Realizing the physics of motile cilia synchronization with driven colloids

Cilia and flagella in biological systems often show large scale cooperative behaviors such as the synchronization of their beats in "metachronal waves". These are beautiful examples of emergent dynamics in biology, and are essential for life, allowing diverse processes from the motility of eukaryotic microorganisms, to nutrient transport and clearance of pathogens from mammalian airways. How these collective states arise is not fully understood, but it is clear that individual cilia interact mechanically,and that a strong and long ranged component of the coupling is mediated by the viscous fluid. We review here the work by ourselves and others aimed at understanding the behavior of hydrodynamically coupled systems, and particularly a set of results that have been obtained both experimentally and theoretically by studying actively driven colloidal systems. In these controlled scenarios, it is possible to selectively test aspects of the living motile cilia, such as the geometrical arrangement, the effects of the driving profile and the distance to no-slip boundaries. We outline and give examples of how it is possible to link model systems to observations on living systems, which can be made on microorganisms, on cell cultures or on tissue sections. This area of research has clear clinical application in the long term, as severe pathologies are associated with compromised cilia function in humans.Comment: 31 pages, to appear in Annual Review of Condensed Matter Physic

Self-organization of microtubules for biomimetic structures

Biological polymers that build up the eukaryotic cytoskeleton exhibit a rich dynamical behaviour that aid a multitude of cellular processes. Microtubules, together with their associated motor proteins in the cell are involved in cell motility, mitosis, intracellular transport and maintaining cellular rigidity. In the recent past, synthetic microtubule-motor protein systems have been extensively studied owing to their collective display of higher-level self-organization through spontaneous beating, dynamic pattern formation in dense suspensions and enhanced transport through cytoplasmic streaming. In this work, we focus on understanding microtubule-motor protein interactions through an in vitro bottom-up approach.We gain information on the motor protein induced dynamics on pairs or bundles of sliding microtubule bundles as well as crosslinked microtubule networks. As a result, we move a step closer towards gaining a better understanding of biological phenomena such as ciliary beating and cytoplasmic streaming.2021-07-1

Understanding the Collective Dynamics of Motile Cilia in Human Airways

Eukaryotic organisms rely on the coordinated beating of motile cilia for a multitude of fundamental reasons. In smaller organisms, such as Paramecium and the single cell alga Chlamydomonas reinhardtii, it is a matter of propulsion, to swim towards a higher concentration of nutrients or away from damaging environments. Larger organisms use instead the coordinated motion of cilia to push fluid along an epithelium: examples common to mammals are the circulation of cerebrospinal fluid in the brain, the transport of ovules in the fallopian tubes, and breaking the left/right symmetry in the embryo. Another notable example, and one that is central to this thesis, is mucociliary clearance in human airways: A carpet of motile cilia helps keeping the cell surface free from pathogens and foreign particles by constantly evacuating from lungs, bronchi, and trachea a barrier of mucus. The question of how motile cilia interact with one another to beat in a coordinated fashion is an open and pressing one, with immediate implications for the medical community. In order for the fluid propulsion to be effective, the motion of cilia needs to be phase-locked across significant distances, in the form of travelling waves (``metachronal waves''). It is still not known how this long-range coordination emerges from local rules, as there is no central node regulating the coordination among cilia. In the first part of this thesis I will focus on studying the coordination in carpets of cilia with a top-down approach, by proposing, implementing, and applying a new method of analysing microscope videos of ciliated epithelia. Chapter 1 provides the reader with an introduction on motile cilia and flagella, treating their structure and motion and reporting the different open questions currently tackled by the scientific community, with particular interest in the coordination mechanisms of cilia and the mucociliary clearance apparatus. Chapter 2 introduces Differential Dynamic Microscopy (DDM), a powerful and versatile image analysis tool that bridges the gap between spectroscopy and microscopy by allowing to perform scattering experiments on a microscope. The most interesting aspects of DDM for this work are that it can be applied to microscope videos where it is not possible to resolve individual objects in the field of view, and it requires no user input. These two characteristics make DDM a perfect candidate for analysing several hundred microscope videos of weakly scattering filaments such as cilia. In Chapter 3 I will present how it is possible to employ DDM to extract a wealth of often-overlooked information from videos of ciliated epithelia: DDM can successfully probe the ciliary beat frequency (CBF) in a sample, measure the direction of beating of the cilia, and detect metachronal waves and read their direction and wavelength. In vitro ciliated epithelia however often do not show perfect coordination or alignment among cilia. For the analysis of these samples, where the metachronal coordination might not be evident, we developed a new approach, called multiscale DDM (multiDDM), to measure a coordination length scale, a characteristic length of the system over which the coordination between cilia is lost. The new technique of multiDDM is employed in Chapter 4 to study how the coordination among cilia changes as a response to changes in the rheology of the mucous layer. In particular, we show that cilia beating under a thick, gel-like mucus layer show a larger coordination length scale, as if the mucus acted as an elastic raft effectively coupling cilia over long distances. This is corroborated by the coordination length scale being larger in samples from patients affected by Cystic Fibrosis than in healthy samples, and much shorter when the mucus layer is washed and cilia therefore beat in a near-Newtonian fluid. We then show how it is possible to employ multiDDM to measure the effectiveness of drugs in recovering, in CF samples, a coordination length scale typical of a healthy phenotype. In the second part I will focus instead on the single cilium scale, showing how we can attempt to link the beating pattern of cilia to numerical simulations studying synchronisation in a model system. In particular in Chapter 5 I will describe our approach to quantitatively describe the beating pattern of single cilia obtained from human airway cells of either healthy individuals or patients affected by Primary Ciliary Dyskinesia. Our description of the beating pattern, and the selection of a few meaningful, summary parameters, are then shown to be accurate enough to discriminate between different mutations within Primary Ciliary Dyskinesia. In Chapter 6 instead I report the results obtained by coarse-graining the ciliary beat pattern into a model system consisting of two ``rotors''. The rotors are simulated colloidal particles driven along closed trajectories while leaving their phase free. In my study, the trajectories followed by the rotors are analytical fits of experimental trajectories of the centre of drag of real cilia. The rotors, that are coupled only via hydrodynamics interactions, are seen to phase-lock, and the shape of the trajectory they are driven along is seen to influence the steady state of the system

