Proximal-isometric (P J) flows

We develop some new tools for the study of minimal transformation groups (flows) and apply these tools to extend the classification theory of minimal flows to a larger class than has previously been classified. The tools we develop arise from a simplification and unification of the techniques used by Furstenberg, Ellis, and Veech in their proofs of structure theorems about distal and point distal flows. This simplification is made possible largely through the use of recent results of Glasner on the structure of 2^X (whose points consist of closed subsets of the phase space X of a given flow).     

X-RAY INDUCED VISIBLE LUMINESCENCE OF PORPHYRINS

A concept has been presented whereby X-ray irradiation can be used to induce visible luminescence of chromophores such as porphyrins. The essential aspects of the idea have been demonstrated in a supramolecular assembly consisting of a water-dispersed polystyrene latex with an embedded scintillating compound, 2,5-diphenyloxa-zole, and an externally attached hematoporphyrin. X-ray excitation of the assembly yields an emission spectra typical for hematoporphyrin with fluorescent yields. of up to 3% with respect to 2,5-diphenyloxazole emission. Significant quenching in the presence of dioxygen indicates that singlet oxygen is formed at atmospheric conditions.     

The signature operator at 2

It is well known that the signature operator on a manifold defines a K-homology class which is an orientation after inverting 2. Here we address the following puzzle: What is this class localized at 2, and what special properties does it have? Our answers include the following:

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the K-homology class Δ_M of the signature operator is a bordism invariant;

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the reduction mod 8 of the K-homology class of the signature operator is an oriented homotopy invariant;

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the reduction mod 16 of the K-homology class of the signature operator is not an oriented homotopy invariant.

     

Backbone conformational preferences and pseudorotational ring puckering of 1-aminocyclopentane-1-carboxylic acid

We have used quantum mechanical calculations at the B3LYP/6-311G(d,p) level to determine the conformational preferences of the N-acetyl-N'-methylamide derivative of 1-aminocyclopentane-1-carboxylic acid in the gas phase, chloroform solution, and water solution. The backbone conformation of this dipeptide has been described through the dihedral angles varphi and psi, while the pseudorotational phase angle was used to define the conformation of the cyclopentane ring. Results indicate that the backbone flexibility of this amino acid is restricted by the cyclic nature of the side chain, the relative stability of the different conformations depending on the polarity of the environment. The potential energy of the pseudorotation was also studied as a function of the backbone conformation. Interestingly, the conformation of the cyclic side chain depends on the backbone arrangement. Furthermore, the number of pseudorotational states accessible at room temperature is high in all the investigated environments, especially in aqueous solution. Finally, a set of force-field parameters for classical molecular mechanics calculations was developed for the investigated amino acid. Molecular dynamics simulations in both chloroform and aqueous solutions were performed to demonstrate the reliability of such parameters.     

Optimization over Young diagrams

Journal of Algebraic Combinatorics - We consider the problem of finding a Young diagram minimizing the sum of evaluations of a given pair of functions on the parts of the associated pair of...     

Application of 1-aminocyclohexane carboxylic acid to protein nanostructure computer design

Conformationally restricted amino acids are promising candidates to serve as basic pieces in redesigned protein motifs which constitute the basic modules in synthetic nanoconstructs. Here we study the ability of constrained cyclic amino acid 1-aminocyclohexane-1-carboxylic acid (Ac6c) to stabilize highly regular beta-helical motifs excised from naturally occurring proteins. Calculations indicate that the conformational flexibility observed in both the ring and the main chain is significantly higher than that detected for other 1-aminocycloalkane-1-carboxylic acids (Acnc, where n refers to the size of the ring) with smaller cycles. Incorporation of Ac6c into the flexible loops of beta-helical motifs indicates that the stability of such excised building blocks as well as the nanoassemblies derived from them is significantly enhanced. Thus, the intrinsic Ac6c tendency to adopt folded conformations combined with the low structural strain of the cyclohexane ring confers the ability to both self-adapt to the beta-helix motif and to stabilize the overall structure by absorbing part of its conformational fluctuations. Comparison with other Acnc residues indicates that the ability to adapt to the targeted position improves considerably with the ring size, i.e., when the rigidity introduced by the strain of the ring decreases.     

The energy landscape of a selective tumor-homing pentapeptide

Recently, a potentially powerful strategy based on phage-display libraries has been presented to target tumors via homing peptides attached to nanoparticles. The Cys-Arg-Glu-Lys-Ala (CREKA) peptide sequence has been identified as a tumor-homing peptide that binds to clotted plasmas proteins present in tumor vessels and interstitium. The aim of this work consists of mapping the conformational profile of CREKA to identify the bioactive conformation. For this purpose, a conformational search procedure based on modified simulated annealing combined with molecular dynamics was applied to three systems that mimic the experimentally used conditions: (i) the free peptide; (ii) the peptide attached to a nanoparticle; and (iii) the peptide inserted in a phage display protein. In addition, the free peptide was simulated in an ionized aqueous solution environment, which mimics the ionic strength of the physiological medium. Accessible minima of all simulated systems reveal a multiple interaction pattern involving the ionized side chains of Arg, Glu, and Lys, which induces a beta-turn motif in the backbone observed in all simulated CREKA systems.     

High-resolution separation of peptides by sodium dodecyl sulfate-polyacrylamide gel "focusing"

As a follow-up of our previous report (Anal. Chem. 2007, 79, 821-827) on analytical SDS-PAGE focusing, a refinement of the method for separation of peptides in the small to medium M(r) range (0.5-10 kDa) is here reported, based on a shallow gradient of immobilized positive charges (0-10 mM) onto a minimally sieving polyacrylamide gel matrix (4%T, 2.5%C). Unlike conventional SDS-PAGE, which rarely can achieve the separations of polypeptide chains below a critical value of 10 kDa, the present method can be fine-tuned to perform such separations even down to a size of only 500 Da. In the case of larger fragments, the major peptide zones are shown, under microscope observation, to be composed by envelopes of bands as narrow as 20-100 microm, spaced at regular intervals of 100-150 microm. It is hypothesized that such larger peptides could form complexes with rather small SDS micelles and that such peptide-SDS complexes could differ in charge by just a single negative charge.