Dynamics and forces in the mitotic spindle

Mikrotubuli sind zylinderförmige Filamente und Teil des Zytoskeletts. Ihre Polymerisationsdynamik zeichnet sich durch eine dynamische Instabilität von Wachstums- und Schrumpfphasen aus. Die zufälligen Wechsel vom schrumpfenden in den wachsenden Zustand und umgekehrt werden als Rettungen bzw. Katastrophen bezeichnet. Letztere können experimentellen Beobachtungen zufolge als Mehrschrittprozesse beschrieben werden. Im ersten Teil dieser Arbeit wird das empirische Dogterom-Leibler-Modell der dynamischen Instabilität erweitert, um auszuarbeiten, welche Auswirkungen eine Mehrschrittkatastrophe auf die Längenverteilung eines Mikrotubulus in den Regimen gebundenen und ungebundenen Wachstums hat. Es zeigt sich, dass die Mikrotubuluslängen im gebundenen Regime nicht mehr exponentiell und weniger endlastig verteilt sind, wenn eine Katastrophe aus mehreren Schritten besteht. Wenn Rettungen möglich sind, hat die Verteilung ein Maximum und der Mikrotubulus somit eine wahrscheinlichste Länge, die größer ist als 0. Im Regime ungebundenen Wachstums nähert sich die Längenverteilung einer Normalverteilung an, die mit steigender Anzahl der Katastrophenschritte schmaler wird. In der Mitosespindel sind Mikrotubuli durch Kinetochore mit den Chromosomen verbunden und üben so Kräfte aus, die in der Metaphase zu stochastischen Oszillationen der Chromosomen führen. Im zweiten Teil dieser Arbeit untersuchen wir in Modellen der Mitosespindel die kollektive Dynamik von Mikrotubuli, die durch elastische Federn an Kinetochore gebunden sind. Die Modelle beinhalten die dynamische Instabilität der Mikrotubuli und die Kräfte, die durch die elastischen Verbindungen wirken. Für ein einseitiges Modell mit nur einem Kinetochor, das einer externen Kraft ausgesetzt ist, können mithilfe einer Molekularfeldnäherung Fokker-Planck-Gleichungen aufgestellt und gelöst werden. Aus der Lösung folgt eine bistabile Abhängigkeit der Kinetochorgeschwindigkeit von der externen Kraft. Im zweiseitigen Modell mit zwei elastisch gekoppelten Kinetochoren führt die Bistabilität zu Oszillationen, die denen der Chromosomen in der Metaphase gleichen. Das Modell kann erklären, warum in Zellen mit einem schnellen polwärtigen Mikrotubulusfluss keine Oszillationen beobachtet wurden. Polare Auswurfkräfte gewährleisten im Modell eine Anordnung der Kinetochore am Spindeläquator und führen zu geregelteren Oszillationen mit verringerter Amplitude. Wenn das Modell so geändert wird, dass die Mikrotubuli nur Zugkräfte auf das Kinetochor ausüben können, treten Oszillationen nur unter der Voraussetzung auf, dass in der Nähe der Kinetochore Katastrophen induziert werden. Die Modellparameter können so angepasst werden, dass die modellierten Oszillationen auch in quantitativer Hinsicht mit Messungen in PtK1-Zellen übereinstimmen. Ein wichtiger Bestandteil des Kinetochors sind stäbchenförmige Ndc80-Komplexe, die den Mikrotubulus binden und deren elastischen Eigenschaften als wichtig für die Kraftübertragung vom Mikrotubulus auf das Chromosom erachtet werden. Im letzten Teil dieser Arbeit wird eine Methode präsentiert, die es erlaubt, den zeitlichen Verlauf der effektiven Steifigkeit von Ndc80-Komplexen zu ermitteln, die in einer optischen Falle entgegen einer Kraft dem schrumpfenden Ende eines Mikrotubulus folgen. Die Anwendung der Methode auf mehrere Experimente zeigt, dass sowohl der Wildtyp als auch drei weitere Ndc80-Varianten steifer werden, wenn der schrumpfende Mikrotubulus sie unter Spannung setzt. Die gemessene Steifigkeit hat eine annähernd lineare Abhängigkeit von der angelegten Kraft und ist unabhängig vom dynamischen Zustand des Mikrotubulus. Mithilfe eines elastischen Modells kann die Versteifung auf die spezielle Architektur des Ndc80-Komplexes sowie auf das Biegen gekrümmter Protofilamente zurückgeführt werden. Ein Modell mit einer kraftabhängigen Bindungsaffinität reproduziert die lineare Beziehung zwischen Steifigkeit und Kraft.Microtubules are cylindrical cytoskeletal filaments. Their polymerization dynamics is characterized by a dynamic instability between phases of growth and shrinkage. The stochastic switches from shrinkage to growth and vice versa are called rescues and catastrophes, respectively. Experimental observations characterized the latter ones as multistep processes. In the first part of this thesis, we extend the empirical Dogterom–Leibler model of dynamic instability to discuss the effect that a multistep catastrophe mechanism has on the distribution of microtubule lengths in the two regimes of bounded and unbounded growth. We show that, in the former case, the steady state length distribution is non-exponential and has a lighter tail if multiple steps are required to undergo a catastrophe. If rescue events are possible, we detect a maximum in the distribution, i.e., the microtubule has a most probable length greater than zero. In the regime of unbounded growth, the length distribution converges to a Gaussian distribution whose variance decreases with the number of catastrophe steps. In the mitotic spindle, microtubules attach to chromosomes via kinetochores, and their depolymerization forces give rise to stochastic chromosome oscillations during metaphase. In the second part of this thesis, we investigate the cooperative stochastic microtubule dynamics in spindle models consisting of ensembles of parallel microtubules, which are attached to kinetochores via elastic linkers. We include the dynamic instability of microtubules and forces on microtubules and kinetochores from elastic linkers. A one-sided model with a single kinetochore exposed to an external force is solved analytically employing a mean-field approach based on Fokker–Planck equations. The solution establishes a bistable force–velocity relation of the kinetochore. Coupling the kinetochores of two such bistable systems elastically in the full two-sided model gives rise to oscillations, which can explain stochastic chromosome oscillations in metaphase. We derive constraints on linker stiffness and microtubule number for these oscillations. Including poleward microtubule flux into the model, we can provide an explanation for the experimentally observed suppression of chromosome oscillations in cells with high flux velocities. Chromosome oscillations persist in the presence of polar ejection forces, however, with a reduced amplitude and a phase shift between sister kinetochores. Moreover, polar ejection forces are necessary to align the chromosomes at the spindle equator and stabilize an alternating oscillation pattern of the two kinetochores. Finally, we modify the model such that microtubules can only exert tensile forces on the kinetochore. Then, induced microtubule catastrophes after reaching the kinetochore are necessary to stimulate oscillations. The model parameters can be adapted to reproduce experimental results for kinetochore oscillations in PtK1 cells quantitatively. The microtubule-binding Ndc80 complex is an integral part of kinetochores and is essential to transmit forces from dynamic microtubule ends to the chromosomes. The Ndc80 complex has a rod-like appearance and its mechanical properties are considered important for the dynamic interaction between kinetochores and microtubules. In the final part of this thesis, we present a novel method that allows us to time-trace the effective stiffness of Ndc80 complexes following shortening microtubule ends against an applied force in optical trap experiments. Applying this method to wild type Ndc80 and three further variants, we reveal that each variant exhibits strain stiffening, i.e., the effective stiffness increases under tension that is built up by a depolymerizing microtubule. The strain stiffening relation is roughly linear and independent of the dynamic state of the microtubule. We introduce an elastic model, which shows that the strain stiffening can be traced back to the specific architecture of the Ndc80 complex and the bending elasticity of flaring protofilaments. The model reproduces the roughly linear strain stiffening behavior if a force-dependent binding affinity is taken into account

