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Proteins are chain molecules built from amino acids. The precise sequence of the 20 different types of amino acids in a protein chain defines into which structure a protein folds, and the three-dimensional structure in turn specifies the biological function of the protein. The reliable folding of proteins is a prerequisite for their robust function. Misfolding can lead to protein aggregates that cause severe diseases, such as Alzheimer's, Parkinson's, or the variant Creutzfeldt-Jakob disease. Small single-domain proteins often fold without experimentally detectable metastable intermediate states. The folding dynamics of these proteins is thought to be governed by a single transition-state barrier between the unfolded and the folded state. The transition state is highly instable and cannot be observed directly. However, mutations in which a single amino acid of the protein is substituted by another one can provide indirect access. The mutations slightly change the transition-state barrier and, thus, the folding and unfolding times of the protein. The central question is how to reconstruct the transition state from the observed changes in folding times. In this habilitation thesis, a novel method to extract structural information on transition states from mutational data is presented. The method is based on (i) the cooperativity of structural elements such as alpha-helices and beta-hairpins, and (ii) on splitting up mutation-induced free-energy changes into components for these elements. By fitting few parameters, the method reveals the degree of structure formation of alpha-helices and beta-hairpins in the transition state. In addition, it is shown in this thesis that the folding routes of small single-domain proteins are dominated by loop-closure dependencies between the structural elements.
In der vorliegenden Arbeit werden Methoden der Erdsystemanalyse auf die Untersuchung der Habitabilität terrestrischer Exoplaneten angewandt. Mit Hilfe eines parametrisierten Konvektionsmodells für die Erde wird die thermische Evolution von terrestrischen Planeten berechnet. Bei zunehmender Leuchtkraft des Zentralsterns wird über den globalen Karbonat-Silikat-Kreislauf das planetare Klima stabilisiert. Für eine photosynthetisch-aktive Biosphäre, die in einem bestimmten Temperaturbereich bei hinreichender CO2-Konzentration existieren kann, wird eine Überlebenspanne abgeschätzt. Der Abstandsbereich um einen Stern, in dem eine solche Biosphäre produktiv ist, wird als photosynthetisch-aktive habitable Zone (pHZ) definiert und berechnet. Der Zeitpunkt, zu dem die pHZ in einem extrasolaren Planetensystem endgültig verschwindet, ist die maximale Lebenspanne der Biosphäre. Für Supererden, massereiche terrestrische Planeten, ist sie umso länger, je massereicher der Planet ist und umso kürzer, je mehr er mit Kontinenten bedeckt ist. Für Supererden, die keine ausgeprägten Wasser- oder Landwelten sind, skaliert die maximale Lebenspanne mit der Planetenmasse mit einem Exponenten von 0,14. Um K- und M-Sterne ist die Überlebensspanne einer Biosphäre auf einem Planeten immer durch die maximale Lebensspanne bestimmt und nicht durch das Ende der Hauptreihenentwicklung des Zentralsterns limitiert. Das pHZ-Konzept wird auf das extrasolare Planetensystem Gliese 581 angewandt. Danach könnte die 8-Erdmassen-Supererde Gliese 581d habitabel sein. Basierend auf dem vorgestellten pHZ-Konzept wird erstmals die von Ward und Brownlee 1999 aufgestellte Rare-Earth-Hypothese für die Milchstraße quantifiziert. Diese Hypothese besagt, dass komplexes Leben im Universum vermutlich sehr selten ist, wohingegen primitives Leben weit verbreitet sein könnte. Unterschiedliche Temperatur- und CO2-Toleranzen sowie ein unterschiedlicher Einfluss auf die Verwitterung für komplexe und primitive Lebensformen führt zu unterschiedlichen Grenzen der pHZ und zu einer unterschiedlichen Abschätzung für die Anzahl der Planeten, die mit den entsprechenden Lebensformen besiedelt sein könnten. Dabei ergibt sich, dass komplex besiedelte Planeten heute etwa 100-mal seltener sein müssten als primitiv besiedelte.
