Kieselalgen – auch Diatomeen genannt – verfügen über die einzigartige Fähigkeit, nanostrukturierte, hierarchisch aufgebaute Zellwände aus Siliziumdioxid – auch als Biosilica bekannt – mit beispielloser Genauigkeit und Reproduzierbarkeit zu bilden. Ein tieferes Verständnis für diesen Prozess, der als “Biomineralisation“ bekannt ist, ist nicht nur auf dem Gebiet der Grundlagenforschung zu Kieselalgen sehr bedeutsam, sondern auch für die Nutzung dieser Nanostrukturierung in den Materialwissenschaften oder der Nanobiotechnologie. Nach dem derzeitigem Stand der Wissenschaft wird diese Strukturierung durch die Selbstorganisation von Proteinmustern, an denen sich das Siliziumdioxid bildet, erreicht. Um die Funktion und das Zusammenspiel einzelner Proteine, die an diesem Biomineralisationsprozess beteiligt sind, entschlüsseln zu können, ist es essentiell ihre strukturelle Organisation aufzuklären und diese mit den morphologischen Zellwandmerkmalen zu korrelieren. Die Größenordnung dieser Merkmale ist im Bereich von Nanometern angesiedelt. Mit Hilfe der Elektronenmikroskopie können diese Biosilicastrukturen aufgelöst werden, jedoch ist keine proteinspezifische Information verfügbar. Ziel dieser Arbeit war es daher, eine Technik zu etablieren, die in der Lage ist, einzelne Biosilica-assozierte Proteine mit Nanometer-Präzision zu lokalisieren. Um dieses Ziel zu erreichen, wurde Einzelmoleküllokalisationsmikroskopie (single-molecule localization microscopy, kurz: SMLM) beispielhaft in der Kieselalge Thalassiosira pseudonana etabliert. Die Position verschiedener Biosilica-assoziierte Proteine innerhalb des Biosilicas und nach dessen chemischer Auflösung wurde mit einer hohen räumlichen Auflösung bestimmt. Um quantitative Ergebnisse zu erhalten, wurde ein Analyse-Workflow entwickelt, der grafische Benutzeroberflächen und Skripte für die Visualisierung, das Clustering und die Kolokalisation von SMLM Daten beinhaltet. Um optimale Markierungen für SMLM an Biosilica-eingebetteten Proteinen zu finden, wurde ein umfassendes Screening von photo-schaltbaren fluoreszierenden Proteinen durchgeführt. Diese wurden als Fusionsproteine mit Silaffin3, einem Protein, welches eng mit der Biosilica-Zellwand assoziiert ist, exprimiert. Es konnte gezeigt werden, dass nur drei von sechs Kandidaten funktional sind, wenn sie in Biosilica eingebettet sind. Silaffin3 konnte indirekt mittels SMLM mit einer Lokalisationsgenauigkeit von 25 nm detektiert werden. Dies erlaubte es, seine strukturelle Organisation aufzulösen und Silaffin3 als eine Hauptkomponente in der Basalkammer der Fultoportulae zu identifizieren.:1 INTRODUCTION 1 1.1 Diatoms – a model system for biomineralization 3 1.2 Imaging of biosilica and associated organic components 8 1.3 Single-molecule localization microscopy (SMLM) 10 2 METHODS & METHOD DEVELOPMENT FOR SMLM DATASETS 17 2.1 Super-resolution reconstruction 19 2.2 Tools for SMLM resolution estimates 21 2.3 Voronoi tessellation for noise-removal and cluster estimation 25 2.4 Tools for SMLM cluster analysis 27 2.5 Coordinate-based co-localization 32 2.6 PairRice – A novel algorithm to extract distances between cluster pairs 33 2.7 SiMoNa – A new GUI for exploring SMLM datasets 35 3 RESOLUTION OF THE SMLM SETUP TESTED WITH DNA ORIGAMI NANOSTRUCTURES 41 3.1 DNA origami as a length standard 42 3.2 Global resolution estimates 44 3.3 Local resolution estimates 47 3.4 Conclusion 53 4 EVALUATION OF PHOTO-CONTROLLABLE FLUORESCENT PROTEINS FOR PALM IN DIATOMS 55 4.1 Selecting PCFPs to minimize interference with the diatom autofluorescence 56 4.2 Screening results for cytosolic and biosilica-embedded PCFPs 58 4.3 The underlying conversion mechanism 61 4.4 Conclusion 63 5 IMAGING THE SIL3 MESHWORK 65 5.1 Analyzing protein layer thickness using tpSil3-Dendra2 65 5.2 Imaging the valve region using tpSil3 68 5.3 Resolution and localization parameters of tpSil3 70 5.4 Conclusion 72 6 DECIPHERING CINGULIN PATTERNS WITH CO LOCALIZATION STUDIES 73 6.1 A two-color cingulin construct for PALM-STORM 73 6.2 Steps towards PALM-STORM: screening, alignment, and imaging routine 76 6.3 Co-localization studies: quantification, clustering, and correlations 83 6.4 Conclusion 91 7 OUTLOOK 93 8 MATERIALS & METHODS 97 8.1 Microscope specifications 97 8.2 DNA origami annealing and AFM measurements 99 8.3 Diatom sample preparations 100 8.4 Fluorescence imaging conditions 102 8.5 Buffer systems 103 9 APPENDICES 105 9.1 Tables and Protocols 105 9.2 Satellite projects 112 9.2.1 Quantitative fluorescence intensity analysis of 3D time-lapse confocal microscopy data in diatoms 112 9.2.2 Applying neural networks to filter SMLM localizations 118 9.2.3 In vivo imaging at super-resolution conditions using SOFI 121 9.2.4 Quantifying chromatic aberrations in the microscope using fiducials 123 10 REFERENCES 127 / Diatoms feature the unique ability to form nanopatterned hierarchical silica cell walls with unprecedented accuracy and reproducibility. Gathering a deeper understanding of this process that is known as “biomineralization” is vitally important not only in the field of diatom research. In fact, the nanopatterning can also be exploited in the fields of material sciences or nanobiotechnology. According to the current understanding, the self-assembly of protein patterns along which biosilica is formed is key to this nanopatterning. Thus, in order to unravel the function of individual proteins that are involved in this biomineralization process, their structural organization has to be deciphered and correlated to morphological cell wall features that are in the order of tens of nanometer. Electron microscopy is able to resolve these features but does not provide protein-specific information. Therefore, a technique has to be established that is able to localize individual biosilica-associated proteins with nanometer precision. To achieve this objective, single-molecule localization microscopy (SMLM) for the diatom Thalassiosira pseudonana has been pioneered and exploited to localize different biosilica associated proteins inside silica and after silica removal. To obtain quantitative data, an analysis workflow was developed including graphical user interfaces and scripts for SMLM visualization, clustering, and co-localization. In order to find optimal labels for SMLM to target biosilica-embedded proteins, a comprehensive screening of photo-controllable fluorescent proteins has been carried out. Only three of six candidates were functional when embedded inside biosilica and fused to Silaffin3 – a protein that is tightly associated with the biosilica cell wall. Silaffin3 could be localized using SMLM with a localization precision of 25 nm. This allowed to resolve its structural organization and therefore identified Silaffin3 as a major component in the basal chamber of the fultoportulae. Additionally, co-localization studies on cingulins – a protein family hypothesized to be involved in silica formation – have been performed to decipher their pattern-function relationship. Towards this end, novel imaging strategies, co-localization calculations and pattern quantifications have been established. With the help of these results, the spatial arrangement of cingulins W2 and Y2 could be compared with unprecedented resolution. In summary, this work has laid ground for quantitative SMLM studies of proteins in diatoms in general and contributed insights into the spatial organization of proteins involved in biomineralization in the diatom T. pseudonana.:1 INTRODUCTION 1 1.1 Diatoms – a model system for biomineralization 3 1.2 Imaging of biosilica and associated organic components 8 1.3 Single-molecule localization microscopy (SMLM) 10 2 METHODS & METHOD DEVELOPMENT FOR SMLM DATASETS 17 2.1 Super-resolution reconstruction 19 2.2 Tools for SMLM resolution estimates 21 2.3 Voronoi tessellation for noise-removal and cluster estimation 25 2.4 Tools for SMLM cluster analysis 27 2.5 Coordinate-based co-localization 32 2.6 PairRice – A novel algorithm to extract distances between cluster pairs 33 2.7 SiMoNa – A new GUI for exploring SMLM datasets 35 3 RESOLUTION OF THE SMLM SETUP TESTED WITH DNA ORIGAMI NANOSTRUCTURES 41 3.1 DNA origami as a length standard 42 3.2 Global resolution estimates 44 3.3 Local resolution estimates 47 3.4 Conclusion 53 4 EVALUATION OF PHOTO-CONTROLLABLE FLUORESCENT PROTEINS FOR PALM IN DIATOMS 55 4.1 Selecting PCFPs to minimize interference with the diatom