Approximate controllability of second-order distributed implicit functional systems

In this paper we study the approximate controllability of control systems with states and controls in Hilbert spaces, and described by a second-order semilinear abstract functional differential equation with infinite delay. Initially we establish a characterization for the approximate controllability of a second-order abstract linear system and, in the last section, we compare the approximate controllability of a semilinear abstract functional system with the approximate controllability of the associated linear system. (C) 2008 Elsevier Ltd. All rights reserved.

Fluorescence spectroscopy of small peptides interacting with microheterogeneous micelles

Many peptides containing tryptophan have therapeutic uses and can be studied by their fluorescent properties. The biological activity of these peptides involves interactions with many cellular components and micelles can function as carriers inside organisms. We report results from the interaction of small peptides containing tryptophan with several microheterogeneous systems: sodium dodecyl sulphate (SDS) micelles; sodium dodecyl sulphate-poly(ethylene oxide) (SDS-PEO) aggregates; and neutral polymeric micelles. We observed that specific parameters, such as wavelength of maximum emission and fluorescence anisotropy, could be used to ascertain the occurrence of interactions. Affinity constants were determined from changes in the intensity of emission while structural modifications in rotameric conformations were verified from time-resolved measurements. Information about the location and diffusion of peptides in the microheterogeneous systems were obtained from tryptophan emission quenching experiments using N-alkylpyridinium ions. The results show the importance of electrostatic and hydrophobic effects, and of the ionization state of charged residues, in the presence of anionic and amphiphilic SDS in the microheterogeneous systems. Conformational stability of peptides is best preserved in the interaction with the neutral polymeric micelles. (C) 2009 Elsevier B.V. All rights reserved.

Interaction of adrenocorticotropin peptides with microheterogeneous systems - A fluorescence study

Adrenocorticotropin (ACM) and alpha-melanocyte stimulating hormone (alpha-MSH) are peptides which present many physiological effects related to pigmentation, motor and sexual behavior, learning and memory, analgesia, anti-inflammatory and antipyretic processes. The 13 amino acid residues of alpha-MSH are the same initial sequence of ACM and due to the presence of a tryptophan residue in position 9 of the peptide chain, fluorescence techniques could be used to investigate the conformational properties of the hormones in different environments and the mechanisms of interaction with biomimetic systems like sodium dodecyl sulphate (SDS) micelles, sodium dodecyl sulphate-poly(ethylene oxide) (SDS-PEO) aggregates and neutral polymeric micelles. In buffer solution, fluorescence parameters were typical of peptides containing tryptophan exposed to the aqueous medium and upon addition of surfactant and polymer molecules, the gradual change of those parameters demonstrated the interaction of the peptides with the microheterogeneous systems. From time-resolved experiments it was shown that the interaction proceeded with conformational changes in both peptides, and further information was obtained from quenching of Trp fluorescence by a family of N-alkylpyridinium ions, which possess affinity to the microheterogeneous systems dependent on the length of the alkyl chain. The quenching of Trp fluorescence was enhanced in the presence of charged micelles, compared to the buffer solution and the accessibility of the fluorophore to the quencher was dependent on the peptide and the alkylpyridinium: in ACTH(1-21) highest collisional constants were obtained using ethylpyridinium as quencher, indicating a location of the residue in the surface of the micelle, while in alpha-MSH the best quencher was hexylpyridinium, indicating insertion of the residue into the non-polar region of the micelles. The results had shown that the interaction between the peptides and the biomimetic systems where driven by combined electrostatic and hydrophobic effects: in ACTH(1-24) the electrostatic interaction between highly positively charged C-terminal and negatively charged surface of micelles; and aggregates predominates over hydrophobic interactions involving residues in the central region of the peptide; in alpha-MSH, which presents one residual positive charge, the hydrophobic interactions are relevant to position the Trp residue in the non-polar region of the microheterogeneous systems. (C) 2008 Elsevier B.V. All rights reserved.

