Applications of equivalent representations of fractional- and integer-order linear time-invariant systems

Nicht-ganzzahlige - fraktionale - Ableitungsoperatoren beschreiben Prozesse mit Gedächtniseffekten, deshalb werden sie zur Modellierung verschiedenster Phänomene, z.B. viskoelastischen Verhaltens, genutzt. In der Regelungstechnik wird das Konzept vor allem wegen des erhöhten Freiheitsgrades im Frequenzbereich verwendet. Deshalb wurden in den vergangenen Dekaden neben einer Verallgemeinerung des PID-Reglers auch fortgeschrittenere Regelungskonzepte auf nicht-ganzzahlige Operatoren erweitert. Das Gedächtnis der nicht-ganzzahligen Ableitung ist zwar essentiell für die Modellbildung, hat jedoch Nachteile, wenn z.B. Zustände geschätzt oder Regler implementiert werden müssen: Das Gedächtnis führt zu einer langsamen, algebraischen Konvergenz der Transienten und da eine numerische Approximation ist speicherintensiv. Im Zentrum der Arbeit steht die Frage, mit welchen Maßnahmen sich das Konvergenzverhalten dieser nicht ganzzahligen Systeme beeinflussen lässt. Es wird vorgeschlagen, die Ordnung der nicht ganzzahligen Ableitung zu ändern. Zunächst werden Beobachter für verschiedene Klassen linearer zeitinvarianter Systeme entworfen. Die Entwurfsmethodik basiert dabei auf einer assoziierten Systemdarstellung, welche einen Differenzialoperator mit höherer Ordnung verwendet. Basierend auf dieser Systembeschreibung können Beobachter entworfen werden, welche das Gedächtnis besser mit einbeziehen und so schneller konvergieren. Anschließend werden ganzzahlige lineare zeitinvariante Systeme mit Hilfe nicht-ganzzahliger Operatoren dargestellt. Dies ermöglicht eine erhöhte Konvergenz im Zeitintervall direkt nach dem Anfangszeitpunkt auf Grund einer unbeschränkten ersten Ableitung. Die periodische Löschung des so eingeführten Gedächtnisses wird erzielt, indem die nicht ganzzahlige Dynamik periodisch zurückgesetzt wird. Damit wird der algebraischen Konvergenz entgegen gewirkt und exponentielle Stabilität erzielt. Der Reset reduziert den Speicherbedarf und induziert eine unterlagerte zeitdiskrete Dynamik. Diese bestimmt die Stabilität des hybriden nicht-ganzzahligen Systems und kann genutzt werden um den Frequenzgang für niedrige Frequenzen zu bestimmen. So lassen sich Beobachter und Regler für ganzzahlige System entwerfen. Im Rahmen des Reglerentwurfs können durch den Resets das Verhalten für niedrige und hohe Frequenzen in gewissen Grenzen getrennt voneinander entworfen werden.Non-integer, so-called fractional-order derivative operators allow to describe systems with infinite memory. Hence they are attractive to model various phenomena, e.g. viscoelastic deformation. In the field of control theory, both the higher degree of freedom in the frequency domain as well as the easy generalization of PID control have been the main motivation to extend various advanced control concepts to the fractional-order domain. The long term memory of these operators which helps to model real life phenomena, has, however, negative effects regarding the application as controllers or observers. Due to the infinite memory, the transients only decay algebraically and the implementation requires a lot of physical memory. The main focus of this thesis is the question of how to influence the convergence rates of these fractional-order systems by changing the type of convergence. The first part is concerned with the observer design for different classes of linear time-invariant fractional-order systems. We derive associated system representations with an increased order of differentiation. Based on these systems, the observers are designed to take the unknown memory into account and lead to higher convergence rates. The second part explores the representation of integer-order linear time-invariant systems in terms of fractional-order derivatives. The application of the fractional-order operator introduces an unbounded first-order derivative at the initial time. This accelerates the convergence for a short time interval. With periodic deletion of the memory - a reset of the fractional-order dynamics - the slow algebraic decay is avoided and exponential stability can be achieved despite the fractional-order terms. The periodic reset leads to a reduced implementation demand and also induces underlying discrete time dynamics which can be used to prove stability of the hybrid fractional-order system and to give an interpretation of the reset in the frequency domain for the low frequency signals. This concept of memory reset is applied to design an observer and improve fractional-order controllers for integer-order processes. For the controller design this gives us the possibility to design the high-frequency response independently from the behavior at lower frequencies within certain limits

