Coiled-coil motifs are part of 5–10 % of the eukaryotic proteome and are involved in important cellular processes such as membrane trafficking, chromosome segregation or mechanosensing. Their canonical form is well understood and based on a heptad repeat with hydrophobic amino acids at positions 1 and 4. A sequence of these peptides folds into an α-helix and two, or more, of these helices bind together by winding around each other, covering up the hydrophobic residues and giving rise to the coiled-coil structure. Coiled-coil proteins appearing in nature do, however, deviate from this form by introducing discontinuities into the heptad repeat. The effect of these imperfections on the structure is only known for few cases and not generally understood or predictable. The additional impact of these discontinuities on the dynamic function of coiled-coil domains is unknown altogether. Here, in order to tackle these questions, the adhesive forces between the α-helices are studied in single-molecule experiments. To measure these small forces (∼ pN) with a high spatial and temporal resolution, a dual-trap optical tweezers setup was constructed. Special emphasis was put on realizing the required high resolution, a large degree of automation and versatility during the building process. The instrument’s performance was assessed by recording force-extension curves of DNA yielding results for the molecular parameters persistence length and stretch modulus in good agreement with those found in the literature. Additionally, the Allan deviation was computed for different configurations of beads and a high stability and resolution of the instrument was found with optimal performance on the time scale of 1–10 s. Optical tweezers require calibration to accurately measure forces. To this end, generally a scheme is used that leverages the Brownian motion of a trapped object in the harmonic potential, created by the laser focus, to determine the parameters required to convert the analog voltage signal to distances and forces. However, this approach requires prior knowledge of the bead’s drag coefficient. A method was suggested previously that allows to measure this parameter by exciting the trapped bead through an external fluid flow and observing its response. Yet, this scheme was proposed for single-trap devices only. The precision and versatility of the new instrument was increased by extending this technique to work with two traps and implementing it in the apparatus. To this aim, the underlying equations of a trapped bead’s motion were modified to include hydrodynamic interactions between the objects resulting from the external fluid flow. It was found that a single multiplicative factor is sufficient to correct the calibration results for the hydrodynamic effects and ensure precise calibration. The drag coefficient of several beads yielded the same result for a single and two traps within the measurement error thus confirming the validity of the method. The newly built instrument was then used to study the coiled-coil protein early endosome antigen 1 (EEA1). This 200 nm long homodimer was shown to undergo an entropic collapse upon binding a small GTPase at the N-terminus. For further investigations of this effect and the adhesives forces at play, an experiment was designed here to unzip the two α-helices of the protein. To this end, DNA handles were attached to each of the two helices using a sortase A based ligation reaction as force moderators and first optical tweezers experiments were performed with the protein-DNA chimera. Thus, the necessary tools for unzipping assays of EEA1 are now at hand to further research the entropic collapse process. To summarize, a dual-trap optical tweezers setup was built, the calibration routine extended and realized in a more precise way and the instrument was used to investigate binding energies of EEA1 α-helices. / Coiled-Coil Strukturmotive sind in 5–10 % aller Proteine von Eukaryoten vertreten und wichtiger Teil zellulärer Prozesse wie Membrantransport, Segregation von Chromosomen oder Mechanoperzeption. Ihre grundlegende Struktur besteht aus dem sogenannten Heptadenmuster, einer Sequenz aus sieben Aminosäuren mit hydrophoben Molekülen an Position eins und vier. Eine Reihe