The role of hydrodynamic forces in synchronisation and alignment of mammalian motile cilia

Fluid flow generated by a ciliated epithelium is a fascinating evidence of collective behaviour in nature. In many organs and eukaryotic organisms, thousands of microscale whip-like structures called `motile cilia' beat aligned at the same frequency and in a coordinated fashion. This dynamics, known as `metachronal wave', has fundamental physiological roles in microorganisms and many organs of vertebrates. In the airways, the coordinated beatings of motile cilia generate a fluid flow that pushes mucus to the pharynx, and so protects the lungs from inhaled contaminants. The failure of this collective dynamics can precipitate or exacerbate severe infections and chronic inflammatory conditions such as cystic fibrosis (CF), primary ciliary dyskinesia (PCD) or asthma. In the brain, the multiciliated ependymal cells cover all the ventricles. Their cilia beat in a coordinated fashion to ensure the cerebrospinal fluid circulation necessary for brain homoeostasis, toxin washout and orientation of the migration of newborn neurons. Despite the fundamental role in nature, the mechanism underpinning such collective behaviour is still unknown. A recent hypothesis, supported by simulations, experiments with microorganisms and with cilia models, proposed that hydrodynamic interactions between cilia could provide a physical mechanism for their coordination. In contrast, others have proposed a role of the cytoskeletal elastic coupling between cilia. While previous works mainly focused on algae and protists, investigating the conditions that are required for the emergence of the metachronal wave in mammalian tissues can provide important progress in the diagnosis and treatment of human medical diseases. Specifically, I tackled this broad topic by studying the hydrodynamic forces necessary for the synchronisation and alignment of motile cilia from brain and airways. This question was addressed experimentally by measuring cilia motility during treatment with oscillatory and constant external fluid flows. We found that synchronisation and alignment of mammalian cilia in the brain is achieved with flows of similar magnitude of the ones generated by cilia themselves. Our results suggest that hydrodynamic forces between cilia are sufficient for the emergence of their collective behaviour. The first chapter provides basic knowledge on motile cilia structure and functions in microorganisms and humans. Additionally, I introduce the reader to the open questions related to the coordination of a pair and a carpet of cilia, with specific attention on previous works on mammals. This first chapter is followed by a description of a novel microfluidic device that I developed to grow $\textit{in vitro}$ airway and brain cells and apply controlled viscous forces. In Chapter 3, I describe how we have investigated cilia synchronisation of mammalian cilia. Applying external oscillatory flow on brain cells, we studied the susceptibility of cilia motility to hydrodynamic forces similar to the ones generated by cilia themselves. We found that cells with few cilia (up to five) can be entrained at flows comparable to the cilia-driven flows reported in vivo. We suggest that hydrodynamic forces between mammalian cilia are sufficiently strong to be the mechanism underpinning frequency synchronisation. In the second part of my thesis, I looked into the hydrodynamic shear forces needed to align permanently the cilia direction of beating. We tackled this problem by using $\textit{in vitro}$ cultures of mouse brain and human airway cells grown in custom flow channels. We found that cilia from mouse brain do not lock their beating direction after \emph{ciliogenesis}, but can respond and align to physiological shear stress found \emph{in vivo} at any time, in contrast with was previously believed. Moreover, we suggest that cilia alignment depends on the density of cilia, in agreement with a hydrodynamic screening effect of the external flow by the nearby cilia that we aim to investigate in the future. These results are described in Chapter 4. Successively in Chapter 5, I report our approach to study whether physiological shear stress can induce cilia alignment in airway cell cultures. The current hypothesis is that these cilia may also be able to align with external hydrodynamic forces - however, experimental evidence is still needed. There is a lack of experiments on this topic mainly because airway cells are cultured in an air-liquid interface, and so shear stress has to be applied with airflows. We developed novel setups for applying long term shear stress with air and fluid flow on this system, leaving further experiments for the future.EU Horizon 2020 research and innovation program under Marie Sklodowska-Curie 641639 ITN BioPol and ERC CoG HydroSyn

