Search

Nanoindentation of viral capsids provides an efficient tool in order to probe their elastic properties. We investigate in the present work the various sources of stiffness heterogeneity as observed in Atomic Force Microscopy (AFM) experiments. By combining experimental results with both numerical and analytical modeling, we first show that for small viruses a position-dependent stiffness is observed. This effect is strong and has not been properly taken into account previously. Moreover, we show that a geometrical model is able to reproduce this effect quantitatively. Our work suggests alternative ways of measuring stiffness heterogeneities on small viral capsids. This is illustrated on two different viral capsids: Adeno Associated Virus serotype 8 (AAV8) and Hepatitis B Virus (HBV with T=4). We discuss our results in the light of continuous elasticity modeling., Comment: Physical Review E , American Physical Society (APS), In press

Les virus biologiques sont des entites fascinantes qui opposent une relative simplicite dans leur structure a une surprenante sophistication dans leur fonction. Bien qu’inertes, leurs centaines voire milliers de composants moleculaires s’assemblent et se desassemblent spontanement dans un milieu cellulaire heterogene et encombre, avec une precision quasi-atomique et un taux d’erreur marginal.Les concepts theoriques et experimentaux de la physique statistique et des fluides complexes permettent aujourd’hui de decrire la thermodynamique et les phenomenes hors equilibre qui regissent l’assemblage et le desassemblage de virus naturels ou synthetiques.

International audience; Molecular self-assembly on a curved substrate leads to the spontaneous inclusion of topological defects in the growing bidimensional crystal, unlike assembly on a flat substrate. We propose in this work a quantitative mechanism for this phenomenon by using standard thin shell elasticity. The Gaussian curvature of the substrate induces large in-plane compressive stress as the surface grows, in particular at the rim of the assembly, and the addition of a single defect relaxes this mechanical stress. We found out that the value of azimutal stress at the rim of the assembly determines the prefered directions for defect nucleation. These results are also discussed as function of different defect combinations, like dislocations and grain boundaries or scars. In particular, the elastic model permits to compare quantitatively the ability of various defects to relax mechanical stress. Moreover, these findings allows to understand the progressive buidling-up of the typical disclinations and grain boundaries pattern observed for ground states of large 2D spherical crystals.

Virus families have evolved different strategies for genome uncoating, which are also followed by recombinant vectors. Vectors derived from adeno-associated viruses (AAV) are considered as leading delivery tools for in vivo gene transfer, and in particular gene therapy. Using a combination of atomic force microscopy (AFM), biochemical experiments, and physical modeling, we investigated here the physical properties and stability of AAV vector particles. We first compared the morphological properties of AAV vectors derived from two different serotypes (AAV8 and AAV9). Furthermore, we triggered ssDNA uncoating by incubating vector particles to increasing controlled temperatures. Our analyses, performed at the single-particle level, indicate that genome release can occur in vitro via two alternative pathways: either the capsid remains intact and ejects linearly the ssDNA molecule, or the capsid is ruptured, leaving ssDNA in a compact entangled conformation. The analysis of the length distributions of ejected genomes further revealed a two-step ejection behavior. We propose a kinetic model aimed at quantitatively describing the evolution of capsids and genomes along the different pathways, as a function of time and temperature. This model allows quantifying the relative stability of AAV8 and AAV9 particles. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1007/s10867-018-9488-5) contains supplementary material, which is available to authorized users.

Chaque etape du cycle viral du VIH-1 s’accompagne d’une modification de la morphologie et/ou des proprietes mecaniques de la particule entiere ou de la capside virale. Le microscope a force atomique (AFM) est un outil physique extremement performant pour caracteriser ces changements a l’echelle d’un virus unique. En effet, l’AFM permet, d’une part, la visualisation de capsides virales dans un environnement physiologique controle, et, d’autre part, de sonder leurs proprietes mecaniques par nano-indentation. Enfin, la spectro-scopie de force AFM peut permettre de caracteriser les affinites entre les proteines d’enveloppe virale et les recepteurs cellulaires a l’echelle de la ­molecule unique.

