempts to design a physiologically viable immobilization technique for following rotein-protein/protein-DNA interactions. The work explores the mechanism for biological interactions related to transcription process in E. coli. Chapter 1 deals with the literary survey of the importance and effects of molecular crowding on biological reactions. It gives a brief history of the efforts been made so far by experimentalists, to mimic macromolecular crowding and the methods applied. The chapter tries to project an all-round perspective of the pros and cons of different immobilization techniques as a means to achieve a high surface density of molecules and the advancements so far. Chapter 2 deals with the detailed technicality and applicability of the Langmuir-Blodgett method. It discusses the rationale behind our developing this technique as an alternate means of bio-affinity immobilization, under physiologically compatible conditions. It then goes on to describe our efforts to follow the sequence-specific and sequential assembly process of a functional RNA polymerase enzyme with one immobilized partner and also explore the role of omega subunit of RNAP in the reconstitution pathway. This chapter uses the assembly process of a multi-subunit enzyme to evaluate the efficiency of the LB system as a universal two-dimensional scaffold to follow sequence-specific protein-ligand interaction. Chapter 3 discusses the application of LB technique to quantitatively evaluate the kinetics and thermodynamics of promoter-RNA polymerase interaction under conditions of reduced dimensionality. Here, we follow the interaction of T7A1 phage promoter with Escherichia coli RNA polymerase using our Langmuir-Blodgett technique. The changes in mechanistic pathway and trapping of kinetic intermediates are discussed in detail due to the imposed restriction in the degrees of freedom of the system. The sensitivity of this detection method is compared vis-a-vis conventional immobilization methods like SPR. This chapter firmly establishes the universal application of LB technique as a means to emulate molecular crowding and as a sensitive assay for studying the effects of such crowding on vital biological reaction pathway. Chapter 4 describes the mechanistic pathway for the physical binding of MsDps1 protein with long dsDNA in order to physically protect DNA during oxidative stress. The chapter describes in detail the mechanism of physical sequestering of non-specific DNA strands and compaction of the genome under conditions where a kinetic bottleneck has been applied. The data obtained is compared with results obtained in the previous chapter for the sequence-specific DNA-protein interaction in order to understand the difference in recognition process between regulatory and structural proteins binding to DNA. Chapter 5 deals with the evaluation of the σ-competition model in E. coli for three different sigma factors (all belonging to the σ-70 family). Here again, we have evaluated the kinetic and thermodynamic parameters governing the binding of core RNAP with its different sigma factors (σ70, σ32and σ38) and performed a comparative study for the binding of each sigma factor to its core using two different non-homogeneous immobilization techniques. The data has been analyzed globally to resolve the discrepancies associated with establishing the relative affinity of the different sigma factors for the same core RNA polymerase under physiological conditions. Chapter 6 summarizes the work presented in this thesis. In the Appendix section we have followed the unzipping of promoter DNA sequence using Optical Tweezers in an attempt to follow the temporal fluctuations occurring in biological reactions in real time and at a single molecule level.

