Exponentially Accurate Semiclassical Tunneling Wave Functions in One Dimension

We study the time behavior of wave functions involved in tunneling through a smooth potential barrier in one dimension in the semiclassical limit. We determine the leading order component of the wave function that tunnels. It is exponentially small in $1/\hbar$. For a wide variety of incoming wave packets, the leading order tunneling component is Gaussian for sufficiently small $\hbar$. We prove this for both the large time asymptotics and for moderately large values of the time variable

Paracrine delivery of therapeutic biologics for cancer

A fundamental goal of cancer drug delivery is to achieve sufficient levels within the tumour without leading to high systemic concentrations that might cause off-target toxicities. In situ production of protein-based therapeutics by tumour cells provides an attractive alternative to treatment with repeated high bolus injections, as secretion by the tumour itself could provide high local concentrations that act in a paracrine fashion over an extended duration. For this purpose, we have developed a non-oncolytic adenoviral delivery system that allows for targeting of Ad5 to discrete cell types by redirecting viral tropism to cell surface biomarkers through the use of interchangeable adapters. Furthermore, we recently described the engineering of a protein-based ‘shield’ that is coated on the Ad5 capsid, which, together with the retargeting adapters, allows for improved tumour specificity and prevention of viral clearance. To test this delivery strategy in vivo, SCID-beige mice bearing orthotopic BT474 xenografts were treated with three doses of either a cancerspecific, non-replicative Ad5 that encodes a secreted anti-HER2 antibody, trastuzumab, in its genome, or with the protein therapeutic itself (Herceptin®). We have employed state-of-the-art whole tumour clearing and imaging with confocal microscopy at high spatial resolution in 3D to assess biodistribution, and large volumetric imaging has revealed that the secreted therapeutic diffuses significantly throughout the tumour leading to a therapeutic effect and delayed tumour outgrowth. Moreover, the systemic concentration of antibody is significantly reduced with viral delivery, suggesting that paracrine delivery may be a promising strategy for delivery of biologics with narrow therapeutic indices

(4Z,6Z,12Z,14Z)-2,10-Dimethyl-2,8,10,16-tetra­hydro­dipyrazolo[3,4-e:3′,4′-l][1,2,4,8,9,11]hexa­azacyclo­tetra­decine-4,12-diamine

The title compound, C12H16N12, is a centrosymmetric mol­ecule which comprises of a hexa­aza[14]annulene macrocyclic ring fused with two pyrazole rings. The macrocyclic ring is essentially planar, with an r.m.s. deviation of 0.0381 Å. The electron pairs of the amino groups are delocalized with the conjugated system of the macrocycle. Strong intra­molecular N—H⋯N hydrogen bonds arranged in an S 2 2(10) graph-set motif are present in the macrocyclic ring. In the crystal, the amino groups act as donors for inter­molecular N—H⋯N inter­actions with the N atoms of the heterocyclic system, forming a network of two types of extended chains oriented parallel to the [101] and [011] directions. The crystal packing is also stabilized by weak inter­molecular C—H⋯N hydrogen bonds formed between pyrazole C—H groups and N atoms of the macrocyclic ring, running in the [10] direction

Use of high-content imaging to quantify transduction of AAV-PHP viruses in the brain following systemic delivery

The engineering of the AAV-PHP capsids was an important development for CNS research and the modulation of gene expression in the brain. They cross the blood brain barrier and transduce brain cells after intravenous systemic delivery, a property dependent on the genotype of Ly6a, the AAV-PHP capsid receptor. It is important to determine the transduction efficiency of a given viral preparation, as well as the comparative tropism for different brain cells; however, manual estimation of adeno-associated viral transduction efficiencies can be biased and time consuming. Therefore, we have used the Opera Phenix high-content screening system, equipped with the Harmony processing and analysis software, to reduce bias and develop an automated approach to determining transduction efficiency in the mouse brain. We used R Studio and ‘gatepoints’ to segment the data captured from coronal brain sections into brain regions of interest. C57BL/6J and CBA/Ca mice were injected with an AAV-PHP.B virus containing a green fluorescent protein reporter with a nuclear localization signal. Coronal sections at 600 μm intervals throughout the entire brain were stained with Hoechst dye, combined with immunofluorescence to NeuN and green fluorescent protein to identify all cell nuclei, neurons and transduced cells, respectively. Automated data analysis was applied to give an estimate of neuronal percentages and transduction efficiencies throughout the entire brain as well as for the cortex, striatum and hippocampus. The data from each coronal section from a given mouse were highly comparable. The percentage of neurons in the C57BL/6J and CBA/Ca brains was approximately 40% and this was higher in the cortex than striatum and hippocampus. The systemic injection of AAV-PHP.B resulted in similar transduction rates across the entire brain for C57BL/6J mice. Approximately 10–15% of all cells were transduced, with neuronal transduction efficiencies ranging from 5% to 15%, estimates that were similar across brain regions, and were in contrast to the much more localized transduction efficiencies achieved through intracerebral injection. We confirmed that the delivery of the AAV-PHP.B viruses to the brain from the vasculature resulted in widespread transduction. Our methodology allows the rapid comparison of transduction rates between brain regions producing comparable data to more time-consuming approaches. The methodology developed here can be applied to the automated quantification of any parameter of interest that can be captured as a fluorescent signal

Intersection local times of independent fractional Brownian motions as generalized white noise functionals

