Semiclassical low energy scattering for one-dimensional Schr\"odinger operators with exponentially decaying potentials

We consider semiclassical Schr\"odinger operators on the real line of the form $$H(\hbar)=-\hbar^2 \frac{d^2}{dx^2}+V(\cdot;\hbar)$$ with $\hbar>0$ small. The potential $V$ is assumed to be smooth, positive and exponentially decaying towards infinity. We establish semiclassical global representations of Jost solutions $f_\pm(\cdot,E;\hbar)$ with error terms that are uniformly controlled for small $E$ and $\hbar$, and construct the scattering matrix as well as the semiclassical spectral measure associated to $H(\hbar)$. This is crucial in order to obtain decay bounds for the corresponding wave and Schr\"odinger flows. As an application we consider the wave equation on a Schwarzschild background for large angular momenta $\ell$ where the role of the small parameter $\hbar$ is played by $\ell^{-1}$. It follows from the results in this paper and \cite{DSS2}, that the decay bounds obtained in \cite{DSS1}, \cite{DS} for individual angular momenta $\ell$ can be summed to yield the sharp $t^{-3}$ decay for data without symmetry assumptions.Comment: 44 pages, minor modifications in order to match the published version, will appear in Annales Henri Poincar

Systemic shRNA mediated knock down of S100A4 in colorectal cancer xenografted mice reduces metastasis formation

The metastasis-inducing protein S100A4 was found to be a prognostic indicator for the development of metachronous metastases. S100A4 expression levels correlate with the formation of human colorectal cancer metastases and shorter patients' survival. Inhibition of S100A4 expression in patients might therefore result in decreased metastasis formation and prolonged survival. In the present study, we used shRNA expression plasmids to inhibit S100A4 expression in the colorectal cancer cell lines HCT116, SW620 and DLD-1. Cell lines with reduced S100A4 expression showed reduced cell migration and invasion in vitro. The knock-down of S100A4 expression also led to significantly diminished formation of liver metastases when intrasplenically transplanted in mice (P = 0.004). We then focused on the therapeutic potential of systemically applied shRNA expression plasmids acting on S100A4 via repeated hydrodynamics-based tail vein injection of plasmid DNA. Mice, intrasplenically transplanted with HCT116 cells and treated systemically with S100A4‑shRNA plasmids, showed a decrease of S100A4 and MMP9 expression levels, resulting in significantly reduced liver metastases (P = 0.005). In summary, we show for the first time the intratumoral knock down of S100A4 via systemic application of S100A4‑shRNA plasmid DNA, which restricts metastasis formation in a xenografted mouse model of colorectal cancer

RAGE mediates S100A4-induced cell motility via MAPK/ERK and hypoxia signaling and is a prognostic biomarker for human colorectal cancer metastasis

Survival of colorectal cancer patients is strongly dependent on development of distant metastases. S100A4 is a prognostic biomarker and inducer for colorectal cancer metastasis. Besides exerting intracellular functions, S100A4 is secreted extracellularly. The receptor for advanced glycation end products (RAGE) is one of its interaction partners. The impact of the S100A4-RAGE interaction for cell motility and metastasis formation in colorectal cancer has not been elucidated so far. Here we demonstrate the RAGE-dependent increase in migratory and invasive capabilities of colorectal cancer cells via binding to extracellular S100A4. We show the direct interaction of S100A4 and RAGE, leading to hyperactivated MAPK/ERK and hypoxia signaling. The S100A4-RAGE axis increased cell migration (P<0.005) and invasion (P<0.005), which was counteracted with recombinant soluble RAGE and RAGE-specific antibodies. In colorectal cancer patients, not distantly metastasized at surgery, high RAGE expression in primary tumors correlated with metachronous metastasis, reduced overall (P=0.022) and metastasis-free survival (P=0.021). In summary, interaction of S100A4-RAGE mediates S100A4-induced colorectal cancer cell motility. RAGE by itself represents a biomarker for prognosis of colorectal cancer. Thus, therapeutic approaches targeting RAGE or intervening in S100A4-RAGE-dependent signaling early in tumor progression might represent alternative strategies restricting S100A4-induced colorectal cancer metastasis

Circulating MACC1 transcripts in colorectal cancer patient plasma predict metastasis and prognosis

