Thesis (Doctoral)--Universiteit van Amsterdam, 1982.

What is flagellar swimming? Cilia and flagella are whip-like cell appendages that can exhibit regular bending waves. This active process emerges from the non-equilibrium dynamics of molecular motors distributed along the length of cilia and flagella. Eukaryotic cells can possess many cilia and flagella that beat in a coordinated fashion, thus transporting fluids, as in mammalian airways or the ventricular system inside the brain. Many unicellular organisms posses just one or two flagella, rendering them microswimmers that are propelled through fluids by the flagellar beat including sperm cells and the biflagellate green alga Chlamydomonas. Objectives. In this thesis in theoretical biological physics, we seek to understand the nonlinear dynamics of flagellar swimming and synchronization. We investigate the flow fields induced by beating flagella and how in turn external hydrodynamic flows change speed and shape of the flagellar beat. This flagellar load-response is a prerequisite for flagellar synchronization. We want to find the physical principals underlying stable synchronization of the two flagella of Chlamydomonas cells. Results. First, we employed realistic hydrodynamic simulations of flagellar swimming based on experimentally measured beat patterns. For this, we developed analysis tools to extract flagellar shapes from high-speed videoscopy data. Flow-signatures of flagellated swimmers are analysed and their effect on a neighboring swimmer is compared to the effect of active noise of the flagellar beat. We were able to estimate a chemomechanical energy efficiency of the flagellar beat and determine its waveform compliance by comparing findings from experiments, in which a clamped Chlamydomonas is exposed to external flow, to predictions from an effective theory that we designed. These mechanical properties have interesting consequences for the synchronization dynamics of Chlamydomonas, which are revealed by computer simulations. We propose that direct elastic coupling between the two flagella of Chlamydomonas, as suggested by recent experiments, in combination with waveform compliance is crucial to facilitate in-phase synchronization of the two flagella of Chlamydomonas.

Für die E. coli K12 Biofilmbildung ist die Expression des Masterregulators CsgD essentiell. Dies erfordert das Signalmolekül c-di-GMP, dessen Auf- und Abbau durch 12 Diguanylatzyklasen (DGCs mit GGDEF-Domänen) und 13 Phosphodiesterasen (PDEs mit EAL-Domänen) erfolgt. DgcE ist mit einer MASE1-umfassenden Transmembranregion (TM), drei PAS-, einer GGDEF- und einer degenerierten EAL-Domäne die strukturell komplexeste DGC und notwendig für die Biofilmbildung. Diese Arbeit zeigt, dass die Aktivität von DgcE einer hoch komplexen Regulation unterliegt. Einzelnen DgcE-Domänen konnten aktivierende bzw. inhibierende Rollen hinsichtlich der Biofilmmatrixsynthese zugeordnet werden. Die Biofilmbildung hängt von DgcE-produziertem c-di-GMP ab, wobei die DgcE-Dimerisierung v.a. durch die PAS-Region vermittelt wird. Die EAL-Domäne wirkt einer aktiven DgcE-Form entgegen. Für die DgcE-vermittelte Matrixproduktion sind die GTPase YjdA und sein Partnerprotein YjcZ nötig. Über Interaktionen mit YjcZ und der TM von DgcE vermittelt YjdA eine Komplexbildung. Die Interaktion von YjdA und DgcE sowie die Matrixproduktion hängen von der GTPase-Aktivität von YjdA ab. GTP wird daher als intrazelluläres Signal vorgeschlagen, das die Aktivierung von DgcE durch YjdA/YjcZ reguliert. Die MASE1-umfassende TM agiert als Zentrale der Signalintegration. Einerseits ist sie nötig für die DgcE-Aktivität und andererseits ist sie an einem massiven Abbau von DgcE beteiligt. Zudem wurden neu identifizierte Curli-regulierende Gene (rbsK, rbsR, ydcI, yieP, puuR) untersucht, wobei keines über das PdeR/DgcM/MlrA-Modul in die c-di-GMP-vermittelte CsgD-Expression eingreift. Flagellare Verknotungen in der unteren Schicht von E. coli Makrokolonien tragen zur Morphogenese dieser Makrokolonien bei. Diese Arbeit zeigt, dass Flagellenverknotungen zu einer verminderten Expression der Master-PDE