dieser Muster kann sich zu einer α-Helix falten und zwei, oder mehr, solcher Helices sich umeinander winden, um die hydrophoben Moleküle abzuschirmen. Das Ergebnis ist eine Coiled-Coil- oder Doppelwendelstruktur. Natürlich vorkommende Coiled-Coil Proteine weichen jedoch durch Fehlstellen im Heptadenmuster von dieser kanonischen Form ab. Die Auswirkung dieser Störstellen auf die Struktur des gesamten Moleküls ist bisher nur für einige wenige Fälle untersucht und nicht allgemein vorstanden oder vorhersagbar. Der zusätzliche Einfluss dieser Fehlstellen auf die Funktion und dynamischen Prozesse solcher Proteine ist gänzlich unbekannt. Um diesen Fragen nachzugehen werden hier die Bindungskräfte zwischen den α-Helices in Einzelmolekülstudien untersucht. Um diese winzigen Kräfte (∼ pN) mit hoher räumlicher und zeitlicher Auflösung untersuchen zu können, wurde im Rahmen der vorliegenden Arbeit eine optische Doppelfalle konstruiert. Besonderes Augenmerk lag dabei auf dem Erreichen der erforderlichen Auflösung, einem hohen Grad an Automatisierung und der vielfälting Einsatzfähigkeit des Instruments. Die Leistungsfähigkeit dieses Kraftmikroskops wurde besonders durch zwei Experimente überprüft und sichergestellt. Zum einen wurden DNA Moleküle gedehnt und die Polymerparameter Persistenzlänge und Zugmodul gemessen, welche sehr gut mit veröffentlichten Referenzwerten übereinstimmten. Zum anderen wurde die Allan Schwankung für verschiedene experimentelle Konfigurationen von mikroskopischen Kugeln ermittelt, was eine hohe Stabilität und Auflösung des Gerätes, mit optimaler Leistung bei Mittelung auf Zeitskalen von 1–10 s, bestätigte. Optische Fallen müssen kalibriert werden, um Kräfte exakt messen zu können. Im Allgemeinen kommt dafür ein Verfahren zum Einsatz, welches die brownsche Bewegung eines gefangenen Objektes im harmonischen Potential des Laserfokus ausnutzt. Aus diesen Fluktuationen werden die benötigten Parameter ermittelt, um das gemessene analoge Spannungssignal in Abstände und Kräfte umzuwandeln. Dieser Ansatz erfordert jedoch die Kenntnis des Reibungskoeffizienten des gehaltenen Objektes, meist einer mikroskopischen Kugel. Daher wurde eine Methode vorgeschlagen, die durch ein oszillierendes Flussfeld eine zusätzliche Bewegung der Kugel anregt aus welcher der Reibungskoeffizient bestimmt werden kann. Dieses Vorgehen reduziert die im vornherein benötigten Informationen, wurde jedoch nur für eine einzelne optische Falle entwickelt. Der Ansatz wurde in dieser Arbeit erweitert, indem die zu zugrundeliegenden Bewegungsgleichungen einer gefangenen Kugel um hydrodynamische Wechselwirkungen zwischen mehreren Objekten ergänzt und die Kalibrationparameter basierend darauf hergeleitet wurden. Im Ergebnis konnte gezeigt werden, dass ein einzelner multiplikativer Faktor ausreicht, um die Hydrodynamik zu berücksichtigen und die exakte Kalibration des Instruments sicherzustellen. Dieses Vorgehen wurde überprüft, indem der Reibungskoeffizient einer einzelnen oder mehrerer mikroskopischer Kugeln gleichzeitig durch Anlegen eines externen Flussfeldes gemessen wurde. Die Ergebnisse stimmen im Rahmen der Messgenauigkeit überein und bestätigen damit den gewählten Ansatz. Das neu implementierte Kraftmikroskop wurde im Folgenden eingesetzt, um das Coiled-Coil Protein Early Endosome Antigen 1 (EEA1) zu erforschen. Dieser 200 nm lange Homodimer kollabiert aufgrund entropischer Kräfte sobald eine kleine GTPase an seinen N-Terminus bindet. Um diesen Effekt und die wirkenden Bindungskräfte besser zu verstehen, wurde hier ein Experiment entwickelt bei dem die beiden α-Helicen auseinandergezogen werden. Dazu wurde mittels einer Sortase A basierten Ligationsreaktion an jede Helix ein DNA-Stück gebunden, über welches Kräfte auf das Molekül übertragen werden können. Erste Experimente wurden mit der optischen Doppelfalle und dieser Protein-DNA Chimäre durchgeführt. Somit sind alle benötigten Werkzeuge zum weiteren Studium des entropischen Kollapses von EEA1 verfügbar, indem die Bindungskräfte der α-Helicen untersucht werden. Zusammenfassend wurde eine hoch auflösende Doppelfalle konstruiert, die Kalibrationsmethode weiterentwickelt und verfeinert und das Kraftmikroskop zur Erforschung der Bindungskräfte der α-Helicen von EEA1 eingesetzt.

