Different Amyloid-β Self-Assemblies Have Distinct Effects on Intracellular Tau Aggregation.

Alzheimer's disease (AD) pathology is characterized by the aggregation of beta-amyloid (Aβ) and tau in the form of amyloid plaques and neurofibrillary tangles in the brain. It has been found that a synergistic relationship between these two proteins may contribute to their roles in disease progression. However, how Aβ and tau interact has not been fully characterized. Here, we analyze how tau seeding or aggregation is influenced by different Aβ self-assemblies (fibrils and oligomers). Our cellular assays utilizing tau biosensor cells show that transduction of Aβ oligomers into the cells greatly enhances seeded tau aggregation in a concentration-dependent manner. In contrast, transduced Aβ fibrils slightly reduce tau seeding while untransduced Aβ fibrils promote it. We also observe that the transduction of α-synuclein fibrils, another amyloid protein, has no effect on tau seeding. The enhancement of tau seeding by Aβ oligomers was confirmed using tau fibril seeds derived from both recombinant tau and PS19 mouse brain extracts containing human tau. Our findings highlight the importance of considering the specific form and cellular location of Aβ self-assembly when studying the relationship between Aβ and tau in future AD therapeutic development

On the genera of semisimple groups defined over an integral domain of a global function field

Let $K=\mathbb{F}_q(C)$ be the global function field of rational functions over a smooth and projective curve $C$ defined over a finite field $\mathbb{F}_q$. The ring of regular functions on $C-S$ where $S \neq \emptyset$ is any finite set of closed points on $C$ is a Dedekind domain $\mathcal{O}_S$ of $K$. For a semisimple $\mathcal{O}_S$-group $\underline{G}$ with a smooth fundamental group $\underline{F}$, we aim to describe both the set of genera of $\underline{G}$ and its principal genus (the latter if $\underline{G} \otimes_{\mathcal{O}_S} K$ is isotropic at $S$) in terms of abelian groups depending on $\mathcal{O}_S$ and $\underline{F}$ only. This leads to a necessary and sufficient condition for the Hasse local-global principle to hold for certain $\underline{G}$. We also use it to express the Tamagawa number $\tau(G)$ of a semisimple $K$-group $G$ by the Euler Poincar\'e invariant. This facilitates the computation of $\tau(G)$ for twisted $K$-groups.Comment: 18 page

On the flat cohomology of binary norm forms

Let $\mathcal{O}$ be an order of index $m$ in the maximal order of a quadratic number field $k=\mathbb{Q}(\sqrt{d})$. Let $\underline{\mathbf{O}}_{d,m}$ be the orthogonal $\mathbb{Z}$-group of the associated norm form $q_{d,m}$. We describe the structure of the pointed set $H^1_{\mathrm{fl}}(\mathbb{Z},\underline{\mathbf{O}}_{d,m})$, which classifies quadratic forms isomorphic (properly or improperly) to $q_{d,m}$ in the flat topology. Gauss classified quadratic forms of fundamental discriminant and showed that the composition of any binary $\mathbb{Z}$-form of discriminant $\Delta_k$ with itself belongs to the principal genus. Using cohomological language, we extend these results to forms of certain non-fundamental discriminants.Comment: 24 pages, submitted. Comments are welcom

Theory of interacting electrons on the honeycomb lattice

The low-energy theory of electrons interacting via repulsive short-range interactions on graphene's honeycomb lattice at half filling is presented. The exact symmetry of the Lagrangian with local quartic terms for the Dirac field dictated by the lattice is D_2 x U_c(1) x (time reversal), where D_2 is the dihedral group, and U_c(1) is a subgroup of the SU_c(2) "chiral" group of the non-interacting Lagrangian, that represents translations in Dirac language. The Lagrangian describing spinless particles respecting this symmetry is parameterized by six independent coupling constants. We show how first imposing the rotational, then Lorentz, and finally chiral symmetry to the quartic terms, in conjunction with the Fierz transformations, eventually reduces the set of couplings to just two, in the "maximally symmetric" local interacting theory. We identify the two critical points in such a Lorentz and chirally symmetric theory as describing metal-insulator transitions into the states with either time-reversal or chiral symmetry being broken. In the site-localized limit of the interacting Hamiltonian the low-energy theory describes the continuous transitions into the insulator with either a finite Haldane's (circulating currents) or Semenoff's (staggered density) masses, both in the universality class of the Gross-Neveu model. The picture of the metal-insulator transition on a honeycomb lattice emerges at which the residue of the quasiparticle pole at the metallic and the mass-gap in the insulating phase both vanish continuously as the critical point is approached. We argue that the Fermi velocity is non-critical as a consequence of the dynamical exponent being fixed to unity by the emergent Lorentz invariance. Effects of long-range interaction and the critical behavior of specific heat and conductivity are discussed.Comment: 16 revtex pages, 4 figures; typos corrected, new and updated references; published versio

Seasonal Variation in the NDVI–Species Richness Relationship in a Prairie Grassland Experiment (Cedar Creek)

Species richness generally promotes ecosystem productivity, although the shape of the relationship varies and remains the subject of debate. One reason for this uncertainty lies in the multitude of methodological approaches to sampling biodiversity and productivity, some of which can be subjective. Remote sensing offers new, objective ways of assessing productivity and biodiversity. In this study, we tested the species richness–productivity relationship using a common remote sensing index, the Normalized Difference Vegetation Index (NDVI), as a measure of productivity in experimental prairie grassland plots (Cedar Creek). Our study spanned a growing season (May to October, 2014) to evaluate dynamic changes in the NDVI–species richness relationship through time and in relation to environmental variables and phenology. We show that NDVI, which is strongly associated with vegetation percent cover and biomass, is related to biodiversity for this prairie site, but it is also strongly influenced by other factors, including canopy growth stage, short-term water stress and shifting flowering patterns. Remarkably, the NDVI-biodiversity correlation peaked at mid-season, a period of warm, dry conditions and anthesis, when NDVI reached a local minimum. These findings confirm a positive, but dynamic, productivity–diversity relationship and highlight the benefit of optical remote sensing as an objective and non-invasive tool for assessing diversity–productivity relationships