A homozygous genome‐edited Sept2‐EGFP fibroblast cell line

Septins are a conserved, essential family of GTPases that interact with actin, microtubules, and membranes and form scaffolds and diffusion barriers in cells. Several of the 13 known mammalian septins assemble into nonpolar, multimeric complexes that can further polymerize into filamentous structures. While some GFP‐coupled septins have been described, overexpression of GFP‐tagged septins often leads to artifacts in localization and function. To overcome this ubiquitous problem, we have here generated a genome‐edited rat fibroblast cell line expressing Septin 2 (Sept2) coupled to enhanced green fluorescent protein (EGFP) from both chromosomal loci. We characterize these cells by genomic polymerase chain reaction (PCR) for genomic integration, by western blot and reverse transcriptase‐PCR for expression, by immunofluorescence and immunoprecipitation for the colocalization of septins with one another and cellular structures and for complex formation of different septins. By live cell imaging, proliferation and migration assays we investigate proper function of septins in these cells. We find that EGFP is incorporated into both chromosomal loci and only EGFP‐coupled Sept2 is expressed in homozygous cells. We find that endogenous Sept2‐EGFP exhibits expression levels, localization and incorporation into cellular septin complexes similar to the wt in these cells. The expression level of other septins is not perturbed and cell division and cell migration proceed normally. We expect our cell line to be a useful tool for the cell biology of septins, especially for quantitative biology

Mass spectrometry data from label-free quantitative proteomic analysis of harmless and pathogenic strains of infectious microalgae, Prototheca spp

Here, we provide the dataset associated with our research article ‘label-free quantitative proteomic analysis of harmless and pathogenic strains of infectious microalgae, Prototheca spp.’ (Murugaiyan et al., 2017) [1]. This dataset describes liquid chromatography–mass spectrometry (LC–MS)-based protein identification and quantification of a non-infectious strain, Prototheca zopfii genotype 1 and two strains associated with severe and mild infections, respectively, P. zopfii genotype 2 and Prototheca blaschkeae. Protein identification and label-free quantification was carried out by analysing MS raw data using the MaxQuant-Andromeda software suit. The expressional level differences of the identified proteins among the strains were computed using Perseus software and the results were presented in [1]. This DiB provides the MaxQuant output file and raw data deposited in the PRIDE repository with the dataset identifier PXD005305

Entnahmemorbidität beim mikrochirurgisch anastomosierten Anterior Lateral Thigh (ALT)-Lappen

Einleitung: Ziel der Studie war es, die Entnahmemorbidität des ALT_Lappens bei Rekonstruktion im Kopf- Halsbereich unter standardisierten und objektivierbaren Methoden zu untersuchen. Methodik: zwischen 07/2006 und 12/2015 wurde bei 138 Patienten ein ALT-Lappen zur Rekonstruktion im Kopf- Halsbereich verwendet. 51 Patienten konnten nachuntersucht werden. Diese bestand aus der Abarbeitung eines standardisierten Fragebogens, einer körperlichen Untersuchung und aus einem isokinetischen Test der Oberschenkelmuskulatur mittels Dynamometer. Ergebnisse: Das mittlere Nachuntersuchungsintervall zwischen Lappentransfer und Nachuntersuchung betrug 29 Monate. Bei den Patientenbefragungen ergag sich aus Patientensicht kein relevanter Unterschied zwischen dem Spenderbein und dem kontralateralen Bein im Hinblick auf die Sensibilität und die Kraft. Die objektive Nachuntersuchung ergab jedoch einen signifikanten Unterschied im Hinblick auf die Hautsensibilität und die Kraft bei Extension und Flexion bei der isokinetischen Untersuchung. Diskussion und Schlussfolgerung: Die Ergebnisse zeigen, dass nach Hebung eines ALT-Lappens signifikante Unterschiede zwischen Spenderbein und kontralateraler Seite im Hinblick auf Sensinsibilität und Kraft bestehen. Diese sind vermutlich durch die Präparation muskulokutaner Perforatoren mit resultierender funktionseinschränkung des M.vastus lateralis zu erklären. Die könnte ebenfalls reflektorisch Auswirkungen auf die antagonistische Muskelgruppe haben. Zusammenfassend konnten wir zeigen, dass durch Hebung des Lappens gewisse Fuktionseinschränkungeb auftreten können, die den Patienten allerdings in seinem täglich Leben nicht beeinträchtigen. Somit besteht keine einschränkung in der Indikation