The final shape of a virus is dictated by the self-assembly pathway of its constituents. Using standard thin-shell elasticity, we highlight the prominent role of the viral shell's spontaneous curvature in determining the assembly pathway. In particular, we demonstrate that the mechanical stress inherent to the growth of a curved surface can be relaxed in two different ways in the early steps of assembly, depending on the value of the spontaneous curvature of the surface. This important result explains why most viral shells have either a compact shape with icosahedral symmetry or an elongated shape lacking this symmetry.

In this work, we explore theoretically the kinetics of molecular self-assembly in the presence of constant monomer flux as an input, and a maximal size. The proposed model is supposed to reproduce the dynamics of viral self-assembly for enveloped virus. It turns out that the kinetics of open self-assembly is rather quantitatively different from the kinetics of similar closed assembly. In particular, our results show that the convergence toward the stationary state is reached through assembly waves. Interestingly, we show that the production of complete clusters is much more efficient in the presence of a constant input flux, rather than providing all monomers at the beginning of the self-assembly.

Each step of the HIV-1 life cycle frequently involves a change in the morphology and/or mechanical properties of the viral particle or core. The atomic force microscope (AFM) constitutes a powerful tool for characterizing these physical changes at the scale of a single virus. Indeed, AFM enables the visualization of viral capsids in a controlled physiological environment and to probe their mechanical properties by nano-indentation. Finally, AFM force spectroscopy allows to characterize the affinities between viral envelope proteins and cell receptors at the single molecule level.

We discuss how a balance can be established between the force acting to eject DNA from viral capsids and the force resisting its entry into a colloidal suspension that mimics the host cell cytoplasm. The ejection force arises from the energy stored in the capsid as a consequence of the viral genome (double-stranded DNA) being strongly bent and crowded on itself. The resisting force is associated with the osmotic pressure exerted by the colloidal particles in the host solution. Indeed, recent experimental work has demonstrated that the extent of ejection can be progressively limited by increasing the external osmotic pressure; at a sufficiently high pressure, the ejection is completely suppressed. We outline here a theoretical analysis that allows a determination of the internal (capsid) pressure by examining the different relations between force and pressure inside and outside the capsid using the experimentally measured position of the force balance.

International audience; Chromatin remodeling factors are enzymes being able to alter locally chromatin structure at the nucleosomal level and they actively participate in the regulation of gene expression. Using simple rules for individual nucleosome motion induced by a remodeling factor, we designed simulations of the remodeling of oligomeric chromatin, in order to address quantitatively collective effects in DNA accessibility upon nucleosome mobilization. Our results suggest that accessibility profiles are inhomogeneous thanks to borders effects like protein binding. Remarkably, we show that the accessibility lifetime of DNA sequence is roughly doubled in the vicinity of borders as compared to its value in bulk regions far from the borders. These results are quantitatively interpreted as resulting from the confined diffusion of a large nucleosome depleted region.

We study theoretically in the present work the self-assembly of molecules in an open system, which is fed by monomers and depleted in partial or complete clusters. Such a scenario is likely to occur for example in the context of viral self-assembly. We provide a general formula for the mean-field size distribution which is valid both at equilibrium in a closed system, and in the stationary state in an open system. This allows us to explore in a simple way out-of-equilibrium features for self-assembly and compare them to equilibrium properties. In particular, we identify a region of parameter space for which the out-of-equilibrium size distribution in the presence of external fluxes is equal to the equilibrium size distribution in the absence of external fluxes, up to a constant renormalization factor. The range of validity of this result and its consequences are discussed., PACS 81.16.Fg - Supramolecular and biochemical assembly PACS 82.39.-k - Chemical kinetics in biological systems PACS 05.65.+b - Self-organized systems