Finite-temperature correlations and density profiles of an inhomogeneous interacting one-dimensional Bose gas

We calculate the density profiles and density correlation functions of the one-dimensional Bose gas in a harmonic trap, using the exact finite-temperature solutions for the uniform case, and applying a local density approximation. The results are valid for a trapping potential that is slowly varying relative to a correlation length. They allow a direct experimental test of the transition from the weak-coupling Gross-Pitaevskii regime to the strong-coupling, fermionic Tonks-Girardeau regime. We also calculate the average two-particle correlation which characterizes the bulk properties of the sample, and find that it can be well approximated by the value of the local pair correlation in the trap center.

Structural and Biochemical Correlates of Na(+), K(+)-ATPase Driven Ion Uptake Across the Posterior Gill Epithelium of the True Freshwater Crab, Dilocarcinus pagei (Brachyura, Trichodactylidae)

To better comprehend the structural and biochemical underpinnings of ion uptake across the gills of true freshwater crabs, we performed an ultrastructural, ultracytochemical and morphometric investigation, and kinetically characterized the Na(+), K(+)-ATPase, in posterior gill lamellae of Dilocarcinus pagei. Ultrastructurally, the lamellar epithelia are markedly asymmetrical: the thick, mushroom-shaped, proximal ionocytes contain elongate mitochondria (41% cell volume) associated with numerous (approximate to 14 mu m(2) membrane per mu m(3) cytoplasm), deep invaginations that house the Na(+), K(+)-ATPase, revealed ultracytochemically. Their apical surface is amplified (7.5 mu m(2) mu m(-2)) by stubby evaginations whose bases adjoin mitochondria below the subcuticular space. The apical membrane of the thin, distal ionocytes shows few evaginations (1.6 mu m(2) mu m(-2)), each surrounding a mitochondrion, abundant in the cytoplasm below the subcuticular space; basolateral invaginations and mitochondria are few. Fine basal cytoplasmic bridges project across the hemolymph space, penetrating into the thick ionocytes, suggesting ion movement between the epithelia. Microsomal Na(+), K(+)-ATPase specific activity resembles marine crabs but is approximate to 5-fold less than in species from fluctuating salinities, and freshwater shrimps, suggesting ion loss compensation by strategies other than Na(+) uptake. Enzyme apparent K(+) affinity attains 14-fold that of marine crabs, emphasizing the relevance of elevated K(+) affinity to the conquest of fresh water. Western blotting and biphasic ouabain inhibition disclose two alpha-subunit isoforms comprising distinct functional isoenzymes. While enzyme activity is not synergistically stimulated by NH(4)(+) and K(+), each increases affinity for the other, possibly assuring appropriate intracellular K(+) concentrations. These findings reveal specific structural and biochemical adaptations that may have allowed the establishment of the Brachyura in fresh water. J. Exp. Zool. 313A:508-523, 2010. (C) 2010 Wiley-Liss, Inc.

Interfacial interactions and structure of organic-inorganic nanohybrids

Understanding the interfacial interactions and structure is important to better design and application of organic-inorganic nanohybrids. This paper presents our recent molecular dynamic studies on organoclays and polymer nanocomposites, including the layering behavior of organoclays, structural and dynamic properties of dioctadecyldimethyl ammoniums in organoclays, and interfacial interactions and structure of polyurethane nanocomposites. The results demonstrate that the layering behaviors of organoclays are closely related to the chain length of quaternary alkyl ammoniums and cation exchangeable capacity of clays. In addition to typical layered structures such as monolayer, bilayer and pseudo-trilayer, a pseudo-quadrilayer structure was also observed in organoclays modified with dioctadecyldimethyl ammoniums (DODDMA). In such a structure, alkyl chains do not lie flat within a single layer but interlace, and also jump to the next layer or even the next nearest layer. Moreover, the diffusion constants of nitrogen and methylene atoms increase with the temperature and methelene towards the tail groups. For polyurethane nanocomposite, the van der Waals interaction between apolar alkyl chains and soft segments of polyurethane predominates the interactions between organoclay and polyurethane. Different from most bulk polyurethane systems, there is no distinct phase-separated structure for the polyurethane.

Semiquantum versus semiclassical mechanics for simple nonlinear systems

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.