Bistability and oscillations in cooperative microtubule and kinetochore dynamics in the mitotic spindle

In the mitotic spindle microtubules attach to kinetochores via catch bonds during metaphase, and microtubule depolymerization forces give rise to stochastic chromosome oscillations. We investigate the cooperative stochastic microtubule dynamics in spindle models consisting of ensembles of parallel microtubules, which attach to a kinetochore via elastic linkers. We include the dynamic instability of microtubules and forces on microtubules and kinetochores from elastic linkers. A one-sided model, where an external force acts on the kinetochore is solved analytically employing a mean-field approach based on Fokker–Planck equations. The solution establishes a bistable force–velocity relation of the microtubule ensemble in agreement with stochastic simulations. We derive constraints on linker stiffness and microtubule number for bistability. The bistable force–velocity relation of the one-sided spindle model gives rise to oscillations in the two-sided model, which can explain stochastic chromosome oscillations in metaphase (directional instability). We derive constraints on linker stiffness and microtubule number for metaphase chromosome oscillations. Including poleward microtubule flux into the model we can provide an explanation for the experimentally observed suppression of chromosome oscillations in cells with high poleward flux velocities. Chromosome oscillations persist in the presence of polar ejection forces, however, with a reduced amplitude and a phase shift between sister kinetochores. Moreover, polar ejection forces are necessary to align the chromosomes at the spindle equator and stabilize an alternating oscillation pattern of the two kinetochores. Finally, we modify the model such that microtubules can only exert tensile forces on the kinetochore resulting in a tug-of-war between the two microtubule ensembles. Then, induced microtubule catastrophes after reaching the kinetochore are necessary to stimulate oscillations. The model can reproduce experimental results for kinetochore oscillations in PtK1 cells quantitatively

Dynamics and length distributions of microtubules with a multistep catastrophe mechanism

