Aktive Filament-Systeme, wie zum Beispiel das Zellskelett, sind Beispiele einer interessanten Klasse neuartiger Materialien, die eine wichtige Rolle in der belebten Natur spielen. Viele wichtige Prozesse in lebenden Zellen wie zum Beispiel die Zellbewegung oder Zellteilung basieren auf dem Zellskelett. Das Zellskelett besteht aus Protein-Filamenten, molekularen Motoren und einer großen Zahl weiterer Proteine, die an die Filamente binden und diese zu einem Netz verbinden können. Die Filamente selber sind semifexible Polymere, typischerweise einige Mikrometer lang und bestehen aus einigen hundert bis tausend Untereinheiten, typischerweise Mono- oder Dimeren. Die Filamente sind strukturell polar, d.h. sie haben eine definierte Richtung, ähnlich einer Ratsche. Diese Polarität begründet unterschiedliche Polymerisierungs- und Depolymerisierungs-Eigenschaften der beiden Filamentenden und legt außerdem die Bewegungsrichtung molekularer Motoren fest. Die Polymerisation von Filamenten sowie Krafterzeugung und Bewegung molekularer Motoren sind aktive Prozesse, die kontinuierlich chemische Energie benötigen. Das Zellskelett ist somit ein aktives Gel, das sich fern vom thermodynamischen Gleichgewicht befindet. In dieser Arbeit präsentieren wir Beschreibungen solcher aktiven Filament-Systeme und wenden sie auf Strukturen an, die eine ähnliche Geometrie wie zellulare Strukturen haben. Beispiele solcher zellularer Strukturen sind Spannungsfasern, kontraktile Ringe oder mitotische Spindeln. Spannungsfasern sind für die Zellbewegung essentiell; sie können kontrahieren und so die Zelle vorwärts bewegen. Die mitotische Spindel trennt Kopien der Erbsubstanz DNS vor der eigentlichen Zellteilung. Der kontraktile Ring schließlich trennt die Zelle am Ende der Zellteilung. In unserer Theorie konzentrieren wir uns auf den Einfluß der Polymerisierung und Depolymerisierung von Filamenten auf die Dynamik dieser Strukturen. Wir zeigen, dass der kontinuierliche Umschlag (d.h. fortwährende Polymerisierung und Depolymerisierung) von Filamenten unabdingbar ist für die kontraktion eines Rings mit konstanter Geschwindigkeit, so wie in Experimenten mit Hefezellen beobachtet. Mit Hilfe einer mikroskopisch motivierten Beschreibung zeigen wir, wie "filament treadmilling", also Filament Polymerisierung an einem Ende mit der gleichen Rate wie Depolymerisierung am anderen Ende, zur Spannung in Filament Bündeln und Ringen beitragen kann. Ein zentrales Ergebnis ist, dass die Depolymerisierung von Filamenten in Anwesenheit von filamentverbindenden Proteinen das Zusammenziehen dieser Bündel sogar in Abwesenheit molekulare Motoren herbeiführen kann. Ferner entwickeln wir eine generische Kontinuumsbeschreibung aktiver Filament-Systeme, die ausschließlich auf Symmetrien der Systeme beruht und von mikroskopischen Details unabhängig ist. Diese Theorie erlaubt uns eine komplementäre Sichtweise auf solche aktiven Filament-Systeme. Sie stellt ein wichtiges Werkzeug dar, um die physikalischen Mechanismen z.B. in Filamentbündeln aber auch bei der Bildung von Filamentringen im Zellkortex zu untersuchen. Schließlich entwickeln wir eine auf einem Kräftegleichgewicht basierende Beschreibung für bipolare Strukturen aktiver Filamente und wenden diese auf die mitotische Spindel an. Wir diskutieren Bedingungen für die Bildung und Stabilität von Spindeln. / Active filament systems such as the cell cytoskeleton represent an intriguing class of novel materials that play an important role in nature. The cytoskeleton for example provides the mechanical basis for many central processes in living cells, such as cell locomotion or cell division. It consists of protein filaments, molecular motors and a host of related proteins that can bind to and cross-link the filaments. The filaments themselves are semiflexible polymers that are typically several micrometers long and made of several hundreds to thousands of subunits. The filaments are structurally polar, i.e. they possess a directionality. This polarity causes the two distinct filament ends to exhibit different properties regarding polymerization and depolymerization and also defines the direction of movement of molecular motors. Filament polymerization as well as force generation and motion of molecular motors are active processes, that constantly use chemical