A double critical mass phenomenon in a no-flux-Dirichlet Keller-Segel system

Derived from a biophysical model for the motion of a crawling cell, the system $$(*)~\begin{cases}u_t=\Delta u-\nabla\cdot(u\nabla v)\\0=\Delta v-kv+u\end{cases}$$ is investigated in a finite domain $\Omega\subset\mathbb{R}^n$, $n\geq2$, with $k\geq0$. While a comprehensive literature is available for cases with $(*)$ describing chemotaxis systems and hence being accompanied by homogeneous Neumann-type boundary conditions, the presently considered modeling context, besides yet requiring the flux $\partial_\nu u-u\partial_\nu v$ to vanish on $\partial\Omega$, inherently involves homogeneous Dirichlet conditions for the attractant $v$, which in the current setting corresponds to the cell's cytoskeleton being free of pressure at the boundary. This modification in the boundary setting is shown to go along with a substantial change with respect to the potential to support the emergence of singular structures: It is, inter alia, revealed that in contexts of radial solutions in balls there exist two critical mass levels, distinct from each other whenever $k>0$ or $n\geq3$, that separate ranges within which (i) all solutions are global in time and remain bounded, (ii) both global bounded and exploding solutions exist, or (iii) all nontrivial solutions blow up in finite time. While critical mass phenomena distinguishing between regimes of type (i) and (ii) belong to the well-understood characteristics of $(*)$ when posed under classical no-flux boundary conditions in planar domains, the discovery of a distinct secondary critical mass level related to the occurrence of (iii) seems to have no nearby precedent. In the planar case with the domain being a disk, the analytical results are supplemented with some numerical illustrations, and it is discussed how the findings can be interpreted biophysically for the situation of a cell on a flat substrate

On a Minimal Model for the Initiation of Cell Movement

Actin-driven motility of eucaryotic cells plays a crucial role in many biological processes and has therefore been under intense experimental and theoretical investigation throughout several decades. In [10], we introduced a minimal model for the preparation of movement in a symmetric resting cell on a flat substrate. This system consists of at least four hyperbolic conservation laws describing the evolution of densities of actin filament tips and at least one parabolic equation for the actin monomer concentration. For this coupled hyperbolic-parabolic system, we shall now formulate a free boundary problem to allow for actual motion of the cell. For this model with some specific boundary conditions, we will show short time well posedness and present several mechanisms by which the solutions might break down for large times. In particular, possible blow-up phenomena are described and investigated, both analytically and numerically. Moreover, we discuss how the cease of existence of solutions can be interpreted physically as the emergence of actin polymerization fronts. Finally, different possible boundary conditions are presented, and their biological meanings are explained. We furthermore reformulate the model under certain assumptions and derive a system of two parabolic equations describing the motion of two interacting species of filaments moving in opposite directions. This simplified model is investigated in part II where we ask for stability of particular steady states and construct traveling wave solutions. The existence of the latter can also be found in simulations, and we will discuss the type and velocity of the evolving wave profiles. Particular attention will be paid to the remarkable differences between different types of nonlinearities describing the mutual interaction. Of special interest are the deviations from the predictions about stability and the traveling wave solutions obtained from the linearization of the model around its equilibria. These predictions are met quite well by some versions of the nonlinear terms whereas for others they are missed significantly. We are thus dealing with a quite minimalistic system of reaction advection diffusion equations whose behavior cannot be predicted by linearization but strongly depends on the particular nonlinearity

