18 research outputs found
Dynamics of active surfaces
Mechano-chemical processes in biological systems play an important role during the morphogenesis of cells and tissues. In particular, they are responsible for the dynamic organisation of active stress, which itself results from non-equilibrium processes and leads to flows and deformations of material. The generation of active stress often occurs in thin biological structures, such as the cellular cortex or epithelial tissues, which motivates the theoretical concept of an active surface. In this thesis, we study the dynamics of curved and deforming active surfaces. More specifically, we are interested in the dynamics of mechano-chemical processes on these surfaces, as well as in their interaction with the surface shape and external forces.
To study the interplay of mechano-chemical processes with shape changes of the material, we consider the fully self-organised shape dynamics using the theory of active fluids on deforming surfaces. We then develop a numerical approach to solve the corresponding force and torque balance equations. We further examine how the stability of surface shapes is affected by mechano-chemical processes. We show that the tight coupling between chemical processes and surface mechanics gives rise to the spontaneous generation of specific surface shapes, to shape oscillations and to directed surface flows that resemble peristaltic motion.
In the following part, we explore the mechano-chemical self-organisation of active fluids on fixed surfaces, focussing on mechanical interactions with surrounding material. We introduce a description in which active surface flows set a surrounding passive fluid into motion. We then study two scenarios. First, inspired by the cellular cortex and its interactions with the cytoplasm, we consider a fluid that is enclosed by the surface. We find that mechanical interactions with the surrounding passive fluid enable an isotropic active surface to spontaneously generate patterns with polar asymmetry and to form a contractile ring in a fully self-organised fashion. Second, we consider the case where the passive fluid surrounds the active surface on the outside. This description leads to the model of a microswimmer, which is characterised by an onset of motion due to spontaneous symmetry breaking on the active surface.
Most biological materials are viscoelastic, such that they show viscous and elastic responses if mechanical stress is applied on different time scales. In the final part of this thesis, we therefore consider a surface whose response to self-organised active stress is described by a Maxwell model. We identify a minimal time scale for the relaxation of elastic stress, beyond which spatio-temporal, mechano-chemical oscillations on the surface can spontaneously emerge.
In summary, we identify and characterise in this thesis various processes that result from the self-organisation of active surfaces. The underlying coupling between surface mechanics and a chemical organisation of stress in the material represents a key feature of morphogenetic processes in biology. Furthermore, we develop several numerical approaches that will enable to study alternative constitutive relations of active surfaces in the future. Overall, we contribute theoretical insights and numerical tools to further the understanding of the emerging spatial organisation and shape generation of active surfaces.Mechanochemische Prozesse spielen eine wichtige Rolle fĂŒr die Morphogenese von biologischen Zellen und Geweben. Sie sind insbesondere verantwortlich fĂŒr die dynamische Organisation von aktiver mechanischer Spannung, welche Nicht-Gleichgewichtsprozessen entstammt und zu FlĂŒssen und Verformungen von Material fĂŒhrt. Aktive mechanische Spannung wird hĂ€ufig in dĂŒnnen biologischen Strukturen erzeugt, wie zum Beispiel dem Zellkortex oder dem Epithelgewebe, was die EinfĂŒhrung von aktiven FlĂ€chen als theoretisches Konzept motiviert. In der vorliegenden Arbeit untersuchen wir die Dynamik von gekrĂŒmmten und sich verformenden aktiven FlĂ€chen. Dabei interessieren wir uns insbesondere fĂŒr die Dynamik mechanochemischer Prozesse auf diesen FlĂ€chen, sowie fĂŒr deren Wechselwirkung mit der FlĂ€chenform und externen KrĂ€ften.
Zur Untersuchung der Wechselwirkung zwischen mechanochemischen Prozessen und FlĂ€chenverformungen nutzen wir die hydrodynamische Theorie aktiver Fluide auf sich verformenden FlĂ€chen und betrachten eine vollstĂ€ndig selbstorganisierte FlĂ€chendynamik. Wir entwickeln eine Methode zur Bestimmung numerischer Lösungen des KrĂ€fte- und Drehmomentgleichgewichts auf FlĂ€chen und untersuchen wie die StabilitĂ€t von FlĂ€chenformen durch mechanochemische Prozesse beeinflusst wird. Wir zeigen, dass die enge Kopplung zwischen chemischen Prozessen und der Mechanik von FlĂ€chen zur spontanen Erzeugung spezifischer Formen, zu Formoszillationen und zu gerichteten FlĂŒssen fĂŒhrt, welche eine peristaltische Bewegung nachbilden.
