The approach to criticality in sandpiles

A popular theory of self-organized criticality relates the critical behavior of driven dissipative systems to that of systems with conservation. In particular, this theory predicts that the stationary density of the abelian sandpile model should be equal to the threshold density of the corresponding fixed-energy sandpile. This "density conjecture" has been proved for the underlying graph Z. We show (by simulation or by proof) that the density conjecture is false when the underlying graph is any of Z^2, the complete graph K_n, the Cayley tree, the ladder graph, the bracelet graph, or the flower graph. Driven dissipative sandpiles continue to evolve even after a constant fraction of the sand has been lost at the sink. These results cast doubt on the validity of using fixed-energy sandpiles to explore the critical behavior of the abelian sandpile model at stationarity.Comment: 30 pages, 8 figures, long version of arXiv:0912.320

Fast approximation of centrality and distances in hyperbolic graphs

We show that the eccentricities (and thus the centrality indices) of all vertices of a $\delta$-hyperbolic graph $G=(V,E)$ can be computed in linear time with an additive one-sided error of at most $c\delta$, i.e., after a linear time preprocessing, for every vertex $v$ of $G$ one can compute in $O(1)$ time an estimate $\hat{e}(v)$ of its eccentricity $ecc_G(v)$ such that $ecc_G(v)\leq \hat{e}(v)\leq ecc_G(v)+ c\delta$ for a small constant $c$. We prove that every $\delta$-hyperbolic graph $G$ has a shortest path tree, constructible in linear time, such that for every vertex $v$ of $G$, $ecc_G(v)\leq ecc_T(v)\leq ecc_G(v)+ c\delta$. These results are based on an interesting monotonicity property of the eccentricity function of hyperbolic graphs: the closer a vertex is to the center of $G$, the smaller its eccentricity is. We also show that the distance matrix of $G$ with an additive one-sided error of at most $c'\delta$ can be computed in $O(|V|^2\log^2|V|)$ time, where $c'< c$ is a small constant. Recent empirical studies show that many real-world graphs (including Internet application networks, web networks, collaboration networks, social networks, biological networks, and others) have small hyperbolicity. So, we analyze the performance of our algorithms for approximating centrality and distance matrix on a number of real-world networks. Our experimental results show that the obtained estimates are even better than the theoretical bounds.Comment: arXiv admin note: text overlap with arXiv:1506.01799 by other author

Mod/Resc Parsimony Inference

We address in this paper a new computational biology problem that aims at understanding a mechanism that could potentially be used to genetically manipulate natural insect populations infected by inherited, intra-cellular parasitic bacteria. In this problem, that we denote by \textsc{Mod/Resc Parsimony Inference}, we are given a boolean matrix and the goal is to find two other boolean matrices with a minimum number of columns such that an appropriately defined operation on these matrices gives back the input. We show that this is formally equivalent to the \textsc{Bipartite Biclique Edge Cover} problem and derive some complexity results for our problem using this equivalence. We provide a new, fixed-parameter tractability approach for solving both that slightly improves upon a previously published algorithm for the \textsc{Bipartite Biclique Edge Cover}. Finally, we present experimental results where we applied some of our techniques to a real-life data set.Comment: 11 pages, 3 figure

Amyloid-β(1-42) aggregation initiates its cellular uptake and cytotoxicity

The accumulation of amyloid beta peptide(1-42) (Abeta(1-42)) in extracellular plaques is one of the pathological hallmarks of Alzheimer disease (AD). Several studies have suggested that cellular reuptake of Abeta(1-42) may be a crucial step in its cytotoxicity, but the uptake mechanism is not yet understood. Abeta may be present in an aggregated form prior to cellular uptake. Alternatively, monomeric peptide may enter the endocytic pathway and conditions in the endocytic compartments may induce the aggregation process. Our study aims to answer the question whether aggregate formation is a prerequisite or a consequence of Abeta endocytosis. We visualized aggregate formation of fluorescently labeled Abeta(1-42) and tracked its internalization by human neuroblastoma cells and neurons. beta-Sheet-rich Abeta(1-42) aggregates entered the cells at low nanomolar concentration of Abeta(1-42). In contrast, monomer uptake faced a concentration threshold and occurred only at concentrations and time scales that allowed Abeta(1-42) aggregates to form. By uncoupling membrane binding from internalization, we found that Abeta(1-42) monomers bound rapidly to the plasma membrane and formed aggregates there. These structures were subsequently taken up and accumulated in endocytic vesicles. This process correlated with metabolic inhibition. Our data therefore imply that the formation of beta-sheet-rich aggregates is a prerequisite for Abeta(1-42) uptake and cytotoxicity

Multipurpose High Frequency Electron Spin Resonance Spectrometer for Condensed Matter Research

We describe a quasi-optical multifrequency ESR spectrometer operating in the 75-225 GHz range and optimized at 210 GHz for general use in condensed matter physics, chemistry and biology. The quasi-optical bridge detects the change of mm wave polarization at the ESR. A controllable reference arm maintains a mm wave bias at the detector. The attained sensitivity of 2x10^10 spin/G/(Hz)1/2, measured on a dilute Mn:MgO sample in a non-resonant probe head at 222.4 GHz and 300 K, is comparable to commercial high sensitive X band spectrometers. The spectrometer has a Fabry-Perot resonator based probe head to measure aqueous solutions, and a probe head to measure magnetic field angular dependence of single crystals. The spectrometer is robust and easy to use and may be operated by undergraduate students. Its performance is demonstrated by examples from various fields of condensed matter physics.Comment: submitted to Journal of Magnetic Resonanc