Gradient based optimization in ligand-receptor docking

In this work, we compared six global search heuristics and two scoring functions in the field of ligand-receptor docking. A new way for the gradient based minimization of a ligand whose position in space is defined by translation, orientation and a set of torsional flexible angles was implemented and thoroughly tested. The default local search method of a Lamarckian genetic algorithm was replaced by our novel gradient based approach and the new hybrid was compared to non-gradient global search heuristics. Finally, we present our docking program BALLDock, in which we incorporated our findings.In der vorliegenden Arbeit wurden sechs populationsbasierte Optmierungsheuristiken und zwei Scoring-Funktionen im Hinblick auf ihre Leistungsfähigkeit im Bereich Ligand-Rezeptor Docking miteinander verglichen. Parallel dazu wurde eine neuer Ansatz entwickelt, der die lokale, gradientenbasierte Optimierung partiell flexibler Moleküle, deren Position und Konformation durch Translation, Orientierung und eine Anzahl flexibler Bindungswinkel definiert ist, erlaubt. Danach wurde die gradientenfreie Methode zur lokalen Optimierung eines Lamarck genetischen Algorithmus durch das neuartige gradientbasierte Verfahren ersetzt und dessen Einfluss auf die Ergebnisse der globalen Suchheuristik analysiert. Abschließend wird das Dockingprogramm BALLDock vorgestellt, in das die neu gewonnenen Erkenntnisse einflossen

IGBT-Kurzschlussverhalten am Beispiel einer schnellen Fehlerstrombegrenzung für Hochvolt-Halbleiterversuchsplätze

In dieser Arbeit wird ein Schutzkonzept für ein Hochvolt-Halbleiterversuchsplatz vorgestellt, dessen zentrales Element ein serieller Insulated-Gate Bipolar Transistor ist, der den Zwischenkreis im Fehlerfall von der Fehlerstelle trennt. In diesem IGBT treten verschiedene Kurzschlussfälle auf. Der Verlauf des Kurzschlusses und das Zusammenspiel der Leistungshalbleiter kann mit Hilfe eines Ersatzschaltbildes erklärt werden. Die Kurzschlussfallverläufe können anhand von Wirkungsketten dargestellt werden. Die Wirksamkeit dieser Fehlerstrombegrenzung wird an einem echten Ausfall demonstriert

The subspace Nevanlinna interpolation problem and the most powerful unfalsified model

A generalization of the tangential Nevanlinna interpolation problem will be studied from a behavioral point of view. Necessary and sufficient conditions for its solvability and a characterization of art its solutions are derived. These results are obtained by associating to the interpolation data a behavior that enjoys a special structure. (C) 1997 Elsevier Science B.V

Effekter på bunnfauna av nytt fangstredskap for haneskjell - Testing av TauTech's Harvester

På oppdrag av TauTech AS gjennomførte Havforskningsinstituttet i samarbeid med NIVA en undersøkelse hvor målsetningen var å studere effekter på bunnfauna og bunnsedimenter ved bruk av et nytt fangstredskap for haneskjell, heretter kalt Harvester. Selve fangstingen baserer seg på å suge skjellene opp fra bunnen, hvor deler av fangsten sorteres fra på bunnen og ønsket fangst (store haneskjell) blir samlet opp. Forsøket foregikk på et haneskjellfelt på Berg ved Tromsø. I tillegg til undervanns videoopptak ble det gjort skrapetrekk med trekantskrape før og etter operasjonene med Harvester, for å undersøke sammensetningen av bunndyr før og etter operasjonene. Materialet som sorteres ut ved fangstingen ble også undersøkt med hensyn på størrelse på utsorterte haneskjell, sammensetningen av dyr og graden av skader på begge deler. Resultatene viste ingen endringer i sammensetningen av dyr unntatt haneskjell før og etter operasjonene med Harvester. Størstedelen av utsorterte haneskjell var små skjell og skadene på disse var moderate. De resterende dyrene ble inndelt i seks sårbarhetsgrupper basert på noen kriterier og det viste seg at dyr i fem av gruppene hadde små og moderate skader, mens dyrene i den ene gruppen for det meste hadde dødelige skader. Denne gruppen inneholdt dyr som små reker og eremittkreps. Eventuelle endringer i bunnsedimenter antas å være den viktigste faktoren for restituering av haneskjellfelt etter fangstoperasjoner siden dette kan endre forutsetningene og nyetablering samt levevilkårene for bunndyr. Påvirkningen av Harvester på bunnsedimentene så ut til å være svært moderate. Videoopptakene indikerte at en del finkornet sediment så ut til å være borte etter at Harvester hadde gått over området. En svakhet med denne undersøkelsen var at intensiteten i fangstingen ved forsøket med Harvester på langt nær var på det nivået en kan forvente ved et ordinært fiskeri. Vi undersøkte heller ikke hvor stor total biomasse av haneskjell og andre bunndyr som ble tatt ut med Harvester. Det anbefales derfor at det gjennomføres nye undersøkelser av påvirkningen på bunnfauna og sediment etter at et eventuelt fiskeri er kommet i gang.publishedVersio

