Determining the mechanical properties of living cells accurately and repeatably is critical to understanding developmental, disease, and repair biology. The cellular environment is composed of fibrous proteins of a mix of diameters organized in random and aligned configurations. In the past two decades, several methods, including modified atomic force microscopy (AFM) and micro-pipette aspiration have been developed to measure cellular viscoelastic properties at single-cell resolution. We inquired if the fibrous environment affected cellular mechanobiology. Using our non-electrospinning Spinneret based Tunable Engineered Parameters (STEP) fiber manufacturing platform, we developed fused nanonets to measure single-cell forces and viscoelasticity. Using computer-controlled probes, we stretched single cells attached to two-fiber and three-fiber systems precisely and recorded the relaxation response of cells. The viscoelastic properties were determined by fitting the data to the standard linear viscoelastic solid model (SLS), which includes a spring (k0) in parallel with a spring (km)-damper (cm) series. In cases in which cells are seeded on two fibers, we tested hMSCs and BJ-5TA cells, and the viscoelastic components measurements k0, km, and cm are 26.16 ± 3.38 nN/µm, 5.81 ± 0.81 nN/µm, and 41.15 ± 5.97 nN-s/µm, respectively for hMSCs, while the k0, km, and cm, measurements of BJ-5TA cells are 20.02 ± 2.89 nN/µm, 4.62 ± 0.75 nN/µm, and 45.46 ± 6.00 nN-s/µm respectively. Transitioning to the three-fiber system resulted in an overall increase in native contractility of the cells while allowing us to understand how the viscoelastic response was distributed with an increasing number of fibers. Viscoelastic experiments were done twice. First, we pulled on the outermost fiber similar to the two-fiber case. The cell was then allowed to rest for two hours, sufficient time to regain its pre-stretching contractility. The cell was then excited by pulling on the middle fiber. The experimental results of cell seeding on three fibers proved that the viscoelastic property measurements depend on the excitation position. Overall, we present new knowledge on the cellular viscoelasticity of cells attached to ECM-mimicking fibers. / Master of Science / Investigating living cell mechanical properties including the viscoelastic properties of single living cell is critical to understanding developmental, disease, and repair biology. With the advancement of micrometer scale technologies, researchers are able to excite individual living cells. Current methods are mostly based on perturbing cells attached to flat 2D surfaces with limited physiological relevance. Since the native environment of cells is fibrous in nature, we inquired if cellular viscoelasticity could be measured of cells attached to suspended fibers. Using our non-electrospinning Spinneret based Tunable Engineered Parameters (STEP) fiber manufacturing platform, we developed fused nanonets to measure single-cell forces and viscoelasticity. Our suspended, aligned nanonet provides a unique way for us to pull on individual living cells using computercontrolled probes. By controlling the aligned fiber spacing, we are able to determine how many fibers the cells were seeded on. We first measured the viscoelastic properties of human mesenchymal stem cells(hMSCs) and human fibroblast BJ-5TA cells seeded on two fibers. The standard linear solid (SLS) model, which includes a spring in parallel with a spring-damper series, was used to quantitatively analyze the viscoelastic properties of cells. By giving the excitation on one fiber and measuring the cell forces on the other fiber, we calculated the corresponding spring constants and damping coefficients of the model. Then we investigated the viscoelastic properties of hMSCs seeded on three fibers by giving the excitation on the outermost fiber and then the middle fiber. Between the two excitations, the cell was allowed to relax for two hours and regain contractility. Our results confirm that the viscoelastic properties measurements depend on the excitation position. Overall, we present a new fiber-based force measurement system capable of determining the viscoelastic response of cells repeatably.

