530 Physik
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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.
Understanding the formation of stars in galaxies is central to much of modern astrophysics. For several decades it has been thought that the star formation process is primarily controlled by the interplay between gravity and magnetostatic support, modulated by neutral-ion drift. Recently, however, both observational and numerical work has begun to suggest that supersonic interstellar turbulence rather than magnetic fields controls star formation. This review begins with a historical overview of the successes and problems of both the classical dynamical theory of star formation, and the standard theory of magnetostatic support from both observational and theoretical perspectives. We then present the outline of a new paradigm of star formation based on the interplay between supersonic turbulence and self-gravity. Supersonic turbulence can provide support against gravitational collapse on global scales, while at the same time it produces localized density enhancements that allow for collapse on small scales. The efficiency and timescale of stellar birth in Galactic gas clouds strongly depend on the properties of the interstellar turbulent velocity field, with slow, inefficient, isolated star formation being a hallmark of turbulent support, and fast, efficient, clustered star formation occurring in its absence. After discussing in detail various theoretical aspects of supersonic turbulence in compressible self-gravitating gaseous media relevant for star forming interstellar clouds, we explore the consequences of the new theory for both local star formation and galactic scale star formation. The theory predicts that individual star-forming cores are likely not quasi-static objects, but dynamically evolving. Accretion onto these objects will vary with time and depend on the properties of the surrounding turbulent flow. This has important consequences for the resulting stellar mass function. Star formation on scales of galaxies as a whole is expected to be controlled by the balance between gravity and turbulence, just like star formation on scales of individual interstellar gas clouds, but may be modulated by additional effects like cooling and differential rotation. The dominant mechanism for driving interstellar turbulence in star-forming regions of galactic disks appears to be supernovae explosions. In the outer disk of our Milky Way or in low-surface brightness galaxies the coupling of rotation to the gas through magnetic fields or gravity may become important.
Biological materials, in addition to having remarkable physical properties, can also change shape and volume. These shape and volume changes allow organisms to form new tissue during growth and morphogenesis, as well as to repair and remodel old tissues. In addition shape or volume changes in an existing tissue can lead to useful motion or force generation (actuation) that may even still function in the dead organism, such as in the well known example of the hygroscopic opening or closing behaviour of the pine cone. Both growth and actuation of tissues are mediated, in addition to biochemical factors, by the physical constraints of the surrounding environment and the architecture of the underlying tissue. This habilitation thesis describes biophysical studies carried out over the past years on growth and swelling mediated shape changes in biological systems. These studies use a combination of theoretical and experimental tools to attempt to elucidate the physical mechanisms governing geometry controlled tissue growth and geometry constrained tissue swelling. It is hoped that in addition to helping understand fundamental processes of growth and morphogenesis, ideas stemming from such studies can also be used to design new materials for medicine and robotics.
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.
In a classical context, synchronization means adjustment of rhythms of self-sustained periodic oscillators due to their weak interaction. The history of synchronization goes back to the 17th century when the famous Dutch scientist Christiaan Huygens reported on his observation of synchronization of pendulum clocks: when two such clocks were put on a common support, their pendula moved in a perfect agreement. In rigorous terms, it means that due to coupling the clocks started to oscillate with identical frequencies and tightly related phases. Being, probably, the oldest scientifically studied nonlinear effect, synchronization was understood only in 1920-ies when E. V. Appleton and B. Van der Pol systematically - theoretically and experimentally - studied synchronization of triode generators. Since that the theory was well developed and found many applications. Nowadays it is well-known that certain systems, even rather simple ones, can exhibit chaotic behaviour. It means that their rhythms are irregular, and cannot be characterized only by one frequency. However, as is shown in the Habilitation work, one can extend the notion of phase for systems of this class as well and observe their synchronization, i.e., agreement of their (still irregular!) rhythms: due to very weak interaction there appear relations between the phases and average frequencies. This effect, called phase synchronization, was later confirmed in laboratory experiments of other scientific groups. Understanding of synchronization of irregular oscillators allowed us to address important problem of data analysis: how to reveal weak interaction between the systems if we cannot influence them, but can only passively observe, measuring some signals. This situation is very often encountered in biology, where synchronization phenomena appear on every level - from cells to macroscopic physiological systems; in normal states as well as in severe pathologies. With our methods we found that cardiovascular and respiratory systems in humans can adjust their rhythms; the strength of their interaction increases with maturation. Next, we used our algorithms to analyse brain activity of Parkinsonian patients. The results of this collaborative work with neuroscientists show that different brain areas synchronize just before the onset of pathological tremor. Morevoever, we succeeded in localization of brain areas responsible for tremor generation.