autofluorescence 56 4.2 Screening results for cytosolic and biosilica-embedded PCFPs 58 4.3 The underlying conversion mechanism 61 4.4 Conclusion 63 5 IMAGING THE SIL3 MESHWORK 65 5.1 Analyzing protein layer thickness using tpSil3-Dendra2 65 5.2 Imaging the valve region using tpSil3 68 5.3 Resolution and localization parameters of tpSil3 70 5.4 Conclusion 72 6 DECIPHERING CINGULIN PATTERNS WITH CO LOCALIZATION STUDIES 73 6.1 A two-color cingulin construct for PALM-STORM 73 6.2 Steps towards PALM-STORM: screening, alignment, and imaging routine 76 6.3 Co-localization studies: quantification, clustering, and correlations 83 6.4 Conclusion 91 7 OUTLOOK 93 8 MATERIALS & METHODS 97 8.1 Microscope specifications 97 8.2 DNA origami annealing and AFM measurements 99 8.3 Diatom sample preparations 100 8.4 Fluorescence imaging conditions 102 8.5 Buffer systems 103 9 APPENDICES 105 9.1 Tables and Protocols 105 9.2 Satellite projects 112 9.2.1 Quantitative fluorescence intensity analysis of 3D time-lapse confocal microscopy data in diatoms 112 9.2.2 Applying neural networks to filter SMLM localizations 118 9.2.3 In vivo imaging at super-resolution conditions using SOFI 121 9.2.4 Quantifying chromatic aberrations in the microscope using fiducials 123 10 REFERENCES 127

Anders als menschengemachte Maschinen verfügen Zellen über keinen festgeschriebenen Bauplan und die Positionen einzelner Elemente sind häufig nicht genau festgelegt, da die Moleküle diffusiven Zufallsbewegungen unterworfen sind. Darüber hinaus sind einzelne Bauteile auch nicht auf eine einzelne Funktion festgelegt, sondern können parallel in verschiedene Prozesse einbezogen sein. Basierend auf Selbstorganisation und Selbstassemblierung muß die Organisation von Anordnung und Funktion einer lebenden Zelle also bereits in ihren einzelnen Komponenten inhärent enthalten sein. Die intrazelluläre Organisation wird zum großen Teil durch ein internes Biopolymergerüst reguliert, das Zytoskelett. Biopolymer-Netzwerke und –Fasern durchdringen die gesamte Zelle und sind verantworlich für mechanische Integrität und die funktionale Architektur. Unzählige essentielle biologische Prozesse hängen direkt von einem funktionierenden Zytoskelett ab. Die vorliegende Arbeit zielt auf ein besser Verständnis und den Nachbau zweier verschiedener funktionaler Module lebender Zellen anhand stark reduzierter Modellsysteme. Als zentrales Element wurde Aktin gewählt, da dieses Biopolymer eine herausragende Rolle in nahezu allen eukaryotischen Zellen spielt. Mit dem ersten Modellsystem wird der bewegliche Aktin-Polymerfilm an der Vorderkante migrierender Zellen betrachtet. Die wichtigsten Elemente dieser hochdynamischen Netzwerke sind bereits bekannt und wurden in dieser Arbeit benutzt um ein experimentelles Modellsystem zu etablieren. Vor allem aber lieferten detailierte Computersimulationen und ein mathematisches Modell neue Erkenntnisse über grundlegende Organisationsprinzipien dieser Aktinnetzwerke. Damit war es nicht nur möglich, experimentelle Daten erfolgreich zu reproduzieren, sondern das Entstehen von Substrukturen und deren Charakteristika auf proteinunabhängige, generelle Mechanismen zurückzuführen. Das zweite studierte System betrachtet die Selbstassemblierung von Aktinnetzwerken durch entropische Kräfte. Aktinfilamente aggregieren hierbei durch Kondensation multivalenter Ionen oder durch Volumenausschluss hochkonzentrierter inerter Polymere. Ein neu entwickelter Experimentalaufbau bietet die Möglichkeit in gut definierten zellähnlichen Volumina, Konvektionseinflüsse zu umgehen und Aggregationseffekte gezielt einzuschalten. Hierbei wurden neuartige, regelmäßige Netzwerkstrukturen entdeckt, die bislang nur im Zusammenhang mit molekularen Motoren bekannt waren. Es konnte ferner gezeigt werden, dass die Physik der Flüssigkristalle entscheidend zu weiteren Variationen dieser Netzwerke beiträgt. Dabei wird ersichtlich, dass entstehende Netzwerke in ihrer Architektur direkt die zuvor herrschenden Anisotropien der Filamentlösung widerspiegeln.:1 Introduction 1 2 General background 7 2.1 General concepts 7 2.1.1 Coarse-graining as hierarchical reduction 8 2.1.2 Functional modules and redundancies 10 2.1.3 Emergence 11 2.1.4 Self-organization and self-assembly 13 2.1.5 Bottom-up and top-down 13 2.2 The cytoskeleton 15 2.2.1 From actin monomers to filaments 16 2.2.2 Accessory proteins and actin networks 21 2.3 Biopolymer pattern formation 25 2.3.1 Random networks and nematic phases 25 2.3.2 Linker and motor induced networks 28 3 Lamellipodial actin network formation 33 3.1 Background: crawling cell migration 33 3.1.1 Leading edge actin structures 35 3.1.2 Lamellipodial self-organization into oriented branches? 