PdeH beitragen, wodurch vermutlich die zelluläre c-di-GMP-Konzentration steigt und somit die Biofilmbildung begünstigt wird. / Biofilm formation of E. coli K12 requires the expression of the biofilm master regulator CsgD. This process depends on the signaling molecule c-di-GMP, which is synthesized by 12 diguanylate cyclases (DGCs with GGDEF domains) and degraded by 13 phosphodiesterases (PDEs with EAL domains). DgcE is the most complex DGC with a MASE1-containing transmembrane region (TM), three PAS, a GGDEF and a degenerate EAL domain, and it is essential for biofilm formation. This work shows that the regulation of the DgcE activity is highly complex. It was possible to assign activating and inhibitory roles to single domains of DgcE with regard to the expression of biofilm matrix components. C-di-GMP produced by DgcE is necessary for biofilm matrix production. The dimerization of DgcE is mainly mediated by the PAS region, whereas the EAL domain counteracts an active form of DgcE. DgcE-mediated matrix synthesis requires the activating signal input of the GTPase YjdA and its partner protein YjcZ. DgcE, YjdA and YjcZ form a protein complex in which YjdA directly interacts with YjcZ and the TM of DgcE. The interaction between DgcE and YjdA as well as the matrix expression depend on the GTPase activity of YjdA. Thus, it is proposed that GTP serves as an intracellular signal regulating the activation of DgcE by YjdA/YjcZ. The MASE1-containing TM proved to be a central hub for signal integration. It is both required for DgcE activity and for a massive degradation of DgcE. Furthermore, newly discovered curli-regulating genes (rbsK, rbsR, ydcI, yieP, puuR) have been analyzed. None of those gene products act on CsgD expression via the PdeR/DgcM/MlrA module. Flagellar entangling within the bottom layer of E. coli macrocolonies determines morphogenesis of macrocolonies. The data presented here suggest that the master PDE PdeH is somehow down-regulated by flagellar entangling, which probably results in a higher cellular c-di-GMP concentration, thereby promoting biofilm formation.

What is flagellar swimming? Cilia and flagella are whip-like cell appendages that can exhibit regular bending waves. This active process emerges from the non-equilibrium dynamics of molecular motors distributed along the length of cilia and flagella. Eukaryotic cells can possess many cilia and flagella that beat in a coordinated fashion, thus transporting fluids, as in mammalian airways or the ventricular system inside the brain. Many unicellular organisms posses just one or two flagella, rendering them microswimmers that are propelled through fluids by the flagellar beat including sperm cells and the biflagellate green alga Chlamydomonas. Objectives. In this thesis in theoretical biological physics, we seek to understand the nonlinear dynamics of flagellar swimming and synchronization. We investigate the flow fields induced by beating flagella and how in turn external hydrodynamic flows change speed and shape of the flagellar beat. This flagellar load-response is a prerequisite for flagellar synchronization. We want to find the physical principals underlying stable synchronization of the two flagella of Chlamydomonas cells. Results. First, we employed realistic hydrodynamic simulations of flagellar swimming based on experimentally measured beat patterns. For this, we developed analysis tools to extract flagellar shapes from high-speed videoscopy data. Flow-signatures of flagellated swimmers are analysed and their effect on a neighboring swimmer is compared to the effect of active noise of the flagellar beat. We were able to estimate a chemomechanical energy efficiency of the flagellar beat and determine its waveform compliance by comparing findings from experiments, in which a clamped Chlamydomonas is exposed to external flow, to predictions from an effective theory that we designed. These mechanical properties have interesting consequences for the synchronization dynamics of Chlamydomonas, which are revealed by computer simulations. We propose that direct elastic coupling between the two