On a Generalization of the Frobenius Number

We consider a generalization of the Frobenius Problem where the object of interest is the greatest integer which has exactly $j$ representations by a collection of positive relatively prime integers. We prove an analogue of a theorem of Brauer and Shockley and show how it can be used for computation.Comment: 5 page

Targeting Angiogenesis and the Tumor Microenvironment

The role of the microenvironment during the initiation and progression of malignancy is appreciated to be of critical importance for improved molecular diagnostics and therapeutics. The tumor microenvironment is the product of a crosstalk between different cells types. Critical elements in the microenvironment include tumor associated fibroblasts, which provide an essential communication network via secretion of growth factors and chemokines, inducing an altered extracellular matrix (ECM), thereby providing additional oncogenic signals that enhance cancer-cell proliferation and invasion. Active contribution of tumor-associated stromal cells to cancer progression has been recognized. Stromal elements consist of the ECM, fibroblasts of various phenotypes, and a scaffold composed of immune and inflammatory cells, blood and lymph vessels, and nerves. This review will focus on therapeutic targets in the microenvironment related to tumor endothelium, tumor associated fibroblasts and the extracellular matrix

Ultrasound Molecular Imaging of Secreted Frizzled Related Protein-2 Expression in Murine Angiosarcoma

Angiosarcoma is a biologically aggressive vascular malignancy with a high metastatic potential. In the era of targeted medicine, knowledge of specific molecular tumor characteristics has become more important. Molecular imaging using targeted ultrasound contrast agents can monitor tumor progression non-invasively. Secreted frizzled related protein 2 (SFRP2) is a tumor endothelial marker expressed in angiosarcoma. We hypothesize that SFRP2-directed imaging could be a novel approach to imaging the tumor vasculature. To develop an SFRP2 contrast agent, SFRP2 polyclonal antibody was biotinylated and incubated with streptavidin-coated microbubbles. SVR angiosarcoma cells were injected into nude mice, and when tumors were established the mice were injected intravenously with the SFRP2 -targeted contrast agent, or a control streptavidin-coated contrast agent. SFRP2 -targeted contrast agent detected tumor vasculature with significantly more signal intensity than control contrast agent: the normalized fold-change was 1.6±0.27 (n = 13, p = 0.0032). The kidney was largely devoid of echogenicity with no significant difference between the control contrast agent and the SFRP2-targeted contrast agent demonstrating that the SFRP2-targeted contrast agent was specific to tumor vessels. Plotting average pixel intensity obtained from SFRP2-targeted contrast agent against tumor volume showed that the average pixel intensity increased as tumor volume increased. In conclusion, molecularly-targeted imaging of SFRP2 visualizes angiosarcoma vessels, but not normal vessels, and intensity increases with tumor size. Molecular imaging of SFRP2 expression may provide a rapid, non-invasive method to monitor tumor regression during therapy for angiosarcoma and other SFRP2 expressing cancers, and contribute to our understanding of the biology of SFRP2 during tumor development and progression

Genome-wide trans-ancestry meta-analysis provides insight into the genetic architecture of type 2 diabetes susceptibility.

To further understanding of the genetic basis of type 2 diabetes (T2D) susceptibility, we aggregated published meta-analyses of genome-wide association studies (GWAS), including 26,488 cases and 83,964 controls of European, east Asian, south Asian and Mexican and Mexican American ancestry. We observed a significant excess in the directional consistency of T2D risk alleles across ancestry groups, even at SNPs demonstrating only weak evidence of association. By following up the strongest signals of association from the trans-ethnic meta-analysis in an additional 21,491 cases and 55,647 controls of European ancestry, we identified seven new T2D susceptibility loci. Furthermore, we observed considerable improvements in the fine-mapping resolution of common variant association signals at several T2D susceptibility loci. These observations highlight the benefits of trans-ethnic GWAS for the discovery and characterization of complex trait loci and emphasize an exciting opportunity to extend insight into the genetic architecture and pathogenesis of human diseases across populations of diverse ancestry

Consensus Recommendation for Mouse Models of Ocular Hypertension to Study Aqueous Humor Outflow and Its Mechanisms.