My thesis is divided into five chapters, starting with a general introduction in first chapter and sample preparation and protein-NMR assignment techniques in second chapter. The remaining three chapters focus on three different areas/projects that I have worked on. Chapter 1: Introduction to nanomaterials and all the experimental techniques This chapter reviews different kinds of nanomaterials and their application utilized for protein-nanomaterial interaction in our study, along with the introduction to different spectroscopy and microscopy techniques used for the interaction studies. Starting with introduction of nanomaterials and all the experimental techniques, which constitute the arsenal for structural studies of the protein-nanomaterial interaction, different steps enroute to structural and dynamic interaction are outlined in detail. Chapter 2: Preparation and Characterization of Proteins used for nanomaterial interaction studies Proteins are generally of three kinds- globular (structured), intrinsically disordered and membrane bound. These proteins have different functions in living organisms and play a major role to maintain metabolism and other important factors. To probe protein-nanomaterial interactions, we have chosen different protein/peptides. This chapter describes the protocol/procedure used for purifying the proteins. For studying a globular protein, ubiquitin was chosen. Nanomaterial-IDP interaction was investigated using the intrinsically disordered central linker domain of human insulin like growth factor binding protein-2 (L-hIGFBP2). The hydrophobic membrane interacting part of the prion protein was chosen as a representative membrane protein. The characterization of the proteins by NMR spectroscopy is also described. Chapter 3: A nanomaterial based novel macromolecular crowding agent Carbon quantum dots (CQD) are nanomaterials with size less than 10 nm, first obtained in 2004 during purification of single-walled carbon-nanotubes. Since then CQDs have been used in a wide range of applications due to their low cost of preparation and favorable properties such as chemical inertness, biocompatibility, non-toxicity and solubility in aqueous medium. One of the applications of CQDs has been their use for imaging and tracking proteins inside cells, based on their intrinsic fluorescence. Further, quantum dots exhibit concentration dependent aggregation while retaining their solubility. Fluorescent carbon quantum dots (CQD) induce macromolecular crowding making them suitable for probing the structure, function and dynamics of both hydrophilic and hydrophobic peptides/ proteins under near in-cell conditions. We have prepared hydrophilic and hydrophobic quantum dots to see the crowding effect. After characterization of CQD, we tested the property of proteins with CQD and found that CQD behaves as a macromolecular crowding agent by mimicking near in-cell conditions. In our study, we have chosen a globular protein, an intrinsically disordered protein (IDP) and one hydrophobic membrane peptide. We have also compared the crowding property of CQD with ficoll which is widely used commercial crowding agent. The overall study tells that the CQD acts like crowding agent and can be used for the study of macromolecular crowding effect. This makes them suitable for structural and functional studies of proteins in near in-cell conditions. Chapter 4: Ubiquitin-Graphene oxide interactions Described here is the interaction of human ubiquitin with GO using NMR spectroscopy and other techniques such as Fluorescence spectroscopy, isothermal titration calorimetry (ITC), UV-Visible spectroscopy, dynamic light scattering (DLS), zeta potential measurements and transmission electron microscopy (TEM). The globular protein ubiquitin interacts with GO and undergoes a dynamic and reversible association-dissociation in a fast exchange regimen as revealed by NMR spectroscopy. The conformation of the protein is not affected and the primary interaction is seen to be electrostatic in nature due to the polar functional groups present on the protein and GO sheet surface. For the first time we have shown that the interaction between ubiquitin and GO is dynamic in nature with fast and reversible adsorption/desorption of protein from the surface of GO. This insight will help in understanding the mechanistic aspects of interaction of GO with cellular proteins and will help in designing appropriate functionalized graphene oxide for its biological application. Chapter 5: Section A: Interaction of an intrinsically disordered protein (L-HIGFBP2) with graphene oxide The interaction between intrinsically disordered linker domain of human insulin-like growth factor binding protein-2 (L-hIGFBP2) with GO was studied using NMR spectroscopy and other techniques such as isothermal titration calorimetry (ITC), dynamic light scattering (DLS), zeta-potential measurements. The study revealed that the disordered protein L-hIGFBP2 interacts with GO through electrostatic interaction and undergoes a dynamic and reversible association-dissociation in a fast exchange regime. The conformation of the protein is not affected. Section B: Stability of an Intrinsically disordered protein through weak interaction with Silver nanoparticles Using NMR spectroscopy and other techniques we probed the mechanism of L-hIGFBP2–AgNP interactions which render the IDP stable. The study reveals a mechanism which involves a relatively fast and reversible association–dissociation of L-hIGFBP2 (dynamic exchange) from the surface of AgNP. The AgNP–L-hIGFBP2 complex remains stable for more than a month. The techniques employed in addition to NMR include UV-Visible spectroscopy, dynamic light scattering (DLS), zeta potential measurements and transmission electron microscopy (TEM) to probe the protein-AgNP interaction here in this section.

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