Modelling,simulation, animation,and real-time control (MoSART) for a class of electromechanical systems: a system-theoretic approach

This paper describes an interactive modelling, simulation, animation, and real-time control (MoSART) environment for a class of ‘cart-pendulum’ electromechanical systems that may be used to enhance learning within differential equations and linear algebra classes. The environment is useful for conveying fundamental mathematical/systems concepts through computer-aided analysis, design, graphical visualization, and 3D animation. Referred to as Cart-Pendulum Control3D-Lab1Control3D-Lab-short for control 3D animation laboratory. The author to whom correspondence should be addressed., the environment is based on Microsoft Windows/Visual C++/Direct-3D and MATLAB/Simulink2MATLAB and Simulant are trademarks of The Masterworks, Inc.. Pull-down menus provide access to systems/models/control laws, exogenous signals, parameters, animation models and visual indicators, a suite of (easy-to-modify) Simulant diagrams containing models and control laws, MATLAB m-files for detailed analysis and design, and detailed documentation for each of the above. Three blocks enable animation, joystick inputs, and real-time animation within Simulant. Examples are presented to illustrate the utility of the environment as a valuable tool for analysing/visualizing the above class of electromechanical systems and for enhancing mathematics instruction.     

High-throughput screening for human lysosomal beta-N-Acetyl hexosaminidase inhibitors acting as pharmacological chaperones

The adult forms of Tay-Sachs and Sandhoff diseases result when the activity of beta-hexosaminidase A (Hex) falls below approximately 10% of normal due to decreased transport of the destabilized mutant enzyme to the lysosome. Carbohydrate-based competitive inhibitors of Hex act as pharmacological chaperones (PC) in patient cells, facilitating exit of the enzyme from the endoplasmic reticulum, thereby increasing the mutant Hex protein and activity levels in the lysosome 3- to 6-fold. To identify drug-like PC candidates, we developed a fluorescence-based real-time enzyme assay and screened the Maybridge library of 50,000 compounds for inhibitors of purified Hex. Three structurally distinct micromolar competitive inhibitors, a bisnaphthalimide, nitro-indan-1-one, and pyrrolo[3,4-d]pyridazin-1-one were identified that specifically increased lysosomal Hex protein and activity levels in patient fibroblasts. These results validate screening for inhibitory compounds as an approach to identifying PCs.     

The Saffman-Taylor problem for an extremely shear-thinning fluid

We consider a steady flow driven by pushing a finger of gasinto a highly shear-thinning power-law fluid, with exponentn, in a Hele-Shaw channel. We formulate the problem in termsof the streamfunction , which satisfies the p-Laplacian equation (with ), and investigate travelling wave solutions in the large-n (extreme shear-thinning) limit.We take a Legendre transform of the free-boundary problem for, which reduces it to a linear problem on a fixed domain. The solution to this problem is foundby using matched asymptotic expansions and the resulting shapeof the finger deduced (being, to leading order, a semi-infinitestrip). The nonlinear problem for the streamfunction is alsotreated using matched asymptotic expansion in the physical plane.The finger-width selection problem is briefly discussed in termsof our results.     

New Expressions for Repeated Upper Tail Integrals of the Normal Distribution

Expressions are given for repeated upper tail integrals of the univariate normal density (and so also for the general Hermite function) for both positive and negative arguments. The expressions involve moments of the form E(x + i N) ⁿ and E1 / (x ² + N ²) ⁿ , where N is a unit normal random variable. Laplace transforms are provided for the Hermite functions and the moments. The practical use of these expressions is illustrated.     

HUMIC MACROMOLECULES IN NATURAL WATERS

Abstract

Humic substances are the major organic constituents of soils and sediments. They also occur in small concentrations in natural surface waters and groundwaters. They form through the breakdown of plant and animal tissues by chemical and biological processes that tend to produce complex chemical structures that are more stable than the original material from which they were derived. One of the more important characteristics of humic substances is their ability to form water-soluble and water-insoluble complexes with metal ions and hydrous oxides and to interact with clay minerals and various organic compounds such as alkanes, fatty acids, and toxic organic substances such as pesticides.     

Escherichia coli glucuronylsynthase: an engineered enzyme for the synthesis of beta-glucuronides

The glycosynthase derived from E. coli beta-glucuronidase catalyzes the glucuronylation of a range of primary, secondary, and aryl alcohols with moderate to excellent yields. The procedure provides an efficient, stereoselective, and scalable single-step synthesis of beta-glucuronides under mild conditions.     

Active site pressurization: a new tool for structure-guided drug design and other studies of protein flexibility

We present a new molecular dynamics methodology to assist in structure-based drug design and other studies that seek to predict protein deformability. Termed Active Site Pressurization (ASP), the new methodology simply injects a resin into the ligand binding-site of a protein during the course of a molecular dynamics simulation such that novel, energetically reasonable protein conformations are generated in an unbiased way that may be better representations of the ligand binding conformation than are currently available. Here we apply two different versions of the ASP methodology to three proteins, cytochrome P450cam, PcrA helicase, and glycogen synthase kinase 3beta (GSK3beta), and show that the method is capable of inducing significant conformational changes when compared to the X-ray crystal structures. Application of the ASP methodology therefore provides a view of binding site flexibility that is a rich source of data for inclusion in a variety of further investigations, including high-throughput virtual screening, lead hopping, revealing alternative modes of deformation, and revealing hidden exit and entrance tunnels.