Fractional-Order Partial Cancellation of Integer-Order Poles and Zeros

The key idea of this contribution is the partial compensation of non-minimum phase zeros or unstable poles. Therefore the integer-order zero/pole is split into a product of fractional-order pseudo zeros/poles. The amplitude and phase response of these fractional-order terms is derived to include these compensators into the loop-shaping design. Such compensators can be generalized to conjugate complex zeros/poles, and also implicit fractional-order terms can be applied. In the case of the non-minimum phase zero, its compensation leads to a higher phase margin and a steeper open-loop amplitude response around the crossover frequency resulting in a reduced undershooting in the step-response, as illustrated in the numerical example.publishedVersio

Well-known surface and extracellular antigens of pathogenic microorganisms among the immunodominant proteins of the infectious microalgae Prototheca zopfii

Microalgae of the genus Prototheca (P.) are associated with rare but severe infections (protothecosis) and represent a potential zoonotic risk. Genotype (GT) 2 of P. zopfii has been established as pathogenic agent for humans, dogs, and cattle, whereas GT1 is considered to be non-pathogenic. Since pathogenesis is poorly understood, the aim of this study was to determine immunogenic proteins and potential virulence factors of P. zopfii GT2. Therefore, 2D western blot analyses with sera and isolates of two dogs naturally infected with P. zopfii GT2 have been performed. Cross-reactivity was determined by including the type strains of P. zopfii GT2, P. zopfii GT1, and P. blaschkeae, a close relative of P. zopfii, which is known to cause subclinical forms of bovine mastitis. The sera showed a high strain-, genotype-, and species-cross- reactivity. A total of 198 immunogenic proteins have been analyzed via MALDI—TOF MS. The majority of the 86 identified proteins are intracellularly located (e.g., malate dehydrogenase, oxidoreductase, 3-dehydroquinate synthase) but some antigens and potential virulence factors, known from other pathogens, have been found (e.g., phosphomannomutase, triosephosphate isomerase). One genotype-specific antigen could be identified as heat shock protein 70 (Hsp70), a well-known antigen of eukaryotic pathogens with immunological importance when located extracellularly. Both sera were reactive to glyceraldehyde-3-phosphate-dehydrogenase of all investigated strains. This house-keeping enzyme is found to be located on the surface of several pathogens as virulence factor. Flow-cytometric analysis revealed its presence on the surface of P. blaschkeae

Expression, purification and structural analysis of functional GABA transporter 1 using the baculovirus expression system

The γ-aminobutyric acid (GABA) transporter 1 (GAT1) belongs to a family of Na+ and Cl−-coupled transport proteins and possesses 12 putative transmembrane domains. To perform structural analyses of the GAT1 protein, the GAT1/green fluorescent protein (GFP) fusion protein was functionally expressed in insect Sf9 cells by the BAC-TO-BAC® baculovirus expression system. A two-step procedure to purify the GAT1/GFP fusion protein from insect Sf9 cells has been established and involves immunoaffinity chromatography using self-prepared anti-GFP antibodies and size-exclusion fast protein liquid chromatography (SE- FPLC). A yield of 200–300 μg of the GAT1/GFP protein could be purified from 400–600 mL of infected Sf9 cells. The purified protein was analyzed by transmission electron microscopy (TEM), which revealed that the GAT1/GFP fusion protein was isolated in its monomeric form