Microtubules are a part of the cell cytoskeleton that performs different functions, such as providing the mechanical support for the shape of a cell, acting as tracks along which the motor protein move organelles from one part of the cell to another, or the forming mitotic spindle during the cell division. The microtubules are dynamic structures, namely they can grow and shrink. The phase of microtubule growth alternates with the phase of shrinkage that results in the dynamic microtubule network in the cell. However, to form stable and spatially well-defined structures, such as a mitotic spindle, the cell needs to control this stochastic process. This is done by microtubule-associated proteins (MAPs). One class of MAPs is the proteins of XMAP216/Dis1 family, which are microtubule polymerases. The founding member of this family is X. laevis XMAP215. XMAP215 is a processive polymerase acting on the microtubule plus end. XMAP215 binds either directly or reaches the microtubule plus end by the diffusion along the microtubule lattice. Being at the microtubule plus-end XMAP215 stays there transiently and helps to incorporate up to 25 tubulin dimers into microtubule lattice before it dissociates and, therefore, it processively tracks the growing microtubule end during polymerization. There are two hypothesis of microtubule assembly promotion: (i) XMAP215 repeatedly releases an associated tubulin dimer into the microtubule growing plus end or (ii) structurally stabilizes a polymerized tubulin intermediate at the growing plus end and, therefore, preventing depolymerization events. The first way results into the increase of on-rate of tubulin dimers at the microtubule end, whereas the second way results into the decrease of off-rate of tubulin dimers at the microtubule end. Here, I show the study of the mechanism of microtubule growth acceleration by XMAP215 and the dependence of XMAP215 polymerization activity on the applied force. To answer these questions, I investigated the addition of tubulin dimers to the plus end of the microtubule by XMAP215 and how this addition depends on the applied force. XMAP215 remains at the microtubule end for several rounds of tubulin addition surfing both growing and shrinking microtubule ends. Therefore, if one could track the position of the XMAP215 molecules at the very tip of a microtubule with sufficient resolution, it would provide the information about the dynamics of the microtubule end. The technique, which can detect the position of the object of interest with high spatial and temporal resolution in addition to being able to exert a force, is an optical trap. A calibrated optical trap not only provides a good measure of displacement but also enables force measurements. To monitor the position of the molecules of interest, the molecules of interest are usually attached to a microsphere. Hence, I tethered XMAP215 to a microsphere held by an optical trap, and used XMAP215 as a handle to interact with the microtubule tip. When the microtubule grows, the XMAP215 coated microsphere will move in the optical trap and this movement can be detected with high temporal and spatial resolution. My work demonstrates that cooperatively working XMAP215 molecules can not only polymerize microtubule but also harness the energy of microtubule polymerization or depolymerization to transport some cargo. There is an evidence that orthologues of XMAP215 in budding yeasts, fission yeasts and Drosophila localize on the kinetochores. Therefore, the ability of the bearing some load during microtubule polymerization could be potentially important for the XMAP215 functioning during cell division. I also showed the influence of external force applied to the XMAP215 molecules. Pointing toward microtubule growth, a force of 0.5 pN applied to the microtubule tip-coupled XMAP215-coated microsphere increases XMAP215 polymerization activity. However, the force of the same magnitude but applied against microtubule growth does not affect XMAP215 polymerization activity. This result can be explained by the fact, that the force acting in the direction of microtubule growth constrains XMAP215 to be at the very microtubule tip. Hence, XMAP215 can not diffuse away from plus-end and there is higher chance to incorporate tubulin dimers into the microtubule plus-end. The on- and off-rate of tubulin dimers at the microtubule end are both decreased when the external force applied either in direction of microtubule growth or opposite to it. The external force affects the off-rate slightly stronger than on-rate of tubulin dimer. Taking together, my study gives new insights into the mechanism of microtubule polymerization by XMAP215 and shows some novel properties of this protein.