Im Folgenden untersuchen wir die mechanochemische Selbstorganisation aktiver Fluide auf festen FlĂ€chen und betrachten mechanische Wechselwirkungen mit umgebendem Material. Dazu beschreiben wir ein umgebendes passives Fluid, welches durch aktive FlĂŒsse auf der FlĂ€che in Bewegung versetzt wird. Im Rahmen dieser Beschreibung untersuchen wir zwei Szenarien. Inspiriert durch die Wechselwirkung des Zellkortex mit dem Zytoplasma, betrachten wir zuerst ein Fluid, welches durch die FlĂ€che eingeschlossen wird. Wir zeigen, dass die mechanische Wechselwirkung einer isotropen, aktiven FlĂ€che mit dem umgebenden Fluid es ermöglicht, Muster mit einer polaren Asymmetrie, sowie einen kontraktilen Ring spontan und selbstorganisiert zu bilden. Danach betrachten wir ein passives Fluid, welches die FlĂ€che auĂen umgibt. Diese Beschreibung fĂŒhrt zu einem Modell fĂŒr einen Mikroschwimmer, welcher durch eine spontane Symmetriebrechung auf der aktiven FlĂ€che beginnt sich durch das passive Fluid zu bewegen.
Die meisten biologischen Materialien verhalten sich viskoelastisch, sodass deren mechanische Antwort je nach Zeitskala einer applizierten mechanischen Spannung viskos und elastisch ausfallen kann. Im abschlieĂenden Teil dieser Arbeit betrachten wir daher eine FlĂ€che, deren mechanische Antwort auf aktive Spannung durch ein Maxwell-Modell beschrieben wird. Wir bestimmen eine minimale Zeitskala fĂŒr die Relaxation von elastischer Spannung, welche das spontane Einsetzen rĂ€umlich-zeitlicher Oszillationen aktiver mechanischer Spannung kennzeichnet.
Zusammengefasst identifizieren und charakterisieren wir in dieser Arbeit eine Reihe von Prozessen, welche der Selbstorganisation aktiver FlĂ€chen entspringen. Die zugrundeliegende Kopplung zwischen der Mechanik von FlĂ€chen und einer chemischen Organisation aktiver mechanischer Spannung stellen ein SchlĂŒsselprinzip morphogenetischer VorgĂ€nge in der Biologie dar. ZusĂ€tzlich entwickeln wir eine Reihe numerischer Methoden, welche es in Zukunft erlauben weitere Beschreibungen aktiver FlĂ€chen zu untersuchen. Damit trĂ€gt diese Arbeit neue theoretische Einsichten und numerische Algorithmen zur Verbesserung des VerstĂ€ndnisses der emergenten rĂ€umlichen Organisation und Formerzeugung aktiver FlĂ€chen bei
Anyonic Defect Braiding and Spontaneous Chiral Symmetry Breaking in Dihedral Liquid Crystals
Dihedral ('-atic') liquid crystals (DLCs) are assemblies of microscopic
constituent particles that exhibit -fold discrete rotational and reflection
symmetries. Generalizing the half-integer defects in nematic liquid crystals,
two-dimensional -atic DLCs can host point defects of fractional topological
charge . Starting from a generic microscopic model, we derive a
unified hydrodynamic description of DLCs with aligning or anti-aligning
short-range interactions in terms of Ginzburg-Landau and
Landau-Brazovskii-Swift-Hohenberg theories for a universal complex
order-parameter field. Building on this framework, we demonstrate in both
particle and continuum simulations how adiabatic braiding protocols,
implemented through suitable boundary conditions, can emulate anyonic exchange
behavior in a classical system. Analytic solutions and simulations of the
mean-field theory further predict a novel spontaneous chiral symmetry breaking
transition in anti-aligning DLCs, in quantitative agreement with the patterns
observed in particle simulations.Comment: Figs. 3, 6 and S1 added; Analytic solutions added (Sec. V.B.4,
Appendix C), Refs. [8], [14], [26], [53]-[60], [80], [81] adde
Lessons from Oxypnictide Thin Films
First experiments on the growth of oxypnictide F-doped LaFeAsO thin films
indicated an incomplete normal-to-superconducting transition and offered a work
programme challenging to overcome possible difficulties in their fabrication.