Ex-vivo and In-vivo Characterization of Human Accommodation

A completely satisfying approach to restoring accommodation still needs to be developed. Besides, there are considerable discrepancies between objective and subjective trials to evaluate the therapeutic success. A substantial biomechanical understanding of all structures and processes involved in accommodation as well as presbyopia are needed to develop promising new strategies. This contribution focuses on developing advanced imaging techniques to create a basic understanding of accommodation and presbyopia and to evaluate existing concepts for restoring accommodation. Besides, the emphasis is also on replacing stiff presbyopic lenses by a material that imitates the young crystalline lens

Nonlinear dynamics and fluctuations in biological systems

The present habilitation thesis in theoretical biological physics addresses two central dynamical processes in cells and organisms: (i) active motility and motility control and (ii) self-organized pattern formation. The unifying theme is the nonlinear dynamics of biological function and its robustness in the presence of strong fluctuations, structural variations, and external perturbations. We theoretically investigate motility control at the cellular scale, using cilia and flagella as ideal model system. Cilia and flagella are highly conserved slender cell appendages that exhibit spontaneous bending waves. This flagellar beat represents a prime example of a chemo-mechanical oscillator, which is driven by the collective dynamics of molecular motors inside the flagellar axoneme. We study the nonlinear dynamics of flagellar swimming, steering, and synchronization, which encompasses shape control of the flagellar beat by chemical signals and mechanical forces. Mechanical forces can synchronize collections of flagella to beat at a common frequency, despite active motor noise that tends to randomize flagellar synchrony. In Chapter 2, we present a new physical mechanism for flagellar synchronization by mechanical self-stabilization that applies to free-swimming flagellated cells. This new mechanism is independent of direct hydrodynamic interactions between flagella. Comparison with experimental data provided by experimental collaboration partners in the laboratory of J. Howard (Yale, New Haven) confirmed our new mechanism in the model organism of the unicellular green alga Chlamydomonas. Further, we characterize the beating flagellum as a noisy oscillator. Using a minimal model of collective motor dynamics, we argue that measured non-equilibrium fluctuations of the flagellar beat result from stochastic motor dynamics at the molecular scale. Noise and mechanical coupling are antagonists for flagellar synchronization. In addition to the control of the flagellar beat by mechanical forces, we study the control of the flagellar beat by chemical signals in the context of sperm chemotaxis. We characterize a fundamental paradigm for navigation in external concentration gradients that relies on active swimming along helical paths. In this helical chemotaxis, the direction of a spatial concentration gradient becomes encoded in the phase of an oscillatory chemical signal. Helical chemotaxis represents a distinct gradient-sensing strategy, which is different from bacterial chemotaxis. Helical chemotaxis is employed, for example, by sperm cells from marine invertebrates with external fertilization. We present a theory of sensorimotor control, which combines hydrodynamic simulations of chiral flagellar swimming with a dynamic regulation of flagellar beat shape in response to chemical signals perceived by the cell. Our theory is compared to three-dimensional tracking experiments of sperm chemotaxis performed by the laboratory of U. B. Kaupp (CAESAR, Bonn). In