Many genetic processes require enzymes or enzyme complexes that interact simultaneously with distant sites along the genome. Such long-range DNA-enzyme interactions are important for example in gene regulation, DNA replication, repair and recombination. In addition many restriction enzymes depend on interactions between two recognition sites and form therefore a model system for studying long-range communications on DNA. Topic of the present work are Type III restriction enzymes. For these enzymes the communication mechanism between their distant target sites has not been resolved and conflicting models including 3D diffusion, 1D translocation and 1D diffusion have been proposed. Also the role of ATP hydrolysis by their superfamily 2 helicase domains which catalyse functions of many enzyme systems is still poorly understood. To cleave DNA, Type III restriction enzymes sense the relative orientation of their distant target sites and cleave DNA only if at least two of them are situated in an inverted repeat. This process strictly depends on ATP hydrolysis. The aim of this PhD thesis was to elucidate this long-range communication. For this a new single molecule assay was developed using a setup combining magnetic tweezers and objective-type total internal reflection fluorescence microscopy. In addition of being able to mechanically manipulate individual DNA molecules, this assay allows to directly visualize the binding and movement of fluorescently labelled enzymes along DNA. Applying this assay to quantum dot labelled Type III restriction enzymes, a 1D diffusion of the enzymes after binding at their target sites could be demonstrated. Furthermore, it was found that the diffusion depends on the nucleotide that is bound to the ATPase domains of these enzymes. This suggested that ATP hydrolysis acts as a switch to license diffusion from the target site which leads to cleavage. In addition to the direct visualization of the enzyme-DNA interaction, the cleavage site selection, the DNA end influence (open or blocked) and the DNA binding kinetics were measured in bulk solution assays (not part of this thesis). The experimental results were compared to Monte Carlo simulations of a diffusion-collision-model which is proposed as long-range communication in this thesis.

Optical tweezers are a sensitive position and force transducer widely employed in physics and biology. In a focussed laser, forces due to radiation pressure enable to trap and manipulate small dielectric particles used as probes for various experiments. For sensitive biophysical measurements, microspheres are often used as a handle for the molecule of interest. The force range of optical traps well covers the piconewton forces generated by individual biomolecules such as kinesin molecular motors. However, cellular processes are often driven by ensembles of molecular machines generating forces exceeding a nanonewton and thus the capabilities of optical tweezers. In this thesis I focused, fifirst, on extending the force range of optical tweezers by improving the trapping e fficiency of the probes and, second, on applying the optical tweezers technology to understand the mechanics of molecular motors. I designed and fabricated photonically-structured probes: Anti-reflection-coated, high-refractive-index, core-shell particles composed of titania. With these probes, I significantly increased the maximum optical force beyond a nanonewton. These particles open up new research possibilities in both biology and physics, for example, to measure hydrodynamic resonances associated with the colored nature of the noise of Brownian motion. With respect to biophysical applications, I used the optical tweezers to study the mechanics of single kinesin-8. Kinesin-8 has been shown to be a very processive, plus-end directed microtubule depolymerase. The underlying mechanism for the high processivity and how stepping is affected by force is unclear. Therefore, I tracked the motion of yeast (Kip3) and human (Kif18A) kinesin-8s with high precision under varying loads. We found that kinesin-8 is a low-force motor protein, which stalled at loads of only 1 pN. In addition, we discovered a force-induced stick-slip motion, which may be an adaptation for the high processivity. Further improvement in optical tweezers probes and the instrument will broaden the scope of feasible optical trapping experiments in the future.