Es wird ein "off-axis" Aufbau zur digitalholographischen Mikroskopie in Durchlicht- und Auflichtanordnung vorgestellt, der gleichzeitig hoch aufgelöste "full-field" Amplituden- und quantitative Phasenkontrastmikroskopie ermöglicht. Dabei werden verschiedene Algorithmen zur numerischen Rekonstruktion der komplexen Objektwelle bzgl. ihrer Eignung für die mikroskopische Anordnung miteinander verglichen. Durch Kombination eines beugungsfreien räumlichen Phasenschiebeverfahrens, das die Rekonstruktion ohne "Twin-Image" und nullte Beugungsordnung ermöglicht, und der Auswertung des Fresnel-Kirchhoff''schen Beugungsintegrals mit der Faltungsmethode werden die besten Ergebnisse erzielt. Die gleichzeitige Rekonstruktion der Amplitude und der Phase der Objektwelle aus einem einzigen Hologramm erfordert die mathematische Beschreibung der räumlichen Phasenverteilung in der Hologrammebene. Zur Bestimmung der Modellparameter wurde ein effizienter Algorithmus entwickelt und hinsichtlich seiner Genauigkeit getestet. Darüber hinaus wurde der Zusammenhang zwischen axialer Probenposition und dem Rekonstruktionsabstand, dessen Kenntnis zur quantitativen Auswertung und für eine rein numerische Fokussierung notwendig ist, hergeleitet. Anhand von Untersuchungen an technischen Objekten werden die laterale Auflösung und die Phasenauflösung des Systems quantifiziert und weitere experimentelle Parameter optimiert. Transparente biologische Proben, wie lebende Zellen, werden in Durchlichtanordnung analysiert. Dabei ist zur Bestimmung der Zelldicke die Kenntnis der Brechungsindizes von Zelle und Medium erforderlich. Hierfür wird ein experimentelles Verfahren vorgestellt, das die Abschätzung des integralen Brechungsindexes von Einzelzellen anhand ihrer rekonstruierten räumlichen Phasenverteilung ermöglicht. Exemplarisch wird Zelldifferenzierung aufgrund morphologischer Eigenschaften nachgewiesen und es werden Ergebnisse dynamischer Untersuchungen an lebenden Zellen gezeigt und diskutiert. / An off-axis setup for digital holographic microscopy in incident and transmission light arrangement for simultaneous high resolution full field amplitude and quantitative phase contrast microscopy is presented. Different kinds of algorithms for numerical reconstruction of the complex object wave are compared concerning their applicability to the microscopy arrangement. By combining a non-diffractive spatial phase shifting algorithm that performs reconstruction without the disturbing terms twin image and zero order with the numerical evaluation of the Fresnel-Kirchhoff diffraction integral by a convolution method we achieve best results. The simultaneous reconstruction of the object wave''s amplitude and phase from a single hologram requires a mathematical model of the spatial phase distribution within the hologram plane. An efficient numerical algorithm has been developed for determining the model''s parameters automatically and tested concerning its accuracy. Furthermore, the relation between the axial position of the object and the distance of reconstruction which is required for the quantitative evaluation of the reconstructed images and the application of a pure numerical focus is derived. Technical objects were used to quantify the lateral resolution and the phase resolution of the system and to optimize several parameters of the setup. Biological probes such as living cells are analyzed in transmission light arrangement. As a result the knowledge of the refractive index of the medium and the cell is required to derive the cell''s thickness from the reconstructed phase. Thus a special experimental method for the approximation of the integral refractive index of single cells from the reconstructed phase has been developed. Finally results of cell differentiation by morphological varieties as well as results of stimulated dynamic morphological changes are presented and discussed.

Ziel dieser Arbeit ist es eine Toolbox zur Charakterisierung der anomalen Diffusion von Tracerpartikeln in dicht gepackten Systemen mit Fluoreszenz-Korrelationsspektroskopie (FCS) zur Verfügung zu stellen. Es wird gezeigt, dass die robusten Informationen über die Wahrscheinlichkeitsdichtefunktion (PDF) der Verschiebung des Tracers im asymptotischen Verhalten der FCS-Kurven auf langen, sowie auf kurzen Zeitskalen enthalten sind. So liefert die Analyse des Kurzzeitverhaltens zuverlässige Aussagen über die Werte des Exponenten der anomalen Diffusion, des Diffusionskoeffizienten und der niedrigeren Momente der PDF. Dies erlaubt es eine Gaußverteilung zu bestätigen oder zu widerlegen. Der Test auf Gaußverteilung könnte als Index verwendet werden, um die richtige Form der PDF aus einer Reihe von konkurrierenden Ergebnissen zu erraten. Darüber hinaus untersuchen wir die Konsequenz der nicht skalierenden PDF auf Ergebnis der FCS-Kurven. Wir berechnen die FCS für ein Continuous Time Random Walk Modell mit Wartezeiten gemäß einer Lévy-stabilen Verteilung mit exponentiellem cut-off. Die Ergebnisse zeigen, dass obwohl die Abweichungen vom Gauß’schen Verhalten bei der asymptotischen Analyse erkannt werden können, ihre Körper immer an Formen für die normale Diffusion perfekt angepasst werden können. Schließlich schlagen wir einen alternativen Ansatz für die Durchführung von Spot Variation FCS mit dem gewöhnlichen FCS-Setup