Subject of study: Cilia and flagella are slender appendages of eukaryotic cells. They are actively bending structures and display regular bending waves. These active flagellar bending waves drive fluid flows on cell surfaces like in the case of the ciliated trachea or propels single cell micro-swimmers like sperm or alga. Objective: The axoneme is the evolutionarily conserved mechanical apparatus within cilia and flagella. It is comprised of a cylindrical arrangement of microtubule doublets, which are the elastic elements and dyneins, which are the force generating elements in the axonemal structure. Dyneins collectively bend the axoneme and must be specifically regulated to generate symmetric and highly asymmetric waveforms. In this thesis, I address the question of the molecular origin of the asymmetric waveform and test different theoretical descriptions for motor regulation. Approach: I introduce the isolated and reactivated Chlamydomonas axoneme as an experimental model for the symmetric and asymmetric flagellar beat. This system allows to study the beat in a controlled and cell free environment. I use high-speed microscopy to record shapes with high spatial and temporal resolution. Through image analysis and shape parameterization I extract a minimal set of parameters that describe the flagellar waveform. Using Chlamydomonas, I make use of different structural and motor mutants to study their effect on the shape in different reactivation conditions. Although the isolated axoneme system has many advantages compared to the cell-bound flagellum, to my knowledge, it has not been characterized yet. Results: I present a shape parameterization of the asymmetric beat using Fourier decomposition methods and find, that the asymmetric waveform can be understood as a sinusoidal beat around a circular arc. This reveals the similarities of the two different beat types: the symmetric and the asymmetric beat. I investigate the origin of the beat-asymmetry and find evidence for a specific dynein motor to be responsible for the asymmetry. I furthermore find experimental evidence for a strong sliding restriction at the basal end of the axoneme, which is important to establish a static bend. In collaboration with P. Sartori and F. Jülicher, I compare theoretical descriptions of different motor control mechanisms and find that a curvature controlled motor-regulation mechanism describes the experimental data best. We furthermore find, that in the dynamic case an additional sliding restriction at the base is unnecessary. By comparing the waveforms of intact cells and isolated reactivated axonemes, I reveal the effect of hydrodynamic loading, and the influence of boundary conditions on the shape of the beating flagella.

Subject of study: Cilia and flagella are slender appendages of eukaryotic cells. They are actively bending structures and display regular bending waves. These active flagellar bending waves drive fluid flows on cell surfaces like in the case of the ciliated trachea or propels single cell micro-swimmers like sperm or alga. Objective: The axoneme is the evolutionarily conserved mechanical apparatus within cilia and flagella. It is comprised of a cylindrical arrangement of microtubule doublets, which are the elastic elements and dyneins, which are the force generating elements in the axonemal structure. Dyneins collectively bend the axoneme and must be specifically regulated to generate symmetric and highly asymmetric waveforms. In this thesis, I address the question of the molecular origin of the asymmetric waveform and test different theoretical descriptions for motor regulation. Approach: I introduce the isolated and reactivated Chlamydomonas axoneme as an experimental model for the symmetric and asymmetric flagellar beat. This system allows to study the beat in a controlled and cell free environment. I use high-speed microscopy to record shapes with high spatial and temporal resolution. Through image analysis and shape parameterization I extract a minimal set of parameters that describe the flagellar waveform. Using Chlamydomonas, I make use of different structural and motor mutants to study their effect on the shape in different reactivation conditions. Although the isolated axoneme system has many advantages compared to the cell-bound flagellum, to my knowledge, it has not been characterized yet. Results: I present a shape parameterization of the asymmetric beat using Fourier decomposition methods and find, that the asymmetric waveform can be understood as a sinusoidal beat around a circular arc. This reveals the similarities of the two different beat types: the symmetric and the asymmetric beat. I investigate the origin of the beat-asymmetry and find evidence for a specific dynein motor to be responsible for the asymmetry. I furthermore find experimental evidence for a strong sliding restriction at the basal end of the axoneme, which is important to establish a static bend. In collaboration with P. Sartori and F. Jülicher, I compare theoretical descriptions of different motor control mechanisms and find that a curvature controlled motor-regulation mechanism describes the experimental data best. We furthermore find, that in the dynamic case an additional sliding restriction at the base is unnecessary. By comparing the waveforms of intact cells and isolated reactivated axonemes, I reveal the effect of hydrodynamic loading, and the influence of boundary conditions on the shape of the beating flagella.:Contents 1 Introduction. . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 Biology of Cilia and Flagella . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 The dimensions of flagellated micro-swimmers . . . . . . . . . . . . . . . . . 4 1.1.2 The symmetric and the asymmetric beat . . . . . . . . .. . . . . . . . . . . . 5 1.1.3 Chlamydomonas reinhardtii as a flagella model . . . . . . . . . . 5 1.2 The axoneme is the internal structure in eukaryotic cilia and flagella . . 6 1.3 Structure and function of microtubules and dyneins . . . . . . . . . . . 9 1.3.1 Microtubules: The structural elements in the axoneme . . . . . . 9 1.3.2 Dyneins: The force generators that drive the axonemal beat . . . 10 1.3.3 The asymmetries in the axoneme and consequences for the beat 17 1.4 Axonemal waveform models and mechanisms: from sliding to bending to beating . . . . . . . . . . . . . . 20 1.5 Geometrical representation and parameterization of the axonemal beat . . . . . . . . . . . . . . . 23 2 Questions addressed in this thesis . . . . . . . . . . . . . . 27 3 Material and Methods . . . . . . . . . . . . . . 29 3.1 Chlamydomonas cells: Axoneme preparation and motility assays . . . . 29 3.1.1 Culturing of Chlamydomonas reinhardtii cells . . . . . . . . . . . 29 3.1.2 Isolation, demembranation and storage of axonemes . . . . . . . 33 3.1.3 Reactivation of axonemes in controlled conditions . . . . . . . . . 35 3.1.4 Axoneme gliding assay using kinesin 1 . . . . . . . . . . . . . . . 36 3.2 Imaging and image processing . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.1 High-speed imaging of the flagella and axonemes . . . . . . . . . 38 3.2.2 Precise tracking of isolated axonemes and the flagella of cells . . 42 3.2.3 High throughput frequency evaluation of isolated axonemes . . . 47 3.2.4 Beat frequency characterization of the reactivated WT axoneme . . . . . . . . . . . . . . 49 4 Results and Discussion . . . . . . . . . . . . . . 53 4.1 The beat of the axoneme propagates from base to tip . . . . . . . . . . . 53 4.1.1 TEM study reveals no sliding at the base of a bend axoneme . . 53 4.1.2 The direction of wave propagation is directly determined from the reactivation of polarity marked axonemes . . . . . . . . . . 57 4.1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.2 The asymmetric beat is the superposition of a static semi-circular arc and a sinusoidal beat . . . . . . .. . . . . . . . . . . . . . . . . 61 4.2.1 The waveform is parameterized by Fourier decomposition in time . . . . . . . . . . . . . . 61 4.2.2 The 0th and 1st Fourier modes describe the axonemal waveform . . . . . . . . . . . . . . 65 4.2.3 General dependence of shape parameters on axoneme length and beat frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.2.4 The isolated axoneme is a good model for the intact flagellum . .. . . . . . . . . . . . . . 71 4.2.5 Summary: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.3 The circular motion is a consequence of the axonemal waveform . . . . . . . . . . . . . . . . . . . 79 4.3.1 Hydrodynamic relations for small amplitude waves explain the relation between swimming and shape of axonemes . . . . 79 4.3.2 The swimming path can be reconstructed using shape information and a hydrodynamic model . . . . . . . . . . . . . . . . 83 4.3.3 Motor mutations alter the direction of rotation of reactivated axonemes. . . . . . . . . . . . . . . . . . . . . . . . 84 4.3.4 Summary: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.4 The molecular origin of the circular mean shape. . . . . . . . . . . . . . 89 4.4.1 Motor Mutations do not abolish the mean shape, a structural mutation does . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.4.2 The axoneme is straight in absence of ATP but bend at low ATP concentrations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.4.3 Viscous load decreases the mean curvature . . . . . . . . . . . . 99 4.4.4 Summary: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.5 Curvature-dependent dynein activation accounts for the shape of the beat of the isolated axoneme . . . . . . . . . . . . . . . . 103 5 Conclusions and Outlook . . . . . . . . . . . . . . . . 109 5.1 Summary of the results . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.2 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Abbreviations . . . . . . . . . . . . . . . . 111 List of figures . . . . . . . . . . . . . . . . 116 List of tables . . . . . . . . . . . . . . . . 118 Bibliography

This thesis is focused on a creating supporting drivers and algorithms for electrical motor control using CPU TriCore TC275 CA. The first part is devoted to processor description and selected peripherals, which are A/D converter, a timer for creating the PWM signals and the second timer for processing singnals from encoder. All drivers are tested on an aplication kit, which is equipped with TC275 CA processor. The second part analyzes the measurement quality of GMR sensor TLE5009. Special testbench was prepared for sin cos data capturing and for their comparison with precise encoder position measurement. It was composed from DC motor having both sensor types on commons shaft. Data are acquired using LabView. Subsequently, it analyzes the sensor data, their compensation and subsequent comparison with measured data from the encoder.