Regarding the experimental observation that microtubule (MT) catastrophe can be described as a multistep process, we extend the Dogterom–Leibler model for dynamic instability in order to discuss the effect that such a multistep catastrophe mechanism has on the distribution of MT lengths in the two regimes of bounded and unbounded growth. We show that in the former case, the steady state length distribution is non-exponential and has a lighter tail if multiple steps are required to undergo a catastrophe. If rescue events are possible, we detect a maximum in the distribution, i.e. the MT has a most probable length greater than zero. In the regime of unbounded growth, the length distribution converges to a Gaussian distribution whose variance decreases with the number of catastrophe steps. We extend our work by applying the multistep catastrophe model to MTs that grow against an opposing force and to MTs that are confined between two rigid walls. We determine critical forces below which the MT is in the bounded regime, and show that the multistep characteristics of the length distribution are largely lost if the growth of an MT in the unbounded regime is restricted by a rigid wall. All results are verified by stochastic simulations

SMALL CHANGES, BIG IMPACT: HOW SINGULAR MODIFICATIONS SHIFTED THE FEDERAL GOVERNMENT FROM ITS CONSTITUTUIONAL ROLES

This paper is an examination of “small” changes to each branch of the United States Federal Government that have had major implications on how the government works and its design. Each chapter focuses on a singular change to one branch of government; explores the historical significance; and assesses the potential future implications of those changes if the trends within the chapters continue. Chapter One examines the changes of post- Seventeenth Amendment split party delegations using the DW-NOMINATE scoring method and senator party support; Chapter Two examines the polarization of the Supreme Court since the New Deal by assessing Supreme Court justices with the Martin-Quinn Scores and the overall polarization of each Court, and Chapter Three examines the power shift of the first fifteen presidential executive orders and how presidents are changing the way they use the power of the pen using the length of time to issue fifteen executive orders and what types of orders that are issued. The conclusions that arise from each chapter highlight the trend that small changes to the federal government have long lasting and large implications that are often overlooked or are lumped into larger changes in the federal government. By understanding the small changes, the bigger picture can become clearer

Hardware Design Improvements to the Major Constituent Analyzer

The Major Constituent Analyzer (MCA) onboard the International Space Station (ISS) is designed to monitor the major constituents of the ISS's internal atmosphere. This mass spectrometer based system is an integral part of the Environmental Control and Life Support System (ECLSS) and is a primary tool for the management of ISS atmosphere composition. As a part of NASA Change Request CR10773A, several alterations to the hardware have been made to accommodate improved MCA logistics. First, the ORU 08 verification gas assembly has been modified to allow the verification gas cylinder to be installed on orbit. The verification gas is an essential MCA consumable that requires periodic replenishment. Designing the cylinder for subassembly transport reduces the size and weight of the maintained item for launch. The redesign of the ORU 08 assembly includes a redesigned housing, cylinder mounting apparatus, and pneumatic connection. The second hardware change is a redesigned wiring harness for the ORU 02 analyzer. The ORU 02 electrical connector interface was damaged in a previous on-orbit installation, and this necessitated the development of a temporary fix while a more permanent solution was developed. The new wiring harness design includes flexible cable as well as indexing fasteners and guide-pins, and provides better accessibility during the on-orbit maintenance operation. This presentation will describe the hardware improvements being implemented for MCA as well as the expected improvement to logistics and maintenance

The first biosimilar approved for the treatment of osteoporosis

To demonstrate the clinical comparability between RGB-10 (a biosimilar teriparatide) and the originator, a comparative pharmacokinetic trial was conducted. The study was successful in establishing bioequivalence. Marketing authorisation for RGB-10 (Terrosa®) was granted by the European Medicines Agency in 2017.Teriparatide, the first bone anabolic agent, is the biologically active fragment of human parathyroid hormone. The imminent patent expiry of the originator will open the door for biosimilars to enter the osteology market, thereby improving access to a highly effective, yet prohibitively expensive therapy.Subsequent to establishing comparability on the quality and non-clinical levels between RGB-10, a biosimilar teriparatide, and its reference product (Forsteo®), a randomised, double-blind, 2-way cross-over comparative study (duration: four days) was conducted in 54 healthy women (ages: 18 to 55 years) to demonstrate the pharmacokinetic/pharmacodynamic (PK/PD) equivalence and comparable safety of these products. Extents of exposure (AUC0-tlast) and peak exposure (Cmax), as measured by means of ELISA, were evaluated as co-primary PK endpoints, and serum calcium levels, as measured using standard automated techniques, were assessed for PD effects. Safety was monitored throughout the study.The 94.12% CIs for the ratio of the test to the reference treatments, used due to the two-stage design (85.20-98.60% and 85.51-99.52% for AUC0-tlast and Cmax, respectively), fell within the 80.00-125.00% acceptance range. The calcium PD parameters were essentially identical with geometric mean ratios (GMRs) of 99.93% and 99.87% for AUC and Cmax, respectively. Analysis of the safety data did not reveal any differences between RGB-10 and its reference.Based on the high level of similarity in the preclinical data and the results of this clinical study, marketing authorisation for RGB-10 (Terrosa®) was granted by the European Medicines Agency (EMA) in 2017