Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that diffusion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarising their densely packed and heterogeneous structures. The most familiar phenomenon is a power-law increase of the MSD, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations, non-gaussian distributions of the displacements, heterogeneous diffusion, and immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarise some widely used theoretical models: gaussian models like FBM and Langevin equations for visco-elastic media, the CTRW model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Emphasis is put on the spatio-temporal properties of the transport in terms of 2-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even for identical MSDs. Then, we review the theory underlying common experimental techniques in the presence of anomalous transport: single-particle tracking, FCS, and FRAP. We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where model systems mimic physiological crowding conditions. Finally, computer simulations play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.Comment: review article, to appear in Rep. Prog. Phy

Dynamical structure of center-of-pressure trajectories in patients recovering from stroke

Contains fulltext : 50308.pdf (publisher's version ) (Closed access)In a recent study, De Haart et al. (Arch Phys Med Rehabil 85:886-895, 2004) investigated the recovery of balance in stroke patients using traditional analyses of center-of-pressure (COP) trajectories to assess the effects of health status, rehabilitation, and task conditions like standing with eyes open or closed and standing while performing a cognitive dual task. To unravel the underlying control processes, we reanalyzed these data in terms of stochastic dynamics using more advanced analyses. Dimensionality, local stability, regularity, and scaling behavior of COP trajectories were determined and compared with shuffled and phase-randomized surrogate data. The presence of long-range correlations discarded the possibility that the COP trajectories were purely random. Compared to the healthy controls, the COP trajectories of the stroke patients were characterized by increased dimensionality and instability, but greater regularity in the frontal plane. These findings were taken to imply that the stroke patients actively (i.e., cognitively) coped with the stroke-induced impairment of posture, as reflected in the increased regularity and decreased local stability, by recruiting additional control processes (i.e., more degrees of freedom) and/or by tightening the present control structure while releasing non-essential degrees of freedom from postural control. In the course of rehabilitation, dimensionality stayed fairly constant, whereas local stability increased and regularity decreased. The progressively less regular COP trajectories were interpreted to indicate a reduction of cognitive involvement in postural control as recovery from stroke progressed. Consistent with this interpretation, the dual task condition resulted in less regular COP trajectories of greater dimensionality, reflecting a task-related decrease of active, cognitive contributions to postural control. In comparison with conventional posturography, our results show a clear surplus value of dynamical measures in studying postural control

New physics in and with gravity

At the center of black holes, the theory of general relativity breaks down. The resolution of such singularities could require a theory of quantum gravity which describes the fundamental nature of space-time at shortest distances. In this thesis, we explore the tensor model approach to quantum gravity and inspect its relation to other theories of quantum gravity, such as, e.g., asymptotic safety, through a universal continuum limit. Even though at microscopic distances, general relativity breaks down, at large distances this theory is highly successful. We will inspect how one of the predictions of general relativity, gravitational waves, can help us to learn more about new physics beyond the Standard Model

USING ASTROBIOLOGY AS A PLATFORM TO STUDY THE IMPACT ON THE MATHEMATICAL CONTENT KNOWLEDGE AND PEDAGOGICAL CONTENT KNOWLEDGE OF ELEMENTARY EDUCATION MAJORS

Early mathematical skills have long been hailed as a cornerstone and as the best predictor of later success in mathematics and literacy. This perception highlights the importance of elementary educator’s mathematical content knowledge (MCK) and pedagogical content knowledge (PCK). This study explored a novel approach to motivating and facilitating preservice elementary educators’ engagement in an interdisciplinary context. Astrobiology is a growing interdisciplinary field with extraordinary educational potential. It has the potential to provide an exciting science framework structure to mathematics for preservice educators. Due to its interdisciplinary content, astrobiology offers preservice educators an opportunity to see math content through a science lens, an approach that may appeal to students with diverse interests. Although astrobiology research has been on the rise and has contributed greatly to the science field and to society, more research on astrobiology education in schools and colleges needs to be done to understand the best pedagogical approaches to such a diverse topic that encompasses multiple disciplines. Using a quasi-experimental design, this study examines whether the implementation of astrobiology modules focused on science questions could be used as an effective platform to deliver mathematical instruction that focuses on MCK and PCK. Specifically, this dissertation investigates the impact of such modules on preservice elementary educators’ MCK and PCK, both quantitatively and qualitatively. A comprehensive analysis involving nonparametric statistics and qualitative analysis found insufficient sample evidence at the alpha level of 0.05 (α=0.05) to warrant rejection that the astrobiology based mathematical modules had no effect on the preservice teachers’ MCK or PCK. However, one test found a positive correlation between the module and an increase in astrobiology knowledge. The qualitative examination exposed a decrease in the quality of responses for the MCK and PCK areas. This affect could be attributed to the limiting factors of the study. These factors have implications for both teaching future research in the intersection of astrobiology education and MCK and PCK

Characterising postural sway fluctuations in humans using linear and nonlinear methods