In this regard the possibility of an all in-situ epitaxial growth appeared to
be a matter of time and growth parameters. The following review clarifies that
F-doped oxypnictide thin films are extremely difficult to grow by in-situ PLD
due to the formation of very stable impurity phases such as oxyfluorides (LaOF)
and oxides (La2O3) and the loss of stoichiometry possibly due to incongruent
evaporation of the target or re-evaporation of volatile elements at the
substrate surface. However, the review also demonstrates that the employed
two-step fabrication process for oxypnictide thin films has been successfully
applied in the preparation of clean polycrystalline as well as of epitaxial
thin films. Fundamental investigations on the upper critical field, its
temperature dependence and its anisotropy contributed to an understanding of
multiband superconductivity in oxypnictides.Comment: accepted, pre-print versio
Rheology of suspensions of flat elastic particles
We consider a suspension of non-interacting flat elastic particles in a
Newtonian fluid. We model a flat shape as three beads, carried along by the
flow according to Stokes' law, and connected by nonlinear springs, chosen such
that the energy is quadratic in the area. In analogy with common dumbbell
models involving two beads connected by linear springs, we solve the stochastic
equations of motion exactly to compute the constitutive law for the stress
tensor of a flat elastic particle suspension. A lower convected time derivative
naturally arises as part of the constitutive law, but surprisingly the
rheological response in strong extensional and strong contracting flows is
similar to that of the classical Oldroyd-B model associated with dumbbell
suspensions.Comment: 8 pages, 1 figur
Learning developmental mode dynamics from single-cell trajectories
Embryogenesis is a multiscale process during which hierarchical symmetry
breaking transitions give rise to a fully developed organism. Recent advances
in high-resolution live-cell microscopy provide unprecedented insights into the
collective cell dynamics at various stages of embryonic development. The rapid
experimental progress poses the theoretical challenge of translating
high-dimensional imaging data into predictive low-dimensional models that
capture the essential ordering principles governing developmental cell
migration in complex geometries. Here, we combine mode decomposition ideas that
have proved successful in condensed matter physics and turbulence theory with
recent advances in sparse dynamical systems inference to realize a
computational framework for learning quantitative continuum models from
single-cell imaging data. Considering pan-embryo cell migration during early
gastrulation in zebrafish as a widely studied example, we show how cell
trajectory data on a curved surface can be coarse-grained and compressed with
suitable harmonic basis functions. The resulting low-dimensional representation
of the early gastrulation process reveals a multilayer interaction network
between dominant dynamical modes that enables the symmetry breaking transition
from a homogeneous animal pole to an increasingly structured cell assembly. Due
to its generic conceptual foundation, we expect this approach to be broadly
applicable to obtain a quantitative biophysical understanding of a wide range
of developmental structure formation processes.Comment: main text: 11 pages, 3 figures; si text: 14 pages, 7 figure
Learning hydrodynamic equations for active matter from particle simulations and experiments
Recent advances in high-resolution imaging techniques and particle-based
simulation methods have enabled the precise microscopic characterization of
collective dynamics in various biological and engineered active matter systems.
In parallel, data-driven algorithms for learning interpretable continuum models
have shown promising potential for the recovery of underlying partial
differential equations (PDEs) from continuum simulation data. By contrast,
learning macroscopic hydrodynamic equations for active matter directly from
experiments or particle simulations remains a major challenge. Here, we present
a framework that leverages spectral basis representations and sparse regression
algorithms to discover PDE models from microscopic simulation and experimental
data, while incorporating the relevant physical symmetries. We illustrate the
practical potential through applications to a chiral active particle model
mimicking swimming cells and to recent microroller experiments. In both cases,
our scheme learns hydrodynamic equations that reproduce quantitatively the
self-organized collective dynamics observed in the simulations and experiments.