40 3.1.3 Lamellipodial modeling 41 3.1.4 Beyond the lamellipodium: adhesion and network contraction 42 3.2 Methods: lamellar treadmilling model 45 3.2.1 Assumptions 45 3.2.2 Choice of model parameters 51 3.2.3 Computer simulation (implementation) 52 3.2.4 Mathematical modeling 56 3.3 Modeling results 63 3.3.1 Reproduction of motile cell characteristics 64 3.3.2 Self-organization into lamellipodium and lamellum 65 3.3.3 Filament severing and annealing influence network properties 70 3.3.4 Unconfined network growth 74 3.4 Feasible model extensions 76 3.4.1 Alternative nucleation mechanisms 77 3.4.2 Convergence zone through myosin-driven network contraction 80 3.5 Experimental bottom-up approach 82 3.6 Discussion: Arp2/3 induced actin networks 87 4 Actin network patterns in confined systems 91 4.1 Background: counterion condensation and depletion forces 91 4.1.1 Actin, a polyelectrolyte: counterion condensation 92 4.1.2 Actin and molecular crowding: depletion forces 95 4.2 Methods: Experimental design and data analysis 97 4.2.1 Protein purification and handling 98 4.2.2 Droplet formation 98 4.2.3 Volume monitoring and pattern analysis 100 4.3 Actin pattern formation 105 4.3.1 Counterion-induced network formation 105 4.3.2 Depletion force induced network formation 111 4.4 First modeling attempts: bundling simulation 116 4.4.1 Model concept and assumptions 116 4.5 Discussion: Counterion and depletion-based network assembly 119 5 Discussion & Outlook 125 Appendix 129 A. Variation of filament orientation 129 B. Analytical solution of the mathematical model 131 C. Pre-alignment of filaments 132 D. Protocols 134 d1. Acetone Powder Prep 134 d2. Actin prep 135 d3. Actin labling with rhodamine dye 137 Bibliography 141 Acknowledgements 157

Titanium alloys are frequently used in the medical field as bone implant materials due to their excellent biocompatibility and corrosion resistance. Yet, their elastic modulus is usually significantly higher than the one of bone, which can lead to a reduction of bone tissue at the implant site. The current research is therefore focused on the development of highly porous implants, which promise a low elastic modulus close to that of bone, an enhanced bone ingrowth and an improved vascularization. However, the appropriate pore size for an optimal osseointegration still remains unclear. To that end, a transparent tubular microsystem is developed to mimic such a porous microenvironment in order to study single bone cell behavior and early bone formation processes. The system is fabricated out of an implant material (β-stabilized Ti-45Nb (wt%)). It is demonstrated that the bulk material composition, which is consisting of a high Nb content, can be closely transferred to transparent thin films by using reactive sputtering. These films then self-assemble into tubular microscaffolds (TS) with a diameter range between 10-42 μm. Biological studies are subsequently performed to investigate the response (e.g. cell adhesion, migration, osteogenic differentiation) of human Mesenchymal Stem Cells (MSC) to the TS. It is shown that cells form fewer, more diffuse focal adhesion points inside the TS compared to a planar surface and the spatial confinement causes a switch in between amoeboid and mesenchymal migration modes. In addition, it is demonstrated that cells can survive inside the TS for at least 12 days during osteogenic differentiation and partly mineralize the TS interior. The observed mineralization process is furthermore linked to the formation of hydroxyapatite crystals inside dead cells bodies, which leads to a crystallization over time. All in all, the TS platform offers an easy way to identify key factors of bone cell-implant interactions that can be used to improve the biocompatibility of the bone-implant interface in the future.