Introduction: Postural control is a prerequisite to many everyday and sporting activities which requires the interaction of multiple sensorimotor processes. As long as we have no balance disorders, the maintenance of an erect standing position is taken for granted with automatic running control processes. It is well known that with increasing age or disease balance problems occur which often cause fall-related injuries. To assess balance performance, posturography is widely applied in which body sway is traditionally viewed as a manifestation of random fluctuations. Thus, the amount of sway is solely used as an index of postural stability, that is, less sway is an indication of better control. But, traditional measures of variability fail to account for the temporal organisation of postural sway. The concept of nonlinear dynamics suggests that variability in the motor output is not random but structured. It provides the stimulus to reveal the functionality of postural sway. This thesis evaluates nonlinear analysis tools in addition to classic linear methods in terms of age-related modifications of postural control and under different standing conditions in order to broaden the existing knowledge of postural control processes. Methods: Static posturographic analyses were conducted which included the recording of centre of pressure (COP) time series by means of a force plate. Linear and nonlinear methods were used to quantify postural sway variability in order to evaluate both the amount and structure of sway. Classic time and frequency domain COP parameters were computed. In addition, wavelet transform (WT), multiscale entropy, detrended fluctuation analysis, and scaled windowed variance method were applied to COP signals in order to derive structural COP parameters. Two experiments were performed. 1) 16 young (26.1 ± 6.7 years), healthy subjects were asked to adopt a bipedal stance under single- and dual-task conditions. Three trials were conduced each with a different sampling duration: 30, 60, and 300 seconds [s]. 2) 26 young (28.15 ± 5.86 years) and 13 elderly (72 ± 7 years) subjects stood quietly for 60 s on five different surfaces which imposed different biomechanical constraints: level ground (LG), one foot on a step (ST), uphill (UH), downhill (DH), and slope (SL). Additional to COP recordings, limb load symmetry was assessed via foot pressure insoles. Results: We found a higher sensitivity of structural COP parameters to modulations of postural control and partly an improved evaluation of sway dynamics in longer COP recordings. WT revealed a reweighing of frequency bands in response to altered standing conditions. Scaling exponents and entropy values of COP signals were task-dependent. Higher entropy values were found under the dual-task and condition ST. The time scales affected under the altered standing positions differed between groups and sway directions. Mainly larger posturograms were found in the elderly. Age effects were especially revealed in position ST and concerning medial-lateral COP signals. Load asymmetry was stronger in elderly subjects for LG, UH, and DH positions. Discussion: Modifications of multiple time scales corresponds to an interplay of control subsystems to cope with the altered task demands. The affected time scales are age-dependent suggesting a change of control processes. Higher irregularity under the dual-task indicates a more complex motor output which is interpreted as less attentional investment into postural control. Larger complexity is evident for ST in contrast to LG position. ST obviously challenges lateral sway which is counteracted differently between groups. Load asymmetry suggests that especially elderly subjects adopt a step-initiation strategy. Conclusion: A continued application of nonlinear methods is necessary to broaden the understanding of postural control mechanisms and to identify classifiers for balance dysfunctions. Structural COP parameters provide a more comprehensive indication of postural control system properties between groups and task demands. COP recordings of at least 60 s are recommended to adequately quantify COP signal structure. The analysis of postural strategies in everyday activities increases the ecological validity of postural control studies and can provide valuable information regarding the development of effective rehabilitation programs.Die posturale Kontrolle ist eine Voraussetzung für viele Alltagsaktivitäten und sportliche Bewegungen. Man weiß heute, dass den Kontrollmechanismen eine komplexe Interaktion sensomotorischer Prozesse unterliegt (Horak and Mcpherson, 1996; Oie et al., 2002). Solange keine Gleichgewichtsdefizite vorliegen, nehmen wir es als selbstverständlich wahr aufrecht Stehen zu können, ohne uns der Komplexität posturaler Kontrollmechanismen bewusst zu sein. Studien haben gezeigt, dass es mit zunehmendem Alter zu Defiziten in der posturalen Kontrolle kommt (Pasquier et al., 2003; Woollacott, 1993). Oftmals ist ein erhöhtes Sturzrisiko die Folge, welches unter anderem mit Verletzungen, einer eingeschränkten Mobilitätsowie einer verminderten Lebensqualität einhergehen kann (Era et al., 1997; Frank and Patla, 2003). Seit vielen Jahren schon werden posturographische Untersuchungen durchgeführt mit dem Ziel, posturale Kontrollmechanismen abzuleiten undDysfunktionen im posturalen System zu diagnostizieren (Piirtola and Era, 2006). Jedoch sind die Mechanismen, die der posturalen Kontrolle unterliegen, bis heute nicht eindeutig verstanden. Neue Erkenntnisse konnten in den letzten Jahrenvor allem durch ein erweitertes Verständnis von Bewegungsvariabilität gewonnen werden (Stergiou and Decker, 2011; Lippens and Nagel, 2009). Traditionell werden posturale Analysen unter der Annahme durchgeführt und interpretiert, dass Variabilität eine Art “Rauschen” (white noise) ist und somit Ausdruck eines Fehlers. Posturale Schwankungen werden als zufällige, nicht intendierte Abweichungen gesehen (Loosch, 1997). Der Parameter “Schwankungsausmaß” wird zur Diagnostik des statischen Gleichgewichts herangezogen und bei einer größeren Schwankung wird eine schlechtere posturale Kontrolle diagnostiziert. Im Gegensatz dazu weist der systemdynamische Modellansatz auf die funktionale Rolle der Variabilität hin (van Emmerik and van Wegen, 2002). Variabilität ist Ausdruck der Anpassung und Flexibilität und somit notwendig, um auf ständige Umweltveränderungen reagieren zu können. Ein erhöhtes Schwankungsausmaß ist demnach nicht ausschließlich ein Zeichen für Instabilität (Newell et al., 1993). Eine größere Variabilität posturaler Schwankungen kann auch positiv im Sinne von mehr Umweltexploration interpretiert werden (Lacour et al., 2008). So konnte gezeigt werden, dass posturale Schwankungen nicht zufällig sind, sondern eine Struktur enthalten (Duarte and Zatsiorsky, 2000), dessen Charakterisierung zusätzliche Informationen über die Organisation des posturalen Kontrollsystems liefert (Stergiou and Decker, 2011). Die vorliegende Arbeit evaluiert nichtlineare Methoden unter dem systemdynamischen Ansatz zusätzlich zu den traditionell eingesetzten linearen Methoden. Ziel ist es, neben der Quantifizierung des Ausmaßes posturaler Schwankungen ihre Struktur zu charakterisieren, um das Verständnis für posturale Kontrollmechanismen zu erweitern. Die Evaluierung erfolgt zunächst über den Vergleich von Stehen mit und ohne kognitiver Zusatzaufgabe, wo Studien erste Hinweise auf eine veränderte COP1 Signalstruktur geben (Cavanaugh et al., 2007; Donker et al., 2007; Stins et al., 2009). Durch das Betrachten unterschiedlicher Signallängen und eines umfangreichen Methodenspektrums sollen Anhaltspunkte für die Applikation vonnichtlinearen in Kombination mit linearen Analyseverfahren abgeleitet werden. In einer zweiten Untersuchung werden diese dann in einem angewandten Studiendesign umgesetzt. Dabei wird die Veränderung posturaler Kontrollstrategien bei unterschiedlichen Standpositionen untersucht, welche alltägliche Situationen simulieren, unter Berücksichtigung altersbedingter Effekte. Dies ist ein erster Ansatz zur Erreichung einer hohen ökologischen Validität posturaler Studien (Frank and Patla, 2003; Visser et al., 2008). Erst kürzlich wurde gezeigt, dass bei älteren Menschen meist interne Auslöser (z.B. Gewichtsverlagerungen) ursächlich für Stürze sind (Robinovitch et al., 2013). Zudem haben ältere Personen größere Schwierigkeiten auf Umgebungsveränderungen zu reagieren (Nardone and Schieppati, 2010). Es ist jedoch bisher unbekannt, wie sich Defizite in der Gleichgewichtskontrolle älterer Menschen auf die Struktur posturaler Schwankungen auswirken. ..

