570 Biowissenschaften; Biologie
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During the last decade, intracellular actin waves have attracted much attention due to their essential role in various cellular functions, ranging from motility to cytokinesis. Experimental methods have advanced significantly and can capture the dynamics of actin waves over a large range of spatio-temporal scales. However, the corresponding coarse-grained theory mostly avoids the full complexity of this multi-scale phenomenon. In this perspective, we focus on a minimal continuum model of activator–inhibitor type and highlight the qualitative role of mass conservation, which is typically overlooked. Specifically, our interest is to connect between the mathematical mechanisms of pattern formation in the presence of a large-scale mode, due to mass conservation, and distinct behaviors of actin waves.
We investigate the transition from incoherence to global collective motion in a three-dimensional swarming model of agents with helical trajectories, subject to noise and global coupling. Without noise this model was recently proposed as a generalization of the Kuramoto model and it was found that alignment of the velocities occurs discontinuously for arbitrarily small attractive coupling. Adding noise to the system resolves this singular limit and leads to a continuous transition, either to a directed collective motion or to center-of-mass rotations.
Biodiversity loss is a result of interacting ecological and economic factors, and it must be addressed through an analysis of biodiversity conservation policies. Ecological-economic modelling is a helpful approach to this analysis, but it is also challenging since modellers often have a specific disciplinary background and tend to misrepresent either the ecological or economic aspects. Here, we introduce some of the most important concepts from both disciplines, and since the two modelling cultures also differ between the two disciplines, we present an integrated, consistent guide through all the steps of generic ecological-economic modelling, such as formulation of the research question, development of the conceptual model, model parametrisation and analysis, and interpretation of model results. Although we focus on generic models aimed at a general understanding of causes and remedies for biodiversity loss, the concepts and guidance provided here may also help in the modelling of more specific conservation problems. This guide is aimed at the intersection of three disciplines: ecology, economics and mathematical modelling, and addresses readers who have some knowledge in at least one of these disciplines and want to learn about the others to build and analyse generic ecological-economic models. Compared to textbooks, the guide focuses on the practice of modelling rather than lengthy explanations of theoretical concepts. We attempt to demonstrate that generic ecological-economic modelling does not require magical powers and instead is a manageable exercise.
A new ion mobility (IM) spectrometer, enabling mobility measurements in the pressure range between 5 and 500 mbar and in the reduced field strength range E/N of 5-90 Td, was developed and characterized. Reduced mobility (K-0) values were studied under low E/N (constant value) as well as high E/N (deviation from low field K-0) for a series of molecular ions in nitrogen. Infrared matrix-assisted laser desorption ionization (IR-MALDI) was used in two configurations: a source working at atmospheric pressure (AP) and, for the first time, an IR-MALDI source working with a liquid (aqueous) matrix at sub-ambient/reduced pressure (RP). The influence of RP on IR-MALDI was examined and new insights into the dispersion process were gained. This enabled the optimization of the IM spectrometer for best analytical performance. While ion desolvation is less efficient at RP, the transport of ions is more efficient, leading to intensity enhancement and an increased number of oligomer ions. When deciding between AP and RP IR-MALDI, a trade-off between intensity and resolving power has to be considered. Here, the low field mobility of peptide ions was first measured and compared with reference values from ESI-IM spectrometry (at AP) as well as collision cross sections obtained from molecular dynamics simulations. The second application was the determination of the reduced mobility of various substituted ammonium ions as a function of E/N in nitrogen. The mobility is constant up to a threshold at high E/N. Beyond this threshold, mobility increases were observed. This behavior can be explained by the loss of hydrated water molecules.
The motility of adherent eukaryotic cells is driven by the dynamics of the actin cytoskeleton. Despite the common force-generating actin machinery, different cell types often show diverse modes of locomotion that differ in their shape dynamics, speed, and persistence of motion. Recently, experiments in Dictyostelium discoideum have revealed that different motility modes can be induced in this model organism, depending on genetic modifications, developmental conditions, and synthetic changes of intracellular signaling. Here, we report experimental evidence that in a mutated D. discoideum cell line with increased Ras activity, switches between two distinct migratory modes, the amoeboid and fan-shaped type of locomotion, can even spontaneously occur within the same cell. We observed and characterized repeated and reversible switchings between the two modes of locomotion, suggesting that they are distinct behavioral traits that coexist within the same cell. We adapted an established phenomenological motility model that combines a reaction-diffusion system for the intracellular dynamics with a dynamic phase field to account for our experimental findings.