Aufgrund einer komplexen Wechselwirkung mit Proteinen ist das Genom in einer Zelle ständig mechanischer Spannung und Torsion ausgesetzt. Daher ist es wichtig die Mechanik und die Dynamik von verdrillter DNA unter Spannung zu verstehen. Diese Situation wurde experimentell mittels einer sog. magnetischen Pinzette nachgestellt, indem sowohl Kraft als auch Drehmoment auf ein einzelnes DNA Molekül ausgeübt und gleichzeitig die mechanische Antwort des Polymers aufgezeichnet wurde. Als erstes Beispiel wurde der Übergang von linearer zu sog. plectonemischer DNA untersucht, d.h. die Absorption eines Teils der induzierten Verdrillung in einer superhelikalen Struktur. Eine abrupte Längenänderung am Anfang dieses Übergangs wurde bereits im Vorfeld publiziert. In der vorliegenden Arbeit wird gezeigt, dass diese abrupte DNA Verkürzung insbesondere von der Länge der DNA und der Ionenkonzentration der Lösung abhängt. Dieses Verhalten kann mittels eines Modells verstanden werden, in dem die Energie pro Verwringung der ersten Schlinge innerhalb der Superhelix größer ist als die aller nachfolgenden. Des Weiteren wurden DNA-DNA Wechselwirkungen in der Umgebung monovalenter Ionen durch die Analyse des Superspiralisierungsverhaltens einzelner DNA Moleküle bei konstanter Kraft charakterisiert. Solche Wechselwirkungen sind für die Kompaktierung des Genoms und die Regulation der Transkription wichtig. Oft wird DNA als gleichmäßig geladener Zylinder modelliert und ihre elektrostatischen Wechselwirkungen im Rahmen der Poisson-Boltzmann-Gleichung mit einem Ladungsanpassungsfaktor berechnet. Trotz erheblicher Anstrengung ist eine präzise Bestimmung dieses Parameters bisher nicht gelungen. Ein theoretisches Modell dieses Prozesses zeigte nun eine erstaunlich kleine effektive DNA Ladung von ~40% der nominalen Ladungsdichte. Abgesehen von Gleichgewichtsprozessen wurde auch die Dynamik eines Faltungsvorgangs von DNA untersucht. Spontane Branch Migration einer homologen Holliday-Struktur wurde genutzt, um die intramolekulare Reibung der DNA zu erforschen. Mittels einer magnetischen Pinzette wurde eine torsionslimitierte Holliday-Struktur gestreckt während die Längenfluktuationen der Zweige mit schneller Videomikroskopie bei ~3 kHz aufgezeichnet wurden. Einzelne diffusive Schritte der Basenpaare sollten auf einer sub-Millisekunden Zeitskala auftreten und viel kleiner als die Gesamtfluktuationen der DNA sein. Eine Analyse der spektralen Leistungsdichte der Längenfluktuationen ermöglicht eine eindeutige Beschreibung der Dynamik der Branch Migration. Die Holliday-Struktur wurde außerdem als nanomechanischer Linearversteller eingesetzt, um einen einzelnen fluoreszierenden Quantenpunkt durch ein exponentiell abfallendes evaneszentes Feld zu bewegen. Durch die Aufzeichnung der Emission des Quantenpunkts sowohl in dem evaneszenten Feld als auch unter gleichmäßiger Beleuchtung kann die Intensitätsverteilung des Anregungsfelds ohne weitere Dekonvolution bestimmt werden. Diese neue Technik ist von besonderem wissenschaftlichen Interesse, weil die Beschreibung dreidimensionaler inhomogener Beleuchtungsfelder eine große Herausforderung in der modernen Mikroskopie darstellt. Die Ergebnisse dieser Arbeit werden dem besseren Verständnis einer Vielzahl biologischer Prozesse, die in Verbindung mit DNA Superspiralisierung stehen, dienen und weitere technische Anwendungen des DNA-basierten Linearverstellers hervorbringen. / The genome inside the cell is continuously subjected to tension and torsion primarily due to a complex interplay with a large variety of proteins. To gain insight into these processes it is crucial to understand the mechanics and dynamics of twisted DNA under tension. Here, this situation is mimicked experimentally by applying force and torque to a single DNA molecule with so called magnetic tweezers and measuring its mechanical response. As a first example a transition from a linear to a plectonemic DNA configuration is studied, i.e. the absorption of part of the applied twist in a superhelical structure. Recent experiments revealed the occurrence of an abrupt extension change at the onset of this transition. Here, it is found that this abrupt DNA shortening strongly depends on the length of the DNA molecule and the ionic strength of the solution. This behavior can be well understood in the framework of a model in which the energy per writhe for the initial plectonemic loop is larger than for subsequent turns of the superhelix. Furthermore DNA-DNA interactions in the presence of monovalent ions were comprehensively characterized by analyzing the supercoiling behavior of single DNA molecules held under constant tension. These interactions are important for genome compaction and transcription regulation. So far DNA is often modeled as a homogeneously charged cylinder and its electrostatic interactions are calculated within the framework of the Poisson-Boltzmann equation including a charge adaptation factor. Despite considerable efforts, until now a rigorous quantitative assessment of this parameter has been lacking. A theoretical model of this process revealed a surprisingly small effective DNA charge of ~40% of the