Non-lethal exposure to H2O2 boosts bacterial survival and evolvability against oxidative stress

Unicellular organisms have the prevalent challenge to survive under oxidative stress of reactive oxygen species (ROS) such as hydrogen peroxide (H2O2). ROS are present as by-products of photosynthesis and aerobic respiration. These reactive species are even employed by multicellular organisms as potent weapons against microbes. Although bacterial defences against lethal and sub-lethal oxidative stress have been studied in model bacteria, the role of fluctuating H2O2 concentrations remains unexplored. It is known that sub-lethal exposure of Escherichia coli to H2O2 results in enhanced survival upon subsequent exposure. Here we investigate the priming response to H2O2 at physiological concentrations. The basis and the duration of the response (memory) were also determined by time-lapse quantitative proteomics. We found that a low level of H2O2 induced several scavenging enzymes showing a long half-life, subsequently protecting cells from future exposure. We then asked if the phenotypic resistance against H2O2 alters the evolution of resistance against oxygen stress. Experimental evolution of H2O2 resistance revealed faster evolution and higher levels of resistance in primed cells. Several mutations were found to be associated with resistance in evolved populations affecting different loci but, counterintuitively, none of them was directly associated with scavenging systems. Our results have important implications for host colonisation and infections where microbes often encounter reactive oxygen species in gradients

Regulation and structure of YahD, a copper-inducible α/β serine hydrolase of Lactococcus lactis IL1403

Lactococcus lactis IL1403 is a lactic acid bacterium that is used widely for food fermentation. Copper homeostasis in this organism chiefly involves copper secretion by the CopA copper ATPase. This enzyme is under the control of the CopR transcriptional regulator. CopR not only controls its own expression and that of CopA, but also that of an additional three operons and two monocistronic genes. One of the genes under the control of CopR, yahD, encodes an α/β-hydrolase. YahD expression was induced by copper and cadmium, but not by other metals or oxidative or nitrosative stress. The three-dimensional structure of YahD was determined by X-ray crystallography to a resolution of 1.88 Å. The protein was found to adopt an α/β-hydrolase fold with the characteristic Ser-His-Asp catalytic triad. Functional testing of YahD for a wide range of substrates for esterases, lipases, epoxide hydrolases, phospholipases, amidases and proteases was, however, unsuccessful. A copper-inducible serine hydrolase has not been described previously and YahD appears to be a new functional member of this enzyme famil

Pine defense against eggs of an herbivorous sawfly is elicited by an annexin-like protein present in egg-associated secretion

Known elicitors of plant defenses against eggs of herbivorous insects are low-molecular-weight organic compounds associated with the eggs. However, previous studies provided evidence that also proteinaceous compounds present in secretion associated with eggs of the herbivorous sawfly Diprion pini can elicit defensive responses in Pinus sylvestris. Pine responses induced by the proteinaceous secretion are known to result in enhanced emission of (E)-β-farnesene, which attracts egg parasitoids killing the eggs. Here, we aimed to identify the defense-eliciting protein and elucidate its function. After isolating the defense-eliciting protein from D. pini egg-associated secretion by ultrafiltration and gel electrophoresis, we identified it by MALDI-TOF mass spectrometry as an annexin-like protein, which we named ‘diprionin’. Further GC-MS analyses showed that pine needles treated with heterologously expressed diprionin released enhanced quantities of (E)-β-farnesene. Our bioassays confirmed attractiveness of diprionin-treated pine to egg parasitoids. Expression of several pine candidate genes involved in terpene biosynthesis and regulation of ROS homeostasis was similarly affected by diprionin and natural sawfly egg deposition. However, the two treatments had different effects on expression of pathogenesis-related genes (PR1, PR5). Diprionin is the first egg-associated proteinaceous elicitor of indirect plant defense against insect eggs described so far