Non-Fermi liquids

Our present understanding of how the interactions between electrons affect the metallic state has, for forty years, rested on the foundations of Landau's Fermi-liquid theory. It provides the basis for understanding metals in terms of weakly interacting electron (-like) particles. Recent years have seen the discovery of metals which appear to fall outside this framework-perhaps most notably in the normal state of the high temperature cuprate superconductors. While the theory for understanding the cuprate metals remains controversial, there are a number of clear examples where we do believe we understand the new underlying theoretical concepts. In this article I illustrate four such routes towards forming a non-Fermi liquid metal and illustrate, where possible, how these have been realized in a number of materials. The proximity to a quantum phase transition and reduced effective dimensionality can both play important roles

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue

Intermittency and Self-Organisation in Turbulence and Statistical Mechanics

There is overwhelming evidence, from laboratory experiments, observations, and computational studies, that coherent structures can cause intermittent transport, dramatically enhancing transport. A proper description of this intermittent phenomenon, however, is extremely difficult, requiring a new non-perturbative theory, such as statistical description. Furthermore, multi-scale interactions are responsible for inevitably complex dynamics in strongly non-equilibrium systems, a proper understanding of which remains a main challenge in classical physics. As a remarkable consequence of multi-scale interaction, a quasi-equilibrium state (the so-called self-organisation) can however be maintained. This special issue aims to present different theories of statistical mechanics to understand this challenging multiscale problem in turbulence. The 14 contributions to this Special issue focus on the various aspects of intermittency, coherent structures, self-organisation, bifurcation and nonlocality. Given the ubiquity of turbulence, the contributions cover a broad range of systems covering laboratory fluids (channel flow, the Von Kármán flow), plasmas (magnetic fusion), laser cavity, wind turbine, air flow around a high-speed train, solar wind and industrial application