No abstract available

We incorporate amphiphilic receptors bearing ß-diketone functional units into large (LUV's) and giant unilamellar vesicles (GUV's). Electrolyte solutions containing di- and trivalent ions were used to induce inter-membrane interactions. Measurements performed with isothermal titration calorimetry (ITC) revealed that interaction between EuCl3 and ß-diketone receptors was characterized by a molar enthalpy 126 ± 5 kcal/mole and an equilibrium binding constant 26 ± 4 mM-1. The results indicate a molecular complex formed binding two ß-diketone receptors to one Eu3+ ion. Dynamic light scattering (DLS) was used to follow changes in LUV diameter indicated in an increase in vesicle size distribution of on average 20 %. Optical microscopy was employed to visualize the inter-membrane interaction measured using DLS and ITC. Depending on membrane composition of the functionalized vesicles we found that local injections of micromolar EuCl¬3 induced membrane pore formation and membrane fusion. Our collection of results leads to the conclusion that formation of intra-molecular ligand receptor complexes leads to pore formation and inter-membrane complex formation leads to membrane fusion. Detailed characterization of the fusion process shows that irreversible opening of the fusion pore can be extrapolated to times below 50 µsec. We have found that formation of membrane bound ligand (Eu3+)-receptor complexes provides versatility to the function of vesicle membranes. / Die Fusion von Membranen ist ein entscheidender Prozeß bei der Entwicklung von Zellen im Körper. Beispielsweise ist sie eine der Voraussetzungen bei der Befruchtung einer Eizelle durch ein Spermium oder für das Eindringen von Viren in eine Zelle. Membranfusion ist auch notwendig für den Stofftransport in die Zelle hinein oder aus ihr heraus. Die Membranfusion ist daher auch von praktischen Interesse auf den Gebieten der Pharmazeutik und des 'Bioengineering'. Oft muss eine Membran mit der infiziertin Zelle fusionieren, um ein Medikament an sein Zeil zu bringen. Deshalb ist ein Verständnis der Membranfusion von großem Interesse für die Entwicklung von gezielten und effizienten Methoden des 'drug delivery'. Dasselbe gilt für die gezielte Zufuhr von Genen bei der Gentherapie. Obwohl die Membranfusion schon vor nahezu 200 Jahren von dem deutschen Biologen und Mediziner Johannes Müller beobachtet wurde, liegt ein vollständiges Verständnis des Fusionsprozesses von Zellen und (Modell-) Membranen auch heute noch in weiter Ferne. Allerdings hat im letzten Jahrzehnt das Interesse für dieses Forschungsgebiet stark zugenommen. Wissenschaftler der unterschiedlichsten Disziplinen arbeiten daran, die Mechanismen der Membranfusion aufzudecken. Biologen untersuchen Proteine, die die Fusion auslösen, Chemiker entwickeln Moleküle, die die Fusion erleichtern, und Physiker versuchen die Antriebsmechanismen der Membranfusion zu verstehen. Neue Mikroskopietechniken und die hohe Rechenleistung moderner Computer helfen die molekulare und die makroskopische Welt der Membranfusion in einem Bild zusammenzufügen. Für unsere Untersuchungen haben wir Modellmembranen, die aus Lipiddoppelschichten bestehen, benutzt. Diese Membranen formen sogenannte Vesikel oder Liposomen, abgeschlossene Membrane, in denen eine bestimmte Menge an Flüssigkeit enthalten ist. Indem wir Rezeptoren in die Membran einbringen, schaffen wir funkionalisierte Vesikel, die sich differenzieren, kooperieren und selektiv reagieren können. Wir benutzen positiv geladene wasserlösliche Ionen, um Wechselwirkungen zwischen den Vesikeln zu vermitteln, und lassen die Rezeptoren und die Ionen den Fusionsprozess auslösen. Die Wechselwirkungen werden unter dem Mikroskop durch spezielle Mikromechanischn Gerätz Mikromechinerien kontrolliert. Mit Hilfe einer sehr schnellen digitale Bildaufnahmetechnik ist es uns gelungen, die Fusion unserer Modellmembranen aufzunehmen und in Echtzeit zu dokumentieren mit einer Auflösung von 50 µs. Unsere Messungen können vergleichen werden mit Computersimulationen des Fusionsprozesses. Diese Simulationen untersuchen Prozesse, die zwischen 0.1 und 1 Mikrosekunde dauern. Eine Herausforderung für die Zukunft wird es sein, die Lücke zwischen den in Experimenten (50µs) und den in Simulationen zugänglichen Zeitskalen von beiden Seiten her zu schließen.