energy. The cytoskeleton is thus an active gel, far from equilibrium. We present theories of such active filament systems and apply them to geometries reminiscent of structures in living cells such as stress fibers, contractile rings or mitotic spindles. Stress fibers are involved in cell locomotion and propel the cell forward, the mitotic spindle mechanically separates the duplicated sets of chromosomes prior to cell division and the contractile ring cleaves the cell during the final stages of cell division. In our theory, we focus in particular on the role of filament polymerization and depolymerization for the dynamics of these structures. Using a mean field description of active filament systems that is based on the microscopic processes of filaments and motors, we show how filament polymerization and depolymerization contribute to the tension in filament bundles and rings. We especially study filament treadmilling, an ubiquitous process in cells, in which one filament end grows at the same rate as the other one shrinks. A key result is that depolymerization of filaments in the presence of linking proteins can induce bundle contraction even in the absence of molecular motors. We extend this description and apply it to the mitotic spindle. Starting from force balance considerations we discuss conditions for spindle formation and stability. We find that motor binding to filament ends is essential for spindle formation. Furthermore we develop a generic continuum description that is based on symmetry considerations and independent of microscopic details. This theory allows us to present a complementary view on filament bundles, as well as to investigate physical mechanisms behind cell cortex dynamics and ring formation in the two dimensional geometry of a cylinder surface. Finally we present a phenomenological description for the dynamics of contractile rings that is based on the balance of forces generated by active processes in the ring with forces necessary to deform the cell. We find that filament turnover is essential for ring contraction with constant velocities such as observed in experiments with fission yeast.

Aktive Filament-Systeme, wie zum Beispiel das Zellskelett, sind Beispiele einer interessanten Klasse neuartiger Materialien, die eine wichtige Rolle in der belebten Natur spielen. Viele wichtige Prozesse in lebenden Zellen wie zum Beispiel die Zellbewegung oder Zellteilung basieren auf dem Zellskelett. Das Zellskelett besteht aus Protein-Filamenten, molekularen Motoren und einer großen Zahl weiterer Proteine, die an die Filamente binden und diese zu einem Netz verbinden können. Die Filamente selber sind semifexible Polymere, typischerweise einige Mikrometer lang und bestehen aus einigen hundert bis tausend Untereinheiten, typischerweise Mono- oder Dimeren. Die Filamente sind strukturell polar, d.h. sie haben eine definierte Richtung, ähnlich einer Ratsche. Diese Polarität begründet unterschiedliche Polymerisierungs- und Depolymerisierungs-Eigenschaften der beiden Filamentenden und legt außerdem die Bewegungsrichtung molekularer Motoren fest. Die Polymerisation von Filamenten sowie Krafterzeugung und Bewegung molekularer Motoren sind aktive Prozesse, die kontinuierlich chemische Energie benötigen. Das Zellskelett ist somit ein aktives Gel, das sich fern vom thermodynamischen Gleichgewicht befindet. In dieser Arbeit präsentieren wir Beschreibungen solcher aktiven Filament-Systeme und wenden sie auf Strukturen an, die eine ähnliche Geometrie wie zellulare Strukturen haben. Beispiele solcher zellularer Strukturen sind Spannungsfasern, kontraktile Ringe oder mitotische Spindeln. Spannungsfasern sind für die Zellbewegung essentiell; sie können kontrahieren und so die Zelle vorwärts bewegen. Die mitotische Spindel trennt Kopien der Erbsubstanz DNS vor der eigentlichen Zellteilung. Der kontraktile Ring schließlich trennt die Zelle am Ende der Zellteilung. In unserer Theorie konzentrieren wir uns auf den Einfluß der Polymerisierung und Depolymerisierung von Filamenten auf die Dynamik dieser Strukturen. Wir zeigen, dass der kontinuierliche Umschlag (d.h. fortwährende Polymerisierung und Depolymerisierung) von Filamenten unabdingbar ist für die kontraktion eines Rings mit konstanter Geschwindigkeit, so wie in Experimenten mit Hefezellen