flagella of Chlamydomonas, as suggested by recent experiments, in combination with waveform compliance is crucial to facilitate in-phase synchronization of the two flagella of Chlamydomonas.:1 Introduction 1.1 Physics of cell motility: flagellated swimmers as model system 2 1.1.1 Tissue cells and unicellular eukaryotic organisms have cilia and flagella 2 1.1.2 The conserved architecture of flagella 3 1.1.3 Synchronization in collections of flagella 5 1.2 Hydrodynamics at the microscale 9 1.2.1 Navier-Stokes equation 10 1.2.2 The limit of low Reynolds number 10 1.2.3 Multipole expansion of flow fields 11 1.3 Self-propulsion by viscous forces 13 1.3.1 Self propulsion requires broken symmetries 13 1.3.2 Signatures of flowfields: pusher & puller 15 1.4 Overview of the thesis 16 2 Flow signatures of flagellar swimming 2.1 Self-propulsion of flagellated swimmers 20 2.1.1 Representation of flagellar shapes 20 2.1.2 Computation of hydrodynamic friction forces 21 2.1.3 Material frame and rigid-body transformations 22 2.1.4 The grand friction matrix 23 2.1.5 Dynamics of swimming 23 2.2 The hydrodynamic far field: pusher and puller 26 2.2.1 The flow generated by a swimmer 26 2.2.2 Force dipole characterization 27 2.2.3 Flagellated swimmers alternate between pusher and puller 29 2.2.4 Implications for two interacting Chlamydomonas cells 31 2.3 Inertial screening of oscillatory flows 32 2.3.1 Convection and oscillatory acceleration 33 2.3.2 The oscilet: fundamental solution of unsteady flow 35 2.3.3 Screening length of oscillatory flows 35 2.4 Energetics of flagellar self-propulsion 36 2.4.1 Impact of inertial screening on hydrodynamic dissipation 37 2.4.2 Case study: the green alga Chlamydomonas 38 2.4.3 Discussion: evolutionary optimization and the number of molecular motors 38 2.5 Summary 39 3 The load-response of the flagellar beat 3.1 Experimental collaboration: flagellated swimmers exposed to flows 41 3.1.1 Description of the experimental setup 42 3.1.2 Computed flow profile in the micro-fluidic device 43 3.1.3 Image processing and flagellar tracking 43 3.1.4 Mode decomposition and limit-cycle reconstruction 47 3.1.5 Changes of limit-cycle dynamics: deformation, translation, acceleration 49 3.2 An effective theory of flagellar oscillations 50 3.2.1 A balance of generalized forces 50 3.2.2 Hydrodynamic friction in generalized coordinates 51 3.2.3 Intra-flagellar friction 52 3.2.4 Calibration of active flagellar driving forces 52 3.2.5 Stability of the limit cycle of the flagellar beat 53 3.2.6 Equations of motion 55 3.3 Comparison of theory and experiment 56 3.3.1 Flagellar mean curvature 57 3.3.2 Susceptibilities of phase speed and amplitude 57 3.3.3 Higher modes and stalling of the flagellar beat at high external load 59 3.3.4 Non-isochrony of flagellar oscillations 63 3.4 Summary 63 4 Flagellar load-response facilitates synchronization 4.1 Synchronization to external driving 65 4.2 Inter-flagellar synchronization in the green alga Chlamydomonas 67 4.2.1 Equations of motion for inter-flagellar synchronization 68 4.2.2 Synchronization strength for free-swimming and clamped cells 70 4.2.3 The synchronization strength depends on energy efficiency and waveform compliance 73 4.2.4 The case of an elastically clamped cell 74 4.2.5 Basal body coupling facilitates in-phase synchronization 75 4.2.6 Predictions for experiments 78 4.3 Summary 80 5 Active flagellar fluctuations 5.1 Effective description of flagellar oscillations 84 5.2 Measuring flagellar noise 84 5.2.1 Active phase fluctuations are much larger than thermal noise 84 5.2.2 Amplitude fluctuations are correlated 85 5.3 Active flagellar fluctuations result in noisy swimming paths 86 5.3.1 Effective diffusion of swimming circles of sperm cell 86 5.3.2 Comparison of the effect of noise and hydrodynamic interactions 87 5.4 Summary 88 6 Summary and outlook 6.1 Summary of our results 89 6.2 Outlook on future work 90 A Solving the Stokes equation A.1 Multipole expansion 95 A.2 Resistive-force theory 96 A.3 Fast multipole boundary element method 97 B Linearized Navier-Stokes equation B.1 Linearized Navier-Stokes equation 