Fully Dynamic Single-Source Reachability in Practice: An Experimental Study

Given a directed graph and a source vertex, the fully dynamic single-source reachability problem is to maintain the set of vertices that are reachable from the given vertex, subject to edge deletions and insertions. It is one of the most fundamental problems on graphs and appears directly or indirectly in many and varied applications. While there has been theoretical work on this problem, showing both linear conditional lower bounds for the fully dynamic problem and insertions-only and deletions-only upper bounds beating these conditional lower bounds, there has been no experimental study that compares the performance of fully dynamic reachability algorithms in practice. Previous experimental studies in this area concentrated only on the more general all-pairs reachability or transitive closure problem and did not use real-world dynamic graphs. In this paper, we bridge this gap by empirically studying an extensive set of algorithms for the single-source reachability problem in the fully dynamic setting. In particular, we design several fully dynamic variants of well-known approaches to obtain and maintain reachability information with respect to a distinguished source. Moreover, we extend the existing insertions-only or deletions-only upper bounds into fully dynamic algorithms. Even though the worst-case time per operation of all the fully dynamic algorithms we evaluate is at least linear in the number of edges in the graph (as is to be expected given the conditional lower bounds) we show in our extensive experimental evaluation that their performance differs greatly, both on generated as well as on real-world instances

Fluorescence correlation spectroscopy in thin films at reflecting substrates as a means to study nanoscale structure and dynamics at soft-matter interfaces

Structure and dynamics at soft-matter interfaces play an important role in nature and technical applications. Optical single-molecule investigations are non-invasive and capable to reveal heterogeneities at the nanoscale. In this work we develop an autocorrelation function (ACF) approach to retrieve tracer diffusion parameters obtained from fluorescence correlation spectroscopy (FCS) experiments in thin liquid films at reflecting substrates. This approach then is used to investigate structure and dynamics in 100 nm thick 8CB liquid crystal films on silicon wafers with five different oxide thicknesses. We find a different extension of the structural reorientation of 8CB at the solid-liquid interface for thin and for thick oxide. For the thin oxides, the perylenediimide tracer diffusion dynamics in general agrees with the hydrodynamic modeling using no-slip boundary conditions with only a small deviation close to the substrate, while a considerably stronger decrease of the interfacial tracer diffusion is found for the thick oxides.Comment: 8 figure

Faster Fully Dynamic Transitive Closure in Practice

The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been thoroughly investigated in theory and many specialized algorithms for solving it have been proposed in the last decades. In two large studies [Frigioni ea, 2001; Krommidas and Zaroliagis, 2008], a number of these algorithms have been evaluated experimentally against simple, static algorithms for graph traversal, showing the competitiveness and even superiority of the simple algorithms in practice, except for very dense random graphs or very high ratios of queries. A major drawback of those studies is that only small and mostly randomly generated graphs are considered. In this paper, we engineer new algorithms to maintain all-pairs reachability information which are simple and space-efficient. Moreover, we perform an extensive experimental evaluation on both generated and real-world instances that are several orders of magnitude larger than those in the previous studies. Our results indicate that our new algorithms outperform all state-of-the-art algorithms on all types of input considerably in practice

Recent Advances in Fully Dynamic Graph Algorithms

In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. Here, we present a quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms

Convergence of Amyloid-β and Tau Pathologies on Mitochondria In Vivo

The histopathological characteristics of Alzheimer's disease (AD) are amyloid-β (Aβ) containing plaques and neurofibrillary tangles (NFTs) as well as neuronal and synaptic loss. Until today, the underlying mechanisms of the interplay of plaques and tangles remained unresolved. There is increasing evidence that mitochondrial dysfunction might be a possible link, as revealed by studies in several APP and tau transgenic mouse models. Recently, we examined mitochondrial function in a novel triple transgenic mouse model (pR5/APP/PS2)—tripleAD mice—that combines both pathologic features of the disease in brain. Using comparative, quantitative proteomics (iTRAQ) and mass spectroscopy, we found a massive deregulation of 24 proteins, of which one third were mitochondrial proteins mainly related to complexes I and IV of the oxidative phosphorylation system (OXPHOS). Remarkably, deregulation of complex I was related to tau, whereas deregulation of complex IV was Aβ dependent, both at the protein and activity levels. The tripleAD mice showed synergistic effects of Aβ and tau already at the age of 8months, resulting in a depolarized mitochondrial membrane potential. At 12months, the strongest defects on OXPHOS, synthesis of ATP and reactive oxygen species, were exhibited in the tripleAD mice, again emphasizing synergistic, age-associated effects of Aβ and tau in impairing mitochondria. This review highlights the convergence of Aβ and tau on mitochondria and establishes a molecular link in AD pathology in viv