HIV-1, an enveloped RNA virus, produces viral particles that are known to be much more heterogeneous in size than is typical of non-enveloped viruses. We present here a novel strategy to study HIV-1 Viral Like Particles (VLP) assembly by measuring the size distribution of these purified VLPs and subsequent viral cores thanks to Atomic Force Microscopy imaging and statistical analysis. This strategy allowed us to identify whether the presence of viral RNA acts as a modulator for VLPs and cores size heterogeneity in a large population of particles. These results are analyzed in the light of a recently proposed statistical physics model for the self-assembly process. In particular, our results reveal that the modulation of size distribution by the presence of viral RNA is qualitatively reproduced, suggesting therefore an entropic origin for the modulation of RNA uptake by the nascent VLP.

We consider the phase behavior of polymeric systems by calculating the structure factors beyond the Random Phase Approximation. The effect of this correction to the mean-field RPA structure factor is shown to be important in the case of Coulombic systems. Two examples are given: simple electrolytes and mixtures of incompatible oppositely charged polyelectrolytes. In this last case, all former studies predicted an enhancement of compatibility for increasing charge densities; we also describe the complexation transition between the polyelectrolytes. We determine a phase diagram of the polyelectrolyte mixture that includes both complexation and incompatibility.

We review some of the theoretical results that we have obtained recently on the adsorption of polyelectrolytes on surfaces of opposite charge. We consider two problems, the formation of polyelectrolyte multilayers and the formation of complexes between rigid polyelectrolytes and small spheres. For polyelectrolyte multilayers, the overcompensation of the adsorbing surface charge and the anchoring between consecutive layers are studied. For polyelectrolyte-sphere complexes, the wrapping of the polymer on the sphere is shown to occur continuously at low ionic strength and discontinuously at high ionic strength. The findings of some recent experiments are briefly compared with our results.

Morphologic diversity is observed across all families of viruses. However, these supra-molecular assemblies are produced most of the time in a spontaneous way through complex molecular self-assembly scenarios. The modeling of these phenomena remains a challenging problem within the emerging field of physical virology. We present in this work a theoretical analysis aiming at highlighting the particular role of configuration entropy in the control of viral particle size distribution. Specializing this model to retroviruses such as HIV-1, we predict a new mechanism of entropic control of both RNA uptake into the viral particle and of the particle's size distribution. Evidence of this peculiar behavior has recently been reported experimentally.

The terminase motors of bacteriophages have been shown to be among the strongest active machines in the biomolecular world, being able to package several tens of kilobase pairs of viral genome into a capsid within minutes. Yet, these motors are hindered at the end of the packaging process by the progressive buildup of a force-resisting packaging associated with already packaged DNA. In this experimental work, we raise the issue of what sets the upper limit on the length of the genome that can be packaged by the terminase motor of phage λ and still yield infectious virions and the conditions under which this can be efficiently performed. Using a packaging strategy developed in our laboratory of building phage λ from scratch, together with plaque assay monitoring, we have been able to show that the terminase motor of phage λ is able to produce infectious particles with up to 110% of the wild-type λ-DNA length. However, the phage production rate, and thus the infectivity, decreased exponentially with increasing DNA length and was a factor of 10(3) lower for the 110% λ-DNA phage. Interestingly, our in vitro strategy was still efficient in fully packaging phages with DNA lengths as high as 114% of the wild-type length, but these viruses were unable to infect bacterial cells efficiently. Further, we demonstrated that the phage production rate is modulated by the presence of multivalent ionic species. The biological consequences of these findings are discussed.