During the last few years there was a tremendous growth of scientific activities in the fields related to both Physics and Control theory: nonlinear dynamics, micro- and nanotechnologies, self-organization and complexity, etc. New horizons were opened and new exciting applications emerged. Experts with different backgrounds starting to work together need more opportunities for information exchange to improve mutual understanding and cooperation. The Conference "Physics and Control 2007" is the third international conference focusing on the borderland between Physics and Control with emphasis on both theory and applications. With its 2007 address at Potsdam, Germany, the conference is located for the first time outside of Russia. The major goal of the Conference is to bring together researchers from different scientific communities and to gain some general and unified perspectives in the studies of controlled systems in physics, engineering, chemistry, biology and other natural sciences. We hope that the Conference helps experts in control theory to get acquainted with new interesting problems, and helps experts in physics and related fields to know more about ideas and tools from the modern control theory.
The mammalian brain is, with its numerous neural elements and structured complex connectivity, one of the most complex systems in nature. Recently, large-scale corticocortical connectivities, both structural and functional, have received a great deal of research attention, especially using the approach of complex networks. Here, we try to shed some light on the relationship between structural and functional connectivities by studying synchronization dynamics in a realistic anatomical network of cat cortical connectivity. We model the cortical areas by a subnetwork of interacting excitable neurons (multilevel model) and by a neural mass model (population model). With weak couplings, the multilevel model displays biologically plausible dynamics and the synchronization patterns reveal a hierarchical cluster organization in the network structure. We can identify a group of brain areas involved in multifunctional tasks by comparing the dynamical clusters to the topological communities of the network. With strong couplings of multilevel model and by using neural mass model, the dynamics are characterized by well-defined oscillations. The synchronization patterns are mainly determined by the node intensity (total input strengths of a node); the detailed network topology is of secondary importance. The biologically improved multilevel model exhibits similar dynamical patterns in the two regimes. Thus, the study of synchronization in a multilevel complex network model of cortex can provide insights into the relationship between network topology and functional organization of complex brain networks.
Nowadays, colloidal rods can be synthesized in large amounts. The rods are typically cylindrically and their length ranges from several nanometers to a few micrometers. In solution, systems of colloidal rodlike molecules or aggregates can form liquid-crystalline phases with long-range orientational and spatial order. In the present work, we investigate structure formation and fractionation in systems of rodlike colloids with the help of Monte Carlo simulations in the NPT ensemble. Repulsive interactions can successfully be mimicked by the hard rod model, which has been studied extensively in the past. In many cases, attractive interactions like van der Waals or depletion forces cannot be neglected, however. In the first part of this work, the phase behavior of monodisperse attractive rods is characterized for different interaction strengths. Phase diagrams as a function of rod length and pressure are presented. Most systems of synthesized mesoscopic rods have a polydisperse length distribution as a consequence of the longitudinal growth process of the rods. For many technical and research applications, a rather small polydispersity is desired in order to have well defined material properties. The polydispersity can be reduced by a spatial demixing (fractionation) of long and short rods. Fractionation and structure formation is studied in a tridisperse and a polydisperse bulk suspension of rods. We observe that the resulting structures depend distinctly on the interaction strength. The fractionation in the system is strongly enhanced with increasing interaction strength. Suspensions are typically confined in a container. We also examine the influence of adjacent substrates in systems of tridisperse and polydisperse rod suspensions. Three different substrate types are studied in detail: a planar wall, a corrugated substrate, and a substrate with rectangular cavities. We analyze the fluid structure close to the substrate and substrate controlled fractionation. The spatial arrangement of long and short rods in front of the substrate depends sensitively on the substrate structure and the pressure. Rods with a predefined length are segregated at substrates with rectangular cavities.
In this thesis the interplay between hydrodynamic transport and specific adhesion is theoretically investigated. An important biological motivation for this work is the rolling adhesion of white blood cells experimentally investigated in flow chambers. There, specific adhesion is mediated by weak bonds between complementary molecular building blocks which are either located on the cell surface (receptors) or attached to the bottom plate of the flow chamber (ligands). The model system under consideration is a hard sphere covered with receptors moving above a planar ligand-bearing wall. The motion of the sphere is influenced by a simple shear flow, deterministic forces, and Brownian motion. An algorithm is given that allows to numerically simulate this motion as well as the formation and rupture of bonds between receptors and ligands. The presented algorithm spatially resolves receptors and ligands. This opens up the perspective to apply the results also to flow chamber experiments done with patterned substrates based on modern nanotechnological developments. In the first part the influence of flow rate, as well as of the number and geometry of receptors and ligands, on the probability for initial binding is studied. This is done by determining the mean time that elapses until the first encounter between a receptor and a ligand occurs. It turns out that besides the number of receptors, especially the height by which the receptors are elevated above the surface of the sphere plays an important role. These findings are in good agreement with observations of actual biological systems like white blood cells or malaria-infected red blood cells. Then, the influence of bonds which have formed between receptors and ligands, but easily rupture in response to force, on the motion of the sphere is studied. It is demonstrated that different states of motion-for example rolling-can be distinguished. The appearance of these states depending on important model parameters is then systematically investigated. Furthermore, it is shown by which bond property the ability of cells to stably roll in a large range of applied flow rates is increased. Finally, the model is applied to another biological process, the transport of spherical cargo particles by molecular motors. In analogy to the so far described systems molecular motors can be considered as bonds that are able to actively move. In this part of the thesis the mean distance the cargo particles are transported is determined.
