Delayed loss of stability of periodic travelling waves: insights from the analysis of essential spectra

Periodic travelling waves (PTW) are a common solution type of partial differential equations. Such models exhibit multistability of PTWs, typically visualised through the Busse balloon, and parameter changes typically lead to a cascade of wavelength changes through the Busse balloon. In the past, the stability boundaries of the Busse balloon have been used to predict such wavelength changes. Here, motivated by anecdotal evidence from previous work, we provide compelling evidence that the Busse balloon provides insufficient information to predict wavelength changes due to a delayed loss of stability phenomenon. Using two different reaction-advection-diffusion systems, we relate the delay that occurs between the crossing of a stability boundary in the Busse balloon and the occurrence of a wavelength change to features of the essential spectrum of the destabilised PTW. This leads to a predictive framework that can estimate the order of magnitude of such a time delay, which provides a novel ``early warning sign'' for pattern destabilization. We illustrate the implementation of the predictive framework to predict under what conditions a wavelength change of a PTW occurs.Comment: 25 pages, 12 figure

Long-range seed dispersal enables almost stationary patterns in a model for dryland vegetation

Spatiotemporal patterns of vegetation are a ubiquitous feature of semi-arid ecosystems. On sloped terrain, vegetation patterns occur as stripes perpendicular to the contours. Field studies report contrasting long-term dynamics between different observation sites; some observe slow uphill migration of vegetation bands while some report stationary patterns. In this paper, we show that long-range seed dispersal provides a mechanism that enables the occurrence of both migrating and stationary patterns. We utilise a nonlocal PDE model in which seed dispersal is accounted for by a convolution term. The model represents vegetation patterns as periodic travelling waves and numerical continuation shows that both migrating and almost stationary patterns are stable if seed dispersal distances are sufficiently large. We use a perturbation theory approach to obtain analytical confirmation of the existence of almost stationary patterned solutions and provide a biological interpretation of the phenomenon

An integrodifference model for vegetation patterns in semi-arid environments with seasonality

Vegetation patterns are a characteristic feature of semi-deserts occurring on all continents except Antarctica. In some semi-arid regions, the climate is characterised by seasonality, which yields a synchronisation of seed dispersal with the dry season or the beginning of the wet season. We reformulate the Klausmeier model, a reaction-advection-diffusion system that describes the plant-water dynamics in semi-arid environments, as an integrodifference model to account for the temporal separation of plant growth processes during the wet season and seed dispersal processes during the dry season. The model further accounts for nonlocal processes involved in the dispersal of seeds. Our analysis focusses on the onset of spatial patterns. The Klausmeier partial differential equations (PDE) model is linked to the integrodifference model in an appropriate limit, which yields a control parameter for the temporal separation of seed dispersal events. We find that the conditions for pattern onset in the integrodifference model are equivalent to those for the continuous PDE model and hence independent of the time between seed dispersal events. We thus conclude that in the context of seed dispersal, a PDE model provides a sufficiently accurate description, even if the environment is seasonal. This emphasises the validity of results that have previously been obtained for the PDE model. Further, we numerically investigate the effects of changes to seed dispersal behaviour on the onset of patterns. We find that long-range seed dispersal inhibits the formation of spatial patterns and that the seed dispersal kernel's decay at infinity is a significant regulator of patterning

Modelling dryland vegetation patterns : nonlocal dispersal, temporal variability in precipitation and species coexistence

