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

Orientador: Carlos Lenz Cesar / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-20T14:50:59Z (GMT). No. of bitstreams: 1 Marques_GustavoPires_M.pdf: 1771357 bytes, checksum: 8ee6919633e2615608f25b33bec98e96 (MD5) Previous issue date: 2005 / Resumo: O microscópio de força atômica é uma ferramenta que possibilita a medida de forças precisamente localizadas com resoluções no tempo, espaço e força jamais vistas. No coração deste instrumento está um sensor a base de uma viga (cantilever) que é responsável pelas características fundamentais do AFM. O objetivo desta pesquisa foi usar a deflexão deste cantilever para obter uma calibração rápida e precisa da força da armadilha da pinça óptica, assim como testar e comparar com os método tradicionalmente utilizados para este propósito. Para isso, foi necessário analisar e entender o condicionamento de sinais utilizados no AFM. Foram estudados cantilever tradicionais, cujo sistema de detecção é baseado na deflexão de um feixe laser em conjunto com fotodetectores, bem como cantilevers piezoresistivos. Cantilevers piezoresistivos fornecem uma alternativa simples e conveniente aos cantilevers ópticos. A integração de um elemento sensorial dentro do cantilever elimina a necessidade de um laser externo e de um detector utilizados na maioria dos AFMs. Isto elimina a etapa delicada de alinhamento da laser ao cantilever e fotodetector que normalmente precede uma medida com AFM, uma simplificação que expande o potencial do AFM para o uso em meios adversos, como câmaras de ultra alto vácuo ou, como no caso específico das Pinças Ópticas, onde existem esferas em solução líquida e também restrições de dimensão / Abstract: The atomic force microscope (AFM) is a tool that enables the measurement of precisely localized forces with unprecedented resolution in time, space and force. At the heart of this instrument is a cantilever probe that sets the fundamental features of the AFM. The objective of this research has been using the deflection of this cantilever to get a fast and accurate calibration of optical tweezers trap force, as well as testing and comparing to the traditionally used methods of calibration for this purpose. For that it was necessary to resolve and understand the sensors signals conditioning used in the AFM. Traditional cantilevers, whose detection system is based on the deflection of a laser beam in addition with a photodetector, as well as piezoresistive cantilevers has been studied. Piezoresistive cantilevers provide a simple and convenient alternative to optically detected cantilevers. Integration of a sensing element into the cantilever eliminates the need for the external laser and detector used in most AFMs. This removes the delicate step of aligning the laser to the cantilever and photodetector which usually precedes an AFM measurement, a simplification which expands the potential of the AFM for use in difficult environments such as ultrahigh vacuum chambers or, as in Optical Tweezers specific case, where there are spheres into a liquid solution as well as dimensional constraints / Mestrado / Física / Mestre em Física

Nous avons étudié expérimentalement les fluctuations de micro-particules browniennes piégées à l'aide de pinces optiques dans un réseau de puits de potentiels voisins. Nous donnons un descriptif général du montage expérimental, puis détaillons quatre utilisations différentes du système. Nous avons d'abord utilisé une unique particule dans un double puits de potentiel pour modéliser un système mémoire à deux niveaux, avec lequel nous avons vérifié le principe de Landauer sur le coût minimal en énergie pour l'effacement d'un bit d'information. Nous avons également appliqué une version détaillée d'un théorème de fluctuation à la procédure d'effacement de l'information pour retrouver la limite énergétique attendue. Nous avons ensuite étudié l'interaction hydrodynamique entre deux particules dont l'une est soumise à une température effective. Nous avons montré qu'il n'y a pas de fluctuations anormales lors de la transition sol-gel de la gélatine, contrairement à ce qui avait été observé précédemment, et que ce système ne pouvait donc pas être utilisé pour étudier des températures effectives. En revanche, nous avons montré que l'ajout d'un forçage aléatoire bien choisi sur la position d'un piège créait une température effective. Nous avons