beobachtet. Mit Hilfe einer mikroskopisch motivierten Beschreibung zeigen wir, wie "filament treadmilling", also Filament Polymerisierung an einem Ende mit der gleichen Rate wie Depolymerisierung am anderen Ende, zur Spannung in Filament Bündeln und Ringen beitragen kann. Ein zentrales Ergebnis ist, dass die Depolymerisierung von Filamenten in Anwesenheit von filamentverbindenden Proteinen das Zusammenziehen dieser Bündel sogar in Abwesenheit molekulare Motoren herbeiführen kann. Ferner entwickeln wir eine generische Kontinuumsbeschreibung aktiver Filament-Systeme, die ausschließlich auf Symmetrien der Systeme beruht und von mikroskopischen Details unabhängig ist. Diese Theorie erlaubt uns eine komplementäre Sichtweise auf solche aktiven Filament-Systeme. Sie stellt ein wichtiges Werkzeug dar, um die physikalischen Mechanismen z.B. in Filamentbündeln aber auch bei der Bildung von Filamentringen im Zellkortex zu untersuchen. Schließlich entwickeln wir eine auf einem Kräftegleichgewicht basierende Beschreibung für bipolare Strukturen aktiver Filamente und wenden diese auf die mitotische Spindel an. Wir diskutieren Bedingungen für die Bildung und Stabilität von Spindeln. / Active filament systems such as the cell cytoskeleton represent an intriguing class of novel materials that play an important role in nature. The cytoskeleton for example provides the mechanical basis for many central processes in living cells, such as cell locomotion or cell division. It consists of protein filaments, molecular motors and a host of related proteins that can bind to and cross-link the filaments. The filaments themselves are semiflexible polymers that are typically several micrometers long and made of several hundreds to thousands of subunits. The filaments are structurally polar, i.e. they possess a directionality. This polarity causes the two distinct filament ends to exhibit different properties regarding polymerization and depolymerization and also defines the direction of movement of molecular motors. Filament polymerization as well as force generation and motion of molecular motors are active processes, that constantly use chemical energy. The cytoskeleton is thus an active gel, far from equilibrium. We present theories of such active filament systems and apply them to geometries reminiscent of structures in living cells such as stress fibers, contractile rings or mitotic spindles. Stress fibers are involved in cell locomotion and propel the cell forward, the mitotic spindle mechanically separates the duplicated sets of chromosomes prior to cell division and the contractile ring cleaves the cell during the final stages of cell division. In our theory, we focus in particular on the role of filament polymerization and depolymerization for the dynamics of these structures. Using a mean field description of active filament systems that is based on the microscopic processes of filaments and motors, we show how filament polymerization and depolymerization contribute to the tension in filament bundles and rings. We especially study filament treadmilling, an ubiquitous process in cells, in which one filament end grows at the same rate as the other one shrinks. A key result is that depolymerization of filaments in the presence of linking proteins can induce bundle contraction even in the absence of molecular motors. We extend this description and apply it to the mitotic spindle. Starting from force balance considerations we discuss conditions for spindle formation and stability. We find that motor binding to filament ends is essential for spindle formation. Furthermore we develop a generic continuum description that is based on symmetry considerations and independent of microscopic details. This theory allows us to present a complementary view on filament bundles, as well as to investigate physical mechanisms behind cell cortex dynamics and ring formation in the two dimensional geometry of a cylinder surface. Finally we present a phenomenological description for the dynamics of contractile rings that is based on the balance of forces generated by active processes in the ring with forces necessary to deform the cell. We find that filament turnover is essential for ring contraction with constant velocities such as observed in experiments with fission yeast.