101 B.2 The case of an oscillating sphere 102 B.3 The small radius limit 103 B.4 Greens function 104 C Hydrodynamic friction C.1 A passive particle 107 C.2 Multiple Particles 107 C.3 Generalized coordinates 108 D Data analysis methods D.1 Nematic filter 111 D.1.1 Nemat 111 D.1.2 Nematic correlation 111 D.2 Principal-component analysis 112 D.3 The quality of the limit-cycle projections of experimental data 113 E Adler equation F Sensitivity analysis for computational results F.1 The distance function of basal coupling 117 F.2 Computed synchronization strength for alternative waveform 118 F.3 Insensitivity of computed load-response to amplitude correlation time 118 List of Symbols List of Figures Bibliography

Durch Parasiten stellen eine starke Gefährdung für die Aquakultur dar. Die durch diplomonaden Flagellaten bei der Regenbogenforelle Oncorhynchus mykiss verursachte Morbidität und Mortalität wurde bisher in Deutschland noch nicht gründlich untersucht. Ich habe diese Parasiten mittels SEM & TEM charakterisiert und wurde die Art Spironucleus salmonis bestimmt. Erstmals konnten die caudale Projektion, sich entleerende Vakuolen und verformbare Kernloben nachgewiesen werden. Ich untersuchte Mikrohabitatpräferenz von des Parasiten sowie pH-Profile in vier Darmabschnitten der Fische. Das Vorkommen und die Dichte von S. salmonis war in der Pylorusregion wesentlich höher als in anderen Bereichen. Das pH-Profil war bei infizierten und nicht infizierten Fischen gleich. Der optimale pH-Wert für S. salmonis war 7,1-7,5. Ich habe die Lebenszyklus der Diplomonaden mittels LM & SEM unter Kulturbedingungen untersucht. Die Enzystierung begann mit der Anheftung von Trophozoiten mit der Spitze der adhäsiven hinteren Flagellen aneinander oder an Fremdkörper. Die pyriformen Trophozoiten wurden kugelförmig, und die vorderen Flagellen inaktiv. Oberflächenbläschen produzierten eine lichtbrechende Zystenwand. Dies ist der erste Beschreibung der Multifunktionalität von Flagellen bei Diplomonaden. Ich untersuchte pathogene Mechanismen und sezierte die Pylorusregion sowie die Leber mittels H&E, PAS/AB. Bei infizierten Fischen trat eine signifikante Hypertrophie der Becherzellen auf. Zu erkennen war eine Hyperaktivität der Becherzellen, jedoch keine Hyperplasie. Ich entwickelte einen in vitro  Plasma-Inkubationstest zur Bestimmung der Suszeptibilität von Regenbogenforelle, Karpfen und Störe. Die unterschiedliche Resistenz von Stör, Karpfen und Regenbogenforelle gegen S. salmonis entsprechend zu den epizootiologischen Daten. Meine Untersuchungen führten zu einem neuen diagnostischen Hilfsmittel, Vorschlägen für neue Behandlungsmethoden, zu verbesserten in vitro-Kulturbedingungen und einem Modellsystem für die Multifunktionalität von Flagellen und flagellaren Signaltransduktion. / Parasitic diseases pose a significant threat to aquaculture. Diplomonad flagellates in rainbow trout Oncorhynchus mykiss are associated with morbidity and mortality; but in Germany has not been thoroughly studied. I characterised the species by SEM & TEM, which revealed Spironucleus salmonis, allowed its complete description including newly showing the caudal projection, discharging vacuoles, and deformable nuclear lobes; diagnostic keys were improved. The microhabitat preference of diplomonads was tested by recording occurrence and density of infection, and pH profile in 4 intestinal regions in fish. Occurrence and density of S. salmonis were significant higher in the pyloric region than elsewhere. The pH profile in uninfected and infected fish was similar; a causal relationship between microhabitat preference and pH was unlikely, and the optimal pH was between 7.1 – 7.5. I described life cycle and encystment using light and SEM. Encystment in culture began by trophozoites attaching at tip of adhesive posterior flagella to each other/debris. Pyriform trophozoites became sub-spherical, anterior flagella inactive, surface blebs produced a refractile cyst wall. Cysts clusters may exceed minimum infective dose for new infection; suggesting new treatment target. This is the first report of multi-functionality of