Most bacteriophages are known to inject their double-stranded DNA into bacteria upon receptor binding in an essentially spontaneous way. This downhill thermodynamic process from the intact virion toward the empty viral capsid plus released DNA is made possible by the energy stored during active packaging of the genome into the capsid. Only indirect measurements of this energy have been available until now using either single-molecule or osmotic suppression techniques. In this paper, we describe for the first time the use of isothermal titration calorimetry to directly measure the heat released (or equivalently the enthalpy) during DNA ejection from phage lambda, triggered in solution by a solubilized receptor. Quantitative analyses of the results lead to the identification of thermodynamic determinants associated with DNA ejection. The values obtained were found to be consistent with those previously predicted by analytical models and numerical simulations. Moreover, the results confirm the role of DNA hydration in the energetics of genome confinement in viral capsids., 24 pages including figures and table

International audience; Chromatin organization and dynamics is studied at scales ranging from single nucleosome to nucleosomal array by using a unique combination of biochemical assays, single molecule imaging technique, and numerical modeling. We show that a subtle modification in the nucleosome structure induced by the histone variant H2A.Bbd drastically modifies the higher order organization of the nucleosomal arrays. Importantly, as directly visualized by atomic force microscopy, conventional H2A nucleosomal arrays exhibit specific local organization, in contrast to H2A.Bbd arrays, which show "beads on a string" structure. The combination of systematic image analysis and theoretical modeling allows a quantitative description relating the observed gross structural changes of the arrays to their local organization. Our results suggest strongly that higher-order organization of H1-free nucleosomal arrays is determined mainly by the fluctuation properties of individual nucleosomes. Moreover, numerical simulations suggest the existence of attractive interactions between nucleosomes to provide the degree of compaction observed for conventional chromatin fibers.

In this review, we discuss recent advances in biophysical virology, presenting experimental and theoretical studies on the physical properties of viruses. We focus on the double-stranded (ds) DNA bacteriophages as model systems for all of the dsDNA viruses both prokaryotic and eukaryotic. Recent studies demonstrate that the DNA packaged into a viral capsid is highly pressurized, which provides a force for the first step of passive injection of viral DNA into a bacterial cell. Moreover, specific studies on capsid strength show a strong correlation between genome length, and capsid size and robustness. The implications of these newly appreciated physical properties of a viral particle with respect to the infection process are discussed.

Recent work has shown that pressures inside dsDNA phage capsids can be as high as many tens of atmospheres; it is this pressure that is responsible for initiation of the delivery of phage genomes to host cells. The forces driving ejection of the genome have been shown to decrease monotonically as ejection proceeds, and hence to be strongly dependent on the genome length. Here we investigate the effects of ambient salts on the pressures inside phage-lambda, for the cases of mono-, di-, and tetravalent cations, and measure how the extent of ejection against a fixed osmotic pressure (mimicking the bacterial cytoplasm) varies with cation concentration. We find, for example, that the ejection fraction is halved in 30 mM Mg(2+) and is decreased by a factor of 10 upon addition of 1 mM spermine. These effects are calculated from a simple model of genome packaging, using DNA-DNA repulsion energies as determined independently from x-ray diffraction measurements on bulk DNA solutions. By comparing the measured ejection fractions with values implied from the bulk DNA solution data, we predict that the bending energy makes the d-spacings inside the capsid larger than those for bulk DNA at the same osmotic pressure.

Recent in vitro experiments have shown that DNA ejection from bacteriophage can be partially stopped by surrounding osmotic pressure when ejected DNA is digested by DNase I in the course of ejection. In this work, we argue by a combination of experimental techniques (osmotic suppression without DNase I monitored by UV absorbance, pulse-field electrophoresis, and cryo-transmission electron microscopy visualization) and simple scaling modeling that intact genome (i.e., undigested) ejection in a crowded environment is, on the contrary, enhanced or eventually complete with the help of a pulling force resulting from DNA condensation induced by the osmotic stress itself. This demonstrates that in vivo, the osmotically stressed cell cytoplasm will promote phage DNA ejection rather than resist it. The further addition of DNA-binding proteins under crowding conditions is shown to enhance the extent of ejection. We also found some optimal crowding conditions for which DNA content remaining in the capsid upon ejection is maximum, which correlates well with the optimal conditions of maximum DNA packaging efficiency into viral capsids observed almost 20 years ago. Biological consequences of this finding are discussed.