montré que le forçage d'une des particules résultait en une corrélation instantanée entre les mouvements des deux particules, et s'accompagnait d'un échange de chaleur de la particule virtuellement chaude à la particule froide en équilibre avec le bain thermique. Nous avons obtenu un bon accord entre les données expérimentales et les prédictions d'un modèle de couplage hydrodynamique. Enfin, nous décrivons l'utilisation de canaux micro-fluidiques pour réaliser un écoulement cisaillé à l'échelle micrométrique, et nous discutons de la possibilité d'interpréter un cisaillement en terme de température effective en testant une relation de fluctuation-dissipation. / We experimentally study the fluctuations of Brownian micro-particles trapped with optical tweezers arranged in various spatial configurations. We give a general description of the set-up and detail four different experiments we conducted. We first use a single particle in a double-well potential to model a two-state memory system. We verify the Landauer principle on the minimal energetic cost to erase one bit of information, and we use a detailed version of a fluctuation theorem to retrieve the expected energetic bound. We then use two particles in two different traps to study the hydrodynamic interactions between two systems kept at different effective temperatures. Contrary to what was previously observed, we show that the sol-gel transition of gelatine does not provide any anomalous fluctuations for the trapped particle when the sample is quenched below gelification temperature. However, we show that an effective temperature is created when a well chosen random noise is added on one trap position. We demonstrate that the random forcing on one particle induces an instantaneous correlation between the two particles motions, and an energy exchange from the virtually hot particle to the cold one, which is in equilibrium with the thermal bath. We show a good agreement between the experimental data and the predictions from an hydrodynamic coupling model. Finally, we describe the use of micro-fluidic channels to create a shear flow at the micron size, and we discuss the possibility to interpret the force due to the shear-flow in terms of an effective temperature by testing a fluctuation-dissipation relation.

Die Proteinfaltung ist ein Prozess der molekularen Selbstorganisation, bei dem sich eine lineare Kette von Aminosäuren zu einer definierten, funktionellen dreidimensionalen Struktur zusammensetzt. Der Prozess der Faltung ist ein thermisch getriebener diffusiver Prozess durch eine Gibbs-Energie-Landschaft im Konformationsraum für die Struktur der minimalen Energie. Während dieses Prozesses zeigt die freie Enthalpie des Systems nicht immer eine monotone Abnahme; stattdessen führt eine suboptimale Kompensation der Enthalpie- und der Entropieänderung während jedes Faltungsschrittes zur Bildung von Freien-Enthalpie-Faltungsbarrieren. Diese Barrieren und damit verbundenen hochenergetischen Übergangszustände, die wichtige Informationen über Mechanismen der Proteinfaltung enthalten, sind jedoch kinetisch unzugänglich. Um den Prozess der Barrierebildung und die strukturellen Merkmale von Übergangszuständen aufzudecken, werden Proteine genutzt, die über barrierefreie Pfade falten – so genannte “downhill folder“. Aufgrund der geringen Faltungsbarrieren werden wichtige Interaktionen der Faltung zugänglich und erlauben Einblicke in die ratenbegrenzenden Faltungsvorgänge. In dieser Arbeit vergleichen wir die Faltungsdynamiken von drei verschiedenen Varianten eines Lambda-Repressor-Fragments, bestehend aus den Aminosäuren 6 bis 85: ein Zwei-Zustands-Falter λWT (Y22W) und zwei downhill-folder-artige Varianten, λYA (Y22W/Q33Y/ G46,48A) und λHA (Y22W/Q33H/G46,48A). Um auf die Kinetik und die strukturelle Dynamik zu greifen zu können, werden Einzelmolekülkraftspektroskopische Experimente mit optische Pinzetten mit Submillisekunden- und Nanometer-Auflösung verwendet. Ich fand, dass die niedrige denaturierende Kraft die Mikrosekunden Faltungskinetik von downhill foldern auf eine Millisekunden-Zeitskala verlangsamt, sodass das System für Einzelmolekülstudien gut zugänglich ist. Interessanterweise zeigten sich unter Krafteinwirkung die downhill-folder-artigen Varianten des Lambda-Repressors als kooperative Zwei-Zustands-Falter mit deutlich unterschiedlicher Faltungskinetik und Kraftabhängigkeit. Drei Varianten des Proteins