During mitosis, adherent animal cells undergo a drastic shape change, from essentially flat to round, in a process known as mitotic cell rounding (MCR). The aim of this thesis was to critically examine the physical and biological basis of MCR. The experimental part of this thesis employed a combined optical microscope-atomic force microscope (AFM) setup in conjunction with flat tipless cantilevers to analyze cell mechanics, shape and volume. To this end, two AFM assays were developed: the constant force assay (CFA), which applies constant force to cells and measures the resultant height, and the constant height assay (CHA), which confines cell height and measures the resultant force. These assays were deployed to analyze the shape and mechanical properties of single cells trans-mitosis. The CFA results showed that cells progressing through mitosis could increase their height against forces as high as 50 nN, and that higher forces can delay mitosis in HeLa cells. The CHA results showed that mitotic cells confined to ~50% of their normal height can generate forces around 50-100 nN without disturbing mitotic progression. Such forces represent intracellular pressures of at least 200 Pascals and cell surface tensions of around 10 nN/µm. Using the CHA to compare mitotic cell rounding with induced cell rounding, it was observed that the intracellular pressure of mitotic cells is at least 3-fold higher than rounded interphase cells. To investigate the molecular basis of the mechanical changes inherent in mitotic cell rounding, inhibitors and toxins were used to pharmacologically dissect the role of candidate cellular processes. These results implicated the actomyosin cortex and osmolyte transporters, the most prominent of which is the Na+/H+ exchanger, in the maintenance of mechanical properties and intracellular hydrostatic pressure. Observations on blebbing cells under the cantilever supported the idea that the actomyosin cortex is required to sustain hydrostatic pressure and direct this pressure into cell shape changes. To gain further insight into the relationship between actomyosin activity and intracellular pressure, dynamic perturbation experiments were conducted. To this end, the CHA was used to evaluate the pressure and volume of mitotic cells before, during and after dynamic perturbations that included tonic shocks, influx of specific inhibitors, and exposure to pore-forming toxins. When osmotic pressure gradients were depleted, pressure and volume decreased. When the actomyosin cytoskeleton was abolished, cell volume increased while rounding pressure decreased. Conversely, stimulation of actomyosin cortex contraction triggered an increase in rounding pressure and a decrease in volume. Taken together, the dynamic perturbation results demonstrated that the actomyosin cortex contracts against an opposing intracellular pressure and that this relationship sets the surface tension, pressure and volume of the cell. The discussion section of this thesis provides a comprehensive overview of the physical basis of MCR by amalgamating the experimental results of this thesis with the literature. Additionally, the biochemal signaling pathways and proteins that drive MCR are collated and discussed. An exhaustive and unprecedented synthesis of the literature on cell rounding (approx. 750 papers as pubmed search hits on “cell rounding”, April 2012) reveals that the spread-to-round transition can be thought of in terms of a surface tension versus adhesion paradigm, and that cell rounding can be physically classified into four main modes, of which one is an MCR-like category characterized by increased actomyosin cortex tension and diminution of focal adhesions. The biochemical pathways and signaling patterns that correspond with these four rounding modes are catalogued and expounded upon in the context of the relevant physiology. This analysis reveals cell rounding as a pertinent topic that can be leveraged to yield insight into core principles of cell biophysics and tissue organization. It furthermore highlights MCR as a model problem to understand the adhesion versus cell surface tension paradigm in cells and its fundamentality to cell shape, mechanics and physiology.