This inference framework makes it possible to measure a large number of
hydrodynamic parameters in parallel and directly from video data.Comment: Added statistical analysis of learned parameters, Added comparison to
analytic coarse-graining approaches, Added spectral comparisons, Added
framework application on fish dat
Dynamics, scaling behavior, and control of nuclear wrinkling
The cell nucleus is enveloped by a complex membrane, whose wrinkling has been
implicated in disease and cellular aging. The biophysical dynamics and spectral
evolution of nuclear wrinkling during multicellular development remain poorly
understood due to a lack of direct quantitative measurements. Here, we combine
live-imaging experiments, theory, and simulations to characterize the onset and
dynamics of nuclear wrinkling during egg development in the fruit fly,
Drosophila melanogaster, when nurse cell nuclei increase in size and display
stereotypical wrinkling behavior. A spectral analysis of three-dimensional
high-resolution data from several hundred nuclei reveals a robust asymptotic
power-law scaling of angular fluctuations consistent with renormalization and
scaling predictions from a nonlinear elastic shell model. We further
demonstrate that nuclear wrinkling can be reversed through osmotic shock and
suppressed by microtubule disruption, providing tunable physical and biological
control parameters for probing mechanical properties of the nuclear envelope.
Our findings advance the biophysical understanding of nuclear membrane
fluctuations during early multicellular development.Comment: Main text: 10 pages, 3 figures. SI: 19 pages, 10 figures, 1 tabl
Dynamics of active surfaces
Mechano-chemical processes in biological systems play an important role during the morphogenesis of cells and tissues. In particular, they are responsible for the dynamic organisation of active stress, which itself results from non-equilibrium processes and leads to flows and deformations of material. The generation of active stress often occurs in thin biological structures, such as the cellular cortex or epithelial tissues, which motivates the theoretical concept of an active surface. In this thesis, we study the dynamics of curved and deforming active surfaces. More specifically, we are interested in the dynamics of mechano-chemical processes on these surfaces, as well as in their interaction with the surface shape and external forces.
To study the interplay of mechano-chemical processes with shape changes of the material, we consider the fully self-organised shape dynamics using the theory of active fluids on deforming surfaces. We then develop a numerical approach to solve the corresponding force and torque balance equations. We further examine how the stability of surface shapes is affected by mechano-chemical processes. We show that the tight coupling between chemical processes and surface mechanics gives rise to the spontaneous generation of specific surface shapes, to shape oscillations and to directed surface flows that resemble peristaltic motion.
In the following part, we explore the mechano-chemical self-organisation of active fluids on fixed surfaces, focussing on mechanical interactions with surrounding material. We introduce a description in which active surface flows set a surrounding passive fluid into motion. We then study two scenarios. First, inspired by the cellular cortex and its interactions with the cytoplasm, we consider a fluid that is enclosed by the surface. We find that mechanical interactions with the surrounding passive fluid enable an isotropic active surface to spontaneously generate patterns with polar asymmetry and to form a contractile ring in a fully self-organised fashion. Second, we consider the case where the passive fluid surrounds the active surface on the outside. This description leads to the model of a microswimmer, which is characterised by an onset of motion due to spontaneous symmetry breaking on the active surface.
Most biological materials are viscoelastic, such that they show viscous and elastic responses if mechanical stress is applied on different time scales. In the final part of this thesis, we therefore consider a surface whose response to self-organised active stress is described by a Maxwell model. We identify a minimal time scale for the relaxation of elastic stress, beyond which spatio-temporal, mechano-chemical oscillations on the surface can spontaneously emerge.
In summary, we identify and characterise in this thesis various processes that result from the self-organisation of active surfaces. The underlying coupling between surface mechanics and a chemical organisation of stress in the material represents a key feature of morphogenetic processes in biology. Furthermore, we develop several numerical approaches that will enable to study alternative constitutive relations of active surfaces in the future. Overall, we contribute theoretical insights and numerical tools to further the understanding of the emerging spatial organisation and shape generation of active surfaces.Mechanochemische Prozesse spielen eine wichtige Rolle fĂŒr die Morphogenese von biologischen Zellen und Geweben. Sie sind insbesondere verantwortlich fĂŒr die dynamische Organisation von aktiver mechanischer Spannung, welche Nicht-Gleichgewichtsprozessen entstammt und zu FlĂŒssen und Verformungen von Material fĂŒhrt. Aktive mechanische Spannung wird hĂ€ufig in dĂŒnnen biologischen Strukturen erzeugt, wie zum Beispiel dem Zellkortex oder dem Epithelgewebe, was die EinfĂŒhrung von aktiven FlĂ€chen als theoretisches Konzept motiviert. In der vorliegenden Arbeit untersuchen wir die Dynamik von gekrĂŒmmten und sich verformenden aktiven FlĂ€chen. Dabei interessieren wir uns insbesondere fĂŒr die Dynamik mechanochemischer Prozesse auf diesen FlĂ€chen, sowie fĂŒr deren Wechselwirkung mit der FlĂ€chenform und externen KrĂ€ften.