Functional and structural changes of mitochondrial function in Tauopathies

Tauopathien sind eine Gruppe von neurodegenerativen Erkrankungen zu denen auch die Alzheimer Demenz zählt, die als gemeinsames pathologisches Merkmal die intrazelluläre Akkumulation von neurofibrillären Bündeln (NFTs) aufweisen. Diese bestehen aus hyperphosphoryliertem Tau-Protein, das hierdurch seine physiologische Funktion, die Assemblierung von Mikrotubuli zu fördern und diese zu stabilisieren, verliert. Der genaue Mechanismus, der bei diesen Erkrankungen zur Neurodegeneration führt und mit Demenz, Parkinsonismus und motorischen Störungen einhergehen kann, ist bisher weitgehend ungeklärt. Da mitochondriale Dysfunktion bei vielen neurodegenerativen Erkrankungen eine entscheidende Rolle spielt, wurde in der vorliegenden Arbeit anhand eines Zellmodells zum Einen der Effekt durch die Überexpression von gesundem Wildtyp-Tau (hTau40) und zum Anderen die Auswirkungen der P301L-Mutation, wie sie auch bei der frontotemporalen Demenz mit Parkinsonismus (FTDP-17) auftritt, auf die mitochondriale Morphologie und Funktion untersucht. Die grundlegende Charakterisierung deckte eine weitreichende Einflussnahme von Tau auf den Energiestoffwechsel der Zellen auf. Die Überexpression von Tau führt zu einer verminderten Expression der Komplexe I, II und IV sowie einer veränderten Aktivität der mitochondrialen Atmungskettenkomplexe I-III. Zudem weist die verminderte Aktivität der Citrat-Synthase auf eine Beeinträchtigung des Citratzyklus hin. Der maßgebliche Unterschied zwischen den Tau überexprimierenden Zellen besteht in dem deutlich erniedrigtem Gehalt (NADH:HAR-Aktivität) und der drastisch erniedrigten Aktivität (NADH:DBQ-Aktivität) von Komplex I in den TauP301L-Zellen, wohingegen die hTau40-Zellen trotz eines vermindertem Gehalts im Vergleich zu den Kontroll-Zellen eine deutlich erhöhte Aktivität (DBQ/HAR-Aktivität) aufweisen. Diese gegensätzliche Aktivität von Komplex I führt zu weitreichenden Veränderungen der Zellphysiologie, was sich am deutlichsten in der daraus resultierenden metabolischen Aktivität (NADH-Spiegeln), den ATP-Spiegeln und dem mitochondrialen Membranpotential zeigt. Diese Parameter sind in den hTau40-Zellen aufgrund der hohen Komplex I-Aktivität erhöht und in den TauP301L-Zellen entsprechend erniedrigt. Ebenso spiegeln sich diese funktionellen Parameter in der veränderten Morphologie, Dynamik sowie der Ultrastruktur der Mitochondrien wieder. Die Cristae-Struktur sowie die Dichte der Matrix lassen eindeutige Rückschlüsse auf die aus den unterschiedlichen Komplex I-Aktivitäten resultierenden ATP-Spiegel zu. Weiterhin gibt es in der Literatur Hinweise, dass zum Einen die Transportrichtung der Mitochondrien von der Affinität der Motormoleküle von dem ATP-Gehalt der Mitochondrien abhängig zu sein scheint und zum Anderen, dass die Hemmung von Komplex I zu einem retrograden Transport und perinukleären Morphologie der Mitochondrien führt. Dies konnte ebenfall in den TauP301L-Zellen gezeigt werden. Zusätzlich sind hier die mitochondriale Bewegung sowie die Dynamik (Fusion und Fission) verringert. Interessanterweise spiegeln viele der funktionellen und strukturellen Veränderungen der TauP301L-Zellen den Alterungsprozess wieder, da es im Alter zu einer erhöhten Rate an oxidativen mtDNA-Schäden, einer verminderten Aktivität von Komplex I sowie zu einer verringerten Effektivität und Kapazität der oxidativen Phosphorylierung kommt, die in niedrigeren ATP-Spiegeln resultiert. Anhaltspunkte aus der Literatur bringen auch die morphologischen und dynamischen Veränderungen der Mitochondrien mit dem Alterungsprozess in Verbindung, wodurch das in dieser Arbeit verwendete Zellmodell anscheinend den Alterungsprozess widerspiegelt, der bei vielen neurodegenerativen Erkrankungen den Hauptrisikofaktor für die Erkrankung darstellt. Die Mutation P301L führt weiterhin dazu, dass die Zellen eine erhöhte Vulnerabilität gegenüber sekundären Insulten aufweisen. Obwohl die Toxizität der einzelnen Stimuli – seien es nun Inhibitoren der einzelnen Atmungskettenkomplexe oder oxidativer sowie nitrosativer Stress – sich unterschiedlich auf die gemessenen physiologischen Parameter der Zellen auswirkte, so zeigt sich durchgängig bei den TauP301L-Zellen ein stärkerer Abfall der metabolischen Aktivität und der ATP-Spiegel. Zudem führte die Überexpression von hTau40 zu einer geringeren Vulnerabilität gegenüber den sekundären Insulten. Trotz der geringen