Spatiotemporal patterns of vegetation are a characteristic feature of dryland ecosystems occurring on all continents except Antarctica. The development of an understanding of their ecosystem dynamics is an issue of considerable socio-economic importance as both the livestock and agricultural sectors in dryland economies heavily depend on ecosystem functioning. Mathematical modelling is a powerful tool to disentangle the complex ecosystem dynamics. In this thesis, I present theoretical models to explore the impact of nonlocal seed dispersal and temporal precipitation variability on dryland vegetation patterns and propose several mechanisms that enable species coexistence within vegetation patterns. To do so, I present extensions of the Klausmeier reaction-advection-diffusion model, a well-established model describing the ecohydrological dynamics of vegetation patterns. Model analyses focus on pattern onset at high precipitation values (i.e. on the transition from uniformly vegetated to spatially patterned states) to assess the impact of nonlocal seed dispersal and precipitation seasonality and intermittency, and on comprehensive bifurcation analyses, including results on pattern existence and stability to investigate coexistence of species in the mathematical framework. Results include the inhibition of pattern onset due to long-range seed dispersal and put emphasis on the functional response of plants to low soil moisture levels to understand effects of rainfall intermittency. Moreover, results suggest that coexistence is facilitated by resource heterogeneities induced by the plant’s spatial self-organisation and highlight the importance of considering out-of-equilibrium solutions.UK Engineering and Physical Sciences Research Council (grant EP/L016508/01) Scottish Funding Council Heriot-Watt Universit

The Aspergillus giganteus antifungal protein AFPNN5353 activates the cell wall integrity pathway and perturbs calcium homeostasis

Background The antifungal protein AFPNN5353 is a defensin-like protein of Aspergillus giganteus. It belongs to a group of secretory proteins with low molecular mass, cationic character and a high content of cysteine residues. The protein inhibits the germination and growth of filamentous ascomycetes, including important human and plant pathogens and the model organsims Aspergillus nidulans and Aspergillus niger. Results We determined an AFPNN5353 hypersensitive phenotype of non-functional A. nidulans mutants in the protein kinase C (Pkc)/mitogen-activated protein kinase (Mpk) signalling pathway and the induction of the α-glucan synthase A (agsA) promoter in a transgenic A. niger strain which point at the activation of the cell wall integrity pathway (CWIP) and the remodelling of the cell wall in response to AFPNN5353. The activation of the CWIP by AFPNN5353, however, operates independently from RhoA which is the central regulator of CWIP signal transduction in fungi. Furthermore, we provide evidence that calcium (Ca2+) signalling plays an important role in the mechanistic function of this antifungal protein. AFPNN5353 increased about 2-fold the cytosolic free Ca2+ ([Ca2+]c) of a transgenic A. niger strain expressing codon optimized aequorin. Supplementation of the growth medium with CaCl2 counteracted AFPNN5353 toxicity, ameliorated the perturbation of the [Ca2+]c resting level and prevented protein uptake into Aspergillus sp. cells. Conclusions The present study contributes new insights into the molecular mechanisms of action of the A. giganteus antifungal protein AFPNN5353. We identified its antifungal activity, initiated the investigation of pathways that determine protein toxicity, namely the CWIP and the Ca2+ signalling cascade, and studied in detail the cellular uptake mechanism in sensitive target fungi. This knowledge contributes to define new potential targets for the development of novel antifungal strategies to prevent and combat infections of filamentous fungi which have severe negative impact in medicine and agriculture.FWF, P19970-B11, Characterization of the toxicity of PA

Entwicklung von RF-Technologie für die Ultrahochfeld-MRT: Optimierung und Anwendung einer Self-Grounded-Bow-Tie-Dipolantenne