vor. Wir führen eine nicht-lineare Transformation ein, die auf das mit Binning oder Kernel smoothing method geglättete Intensitätsprofil der detektierten Fluoreszenzphotonen angewendet wird. Ihre Autokorrelation imitiert die FCS-Kurven für die Größen des Laserspots, die im Experiment effektiv kleiner als die anfängliche Größe sind. Die erhaltenen FCS-Kurven werden verwendet, um künstliche dicht gepackte Systeme sowie lebende Zellen auf Nano-Domänen oder Barrieren hin zu untersuchen. / The objective of this thesis is to provide a toolbox for characterization of anomalous diffusion of tracer particle in crowded systems using fluorescence correlation spectroscopy (FCS). We discuss that the robust information about the probability density function (PDF) of the particle’s displacement is contained in the asymptotic behaviour of the FCS curves at long and short times. Thus, analysis of the short-time behaviour provides reliable values of exponent of anomalous, diffusion coefficient and lower moments of the PDF. This allows one to to confirm or reject its Gaussian nature. The Gaussianity test could be then used to guess the correct form of the PDF from a set of competing models. We show the applicability of the proposed analysis protocol in artificially crowded systems and in living cell experiments. Furthermore, we investigate the consequence of non-scaling PDF on the possible results of the FCS data. As an example of such processes, we calculate the FCS curve for a continues time random walk model with waiting times delivered from Lévy-stable distribution with an exponential cut-off in equilibrium. The results indicate that, although the deviations from Gaussian behaviour may be detected when analyzing the short- and long-time asymptotic of the corresponding curves, their bodies are still perfectly fitted by the fit form used for normal diffusion. Finally, we propose an alternative approach for performing spot variation FCS using an ordinary FCS set-up. We introduce a non-linear transformation which applies on the smoothed intensity profile of the detected fluorescence photons with binning or smoothing kernel method. Autocorrelation of the generated intensity profiles mimic the FCS curves for the sizes of laser spots which are effectively smaller than the initial one in the experiment. The obtained FCS curves are used to investigate the presence of nano-domains or barriers in artificially crowded systems and in living cells.

Hyaluronic acid (HA) is one of the primary chemical building blocks of the extracellular matrix and thus is an attractive material for biomedical applications. FDA approved HA-based materials are available as dermal fillers, joint viscosupplements, vitreous substitutes, and abdominal adhesion barriers. The engineering of new HA-based materials and applications is an active area of research. Here we develop several new types of HA-based hydrogels with unique and useful properties. To address the challenge of delivering hydrophobic drugs from hydrophilic hydrogel matrices we have grafted HA hydrogels with [Beta]-cyclodextrin to create hydrogels capable of binding poorly water soluble drugs. To create HA hydrogels with unique anisotropic swelling behavior we have developed a dual-crosslinking technique in which a super-swelling chemically crosslinked hydrogel is patterned with low-swelling photocrosslinked domains. When this dual-crosslinked hydrogel is swelled it contorts into a new shape because of differential swelling among photopatterned regions. To address the challenge of creating hydrogel scaffolds with biomimetic branched porosity we have invented a "crystal templating" technique. This technique grows dendritic crystals throughout a biopolymer solution, crosslinks the biopolymer around the crystals, and washes the crystals away to yield a hydrogel with a dendritic macroporous network. Lastly, we invented a method for patterning a substrate with a microarray of hydrogel compartments. A microarray of living cells is obtained when cells are seeded on the hydrogel patterned substrate. This method addresses the need for an inexpensive, simple method for obtaining living cell microarrays that does not require clean room labs and lithographic expertise. Each of these new materials were based on hyaluronic acid hydrogels but the methods are generalizable to hydrogels of other polymers too. In conclusion, the novel methods in this dissertation are a significant contribution to the engineering of HA-based materials. / text

Ziel dieser Arbeit ist es eine Toolbox zur Charakterisierung der anomalen Diffusion von Tracerpartikeln in dicht gepackten Systemen mit Fluoreszenz-Korrelationsspektroskopie (FCS) zur Verfügung zu stellen. Es wird gezeigt, dass die robusten Informationen über die Wahrscheinlichkeitsdichtefunktion (PDF) der Verschiebung des Tracers im asymptotischen Verhalten der FCS-Kurven auf langen, sowie auf kurzen Zeitskalen enthalten sind. So liefert die Analyse des Kurzzeitverhaltens zuverlässige Aussagen über die Werte des Exponenten der anomalen Diffusion, des Diffusionskoeffizienten und der niedrigeren Momente der PDF. Dies erlaubt es eine Gaußverteilung zu bestätigen oder zu widerlegen. Der Test auf Gaußverteilung könnte als Index verwendet werden, um die richtige Form der PDF aus einer Reihe von konkurrierenden Ergebnissen