We propose a combined experimental (atomic force microscopy) and theoretical study of the structural and dynamical properties of nucleosomes. In contrast to biochemical approaches, this method allows us to determine simultaneously the DNA-complexed length distribution and nucleosome position in various contexts. First, we show that differences in the nucleoproteic structure observed between conventional H2A and H2A.Bbd variant nucleosomes induce quantitative changes in the length distribution of DNA-complexed with histones. Then, the sliding action of remodeling complex SWI/SNF is characterized through the evolution of the nucleosome position and wrapped DNA length mapping. Using a linear energetic model for the distribution of DNA-complexed length, we extract the net-wrapping energy of DNA onto the histone octamer and compare it to previous studies.

International audience; We present in this work in vitro measurements of the force ejecting DNA from two distinct bacteriophages (T5 and lambda) using the smotic-suppression technique. Our data are analyzed by revisiting the current theories of DNA packaging in spherical capsids. In particular we show that a simplified analytical model based on bending considerations only is able to account quantitatively for the experimental findings. Physical and biological consequences are discussed.

We present in this paper an original approach to compute the electrophoretic mobility of rigid nucleo-protein complexes like nucleosomes. This model allows to address theoretically the influence of complex position along DNA, as well as wrapped length of DNA on the electrophoretic mobility of the complex. The predictions of the model are in qualitative agreement with experimental results on mononucleosomes assembled on short DNA fragments (, to appear in Biophys. J. 29 pages

International audience; The classical Gibbs-Donnan equilibrium describes excess osmotic pressure associated with confined colloidal charges embedded in an electrolyte solution. In this work, we extend this approach to describe the influence of multivalent ion binding on the equilibrium force acting on a charged rod translocating between two compartments, thereby mimicking ionic effects on force balance during in vitro DNA ejection from bacteriophage. The subtle interplay between Gibbs-Donnan equilibrium and adsorption equilibrium leads to a non-monotonic variation of the ejection force as multivalent salt concentration is increased, in qualitative agreement with experimental observations.

We consider the problem of inserting a stiff chain into a colloidal suspension of particles that interact with it through excluded volume forces. The free energy of insertion is associated with the work of creating a cavity devoid of colloid and sufficiently large to accomodate the chain. The corresponding work per unit length is the force that resists the entry of the chain into the colloidal suspension. In the case of a hard sphere fluid, this work can be calculated straightforwardly within the scaled particle theory; for solutions of flexible polymers, on the other hand, we employ simple scaling arguments. The forces computed in these ways are shown, for nanometer chain and colloid diameters, to be of the order of tens of pN for solution volume fraction for biophysical processes such as the ejection of DNA from viral capsids into the cell cytoplasm., 16 pages,3 figures. Accepted for publication in European Physical Journal E

The complexation of oppositely charged colloidal objects is considered in this paper as a thermodynamic micellization process where each kind of object needs the others to micellize. This requirement gives rise to quantitatively different behaviors than the so-called mixed-micellization where each specie can micellize separately. A simple model of the grand potential for micelles is proposed to corroborate the predictions of this general approach., Comment: 7 pages, 2 figures. Accepted for publication in Europhysics Letters

We discuss in this paper the phase diagram of a diblock polyampholyte solution in the limit of high ionic strength as a function of concentration and charge asymmetry. This system is shown to be very similar to solutions of so-called charged-neutral diblock copolymers: at zero charge asymmetry the solution phase separates into a polyelectrolyte complex and almost pure solvent. Above a charge asymmetry threshold, the copolymers are soluble as finite size aggregates. Scaling laws of the aggregates radius as a function of pH of the solution are in qualitative agreement with experiments., 12 pages, 2 figures

We investigate the equilibrium charge distribution along a single annealed polyelectrolyte chain under different conditions. The coupling between the conformation of the chain and the local charge distribution is described for various solvent qualities and salt concentration. In salt free solution, we find a slight charge depletion in the central part of the chain: the charges accumulate at the ends. The effect is less important if salt is added to the solution since the charge inhomogeneity is localized close to the chain ends over a distance of order of the Debye length. In the case of poor solvent conditions we find a different charging of beads and strings in the framework of the necklace model. This inhomogeneity leads to a charge instability and a first order transition between spherical globules and elongated chains., Comment: 20 pages, 4 figures