Magnetic resonance imaging (MRI) is an important diagnostic imaging modality free of ionizing radiation. Sensitivity gain, signal-to-noise ratio (SNR) considerations, and changes in the tissue dependent MRI properties. Together with technical and scientific developments further research into increasing the magnetic field strength is justified, culminating in human applications at ultrahigh magnetic field (UHF, B0 ≥ 7.0 T) MRI. Elevating the field strength results in an increased radiofrequency (RF) for signal transmission and reception in MRI (= Larmor frequency, f ≈ 298 MHz at B0 = 7.0 T). The wavelength of this RF signal becomes sufficiently short when passing through tissue relative to the size of the target anatomy of the brain, upper torso, or abdomen. This phenomenon leads to constructive and deconstructive interference of the electromagnetic field (EMF) distribution, which results in a high susceptibility for non-uniformities in the magnetic RF transmission field (B1+). This detrimental excitation field distribution can cause shading, massive signal drop-off or even signal voids, and potentially offset the benefits of UHF-MRI due to compromised image quality. UHF cardiovascular MR (CMR) benefits from SNR gains and changes in the tissue dependent MRI properties, but the B1+ distribution – in addition to the wavelength dependent non-uniformities – is further compromised by a dielectrically heterogeneous tissue environment. Research on UHF-CMR focuses on the improvement of the cardiac chamber morphology quantification, myocardial T1- and T2*-mapping, fat-water imaging, and vascular imaging (4D-flow). These applications benefit from a homogenous B1+ within the heart and the vascular structure. Several published reports on the development of RF antenna array technology tailored for UHF-CMR address this challenge with ideas and achievements to enable broad clinical UHF-CMR applications in the future. The primary objective of advancing this RF technology is to achieve a uniform B1+ distribution in the heart and the vascular structure with optimizing the magnetic field pattern. The second objective is the improvement of the RF antenna’s efficiency with the reduction of the specific absorption rate (SAR), which is achieved by an optimization of the electric field pattern. The control of the electric field is furthermore conceptually appealing beyond conventional MR imaging modalities and useful for localized and targeted RF induced thermal intervention. Combining MRI with a thermal intervention modality in an integrated Thermal MR system permits direct supervision of the treatment via MR-thermometry, as well as adapting and improving the focal point quality of the RF power deposition. The Thermal MR system is a platform for comprehensive investigation of the effects of temperature on molecular, biochemical, and physiological processes, ultimately yielding insights into temperature utilization for diagnosis and therapy in vivo. EMF control of an RF antenna array depends on the radiation pattern of the antenna elements. Electrical dipoles are promising for UHF-MRI due to a linear polarized current pattern and an energy deposition perpendicular to the antenna. However, the channel count and therefore the degree of freedom for EMF shaping of previously reported antenna concepts is limited by the geometric extent and the coupling between the elements. The first section of this work addresses the design, implementation, and validation of a novel small-sized Self-Grounded Bow-Tie (SGBT) antenna, in combination with a dielectrically filled housing. The narrowband SGBT antenna variant is used in a 32-channel transmit/receive array configuration for UHF-CMR at 7.0 T. The second section focuses on the development of a modified broadband SGBT concept for the Thermal MR system. The broadband antenna increases the degree of freedom with an adaptation of the intervention frequency to improve the focal point quality (size, homogeneity, and specificity). The third section presents the implementation and validation of a signal generator in conjunction with the broadband SGBT variant introduced in section two. The device allows the generation of the intervention signal with a time dependent, channel-wise adaptation of amplitude, phase, and frequency. The work of this thesis offers a technical and conceptual framework for an increased degree of freedom for EMF shaping for a multitude of applications ranging from UHF-MRI to interventional MRI.Die Magnetresonanztomographie (MRI) ist ein wichtiges bildgebendes Diagnoseverfahren mit der Anwendung in vielen medizinischen Disziplinen. Die