1,645 research outputs found
A three-sphere swimmer for flagellar synchronization
In a recent letter (Friedrich et al., Phys. Rev. Lett. 109:138102, 2012), a
minimal model swimmer was proposed that propels itself at low Reynolds numbers
by a revolving motion of a pair of spheres. The motion of the two spheres can
synchronize by virtue of a hydrodynamic coupling that depends on the motion of
the swimmer, but is rather independent of direct hydrodynamic interactions.
This novel synchronization mechanism could account for the synchronization of a
pair of flagella, e.g. in the green algae Chlamydomonas. Here, we discuss in
detail how swimming and synchronization depend on the geometry of the model
swimmer and compute the swimmer design for optimal synchronization. Our
analysis highlights the role of broken symmetries for swimming and
synchronization.Comment: 25 pages, 4 color figures, provisionally accepted for publication in
the New Journal of Physic
Nematic order by elastic interactions and cellular rigidity sensing
We predict spontaneous nematic order in an ensemble of active force
generators with elastic interactions as a minimal model for early nematic
alignment of short stress fibers in non-motile, adhered cells. Mean-field
theory is formally equivalent to Maier-Saupe theory for a nematic liquid.
However, the elastic interactions are long-ranged (and thus depend on cell
shape and matrix elasticity) and originate in cell activity. Depending on the
density of force generators, we find two regimes of cellular rigidity sensing
for which orientational, nematic order of stress fibers depends on matrix
rigidity either in a step-like manner or with a maximum at an optimal rigidity.Comment: 12 pages, 4 figure
Flagellar swimmers oscillate between pusher- and puller-type swimming
Self-propulsion of cellular microswimmers generates flow signatures, commonly
classified as pusher- and puller-type, which characterize hydrodynamic
interactions with other cells or boundaries. Using experimentally measured beat
patterns, we compute that flagellated alga and sperm oscillate between pusher
and puller. Beyond a typical distance of 100 um from the swimmer, inertia
attenuates oscillatory micro-flows. We show that hydrodynamic interactions
between swimmers oscillate in time and are of similar magnitude as stochastic
swimming fluctuations.Comment: 12 pages, 4 color figure
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 Turingâs 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 âFlagellar synchronization independent of hydrodynamic interactionsâ 56
2.2 âCell body rocking is a dominant mechanism for flagellar synchronizationâ 57
2.3 âActive phase and amplitude fluctuations of the flagellar beatâ 58
2.4 âSperm navigation in 3D chemoattractant landscapesâ 59
3 Selected publications: Self-organized pattern formation in cells and tissues 60
3.1 âSarcomeric pattern formation by actin cluster coalescenceâ 60
3.2 âScaling and regeneration of self-organized patternsâ 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 gegenĂŒber Fluktuationen und Ă€uĂeren Störungen. Wir entwickeln hierzu theoretische Beschreibungen fĂŒr 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 zellulĂ€rer Ebene am Modelsystem von Zilien und GeiĂeln. Spontane Biegewellen dieser dĂŒnnen ZellfortsĂ€tze ermöglichen es eukaryotischen Zellen, in einer FlĂŒssigkeit zu schwimmen. Wir beschreiben einen neuen physikalischen Mechanismus fĂŒr die Synchronisation zweier schlagender GeiĂeln, unabhĂ€ngig von direkten hydrodynamischen Wechselwirkungen. Der Vergleich mit experimentellen Daten, zur VerfĂŒgung gestellt von unseren experimentellen Kooperationspartnern im Labor von J. Howard (Yale, New Haven), bestĂ€tigt diesen neuen Mechanismus im Modellorganismus der einzelligen GrĂŒnalge Chlamydomonas. Der Gegenspieler dieser Synchronisation durch mechanische Kopplung sind Fluktuationen. Wir bestimmen erstmals Nichtgleichgewichts-Fluktuationen