International audience; A mechanism for the formation of polyelectrolyte multilayers is proposed. All of the experiments on such systems show that there is strong interpenetration of consecutive layers. We explain the very strong stability of the multilayers by the complexation between polyelectrolytes of opposite signs. Scaling laws on bulk polyelectrolyte complexation and their applications to the case of multilayers are derived in analogy with the description of neutral polymers under poor solvent conditions. Qualitative agreement is reached with some recent experiments.

The organization of DNA into nucleosome can be seen as a barrier for the transcription factors binding to their target DNA sequences and interferes with several basic cellular processes. ATP-remodeling machines and the incorporation of histone variants into chromatin are used by the cell to overcome the nucleosomal barrier and modulate DNA accessibility by the control of nucleosome dynamics. In this work, we use a single molecule technique (Atomic Force Microscopy, AFM) to visualize isolated mono- and oligo-nucleosomes and quantify their structure and dynamics at thermodynamical equilibrium and out of equilibrium.We have studied the impact of H2A.Bbd histone variant incorporation at the mono-nucleosome and oligo-nucleosome level, and we have shown that this variant modifies both the structure and the dynamics of the nucleosome altering the ability to form a higher structure organization of the chromatin. Using a polymer physics model, we demonstrated that the behavior of variant chromatin can be quantitatively explained by the mono-nucleosome flexibility [1].We are also interested in the mechanism of nucleosome remodeling by SWI/SNF and RSC on mono- and di-nucleosomes. Focusing on the di-nucleosomes, AFM imaging showed only a limited set of distinct configurational states for the remodeling products. No stepwise or preferred directionality of the nucleosome motion was observed [2]. Analysis of the corresponding reaction pathways allows deciphering the mechanistic features of RSC-induced nucleosome relocation. The final outcome of RSC remodeling of oligosomal templates is the packing of the nucleosomes at the edge of the template, providing large stretches of nucleosome depleted DNA.[1] F. Montel, H. Menoni, M. Castelnovo, J. Bednar, S. Dimitrov, D. Angelov & C. Faivre-Moskalenko; Biophys. J. 97, 544-553 (2009).[2] F. Montel, M. Castelnovo, H. Menoni, D. Angelov, S. Dimitrov & C. Faivre-Moskalenko; Nucleic Acids Res. 39, 2571-9 (2011).

The fundamental unit of chromatin, the nucleosome, constitutes a barrier for several processes including transcription, repair and replication. One of the main tools that the cell uses to overcome this barrier is the recruitment of chromatin remodeling factors. The yeast RSC remodeling complex, a sophisticated nanomachine belonging to the SWI/SNF family, is able both to alter the histone-DNA interactions and to relocate nucleosomes. How RSC or the other complexes from the SWI/SNF family act on polynucleosomal templates is not fully understood and few quantitative data are available. Nevertheless, such quantification is required for both the understanding of the mechanism of action of RSC and the key role that it plays in the numerous vital processes for the cell.In order to gap this lack of quantitative information, we have used Atomic Force Microscopy (AFM) to visualize directly and at the single molecule level, the result of RSC action on oligo-nucleosomes. In parallel, we developed numerical simulations of the RSC sliding action, which quantitatively reproduce our experimental data. We demonstrate that RSC acts as an isotropic, processive and sequence-independent nucleosome randomizer. This multidisciplinary approach is very suitable to extend to other remodelers exhibiting different modes of action.