The 2.0 angstrom crystal structure of a pocilloporin at pH 3.5: The structural basis for the linkage between color transition and halide binding

The pocilloporin Rtms5 and an engineered variant Rtms5(H146S) undergo distinct color transitions (from blue to red to yellow to colorless) in a pH-dependent manner. pK(a) values of 4.1 and 3.2 were determined for the blue (absorption lambda(max), 590 nm) to yellow (absorption lambda(max), similar to 453 nm) transitions of Rtms5 and Rtms5H(146). The pK(a) for the blue-yellow transition of Rtms5H(146S) increased by 1.4 U in the presence of 0.1 M KI, whereas the pK(a) for the same transition of Rtms5 was relatively insensitive to added halides. To understand the structural basis for these observations, we have determined to 2.0 A resolution the crystal structure of a yellow form of Rtms5(H146S) at pH 3.5 in the presence of iodide. Iodide was found occupying a pocket in the structure with a pH of 3.5, forming van der Waals contacts with the tyrosyl moiety of the chromophore. Elsewhere, it was determined that this pocket is occupied by a water molecule in the Rtms5(H141S) structure (pH 8.0) and by the side chain of histidine 146 in the wild-type Rtms5 structure. Collectively, our data provide an explanation for the observed linkage between color transitions for Rtms5(H146S) and binding to halides.

2-perfect directed m-cycle systems can be equationally defined for m=3,4, and 5 only

It is shown that quasigroups constructed using the standard construction from 2-perfect directed m-cycle systems are precisely the finite members of a variety if and only if m=3, 4 or 5.

Structural shifts of aldehyde dehydrogenase enzymes were instrumental for the early evolution of retinoid-dependent axial patterning in metazoans

Aldehyde dehydrogenases (ALDHs) catabolize toxic aldehydes and process the vitamin A-derived retinaldehyde into retinoic acid (RA), a small diffusible molecule and a pivotal chordate morphogen. In this study, we combine phylogenetic, structural, genomic, and developmental gene expression analyses to examine the evolutionary origins of ALDH substrate preference. Structural modeling reveals that processing of small aldehydes, such as acetaldehyde, by ALDH2, versus large aldehydes, including retinaldehyde, by ALDH1A is associated with small versus large substrate entry channels (SECs), respectively. Moreover, we show that metazoan ALDH1s and ALDH2s are members of a single ALDH1/2 clade and that during evolution, eukaryote ALDH1/2s often switched between large and small SECs after gene duplication, transforming constricted channels into wide opened ones and vice versa. Ancestral sequence reconstructions suggest that during the evolutionary emergence of RA signaling, the ancestral, narrow-channeled metazoan ALDH1/2 gave rise to large ALDH1 channels capable of accommodating bulky aldehydes, such as retinaldehyde, supporting the view that retinoid-dependent signaling arose from ancestral cellular detoxification mechanisms. Our analyses also indicate that, on a more restricted evolutionary scale, ALDH1 duplicates from invertebrate chordates (amphioxus and ascidian tunicates) underwent switches to smaller and narrower SECs. When combined with alterations in gene expression, these switches led to neofunctionalization from ALDH1-like roles in embryonic patterning to systemic, ALDH2-like roles, suggesting functional shifts from signaling to detoxification.

Giant protein kinases: Domain interactions and structural basis of autoregulation

The myosin-associated giant protein kinases twitchin and titin are composed predominantly of fibronectin- and immunoglobulin-like modules, We report the crystal structures of two autoinhibited twitchin kinase fragments, one from Aplysia and a larger fragment from Caenorhabditis elegans containing an additional C-terminal immunoglobulin-like domain, The structure of the longer fragment shoes that the immunoglobulin domain contacts the protein kinase domain on the opposite side from the catalytic cleft, laterally exposing potential myosin binding residues, Together, the structures reveal the cooperative interactions between the autoregulatory region and the residues from the catalytic domain involved in protein substrate binding, ATP binding, catalysis and the activation loop, and explain the differences between the observed autoinhibitory mechanism and the one found in the structure of calmodulin-dependent kinase I.

Lambda-fold 3-perfect 9-cycle systems

The spectrum for the decomposition of lambda K-v into 3-perfect 9-cycles is found for all lambda > 1. (The case lambda = 1 was dealt with in an earlier paper by the authors and Lindner.) The necessary conditions for the existence of a suitable decomposition turn out to be sufficient.