zeigten ein hoch konformes Verhalten unter Last. Die modellfreie Rekonstruktion von Freien-Enthalpie-Landschaften ermöglichte es uns, die feinen Details der Transformation des Zwei-Zustands-Faltungspfad direkt in einen downhill-artigen Pfad aufzulösen. Die Auswirkungen von einzelnen Mutationen auf die Proteinstabilität, Bildung der Übergangszustände und die konformationelle Heterogenität der Faltungs- und Entfaltungszustände konnten beobachtet werden. Interessanterweise zeigen unsere Ergebnisse, dass sich die untersuchten Varianten trotz der ultraschnellen Faltungszeit im Bereich von 2 μs in einem kooperativen Prozess über verbleibende Energiebarrieren falten und entfalten, was darauf hindeutet, dass wesentlich schnellere Faltungsraten notwendig sind um ein downhill Limit vollständig zu erreichen.:I Theoretical background 1 1 Introduction 3 2 Protein folding: the downhill scenario 5 2.1 Protein folding as a diffusion on a multidimensional energy landscape 5 2.2 Downhill folding proteins 7 2.2.1 Thermodynamic description of downhill folders 7 2.2.2 Identification criteria for downhill folders 8 2.3 Lambda repressor as a model system for studying downhill folding 9 2.3.1 Wild-type lambda repressor fragment λ{6-85} 10 2.3.2 Acceleration of λ{6-85} folding by specifific point mutations 11 2.3.3 The incipient-downhill λYA and downhill λHA variants 14 2.4 Single-molecule techniques as a promising tool for probing downhill folding dynamics 17 3 Single-molecule protein folding with optical tweezers 19 3.1 Optical tweezers 19 3.1.1 Working principle of optical tweezers 19 3.1.2 The optical tweezers setup 21 3.2 The dumbbell assay 22 3.3 Measurement protocols 23 3.3.1 Constant-velocity experiments 23 3.3.2 Constant-trap-distance experiments (equilibrium experiments) 24 4 Theory and analysis of single-molecule trajectories 27 4.1 Polymer elasticity models 27 4.2 Equilibrium free energies of protein folding in optical tweezers 28 4.3 Signal-pair correlation analysis 29 4.4 Force dependence of transition rate constants 29 4.4.1 Zero-load extrapolation of rates: the Berkemeier-Schlierf model 30 4.4.2 Detailed balance for unfolding and refolding data 31 4.5 Direct measurement of the energy landscape via deconvolution 32 II Results 33 5 Efficient strategy for protein-DNA hybrid formation 35 5.1 Currently available strategies for protein-DNA hybrid formation 35 5.2 Novel assembly of protein-DNA hybrids based on copper-free click chemistry 37 5.3 Click-chemistry based assembly preserves the native protein structure 40 5.4 Summary 42 6 Non-equilibrium mechanical unfolding and refolding of lambda repressor variants 45 6.1 Non-equilibrium unfolding and refolding of lambda repressor λWT 45 6.2 Non-equilibrium unfolding and refolding of incipient-downhill λYA and downhill λHA variants of lambda repressor 48 6.3 Summary 52 7 Equilibrium unfolding and refolding of lambda repressor variants 53 7.1 Importance of the trap stiffness to resolve low-force nanometer transitions 54 7.2 Signal pair-correlation analysis to achieve millisecond transitions 56 7.3 Force-dependent equilibrium kinetics of λWT 59 7.4 Equilibrium folding of incipient-downhill λYA and downhill λHA variants of lambda repressor 61 7.5 Summary 65 8 Model-free energy landscape reconstruction for λWT, incipient-downhill λYA and downhill λHA variants 69 8.1 Direct observation of the effect of a single mutation on the conformational heterogeneity and protein stability 71 8.2 Artifacts of barrier-height determination during deconvolution 75 8.3 Summary 76 9 Conclusions and Outlook 79 / Protein folding is a process of molecular self-assembly in which a linear chain of amino acids assembles into a defined, functional three-dimensional structure. The process of folding is a thermally driven diffusive search on a free-energy landscape in the conformational space for the minimal-energy structure. During that process, the free energy of the system does not always show a monotonic decrease; instead, sub-optimal compensation of enthalpy and entropy change during each folding step leads to formation of folding free-energy barriers. However, these barriers, and associated high-energy transition states, that contain key information about mechanisms of protein folding, are kinetically inaccessible. To reveal the barrier-formation process and structural characteristics of transition states, proteins are employed that fold via barrierless