Synchronization of coupled oscillators manifests itself in many natural and man-made systems, including cyrcadian clocks, central pattern generators, laser arrays, power grids, chemical and electrochemical oscillators, only to name a few. The mathematical description of this phenomenon is often based on the paradigmatic Kuramoto model, which represents each oscillator by one scalar variable, its phase. When coupled, phase oscillators constitute a high-dimensional dynamical system, which exhibits complex behaviour, ranging from synchronized uniform oscillation to quasiperiodicity and chaos. The corresponding collective rhythms can be useful or harmful to the normal operation of various systems, therefore they have been the subject of much research.
Initially, synchronization phenomena have been studied in systems with all-to-all (global) and nearest-neighbour (local) coupling, or on random networks. However, in recent decades there has been a lot of interest in more complicated coupling structures, which take into account the spatially distributed nature of real-world oscillator systems and the distance-dependent nature of the interaction between their components. Examples of such systems are abound in biology and neuroscience. They include spatially distributed cell populations, cilia carpets and neural networks relevant to working memory. In many cases, these systems support a rich variety of patterns of synchrony and disorder with remarkable properties that have not been observed in other continuous media. Such patterns are usually referred to as the coherence-incoherence patterns, but in symmetrically coupled oscillator systems they are also known by the name chimera states.
The main goal of this work is to give an overview of different types of collective behaviour in large networks of spatially distributed phase oscillators and to develop mathematical methods for their analysis. We focus on the Kuramoto models for one-, two- and three-dimensional oscillator arrays with nonlocal coupling, where the coupling extends over a range wider than nearest neighbour coupling and depends on separation. We use the fact that, for a special (but still quite general) phase interaction function, the long-term coarse-grained dynamics of the above systems can be described by a certain integro-differential equation that follows from the mathematical approach called the Ott-Antonsen theory. We show that this equation adequately represents all relevant patterns of synchrony and disorder, including stationary, periodically breathing and moving coherence-incoherence patterns. Moreover, we show that this equation can be used to completely solve the existence and stability problem for each of these patterns and to reliably predict their main properties in many application relevant situations.
Our every-day experience is connected with different acoustical noise or music. Usually noise plays the role of nuisance in any communication and destroys any order in a system. Similar optical effects are known: strong snowing or raining decreases quality of a vision. In contrast to these situations noisy stimuli can also play a positive constructive role, e.g. a driver can be more concentrated in a presence of quiet music. Transmission processes in neural systems are of especial interest from this point of view: excitation or information will be transmitted only in the case if a signal overcomes a threshold. Dr. Alexei Zaikin from the Potsdam University studies noise-induced phenomena in nonlinear systems from a theoretical point of view. Especially he is interested in the processes, in which noise influences the behaviour of a system twice: if the intensity of noise is over a threshold, it induces some regular structure that will be synchronized with the behaviour of neighbour elements. To obtain such a system with a threshold one needs one more noise source. Dr. Zaikin has analyzed further examples of such doubly stochastic effects and developed a concept of these new phenomena. These theoretical findings are important, because such processes can play a crucial role in neurophysics, technical communication devices and living sciences.