nominal charge density. Besides describing equilibrium processes, also the dynamics during refolding of nucleic acids is investigated. Spontaneous branch migration of a homologous Holliday junction serves as an ideal system where the friction within the biomolecule can be studied. This is realized by stretching a torsionally constrained Holliday junction using magnetic tweezers and recording the length fluctuations of the arms with high-speed videomicroscopy at ~3 kHz. Single base pair diffusive steps are expected to occur on a sub-millisecond time scale and to be much smaller than the overall DNA length fluctuations. Power-spectral-density analysis of the length fluctuations is able to clearly resolve the overall dynamics of the branch migration process. Apart from studying intramolecular friction, the four-arm DNA junction was also used as a nanomechanical translation stage to move a single fluorescent quantum dot through an exponentially decaying evanescent field. Recording the emission of the quantum dot within the evanescent field as well as under homogeneous illumination allows to directly obtain the intensity distribution of the excitation field without additional deconvolution. This new technique is of particular scientific interest because the characterization of three-dimensional inhomogeneous illumination fields is a challenge in modern microscopy. The results presented in this work will help to better understand a large variety of biological processes related to DNA supercoiling and inspire further technical applications of the nanomechanical DNA gear.

Des atomes individuels piégés dans des matrices de pinces optiques et excités vers des états de Rydberg forment une plateforme expérimentale prometteuse pour la simulation quantique de modèles de spins. Lors de cette thèse, nous avons d’abord résolu le problème du chargement aléatoire des pièges, seulement 50 % d’entre eux étant chargés avec un atome. Nous avons développé une technique pour préparer des matrices 2D, puis 3D, d’atomes de 87Rb en les déplaçant un par un avec une pince optique mobile contrôlée par ordinateur. Nous avons ensuite réalisé le modèle d’Ising en excitant de manière cohérente les atomes depuis leur état électronique fondamental vers un niveau de Rydberg. Après avoir trouvé un régime optimal où l’interaction dipolaire entre deux atomes de Rydberg se réduit à une énergie de van der Waals, nous avons tenté de préparer adiabatiquement l’état de Néel qui minimise l’énergie d’interaction. Nous avons montré que l’efficacité de préparation étaitlimitée par la décohérence induite par les lasers d’excitation. Nous avons ensuite utilisé un autre régime d’interaction, le couplage dipolaire résonant, pour étudier des modèles de spins de type XY, dont le modèle Su-Schrieffer-Heeger, connu pour sa phase fermionique topologique protégée par une symétrie chirale. Ici, nous avons remplacé les fermions par des particules effectives de type `boson de cœur dur’, ce qui modifie les propriétés de cette phase. Nous avons d’abord retrouvé les propriétés à une particule, comme l’existence d’états de bords à énergie nulle. Nous avons ensuite préparé l’état fondamental à N corps pour un remplissage moitié, et observé sa dégénérescence causée par les états de bords, même en présence d’une perturbation qui lèverait cette dégénérescence dans le cas fermionique. Nous avons expliqué ce résultat par l’existence d’une symétrie plus générale, qui protège la phase bosonique. / Single atoms trapped in arrays of optical tweezers and excited to Rydberg states are a promising experimental platform for the quantum simulation of spin models. In this thesis, we first solved a long-standing challenge to this approach caused by the random loading of the traps, with only 50% of them filled with single atoms. We have engineered a robust and easy-to-use method to assemble perfectly filled two-dimensional arrays of 87Rb atoms by moving them one by one with a moveable optical tweezers controlled by computer, a technique further enhanced to trap, image and assemble three-dimensional arrays. We then implemented the quantum Ising model by coherently coupling ground-state atoms to a Rydberg level. After finding experimental parameters where the dipole-dipole interaction takes the ideal form of a van der Waals shift, we performed adiabatic preparation of the Néel state. We showed that the coherence time of our excitation lasers limited the efficiency of this technique. We then used a different type of interaction, a resonant dipolar coupling, to implement XY spin models and notably the Su-Schrieffer-Heeger model, known for its fermionic topological phase protected by the chiral symmetry. Here, we used effective hard-core bosons, which modify the properties of the topological phase. We first recovered known properties at the single particle level, such as the existence of localized zero-energy edge-states. Then, preparing the many-body ground state at half-filling, we observed a surprising robustness of its four-fold degeneracy upon applying a perturbation. This result was explained by the existence of a more general symmetry protecting the bosonic phase.

