Application of Discrete Differential Forms to Spherically Symmetric Systems in General Relativity

In this article we describe applications of Discrete Differential Forms in computational GR. In particular we consider the initial value problem in vacuum space-times that are spherically symmetric. The motivation to investigate this method is mainly its manifest coordinate independence. Three numerical schemes are introduced, the results of which are compared with the corresponding analytic solutions. The error of two schemes converges quadratically to zero. For one scheme the errors depend strongly on the initial data.Comment: 22 pages, 6 figures, accepted by Class. Quant. Gra

From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the L\'evy area of fractional Brownian motion with Hurst index α∈(1/8,1/4)\alpha\in(1/8,1/4)

{Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\alpha<1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a difficult task because of the low H\"older regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates, and call for an extension of Gaussian tools such as for instance the Malliavin calculus. After a first introductory paper \cite{MagUnt1}, this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as L\'evy area

Exploring the structure of the N-terminal domain of CP29 with ultrafast fluorescence spectroscopy

A high-throughput Förster resonance energy transfer (FRET) study was performed on the approximately 100 amino acids long N-terminal domain of the photosynthetic complex CP29 of higher plants. For this purpose, CP29 was singly mutated along its N-terminal domain, replacing one-by-one native amino acids by a cysteine, which was labeled with a BODIPY fluorescent probe, and reconstituted with the natural pigments of CP9, chlorophylls and xanthophylls. Picosecond fluorescence experiments revealed rapid energy transfer (~20–70 ps) from BODIPY at amino-acid positions 4, 22, 33, 40, 56, 65, 74, 90, and 97 to Chl a molecules in the hydrophobic part of the protein. From the energy transfer times, distances were estimated between label and chlorophyll molecules, using the Förster equation. When the label was attached to amino acids 4, 56, and 97, it was found to be located very close to the protein core (~15 Å), whereas labels at positions 15, 22, 33, 40, 65, 74, and 90 were found at somewhat larger distances. It is concluded that the entire N-terminal domain is in close contact with the hydrophobic core and that there is no loop sticking out into the stroma. Most of the results support a recently proposed topological model for the N-terminus of CP29, which was based on electron-spin-resonance measurements on spin-labeled CP29 with and without its natural pigment content. The present results lead to a slight refinement of that model

A gut bacterial amyloid promotes α-synuclein aggregation and motor impairment in mice

Amyloids are a class of protein with unique self-aggregation properties, and their aberrant accumulation can lead to cellular dysfunctions associated with neurodegenerative diseases. While genetic and environmental factors can influence amyloid formation, molecular triggers and/or facilitators are not well defined. Growing evidence suggests that non-identical amyloid proteins may accelerate reciprocal amyloid aggregation in a prion-like fashion. While humans encode ~30 amyloidogenic proteins, the gut microbiome also produces functional amyloids. For example, curli are cell surface amyloid proteins abundantly expressed by certain gut bacteria. In mice overexpressing the human amyloid α-synuclein (αSyn), we reveal that colonization with curli-producing Escherichia coli promotes αSyn pathology in the gut and the brain. Curli expression is required for E. coli to exacerbate αSyn-induced behavioral deficits, including intestinal and motor impairments. Purified curli subunits accelerate αSyn aggregation in biochemical assays, while oral treatment of mice with a gut-restricted amyloid inhibitor prevents curli-mediated acceleration of pathology and behavioral abnormalities. We propose that exposure to microbial amyloids in the gastrointestinal tract can accelerate αSyn aggregation and disease in the gut and the brain

Anthocyanins, phenols, and antioxidant activity in blackberry juice with plant extracts addition during heating

In this work the influence of addition of different plant extracts (olive leaf, green tea, pine bark PE 95%, pine bark PE 5:1, red wine PE 30%, red wine PE 4:1, and bioflavonoids) to blackberry juice during heating (at 30, 50, 70 and 90 °C) on the anthocyanin and phenol contents, polymeric colour, and antioxidant activity was investigated. Also, reaction rate constant, half-lives of degradation, and activation energy were calculated. Control sample was juice without addition of extracts. The highest anthocyanin content at 30 °C was in samples with the addition of olive leaf and green tea. At 90 °C the highest anthocyanin content was measured in samples with the addition of extract of red wine and bioflavonoides. Samples supplemented with the extracts had much higher antioxidant activity in comparison to the control sample. Results showed that at 90 °C the sample with green tea supplementation had the lowest reaction rate constant and the highest half-life. Activation energy ranged from 29 to 44 kJ mol−1

Precise Spatiotemporal Control of Optogenetic Activation Using an Acousto-Optic Device

Light activation and inactivation of neurons by optogenetic techniques has emerged as an important tool for studying neural circuit function. To achieve a high resolution, new methods are being developed to selectively manipulate the activity of individual neurons. Here, we report that the combination of an acousto-optic device (AOD) and single-photon laser was used to achieve rapid and precise spatiotemporal control of light stimulation at multiple points in a neural circuit with millisecond time resolution. The performance of this system in activating ChIEF expressed on HEK 293 cells as well as cultured neurons was first evaluated, and the laser stimulation patterns were optimized. Next, the spatiotemporally selective manipulation of multiple neurons was achieved in a precise manner. Finally, we demonstrated the versatility of this high-resolution method in dissecting neural circuits both in the mouse cortical slice and the Drosophila brain in vivo. Taken together, our results show that the combination of AOD-assisted laser stimulation and optogenetic tools provides a flexible solution for manipulating neuronal activity at high efficiency and with high temporal precision

Selective Optical Control of Synaptic Transmission in the Subcortical Visual Pathway by Activation of Viral Vector-Expressed Halorhodopsin

The superficial layer of the superior colliculus (sSC) receives visual inputs via two different pathways: from the retina and the primary visual cortex. However, the functional significance of each input for the operation of the sSC circuit remains to be identified. As a first step toward understanding the functional role of each of these inputs, we developed an optogenetic method to specifically suppress the synaptic transmission in the retino-tectal pathway. We introduced enhanced halorhodopsin (eNpHR), a yellow light-sensitive, membrane-targeting chloride pump, into mouse retinal ganglion cells (RGCs) by intravitreously injecting an adeno-associated virus serotype-2 vector carrying the CMV-eNpHR-EYFP construct. Several weeks after the injection, whole-cell recordings made from sSC neurons in slice preparations revealed that yellow laser illumination of the eNpHR-expressing retino-tectal axons, putatively synapsing onto the recorded cells, effectively inhibited EPSCs evoked by electrical stimulation of the optic nerve layer. We also showed that sSC spike activities elicited by visual stimulation were significantly reduced by laser illumination of the sSC in anesthetized mice. These results indicate that photo-activation of eNpHR expressed in RGC axons enables selective blockade of retino-tectal synaptic transmission. The method established here can most likely be applied to a variety of brain regions for studying the function of individual inputs to these regions