Ziel dieser Arbeit ist die phänomenologische Untersuchung der Feuchteempfindlichkeit der elektrischen Eigenschaften dünner Polymerschichten. Diese Untersuchungen stellen gleichzeitig Vorarbeiten zur Entwicklung von Prototypen von zwei polymeren Dünnschicht-Feuchtesensoren dar, die sich durch die spezielle Auswahl der feuchtesensitiven Materialien jeweils durch eine besondere Eigenschaft gegenüber kommerziellen Massenprodukten auszeichnen. Ziel der Entwicklungsarbeiten für den ersten Prototypen war die Konstruktion eines schnellen Feuchtesensors, der plötzliche und sprunghafte Feuchteänderungen in der umgebenden Atmosphäre möglichst rasch detektieren kann. Dafür wurden dünne Schichten von Poly-DADMAC auf Interdigitalstrukturen aufgebracht, die einen möglichst direkten Kontakt zwischen feuchtesensitiver Schicht und umgebender, feuchter Atmosphäre gewährleisten. Als Messgrößen dienten die Wechselstromgrößen Widerstand und Kapazität der Schichten. Die Feuchtekennlinien der Schichten zeigen gute Konstanz und hohe Reproduzierbarkeit. Der Widerstand der Schichten ändert sich durch den Einfluss von Feuchte je nach Schichtdicke um 3 bis 5 Größenordnungen und eignet sich als Messgröße für die Feuchtigkeit im gesamten Feuchtebereich. Die Hysterese der Filme konnte auf kleiner als 2,5% r.F. bestimmt werden, die Reproduzierbarkeit auf besser als 1% r.F. Die Ansprechzeit der Schichten lässt sich schichtdickenabhängig zu 1 bis 10 Sekunden bestimmen. Hierbei zeigen besonders die dünnen Schichten kurze Ansprechzeiten. Zielstellung für den zweiten Feuchtesensor war die Entwicklung eines Prototypen, dessen sensitive Schicht sich biostatisch und biozid verhält, so dass er in biotischen Umgebungen eingesetzt werden kann. Es wurden fünf Polysulfobetaine synthetisiert, deren Biozidität und Biostatik mit dem Kontakttest nach Rönnpagel, dem ISO846-Test und Abbautests bestimmt wurde. Zwei Polymere – Poly-DMMAAPS (BT2) und Poly-[MSA-Styren-Sulfobetain] (BT5) – erwiesen sich als ausreichend biozid und biostatisch. Schichten dieser Polymere wurden auf Interdigitalstrukturen aufgezogen, anschließend wurden die Kennlinien dieser Proben aufgenommen. Die Messwerte zeigen für beide Polymere gute Konstanz und eine hohe Reproduzierbarkeit. BT2-Proben sind zwischen 20% und 80% r.F. besonders empfindlich und zeigen über einen Monat keine Langzeitdrift. Vernetzte Proben zeigen bis 50°C keinen temperaturbedingten Abfall der Feuchteempfindlichkeit. Der Einsatz vernetzter BT5-Schichten als kapazitiver Feuchtesensor ist bis etwa 70°C möglich, die Schichten sind selbst nach Lagerung im Hochvakuum und mehrfacher Betauung stabil. Damit liegen zwei funktionsfähige Prototypen von Feuchtesensoren vor, für die die meisten Kennwerte denen von vergleichbaren kommerziellen Feuchtesensoren entsprechen. Gleichzeitig zeichnen sie sich aber durch eine sehr niedrige Ansprechzeit bzw. eine ausreichende Lebensdauer unter biotischen Bedingungen aus.