Viruses are in many ways fascinating biological systems. They vary in their structure, their replication methods, and in their target hosts. They are the smallest self-replicating and self-assembling entities on Earth. Viruses are partly made of a protein shell called the capsid, the most important and interesting component as it encloses their genetic material. The main role of the capsid is to protect the viral genome. As a result and despite their smallness, they have evolved to sustain high external or internal constraints. However, the mechanisms underlying the appearance of viruses (through the capsids shape) and those that bring their high resistances are still poorly understood. Such problematics are of great interest as they could lead to the development of artificial nanocages. Viral derived nanocages are promising for various bioappplications, such as gene therapies or nanoapplications, such as drug delivery. The work I propose in my Ph.D. aims to contribute modestly to the understanding of viral assembly and stability using both analytical and numerical investigations.Viruses are biological structures produced thanks to molecular self-assembly. Because the final crystal is too be curved, the induced elastic stress is relaxed thanks to the introduction of topological defects in the protein lattice. We propose in the Ph.D. thesis a quantitative mechanism for this phenomenon by using standard thin shell elasticity. In particular, we show that the type and the angular location of a defect is determined by the value of the azimuthal stress that characterizes compressive or tensile regions. The elastic model proposed permits us to compare quantitatively the relaxation of mechanical stress induced by various defect distributions.Testing the mechanical stability of viral particles is possible thanks to nanoindentation experiments by atomic force microscopy. Using a coarse-grained molecular simulation of a viral structure, we build in the Ph.D. thesis a framework to help interpret mechanical information obtained by such nanoexperiments. More specifically, non-vanishing Gaussian curvature of viruses and the geometry of the tip have an influence on the viral quantitative stiffnesses that can be extracted. The coalescence of analytical and numerical results enables us to capture and rationalize the latter influence. We hope the latter work to be of interest for following investigations regarding mechanical aspects of viruses.; Les différentes propriétés des virus en font des objets intéressants et fascinants. On peut en trouver de différentes structures, avec des méthodes de réplication différentes et ils sont spécifiques à leurs cibles. Ils constituent la plus petite entité auto-assemblée, elle-même encodée par un matériel génétique. Ce génome est protégé par une capside à l'intérieur virus lui-même. La capside est le constituant le plus important d'un virus. Son rôle est de protéger le génome viral des agressions extérieures. De fait, elle peut supporter de hautes contraintes mécaniques ou chimiques externes et/ou internes. Cependant, les mécanismes conduisant à leur construction, influençant leurs formes et leur conférant cette résistance sont toujours assez peu compris. Ces problématiques présentent un intérêt majeur car elles ouvrent la porte au développement de nanocages. Ces nanocages inspirées des virus pourraient être particulièrement utiles pour des applications biologiques, en thérapie génique par exemple, ou des applications technologiques, comme la délivrance de médicaments à des cibles spécifiques. Le travail présenté dans cette thèse se propose modestement de contribuer à la compréhension de l'auto-assemblage et de la stabilité virale en utilisant des modèles numériques et analytiques.Les virus sont des échafaudages biologiques auto-assemblés. La structure finale étant nécessairement courbée, la contrainte élastique au cours de l'auto-assemblage due à la courbure est relachée par l'inclusion de défauts topologiques dans le réseau protéique. Dans cette thèse, par l'utilisation de la physique de l'élasticité en milieu continu, on propose un mécanisme pour ce phénomène. En particulier, on montre que le type et la localisation angulaire du défaut à la frontière de l'assemblage sont deux paramètres fixés par la contrainte azimuthale, celle-ci pouvant être compressive ou extensive. Le modèle élastique proposé permet de comparer et d'évaluer l'effet relaxant de différentes distributions de défauts topologiques dans la structure.L'évaluation et les tests de stabilité mécaniques des structures virales ont été rendus possible par les expériences de nanoindentation par microscopie à force atomique. En utilisant une simulation numérique de dynamique moléculaire d'une structure virale gros-grains, on construit dans cette thèse un cadre de travail permettant d'aider à l'interprétation des informations mécaniques tirées de ces expériences. Plus spécifiquement, la courbure Gaussienne non-nulle du virus indenté et la géométrie de la pointe utilisée pour l'indentation ont des influences sur la rigidité mécanique effective pouvant être extraite expérimentalement. La coalescence de résultats numériques et théoriques nous permet de capturer et de rationaliser cette influence. On espère que ce travail pourra être d'intérêt pour des recherches futures portant sur les propriétés mécaniques des virus.

