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Was lebt ist in Bewegung. Diese einfache Assoziation gilt nicht nur für ausgewachsene Organismen, sondern auch für einzelne Zellen, die kleinsten lebenden Bausteine der Natur. Die Beweglichkeit von Zellen spielt eine zentrale Rolle bei einer Vielzahl biologischer Vorgänge, wie zum Beispiel der Embryonalentwicklung, der Heilung von Wunden oder der krankhaften Ausbreitung von Krebszellen im Körper. Am Beispiel der Beweglichkeit einer einfachen Amöbe können grundlegende Mechanismen der Zelldynamik untersucht und auf der Grundlage physikalischer Konzepte erklärt werden.
We present an analysis of concentration switching times in microfluidic devices. The limits of rapid switching are analyzed based on the theory of dispersion by Taylor and Aris and compared to both experiments and numerical simulations. We focus on switching times obtained by photo-activation of caged compounds in a micro-flow (flow photolysis). The performance of flow photolysis is compared to other switching techniques. A flow chart is provided to facilitate the application of our theoretical analysis to microfluidic switching devices.
We quantify random migration of the social ameba Dictyostelium discoideum. We demonstrate that the statistics of cell motion can be described by an underlying Langevin-type stochastic differential equation. An analytic expression for the velocity distribution function is derived. The separation into deterministic and stochastic parts of the movement shows that the cells undergo a damped motion with multiplicative noise. Both contributions to the dynamics display a distinct response to external physiological stimuli. The deterministic component depends on the developmental state and ambient levels of signaling substances, while the stochastic part does not.
We consider the suppression of spatiotemporal chaos in the complex Ginzburg-Landau equation by a combined global and local time-delay feedback. Feedback terms are implemented as a control scheme, i.e., they are proportional to the difference between the time-delayed state of the system and its current state. We perform a linear stability analysis of uniform oscillations with respect to space-dependent perturbations and compare with numerical simulations. Similarly, for the fixed-point solution that corresponds to amplitude death in the spatially extended system, a linear stability analysis with respect to space-dependent perturbations is performed and complemented by numerical simulations.
Standing waves are studied as solutions of a complex Ginsburg-Landau equation subjected to local and global time-delay feedback terms. The onset of standing waves is studied at the instability of the homogeneous periodic solution with respect to spatially periodic perturbations. The solution of this spatiotemporal wave pattern is given and is compared to the homogeneous periodic solution.
We have used x-ray waveguides as highly confining optical elements for nanoscale imaging of unstained biological cells using the simple geometry of in-line holography. The well-known twin-image problem is effectively circumvented by a simple and fast iterative reconstruction. The algorithm which combines elements of the classical Gerchberg-Saxton scheme and the hybrid-input-output algorithm is optimized for phase-contrast samples, well-justified for imaging of cells at multi-keV photon energies. The experimental scheme allows for a quantitative phase reconstruction from a single holographic image without detailed knowledge of the complex illumination function incident on the sample, as demonstrated for freeze-dried cells of the eukaryotic amoeba Dictyostelium discoideum. The accessible resolution range is explored by simulations, indicating that resolutions on the order of 20 nm are within reach applying illumination times on the order of minutes at present synchrotron sources.
We report spatiotemporal chaos in the Oregonator model of the Belousov-Zhabotinsky reaction. Spatiotemporal chaos spontaneously develops in a regime, where the underlying local dynamics show stable limit cycle oscillations (diffusion-induced turbulence). We show that spatiotemporal chaos can be suppressed by a unidirectional flow in the system. With increasing flow velocity, we observe a transition scenario from spatiotemporal chaos via a regime of travelling waves to a stationary steady state. At large flow velocities, we recover the known regime of flow distributed oscillations.
Over the past decade, microfluidic techniques have been established as a versatile platform to perform live cell experiments under well-controlled conditions. To investigate the directional responses of cells, stable concentration profiles of chemotactic factors can be generated in microfluidic gradient mixers that provide a high degree of spatial control. However, the times for built-up and switching of gradient profiles are in general too slow to resolve the intracellular protein translocation events of directional sensing of eukaryotes. Here, we review an example of a conventional microfluidic gradient mixer as well as the novel flow photolysis technique that achieves an increased temporal resolution by combining the photo-activation of caged compounds with the advantages of microfluidic chambers.
Chemotaxis, the directed motion of a cell toward a chemical source, plays a key role in many essential biological processes. Here, we derive a statistical model that quantitatively describes the chemotactic motion of eukaryotic cells in a chemical gradient. Our model is based on observations of the chemotactic motion of the social ameba Dictyostelium discoideum, a model organism for eukaryotic chemotaxis. A large number of cell trajectories in stationary, linear chemoattractant gradients is measured, using microfluidic tools in combination with automated cell tracking. We describe the directional motion as the interplay between deterministic and stochastic contributions based on a Langevin equation. The functional form of this equation is directly extracted from experimental data by angle-resolved conditional averages. It contains quadratic deterministic damping and multiplicative noise. In the presence of an external gradient, the deterministic part shows a clear angular dependence that takes the form of a force pointing in gradient direction. With increasing gradient steepness, this force passes through a maximum that coincides with maxima in both speed and directionality of the cells. The stochastic part, on the other hand, does not depend on the orientation of the directional cue and remains independent of the gradient magnitude. Numerical simulations of our probabilistic model yield quantitative agreement with the experimental distribution functions. Thus our model captures well the dynamics of chemotactic cells and can serve to quantify differences and similarities of different chemotactic eukaryotes. Finally, on the basis of our model, we can characterize the heterogeneity within a population of chemotactic cells.