A Hyland-Bernstein approach to the digital control of Pritchard-Salamon systems

In this paper we consider the fixed finite-order digital linear-quadraticcontrol of Pritchard-Salamon infinite-dimensional systems withunbounded input and output operators under gaussian disturbances.A set of necessary conditions is given in terms of the solvabilityof a discrete-time Hyland-Bernstein system of equations (twomodified Riccati equations and two modified Lyapunov equationscoupled by an projection operator).     

An Inverse Problem for the Matrix Schrödinger Equation

By modifying and generalizing some old techniques of N. Levinson, a uniqueness theorem is established for an inverse problem related to periodic and Sturm-Liouville boundary value problems for the matrix Schrödinger equation.     

An investigation of the parametric excitation of an eccentrically tensioned bar

Results of an investigation of the parametric excitation of an eccentrically tensioned bar are presented. Two distinct types of resonant behavior are observed. For one, the excitation-response frequency ratio is one and, for the other, the ratio is two. In germs of oscillation amplitude and size of the region of parameter space in which resonance occurs, the latter response exhibits the greater potential for producing damage. The transition from small to large amplitude oscillations occurs abruptly and coincides with the occurrence of a snap-through behavior.     

A Simple Model for the Variation of Permeability due to Partial Saturation in Dual Scale Porous Media

The main focus of this work is to model macroscopically the effects of partial saturation upon the permeability of dual scale fibrous media made of fiber bundles when a Newtonian viscous fluid impregnates it. A new phenomenological model is proposed to explain the discrepancies between experimental pressure results and analytical predictions based on Darcy's law. This model incorporates the essential features of relative permeability but without the necessity of measuring saturation of the liquid for its prediction. The model is very relevant for the small scale industrial systems where a liquid is forced to flow through a fibrous porous medium. It requires four parameters. Two of them are the two permeability values based on the two length scales. One length scale is of the order of magnitude of the individual fiber radius and corresponds to the permeability of the completely staurated medium, the other is of the order of magnitude of the distance between the fiber bundles and corresponds to the permeability of the partially saturated medium. The other two parameters are the lengths of the two partially saturated regions of the flow domain. The two lengths of the partially saturated region and the permeability of the fully saturated flow domain can be directly measured from the experiments. The excellent agreement between the model and the experimental results of inlet pressure profile with respect to time suggests that this model may be used to describe the variation of the permeability behind a moving front in such porous media for correct pressure prediction. It may also be used to characterize the fibrous medium by determining the two different permeabilities and the relative importance of the unsaturated portion of the flow domain for a given architecture.     

Comparing pharmacophore models derived from crystallography and NMR ensembles

NMR and X-ray crystallography are the two most widely used methods for determining protein structures. Our previous study examining NMR versus X-Ray sources of protein conformations showed improved performance with NMR structures when used in our Multiple Protein Structures (MPS) method for receptor-based pharmacophores (Damm, Carlson, J Am Chem Soc 129:8225–8235, 2007). However, that work was based on a single test case, HIV-1 protease, because of the rich data available for that system. New data for more systems are available now, which calls for further examination of the effect of different sources of protein conformations. The MPS technique was applied to Growth factor receptor bound protein 2 (Grb2), Src SH2 homology domain (Src-SH2), FK506-binding protein 1A (FKBP12), and Peroxisome proliferator-activated receptor-γ (PPAR-γ). Pharmacophore models from both crystal and NMR ensembles were able to discriminate between high-affinity, low-affinity, and decoy molecules. As we found in our original study, NMR models showed optimal performance when all elements were used. The crystal models had more pharmacophore elements compared to their NMR counterparts. The crystal-based models exhibited optimum performance only when pharmacophore elements were dropped. This supports our assertion that the higher flexibility in NMR ensembles helps focus the models on the most essential interactions with the protein. Our studies suggest that the “extra” pharmacophore elements seen at the periphery in X-ray models arise as a result of decreased protein flexibility and make very little contribution to model performance.     

Dependence of linear elasticity solutions on the elastic constants

Necessary and sufficient conditions for the displacement and/or the stress to be independent of Poisson's ratio or the shear modulus or the mass density in the standard boundary-initial-value problems of three-dimensional classical elastodynamics are determined.

---

Résumé On détermine des conditions nécessaires et suffisantes pour que les déplacements et (ou) les contraintes soient indépendants du coefficient de Poisson ou du module de rigidité ou du densité de masse dans les problémes classiques de l'élasticité tri-dimensionnelle dynamique.

---

---

Department of Theoretical and Applied Mechanics, University of Illinois at Urbana     

Direct interaction between an allosteric agonist pepducin and the chemokine receptor CXCR4

Cell surface heptahelical G protein-coupled receptors (GPCRs) mediate critical cellular signaling pathways and are important pharmaceutical drug targets. (1) In addition to traditional small-molecule approaches, lipopeptide-based GPCR-derived pepducins have emerged as a new class of pharmaceutical agents. (2, 3) To better understand how pepducins interact with targeted receptors, we developed a cell-based photo-cross-linking approach to study the interaction between the pepducin agonist ATI-2341 and its target receptor, chemokine C-X-C-type receptor 4 (CXCR4). A pepducin analogue, ATI-2766, formed a specific UV-light-dependent cross-link to CXCR4 and to mutants with truncations of the N-terminus, the known chemokine docking site. These results demonstrate that CXCR4 is the direct binding target of ATI-2341 and suggest a new mechanism for allosteric modulation of GPCR activity. Adaptation and application of our findings should prove useful in further understanding pepducin modulation of GPCRs as well as enable new experimental approaches to better understand GPCR signal transduction.