Nitrogen fertilizer fate after introducing maize and upland-rice into continuous paddy rice cropping systems

Water scarcity and economic incentives favor the introduction of upland crops into permanent paddy rice systems during dry seasons. However, introducing upland crops into permanently flooded cropping systems temporarily changes soil conditions from anaerobic to aerobic, affecting nitrogen (N) dynamics profoundly. We hypothesized that under maize and dry rice, total fertilizer $^{15}$N recovery in soil as well as the immobilization of fertilizer $^{15}$N in microbial residues is reduced compared with continuous paddy rice cropping. Furthermore, we expected enhanced emissions of fertilizer $^{15}$N in form of nitrous oxide (N₂O) under maize and dry rice. To test these hypotheses, we traced the fate of a $^{15}$N-urea pulse in a field experiment in the Philippines with three different crop rotations: continuous paddy rice, paddy rice – dry rice, and paddy rice – maize for two years. Indeed, the $^{15}$N recovery in the first 5 cm of bulk soil was lowest in the paddy rice – maize rotation (arithmetic mean with standard error: 19.2 ± 1.8% of applied $^{15}$N), while twice as much was recovered in the first 5 cm of bulk soil of the continuous paddy rice cropping systems (37.8 ± 2.2% of applied $^{15}$N) during the first dry season. The $^{15}$N recovery in the plant biomass (shoots and roots) in the continuous paddy rice cropping was 13% larger than in the dry rice plant biomass and 5% larger than in the maize plant biomass during the first dry season. Fertilizer $^{15}$N remained longest in paddy rice – maize (mean residence time=90 ± 25 days) and in continuous paddy rice (mean residence time=77 ± 30 days), compared with dry rice – paddy rice rotation (mean residence time=16 ± 5 days). After 2 years, 10% (paddy rice – dry rice, paddy rice – maize) to 23% (continuous paddy rice) of the applied fertilizer 15N were still stored in soil. The largest fraction of this $^{15}$N was immobilized by soil microbes, which stored 3-4% of applied 15N in the form of amino sugars as specific cell wall constituents, in all cropping systems. Nevertheless, introducing upland crops into continuous paddy rice systems likely increased N leaching losses and resulted in initial losses of urea- $^{15}$N to N₂O, which thus has to be considered in climate smart mitigation strategies

An Outer Membrane Vesicle-Based Permeation Assay (OMPA) for Assessing Bacterial Bioavailability

When searching for new antibiotics against Gram-negative bacterial infections, a better understanding of the permeability across the cell envelope and tools to discriminate high from low bacterial bioavailability compounds are urgently needed. Inspired by the phospholipid vesicle-based permeation assay (PVPA), which is designed to predict non-facilitated permeation across phospholipid membranes, outer membrane vesicles (OMVs) of Escherichia coli either enriched or deficient of porins are employed to coat filter supports for predicting drug uptake across the complex cell envelope. OMVs and the obtained in vitro model are structurally and functionally characterized using cryo-TEM, SEM, CLSM, SAXS, and light scattering techniques. In vitro permeability, obtained from the membrane model for a set of nine antibiotics, correlates with reported in bacterio accumulation data and allows to discriminate high from low accumulating antibiotics. In contrast, the correlation of the same data set generated by liposome-based comparator membranes is poor. This better correlation of the OMV-derived membranes points to the importance of hydrophilic membrane components, such as lipopolysaccharides and porins, since those features are lacking in liposomal comparator membranes. This approach can offer in the future a high throughput screening tool with high predictive capacity or can help to identify compound- and bacteria-specific passive uptake pathways