A Recipe for State Dependent Distributed Delay Differential Equations

We use the McKendrick equation with variable ageing rate and randomly distributed maturation time to derive a state dependent distributed delay differential equation. We show that the resulting delay differential equation preserves non-negativity of initial conditions and we characterise local stability of equilibria. By specifying the distribution of maturation age, we recover state dependent discrete, uniform and gamma distributed delay differential equations. We show how to reduce the uniform case to a system of state dependent discrete delay equations and the gamma distributed case to a system of ordinary differential equations. To illustrate the benefits of these reductions, we convert previously published transit compartment models into equivalent distributed delay differential equations.Comment: 28 page

Complex formation and regulation of Escherichia coli acetyl-CoA carboxylase

Acetyl-CoA carboxylase is a biotin-dependent, multifunctional enzyme that catalyzes the first committed step in fatty acid synthesis. The Escherichia coli enzyme is composed of a homodimeric biotin carboxylase, biotinylated biotin carboxyl carrier protein (BCCP), and an α2β2 heterotetrameric carboxyltransferase. Catalysis by acetyl-CoA carboxylase proceeds via two half-reactions. In the first half-reaction, biotin carboxylase catalyzes the ATP-dependent carboxylation of biotin, which is covalently attached to BCCP, to form carboxybiotin. In the second half-reaction, carboxyltransferase transfers the carboxyl group from carboxybiotin to acetyl-CoA to form malonyl-CoA. All biotin-dependent carboxylases are proposed to have a two-site ping-pong mechanism where the carboxylase and transferase activities are separate and do not interact. This posits two hypotheses: either biotin carboxylase and BCCP undergo the first half-reaction, BCCP dissociates, and then BCCP interacts with carboxyltransferase to complete the second-half reaction, or all three components form a macromolecular enzyme complex. To determine which hypothesis is correct, a steady-state enzyme kinetic analysis of E. coli acetyl-CoA carboxylase was carried out. The results indicated the two active sites of acetyl-CoA carboxylase interact. Both in vitro and in vivo pull-down assays demonstrated that the three components of E. coli acetyl-CoA carboxylase form a multimeric complex and that complex formation is unaffected by acetyl-CoA, AMPPNP, and mRNA coding for carboxyltransferase. The second study focuses on the crystallization of part of the acetyl-CoA carboxylase complex. To date, the three-dimensional structures of the individual subunits, except the N-terminal domain of BCCP, have been solved; however, the structural basis for how BCCP reacts with biotin carboxylase or carboxyltransferase is unknown. Therefore, we report here the first crystal structure of E. coli BCCP complexed with biotin carboxylase to a resolution of 2.49 Å. The protein-protein complex shows unique quaternary structure and two distinct interfaces for each BCCP monomer. The structure supports a model by which biotin protein ligase can biotinylate the complex. The BCCP binding sites are unique compared to phylogenetically related biotin-dependent carboxylases and therefore, provide novel targets for developing antibiotics against bacterial acetyl-CoA carboxylase. Taken together, these findings provide structural and functional insight into the regulation and complex formation of E. coli acetyl-CoA carboxylase

Reach Out and Touch Someone: Reflections on the 25th Anniversary of Feist Publications, Inc. v. Rural Telephone Service Co.

2016 marks the 25th anniversary of the Supreme Court’s opinion in Feist Publications, Inc. v. Rural Telephone Service Co., one of the Court’s landmark opinions in copyright law, and one that continues to define the standard of originality for copyrighted works in general and compilations of data in particular. The Feist case, however, was an unlikely candidate for landmark status. Only a handful of court opinions and academic authors had expressed dissatisfaction with the existing state of the law concerning originality and data compilations.scure sources which have enhanced greatly the pages that follow. Further, the Tenth Circuit’s opinion in Feist was a two-page, unpublished decision that could not be cited as precedent. The Supreme Court nonetheless granted certiorari and resolved a circuit split by rejecting decisively the “sweat of the brow” doctrine. In doing so, and in unexpectedly grounding its opinion in the Constitution’s Copyright Clause, the Court firmly reinvigorated a standard for originality that has proven durable, flexible, and occasionally controversial in meeting the challenges of copyright law in the 21st century

From Tank to Treatment: Modeling Melanoma in Zebrafish

Melanoma is the deadliest form of skin cancer and one of few cancers with a growing incidence. A thorough understanding of its pathogenesis is fundamental to developing new strategies to combat mortality and morbidity. Zebrafish-due in large part to their tractable genetics, conserved pathways, and optical properties-have emerged as an excellent system to model melanoma. Zebrafish have been used to study melanoma from a single tumor initiating cell, through metastasis, remission, and finally into relapse. In this review, we examine seminal zebrafish studies that have advanced our understanding of melanoma

Spatiotemporal Statistical Downscaling for the Fusion of In-lake and Remote Sensing Data

This paper addresses the problem of fusing data from in-lake monitoring programmes with remote sensing data, through statistical downscaling. A Bayesian hierarchical model is developed, in order to fuse the in-lake and remote sensing data using spatially-varying coefficients. The model is applied to an example dataset of log(chlorophyll-a) data for Lake Erie, one of the Great Lakes of North America

Safran Seat Attachment System

This final design review (FDR) document outlines the senior design project being carried out by a team of mechanical engineering undergraduate students attending California Polytechnic State University, San Luis Obispo for Safran Seats in Santa Maria, CA. The project originally was to design, build, and test a universal attachment to secure a widebody business class seat to seven aircraft models with different seat track geometry. The goal was to design, document, and create a finished product that fits design, weight, and manufacturing requirements, as well as passes static 9G FWD testing. Structural analysis, manufacturing analysis, FEA, and CAD assemblies will also be handed over to Safran as the last step in the delivery of the final prototype. Additionally, any necessary bending, torsion, and stress concentration analysis will be completed and summarized for structural parts. Due to the COVID-19 outbreak in the state of California, deliverables had to be modified as the team was no longer allowed to finish the physical prototype and perform the final 9G test within the Safran facilities. This document describes the full timeline of the project, including background research, project requirements, expected final deliverables, concept ideation and preliminary concept design, final design and supporting analysis, the manufacturing plan for all components, the planned tests for design verification, and next steps for the project. Additionally, it outlines progress since the Critical Design Review (CDR) document was released with the modified deliverables due to the COVID-19 outbreak and shelter in place orders