Dynamical Properties of Weierstrass Elliptic Functions on Square Lattices

In this dissertation we prove that the Julia set of a Weierstrass elliptic function on a square lattice is connected. We further show that the parameter space contains an infinite number of Mandelbrot sets. As a consequence, this proves the existence of Siegel disks and gives a description of the bifurcation locus about super-attracting parameters corresponding to super-attracting fixed points. We conclude with a description of a family of rational maps that approximate the Weierstrass elliptic function on a square lattice

SpectralNET – an application for spectral graph analysis and visualization

BACKGROUND: Graph theory provides a computational framework for modeling a variety of datasets including those emerging from genomics, proteomics, and chemical genetics. Networks of genes, proteins, small molecules, or other objects of study can be represented as graphs of nodes (vertices) and interactions (edges) that can carry different weights. SpectralNET is a flexible application for analyzing and visualizing these biological and chemical networks. RESULTS: Available both as a standalone .NET executable and as an ASP.NET web application, SpectralNET was designed specifically with the analysis of graph-theoretic metrics in mind, a computational task not easily accessible using currently available applications. Users can choose either to upload a network for analysis using a variety of input formats, or to have SpectralNET generate an idealized random network for comparison to a real-world dataset. Whichever graph-generation method is used, SpectralNET displays detailed information about each connected component of the graph, including graphs of degree distribution, clustering coefficient by degree, and average distance by degree. In addition, extensive information about the selected vertex is shown, including degree, clustering coefficient, various distance metrics, and the corresponding components of the adjacency, Laplacian, and normalized Laplacian eigenvectors. SpectralNET also displays several graph visualizations, including a linear dimensionality reduction for uploaded datasets (Principal Components Analysis) and a non-linear dimensionality reduction that provides an elegant view of global graph structure (Laplacian eigenvectors). CONCLUSION: SpectralNET provides an easily accessible means of analyzing graph-theoretic metrics for data modeling and dimensionality reduction. SpectralNET is publicly available as both a .NET application and an ASP.NET web application from . Source code is available upon request

Advancing Biological Understanding and Therapeutics Discovery with Small-Molecule Probes

Small-molecule probes can illuminate biological processes and aid in the assessment of emerging therapeutic targets by perturbing biological systems in a manner distinct from other experimental approaches. Despite the tremendous promise of chemical tools for investigating biology and disease, small-molecule probes were unavailable for most targets and pathways as recently as a decade ago. In 2005, the U.S. National Institutes of Health launched the decade-long Molecular Libraries Program with the intent of innovating in and broadening access to small-molecule science. This Perspective describes how novel small-molecule probes identified through the program are enabling the exploration of biological pathways and therapeutic hypotheses not otherwise testable. These experiences illustrate how small-molecule probes can help bridge the chasm between biological research and the development of medicines, but also highlight the need to innovate the science of therapeutic discovery.Chemistry and Chemical Biolog

Renal cell carcinoma bone metastases: clinical advances

Bone is a common site of metastatic spread in patients with advanced renal cell carcinoma (RCC) occurring in around one-third of patients enrolled in clinical trials evaluating modern systemic therapies for this disease. Until recently, limited systemic therapeutic options were available for advanced RCC. Nowadays, a quiver of agents have demonstrated activity, including compounds targeting the vascular endothelial growth factor (VEGF) axis and those targeting the mammalian target of rapamycin (mTOR). Despite a detailed biological understanding of how these drugs work, their effect on bony metastases is less clear. Data suggesting that bisphosphonates (namely zoledronic acid) benefit patients with bone metastases from advanced RCC was gathered prior to the targeted therapy era; therefore, there is some uncertainty about their role in patients on modern RCC therapies. This review summarizes the current targeted therapies registered for use in advanced RCC and postulates how some of them might affect the behavior of bone metastases. It also explores the data available on the role of bisphosphonates for bone metastases from RCC, describes methods of assessing response to therapy for bone metastases and delineates future expectations for the treatment of bone metastases from advanced RCC

Mapping the landscape of genetic dependencies in chordoma

Cancer cells possess unique molecular features that can confer an increased dependence on specific genes. Here, the authors use CRISPR-Cas9 screens to identify selectively essential genes and therapeutic targets in chordoma

Harnessing connectivity in a large-scale small-molecule sensitivity dataset

Identifying genetic alterations that prime a cancer cell to respond to a particular therapeutic agent can facilitate the development of precision cancer medicines. Cancer cell-line (CCL) profiling of small-molecule sensitivity has emerged as an unbiased method to assess the relationships between genetic or cellular features of CCLs and small-molecule response. Here, we developed annotated cluster multidimensional enrichment analysis to explore the associations between groups of small molecules and groups of CCLs in a new, quantitative sensitivity dataset. This analysis reveals insights into small-molecule mechanisms of action, and genomic features that associate with CCL response to small-molecule treatment. We are able to recapitulate known relationships between FDA-approved therapies and cancer dependencies and to uncover new relationships, including for KRAS-mutant cancers and neuroblastoma. To enable the cancer community to explore these data, and to generate novel hypotheses, we created an updated version of the Cancer Therapeutic Response Portal (CTRP v2). SIGNIFICANCE: We present the largest CCL sensitivity dataset yet available, and an analysis method integrating information from multiple CCLs and multiple small molecules to identify CCL response predictors robustly. We updated the CTRP to enable the cancer research community to leverage these data and analyses

A dataset of images and morphological profiles of 30 000 small-molecule treatments using the Cell Painting assay

Abstract Background: Large-scale image sets acquired by automated microscopy of perturbed samples enable a detailed comparison of cell states induced by each perturbation, such as a small molecule from a diverse library. Highly multiplexed measurements of cellular morphology can be extracted from each image and subsequently mined for a number of applications. Findings: This microscopy dataset includes 919 265 five-channel fields of view, representing 30 616 tested compounds, available at “The Cell Image Library” (CIL) repository. It also includes data files containing morphological features derived from each cell in each image, both at the single-cell level and population-averaged (i.e., per-well) level; the image analysis workflows that generated the morphological features are also provided. Quality-control metrics are provided as metadata, indicating fields of view that are out-of-focus or containing highly fluorescent material or debris. Lastly, chemical annotations are supplied for the compound treatments applied. Conclusions: Because computational algorithms and methods for handling single-cell morphological measurements are not yet routine, the dataset serves as a useful resource for the wider scientific community applying morphological (image-based) profiling. The dataset can be mined for many purposes, including small-molecule library enrichment and chemical mechanism-of-action studies, such as target identification. Integration with genetically perturbed datasets could enable identification of small-molecule mimetics of particular disease- or gene-related phenotypes that could be useful as probes or potential starting points for development of future therapeutics