paths – so-called downhill folders. Due to the low folding barriers, the key folding interactions become accessible, yielding insights about the rate-limiting folding events. Here, I compared the folding dynamics of three different variants of a lambda repressor fragment, containing amino acids 6 to 85: a two-state folder λWT (Y22W) and two downhill-like folding variants, λYA (Y22W/Q33Y/G46,48A) and λHA (Y22W/Q33H/G46,48A). To access the kinetics and structural dynamics, single-molecule optical tweezers with submillisecond and nanometer resolution are used. I found that force perturbation slowed down the microsecond kinetics of downhill folders to a millisecond time-scale, making it accessible to single-molecule studies. Interestingly, under load, the downhill-like variants of lambda repressor appeared as cooperative two-state folders with significantly different folding kinetics and force dependence. The three protein variants displayed a highly compliant behaviour under load. Model-free reconstruction of free-energy landscapes allowed us to directly resolve the fine details of the transformation of the two-state folding path into a downhill-like path. The effect of single mutations on protein stability, transition state formation and conformational heterogeneity of folding and unfolding states was observed. Noteworthy, our results demonstrate, that despite the ultrafast folding time in a range of 2 µs, the studied variants fold and unfold in a cooperative process via residual barriers, suggesting that much faster folding rate constants are required to reach the full-downhill limit.:I Theoretical background 1 1 Introduction 3 2 Protein folding: the downhill scenario 5 2.1 Protein folding as a diffusion on a multidimensional energy landscape 5 2.2 Downhill folding proteins 7 2.2.1 Thermodynamic description of downhill folders 7 2.2.2 Identification criteria for downhill folders 8 2.3 Lambda repressor as a model system for studying downhill folding 9 2.3.1 Wild-type lambda repressor fragment λ{6-85} 10 2.3.2 Acceleration of λ{6-85} folding by specifific point mutations 11 2.3.3 The incipient-downhill λYA and downhill λHA variants 14 2.4 Single-molecule techniques as a promising tool for probing downhill folding dynamics 17 3 Single-molecule protein folding with optical tweezers 19 3.1 Optical tweezers 19 3.1.1 Working principle of optical tweezers 19 3.1.2 The optical tweezers setup 21 3.2 The dumbbell assay 22 3.3 Measurement protocols 23 3.3.1 Constant-velocity experiments 23 3.3.2 Constant-trap-distance experiments (equilibrium experiments) 24 4 Theory and analysis of single-molecule trajectories 27 4.1 Polymer elasticity models 27 4.2 Equilibrium free energies of protein folding in optical tweezers 28 4.3 Signal-pair correlation analysis 29 4.4 Force dependence of transition rate constants 29 4.4.1 Zero-load extrapolation of rates: the Berkemeier-Schlierf model 30 4.4.2 Detailed balance for unfolding and refolding data 31 4.5 Direct measurement of the energy landscape via deconvolution 32 II Results 33 5 Efficient strategy for protein-DNA hybrid formation 35 5.1 Currently available strategies for protein-DNA hybrid formation 35 5.2 Novel assembly of protein-DNA hybrids based on copper-free click chemistry 37 5.3 Click-chemistry based assembly preserves the native protein structure 40 5.4 Summary 42 6 Non-equilibrium mechanical unfolding and refolding of lambda repressor variants 45 6.1 Non-equilibrium unfolding and refolding of lambda repressor λWT 45 6.2 Non-equilibrium unfolding and refolding of incipient-downhill λYA and downhill λHA variants of lambda repressor 48 6.3 Summary 52 7 Equilibrium unfolding and refolding of lambda repressor variants 53 7.1 Importance of the trap stiffness to resolve low-force nanometer transitions 54 7.2 Signal pair-correlation analysis to achieve millisecond transitions 56 7.3 Force-dependent equilibrium kinetics of λWT 59 7.4 Equilibrium folding of incipient-downhill λYA and downhill λHA variants of lambda repressor 61 7.5 Summary 65 8 Model-free energy landscape reconstruction for λWT, incipient-downhill λYA and downhill λHA variants 69 8.1 Direct observation of the effect of a single mutation on the conformational heterogeneity and protein stability 71 8.2 Artifacts of barrier-height determination during deconvolution 75 8.3 Summary 76 9 Conclusions and Outlook 79

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