Amyloid-β(1-42) Aggregation Initiates Its Cellular Uptake and Cytotoxicity

The accumulation of amyloid β peptide(1-42) (Aβ(1-42)) in extracellular plaques is one of the pathological hallmarks of Alzheimer disease (AD). Several studies have suggested that cellular reuptake of Aβ(1-42) may be a crucial step in its cytotoxicity, but the uptake mechanism is not yet understood. Aβ may be present in an aggregated form prior to cellular uptake. Alternatively, monomeric peptide may enter the endocytic pathway and conditions in the endocytic compartments may induce the aggregation process. Our study aims to answer the question whether aggregate formation is a prerequisite or a consequence of Aβ endocytosis. We visualized aggregate formation of fluorescently labeled Aβ(1-42) and tracked its internalization by human neuroblastoma cells and neurons. β-Sheet-rich Aβ(1-42) aggregates entered the cells at low nanomolar concentration of Aβ(1-42). In contrast, monomer uptake faced a concentration threshold and occurred only at concentrations and time scales that allowed Aβ(1-42) aggregates to form. By uncoupling membrane binding from internalization, we found that Aβ(1-42) monomers bound rapidly to the plasma membrane and formed aggregates there. These structures were subsequently taken up and accumulated in endocytic vesicles. This process correlated with metabolic inhibition. Our data therefore imply that the formation of β-sheet-rich aggregates is a prerequisite for Aβ(1-42) uptake and cytotoxicity

Amyloid-β(1-42) Aggregation Initiates Its Cellular Uptake and Cytotoxicity

The accumulation of amyloid β peptide(1-42) (Aβ(1-42)) in extracellular plaques is one of the pathological hallmarks of Alzheimer disease (AD). Several studies have suggested that cellular reuptake of Aβ(1-42) may be a crucial step in its cytotoxicity, but the uptake mechanism is not yet understood. Aβ may be present in an aggregated form prior to cellular uptake. Alternatively, monomeric peptide may enter the endocytic pathway and conditions in the endocytic compartments may induce the aggregation process. Our study aims to answer the question whether aggregate formation is a prerequisite or a consequence of Aβ endocytosis. We visualized aggregate formation of fluorescently labeled Aβ(1-42) and tracked its internalization by human neuroblastoma cells and neurons. β-Sheet-rich Aβ(1-42) aggregates entered the cells at low nanomolar concentration of Aβ(1-42). In contrast, monomer uptake faced a concentration threshold and occurred only at concentrations and time scales that allowed Aβ(1-42) aggregates to form. By uncoupling membrane binding from internalization, we found that Aβ(1-42) monomers bound rapidly to the plasma membrane and formed aggregates there. These structures were subsequently taken up and accumulated in endocytic vesicles. This process correlated with metabolic inhibition. Our data therefore imply that the formation of β-sheet-rich aggregates is a prerequisite for Aβ(1-42) uptake and cytotoxicity

Nitroxide-nitroxide and nitroxide-metal distance measurements in transition metal complexes with two or three paramagnetic centres give access to thermodynamic and kinetic stabilities

AG was supported by the EPSRC funded Centre for Doctoral Training in ‘integrated magnetic resonance’ (EP/J500045/1). BEB is grateful for funding from the European Union (REA 334496). This work was supported by the EPSRC (EP/M024660/1), the DFG (Schwerpunktprogramm 1601) and a Wellcome Trust multiuser equipment grant [099149/Z/12/Z].Fundamentally, the stability of coordination complexes and of templated (bio)macromolecular assemblies depends on the thermodynamic and kinetic properties of the intermediates and final complexes formed. Here, we used pulse EPR (electron paramagnetic resonance) spectroscopy to determine the stabilities of nanoscopic assemblies formed between one or two nitroxide spin-labelled tridentate 2,2′:6′,2′′-terpyridine (tpy) ligands and divalent metal ions (FeII, ZnII, CoII and CuII). In three distinct approaches we exploited (a) the modulation depth of pulsed electron–electron double resonance (PELDOR) experiments in samples with increasing metal-to-ligand ratios, (b) the frequencies of PELDOR under broadband excitation using shaped pulses and (c) the distances recovered from well-resolved PELDOR data in fully deuterated solvents measured at 34 GHz. The results demonstrate that PELDOR is highly sensitive to resolving the stability of templated dimers and allows to readily distinguish anti-cooperative binding (for CuII ions) from cooperative binding (for CoII or FeII ions). In the case of paramagnetic ions (CoII and CuII) the use of broadband PELDOR allowed to identify the cooperativity of binding from the time domain and distance data. By using a second labelled tpy ligand and by mixing two homoleptic complexes of the same metal centre we could probe the kinetic stability on a timescale of tens of seconds. Here, tpy complexes of CuII and ZnII were found to be substitutionally labile, CoII showed very slow exchange and FeII was inert under our conditions. Not only do our chemical models allow studying metal–ligand interactions via PELDOR spectroscopy, the design of our study is directly transferable to (bio)macromolecular systems for determining the kinetic and thermodynamic stabilities underpinning (templated) multimerisation. Considering the limited methods available to obtain direct information on the composition and stability of complex assemblies we believe our approach to be a valuable addition to the armoury of methods currently used to study these systems.PostprintPeer reviewe