This work is a numerical examination of a semiflexible polymer exposed to a disorder landscape consisting of hard disks. For a small parameter range and simple constraints it is known that disorder leads to structural transitions of the equilibrium properties of polymers. The scope of this work strongly extends this range by going to both high disorder densities and large stiffnesses of the polymers. The competing length scales of polymer stiffness and average distance between the obstacles of the potential along with the way of assembling the disorder lead to a wide range of effects such as crumpling and stretching of polymer configurations due to the disorder or a modulation of the polymer’s characterizing observables with the correlation function of the potential. The high accuracy results presented in this work have been obtained by means of sophisticated Monte Carlo simulations. The refinement of a rarely applied but highly promising method to a state of the art algorithm in connection with latest numerical techniques made it possible to investigate the impact of hard-disk disorder on semiflexible polymer conformations on a broad scale.

During embryonic development, precursor germ cells contain aggregates of protein and RNA known as germ granules. These germ granules are important in the specifi- cation of a functioning germ line, i.e. functioning sex cells within mature organisms. In the single cell fertilized embryo of the nematode worm C.elegans, germ granules (referred to as P granules) localize to the posterior side of the cell. After cell division occurs, they are found only in the posterior daughter cell. The localization behav- ior of P granules has been a topic of much interest, and considered an important aspect of symmetry breaking during development. We learn the fundamental prop- erties of P granule localization, and determine possible parameters and features of this biological system by developing theory in close collaboration with experimental evidence. In this study, experimental evidence is presented which shows that P granules are liquid droplets, and that their localization occurs through preferential nucleation and growth behavior on one side of the cell and simultaneous preferential dissolution on the opposite side. It is also shown that this behavior is linked to the concentration gradient of the protein Mex-5 along the anterio-posterior axis of the cell, which is necessary to induce the preferential growth of P granules. From this experimental data, a theoretical model for the preferential growth of P granules is developed, where the localization of P granules occurs by phase separa- tion. That is, P granules separate from the bulk cytoplasm by a process described by a first order liquid-liquid phase transitition, where a liquid droplet granule phase nucleates and then grows out of the bulk liquid cytoplasmic phase. In this model, a spatial gradient is imposed on the saturation point, the boundary point between the single phase state consisting only of the cytoplasm, and a metastable state which includes both a P granule and cytoplasm phase. This gradient mimics the properties of the Mex-5 gradient and is sufficient in explaining P granule localization. Using numerical simulations, the theoretical model is studied. It is found suffi- cient to both successfully describe P granule localizaion, and to describe interesting behavior in a system with assymetric growth due to a spatial gradient. From a purely theoretical standpoint, we observe cyclical non-equilibrium steady states, where material is cycled back and forth along the gradient. From the biological side, experimental properties of the system, such as the diffusion coefficient of P granules and P granule growth rates are determined through both simulation and image analysis of data. In addition, the possiblility of different types of growth behavior at later cell stages, and a method of long range intracellular signalling are suggested from the theoretical model.