Due to their similarities in anatomy, physiology, and pharmacology to humans, mice are a valuable model system to study the generation and mechanisms modulating conventional outflow resistance and thus intraocular pressure. In addition, mouse models are critical for understanding the complex nature of conventional outflow homeostasis and dysfunction that results in ocular hypertension. In this review, we describe a set of minimum acceptable standards for developing, characterizing, and utilizing mouse models of open-angle ocular hypertension. We expect that this set of standard practices will increase scientific rigor when using mouse models and will better enable researchers to replicate and build upon previous findings

Ultrasound molecular imaging of secreted frizzled related protein-2 expression in murine angiosarcoma.

Angiosarcoma is a biologically aggressive vascular malignancy with a high metastatic potential. In the era of targeted medicine, knowledge of specific molecular tumor characteristics has become more important. Molecular imaging using targeted ultrasound contrast agents can monitor tumor progression non-invasively. Secreted frizzled related protein 2 (SFRP2) is a tumor endothelial marker expressed in angiosarcoma. We hypothesize that SFRP2-directed imaging could be a novel approach to imaging the tumor vasculature. To develop an SFRP2 contrast agent, SFRP2 polyclonal antibody was biotinylated and incubated with streptavidin-coated microbubbles. SVR angiosarcoma cells were injected into nude mice, and when tumors were established the mice were injected intravenously with the SFRP2 -targeted contrast agent, or a control streptavidin-coated contrast agent. SFRP2 -targeted contrast agent detected tumor vasculature with significantly more signal intensity than control contrast agent: the normalized fold-change was 1.6 ± 0.27 (n = 13, p = 0.0032). The kidney was largely devoid of echogenicity with no significant difference between the control contrast agent and the SFRP2-targeted contrast agent demonstrating that the SFRP2-targeted contrast agent was specific to tumor vessels. Plotting average pixel intensity obtained from SFRP2-targeted contrast agent against tumor volume showed that the average pixel intensity increased as tumor volume increased. In conclusion, molecularly-targeted imaging of SFRP2 visualizes angiosarcoma vessels, but not normal vessels, and intensity increases with tumor size. Molecular imaging of SFRP2 expression may provide a rapid, non-invasive method to monitor tumor regression during therapy for angiosarcoma and other SFRP2 expressing cancers, and contribute to our understanding of the biology of SFRP2 during tumor development and progression

SFRP2 -targeted microbubbles bound specifically to vasculature within angiosarcoma.

<p>B-mode images of the SVR angiosarcoma tumors were overlaid in green with molecular images of (A) control streptavidin loaded microbubbles or (B) SFRP2 -targeted microbubbles after three-dimensional molecular imaging. The average pixel intensity observed for SFRP2 -targeted imaging was significantly higher (*p = 0.003, n = 13, paired t-test, two-tailed) than observed for the streptavidin control (C). Immunohistochemistry demonstrated high levels of expression for SFRP2 in angiosarcoma (D). Black scale bars in panels A and B represent 1 mm. Black scale bars in panels D and E represent 35 µm.</p

Microbubbles targeted with anti-chicken IgY were retained within angiosarcoma vasculature at significantly lower levels than microbubbles loaded with streptavidin.

<p>Streptavidin-coated microbubbles were bound to a mixture of biotinylated anti-chicken IgY (raised in rabbit and goat) to produce anti-chicken IgY control microbubbles. Three-dimensional molecular imaging with the anti-chicken IgY control microbubbles resulted in significantly lower average pixel intensity (*p = 0.0002, n = 10, unpaired t-test, two-tailed) than observed with microbubbles coated only with streptavidin.</p