addition to motility control, we investigate in Chapter 3 self-organized pattern formation in two selected biological systems at the cell and organism scale, respectively. On the cellular scale, we present a minimal physical mechanism for the spontaneous self-assembly of periodic cytoskeletal patterns, as observed in myofibrils in striated muscle cells. This minimal mechanism relies on the interplay of a passive coarsening process of crosslinked actin clusters and active cytoskeletal forces. This mechanism of cytoskeletal pattern formation exemplifies how local interactions can generate large-scale spatial order in active systems. On the organism scale, we present an extension of Turing’s framework for self-organized pattern formation that is capable of a proportionate scaling of steady-state patterns with system size. This new mechanism does not require any pre-pattering clues and can restore proportional patterns in regeneration scenarios. We analytically derive the hierarchy of steady-state patterns and analyze their stability and basins of attraction. We demonstrate that this scaling mechanism is structurally robust. Applications to the growth and regeneration dynamics in flatworms are discussed (experiments by J. Rink, MPI CBG, Dresden).:1 Introduction 10 1.1 Overview of the thesis 10 1.2 What is biological physics? 12 1.3 Nonlinear dynamics and control 14 1.3.1 Mechanisms of cell motility 16 1.3.2 Self-organized pattern formation in cells and tissues 28 1.4 Fluctuations and biological robustness 34 1.4.1 Sources of fluctuations in biological systems 34 1.4.2 Example of stochastic dynamics: synchronization of noisy oscillators 36 1.4.3 Cellular navigation strategies reveal adaptation to noise 39 2 Selected publications: Cell motility and motility control 56 2.1 “Flagellar synchronization independent of hydrodynamic interactions” 56 2.2 “Cell body rocking is a dominant mechanism for flagellar synchronization” 57 2.3 “Active phase and amplitude fluctuations of the flagellar beat” 58 2.4 “Sperm navigation in 3D chemoattractant landscapes” 59 3 Selected publications: Self-organized pattern formation in cells and tissues 60 3.1 “Sarcomeric pattern formation by actin cluster coalescence” 60 3.2 “Scaling and regeneration of self-organized patterns” 61 4 Contribution of the author in collaborative publications 62 5 Eidesstattliche Versicherung 64 6 Appendix: Reprints of publications 66Das Thema der vorliegenden Habilitationsschrift in Theoretischer Biologischer Physik ist die nichtlineare Dynamik funktionaler biologischer Systeme und deren Robustheit gegenüber Fluktuationen und äußeren Störungen. Wir entwickeln hierzu theoretische Beschreibungen für zwei grundlegende biologische Prozesse: (i) die zell-autonome Kontrolle aktiver Bewegung, sowie (ii) selbstorganisierte Musterbildung in Zellen und Organismen. In Kapitel 2, untersuchen wir Bewegungskontrolle auf zellulärer Ebene am Modelsystem von Zilien und Geißeln. Spontane Biegewellen dieser dünnen Zellfortsätze ermöglichen es eukaryotischen Zellen, in einer Flüssigkeit zu schwimmen. Wir beschreiben einen neuen physikalischen Mechanismus für die Synchronisation zweier schlagender Geißeln, unabhängig von direkten hydrodynamischen Wechselwirkungen. Der Vergleich mit experimentellen Daten, zur Verfügung gestellt von unseren experimentellen Kooperationspartnern im Labor von J. Howard (Yale, New Haven), bestätigt diesen neuen Mechanismus im Modellorganismus der einzelligen Grünalge Chlamydomonas. Der Gegenspieler dieser Synchronisation durch mechanische Kopplung sind Fluktuationen. Wir bestimmen erstmals Nichtgleichgewichts-Fluktuationen des Geißel-Schlags direkt, wofür wir eine neue Analyse-Methode der Grenzzykel-Rekonstruktion entwickeln. Die von uns gemessenen Fluktuationen entstehen mutmaßlich