Generalized (non-Markovian) diffusion equations with different memory kernels and subordination schemes based on random time change in the Brownian diffusion process are popular mathematical tools for description of a variety of non-Fickian diffusion processes in physics, biology, and earth sciences. Some of such processes (notably, the fluid limits of continuous time random walks) allow for either kind of description, but other ones do not. In the present work we discuss the conditions under which a generalized diffusion equation does correspond to a subordination scheme, and the conditions under which a subordination scheme does possess the corresponding generalized diffusion equation. Moreover, we discuss examples of random processes for which only one, or both kinds of description are applicable.
We report on rendering polyelectrolyte brushes photosensitive by loading them with azobenzene-containing cationic surfactants. Planar poly(methacrylic acid) (PMAA) brushes are synthesized using the “grafting from” free-radical polymerization scheme followed by exposure to a solution of photosensitive surfactants consisting of positively-charged head groups and hydrophobic tails into which azobenzene moieties are inserted. In this study the length of the hydrophobic methylene spacer connecting the azobenzene and the charged head group ranges from 4 to 10 CH2 groups. Under irradiation with UV light, the photo-isomerization of azobenzene integrated into a surfactant results in a change in size, geometry, dipole moment and free volume of the whole molecule. When the brush loaded with photosensitive surfactants is exposed to irradiation with UV interference patterns, the topography of the brush deforms following the distribution of the light intensity, exhibiting surface relief gratings (SRG). Since SRG formation is accompanied by a local rupturing of polymer chains in areas from which the polymer material is receding, most of the polymer material is removed from the surface during treatment with good solvent, leaving behind characteristic patterns of lines or dots. The azobenzene molecules still integrated within the polymer film can be removed by washing the brush with water. The remaining nano-structured brush can then be re-used for further functionalization. Although the opto-mechanically induced rupturing occurs for all surfactants, larger species do not penetrate deep enough into the brush such that after rupturing a leftover layer of polymer material remains on the substrate. This indicates that rupturing occurs predominantly in regions of high surfactant density.
Low-dimensional description for ensembles of identical phase oscillators subject to Cauchy noise
(2020)
We study ensembles of globally coupled or forced identical phase oscillators subject to independent white Cauchy noise. We demonstrate that if the oscillators are forced in several harmonics, stationary synchronous regimes can be exactly described with a finite number of complex order parameters. The corresponding distribution of phases is a product of wrapped Cauchy distributions. For sinusoidal forcing, the Ott-Antonsen low-dimensional reduction is recovered.
Predator-prey cycles rank among the most fundamental concepts in ecology, are predicted by the simplest ecological models and enable, theoretically, the indefinite persistence of predator and prey(1-4). However, it remains an open question for how long cyclic dynamics can be self-sustained in real communities. Field observations have been restricted to a few cycle periods(5-8) and experimental studies indicate that oscillations may be short-lived without external stabilizing factors(9-19). Here we performed microcosm experiments with a planktonic predator-prey system and repeatedly observed oscillatory time series of unprecedented length that persisted for up to around 50 cycles or approximately 300 predator generations. The dominant type of dynamics was characterized by regular, coherent oscillations with a nearly constant predator-prey phase difference. Despite constant experimental conditions, we also observed shorter episodes of irregular, non-coherent oscillations without any significant phase relationship. However, the predator-prey system showed a strong tendency to return to the dominant dynamical regime with a defined phase relationship. A mathematical model suggests that stochasticity is probably responsible for the reversible shift from coherent to non-coherent oscillations, a notion that was supported by experiments with external forcing by pulsed nutrient supply. Our findings empirically demonstrate the potential for infinite persistence of predator and prey populations in a cyclic dynamic regime that shows resilience in the presence of stochastic events.
We present a systematic study on the properties of Na(Y,Gd)F-4-based upconverting nanoparticles (UCNP) doped with 18% Yb3+, 2% Tm3+, and the influence of Gd3+ (10-50 mol% Gd3+). UCNP were synthesized via the solvothermal method and had a range of diameters within 13 and 50 nm. Structural and photophysical changes were monitored for the UCNP samples after a 24-month incubation period in dry phase and further redispersion. Structural characterization was performed by means of X-ray diffraction (XRD), transmission electron microscopy (TEM) as well as dynamic light scattering (DLS), and the upconversion luminescence (UCL) studies were executed at various temperatures (from 4 to 295 K) using time-resolved and steady-state spectroscopy. An increase in the hexagonal lattice phase with the increase of Gd3+ content was found, although the cubic phase was prevalent in most samples. The Tm3+-luminescence intensity as well as the Tm3+-luminescence decay times peaked at the Gd3+ concentration of 30 mol%. Although the general upconverting luminescence properties of the nanoparticles were preserved, the 24-month incubation period lead to irreversible agglomeration of the UCNP and changes in luminescence band ratios and lifetimes.