Zur Untersuchung der Wechselwirkung zwischen mechanochemischen Prozessen und FlĂ€chenverformungen nutzen wir die hydrodynamische Theorie aktiver Fluide auf sich verformenden FlĂ€chen und betrachten eine vollstĂ€ndig selbstorganisierte FlĂ€chendynamik. Wir entwickeln eine Methode zur Bestimmung numerischer Lösungen des KrĂ€fte- und Drehmomentgleichgewichts auf FlĂ€chen und untersuchen wie die StabilitĂ€t von FlĂ€chenformen durch mechanochemische Prozesse beeinflusst wird. Wir zeigen, dass die enge Kopplung zwischen chemischen Prozessen und der Mechanik von FlĂ€chen zur spontanen Erzeugung spezifischer Formen, zu Formoszillationen und zu gerichteten FlĂŒssen fĂŒhrt, welche eine peristaltische Bewegung nachbilden.
Im Folgenden untersuchen wir die mechanochemische Selbstorganisation aktiver Fluide auf festen FlĂ€chen und betrachten mechanische Wechselwirkungen mit umgebendem Material. Dazu beschreiben wir ein umgebendes passives Fluid, welches durch aktive FlĂŒsse auf der FlĂ€che in Bewegung versetzt wird. Im Rahmen dieser Beschreibung untersuchen wir zwei Szenarien. Inspiriert durch die Wechselwirkung des Zellkortex mit dem Zytoplasma, betrachten wir zuerst ein Fluid, welches durch die FlĂ€che eingeschlossen wird. Wir zeigen, dass die mechanische Wechselwirkung einer isotropen, aktiven FlĂ€che mit dem umgebenden Fluid es ermöglicht, Muster mit einer polaren Asymmetrie, sowie einen kontraktilen Ring spontan und selbstorganisiert zu bilden. Danach betrachten wir ein passives Fluid, welches die FlĂ€che auĂen umgibt. Diese Beschreibung fĂŒhrt zu einem Modell fĂŒr einen Mikroschwimmer, welcher durch eine spontane Symmetriebrechung auf der aktiven FlĂ€che beginnt sich durch das passive Fluid zu bewegen.
Die meisten biologischen Materialien verhalten sich viskoelastisch, sodass deren mechanische Antwort je nach Zeitskala einer applizierten mechanischen Spannung viskos und elastisch ausfallen kann. Im abschlieĂenden Teil dieser Arbeit betrachten wir daher eine FlĂ€che, deren mechanische Antwort auf aktive Spannung durch ein Maxwell-Modell beschrieben wird. Wir bestimmen eine minimale Zeitskala fĂŒr die Relaxation von elastischer Spannung, welche das spontane Einsetzen rĂ€umlich-zeitlicher Oszillationen aktiver mechanischer Spannung kennzeichnet.
Zusammengefasst identifizieren und charakterisieren wir in dieser Arbeit eine Reihe von Prozessen, welche der Selbstorganisation aktiver FlĂ€chen entspringen. Die zugrundeliegende Kopplung zwischen der Mechanik von FlĂ€chen und einer chemischen Organisation aktiver mechanischer Spannung stellen ein SchlĂŒsselprinzip morphogenetischer VorgĂ€nge in der Biologie dar. ZusĂ€tzlich entwickeln wir eine Reihe numerischer Methoden, welche es in Zukunft erlauben weitere Beschreibungen aktiver FlĂ€chen zu untersuchen. Damit trĂ€gt diese Arbeit neue theoretische Einsichten und numerische Algorithmen zur Verbesserung des VerstĂ€ndnisses der emergenten rĂ€umlichen Organisation und Formerzeugung aktiver FlĂ€chen bei