Objetivo: Verificar resposta após debridamento epitelial de córneas humanas. Métodos: Córneas normais foram submetidas a debridamento antes da cirurgia de enucleação. Realizou-se histologia, TUNEL, Ki67, SMA e microscopia eletrônica. Resultados: Seis córneas foram debridadas e preservadas entre ½ e 65 horas, apresentando apoptose nos ceratócitos do estroma anterior. Células estromais em proliferação foram observadas apenas no tempo de 65 horas. Miofibroblastos não foram encontrados. Uma córnea serviu de controle. Conclusões: Os eventos observados em córneas humanas após debridamento epitelial, apoptose e proliferação dos ceratócitos, foram semelhantes aos descritos em animais de experimentação / Purpose: To examine the early wound healing response to epithelial scrape in human corneas. Methods: Normal corneas had epithelial scrape prior to enucleation. Histology, TUNEL assay, Ki67, SMA and transmission electron microscopy were performed. Results: Epithelial scrape was performed in six corneas from ½ to 65 hours prior to preservation. Keratocyte apoptosis was detected in the anterior stroma in all scraped corneas. Keratocyte proliferation was detected exclusively 65 hours after scrape. No myofibroblast was detected. One cornea was not scraped (control). Conclusion: Results obtained in human corneas (keratocyte apoptosis and proliferation) were similar to animal models

It is known that fission yeast Schizosaccharomyces pombe maintains its nuclear envelope during mitosis and it undergoes an interesting shape change during cell division - from a spherical via an ellipsoidal and a peanut-like to a dumb-bell shape. However, the biomechanical system behind this amazing transformation is still not understood. What we know is, that the shape must change due to forces acting on the membrane surrounding the nucleus and the microtubule based mitotic spindle is thought to play a key role. To estimate the locations and directions of the forces, the shape of the nucleus was recorded by confocal light microscopy. But such data is often inhomogeneously labeled with gaps in the boundary, making classical segmentation impractical. In order to accurately determine the shape we developed a global parametric shape description method, based on a Fourier coordinate expansion. The method implicitly assumes a closed and smooth surface. We will calculate the geometrical properties of the 2-dimensional shape and extend it to 3-dimensional properties, assuming rotational symmetry. Using a mechanical model for the lipid bilayer and the so called Helfrich-Canham free energy we want to calculate the minimum energy shape while respecting system-specific constraints to the surface and the enclosed volume. Comparing it with the observed shape leads to the forces. This provides the needed research tools to study forces based on images.

Objetivo: Verificar resposta após debridamento epitelial de córneas humanas. Métodos: Córneas normais foram submetidas a debridamento antes da cirurgia de enucleação. Realizou-se histologia, TUNEL, Ki67, SMA e microscopia eletrônica. Resultados: Seis córneas foram debridadas e preservadas entre ½ e 65 horas, apresentando apoptose nos ceratócitos do estroma anterior. Células estromais em proliferação foram observadas apenas no tempo de 65 horas. Miofibroblastos não foram encontrados. Uma córnea serviu de controle. Conclusões: Os eventos observados em córneas humanas após debridamento epitelial, apoptose e proliferação dos ceratócitos, foram semelhantes aos descritos em animais de experimentação / Purpose: To examine the early wound healing response to epithelial scrape in human corneas. Methods: Normal corneas had epithelial scrape prior to enucleation. Histology, TUNEL assay, Ki67, SMA and transmission electron microscopy were performed. Results: Epithelial scrape was performed in six corneas from ½ to 65 hours prior to preservation. Keratocyte apoptosis was detected in the anterior stroma in all scraped corneas. Keratocyte proliferation was detected exclusively 65 hours after scrape. No myofibroblast was detected. One cornea was not scraped (control). Conclusion: Results obtained in human corneas (keratocyte apoptosis and proliferation) were similar to animal models

It is known that fission yeast Schizosaccharomyces pombe maintains its nuclear envelope during mitosis and it undergoes an interesting shape change during cell division - from a spherical via an ellipsoidal and a peanut-like to a dumb-bell shape. However, the biomechanical system behind this amazing transformation is still not understood. What we know is, that the shape must change due to forces acting on the membrane surrounding the nucleus and the microtubule based mitotic spindle is thought to play a key role. To estimate the locations and directions of the forces, the shape of the nucleus was recorded by confocal light microscopy. But such data is often inhomogeneously labeled with gaps in the boundary, making classical segmentation impractical. In order to accurately determine the shape we developed a global parametric shape description method, based on a Fourier coordinate expansion. The method implicitly assumes a closed and smooth surface. We will calculate the geometrical properties of the 2-dimensional shape and extend it to 3-dimensional properties, assuming rotational symmetry. Using a mechanical model for the lipid bilayer and the so called Helfrich-Canham free energy we want to calculate the minimum energy shape while respecting system-specific constraints to the surface and the enclosed volume. Comparing it with the observed shape leads to the forces. This provides the needed research tools to study forces based on images.