In this work we present expansions of intersection local times of fractional Brownian motions in $\R^d$, for any dimension $d\geq 1$, with arbitrary Hurst coefficients in $(0,1)^d$. The expansions are in terms of Wick powers of white noises (corresponding to multiple Wiener integrals), being well-defined in the sense of generalized white noise functionals. As an application of our approach, a sufficient condition on $d$ for the existence of intersection local times in $L^2$ is derived, extending the results of D. Nualart and S. Ortiz-Latorre in "Intersection Local Time for Two Independent Fractional Brownian Motions" (J. Theoret. Probab.,20(4)(2007), 759-767) to different and more general Hurst coefficients.Comment: 28 page

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

Paracrine delivery of therapeutic biologics for cancer

A fundamental goal of cancer drug delivery is to achieve sufficient levels within the tumour without leading to high systemic concentrations that might cause off-target toxicities. In situ production of protein-based therapeutics by tumour cells provides an attractive alternative to treatment with repeated high bolus injections, as secretion by the tumour itself could provide high local concentrations that act in a paracrine fashion over an extended duration. For this purpose, we have developed a non-oncolytic adenoviral delivery system that allows for targeting of Ad5 to discrete cell types by redirecting viral tropism to cell surface biomarkers through the use of interchangeable adapters. Furthermore, we recently described the engineering of a protein-based ‘shield’ that is coated on the Ad5 capsid, which, together with the retargeting adapters, allows for improved tumour specificity and prevention of viral clearance. To test this delivery strategy in vivo, SCID-beige mice bearing orthotopic BT474 xenografts were treated with three doses of either a cancerspecific, non-replicative Ad5 that encodes a secreted anti-HER2 antibody, trastuzumab, in its genome, or with the protein therapeutic itself (Herceptin®). We have employed state-of-the-art whole tumour clearing and imaging with confocal microscopy at high spatial resolution in 3D to assess biodistribution, and large volumetric imaging has revealed that the secreted therapeutic diffuses significantly throughout the tumour leading to a therapeutic effect and delayed tumour outgrowth. Moreover, the systemic concentration of antibody is significantly reduced with viral delivery, suggesting that paracrine delivery may be a promising strategy for delivery of biologics with narrow therapeutic indices

Optical Dissection of Neural Circuits Responsible for Drosophila Larval Locomotion with Halorhodopsin

Halorhodopsin (NpHR), a light-driven microbial chloride pump, enables silencing of neuronal function with superb temporal and spatial resolution. Here, we generated a transgenic line of Drosophila that drives expression of NpHR under control of the Gal4/UAS system. Then, we used it to dissect the functional properties of neural circuits that regulate larval peristalsis, a continuous wave of muscular contraction from posterior to anterior segments. We first demonstrate the effectiveness of NpHR by showing that global and continuous NpHR-mediated optical inhibition of motor neurons or sensory feedback neurons induce the same behavioral responses in crawling larvae to those elicited when the function of these neurons are inhibited by Shibirets, namely complete paralyses or slowed locomotion, respectively. We then applied transient and/or focused light stimuli to inhibit the activity of motor neurons in a more temporally and spatially restricted manner and studied the effects of the optical inhibition on peristalsis. When a brief light stimulus (1–10 sec) was applied to a crawling larva, the wave of muscular contraction stopped transiently but resumed from the halted position when the light was turned off. Similarly, when a focused light stimulus was applied to inhibit motor neurons in one or a few segments which were about to be activated in a dissected larva undergoing fictive locomotion, the propagation of muscular constriction paused during the light stimulus but resumed from the halted position when the inhibition (>5 sec) was removed. These results suggest that (1) Firing of motor neurons at the forefront of the wave is required for the wave to proceed to more anterior segments, and (2) The information about the phase of the wave, namely which segment is active at a given time, can be memorized in the neural circuits for several seconds

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

Amygdala circuitry mediating reversible and bidirectional control of anxiety

Anxiety—a sustained state of heightened apprehension in the absence of immediate threat—becomes severely debilitating in disease states. Anxiety disorders represent the most common of psychiatric diseases (28% lifetime prevalence) and contribute to the aetiology of major depression and substance abuse. Although it has been proposed that the amygdala, a brain region important for emotional processing, has a role in anxiety, the neural mechanisms that control anxiety remain unclear. Here we explore the neural circuits underlying anxiety-related behaviours by using optogenetics with two-photon microscopy, anxiety assays in freely moving mice, and electrophysiology. With the capability of optogenetics to control not only cell types but also specific connections between cells, we observed that temporally precise optogenetic stimulation of basolateral amygdala (BLA) terminals in the central nucleus of the amygdala (CeA)—achieved by viral transduction of the BLA with a codon-optimized channelrhodopsin followed by restricted illumination in the downstream CeA—exerted an acute, reversible anxiolytic effect. Conversely, selective optogenetic inhibition of the same projection with a third-generation halorhodopsin (eNpHR3.0) increased anxiety-related behaviours. Importantly, these effects were not observed with direct optogenetic control of BLA somata, possibly owing to recruitment of antagonistic downstream structures. Together, these results implicate specific BLA–CeA projections as critical circuit elements for acute anxiety control in the mammalian brain, and demonstrate the importance of optogenetically targeting defined projections, beyond simply targeting cell types, in the study of circuit function relevant to neuropsychiatric disease