Forschung zu ultrahohen Magnetfeldern (UHF, B0 ≥ 7.0 T) im humanen Bereich wird durch technische und wissenschaftliche Errungenschaften getrieben und basiert auf einer höheren Sensitivität, einem verbesserten Signal-Rausch-Verhältnisses (SNR) sowie eine Veränderung der gewebsspezifischen MR Eigenschaften. Die höhere Feldstärke resultiert auch in einer erhöhten Radiofrequenz (RF) für die MRI Signalübertragung (= Larmorfrequenz, f ≈ 298 MHz bei B0 = 7.0 T). Die Wellenlänge des RF Signals im Gewebe ist dabei bezogen zur Zielanatomie (e.g. Schädel, Oberkörper und Abdomen) verkürzt was zu konstruktiven und destruktiven Interferenzen des elektromagnetischen Feldes (EMF) führt. Diese Interferenzen ergeben ein heterogenes RF Transmissionsfeld (B1+) mit Abschattungen, massiven Signalabfällen oder Signalausfällen welche die Vorteile der UHF-MRI durch eine beeinträchtigte Bildqualität schmälert. Die UHF Herz MR (CMR) profitiert von einem SNR-Gewinn sowie von veränderten gewebsspezifischen MR Eigenschaften bei höheren Feldstärken. Jedoch wird die B1+ Verteilung, neben der gegebenen RF wellenlängenabhängigen Heterogenität, durch dielektrische Gradienten im Bereich des Thorax zusätzlich beeinträchtigt. Die anwendungsbezogene Forschung und Entwicklung auf dem Gebiet der UHF-CMR konzentriert sich auf die Verbesserung der Quantifizierung der Herzkammermorphologie, des myokardialen T1- und T2*-Mappings, der Fett-Wasser-Bildgebung und der Gefäßbildgebung inklusive der Flussbildgebung (4D-Flow). Die Weiterentwicklung dieser Methoden streben eine breite klinische Anwendung an und profitieren von einer homogenen B1+ Verteilung im Herzen und in der Gefäßstruktur. Das primäre Ziel der der Forschung und Entwicklung von RF Antennenarraytechnologie ist eine Optimierung der B1+ Verteilung. Das sekundäre Ziel ist die Verbesserung der Effizienz durch die Verringerung der spezifischen Absorptionsrate (SAR) mittels einer elektrischen Feldoptimierung. Die Kontrolle des elektrischen Feldes kann aber auch über die konventionelle MR Bildgebung hinaus genutzt werden und ermöglicht konzeptionell eine lokalisierte und gezielte RF induzierte thermische Intervention. Die Kombination von MRI und thermischen Interventionen in einem integrierten Thermal MR System ermöglicht die Anpassung und Verbesserung der lokalen Intervention durch eine Supervision der Behandlung mittels MR-Thermometrie. Das Thermal MR System stellt damit eine technologische Plattform dar, welche eine umfassende Untersuchung der Auswirkungen der Temperatur auf molekulare, biochemische und physiologische Prozesse erlaubt. Letztlich kann die Plattform Erkenntnisse darüber liefern, wie die Temperatur für Diagnosen und Therapien in vivo genutzt werden kann. Die Kontrolle der EMF Verteilung durch ein RF Antennen Array ist abhängig von den Abstrahlungseigenschaften der einzelnen Antennenelemente. Elektrische Dipole stellen durch eine linear polarisierte Stromverteilung und eine Abstrahlungsrichtung orthogonal zur Antenne eine vielversprechende Option dar. Allerdings ist die Kanalzahl und damit der Freiheitsgrad für die EMF Optimierung bei bisher vorgestellten Antennenkonzepten durch die Größe und die Kopplung zwischen den Elementen begrenzt. Der erste Abschnitt dieser Arbeit befasst sich mit dem Entwurf, der Implementierung und der Validierung einer Self-Grounded Bow-Tie (SGBT) Antenne in Kombination mit einem dielektrisch gefüllten Gehäuse. Eine schmalbandige Antennenvariante wird in einer 32-Kanal Sende-/Empfangs-Array Konfiguration für UHF-CMR bei 7,0 T vorgestellt. Der zweite Abschnitt befasst sich mit der Entwicklung eines modifizierten breitbandigen SGBT-Konzepts für das Thermal MR System. Diese Antennenvariante erhöht die Freiheitsgrade für die Optimierung der elektrischen Feldverteilung um die Interventionsfrequenz und erlaubt eine Verbesserung der lokalen Erwärmung (Größe, Homogenität und Spezifität). Im dritten Abschnitt dieser Arbeit wird die Implementierung und Validierung eines Signalgenerators in Verbindung mit der im zweiten Abschnitt vorgestellten Breitbandantennenvariante vorgestellt. Der Signalgenerator erzeugt einen Interventionssignal mit der zeitabhängigen Anpassung von Amplitude, Phase und Frequenz für jeden Kanal. Die Entwicklungen und Erkenntnisse dieser Arbeit bieten einen konzeptionellen Rahmen für eine Vielzahl von realen Anwendungen, welche von der konventionellen MRI bis zu einem integrierten interventionellen Thermal MR System reichen.EC/H2020/743077/EU/Thermal Magnetic Resonance: A New Instrument to Define the Role of Temperature in Biological Systems and Disease for Diagnosis and Therapy/ThermalM