flagella in diplomonads. I investigated pathogenic mechanism of diplomonads by sectioning and staining the pyloric region of the intestine and liver with H&E, and PAS/AB. There was significant hypertrophy of goblet cells in infected fish. The hyperactivity of goblet cells was seen, but no hyperplasia. This hyper-production of mucus may decrease nutrient absorption, underlying impaired growth in S. salmonis infected fish. I developed an in vitro plasma incubation test to predict host susceptibility of rainbow trout, carp, and sturgeon. The test showed the hierarchy of resistance of S. salmonis in sturgeon > carp > rainbow trout; this parallels epizootiological data. My research yielded new diagnostic tool, suggested new treatment target, improved in vitro conditions, and new model system for multi-functionality of flagella and flagellar signalling.

Cilia and flagella are hair-like appendages of eukaryotic cells. They are actively bending structures that exhibit regular beat patterns and thereby play an important role in many different circumstances where motion on a cellular level is required. Most dramatic is the effect of nodal cilia whose vortical motion leads to a fluid flow that is directly responsible for establishing the left-right axis during embryological development in many vertebrate species, but examples range from the propulsion of single cells, such as the swimming of sperm, to the transport of mucus along epithelial cells, e.g. in the ciliated trachea. Cilia and flagella contain an evolutionary highly conserved structure called the axoneme, whose characteristic architecture is based on a cylindrical arrangement of elastic filaments (microtubules). In the presence of a chemical fuel (ATP), molecular motors (dynein) exert shear forces between neighbouring microtubules, leading to a bending of the axoneme through structural constraints. We address the following two questions: How can these organelles generate regular oscillatory beat patterns in the absence of a biochemical signal regulating the activity of the force generating elements? And how can the beat patterns be so different for apparently very similar structures? We present a theoretical description of the axonemal structure as an actively bending elastic cylinder, and show that in such a system bending waves emerge from a non-oscillatory state via a dynamic instability. The corresponding beat patterns are solutions to a set of coupled partial differential equations presented herein.

Cilia and flagella are hair-like appendages of eukaryotic cells. They are actively bending structures that exhibit regular beat patterns and thereby play an important role in many different circumstances where motion on a cellular level is required. Most dramatic is the effect of nodal cilia whose vortical motion leads to a fluid flow that is directly responsible for establishing the left-right axis during embryological development in many vertebrate species, but examples range from the propulsion of single cells, such as the swimming of sperm, to the transport of mucus along epithelial cells, e.g. in the ciliated trachea. Cilia and flagella contain an evolutionary highly conserved structure called the axoneme, whose characteristic architecture is based on a cylindrical arrangement of elastic filaments (microtubules). In the presence of a chemical fuel (ATP), molecular motors (dynein) exert shear forces between neighbouring microtubules, leading to a bending of the axoneme through structural constraints. We address the following two questions: How can these organelles generate regular oscillatory beat patterns in the absence of a biochemical signal regulating the activity of the force generating elements? And how can the beat patterns be so different for apparently very similar structures? We present a theoretical description of the axonemal structure as an actively bending elastic cylinder, and show that in such a system bending waves emerge from a non-oscillatory state via a dynamic instability. The corresponding beat patterns are solutions to a set of coupled partial differential equations presented herein.