It has been known for almost two decades that the water proton NMR signal of diffusing water molecules in brain white matter undergoes a non-monoexponential decay with increasing diffusion gradient factor b. With the help of numerical simulations and analytical expressions, much effort has been directed to describing the signal decay and to extracting relevant biophysical features of the system under investigation. However, the physical basis of such nonmonoexponential behavior is still not properly understood. The primary difficulty in characterizing this phenomenon is the variation in behavior in the different directions of diffusion measurement. A combined framework that accounts for the diffusion process in all directions requires several parameters. Addition of many such parameters renders a model to be unwieldy and over-complicated, but over-simplifications can be shown to miss crucially relevant information in the data. In this thesis, I have attempted to handle this problem with simple measurements that span a wide range of parameter space. Compared to often-performed measurements that probe diffusion over a time-scale of 50-100 ms with relatively low diffusion weighting, the measurements here have been done for very short diffusion times of 2 ms and also very long diffusion times up to 2 s. The temperature dependence of the diffusion coefficients has also been extensively probed. To avoid problems related to gross tissue heterogeneity, diffusion-weighted MR imaging in vivo was performed with ultra-high resolution. These simple measurements allowed sequential assessment of many possible arguments that could have led to such non-monoexponential decay curves. Finally, it was concluded that the water in the glial processes was the major contributor to the non-exponential decay, giving rise to a \'slow\' component both along the axonal fibers and transverse to them.

No description available.

During development, cells consume energy, divide, rearrange, and die. Bulk properties such as viscosity and elasticity emerge from cell-scale mechanics and dynamics. Order appears, for example in patterns of hair outgrowth, or in the predominately hexagonal pattern of cell boundaries in the wing of a fruit fly. In the past fifty years, much progress has been made in understanding tissues as living materials. However, the physical mechanisms underlying tissue-scale behaviour are not completely understood. Here we apply theories from statistical physics and fluid dynamics to understand mechanics and order in two-dimensional tissues. We restrict our attention to the mechanics and dynamics of cell boundaries and vertices, and to planar polarity, a type of long-ranged order visible in anisotropic patterns of proteins and hair outgrowth. Our principle tool for understanding mechanics and dynamics is a vertex model where cell shapes are represented using polygons. We analytically derive the ground-state diagram of this vertex model, finding it to be dominated by the geometric requirement that cells be polygons, and the topological requirement that those polygons tile the plane. We present a simplified algorithm for cell division and growth, and furthermore derive a dynamic equation for the vertex model, which we use to demonstrate the emergence of quasistatic behaviour in the limit of slow growth. All our results relating to the vertex model are consistent with and build off past calculations and experiments. To investigate the emergence of planar polarity, we develop quantification methods for cell flow and planar polarity based on confocal microscope images of developing fly wings. We analyze cell flow using a velocity gradient tensor, which is uniquely decomposed into terms corresponding to local compression, shear, and rotations. We argue that a pattern in an inhomogeneously flowing tissue will necessarily be reorganized, motivating a hydrodynamic theory of polarity reorientation. Using such a coarse-grained theory of polarity reorientation, we show that the quantified patterns of shear and rotation in the wing are consistent with the observed polarity reorganization, and conclude that cell flow reorients planar polarity in the wing of the fruit fly. Finally, we present a cell-scale model of planar polarity based on the vertex model, unifying the themes of this thesis.