The role played by azobenzene polymers in the modern photonic, electronic and opto-mechanical applications cannot be underestimated. These polymers are successfully used to produce alignment layers for liquid crystalline fluorescent polymers in the display and semiconductor technology, to build waveguides and waveguide couplers, as data storage media and as labels in quality product protection. A very hot topic in modern research are light-driven artificial muscles based on azobenzene elastomers. The incorporation of azobenzene chromophores into polymer systems via covalent bonding or even by blending gives rise to a number of unusual effects under visible (VIS) and ultraviolet light irradiation. The most amazing effect is the inscription of surface relief gratings (SRGs) onto thin azobenzene polymer films. At least seven models have been proposed to explain the origin of the inscribing force but none of them describes satisfactorily the light induced material transport on the molecular level. In most models, to explain the mass transport over micrometer distances during irradiation at room temperature, it is necessary to assume a considerable degree of photoinduced softening, at least comparable with that at the glass transition. Contrary to this assumption, we have gathered a convincing evidence that there is no considerable softening of the azobenzene layers under illumination. Presently we can surely say that light induced softening is a very weak accompanying effect rather than a necessary condition for the formation of SRGs. This means that the inscribing force should be above the yield point of the azobenzene polymer. Hence, an appropriate approach to describe the formation and relaxation of SRGs is a viscoplastic theory. It was used to reproduce pulse-like inscription of SRGs as measured by VIS light scattering. At longer inscription times the VIS scattering pattern exhibits some peculiarities which can be explained by the appearance of a density grating that will be shown to arise due to the final compressibility of the polymer film. As a logical consequence of the aforementioned research, a thermodynamic theory explaining the light-induced deformation of free standing films and the formation of SRGs is proposed. The basic idea of this theory is that under homogeneous illumination an initially isotropic sample should stretch itself along the polarization direction to compensate the entropy decrease produced by the photoinduced reorientation of azobenzene chromophores. Finally, some ideas about further development of this controversial topic will be discussed.
This work is concerned with the spatio-temporal structures that emerge when non-identical, diffusively coupled oscillators synchronize. It contains analytical results and their confirmation through extensive computer simulations. We use the Kuramoto model which reduces general oscillatory systems to phase dynamics. The symmetry of the coupling plays an important role for the formation of patterns. We have studied the ordering influence of an asymmetry (non-isochronicity) in the phase coupling function on the phase profile in synchronization and the intricate interplay between this asymmetry and the frequency heterogeneity in the system. The thesis is divided into three main parts. Chapter 2 and 3 introduce the basic model of Kuramoto and conditions for stable synchronization. In Chapter 4 we characterize the phase profiles in synchronization for various special cases and in an exponential approximation of the phase coupling function, which allows for an analytical treatment. Finally, in the third part (Chapter 5) we study the influence of non-isochronicity on the synchronization frequency in continuous, reaction diffusion systems and discrete networks of oscillators.
This dissertation contains theoretical investigations on the morphology and statistical mechanics of vesicles. The shapes of homogeneous fluid vesicles and inhomogeneous vesicles with fluid and solid membrane domains are calculated. The influence of thermal fluctuations is investigated. The obtained results are valid on mesoscopic length scales and are based on a geometrical membrane model, where the vesicle membrane is described as either a static or a thermal fluctuating surface. The thesis consists of three parts. In the first part, homogeneous vesicles are considered. The focus in this part is on the thermally induced morphological transition between vesicles with prolate and oblate shape. With the help of Monte Carlo simulations, the free energy profile of these vesicles is determined. It can be shown that the shape transformation between prolate and oblate vesicles proceeds continuously and is not hampered by a free energy barrier. The second and third part deal with inhomogeneous vesicles which contain intramembrane domains. These investigations are motivated by experimental results on domain formation in single or multicomponent vesicles, where phase separation occurs and different membrane phases coexist. The resulting domains differ with regard to their membrane structure (solid, fluid). The membrane structure has a distinct effect on the form of the domain and the morphology of the vesicle. In the second part, vesicles with coexisting solid and fluid membrane domains are studied, while the third part addresses vesicles with coexisting fluid domains. The equilibrium morphology of vesicles with simple and complex domain forms, derived through minimisation of the membrane energy, is determined as a function of material parameters. The results are summarised in morphology diagrams. These diagrams show previously unknown morphological transitions between vesicles with different domain shapes. The impact of thermal fluctuations on the vesicle and the form of the domains is investigated by means of Monte Carlo simulations.