Auswirkungen von oligomerem und fibrillärem Aß1-42 auf die mitochondriale Funktion der SH-SY5Y Zellen kann nicht ausgeschlossen werden, dass in vivo nicht doch ein Teufelskreislauf besteht, sodass sich die Toxizität von Aß und Tau potenziert. Insgesamt machen die Ergebnisse dieser Arbeit deutlich, dass mitochondriale Dysfunktion auch bei Tauopathien eine entscheidende Rolle in der Pathogenese spielt und sich hierdurch neue Aspekte zur therapeutischen Intervention ergeben.Tauopathies – including Alzheimer’s disease – are a class of neurodegenerative disorders that share as their common pathological feature the cytoplasmic accumulation of neurofibrillary tangles (NFTs). These tangles consist of hyperphosphorylated tau protein, which in this state is no more able to bind and stabilize microtubules. Until today, the exact mechanisms about how this leads to dementia, Parkinsonism, motoric dysfunction and finally results in neurodegeneration is still not known. Because mitochondrial dysfunction plays a key role in several neurodegenerative diseases, the impact from overexpression of wild-type (hTau40) and mutant tau (TauP301L) on mitochondrial morphology and function was investigated in a neuroblastoma cell line. The results revealed an extensive influence of tau on energy metabolism. The overexpression of tau independently led to a down regulation of subunits from complex I, II and IV of the respiratory chain as well as changes in the activities of complex I-III. Additionally, the reduced activities from citrate synthase give evidence for an interference with the citric acid cycle. The significant difference between both tau overexpressing cells, was the attenuated amount (NADH:HAR activity) and the varying activity of complex I (NADH:DBQ activity). This resulted in an improved activity of complex I in hTau40 cells and a dramatic decrease in TauP301L cells both compared to control cells. These opposed complex I activities led to wide-ranging changes in cell physiology of the SH-SY5Y cells. The hTau40 cells showed an increase in metabolic activity (NADH level), ATP level and mitochondrial membrane potential (MMP), whereas these parameters were decreased in TauP301L cells. Furthermore, the morphology, dynamic and ultrastructure of mitochondria reflected the functional parameters. The cristae structure and the density of the matrix mirror clearly the differences in ATP levels that result from the opposed complex I activities. There is some evidence in the literature that on one hand, the direction of transport from mitochondria seems to be dependent on the affinity from the motor molecules to the ATP content of the transported mitochondria and on the other hand, that the inhibition of complex I results in a retrograde transport and perinuclear localization of mitochondria. These outcomes were also seen in the TauP301L cells. Additionally, mitochondrial movements and dynamic (fusion and fission) were reduced in these cells. Interestingly, the functional and structural changes in the TauP301L cells reflect some aspects of the aging process. Aging results in a higher amount of oxidative mtDNA damage, a diminished activity of complex I as well as a disturbed capacity of the oxidative phosphorylation system leading to decreased energy production. Furthermore, there is evidence that also morphological and dynamic changes are associated with the aging process. Therefore, the used cell model reflects aspects of the aging process, which is the main risk factor for many neurodegenerative diseases. Furthermore, the expression of the P301L mutation resulted in a higher vulnerability against secondary insults. Although the toxicity of the stimuli – inhibitors of the respiratory chain as well as oxidative and nitrosative stress – differ on their impact on physiological parameters, they resulted always in a stronger decrease of metabolic activity and ATP level in TauP301L cells. Compared to this, the overexression of hTau40 diminished the vulnerability against secondary insults. Even though oligomeric and fibrillar Aß1-42 showed only slight effect on mitochondrial function in this experimental design it can not be excluded that a vicious cycle exist in vivo and the toxicity of Aß and Tau potentiate each other. Altogether, the results from this work clearly show that mitochondrial dysfunction plays a critical role in the pathogenesis of Tauopathies, which could lead to new intervention strategies for therapy