durch die stochastische Dynamik molekularen Motoren im Innern der Geißeln, welche auch den Geißelschlag antreiben. Um die statistische Physik dieser Nichtgleichgewichts-Fluktuationen zu verstehen, entwickeln wir eine analytische Theorie der Fluktuationen in einem minimalen Modell kollektiver Motor-Dynamik. Zusätzlich zur Regulation des Geißelschlags durch mechanische Kräfte untersuchen wir dessen Regulation durch chemische Signale am Modell der Chemotaxis von Spermien-Zellen. Dabei charakterisieren wir einen grundlegenden Mechanismus für die Navigation in externen Konzentrationsgradienten. Dieser Mechanismus beruht auf dem aktiven Schwimmen entlang von Spiralbahnen, wodurch ein räumlicher Konzentrationsgradient in der Phase eines oszillierenden chemischen Signals kodiert wird. Dieser Chemotaxis-Mechanismus unterscheidet sich grundlegend vom bekannten Chemotaxis-Mechanismus von Bakterien. Wir entwickeln eine Theorie der senso-motorischen Steuerung des Geißelschlags während der Spermien-Chemotaxis. Vorhersagen dieser Theorie werden durch Experimente der Gruppe von U.B. Kaupp (CAESAR, Bonn) quantitativ bestätigt. In Kapitel 3, untersuchen wir selbstorganisierte Strukturbildung in zwei ausgewählten biologischen Systemen. Auf zellulärer Ebene schlagen wir einen einfachen physikalischen Mechanismus vor für die spontane Selbstorganisation von periodischen Zellskelett-Strukturen, wie sie sich z.B. in den Myofibrillen gestreifter Muskelzellen finden. Dieser Mechanismus zeigt exemplarisch auf, wie allein durch lokale Wechselwirkungen räumliche Ordnung auf größeren Längenskalen in einem Nichtgleichgewichtssystem entstehen kann. Auf der Ebene des Organismus stellen wir eine Erweiterung der Turingschen Theorie für selbstorganisierte Musterbildung vor. Wir beschreiben eine neue Klasse von Musterbildungssystemen, welche selbst-organisierte Muster erzeugt, die mit der Systemgröße skalieren. Dieser neue Mechanismus erfordert weder eine vorgegebene Kompartimentalisierung des Systems noch spezielle Randbedingungen. Insbesondere kann dieser Mechanismus proportionale Muster wiederherstellen, wenn Teile des Systems amputiert werden. Wir bestimmen analytisch die Hierarchie aller stationären Muster und analysieren deren Stabilität und Einzugsgebiete. Damit können wir zeigen, dass dieser Skalierungs-Mechanismus strukturell robust ist bezüglich Variationen von Parametern und sogar funktionalen Beziehungen zwischen dynamischen Variablen. Zusammen mit Kollaborationspartnern im Labor von J. Rink (MPI CBG, Dresden) diskutieren wir Anwendungen auf das Wachstum von Plattwürmern und deren Regeneration in Amputations-Experimenten.:1 Introduction 10 1.1 Overview of the thesis 10 1.2 What is biological physics? 12 1.3 Nonlinear dynamics and control 14 1.3.1 Mechanisms of cell motility 16 1.3.2 Self-organized pattern formation in cells and tissues 28 1.4 Fluctuations and biological robustness 34 1.4.1 Sources of fluctuations in biological systems 34 1.4.2 Example of stochastic dynamics: synchronization of noisy oscillators 36 1.4.3 Cellular navigation strategies reveal adaptation to noise 39 2 Selected publications: Cell motility and motility control 56 2.1 “Flagellar synchronization independent of hydrodynamic interactions” 56 2.2 “Cell body rocking is a dominant mechanism for flagellar synchronization” 57 2.3 “Active phase and amplitude fluctuations of the flagellar beat” 58 2.4 “Sperm navigation in 3D chemoattractant landscapes” 59 3 Selected publications: Self-organized pattern formation in cells and tissues 60 3.1 “Sarcomeric pattern formation by actin cluster coalescence” 60 3.2 “Scaling and regeneration of self-organized patterns” 61 4 Contribution of the author in collaborative publications 62 5 Eidesstattliche Versicherung 64 6 Appendix: Reprints of publications 6