In this thesis work, we study the self-assembly of viral particles and focus on the analysis of measurements based on fluorescence labeling of viral proteins. We propose a theoretical model of the dynamic of viral proteins self-assembly at the cell membrane based on previous models developed to describe the in-vitro assembly of spherical viruses. We study the evolution of the populations in the successive stages of viral budding as well as the evolution of single particle within this framework. We also provide various data analysis to measure the physical values involved in the process: rate of aggregation during the bud growth, size and shape of the eventual structure. Viruses are biological objects unable to replicate without infecting an host cell since they lack part of the molecular machinery mandatory for genetic code replication and proteins production. Originally aimed at controlling the diseases they cause, the study of viruses is now rich of applications in medical and technological field (gene therapy, phage therapy, targeted therapy, bio-templating, cargo specific encapsulation, etc.). The existent models describing the self-assembly of viral proteins have successfully captured many features observed in the in-vitro experiments. We study the expected evolution when an open system is considered with an input flux of proteins and an output flux of released virion, characteristic of the in-vivo situation. We derive the population distribution at steady state and numerically study their dynamic under constant viral protein input flux. We also study the case of a single bud evolution which can be followed by its fluorescence emission. We study the possibility to estimate shape parameters at the single viral particle level such as radius and completion for the human immunodeficiency virus (HIV) from single molecule localization superresolution microscopy. These techniques known as (f)PALM or (d)STORM, record labeled proteins position with a precision of few to tens of nanometers. We propose an approach base on the maximum likelihood statistical method which is tested on both real and simulated images of fully formed particles. Our results suggest that it can offer a precision on the determination of the global structure finner than the positioning precision of the single proteins. This efficiency is however tempered when the parameter of interest does not affect the figures of merit to which the method is sensitive such as the apparent area and the image contours, Cette thèse porte sur la description de l'assemblage des virus dans le cadre de la physique statistique ainsi que sur les méthodes de mesure de cet assemblage utilisant les marqueurs fluorescents. Nous nous y attachons à décrire la dynamique de l'agrégation des protéines aux échelles de la population et du virus unique. Nous proposons deux méthodes pour mesurer les grandeurs physiques associées : taille et forme de la structure finale d'une part, taux d'agrégation au cours de la croissance d'autre part. Dans ce travail, nous nous sommes intéressés à la description physique de l'auto-assemblage des protéines virales. La physique de l'auto-assemblage in-vitro des virus sphériques, dont la structure est déterminée par l'agencement régulier de leurs constituants protéiques, a été théoriquement et expérimentalement caractérisée auparavant par des modèles d'agrégation. Les modèles existants décrivaient l'assemblage à quantité de composants viraux fixée dans un système ferme à partir des constituants élémentaires du virus. In-vivo, la situation est bien entendu différente. Abstraction faite de la grande complexité du milieu cellulaire, les virus s'échappent de la cellule une fois formés pour aller infecter de nouvelles cellules. De plus, la quantité de constituants est sans cesse modifiée par la fabrication ou la dégradation des protéines virales. Enfin les méthodes de mesures utilisées in-vitro ne sont généralement plus envisageables in-vivo. Nous avons donc étudié les effets d'un flux de matière dans système ouvert via le calcul de l'état stationnaire, et via la résolution numérique des équations d'évolution des populations d'agrégats qui décrivent la cinétique d'agrégation des protéines virales. Dans ce cadre, nous avons mis en valeur le lien entre la description de l'état général du système en termes de populations et le devenir individuel d'un virus en formation pour le suivi duquel des méthodes expérimentales existent. Nous nous sommes alors attachés à proposer un traitement approprié de telles données expérimentales pour déterminer les valeurs des paramètres physiques du modèle