zu erraten. Darüber hinaus untersuchen wir die Konsequenz der nicht skalierenden PDF auf Ergebnis der FCS-Kurven. Wir berechnen die FCS für ein Continuous Time Random Walk Modell mit Wartezeiten gemäß einer Lévy-stabilen Verteilung mit exponentiellem cut-off. Die Ergebnisse zeigen, dass obwohl die Abweichungen vom Gauß’schen Verhalten bei der asymptotischen Analyse erkannt werden können, ihre Körper immer an Formen für die normale Diffusion perfekt angepasst werden können. Schließlich schlagen wir einen alternativen Ansatz für die Durchführung von Spot Variation FCS mit dem gewöhnlichen FCS-Setup vor. Wir führen eine nicht-lineare Transformation ein, die auf das mit Binning oder Kernel smoothing method geglättete Intensitätsprofil der detektierten Fluoreszenzphotonen angewendet wird. Ihre Autokorrelation imitiert die FCS-Kurven für die Größen des Laserspots, die im Experiment effektiv kleiner als die anfängliche Größe sind. Die erhaltenen FCS-Kurven werden verwendet, um künstliche dicht gepackte Systeme sowie lebende Zellen auf Nano-Domänen oder Barrieren hin zu untersuchen. / The objective of this thesis is to provide a toolbox for characterization of anomalous diffusion of tracer particle in crowded systems using fluorescence correlation spectroscopy (FCS). We discuss that the robust information about the probability density function (PDF) of the particle’s displacement is contained in the asymptotic behaviour of the FCS curves at long and short times. Thus, analysis of the short-time behaviour provides reliable values of exponent of anomalous, diffusion coefficient and lower moments of the PDF. This allows one to to confirm or reject its Gaussian nature. The Gaussianity test could be then used to guess the correct form of the PDF from a set of competing models. We show the applicability of the proposed analysis protocol in artificially crowded systems and in living cell experiments. Furthermore, we investigate the consequence of non-scaling PDF on the possible results of the FCS data. As an example of such processes, we calculate the FCS curve for a continues time random walk model with waiting times delivered from Lévy-stable distribution with an exponential cut-off in equilibrium. The results indicate that, although the deviations from Gaussian behaviour may be detected when analyzing the short- and long-time asymptotic of the corresponding curves, their bodies are still perfectly fitted by the fit form used for normal diffusion. Finally, we propose an alternative approach for performing spot variation FCS using an ordinary FCS set-up. We introduce a non-linear transformation which applies on the smoothed intensity profile of the detected fluorescence photons with binning or smoothing kernel method. Autocorrelation of the generated intensity profiles mimic the FCS curves for the sizes of laser spots which are effectively smaller than the initial one in the experiment. The obtained FCS curves are used to investigate the presence of nano-domains or barriers in artificially crowded systems and in living cells.

Cette thèse est dédiée à l’analyse et la modélisation d'expériences où la position d'un traceur dans le milieu cellulaire est enregistrée au cours du temps. Il s’agit de pouvoir de retirer le maximum d’information à partir d’une seule trajectoire observée expérimentalement. L’enjeu principal consiste à identifier les mécanismes de transport sous-jacents au mouvement observé. La difficulté de cette tâche réside dans l’analyse de trajectoires individuelles, qui requiert de développer de nouveaux outils d’analyse statistique. Dans le premier chapitre, un aperçu est donné de la grande variété des dynamiques observables dans le milieu cellulaire. Notamment, une revue de différents modèles de diffusion anormale et non-Gaussienne est réalisée. Dans le second chapitre, un test est proposé afin de révéler la rupture d'ergodicité faible à partir d’une trajectoire unique. C’est une généralisation de l’approche de M. Magdziarz et A. Weron basée sur la fonction caractéristique du processus moyennée au cours du temps. Ce nouvel estimateur est capable d’identifier la rupture d’ergodicité de la marche aléatoire à temps continu où les temps d'attente sont distribués selon une loi puissance. Par le calcul de la moyenne de l’estimateur pour plusieurs modèles typiques de sous diffusion, l’applicabilité de la méthode est démontrée. Dans le troisième chapitre, un algorithme est proposé afin reconnaître à partir d’une seule trajectoire les différentes phases d'un processus intermittent (e.g. le transport actif/passif à l'intérieur des cellules, etc.). Ce test suppose que le processus alterne entre deux phases distinctes mais ne nécessite aucune hypothèse sur la dynamique propre dans chacune des phases. Les changements de phase sont capturés par le calcul de quantités associées à l’enveloppe convexe locale (volume, diamètre) évaluées au long de la trajectoire. Il est montré que cet algorithme est efficace pour distinguer les états d’une large classe de processus intermittents (6 modèles testés). De plus, cet algorithme est robuste à de forts niveaux de bruit en raison de la nature intégrale de l’enveloppe convexe. Dans le quatrième chapitre, un modèle de diffusion dans un milieu hétérogène où le coefficient de diffusion évolue aléatoirement est introduit et