Ce manuscrit détaille le développement d'un montage de pince optique permettant d'étudier les propriétés mécaniques des cellules endothéliales, impliquées dans le développement de l'athérosclérose. Le but est de déterminer les propriétés viscoélastiques des cellules, et de suivre la propagation d’une contrainte mécanique au sein de la cellule. Cette contrainte mécanique est appliquée via une bille liée à la membrane de la cellule et soumise à un piège optique.Le dispositif réalisé combine le piégeage optique et la microscopie à contraste de phase, permettant d'exercer une force tout en imageant les cellules via le même objectif de microscope. L'originalité du montage de pince optique repose sur la détection du signal rétrodiffusé par la bille piégée, dans un plan conjugué du plan focal arrière de l'objectif, afin de mesurer la position relative de la bille par rapport au piège.Une part importante de ce travail a consisté à comprendre l'allure du signal détecté présentant un système d'interférences en anneaux, et à l’expliquer par un modèle simple. Ce modèle a permis de comprendre la présence d’artefacts de mesure de position dus à la superposition de l'anneau de phase sur la figure d’interférence. Pour y remédier, l'anneau de phase est déporté dans un plan conjugué intervenant uniquement dans l'imagerie de l'échantillon.La figure d'interférence présente un atout majeur : elle donne accès à la hauteur précise de la bille piégée, généralement difficile à mesurer. Cette information est nécessaire pour calibrer la constante de raideur du piège optique à la hauteur des cellules, que ce soit par l'analyse de la densité spectrale de puissance du mouvement brownien de la bille piégée ou par sa réponse à un échelon de position du piège. Ces deux méthodes de calibration, ainsi que l'application du théorème d’équipartition et l'analyse par inférence bayésienne, ont été mises en œuvre. Tous les résultats s'avèrent en bon accord. La calibration complète du dispositif en fait un outil prêt à l'emploi pour exercer des forces locales contrôlées en direction et en amplitude sur les cellules. / This manuscript details the development of an optical tweezer setup to study the mechanical properties of endothelial cells, involved in the development of atherosclerosis. The goal is to determine the viscoelastic properties of the cells, and to follow the propagation of the mechanical constraint inside the cell. This mechanical constraint is applied via a bead attached to the cell membrane and subjected to an optical trap.The setup built combines optical trapping with phase contrast microscopy, to apply a force while imaging the cells with the same microscope objective. The originality of the optical tweezer setup relies on the detection of the signal backscattered by the trapped bead, in a plane conjugate to the back focal plane of the objective, in order to measure the relative position of the bead with respect to the center of the trap.An important part of this work was dedicated to the understanding of the detected signal presenting an interference pattern with rings, explained by a simple model. This model provides an explanation for the position measurement artifacts arising from the superposition of the phase ring and the interference pattern. To solve the problem, the phase ring was moved in a conjugate plane involved only in the imaging path of the sample.The interference pattern has the main advantage of giving access to the precise height of the trapped bead, usually difficult to measure. This information is necessary to calibrate the optical trap stiffness at the height of the cells, either by the power spectrum analysis of the Brownian motion of the trapped bead, or by its response to a step motion of the trap. These two calibration methods, along with the application of the equipartition theorem and Bayesian inference analysis, were implemented and their results compared, showing a good agreement. The complete calibration of the setup makes it a ready-to-use tool to exert local forces controlled in direction and amplitude on cells.