BACKGROUND: Metastasis is the most frequent cause of treatment failure and death in colorectal cancer. Early detection of tumors and metastases is crucial for improving treatment strategies and patient outcome. Development of reliable biomarkers and simple tests routinely applicable in the clinic for detection, prognostication, and therapy monitoring is of special interest. We recently identified the novel gene Metastasis-Associated in Colon Cancer 1 (MACC1), a key regulator of the HGF/Met-pathway. MACC1 is a strong prognostic biomarker for colon cancer metastasis and allows identification of high-risk subjects in early stages, when determined in patients' primary tumors. To overcome the limitation of a restricted number of molecular analyses in tumor tissue, the establishment of a non-invasive blood test for early identification of high-risk cancer patients, for monitoring disease course and therapy response is strongly needed. METHODOLOGY/PRINCIPAL FINDINGS: For the first time, we describe a non-invasive assay for quantification of circulating MACC1 transcripts in blood of more than 300 colorectal cancer patients. MACC1 transcript levels are increased in all disease stages of the cancer patients compared to tumor-free volunteers. Highest MACC1 levels were determined in individuals with metastases (all P<0.05). Importantly, high MACC1 levels correlate with unfavorable survival (P<.0001). Combining MACC1 with circulating transcripts of the metastasis gene S100A4, a transcriptional target of the Wnt/beta-catenin-pathway, improves survival prediction for newly diagnosed cancer patients. CONCLUSION/SIGNIFICANCE: This blood-based assay for circulating MACC1 transcripts, which can be quantitated on a routine basis, is clinically applicable for diagnosis, prognosis, and therapeutic monitoring of cancer patients. Here we demonstrate the diagnostic and prognostic value of circulating MACC1 transcripts in patient plasma for metastasis and survival. Since MACC1 represents a promising target for anti-metastatic therapies, circulating MACC1 transcripts may prove to be an ideal read-out for monitoring therapeutic response of future interventions targeting MACC1-induced metastasis in cancer patients

On the spectral properties of L_{+-} in three dimensions

This paper is part of the radial asymptotic stability analysis of the ground state soliton for either the cubic nonlinear Schrodinger or Klein-Gordon equations in three dimensions. We demonstrate by a rigorous method that the linearized scalar operators which arise in this setting, traditionally denoted by L_{+-}, satisfy the gap property, at least over the radial functions. This means that the interval (0,1] does not contain any eigenvalues of L_{+-} and that the threshold 1 is neither an eigenvalue nor a resonance. The gap property is required in order to prove scattering to the ground states for solutions starting on the center-stable manifold associated with these states. This paper therefore provides the final installment in the proof of this scattering property for the cubic Klein-Gordon and Schrodinger equations in the radial case, see the recent theory of Nakanishi and the third author, as well as the earlier work of the third author and Beceanu on NLS. The method developed here is quite general, and applicable to other spectral problems which arise in the theory of nonlinear equations

Electromagnetic Anchor Tracking for Soft Tissue Navigation

Abstract The compensation of intraoperative (rigid) Problem The exact intraoperative location of the tumor and adjacent vessels is an important information for the surgeon in oncological liver surgery, which can be provided by navigation systems. In contrary to conventional navigation in neurosurgery or orthopaedic surgery the liver like other soft tissues changes its shape significantly between preoperative image acquisition and the intraoperative intervention. Therefore optical navigation systems based on intraoperative 2D [1] and 3D [2] ultrasound have been developed to capture the current liver position and shape. To detect movements or deformations during the actual resection new ultrasound acquisitions have to be performed, which disturb the surgical procedure. A continuous monitoring of movements and deformations at relevant locations would improve the efficiency and accuracy of the navigation. One possibility for such a monitoring are optical fiducial needles introduced by Meier-Hein et al. Methods

A network model to investigate structural and electrical properties of proteins

One of the main trend in to date research and development is the miniaturization of electronic devices. In this perspective, integrated nanodevices based on proteins or biomolecules are attracting a major interest. In fact, it has been shown that proteins like bacteriorhodopsin and azurin, manifest electrical properties which are promising for the development of active components in the field of molecular electronics. Here we focus on two relevant kinds of proteins: The bovine rhodopsin, prototype of GPCR protein, and the enzyme acetylcholinesterase (AChE), whose inhibition is one of the most qualified treatments of Alzheimer disease. Both these proteins exert their functioning starting with a conformational change of their native structure. Our guess is that such a change should be accompanied with a detectable variation of their electrical properties. To investigate this conjecture, we present an impedance network model of proteins, able to estimate the different electrical response associated with the different configurations. The model resolution of the electrical response is found able to monitor the structure and the conformational change of the given protein. In this respect, rhodopsin exhibits a better differential response than AChE. This result gives room to different interpretations of the degree of conformational change and in particular supports a recent hypothesis on the existence of a mixed state already in the native configuration of the protein.Comment: 25 pages, 12 figure

Spectral Analysis for Matrix Hamiltonian Operators

In this work, we study the spectral properties of matrix Hamiltonians generated by linearizing the nonlinear Schr\"odinger equation about soliton solutions. By a numerically assisted proof, we show that there are no embedded eigenvalues for the three dimensional cubic equation. Though we focus on a proof of the 3d cubic problem, this work presents a new algorithm for verifying certain spectral properties needed to study soliton stability. Source code for verification of our comptuations, and for further experimentation, are available at http://www.math.toronto.edu/simpson/files/spec_prop_code.tgz.Comment: 57 pages, 22 figures, typos fixe

Renormalization and blow up for charge one equivariant critical wave maps

We prove the existence of equivariant finite time blow up solutions for the wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the sum of a dynamically rescaled ground-state harmonic map plus a radiation term. The local energy of the latter tends to zero as time approaches blow up time. This is accomplished by first "renormalizing" the rescaled ground state harmonic map profile by solving an elliptic equation, followed by a perturbative analysis