Protein folding is the process during which an extended and unstructured polypeptide converts to its compact folded structure that is most often the functional state. The process has been characterized extensively in dilute buffer in-vitro during the last decades but the actual biological place for this process is the inside of living cells. The cytoplasm of a cell is filled with a plethora of different macromolecules that together occupy up to 40% of the total volume. This large amount of macromolecules restricts the available space to each individual molecule, which has been termed macromolecular crowding. Macromolecular crowding results in excluded volume effects and also increases chances for non-specific interactions. Macromolecular crowding should favor reactions that lead to a decrease in the total occupied volume by all molecules, such as folding reactions. Theoretical models have predicted that the stability of protein folded states should increase in presence of macromolecular crowding due to unfavorable effects on the extended unfolded state. To understand protein folding and function in living systems, we need to have a defined quantitative link between in-vitro dilute conditions (where most biophysical experiments are made) and in-vivo crowded conditions. An important question is thus how macromolecular crowding modifies the biophysical properties of a protein. The work underlying this thesis focused on how macromolecular crowding tunes protein equilibrium stability and kinetic folding processes. To mimic the crowded cellular environment, synthetic sugar-based polymers (Dextrans of different sizes and Ficoll 70) were used as crowding agents (crowders) in controlled in-vitro experiments. In contrast to previous studies which often have focused on one protein and one crowder at a time, the goal here was to make systematic analyses of how size, shape and concentration of the crowders affect both equilibrium and kinetic properties of structurally-different proteins. Three model proteins (cytochrome c, apoazurin and apoflavodoxin) were investigated under crowding by Ficoll 70 and different-size Dextrans, using various spectroscopic techniques such as far-UV circular dichroism and intrinsic tryptophan fluorescence. Thermodynamic models were applied to explain the experimental results. It was discovered that equilibrium stability of all three proteins increased in presence of crowding agents in a crowder concentration dependent manner. The stabilization effect was around 2-3 kJ/mol, larger for the various Dextrans than for Ficoll 70 at the same g/l, but independent of Dextran size (in the range 20 to 70 kDa). To further investigate the cause for the stabilization a theoretical crowding model was applied. In this model, Dextran and Ficoll were modeled as elongated rods and the protein was represented as a sphere, where the folded sphere representation was smaller than the unfolded sphere representation. It is notable that the observed stability changes could be reproduced by this model taking only steric interactions into account. This correlation showed that when using sugar-based crowding agents, excluded volume effects could be studied in isolation and there were no contributions from nonspecific interactions. Time-resolved experiments with apoazurin and apoflavodoxin revealed an increase in the folding rate constants while the unfolding rates were invariant in the presence of crowding agents. For apoflavodoxin and cytochrome c, the presence of crowding agents also altered the folding pathway such that it became more homogeneous (cytochrome c) and it gave less misfolding (apoflavodoxin). These results showed that macromolecular crowding restricts the conformational space of the unfolded polypeptide chain, makes the conformations more compact which, in turn, eliminates access to certain pathways. The results from kinetic and equilibrium measurements on three model proteins, together with available data from the literature, demonstrate that macromolecular crowding effects due to volume exclusion are in the order of a few kJ/mol. Considering the numerous concentration balances and cross-dependent reactions of the cellular machinery, small changes in energetics/kinetics of the magnitudes found here can still have dramatic consequences for cellular fitness. In fact local and transient changes in macromolecular crowding levels may be a way to tune biochemical reactions without invoking gene expression.

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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.

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.

This thesis has the dual purpose of raising awareness of the importance of the mixing protocol on the end products of polyelectrolyte-oppositely charged surfactant systems, and to contribute to a better understanding of the properties of bottle-brush polyelectrolytes when adsorbed onto interfaces. In the first part of this thesis work, the effects of the mixing protocol and the mixing procedure on formed polyelectrolyte-oppositely charged surfactant aggregates were investigated. It was shown that the initial properties of the aggregates were highly dependent on the mixing parameters, and that the difference between the resulting aggregates persisted for long periods of time. The second part of the studies was devoted to the surface properties of a series of bottle-brush polyelectrolytes made of charged segments and segments bearing poly(ethylene oxide) side chains; particular attention was paid to the effect of side chain to charge density ratio of the polyelectrolytes. It was shown that the adsorbed mass of the polyelectrolytes, and the corresponding number of poly(ethylene oxide) bearing segments at the interface, went through a maximum as the charge density of the polyelectrolyte was increased. Also, it was found that bottle-brush polyelectrolyte layers were desorbed quite easily when subjected to salt solutions. This observation was rationalized by the unfavourable excluded volume interactions between the side chains and the entropic penalty of confining them at an interface, which weaken the strength of the binding of the polyelectrolytes to the interface. However, it was shown that the same side chains effectively protect the adsorbed layer against desorption when the layer is exposed to solutions containing an oppositely charged surfactant. Investigation of the lubrication properties of the bottle-brush polyelectrolytes in an asymmetric (mica-silica) system also related the observed favourable frictional properties to the protective nature of the side chains. The decisive factor for achieving very low coefficients of friction was found to be the concentration of the side chains in the gap between the surfaces. Interestingly, it was shown that a brush-like conformation of the bottle-brush polyelectrolyte at the interface has little effect on achieving favourable lubrication properties. However, a brush-like conformation is vital for the resilience of the adsorbed layer against the competitive adsorption of species with a higher surface affinity. / QC 20100830