résolu analytiquement. La densité de probabilité des déplacements présente des queues exponentielles et converge vers une Gaussienne au temps long. Ce modèle généralise les approches précédentes et permet ainsi d’étudier en détail les hétérogénéités dynamiques. En particulier, il est montré que ces hétérogénéités peuvent affecter de manière drastique la précision de mesures effectuées sur une trajectoire par des moyennes temporelles. Dans le dernier chapitre, les méthodes d’analyses de trajectoires individuelles sont utilisées pour étudier deux expériences. La première analyse effectuée révèle que les traceurs explorant le cytoplasme montrent que la densité de probabilité des déplacements présente des queues exponentielles sur des temps plus longs que la seconde. Ce comportement est indépendant de la présence de microtubules ou du réseau d’actine dans la cellule. Les trajectoires observées présentent donc des fluctuations de diffusivité témoignant pour la première fois de la présence d’hétérogénéités dynamiques au sein du cytoplasme. La seconde analyse traite une expérience dans laquelle un ensemble de disques de 4mm de diamètre a été vibré verticalement sur une plaque, induisant un mouvement aléatoire des disques. Par une analyse statistique approfondie, il est démontré que cette expérience est proche d'une réalisation macroscopique d'un mouvement Brownien. Cependant les densités de probabilité des déplacements des disques présentent des déviations par rapport à la Gaussienne qui sont interprétées comme le résultat des chocs inter-disque. Dans la conclusion, les limites des approches adoptées ainsi que les futures pistes de recherches ouvertes par ces travaux sont discutées en détail. / This thesis is dedicated to the analysis and modeling of experiments where the position of a tracer in the cellular medium is recorded over time. The goal is to be able to extract as much information as possible from a single experimentally observed trajectory. The main challenge is to identify the transport mechanisms underlying the observed movement. The difficulty of this task lies in the analysis of individual trajectories, which requires the development of new statistical analysis tools. In the first chapter, an overview is given of the wide variety of dynamics that can be observed in the cellular medium. In particular, a review of different models of anomalous and non-Gaussian diffusion is carried out. In the second chapter, a test is proposed to reveal weak ergodicity breaking from a single trajectory. This is a generalization of the approach of M. Magdziarz and A. Weron based on the time-averaged characteristic function of the process. This new estimator is able to identify the ergodicity breaking of continuous random walking where waiting times are power law distributed. By calculating the average of the estimator for several subdiffusion models, the applicability of the method is demonstrated. In the third chapter, an algorithm is proposed to recognize the different phases of an intermittent process from a single trajectory (e.g. active/passive transport within cells, etc.).This test assumes that the process alternates between two distinct phases but does not require any hypothesis on the dynamics of each phase. Phase changes are captured by calculating quantities associated with the local convex hull (volume, diameter) evaluated along the trajectory. It is shown that this algorithm is effective in distinguishing states from a large class of intermittent processes (6 models tested). In addition, this algorithm is robust at high noise levels due to the integral nature of the convex hull. In the fourth chapter, a diffusion model in a heterogeneous medium where the diffusion coefficient evolves randomly is introduced and solved analytically. The probability density function of the displacements presents exponential tails and converges towards a Gaussian one at long time. This model generalizes previous approaches and thus makes it possible to study dynamic heterogeneities in detail. In particular, it is shown that these heterogeneities can drastically affect the accuracy of measurements made by time averages along a trajectory. In the last chapter, single-trajectory based methods are used for the analysis of two experiments. The first analysis carried out shows that the tracers exploring the cytoplasm show that the probability density of displacements has exponential tails over periods of time longer than the second. This behavior is independent of the presence of both microtubules and the actin network in the cell. The trajectories observed therefore show fluctuations in diffusivity, indicating for the first time the presence of dynamic heterogeneities within the cytoplasm. The second analysis deals with an experiment in which a set of 4mm diameter discs was vibrated vertically on a plate, inducing random motion of the disks. Through an in-depth statistical analysis, it is demonstrated that this experiment is close to a macroscopic realization of a Brownian movement. However, the probability densities of disks’ displacements show deviations from Gaussian which are interpreted as the result of inter-disk shocks. In the conclusion, the limits of the approaches adopted as well as the future research orientation opened by this thesis are discussed in detail.