[pt] Nas últimas décadas, interações entre luz e matéria provaram ser uma ferramenta versátil para medir e controlar sistemas mecânicos, encontrando aplicações desde detecção de forças até resfriamento ao estado fundamental de nanoesferas. Nesta dissertação, nós apresentamos algumas das ferramentas teóricas necessárias para descrever interferômetros, pinças ópticas e cavidades ópticas, constituintes fundamentais da caixa de ferramentas optomecânica. No regime clássico, estudamos o campo eletromagnético circulante em interferômetros lineares e mostramos como encontrar o campo resultante transmitido, apresentando exemplos de cavidades ópticas com um número arbitrário de elementos dispersivos. Nós também estudamos as forças de pressão de radiação que feixes ópticos podem imprimir em partículas dielétricas e mostramos como o aprisionamento óptico 3D é possível em focos claros e escuros. A potencial aplicação para captura de organismos vivos é estudada. No regime quântico, nós estudamos como o campo ressonante de cavidades ópticas pode interagir de forma dispersiva com diferentes sistemas mecânicos, dando origem a uma dinâmica quântica fechada emaranhante. Ao considerar uma nuvem ultra resfriada de átomos interagindo com dois modos ópticos, mostramos o surgimento de emaranhamento óptico que evidencia a natureza não-clássica do conjunto atômico macroscópico. A viabilidade experimental deste experimento com tecnologia atual é estudada. Além disso, nós investigamos o cenário em que uma pinça óptica posiciona uma partícula levitada dentro de uma cavidade óptica de forma que os fótons da pinça espalhados pela partícula possam sobreviver dentro da cavidade. Já foi demonstrado que esta interação, chamada de espalhamento coerente, pode resfriar nanopartículas até números de fônons menores do que um, atingindo profundamente o regime quântico. Nós mostramos que esta interação também pode gerar emaranhamento mecânico entre muitas partículas levitadas, mesmo em um ambiente a temperatura de 300K. Um resumo sobre sistemas de variáveis contínuas e a caixa de ferramentas numérica customizada usada ao longo deste trabalho são apresentados. / [en] Over the last decades, light-matter interactions have proven to be a versatile tool to measure and control mechanical systems, finding application from force sensing to ground state cooling of nanospheres. In this dissertation, we present some of the theoretical tools that describe interferometers, optical tweezers and optical cavities, fundamental constituents of the optomechanical toolbox. In the classical regime, we study the circulating electromagnetic field within linear interferometers and show how one can find the resulting transmitted field, presenting examples of optical cavities with an arbitrary number of dispersive elements. Moreover, we also study the radiation-pressure forces that optical beams can imprint on dielectric particles and show how 3D optical trapping is possible in both bright and dark focuses. Potential application to trapping of living organisms is studied. In the quantum regime, we study how the resonant field of optical cavities can dispersivelly interact with different mechanical systems, giving rise to an entangling closed quantum dynamics. When considering an ultracold cloud of atoms interacting with two optical modes, we show the emergence of optical entanglement which evidences the nonclassical nature of the macroscopic atomic ensemble. The experimental feasibility of this experiment with current technology is studied. Furthermore, we investigate the scenario where a finely tuned optical tweezer places a trapped particle inside an optical cavity such that the tweezer s scattered photons can survive inside the cavity. This so-called coherent scattering interaction has been shown to cool nanoparticles to phonon numbers lower than one deep into the quantum regime. We show that it also can generate mechanical entanglement between many levitated particles even in a room temperature environment. An overview on continuous variable systems and the custom numerical toolbox used throughout this work are presented.

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