des GeiĂel-Schlags direkt, wofĂŒr wir eine neue Analyse-Methode der Grenzzykel-Rekonstruktion entwickeln. Die von uns gemessenen Fluktuationen entstehen mutmaĂlich durch die stochastische Dynamik molekularen Motoren im Innern der GeiĂeln, welche auch den GeiĂelschlag antreiben. Um die statistische Physik dieser Nichtgleichgewichts-Fluktuationen zu verstehen, entwickeln wir eine analytische Theorie der Fluktuationen in einem minimalen Modell kollektiver Motor-Dynamik. ZusĂ€tzlich zur Regulation des GeiĂelschlags durch mechanische KrĂ€fte untersuchen wir dessen Regulation durch chemische Signale am Modell der Chemotaxis von Spermien-Zellen. Dabei charakterisieren wir einen grundlegenden Mechanismus fĂŒr die Navigation in externen Konzentrationsgradienten. Dieser Mechanismus beruht auf dem aktiven Schwimmen entlang von Spiralbahnen, wodurch ein rĂ€umlicher 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 GeiĂelschlags wĂ€hrend der Spermien-Chemotaxis. Vorhersagen dieser Theorie werden durch Experimente der Gruppe von U.B. Kaupp (CAESAR, Bonn) quantitativ bestĂ€tigt.
In Kapitel 3, untersuchen wir selbstorganisierte Strukturbildung in zwei ausgewĂ€hlten biologischen Systemen. Auf zellulĂ€rer Ebene schlagen wir einen einfachen physikalischen Mechanismus vor fĂŒr 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 rĂ€umliche Ordnung auf gröĂeren LĂ€ngenskalen in einem Nichtgleichgewichtssystem entstehen kann. Auf der Ebene des Organismus stellen wir eine Erweiterung der Turingschen Theorie fĂŒr selbstorganisierte Musterbildung vor. Wir beschreiben eine neue Klasse von Musterbildungssystemen, welche selbst-organisierte Muster erzeugt, die mit der SystemgröĂe 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 stationĂ€ren Muster und analysieren deren StabilitĂ€t und Einzugsgebiete. Damit können wir zeigen, dass dieser Skalierungs-Mechanismus strukturell robust ist bezĂŒglich 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 PlattwĂŒrmern 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 âFlagellar synchronization independent of hydrodynamic interactionsâ 56
2.2 âCell body rocking is a dominant mechanism for flagellar synchronizationâ 57
2.3 âActive phase and amplitude fluctuations of the flagellar beatâ 58
2.4 âSperm navigation in 3D chemoattractant landscapesâ 59
3 Selected publications: Self-organized pattern formation in cells and tissues 60
3.1 âSarcomeric pattern formation by actin cluster coalescenceâ 60
3.2 âScaling and regeneration of self-organized patternsâ 61
4 Contribution of the author in collaborative publications 62
5 Eidesstattliche Versicherung 64
6 Appendix: Reprints of publications 6
Cell body rocking is a dominant mechanism for flagellar synchronization in a swimming alga
The unicellular green algae Chlamydomonas swims with two flagella, which can
synchronize their beat. Synchronized beating is required to swim both fast and
straight. A long-standing hypothesis proposes that synchronization of flagella
results from hydrodynamic coupling, but the details are not understood. Here,
we present realistic hydrodynamic computations and high-speed tracking
experiments of swimming cells that show how a perturbation from the
synchronized state causes rotational motion of the cell body. This rotation
feeds back on the flagellar dynamics via hydrodynamic friction forces and
rapidly restores the synchronized state in our theory. We calculate that this
`cell body rocking' provides the dominant contribution to synchronization in
swimming cells, whereas direct hydrodynamic interactions between the flagella
contribute negligibly. We experimentally confirmed the coupling between
flagellar beating and cell body rocking predicted by our theory. This work
appeared also in the Proceedings of the National Academy of Science of the
U.S.A as: Geyer et al., PNAS 110(45), p. 18058(6), 2013.Comment: 40 pages, 15 color figure
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